TSTP Solution File: ITP238_1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : ITP238_1 : TPTP v8.1.2. Released v8.0.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n014.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 03:23:53 EDT 2023
% Result : Theorem 26.56s 26.76s
% Output : Proof 26.60s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 7.37/7.48 % Problem : ITP238_1 : TPTP v8.1.2. Released v8.0.0.
% 7.37/7.49 % Command : do_cvc5 %s %d
% 7.50/7.70 % Computer : n014.cluster.edu
% 7.50/7.70 % Model : x86_64 x86_64
% 7.50/7.70 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 7.50/7.70 % Memory : 8042.1875MB
% 7.50/7.70 % OS : Linux 3.10.0-693.el7.x86_64
% 7.50/7.70 % CPULimit : 300
% 7.50/7.70 % WCLimit : 300
% 7.50/7.70 % DateTime : Sun Aug 27 14:34:39 EDT 2023
% 7.50/7.70 % CPUTime :
% 15.16/15.37 %----Proving TF0_NAR, FOF, or CNF
% 26.56/26.76 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.XWQAaxUSJg/cvc5---1.0.5_29271.p...
% 26.56/26.76 ------- get file name : TPTP file name is ITP238_1
% 26.56/26.76 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_29271.smt2...
% 26.56/26.76 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 26.56/26.76 % SZS status Theorem for ITP238_1
% 26.56/26.76 % SZS output start Proof for ITP238_1
% 26.56/26.76 (
% 26.56/26.76 (let ((_let_1 (not tptp.thesis))) (let ((_let_2 (forall ((Minilow tptp.nat)) (=> (= (tptp.vEBT_vebt_mint (tptp.nth_VEBT_VEBT tptp.treeList (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high tptp.xa) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat tptp.deg) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))))) (tptp.some_nat Minilow)) tptp.thesis)))) (let ((_let_3 (tptp.produc4528391901023682385at_nat tptp.aTP_Lamm_xc))) (let ((_let_4 (tptp.bNF_re2241393799969408733at_nat tptp.intrel tptp.intrel))) (let ((_let_5 (tptp.produc4528391901023682385at_nat tptp.aTP_Lamm_xe))) (let ((_let_6 (tptp.produc5023667602222594023t_bool tptp.aTP_Lamm_xa))) (let ((_let_7 (tptp.bNF_re3189209160384574813l_bool tptp.intrel tptp.fequal_bool))) (let ((_let_8 (tptp.produc5023667602222594023t_bool tptp.aTP_Lamm_wy))) (let ((_let_9 (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat tptp.zero_zero_nat) tptp.zero_zero_nat))) (let ((_let_10 (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat tptp.one_one_nat) tptp.zero_zero_nat))) (let ((_let_11 (tptp.produc2626176000494625587at_nat tptp.aTP_Lamm_ww))) (let ((_let_12 (tptp.produc6842872674320459806at_nat tptp.minus_minus_nat))) (let ((_let_13 (tptp.produc4528391901023682385at_nat tptp.aTP_Lamm_wv))) (let ((_let_14 (tptp.bNF_re7400052026677387805at_int tptp.pcr_int tptp.pcr_int))) (let ((_let_15 (tptp.bNF_re1498568104593929552l_bool tptp.pcr_int tptp.fequal_bool))) (let ((_let_16 (tptp.bNF_re8279943556446156061nt_rat tptp.pcr_rat tptp.pcr_rat))) (let ((_let_17 (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int))) (let ((_let_18 (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int tptp.one_one_int) tptp.one_one_int))) (let ((_let_19 (tptp.bNF_re7145576690424134365nt_int tptp.ratrel tptp.ratrel))) (let ((_let_20 (tptp.bNF_re9007465950226028919l_bool tptp.fequal_int tptp.fequal_bool))) (let ((_let_21 (tptp.bNF_re6223507645442431167l_bool tptp.fequal_nat tptp.fequal_bool))) (let ((_let_22 (tptp.bNF_re5653821019739307937at_nat tptp.fequal_nat tptp.fequal_nat))) (let ((_let_23 (tptp.set_or5849166863359141190n_real tptp.zero_zero_real))) (let ((_let_24 (tptp.aa_num_num tptp.bit0 tptp.one))) (let ((_let_25 (tptp.aa_num_num tptp.bit0 _let_24))) (let ((_let_26 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit0 _let_25))))))))) (let ((_let_27 (tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat _let_26))) (let ((_let_28 (tptp.aa_num_real tptp.numeral_numeral_real _let_24))) (let ((_let_29 (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi))) (let ((_let_30 (tptp.aa_real_real _let_29 _let_28))) (let ((_let_31 (tptp.aa_real_real tptp.uminus_uminus_real _let_30))) (let ((_let_32 (tptp.map_fu5673905371560938248nt_rat tptp.rep_Rat tptp.abs_Rat))) (let ((_let_33 (tptp.aa_num_nat tptp.numeral_numeral_nat _let_24))) (let ((_let_34 (tptp.map_fu6608131713810608381l_bool tptp.rep_Integ tptp.id_bool))) (let ((_let_35 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger _let_24))) (let ((_let_36 (tptp.map_fu3667384564859982768at_int tptp.rep_Integ tptp.abs_Integ))) (let ((_let_37 (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int))) (let ((_let_38 (tptp.aa_rat_rat tptp.uminus_uminus_rat tptp.one_one_rat))) (let ((_let_39 (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger))) (let ((_let_40 (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (let ((_let_41 (tptp.aa_int_int tptp.bit_ri7919022796975470100ot_int tptp.one_one_int))) (let ((_let_42 (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat))) (let ((_let_43 (tptp.aa_nat_nat tptp.suc _let_42))) (let ((_let_44 (tptp.aa_num_int tptp.numeral_numeral_int _let_24))) (let ((_let_45 (tptp.the_real tptp.aTP_Lamm_vn))) (let ((_let_46 (tptp.aa_rea7340605660300375871l_real tptp.times_times_real _let_28))) (let ((_let_47 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat _let_33))) (let ((_let_48 (tptp.aa_real_real tptp.sqrt _let_28))) (let ((_let_49 (tptp.plus_plus_complex tptp.one_one_complex))) (let ((_let_50 (tptp.numera6690914467698888265omplex _let_24))) (let ((_let_51 (tptp.aa_real_complex tptp.real_V4546457046886955230omplex tptp.pi))) (let ((_let_52 (tptp.times_times_complex _let_51))) (let ((_let_53 (tptp.times_times_complex tptp.imaginary_unit))) (let ((_let_54 (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex tptp.one_one_complex))) (let ((_let_55 (tptp.aa_real_real _let_46 tptp.pi))) (let ((_let_56 (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex tptp.imaginary_unit))) (let ((_let_57 (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real))) (let ((_let_58 (tptp.aa_num_num tptp.bit1 tptp.one))) (let ((_let_59 (tptp.aa_num_real tptp.numeral_numeral_real _let_58))) (let ((_let_60 (tptp.aa_real_real tptp.sqrt _let_59))) (let ((_let_61 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real _let_60) _let_28))) (let ((_let_62 (tptp.aa_real_real _let_29 _let_59))) (let ((_let_63 (tptp.aa_real_real _let_29 (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 _let_58))))) (let ((_let_64 (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.one_one_real))) (let ((_let_65 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real _let_48) _let_28))) (let ((_let_66 (tptp.aa_num_real tptp.numeral_numeral_real _let_25))) (let ((_let_67 (tptp.aa_real_real _let_29 _let_66))) (let ((_let_68 (tptp.aa_real_real _let_64 _let_28))) (let ((_let_69 (tptp.aa_num_rat tptp.numeral_numeral_rat _let_24))) (let ((_let_70 (tptp.aa_real_real tptp.cos_real _let_28))) (let ((_let_71 (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real _let_59))) (let ((_let_72 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real _let_71 _let_28)) tptp.pi))) (let ((_let_73 (tptp.aa_num_num tptp.bit1 _let_58))) (let ((_let_74 (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit1 _let_24)))) (let ((_let_75 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (let ((_let_76 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real))) (let ((_let_77 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.pi))) (let ((_let_78 (tptp.power_power_complex tptp.zero_zero_complex))) (let ((_let_79 (tptp.power_power_int tptp.zero_zero_int))) (let ((_let_80 (tptp.aa_real_fun_nat_real tptp.power_power_real tptp.zero_zero_real))) (let ((_let_81 (= (tptp.aa_nat_int tptp.semiri1314217659103216013at_int tptp.one_one_nat) tptp.one_one_int))) (let ((_let_82 (= (tptp.aa_nat_int tptp.semiri1314217659103216013at_int tptp.zero_zero_nat) tptp.zero_zero_int))) (let ((_let_83 (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (let ((_let_84 (tptp.aa_num_int tptp.numeral_numeral_int _let_58))) (let ((_let_85 (tptp.aa_num_rat tptp.numeral_numeral_rat _let_58))) (let ((_let_86 (tptp.numera6690914467698888265omplex _let_58))) (let ((_let_87 (= (tptp.aa_int_int tptp.abs_abs_int tptp.one_one_int) tptp.one_one_int))) (let ((_let_88 (= (tptp.aa_rat_rat tptp.abs_abs_rat tptp.one_one_rat) tptp.one_one_rat))) (let ((_let_89 (= (tptp.aa_real_real tptp.abs_abs_real tptp.one_one_real) tptp.one_one_real))) (let ((_let_90 (= (tptp.abs_abs_Code_integer tptp.one_one_Code_integer) tptp.one_one_Code_integer))) (let ((_let_91 (= (tptp.aa_int_int tptp.abs_abs_int tptp.zero_zero_int) tptp.zero_zero_int))) (let ((_let_92 (= (tptp.aa_rat_rat tptp.abs_abs_rat tptp.zero_zero_rat) tptp.zero_zero_rat))) (let ((_let_93 (= (tptp.aa_real_real tptp.abs_abs_real tptp.zero_zero_real) tptp.zero_zero_real))) (let ((_let_94 (= (tptp.abs_abs_Code_integer tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger))) (let ((_let_95 (tptp.aa_num_rat tptp.numeral_numeral_rat tptp.one))) (let ((_let_96 (tptp.numera6690914467698888265omplex tptp.one))) (let ((_let_97 (tptp.aa_num_int tptp.numeral_numeral_int tptp.one))) (let ((_let_98 (tptp.aa_num_real tptp.numeral_numeral_real tptp.one))) (let ((_let_99 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat _let_38))) (let ((_let_100 (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger _let_83))) (let ((_let_101 (tptp.aa_int_fun_int_bool tptp.ord_less_int _let_37))) (let ((_let_102 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real _let_57))) (let ((_let_103 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat))) (let ((_let_104 (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int))) (let ((_let_105 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int _let_37))) (let ((_let_106 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat _let_38))) (let ((_let_107 (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger _let_83))) (let ((_let_108 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real _let_57))) (let ((_let_109 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_110 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat))) (let ((_let_111 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.one_one_rat))) (let ((_let_112 (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.one_one_int))) (let ((_let_113 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real))) (let ((_let_114 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.one_one_int))) (let ((_let_115 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.one_one_rat))) (let ((_let_116 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.one_one_real))) (let ((_let_117 (tptp.aa_rat_rat tptp.uminus_uminus_rat _let_69))) (let ((_let_118 (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger _let_35))) (let ((_let_119 (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex _let_50))) (let ((_let_120 (tptp.aa_int_int tptp.uminus_uminus_int _let_44))) (let ((_let_121 (tptp.aa_real_real tptp.uminus_uminus_real _let_28))) (let ((_let_122 (= (tptp.modulo364778990260209775nteger _let_83 _let_35) tptp.one_one_Code_integer))) (let ((_let_123 (= (tptp.aa_int_int (tptp.modulo_modulo_int _let_37) _let_44) tptp.one_one_int))) (let ((_let_124 (tptp.minus_minus_rat _let_38))) (let ((_let_125 (tptp.minus_minus_complex _let_54))) (let ((_let_126 (tptp.aa_int_fun_int_int tptp.minus_minus_int _let_37))) (let ((_let_127 (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real _let_57))) (let ((_let_128 (tptp.minus_minus_rat tptp.one_one_rat))) (let ((_let_129 (tptp.minus_minus_complex tptp.one_one_complex))) (let ((_let_130 (tptp.aa_int_fun_int_int tptp.minus_minus_int tptp.one_one_int))) (let ((_let_131 (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real tptp.one_one_real))) (let ((_let_132 (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat _let_38))) (let ((_let_133 (tptp.plus_plus_complex _let_54))) (let ((_let_134 (tptp.aa_int_fun_int_int tptp.plus_plus_int _let_37))) (let ((_let_135 (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real _let_57))) (let ((_let_136 (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat tptp.one_one_rat))) (let ((_let_137 (tptp.aa_int_fun_int_int tptp.plus_plus_int tptp.one_one_int))) (let ((_let_138 (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real tptp.one_one_real))) (let ((_let_139 (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int _let_44))) (let ((_let_140 (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat _let_33))) (let ((_let_141 (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer _let_35))) (let ((_let_142 (tptp.pp (tptp.aa_int_bool _let_109 tptp.zero_zero_int)))) (let ((_let_143 (not (tptp.pp (tptp.aa_int_bool _let_104 tptp.zero_zero_int))))) (let ((_let_144 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat))) (let ((_let_145 (tptp.aa_num_nat tptp.numeral_numeral_nat tptp.one))) (let ((_let_146 (tptp.aa_int_int _let_137 tptp.one_one_int))) (let ((_let_147 (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat tptp.one_one_nat))) (let ((_let_148 (tptp.aa_nat_nat _let_147 tptp.one_one_nat))) (let ((_let_149 (tptp.aa_rat_rat _let_136 tptp.one_one_rat))) (let ((_let_150 (tptp.aa_real_real _let_138 tptp.one_one_real))) (let ((_let_151 (tptp.pp (tptp.aa_int_bool _let_104 tptp.one_one_int)))) (let ((_let_152 (tptp.pp (tptp.aa_nat_bool _let_144 tptp.one_one_nat)))) (let ((_let_153 (tptp.pp (tptp.aa_rat_bool _let_103 tptp.one_one_rat)))) (let ((_let_154 (tptp.pp (tptp.aa_real_bool _let_76 tptp.one_one_real)))) (let ((_let_155 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.one_one_nat))) (let ((_let_156 (tptp.pp (tptp.aa_int_bool _let_109 tptp.one_one_int)))) (let ((_let_157 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat))) (let ((_let_158 (tptp.pp (tptp.aa_nat_bool _let_157 tptp.one_one_nat)))) (let ((_let_159 (tptp.pp (tptp.aa_rat_bool _let_110 tptp.one_one_rat)))) (let ((_let_160 (tptp.pp (tptp.aa_real_bool _let_75 tptp.one_one_real)))) (let ((_let_161 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.one_one_nat))) (let ((_let_162 (= (tptp.aa_int_int (tptp.divide_divide_int tptp.one_one_int) _let_44) tptp.zero_zero_int))) (let ((_let_163 (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat tptp.one_one_nat) _let_33) tptp.zero_zero_nat))) (let ((_let_164 (= (tptp.modulo364778990260209775nteger tptp.one_one_Code_integer _let_35) tptp.one_one_Code_integer))) (let ((_let_165 (= (tptp.aa_int_int (tptp.modulo_modulo_int tptp.one_one_int) _let_44) tptp.one_one_int))) (let ((_let_166 (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat tptp.one_one_nat) _let_33) tptp.one_one_nat))) (let ((_let_167 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat tptp.deg) _let_33))) (let ((_let_168 (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high tptp.xa))) (let ((_let_169 (tptp.aa_nat_nat _let_168 _let_167))) (let ((_let_170 (tptp.vEBT_vebt_pred tptp.summary _let_169))) (let ((_let_171 (tptp.aa_opt7711074727033721499on_nat tptp.vEBT_VEBT_mul (tptp.some_nat (tptp.aa_nat_nat _let_47 _let_167))))) (let ((_let_172 (tptp.aa_opt1882420858203594238on_nat (tptp.aa_opt7711074727033721499on_nat tptp.vEBT_VEBT_add (tptp.aa_opt1882420858203594238on_nat _let_171 _let_170)) (tptp.vEBT_vebt_maxt (tptp.nth_VEBT_VEBT tptp.treeList (tptp.the_nat _let_170)))))) (let ((_let_173 (tptp.some_nat tptp.mi))) (let ((_let_174 (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.mi) tptp.xa))) (let ((_let_175 (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat tptp.mi) tptp.ma)) tptp.deg tptp.treeList tptp.summary))) (let ((_let_176 (tptp.vEBT_vebt_pred _let_175 tptp.xa))) (let ((_let_177 (tptp.nth_VEBT_VEBT tptp.treeList _let_169))) (let ((_let_178 (tptp.vEBT_vebt_mint _let_177))) (let ((_let_179 (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low tptp.xa))) (let ((_let_180 (tptp.aa_nat_nat _let_179 _let_167))) (let ((_let_181 (tptp.some_nat _let_180))) (let ((_let_182 (tptp.pp (tptp.aa_option_nat_bool (tptp.aa_opt7943525813896274546t_bool tptp.vEBT_VEBT_greater _let_181) _let_178)))) (let ((_let_183 (= _let_178 tptp.none_nat))) (let ((_let_184 (not _let_183))) (let ((_let_185 (and _let_184 _let_182))) (let ((_let_186 (= _let_148 _let_33))) (let ((_let_187 (= _let_145 tptp.one_one_nat))) (let ((_let_188 (= _let_170 tptp.none_nat))) (let ((_let_189 (tptp.pp _let_174))) (let ((_let_190 (= tptp.mi tptp.ma))) (let ((_let_191 (forall ((Option tptp.option_nat) (X2 tptp.nat)) (=> (= Option (tptp.some_nat X2)) (not (= Option tptp.none_nat)))))) (let ((_let_192 (forall ((X tptp.option_nat) (P tptp.fun_op7792301606653096457t_bool) (Y tptp.option_nat)) (let ((_let_1 (tptp.pp (tptp.aa_option_nat_bool (tptp.aa_opt7943525813896274546t_bool P X) Y)))) (=> (=> (= X tptp.none_nat) _let_1) (=> (=> (= Y tptp.none_nat) _let_1) (=> (forall ((A3 tptp.nat) (B3 tptp.nat)) (=> (= X (tptp.some_nat A3)) (=> (= Y (tptp.some_nat B3)) (tptp.pp (tptp.aa_option_nat_bool (tptp.aa_opt7943525813896274546t_bool P X) Y))))) _let_1))))))) (let ((_let_193 (tptp.aa_nat_nat _let_47 tptp.na))) (let ((_let_194 (tptp.size_s6755466524823107622T_VEBT tptp.treeList))) (let ((_let_195 (not _let_182))) (let ((_let_196 (or _let_183 _let_195))) (let ((_let_197 (forall ((B3 tptp.nat)) (not (= (tptp.vEBT_vebt_mint (tptp.nth_VEBT_VEBT tptp.treeList (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high tptp.xa) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat tptp.deg) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))))) (tptp.some_nat B3)))))) (let ((_let_198 (not _let_197))) (let ((_let_199 (and _let_195 (not (forall ((A3 tptp.nat)) (not (= (tptp.some_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low tptp.xa) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat tptp.deg) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (tptp.some_nat A3))))) _let_198))) (let ((_let_200 (= tptp.none_nat _let_178))) (let ((_let_201 (and _let_200 _let_195))) (let ((_let_202 (= tptp.none_nat _let_181))) (let ((_let_203 (and _let_202 _let_195))) (let ((_let_204 (or _let_203 _let_201 _let_199 _let_182))) (let ((_let_205 (SYMM (ASSUME :args (_let_184))))) (let ((_let_206 (forall ((X tptp.option_nat) (P tptp.fun_op7792301606653096457t_bool) (Y tptp.option_nat)) (let ((_let_1 (tptp.pp (tptp.aa_option_nat_bool (tptp.aa_opt7943525813896274546t_bool P X) Y)))) (let ((_let_2 (not _let_1))) (or (and (= tptp.none_nat X) _let_2) (and (= tptp.none_nat Y) _let_2) (and _let_2 (not (forall ((A3 tptp.nat)) (not (= X (tptp.some_nat A3))))) (not (forall ((B3 tptp.nat)) (not (= Y (tptp.some_nat B3)))))) _let_1)))))) (let ((_let_207 (EQ_RESOLVE (ASSUME :args (_let_192)) (MACRO_SR_EQ_INTRO :args (_let_192 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_208 (not _let_201))) (let ((_let_209 (not _let_199))) (let ((_let_210 (forall ((Minilow tptp.nat)) (not (= (tptp.vEBT_vebt_mint (tptp.nth_VEBT_VEBT tptp.treeList (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high tptp.xa) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat tptp.deg) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))))) (tptp.some_nat Minilow)))))) (let ((_let_211 (not _let_203))) (let ((_let_212 (forall ((X2 tptp.nat)) (not (= tptp.none_nat (tptp.some_nat X2)))))) (let ((_let_213 (EQ_RESOLVE (ASSUME :args (_let_191)) (MACRO_SR_EQ_INTRO :args (_let_191 SB_DEFAULT SBA_FIXPOINT))))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_204)) :args ((or _let_182 _let_203 _let_201 _let_199 (not _let_204)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_203 0)) :args ((or _let_202 _let_211))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_213 :args (_let_180 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.some_nat X2)))) :args (_let_212))) _let_213 :args ((not _let_202) false _let_212)) :args (_let_211 true _let_202)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_199 2)) :args ((or _let_198 _let_209))) (MACRO_RESOLUTION_TRUST (EQUIV_ELIM1 (ALPHA_EQUIV :args (_let_210 (= Minilow B3)))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))) (ASSUME :args (_let_1)) :args (_let_210 true tptp.thesis)) :args (_let_197 false _let_210)) :args (_let_209 false _let_197)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_201 0)) :args ((or _let_200 _let_208))) _let_205 :args (_let_208 true _let_200)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_207 :args (_let_181 tptp.vEBT_VEBT_greater _let_178 QUANTIFIERS_INST_E_MATCHING ((tptp.aa_option_nat_bool (tptp.aa_opt7943525813896274546t_bool P X) Y)))) :args (_let_206))) _let_207 :args (_let_204 false _let_206)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (ASSUME :args (_let_196)) (MACRO_SR_EQ_INTRO :args (_let_196 SB_DEFAULT SBA_FIXPOINT))) :args ((or _let_195 _let_200))) _let_205 :args (_let_195 true _let_200)) :args (false true _let_203 true _let_199 true _let_201 false _let_204 true _let_182)) :args (_let_184 (= _let_167 tptp.na) (forall ((M tptp.num)) (not (= (tptp.aa_num_num tptp.bit0 M) tptp.one))) (forall ((N tptp.num)) (not (= tptp.one (tptp.aa_num_num tptp.bit0 N)))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat _let_33) tptp.deg)) (forall ((N tptp.num)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 N))) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_num_nat tptp.numeral_numeral_nat N))) (forall ((N tptp.num)) (= (tptp.aa_int_int (tptp.divide_divide_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 N))) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_num_int tptp.numeral_numeral_int N))) (forall ((X tptp.nat) (N tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high X) N) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat X) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N)))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_169) _let_194)) _let_196 (forall ((A tptp.complex)) (= (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex A) (tptp.numera6690914467698888265omplex tptp.one)) A)) (forall ((A tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real A) (tptp.aa_num_real tptp.numeral_numeral_real tptp.one)) A)) (forall ((A tptp.rat)) (= (tptp.aa_rat_rat (tptp.divide_divide_rat A) (tptp.aa_num_rat tptp.numeral_numeral_rat tptp.one)) A)) (forall ((X2 tptp.nat) (Y2 tptp.nat)) (= (= (tptp.some_nat X2) (tptp.some_nat Y2)) (= X2 Y2))) (forall ((X2 tptp.product_prod_nat_nat) (Y2 tptp.product_prod_nat_nat)) (= (= (tptp.some_P7363390416028606310at_nat X2) (tptp.some_P7363390416028606310at_nat Y2)) (= X2 Y2))) (forall ((X2 tptp.num) (Y2 tptp.num)) (= (= (tptp.some_num X2) (tptp.some_num Y2)) (= X2 Y2))) (forall ((X2 tptp.num) (Y2 tptp.num)) (= (= (tptp.aa_num_num tptp.bit0 X2) (tptp.aa_num_num tptp.bit0 Y2)) (= X2 Y2))) (forall ((M tptp.num) (N tptp.num)) (= (= (tptp.aa_num_num tptp.bit0 M) (tptp.aa_num_num tptp.bit0 N)) (= M N))) (= tptp.m tptp.na) (forall ((Xs tptp.set_nat) (X tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_VEBT_max_in_set Xs) X)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X) Xs)) (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) Xs)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X3) X))))))) (forall ((Y tptp.nat) (X tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Y) X)) (tptp.pp (tptp.aa_option_nat_bool (tptp.aa_opt7943525813896274546t_bool tptp.vEBT_VEBT_greater (tptp.some_nat X)) (tptp.some_nat Y))))) (forall ((Xs tptp.set_nat) (X tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_VEBT_min_in_set Xs) X)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X) Xs)) (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) Xs)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X) X3))))))) (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat X) Y) Z) (= (tptp.aa_opt1882420858203594238on_nat (tptp.aa_opt7711074727033721499on_nat tptp.vEBT_VEBT_power (tptp.some_nat X)) (tptp.some_nat Y)) (tptp.some_nat Z)))) (forall ((X tptp.nat) (D tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.vEBT_VEBT_bit_concat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high X) D)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low X) D)) D) X)) (forall ((M tptp.num) (N tptp.num)) (= (= (tptp.numera6690914467698888265omplex M) (tptp.numera6690914467698888265omplex N)) (= M N))) (forall ((M tptp.num) (N tptp.num)) (= (= (tptp.aa_num_real tptp.numeral_numeral_real M) (tptp.aa_num_real tptp.numeral_numeral_real N)) (= M N))) (forall ((M tptp.num) (N tptp.num)) (= (= (tptp.aa_num_rat tptp.numeral_numeral_rat M) (tptp.aa_num_rat tptp.numeral_numeral_rat N)) (= M N))) (forall ((M tptp.num) (N tptp.num)) (= (= (tptp.aa_num_nat tptp.numeral_numeral_nat M) (tptp.aa_num_nat tptp.numeral_numeral_nat N)) (= M N))) (forall ((M tptp.num) (N tptp.num)) (= (= (tptp.aa_num_int tptp.numeral_numeral_int M) (tptp.aa_num_int tptp.numeral_numeral_int N)) (= M N))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_num_real tptp.numeral_numeral_real M)) (tptp.aa_num_real tptp.numeral_numeral_real N))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num M) N)))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_num_rat tptp.numeral_numeral_rat M)) (tptp.aa_num_rat tptp.numeral_numeral_rat N))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num M) N)))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_num_nat tptp.numeral_numeral_nat M)) (tptp.aa_num_nat tptp.numeral_numeral_nat N))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num M) N)))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_num_int tptp.numeral_numeral_int M)) (tptp.aa_num_int tptp.numeral_numeral_int N))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num M) N)))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_num_real tptp.numeral_numeral_real M)) (tptp.aa_num_real tptp.numeral_numeral_real N))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num M) N)))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_num_rat tptp.numeral_numeral_rat M)) (tptp.aa_num_rat tptp.numeral_numeral_rat N))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num M) N)))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_num_nat tptp.numeral_numeral_nat M)) (tptp.aa_num_nat tptp.numeral_numeral_nat N))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num M) N)))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_num_int tptp.numeral_numeral_int M)) (tptp.aa_num_int tptp.numeral_numeral_int N))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num M) N)))) (forall ((X tptp.option_nat)) (= (forall ((Y3 tptp.nat)) (not (= X (tptp.some_nat Y3)))) (= X tptp.none_nat))) (forall ((X tptp.option4927543243414619207at_nat)) (= (forall ((Y3 tptp.product_prod_nat_nat)) (not (= X (tptp.some_P7363390416028606310at_nat Y3)))) (= X tptp.none_P5556105721700978146at_nat))) (forall ((X tptp.option_num)) (= (forall ((Y3 tptp.num)) (not (= X (tptp.some_num Y3)))) (= X tptp.none_num))) (forall ((X tptp.option_nat)) (= (not (= X tptp.none_nat)) (exists ((Y3 tptp.nat)) (= X (tptp.some_nat Y3))))) (forall ((X tptp.option4927543243414619207at_nat)) (= (not (= X tptp.none_P5556105721700978146at_nat)) (exists ((Y3 tptp.product_prod_nat_nat)) (= X (tptp.some_P7363390416028606310at_nat Y3))))) (forall ((X tptp.option_num)) (= (not (= X tptp.none_num)) (exists ((Y3 tptp.num)) (= X (tptp.some_num Y3))))) (= _let_194 (tptp.aa_nat_nat _let_47 tptp.m)) (= _let_194 _let_193) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat _let_168 tptp.na)) _let_193)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat _let_179 tptp.na)) _let_193))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.ma) (tptp.aa_nat_nat _let_47 tptp.deg))) (forall ((X tptp.nat) (Y tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Y)) (tptp.pp (tptp.aa_option_nat_bool (tptp.aa_opt7943525813896274546t_bool tptp.vEBT_VEBT_less (tptp.some_nat X)) (tptp.some_nat Y))))) (forall ((X tptp.nat) (Y tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X) Y)) (tptp.pp (tptp.aa_option_nat_bool (tptp.aa_opt7943525813896274546t_bool tptp.vEBT_VEBT_lesseq (tptp.some_nat X)) (tptp.some_nat Y))))) (forall ((B tptp.real) (A2 tptp.real)) (= (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real B) A2))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A2) B)))) (forall ((B tptp.rat) (A2 tptp.rat)) (= (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) A2))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A2) B)))) (forall ((B tptp.num) (A2 tptp.num)) (= (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num B) A2))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num A2) B)))) (forall ((B tptp.nat) (A2 tptp.nat)) (= (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B) A2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A2) B)))) (forall ((B tptp.int) (A2 tptp.int)) (= (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B) A2))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A2) B)))) (forall ((A tptp.set_int)) (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int A) A))) (forall ((A tptp.rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) A))) (forall ((A tptp.num)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A) A))) (forall ((A tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) A))) (forall ((A tptp.int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) A))) (forall ((A tptp.real)) (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) A)))) (forall ((A tptp.rat)) (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) A)))) (forall ((A tptp.num)) (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num A) A)))) (forall ((A tptp.nat)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) A)))) (forall ((A tptp.int)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) A)))) (forall ((A tptp.rat) (B2 tptp.rat)) (or (= A B2) (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B2))) (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B2) A))))) (forall ((A tptp.num) (B2 tptp.num)) (or (= A B2) (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A) B2))) (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num B2) A))))) (forall ((A tptp.nat) (B2 tptp.nat)) (or (= A B2) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B2))) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B2) A))))) (forall ((A tptp.int) (B2 tptp.int)) (or (= A B2) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B2))) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B2) A))))) (forall ((M tptp.nat) (N tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat M) N)) M))) (forall ((M tptp.nat) (N tptp.nat) (K tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat M) K)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat N) K))))) _let_192 (forall ((X tptp.option_nat) (P tptp.fun_op5698422665285572208t_bool) (Y tptp.option4927543243414619207at_nat)) (let ((_let_1 (tptp.pp (tptp.aa_opt6800557945374683724t_bool (tptp.aa_opt9009324110926966577t_bool P X) Y)))) (=> (=> (= X tptp.none_nat) _let_1) (=> (=> (= Y tptp.none_P5556105721700978146at_nat) _let_1) (=> (forall ((A3 tptp.nat) (B3 tptp.product_prod_nat_nat)) (=> (= X (tptp.some_nat A3)) (=> (= Y (tptp.some_P7363390416028606310at_nat B3)) (tptp.pp (tptp.aa_opt6800557945374683724t_bool (tptp.aa_opt9009324110926966577t_bool P X) Y))))) _let_1))))) (forall ((X tptp.option_nat) (P tptp.fun_op8690601775248757823m_bool) (Y tptp.option_num)) (let ((_let_1 (tptp.pp (tptp.aa_option_num_bool (tptp.aa_opt1914333813751119784m_bool P X) Y)))) (=> (=> (= X tptp.none_nat) _let_1) (=> (=> (= Y tptp.none_num) _let_1) (=> (forall ((A3 tptp.nat) (B3 tptp.num)) (=> (= X (tptp.some_nat A3)) (=> (= Y (tptp.some_num B3)) (tptp.pp (tptp.aa_option_num_bool (tptp.aa_opt1914333813751119784m_bool P X) Y))))) _let_1))))) (forall ((X tptp.option4927543243414619207at_nat) (P tptp.fun_op9100744243108201484t_bool) (Y tptp.option_nat)) (let ((_let_1 (tptp.pp (tptp.aa_option_nat_bool (tptp.aa_opt5915962183577952389t_bool P X) Y)))) (=> (=> (= X tptp.none_P5556105721700978146at_nat) _let_1) (=> (=> (= Y tptp.none_nat) _let_1) (=> (forall ((A3 tptp.product_prod_nat_nat) (B3 tptp.nat)) (=> (= X (tptp.some_P7363390416028606310at_nat A3)) (=> (= Y (tptp.some_nat B3)) (tptp.pp (tptp.aa_option_nat_bool (tptp.aa_opt5915962183577952389t_bool P X) Y))))) _let_1))))) (forall ((X tptp.option4927543243414619207at_nat) (P tptp.fun_op5682630191948829869t_bool) (Y tptp.option4927543243414619207at_nat)) (let ((_let_1 (tptp.pp (tptp.aa_opt6800557945374683724t_bool (tptp.aa_opt7606875699174042974t_bool P X) Y)))) (=> (=> (= X tptp.none_P5556105721700978146at_nat) _let_1) (=> (=> (= Y tptp.none_P5556105721700978146at_nat) _let_1) (=> (forall ((A3 tptp.product_prod_nat_nat) (B3 tptp.product_prod_nat_nat)) (=> (= X (tptp.some_P7363390416028606310at_nat A3)) (=> (= Y (tptp.some_P7363390416028606310at_nat B3)) (tptp.pp (tptp.aa_opt6800557945374683724t_bool (tptp.aa_opt7606875699174042974t_bool P X) Y))))) _let_1))))) (forall ((X tptp.option4927543243414619207at_nat) (P tptp.fun_op775672374849087042m_bool) (Y tptp.option_num)) (let ((_let_1 (tptp.pp (tptp.aa_option_num_bool (tptp.aa_opt9110142220287573435m_bool P X) Y)))) (=> (=> (= X tptp.none_P5556105721700978146at_nat) _let_1) (=> (=> (= Y tptp.none_num) _let_1) (=> (forall ((A3 tptp.product_prod_nat_nat) (B3 tptp.num)) (=> (= X (tptp.some_P7363390416028606310at_nat A3)) (=> (= Y (tptp.some_num B3)) (tptp.pp (tptp.aa_option_num_bool (tptp.aa_opt9110142220287573435m_bool P X) Y))))) _let_1))))) (forall ((X tptp.option_num) (P tptp.fun_op1064277265382982207t_bool) (Y tptp.option_nat)) (let ((_let_1 (tptp.pp (tptp.aa_option_nat_bool (tptp.aa_opt1215501472626160296t_bool P X) Y)))) (=> (=> (= X tptp.none_num) _let_1) (=> (=> (= Y tptp.none_nat) _let_1) (=> (forall ((A3 tptp.num) (B3 tptp.nat)) (=> (= X (tptp.some_num A3)) (=> (= Y (tptp.some_nat B3)) (tptp.pp (tptp.aa_option_nat_bool (tptp.aa_opt1215501472626160296t_bool P X) Y))))) _let_1))))) (forall ((X tptp.option_num) (P tptp.fun_op7732454363416259258t_bool) (Y tptp.option4927543243414619207at_nat)) (let ((_let_1 (tptp.pp (tptp.aa_opt6800557945374683724t_bool (tptp.aa_opt1819983772202877819t_bool P X) Y)))) (=> (=> (= X tptp.none_num) _let_1) (=> (=> (= Y tptp.none_P5556105721700978146at_nat) _let_1) (=> (forall ((A3 tptp.num) (B3 tptp.product_prod_nat_nat)) (=> (= X (tptp.some_num A3)) (=> (= Y (tptp.some_P7363390416028606310at_nat B3)) (tptp.pp (tptp.aa_opt6800557945374683724t_bool (tptp.aa_opt1819983772202877819t_bool P X) Y))))) _let_1))))) (forall ((X tptp.option_num) (P tptp.fun_op1962577433978643573m_bool) (Y tptp.option_num)) (let ((_let_1 (tptp.pp (tptp.aa_option_num_bool (tptp.aa_opt4409681509335781342m_bool P X) Y)))) (=> (=> (= X tptp.none_num) _let_1) (=> (=> (= Y tptp.none_num) _let_1) (=> (forall ((A3 tptp.num) (B3 tptp.num)) (=> (= X (tptp.some_num A3)) (=> (= Y (tptp.some_num B3)) (tptp.pp (tptp.aa_option_num_bool (tptp.aa_opt4409681509335781342m_bool P X) Y))))) _let_1))))) (forall ((P tptp.fun_option_nat_bool)) (= (forall ((X_1 tptp.option_nat)) (tptp.pp (tptp.aa_option_nat_bool P X_1))) (and (tptp.pp (tptp.aa_option_nat_bool P tptp.none_nat)) (forall ((X3 tptp.nat)) (tptp.pp (tptp.aa_option_nat_bool P (tptp.some_nat X3))))))) (forall ((P tptp.fun_op2627489687811228755t_bool)) (= (forall ((X_1 tptp.option4927543243414619207at_nat)) (tptp.pp (tptp.aa_opt6800557945374683724t_bool P X_1))) (and (tptp.pp (tptp.aa_opt6800557945374683724t_bool P tptp.none_P5556105721700978146at_nat)) (forall ((X3 tptp.product_prod_nat_nat)) (tptp.pp (tptp.aa_opt6800557945374683724t_bool P (tptp.some_P7363390416028606310at_nat X3))))))) (forall ((P tptp.fun_option_num_bool)) (= (forall ((X_1 tptp.option_num)) (tptp.pp (tptp.aa_option_num_bool P X_1))) (and (tptp.pp (tptp.aa_option_num_bool P tptp.none_num)) (forall ((X3 tptp.num)) (tptp.pp (tptp.aa_option_num_bool P (tptp.some_num X3))))))) (forall ((P tptp.fun_option_nat_bool)) (= (exists ((X_1 tptp.option_nat)) (tptp.pp (tptp.aa_option_nat_bool P X_1))) (or (tptp.pp (tptp.aa_option_nat_bool P tptp.none_nat)) (exists ((X3 tptp.nat)) (tptp.pp (tptp.aa_option_nat_bool P (tptp.some_nat X3))))))) (forall ((P tptp.fun_op2627489687811228755t_bool)) (= (exists ((X_1 tptp.option4927543243414619207at_nat)) (tptp.pp (tptp.aa_opt6800557945374683724t_bool P X_1))) (or (tptp.pp (tptp.aa_opt6800557945374683724t_bool P tptp.none_P5556105721700978146at_nat)) (exists ((X3 tptp.product_prod_nat_nat)) (tptp.pp (tptp.aa_opt6800557945374683724t_bool P (tptp.some_P7363390416028606310at_nat X3))))))) (forall ((P tptp.fun_option_num_bool)) (= (exists ((X_1 tptp.option_num)) (tptp.pp (tptp.aa_option_num_bool P X_1))) (or (tptp.pp (tptp.aa_option_num_bool P tptp.none_num)) (exists ((X3 tptp.num)) (tptp.pp (tptp.aa_option_num_bool P (tptp.some_num X3))))))) (forall ((Y tptp.option_nat)) (=> (not (= Y tptp.none_nat)) (not (forall ((X22 tptp.nat)) (not (= Y (tptp.some_nat X22))))))) (forall ((Y tptp.option4927543243414619207at_nat)) (=> (not (= Y tptp.none_P5556105721700978146at_nat)) (not (forall ((X22 tptp.product_prod_nat_nat)) (not (= Y (tptp.some_P7363390416028606310at_nat X22))))))) (forall ((Y tptp.option_num)) (=> (not (= Y tptp.none_num)) (not (forall ((X22 tptp.num)) (not (= Y (tptp.some_num X22))))))) _let_191 (forall ((Option tptp.option4927543243414619207at_nat) (X2 tptp.product_prod_nat_nat)) (=> (= Option (tptp.some_P7363390416028606310at_nat X2)) (not (= Option tptp.none_P5556105721700978146at_nat)))) (forall ((Option tptp.option_num) (X2 tptp.num)) (=> (= Option (tptp.some_num X2)) (not (= Option tptp.none_num)))) (forall ((X2 tptp.nat)) (not (= tptp.none_nat (tptp.some_nat X2)))) (forall ((X2 tptp.product_prod_nat_nat)) (not (= tptp.none_P5556105721700978146at_nat (tptp.some_P7363390416028606310at_nat X2)))) (forall ((X2 tptp.num)) (not (= tptp.none_num (tptp.some_num X2)))) (forall ((A tptp.complex) (P tptp.fun_complex_bool)) (= (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex A) (tptp.collect_complex P))) (tptp.pp (tptp.aa_complex_bool P A)))) (forall ((A tptp.real) (P tptp.fun_real_bool)) (= (tptp.member_real A (tptp.collect_real P)) (tptp.pp (tptp.aa_real_bool P A)))) (forall ((A tptp.list_nat) (P tptp.fun_list_nat_bool)) (= (tptp.member_list_nat A (tptp.collect_list_nat P)) (tptp.pp (tptp.aa_list_nat_bool P A)))) (forall ((A tptp.nat) (P tptp.fun_nat_bool)) (= (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat A) (tptp.collect_nat P))) (tptp.pp (tptp.aa_nat_bool P A)))) (forall ((A tptp.int) (P tptp.fun_int_bool)) (= (tptp.pp (tptp.aa_set_int_bool (tptp.member_int A) (tptp.collect_int P))) (tptp.pp (tptp.aa_int_bool P A)))) (forall ((A4 tptp.set_complex)) (= (tptp.collect_complex (tptp.aTP_Lamm_a A4)) A4)) (forall ((A4 tptp.set_real)) (= (tptp.collect_real (tptp.aTP_Lamm_aa A4)) A4)) (forall ((A4 tptp.set_list_nat)) (= (tptp.collect_list_nat (tptp.aTP_Lamm_ab A4)) A4)) (forall ((A4 tptp.set_nat)) (= (tptp.collect_nat (tptp.aTP_Lamm_ac A4)) A4)) (forall ((A4 tptp.set_int)) (= (tptp.collect_int (tptp.aTP_Lamm_ad A4)) A4)) (forall ((P tptp.fun_complex_bool) (Q tptp.fun_complex_bool)) (=> (forall ((X4 tptp.complex)) (= (tptp.pp (tptp.aa_complex_bool P X4)) (tptp.pp (tptp.aa_complex_bool Q X4)))) (= (tptp.collect_complex P) (tptp.collect_complex Q)))) (forall ((P tptp.fun_real_bool) (Q tptp.fun_real_bool)) (=> (forall ((X4 tptp.real)) (= (tptp.pp (tptp.aa_real_bool P X4)) (tptp.pp (tptp.aa_real_bool Q X4)))) (= (tptp.collect_real P) (tptp.collect_real Q)))) (forall ((P tptp.fun_list_nat_bool) (Q tptp.fun_list_nat_bool)) (=> (forall ((X4 tptp.list_nat)) (= (tptp.pp (tptp.aa_list_nat_bool P X4)) (tptp.pp (tptp.aa_list_nat_bool Q X4)))) (= (tptp.collect_list_nat P) (tptp.collect_list_nat Q)))) (forall ((P tptp.fun_nat_bool) (Q tptp.fun_nat_bool)) (=> (forall ((X4 tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool P X4)) (tptp.pp (tptp.aa_nat_bool Q X4)))) (= (tptp.collect_nat P) (tptp.collect_nat Q)))) (forall ((P tptp.fun_int_bool) (Q tptp.fun_int_bool)) (=> (forall ((X4 tptp.int)) (= (tptp.pp (tptp.aa_int_bool P X4)) (tptp.pp (tptp.aa_int_bool Q X4)))) (= (tptp.collect_int P) (tptp.collect_int Q)))) (forall ((X2 tptp.num)) (not (= tptp.one (tptp.aa_num_num tptp.bit0 X2)))) (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt _let_177) tptp.na)) (forall ((T tptp.vEBT_VEBT)) (=> (= (tptp.vEBT_vebt_mint T) tptp.none_nat) (tptp.pp (tptp.aa_VEBT_VEBT_bool tptp.vEBT_VEBT_minNull T)))) (forall ((T tptp.vEBT_VEBT)) (=> (tptp.pp (tptp.aa_VEBT_VEBT_bool tptp.vEBT_VEBT_minNull T)) (= (tptp.vEBT_vebt_mint T) tptp.none_nat))) (forall ((M tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat M) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) N)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat M) _let_1)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat N) _let_1))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N))))) (forall ((K tptp.nat) (M tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) K)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat K) M))))) (forall ((N tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N)))) (forall ((Ma tptp.nat) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Ma) (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N) M)))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high Ma) N)) (tptp.aa_nat_nat _let_1 M)))))) (forall ((B2 tptp.nat) (A tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B2) A)) (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat A) B2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat _let_1 A)) (tptp.aa_nat_nat _let_1 B2)))))) (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (M tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt T) N)) (=> (= (tptp.some_nat M) (tptp.vEBT_vebt_mint T)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N)))))) (forall ((A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) B2))) (tptp.aa_nat_nat _let_1 A)) (tptp.aa_nat_nat _let_1 B2)))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.xa) tptp.ma)) (= tptp.deg (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat tptp.na) tptp.m)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.mi) tptp.ma)) (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt tptp.summary) tptp.m)) (forall ((V tptp.num) (W tptp.num) (Z tptp.complex)) (= (tptp.aa_complex_complex (tptp.plus_plus_complex (tptp.numera6690914467698888265omplex V)) (tptp.aa_complex_complex (tptp.plus_plus_complex (tptp.numera6690914467698888265omplex W)) Z)) (tptp.aa_complex_complex (tptp.plus_plus_complex (tptp.numera6690914467698888265omplex (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num V) W))) Z))) (forall ((V tptp.num) (W tptp.num) (Z tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_num_real tptp.numeral_numeral_real V)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_num_real tptp.numeral_numeral_real W)) Z)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num V) W))) Z))) (forall ((V tptp.num) (W tptp.num) (Z tptp.rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat V)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat W)) Z)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num V) W))) Z))) (forall ((V tptp.num) (W tptp.num) (Z tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_num_nat tptp.numeral_numeral_nat V)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_num_nat tptp.numeral_numeral_nat W)) Z)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num V) W))) Z))) (forall ((V tptp.num) (W tptp.num) (Z tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_num_int tptp.numeral_numeral_int V)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_num_int tptp.numeral_numeral_int W)) Z)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num V) W))) Z))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.aa_complex_complex (tptp.plus_plus_complex (tptp.numera6690914467698888265omplex M)) (tptp.numera6690914467698888265omplex N)) (tptp.numera6690914467698888265omplex (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num M) N)))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_num_real tptp.numeral_numeral_real M)) (tptp.aa_num_real tptp.numeral_numeral_real N)) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num M) N)))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat M)) (tptp.aa_num_rat tptp.numeral_numeral_rat N)) (tptp.aa_num_rat tptp.numeral_numeral_rat (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num M) N)))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_num_nat tptp.numeral_numeral_nat M)) (tptp.aa_num_nat tptp.numeral_numeral_nat N)) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num M) N)))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_num_int tptp.numeral_numeral_int M)) (tptp.aa_num_int tptp.numeral_numeral_int N)) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num M) N)))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num (tptp.aa_num_num tptp.bit0 M)) (tptp.aa_num_num tptp.bit0 N))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num M) N)))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_num_num tptp.bit0 M)) (tptp.aa_num_num tptp.bit0 N))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num M) N)))) (forall ((M tptp.num)) (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num M) tptp.one)))) (forall ((N tptp.num)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num tptp.one) N))) (forall ((N tptp.num)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num tptp.one) (tptp.aa_num_num tptp.bit0 N)))) (forall ((M tptp.num)) (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_num_num tptp.bit0 M)) tptp.one)))) (forall ((M tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) M)) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) M)) (= tptp.vEBT_VEBT_power (tptp.vEBT_V4262088993061758097ft_nat tptp.power_power_nat)) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A))) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real _let_1 B2)) C) (tptp.aa_real_real _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real B2) C))))) (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A))) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat _let_1 B2)) C) (tptp.aa_rat_rat _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat B2) C))))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.plus_plus_int A))) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int _let_1 B2)) C) (tptp.aa_int_int _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int B2) C))))) (forall ((X tptp.num)) (= (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X) tptp.one)) (= X tptp.one))) (forall ((N tptp.num)) (let ((_let_1 (tptp.numera6690914467698888265omplex N))) (= (tptp.numera6690914467698888265omplex (tptp.aa_num_num tptp.bit0 N)) (tptp.aa_complex_complex (tptp.plus_plus_complex _let_1) _let_1)))) (forall ((N tptp.num)) (let ((_let_1 (tptp.aa_num_real tptp.numeral_numeral_real N))) (= (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 N)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real _let_1) _let_1)))) (forall ((N tptp.num)) (let ((_let_1 (tptp.aa_num_rat tptp.numeral_numeral_rat N))) (= (tptp.aa_num_rat tptp.numeral_numeral_rat (tptp.aa_num_num tptp.bit0 N)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat _let_1) _let_1)))) (forall ((N tptp.num)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat N))) (= (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 N)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat _let_1) _let_1)))) (forall ((N tptp.num)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int N))) (= (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 N)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int _let_1) _let_1)))) (forall ((X tptp.complex) (Y tptp.complex)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.aa_nat_complex (tptp.power_power_complex (tptp.aa_complex_complex (tptp.minus_minus_complex X) Y)) _let_1) (tptp.aa_nat_complex (tptp.power_power_complex (tptp.aa_complex_complex (tptp.minus_minus_complex Y) X)) _let_1)))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real X) Y)) _let_1) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real Y) X)) _let_1)))) (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_rat_rat (tptp.minus_minus_rat X) Y)) _let_1) (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_rat_rat (tptp.minus_minus_rat Y) X)) _let_1)))) (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int X) Y)) _let_1) (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int Y) X)) _let_1)))) (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat K))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) K)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) N)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat _let_1 M)) (tptp.aa_nat_nat _let_1 N))))))) (forall ((A tptp.complex) (B2 tptp.complex) (N tptp.nat)) (= (tptp.aa_nat_complex (tptp.power_power_complex (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex A) B2)) N) (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex (tptp.aa_nat_complex (tptp.power_power_complex A) N)) (tptp.aa_nat_complex (tptp.power_power_complex B2) N)))) (forall ((A tptp.real) (B2 tptp.real) (N tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real A) B2)) N) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real A) N)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real B2) N)))) (forall ((A tptp.rat) (B2 tptp.rat) (N tptp.nat)) (= (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_rat_rat (tptp.divide_divide_rat A) B2)) N) (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_nat_rat (tptp.power_power_rat A) N)) (tptp.aa_nat_rat (tptp.power_power_rat B2) N)))) (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt T) N)) (=> (= (tptp.vEBT_vebt_mint T) (tptp.some_nat X)) (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_VEBT_min_in_set (tptp.vEBT_VEBT_set_vebt T)) X))))) (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt T) N)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_VEBT_min_in_set (tptp.vEBT_VEBT_set_vebt T)) X)) (= (tptp.vEBT_vebt_mint T) (tptp.some_nat X))))) (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat X) Y) Z) (= (tptp.aa_opt1882420858203594238on_nat (tptp.aa_opt7711074727033721499on_nat tptp.vEBT_VEBT_add (tptp.some_nat X)) (tptp.some_nat Y)) (tptp.some_nat Z)))) (forall ((K tptp.nat) (J tptp.nat) (I tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat I))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) J)) (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat J) K)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat _let_1 J)) K))))) (forall ((K tptp.nat) (J tptp.nat) (I tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) J)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat J) K)) I) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat J) I)) K)))) (forall ((K tptp.nat) (J tptp.nat) (I tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) J)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat I) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat J) K)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat I) K)) J)))) (forall ((B2 tptp.real) (A tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real B2) A)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real B2) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A) B2)) A))) (forall ((B2 tptp.rat) (A tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B2) A)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat B2) (tptp.aa_rat_rat (tptp.minus_minus_rat A) B2)) A))) (forall ((B2 tptp.nat) (A tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B2) A)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat B2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat A) B2)) A))) (forall ((B2 tptp.int) (A tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B2) A)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int B2) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) B2)) A))) (forall ((B2 tptp.real) (A tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real B2) A)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A) B2)) B2) A))) (forall ((B2 tptp.rat) (A tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B2) A)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.minus_minus_rat A) B2)) B2) A))) (forall ((B2 tptp.nat) (A tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B2) A)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat A) B2)) B2) A))) (forall ((B2 tptp.int) (A tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B2) A)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) B2)) B2) A))) (forall ((Tree tptp.vEBT_VEBT) (X tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_vebt_member Tree) X)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt Tree) N)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N)))))) (=> (not _let_190) (forall ((I2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) tptp.m))) (and (=> (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high tptp.ma) tptp.na) I2) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions (tptp.nth_VEBT_VEBT tptp.treeList I2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low tptp.ma) tptp.na)))) (forall ((X5 tptp.nat)) (=> (and (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high X5) tptp.na) I2) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions (tptp.nth_VEBT_VEBT tptp.treeList I2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low X5) tptp.na)))) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.mi) X5)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X5) tptp.ma))))))))) (forall ((A tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_2 (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat _let_2 (tptp.aa_nat_nat _let_1 M))) (tptp.aa_nat_nat _let_1 N)) (tptp.aa_nat_nat _let_2 (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) N))))))) (forall ((A tptp.int) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_2 (tptp.divide_divide_int A))) (= (tptp.aa_int_int (tptp.divide_divide_int (tptp.aa_int_int _let_2 (tptp.aa_nat_int _let_1 M))) (tptp.aa_nat_int _let_1 N)) (tptp.aa_int_int _let_2 (tptp.aa_nat_int _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) N))))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X))) (=> (tptp.pp (tptp.aa_real_bool _let_1 Y)) (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) Y)) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))))))) (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 Y)) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat X) Y)) (tptp.aa_num_rat tptp.numeral_numeral_rat (tptp.aa_num_num tptp.bit0 tptp.one)))))))) (forall ((T tptp.vEBT_VEBT)) (=> (not (tptp.pp (tptp.aa_VEBT_VEBT_bool tptp.vEBT_VEBT_minNull T))) (exists ((X_12 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions T) X_12))))) (forall ((T tptp.vEBT_VEBT) (X tptp.nat)) (=> (tptp.pp (tptp.aa_VEBT_VEBT_bool tptp.vEBT_VEBT_minNull T)) (not (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_vebt_member T) X))))) (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt T) N)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions T) X)) (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_vebt_member T) X))))) (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt T) N)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions T) X)) (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_vebt_member T) X))))) (= tptp.vEBT_VEBT_add (tptp.vEBT_V4262088993061758097ft_nat tptp.plus_plus_nat)) (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (Maxi tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt T) N)) (=> (= (tptp.vEBT_vebt_mint T) (tptp.some_nat Maxi)) (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_vebt_member T) Maxi))))) (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt T) N)) (= (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_vebt_member T) X)) (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X) (tptp.vEBT_set_vebt T)))))) (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (Mini tptp.nat) (X tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt T) N)) (=> (= (tptp.vEBT_vebt_mint T) (tptp.some_nat Mini)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_vebt_member T) X)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Mini) X)))))) (forall ((T tptp.vEBT_VEBT) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt T) N)) (= (tptp.vEBT_set_vebt T) (tptp.vEBT_VEBT_set_vebt T)))) (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat K))) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat _let_1 M)) (tptp.aa_nat_nat _let_1 N))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N))))) (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat K))) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat _let_1 M)) (tptp.aa_nat_nat _let_1 N))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N))))) (forall ((I tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I) N)) (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat _let_1 I)) I)))) (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat I))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat _let_1 J)) K) (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat J) K))))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num (tptp.aa_num_num tptp.bit0 M)) (tptp.aa_num_num tptp.bit0 N)) (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num M) N)))) (= (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num tptp.one) tptp.one) _let_24) (forall ((T tptp.vEBT_VEBT) (X tptp.nat) (Y tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool (tptp.vEBT_is_pred_in_set (tptp.vEBT_VEBT_set_vebt T)) X) Y)) (and (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_vebt_member T) Y)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Y) X)) (forall ((Z2 tptp.nat)) (=> (and (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_vebt_member T) Z2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Z2) X))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Z2) Y))))))) (forall ((I2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) tptp.m))) (= (exists ((X_1 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions (tptp.nth_VEBT_VEBT tptp.treeList I2)) X_1))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions tptp.summary) I2))))) (forall ((N tptp.num)) (= (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num tptp.one) N) (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num N) tptp.one))) (forall ((X tptp.real) (Y tptp.real)) (=> (not (= X Y)) (=> (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Y))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y) X))))) (forall ((X tptp.rat) (Y tptp.rat)) (=> (not (= X Y)) (=> (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) Y))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Y) X))))) (forall ((X tptp.int) (Y tptp.int)) (=> (not (= X Y)) (=> (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) Y))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Y) X))))) (forall ((M tptp.nat) (N tptp.nat)) (= (not (= M N)) (or (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N) M))))) (forall ((N tptp.nat)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N) N)))) (forall ((N tptp.nat) (M tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N) M)) (not (= M N)))) (forall ((S tptp.nat) (T tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat S) T)) (not (= S T)))) (forall ((N tptp.nat)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N) N)))) (forall ((P tptp.fun_nat_bool) (N tptp.nat)) (=> (forall ((N2 tptp.nat)) (=> (forall ((M2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M2) N2)) (tptp.pp (tptp.aa_nat_bool P M2)))) (tptp.pp (tptp.aa_nat_bool P N2)))) (tptp.pp (tptp.aa_nat_bool P N)))) (forall ((P tptp.fun_nat_bool) (N tptp.nat)) (=> (forall ((N2 tptp.nat)) (=> (not (tptp.pp (tptp.aa_nat_bool P N2))) (exists ((M2 tptp.nat)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M2) N2)) (not (tptp.pp (tptp.aa_nat_bool P M2))))))) (tptp.pp (tptp.aa_nat_bool P N)))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (not (= X Y)) (=> (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Y))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Y) X))))) (forall ((N tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N) N))) (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 J)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat J) K)) (tptp.pp (tptp.aa_nat_bool _let_1 K)))))) (forall ((M tptp.nat) (N tptp.nat)) (=> (= M N) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)))) (forall ((M tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N) M)) (= M N)))) (forall ((M tptp.nat) (N tptp.nat)) (or (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N) M)))) (forall ((P tptp.fun_nat_bool) (K tptp.nat) (B2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool P K)) (=> (forall ((Y4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool P Y4)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Y4) B2)))) (exists ((X4 tptp.nat)) (and (tptp.pp (tptp.aa_nat_bool P X4)) (forall ((Y5 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool P Y5)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Y5) X4))))))))) (forall ((X tptp.list_VEBT_VEBT) (Y tptp.list_VEBT_VEBT)) (=> (not (= (tptp.size_s6755466524823107622T_VEBT X) (tptp.size_s6755466524823107622T_VEBT Y))) (not (= X Y)))) (forall ((X tptp.num) (Y tptp.num)) (=> (not (= (tptp.aa_num_nat tptp.size_size_num X) (tptp.aa_num_nat tptp.size_size_num Y))) (not (= X Y)))) (forall ((X tptp.list_bool) (Y tptp.list_bool)) (=> (not (= (tptp.size_size_list_bool X) (tptp.size_size_list_bool Y))) (not (= X Y)))) (forall ((X tptp.list_nat) (Y tptp.list_nat)) (=> (not (= (tptp.size_size_list_nat X) (tptp.size_size_list_nat Y))) (not (= X Y)))) (forall ((X tptp.vEBT_VEBT) (Y tptp.vEBT_VEBT)) (=> (not (= (tptp.aa_VEBT_VEBT_nat tptp.size_size_VEBT_VEBT X) (tptp.aa_VEBT_VEBT_nat tptp.size_size_VEBT_VEBT Y))) (not (= X Y)))) (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat I))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat _let_1 J)) K) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat _let_1 K)) J)))) (forall ((A tptp.complex) (C tptp.complex) (B2 tptp.complex) (D tptp.complex)) (= (tptp.aa_complex_complex (tptp.minus_minus_complex (tptp.aa_complex_complex (tptp.plus_plus_complex A) C)) (tptp.aa_complex_complex (tptp.plus_plus_complex B2) D)) (tptp.aa_complex_complex (tptp.plus_plus_complex (tptp.aa_complex_complex (tptp.minus_minus_complex A) B2)) (tptp.aa_complex_complex (tptp.minus_minus_complex C) D)))) (forall ((A tptp.real) (C tptp.real) (B2 tptp.real) (D tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) C)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real B2) D)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A) B2)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real C) D)))) (forall ((A tptp.rat) (C tptp.rat) (B2 tptp.rat) (D tptp.rat)) (= (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) C)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat B2) D)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.minus_minus_rat A) B2)) (tptp.aa_rat_rat (tptp.minus_minus_rat C) D)))) (forall ((A tptp.int) (C tptp.int) (B2 tptp.int) (D tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int B2) D)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) B2)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int C) D)))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)) (not (= M N))))) (forall ((M tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)) (or (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N)) (= M N)))) (forall ((M tptp.nat) (N tptp.nat)) (=> (or (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N)) (= M N)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)))) (forall ((M tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)) (=> (not (= M N)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N))))) (forall ((F tptp.fun_nat_nat) (I tptp.nat) (J tptp.nat)) (=> (forall ((I3 tptp.nat) (J2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I3) J2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat F I3)) (tptp.aa_nat_nat F J2))))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I) J)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat F I)) (tptp.aa_nat_nat F J)))))) (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat I) J)) K)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I) K)))) (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I) J)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat K) L)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat I) K)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat J) L)))))) (forall ((I tptp.nat) (J tptp.nat)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat I) J)) I)))) (forall ((J tptp.nat) (I tptp.nat)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat J) I)) I)))) (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I) J)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat I) K)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat J) K))))) (forall ((I tptp.nat) (J tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 J)) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat J) M)))))) (forall ((I tptp.nat) (J tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 J)) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) J)))))) (forall ((K tptp.nat) (L tptp.nat) (M tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat K) L)) (=> (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) L) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat K) N)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N))))) (forall ((M tptp.nat) (K tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) K)) N)) (not (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) N))))))) (forall ((N tptp.nat) (M tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N) M)))) (forall ((N tptp.nat) (M tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) N)))) (forall ((M tptp.nat) (K tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) K)) N)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)))) (forall ((M tptp.nat) (K tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) K)) N)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) N)))) (forall ((K tptp.nat) (L tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) L)) (exists ((N2 tptp.nat)) (= L (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat K) N2))))) (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I) J)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) L)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat I) K)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat J) L)))))) (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I) J)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat I) K)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat J) K))))) (forall ((I tptp.nat) (J tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 J)) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat J) M)))))) (forall ((I tptp.nat) (J tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 J)) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) J)))))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)) (exists ((K2 tptp.nat)) (= N (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) K2))))) (forall ((M tptp.nat) (N tptp.nat) (L tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat L))) (let ((_let_2 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M))) (=> (tptp.pp (tptp.aa_nat_bool _let_2 N)) (=> (tptp.pp (tptp.aa_nat_bool _let_2 L)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat _let_1 N)) (tptp.aa_nat_nat _let_1 M)))))))) (forall ((J tptp.nat) (K tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat J) K)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat J) N)) K)))) (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 M)) (=> (tptp.pp (tptp.aa_nat_bool _let_1 N)) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) K) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) K)) (= M N)))))) (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 M)) (=> (tptp.pp (tptp.aa_nat_bool _let_1 N)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) K)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) K))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N))))))) (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M))) (let ((_let_2 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K))) (=> (tptp.pp (tptp.aa_nat_bool _let_2 M)) (=> (tptp.pp (tptp.aa_nat_bool _let_2 N)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat _let_1 K)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) K)) (tptp.aa_nat_nat _let_1 N))))))) (forall ((M tptp.nat) (N tptp.nat) (L tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) L)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) L))))) (forall ((M tptp.nat) (N tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) N)) M))) (forall ((A tptp.nat) (C tptp.nat) (B2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B2))) (let ((_let_2 (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat C))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) C)) (=> (tptp.pp (tptp.aa_nat_bool _let_1 C)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat _let_2 A)) (tptp.aa_nat_nat _let_2 B2))) (tptp.pp (tptp.aa_nat_bool _let_1 A)))))))) (forall ((M tptp.nat) (N tptp.nat) (L tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat L))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat _let_1 N)) (tptp.aa_nat_nat _let_1 M)))))) (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat K))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat _let_1 M)) (tptp.aa_nat_nat _let_1 N)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) N)))) (forall ((M tptp.nat) (K tptp.nat) (N tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) K)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N) K)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) N))) (forall ((N tptp.nat) (M tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N) M)) N) M)) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) N)) N) M)) (forall ((I tptp.real) (K tptp.real) (N tptp.real) (J tptp.real)) (let ((_let_1 (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real N) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real J) K))))) (let ((_let_2 (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real I) K)) N)))) (=> _let_2 (=> _let_1 (=> _let_2 (=> _let_1 (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real N) K)) J))))))))) (forall ((I tptp.rat) (K tptp.rat) (N tptp.rat) (J tptp.rat)) (let ((_let_1 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat N) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat J) K))))) (let ((_let_2 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat I) K)) N)))) (=> _let_2 (=> _let_1 (=> _let_2 (=> _let_1 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.minus_minus_rat N) K)) J))))))))) (forall ((I tptp.nat) (K tptp.nat) (N tptp.nat) (J tptp.nat)) (let ((_let_1 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat J) K))))) (let ((_let_2 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat I) K)) N)))) (=> _let_2 (=> _let_1 (=> _let_2 (=> _let_1 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) K)) J))))))))) (forall ((I tptp.int) (K tptp.int) (N tptp.int) (J tptp.int)) (let ((_let_1 (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int N) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int J) K))))) (let ((_let_2 (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int I) K)) N)))) (=> _let_2 (=> _let_1 (=> _let_2 (=> _let_1 (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int N) K)) J))))))))) (forall ((I tptp.real) (K tptp.real) (N tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real I) K)) N)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real I) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real N) K))))) (forall ((I tptp.rat) (K tptp.rat) (N tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat I) K)) N)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat I) (tptp.aa_rat_rat (tptp.minus_minus_rat N) K))))) (forall ((I tptp.nat) (K tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat I) K)) N)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) K))))) (forall ((I tptp.int) (K tptp.int) (N tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int I) K)) N)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int I) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int N) K))))) (forall ((A tptp.real) (B2 tptp.real)) (=> (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B2))) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real B2) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A) B2)) A))) (forall ((A tptp.rat) (B2 tptp.rat)) (=> (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B2))) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat B2) (tptp.aa_rat_rat (tptp.minus_minus_rat A) B2)) A))) (forall ((A tptp.nat) (B2 tptp.nat)) (=> (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) B2))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat B2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat A) B2)) A))) (forall ((A tptp.int) (B2 tptp.int)) (=> (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B2))) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int B2) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) B2)) A))) (forall ((F tptp.fun_nat_nat) (M tptp.nat) (K tptp.nat)) (=> (forall ((M3 tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M3) N2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat F M3)) (tptp.aa_nat_nat F N2))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat F M)) K)) (tptp.aa_nat_nat F (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) K)))))) (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 M)) (=> (tptp.pp (tptp.aa_nat_bool _let_1 N)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) K)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) K))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N))))))) (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) B2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat C) A)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat A) C)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat B2) C)))))) (forall ((M tptp.nat) (N tptp.nat)) (=> (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) N)) M))) (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat J) K))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat I) K)) J)))) (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I) J)) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat J) I) K) (= J (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat K) I))))) (forall ((K tptp.nat) (J tptp.nat) (I tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) J)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat J) I)) K) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat J) K)) I)))) (forall ((K tptp.nat) (J tptp.nat) (I tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat I))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) J)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat _let_1 J)) K) (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat J) K)))))) (forall ((K tptp.nat) (J tptp.nat) (I tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) J)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat J) K))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat I) K)) J))))) (forall ((J tptp.nat) (K tptp.nat) (I tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat J) K)) I)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat J) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat I) K))))) (forall ((K tptp.nat) (J tptp.nat) (I tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) J)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat J) K)) I)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat J) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat I) K)))))) (forall ((X tptp.real)) (let ((_let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real X) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real _let_1) _let_1) X))) (forall ((X tptp.rat)) (let ((_let_1 (tptp.aa_rat_rat (tptp.divide_divide_rat X) (tptp.aa_num_rat tptp.numeral_numeral_rat (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat _let_1) _let_1) X))) (forall ((N tptp.nat) (TreeList tptp.list_VEBT_VEBT) (X tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_V5917875025757280293ildren N TreeList) X)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions (tptp.nth_VEBT_VEBT TreeList (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high X) N))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low X) N))))) (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt T) N)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_VEBT_max_in_set (tptp.vEBT_VEBT_set_vebt T)) X)) (= (tptp.vEBT_vebt_maxt T) (tptp.some_nat X))))) (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt T) N)) (=> (= (tptp.vEBT_vebt_maxt T) (tptp.some_nat X)) (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_VEBT_max_in_set (tptp.vEBT_VEBT_set_vebt T)) X))))) (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt T) N)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) _let_1)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Y) _let_1)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_vebt_member (tptp.vEBT_vebt_insert T X)) Y)) (or (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_vebt_member T) Y)) (= X Y)))))))) (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt T) N)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) _let_1)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Y) _let_1)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions T) X)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions (tptp.vEBT_vebt_insert T Y)) X)))))))) (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt T) N)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions (tptp.vEBT_vebt_insert T X)) X))))) (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (Maxi tptp.nat) (X tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt T) N)) (=> (= (tptp.vEBT_vebt_maxt T) (tptp.some_nat Maxi)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_vebt_member T) X)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X) Maxi)))))) (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (Maxi tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt T) N)) (=> (= (tptp.vEBT_vebt_maxt T) (tptp.some_nat Maxi)) (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_vebt_member T) Maxi))))) (forall ((Info tptp.option4927543243414619207at_nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (N tptp.nat) (X tptp.nat)) (let ((_let_1 (tptp.vEBT_Node Info Deg TreeList Summary))) (let ((_let_2 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_3 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat Deg) _let_2))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt _let_1) N)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat _let_2) Deg))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions (tptp.nth_VEBT_VEBT TreeList (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high X) _let_3))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low X) _let_3))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions _let_1) X))))))))) (forall ((T tptp.vEBT_VEBT) (X tptp.nat)) (=> (= (tptp.vEBT_vebt_maxt T) (tptp.some_nat X)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions T) X)))) (forall ((H tptp.nat) (L tptp.nat) (D tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.vEBT_VEBT_bit_concat H) L) D) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat H) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) D))) L))) (forall ((X tptp.nat) (N tptp.nat) (Y tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) _let_1)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat Y) _let_1)) X)) N) X)))) (forall ((Info tptp.option4927543243414619207at_nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt (tptp.vEBT_Node Info Deg TreeList Summary)) N)) (= Deg N))) (forall ((V tptp.num) (W tptp.num) (Z tptp.complex)) (= (tptp.aa_complex_complex (tptp.times_times_complex (tptp.numera6690914467698888265omplex V)) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.numera6690914467698888265omplex W)) Z)) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.numera6690914467698888265omplex (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.times_times_num V) W))) Z))) (forall ((V tptp.num) (W tptp.num) (Z tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_num_real tptp.numeral_numeral_real V)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_num_real tptp.numeral_numeral_real W)) Z)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.times_times_num V) W))) Z))) (forall ((V tptp.num) (W tptp.num) (Z tptp.rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_num_rat tptp.numeral_numeral_rat V)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_num_rat tptp.numeral_numeral_rat W)) Z)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_num_rat tptp.numeral_numeral_rat (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.times_times_num V) W))) Z))) (forall ((V tptp.num) (W tptp.num) (Z tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat V)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat W)) Z)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.times_times_num V) W))) Z))) (forall ((V tptp.num) (W tptp.num) (Z tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_num_int tptp.numeral_numeral_int V)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_num_int tptp.numeral_numeral_int W)) Z)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.times_times_num V) W))) Z))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.aa_complex_complex (tptp.times_times_complex (tptp.numera6690914467698888265omplex M)) (tptp.numera6690914467698888265omplex N)) (tptp.numera6690914467698888265omplex (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.times_times_num M) N)))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_num_real tptp.numeral_numeral_real M)) (tptp.aa_num_real tptp.numeral_numeral_real N)) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.times_times_num M) N)))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_num_rat tptp.numeral_numeral_rat M)) (tptp.aa_num_rat tptp.numeral_numeral_rat N)) (tptp.aa_num_rat tptp.numeral_numeral_rat (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.times_times_num M) N)))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat M)) (tptp.aa_num_nat tptp.numeral_numeral_nat N)) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.times_times_num M) N)))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_num_int tptp.numeral_numeral_int M)) (tptp.aa_num_int tptp.numeral_numeral_int N)) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.times_times_num M) N)))) (forall ((X tptp.nat) (N tptp.nat) (Y tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) _let_1)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat Y) _let_1)) X)) N) Y)))) (forall ((A tptp.complex) (B2 tptp.complex) (V tptp.num)) (let ((_let_1 (tptp.numera6690914467698888265omplex V))) (= (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_complex_complex (tptp.plus_plus_complex A) B2)) _let_1) (tptp.aa_complex_complex (tptp.plus_plus_complex (tptp.aa_complex_complex (tptp.times_times_complex A) _let_1)) (tptp.aa_complex_complex (tptp.times_times_complex B2) _let_1))))) (forall ((A tptp.real) (B2 tptp.real) (V tptp.num)) (let ((_let_1 (tptp.aa_num_real tptp.numeral_numeral_real V))) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) B2)) _let_1) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) _let_1)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real B2) _let_1))))) (forall ((A tptp.rat) (B2 tptp.rat) (V tptp.num)) (let ((_let_1 (tptp.aa_num_rat tptp.numeral_numeral_rat V))) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) B2)) _let_1) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) _let_1)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat B2) _let_1))))) (forall ((A tptp.nat) (B2 tptp.nat) (V tptp.num)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat V))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) B2)) _let_1) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) _let_1)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B2) _let_1))))) (forall ((A tptp.int) (B2 tptp.int) (V tptp.num)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int V))) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) B2)) _let_1) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) _let_1)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B2) _let_1))))) (forall ((V tptp.num) (B2 tptp.complex) (C tptp.complex)) (let ((_let_1 (tptp.times_times_complex (tptp.numera6690914467698888265omplex V)))) (= (tptp.aa_complex_complex _let_1 (tptp.aa_complex_complex (tptp.plus_plus_complex B2) C)) (tptp.aa_complex_complex (tptp.plus_plus_complex (tptp.aa_complex_complex _let_1 B2)) (tptp.aa_complex_complex _let_1 C))))) (forall ((V tptp.num) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_num_real tptp.numeral_numeral_real V)))) (= (tptp.aa_real_real _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real B2) C)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real _let_1 B2)) (tptp.aa_real_real _let_1 C))))) (forall ((V tptp.num) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_num_rat tptp.numeral_numeral_rat V)))) (= (tptp.aa_rat_rat _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat B2) C)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat _let_1 B2)) (tptp.aa_rat_rat _let_1 C))))) (forall ((V tptp.num) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat V)))) (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat B2) C)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat _let_1 B2)) (tptp.aa_nat_nat _let_1 C))))) (forall ((V tptp.num) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_num_int tptp.numeral_numeral_int V)))) (= (tptp.aa_int_int _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int B2) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int _let_1 B2)) (tptp.aa_int_int _let_1 C))))) (forall ((V tptp.num) (B2 tptp.complex) (C tptp.complex)) (let ((_let_1 (tptp.times_times_complex (tptp.numera6690914467698888265omplex V)))) (= (tptp.aa_complex_complex _let_1 (tptp.aa_complex_complex (tptp.minus_minus_complex B2) C)) (tptp.aa_complex_complex (tptp.minus_minus_complex (tptp.aa_complex_complex _let_1 B2)) (tptp.aa_complex_complex _let_1 C))))) (forall ((V tptp.num) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_num_real tptp.numeral_numeral_real V)))) (= (tptp.aa_real_real _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real B2) C)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real _let_1 B2)) (tptp.aa_real_real _let_1 C))))) (forall ((V tptp.num) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_num_rat tptp.numeral_numeral_rat V)))) (= (tptp.aa_rat_rat _let_1 (tptp.aa_rat_rat (tptp.minus_minus_rat B2) C)) (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_rat_rat _let_1 B2)) (tptp.aa_rat_rat _let_1 C))))) (forall ((V tptp.num) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_num_int tptp.numeral_numeral_int V)))) (= (tptp.aa_int_int _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int B2) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_int_int _let_1 B2)) (tptp.aa_int_int _let_1 C))))) (forall ((A tptp.complex) (B2 tptp.complex) (V tptp.num)) (let ((_let_1 (tptp.numera6690914467698888265omplex V))) (= (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_complex_complex (tptp.minus_minus_complex A) B2)) _let_1) (tptp.aa_complex_complex (tptp.minus_minus_complex (tptp.aa_complex_complex (tptp.times_times_complex A) _let_1)) (tptp.aa_complex_complex (tptp.times_times_complex B2) _let_1))))) (forall ((A tptp.real) (B2 tptp.real) (V tptp.num)) (let ((_let_1 (tptp.aa_num_real tptp.numeral_numeral_real V))) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A) B2)) _let_1) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) _let_1)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real B2) _let_1))))) (forall ((A tptp.rat) (B2 tptp.rat) (V tptp.num)) (let ((_let_1 (tptp.aa_num_rat tptp.numeral_numeral_rat V))) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat (tptp.minus_minus_rat A) B2)) _let_1) (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) _let_1)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat B2) _let_1))))) (forall ((A tptp.int) (B2 tptp.int) (V tptp.num)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int V))) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) B2)) _let_1) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) _let_1)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B2) _let_1))))) (forall ((B2 tptp.real) (W tptp.num) (A tptp.real)) (let ((_let_1 (tptp.aa_num_real tptp.numeral_numeral_real W))) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real B2) _let_1)) A)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real B2) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) _let_1)))))) (forall ((B2 tptp.rat) (W tptp.num) (A tptp.rat)) (let ((_let_1 (tptp.aa_num_rat tptp.numeral_numeral_rat W))) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.divide_divide_rat B2) _let_1)) A)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B2) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) _let_1)))))) (forall ((A tptp.real) (B2 tptp.real) (W tptp.num)) (let ((_let_1 (tptp.aa_num_real tptp.numeral_numeral_real W))) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real B2) _let_1))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) _let_1)) B2))))) (forall ((A tptp.rat) (B2 tptp.rat) (W tptp.num)) (let ((_let_1 (tptp.aa_num_rat tptp.numeral_numeral_rat W))) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) (tptp.aa_rat_rat (tptp.divide_divide_rat B2) _let_1))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) _let_1)) B2))))) (forall ((B2 tptp.real) (W tptp.num) (A tptp.real)) (let ((_let_1 (tptp.aa_num_real tptp.numeral_numeral_real W))) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real B2) _let_1)) A)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B2) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) _let_1)))))) (forall ((B2 tptp.rat) (W tptp.num) (A tptp.rat)) (let ((_let_1 (tptp.aa_num_rat tptp.numeral_numeral_rat W))) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.divide_divide_rat B2) _let_1)) A)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B2) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) _let_1)))))) (forall ((A tptp.real) (B2 tptp.real) (W tptp.num)) (let ((_let_1 (tptp.aa_num_real tptp.numeral_numeral_real W))) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real B2) _let_1))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) _let_1)) B2))))) (forall ((A tptp.rat) (B2 tptp.rat) (W tptp.num)) (let ((_let_1 (tptp.aa_num_rat tptp.numeral_numeral_rat W))) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) (tptp.aa_rat_rat (tptp.divide_divide_rat B2) _let_1))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) _let_1)) B2))))) (forall ((A tptp.complex) (M tptp.num) (N tptp.num) (B2 tptp.complex)) (let ((_let_1 (tptp.power_power_complex A))) (= (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_nat_complex _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat M))) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_nat_complex _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat N))) B2)) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_nat_complex _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num M) N)))) B2)))) (forall ((A tptp.real) (M tptp.num) (N tptp.num) (B2 tptp.real)) (let ((_let_1 (tptp.aa_real_fun_nat_real tptp.power_power_real A))) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat M))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat N))) B2)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num M) N)))) B2)))) (forall ((A tptp.rat) (M tptp.num) (N tptp.num) (B2 tptp.rat)) (let ((_let_1 (tptp.power_power_rat A))) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat M))) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat N))) B2)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num M) N)))) B2)))) (forall ((A tptp.nat) (M tptp.num) (N tptp.num) (B2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat M))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat N))) B2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num M) N)))) B2)))) (forall ((A tptp.int) (M tptp.num) (N tptp.num) (B2 tptp.int)) (let ((_let_1 (tptp.power_power_int A))) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat M))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat N))) B2)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num M) N)))) B2)))) (forall ((A tptp.complex) (M tptp.num) (N tptp.num)) (let ((_let_1 (tptp.power_power_complex A))) (= (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_nat_complex _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat M))) (tptp.aa_nat_complex _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat N))) (tptp.aa_nat_complex _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num M) N)))))) (forall ((A tptp.real) (M tptp.num) (N tptp.num)) (let ((_let_1 (tptp.aa_real_fun_nat_real tptp.power_power_real A))) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat M))) (tptp.aa_nat_real _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat N))) (tptp.aa_nat_real _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num M) N)))))) (forall ((A tptp.rat) (M tptp.num) (N tptp.num)) (let ((_let_1 (tptp.power_power_rat A))) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat M))) (tptp.aa_nat_rat _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat N))) (tptp.aa_nat_rat _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num M) N)))))) (forall ((A tptp.nat) (M tptp.num) (N tptp.num)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat M))) (tptp.aa_nat_nat _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat N))) (tptp.aa_nat_nat _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num M) N)))))) (forall ((A tptp.int) (M tptp.num) (N tptp.num)) (let ((_let_1 (tptp.power_power_int A))) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat M))) (tptp.aa_nat_int _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat N))) (tptp.aa_nat_int _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num M) N)))))) (=> _let_190 (forall ((X5 tptp.vEBT_VEBT)) (=> (tptp.pp (tptp.aa_set8260762808118238015T_bool (tptp.aa_VEB289770264548726718T_bool tptp.member_VEBT_VEBT X5) (tptp.set_VEBT_VEBT2 tptp.treeList))) (not (exists ((X_13 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions X5) X_13))))))) (forall ((A tptp.real) (E tptp.real) (B2 tptp.real) (C tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) E)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real B2) E)) C)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) B2)) E)) C))) (forall ((A tptp.rat) (E tptp.rat) (B2 tptp.rat) (C tptp.rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) E)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat B2) E)) C)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) B2)) E)) C))) (forall ((A tptp.nat) (E tptp.nat) (B2 tptp.nat) (C tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) E)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B2) E)) C)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) B2)) E)) C))) (forall ((A tptp.int) (E tptp.int) (B2 tptp.int) (C tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) E)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B2) E)) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) B2)) E)) C))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) B2)) C) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) C)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real B2) C)))) (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) B2)) C) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) C)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat B2) C)))) (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) B2)) C) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) C)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B2) C)))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) B2)) C) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B2) C)))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A))) (= (tptp.aa_real_real _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real B2) C)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real _let_1 B2)) (tptp.aa_real_real _let_1 C))))) (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A))) (= (tptp.aa_rat_rat _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat B2) C)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat _let_1 B2)) (tptp.aa_rat_rat _let_1 C))))) (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A))) (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat B2) C)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat _let_1 B2)) (tptp.aa_nat_nat _let_1 C))))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.times_times_int A))) (= (tptp.aa_int_int _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int B2) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int _let_1 B2)) (tptp.aa_int_int _let_1 C))))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) B2)) C) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) C)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real B2) C)))) (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) B2)) C) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) C)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat B2) C)))) (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) B2)) C) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) C)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B2) C)))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) B2)) C) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B2) C)))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A))) (= (tptp.aa_real_real _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real B2) C)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real _let_1 B2)) (tptp.aa_real_real _let_1 C))))) (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A))) (= (tptp.aa_rat_rat _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat B2) C)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat _let_1 B2)) (tptp.aa_rat_rat _let_1 C))))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.times_times_int A))) (= (tptp.aa_int_int _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int B2) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int _let_1 B2)) (tptp.aa_int_int _let_1 C))))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) B2)) C) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) C)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real B2) C)))) (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) B2)) C) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) C)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat B2) C)))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) B2)) C) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B2) C)))) (forall ((A tptp.complex) (B2 tptp.complex) (C tptp.complex)) (let ((_let_1 (tptp.times_times_complex A))) (= (tptp.aa_complex_complex _let_1 (tptp.aa_complex_complex (tptp.minus_minus_complex B2) C)) (tptp.aa_complex_complex (tptp.minus_minus_complex (tptp.aa_complex_complex _let_1 B2)) (tptp.aa_complex_complex _let_1 C))))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A))) (= (tptp.aa_real_real _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real B2) C)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real _let_1 B2)) (tptp.aa_real_real _let_1 C))))) (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A))) (= (tptp.aa_rat_rat _let_1 (tptp.aa_rat_rat (tptp.minus_minus_rat B2) C)) (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_rat_rat _let_1 B2)) (tptp.aa_rat_rat _let_1 C))))) (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A))) (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat B2) C)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat _let_1 B2)) (tptp.aa_nat_nat _let_1 C))))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.times_times_int A))) (= (tptp.aa_int_int _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int B2) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_int_int _let_1 B2)) (tptp.aa_int_int _let_1 C))))) (forall ((B2 tptp.complex) (C tptp.complex) (A tptp.complex)) (= (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_complex_complex (tptp.minus_minus_complex B2) C)) A) (tptp.aa_complex_complex (tptp.minus_minus_complex (tptp.aa_complex_complex (tptp.times_times_complex B2) A)) (tptp.aa_complex_complex (tptp.times_times_complex C) A)))) (forall ((B2 tptp.real) (C tptp.real) (A tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real B2) C)) A) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real B2) A)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real C) A)))) (forall ((B2 tptp.rat) (C tptp.rat) (A tptp.rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat (tptp.minus_minus_rat B2) C)) A) (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat B2) A)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat C) A)))) (forall ((B2 tptp.nat) (C tptp.nat) (A tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat B2) C)) A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B2) A)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat C) A)))) (forall ((B2 tptp.int) (C tptp.int) (A tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int B2) C)) A) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B2) A)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int C) A)))) (forall ((A tptp.complex) (B2 tptp.complex) (C tptp.complex)) (let ((_let_1 (tptp.times_times_complex A))) (= (tptp.aa_complex_complex _let_1 (tptp.aa_complex_complex (tptp.minus_minus_complex B2) C)) (tptp.aa_complex_complex (tptp.minus_minus_complex (tptp.aa_complex_complex _let_1 B2)) (tptp.aa_complex_complex _let_1 C))))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A))) (= (tptp.aa_real_real _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real B2) C)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real _let_1 B2)) (tptp.aa_real_real _let_1 C))))) (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A))) (= (tptp.aa_rat_rat _let_1 (tptp.aa_rat_rat (tptp.minus_minus_rat B2) C)) (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_rat_rat _let_1 B2)) (tptp.aa_rat_rat _let_1 C))))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.times_times_int A))) (= (tptp.aa_int_int _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int B2) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_int_int _let_1 B2)) (tptp.aa_int_int _let_1 C))))) (forall ((A tptp.complex) (B2 tptp.complex) (C tptp.complex)) (= (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_complex_complex (tptp.minus_minus_complex A) B2)) C) (tptp.aa_complex_complex (tptp.minus_minus_complex (tptp.aa_complex_complex (tptp.times_times_complex A) C)) (tptp.aa_complex_complex (tptp.times_times_complex B2) C)))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A) B2)) C) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) C)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real B2) C)))) (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat (tptp.minus_minus_rat A) B2)) C) (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) C)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat B2) C)))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) B2)) C) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B2) C)))) (forall ((X tptp.complex) (Y tptp.complex) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_complex (tptp.power_power_complex X) N))) (let ((_let_2 (tptp.times_times_complex Y))) (=> (= (tptp.aa_complex_complex (tptp.times_times_complex X) Y) (tptp.aa_complex_complex _let_2 X)) (= (tptp.aa_complex_complex (tptp.times_times_complex _let_1) Y) (tptp.aa_complex_complex _let_2 _let_1)))))) (forall ((X tptp.real) (Y tptp.real) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) N))) (let ((_let_2 (tptp.aa_rea7340605660300375871l_real tptp.times_times_real Y))) (=> (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real X) Y) (tptp.aa_real_real _let_2 X)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real _let_1) Y) (tptp.aa_real_real _let_2 _let_1)))))) (forall ((X tptp.rat) (Y tptp.rat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_rat (tptp.power_power_rat X) N))) (let ((_let_2 (tptp.aa_rat_fun_rat_rat tptp.times_times_rat Y))) (=> (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat X) Y) (tptp.aa_rat_rat _let_2 X)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat _let_1) Y) (tptp.aa_rat_rat _let_2 _let_1)))))) (forall ((X tptp.nat) (Y tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat X) N))) (let ((_let_2 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat Y))) (=> (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat X) Y) (tptp.aa_nat_nat _let_2 X)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat _let_1) Y) (tptp.aa_nat_nat _let_2 _let_1)))))) (forall ((X tptp.int) (Y tptp.int) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_int (tptp.power_power_int X) N))) (let ((_let_2 (tptp.aa_int_fun_int_int tptp.times_times_int Y))) (=> (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int X) Y) (tptp.aa_int_int _let_2 X)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int _let_1) Y) (tptp.aa_int_int _let_2 _let_1)))))) (forall ((A tptp.complex) (B2 tptp.complex) (N tptp.nat)) (= (tptp.aa_nat_complex (tptp.power_power_complex (tptp.aa_complex_complex (tptp.times_times_complex A) B2)) N) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_nat_complex (tptp.power_power_complex A) N)) (tptp.aa_nat_complex (tptp.power_power_complex B2) N)))) (forall ((A tptp.real) (B2 tptp.real) (N tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) B2)) N) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real A) N)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real B2) N)))) (forall ((A tptp.rat) (B2 tptp.rat) (N tptp.nat)) (= (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) B2)) N) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat (tptp.power_power_rat A) N)) (tptp.aa_nat_rat (tptp.power_power_rat B2) N)))) (forall ((A tptp.nat) (B2 tptp.nat) (N tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) B2)) N) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A) N)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat B2) N)))) (forall ((A tptp.int) (B2 tptp.int) (N tptp.nat)) (= (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) B2)) N) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int (tptp.power_power_int A) N)) (tptp.aa_nat_int (tptp.power_power_int B2) N)))) (forall ((A tptp.complex) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_complex (tptp.power_power_complex A) N))) (= (tptp.aa_complex_complex (tptp.times_times_complex _let_1) A) (tptp.aa_complex_complex (tptp.times_times_complex A) _let_1)))) (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real A) N))) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real _let_1) A) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) _let_1)))) (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_rat (tptp.power_power_rat A) N))) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat _let_1) A) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) _let_1)))) (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A) N))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat _let_1) A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) _let_1)))) (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_int (tptp.power_power_int A) N))) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int _let_1) A) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) _let_1)))) (forall ((A tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A))) (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat M) N)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_nat_nat _let_1 M)) N)))) (forall ((A tptp.real) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_real_fun_nat_real tptp.power_power_real A))) (= (tptp.aa_nat_real _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat M) N)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_nat_real _let_1 M)) N)))) (forall ((A tptp.int) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.power_power_int A))) (= (tptp.aa_nat_int _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat M) N)) (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_nat_int _let_1 M)) N)))) (forall ((A tptp.complex) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.power_power_complex A))) (= (tptp.aa_nat_complex _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat M) N)) (tptp.aa_nat_complex (tptp.power_power_complex (tptp.aa_nat_complex _let_1 M)) N)))) (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat K))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I) J)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat _let_1 I)) (tptp.aa_nat_nat _let_1 J)))))) (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I) J)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat I) K)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat J) K))))) (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I) J)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) L)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat I) K)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat J) L)))))) (forall ((M tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat M) M)))) (forall ((M tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat M))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat _let_1 M)))))) (forall ((I tptp.nat) (U tptp.nat) (J tptp.nat) (K tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat I) U)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat J) U)) K)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat I) J)) U)) K))) (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat K))) (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) N)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat _let_1 M)) (tptp.aa_nat_nat _let_1 N))))) (forall ((M tptp.nat) (N tptp.nat) (K tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) N)) K) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat M) K)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat N) K)))) (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat K))) (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) N)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat _let_1 M)) (tptp.aa_nat_nat _let_1 N))))) (forall ((M tptp.nat) (N tptp.nat) (K tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) N)) K) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat M) K)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat N) K)))) (forall ((M tptp.nat) (N tptp.nat) (Q2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat M))) (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat N) Q2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat _let_1 N)) Q2)))) (forall ((A tptp.complex)) (= (tptp.aa_complex_complex (tptp.times_times_complex (tptp.numera6690914467698888265omplex tptp.one)) A) A)) (forall ((A tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_num_real tptp.numeral_numeral_real tptp.one)) A) A)) (forall ((A tptp.rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_num_rat tptp.numeral_numeral_rat tptp.one)) A) A)) (forall ((A tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat tptp.one)) A) A)) (forall ((A tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_num_int tptp.numeral_numeral_int tptp.one)) A) A)) (forall ((A tptp.complex)) (= (tptp.aa_complex_complex (tptp.times_times_complex A) (tptp.numera6690914467698888265omplex tptp.one)) A)) (forall ((A tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) (tptp.aa_num_real tptp.numeral_numeral_real tptp.one)) A)) (forall ((A tptp.rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) (tptp.aa_num_rat tptp.numeral_numeral_rat tptp.one)) A)) (forall ((A tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) (tptp.aa_num_nat tptp.numeral_numeral_nat tptp.one)) A)) (forall ((A tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) (tptp.aa_num_int tptp.numeral_numeral_int tptp.one)) A)) (forall ((X tptp.complex) (Y tptp.complex) (A tptp.complex) (B2 tptp.complex)) (let ((_let_1 (tptp.times_times_complex X))) (= (tptp.aa_complex_complex (tptp.minus_minus_complex (tptp.aa_complex_complex _let_1 Y)) (tptp.aa_complex_complex (tptp.times_times_complex A) B2)) (tptp.aa_complex_complex (tptp.plus_plus_complex (tptp.aa_complex_complex _let_1 (tptp.aa_complex_complex (tptp.minus_minus_complex Y) B2))) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_complex_complex (tptp.minus_minus_complex X) A)) B2))))) (forall ((X tptp.real) (Y tptp.real) (A tptp.real) (B2 tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.times_times_real X))) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real _let_1 Y)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) B2)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real Y) B2))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real X) A)) B2))))) (forall ((X tptp.rat) (Y tptp.rat) (A tptp.rat) (B2 tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_rat tptp.times_times_rat X))) (= (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_rat_rat _let_1 Y)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) B2)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat _let_1 (tptp.aa_rat_rat (tptp.minus_minus_rat Y) B2))) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat (tptp.minus_minus_rat X) A)) B2))))) (forall ((X tptp.int) (Y tptp.int) (A tptp.int) (B2 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.times_times_int X))) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_int_int _let_1 Y)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) B2)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int Y) B2))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int X) A)) B2))))) (forall ((X tptp.complex) (Y tptp.complex)) (= (tptp.aa_complex_complex (tptp.minus_minus_complex (tptp.aa_complex_complex (tptp.times_times_complex X) X)) (tptp.aa_complex_complex (tptp.times_times_complex Y) Y)) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_complex_complex (tptp.plus_plus_complex X) Y)) (tptp.aa_complex_complex (tptp.minus_minus_complex X) Y)))) (forall ((X tptp.real) (Y tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real X) X)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real Y) Y)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) Y)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real X) Y)))) (forall ((X tptp.rat) (Y tptp.rat)) (= (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat X) X)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat Y) Y)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat X) Y)) (tptp.aa_rat_rat (tptp.minus_minus_rat X) Y)))) (forall ((X tptp.int) (Y tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int X) X)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int Y) Y)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int X) Y)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int X) Y)))) (forall ((A tptp.complex) (E tptp.complex) (C tptp.complex) (B2 tptp.complex) (D tptp.complex)) (= (= (tptp.aa_complex_complex (tptp.plus_plus_complex (tptp.aa_complex_complex (tptp.times_times_complex A) E)) C) (tptp.aa_complex_complex (tptp.plus_plus_complex (tptp.aa_complex_complex (tptp.times_times_complex B2) E)) D)) (= C (tptp.aa_complex_complex (tptp.plus_plus_complex (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_complex_complex (tptp.minus_minus_complex B2) A)) E)) D)))) (forall ((A tptp.real) (E tptp.real) (C tptp.real) (B2 tptp.real) (D tptp.real)) (= (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) E)) C) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real B2) E)) D)) (= C (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real B2) A)) E)) D)))) (forall ((A tptp.rat) (E tptp.rat) (C tptp.rat) (B2 tptp.rat) (D tptp.rat)) (= (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) E)) C) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat B2) E)) D)) (= C (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat (tptp.minus_minus_rat B2) A)) E)) D)))) (forall ((A tptp.int) (E tptp.int) (C tptp.int) (B2 tptp.int) (D tptp.int)) (= (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) E)) C) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B2) E)) D)) (= C (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int B2) A)) E)) D)))) (forall ((A tptp.complex) (E tptp.complex) (C tptp.complex) (B2 tptp.complex) (D tptp.complex)) (= (= (tptp.aa_complex_complex (tptp.plus_plus_complex (tptp.aa_complex_complex (tptp.times_times_complex A) E)) C) (tptp.aa_complex_complex (tptp.plus_plus_complex (tptp.aa_complex_complex (tptp.times_times_complex B2) E)) D)) (= (tptp.aa_complex_complex (tptp.plus_plus_complex (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_complex_complex (tptp.minus_minus_complex A) B2)) E)) C) D))) (forall ((A tptp.real) (E tptp.real) (C tptp.real) (B2 tptp.real) (D tptp.real)) (= (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) E)) C) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real B2) E)) D)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A) B2)) E)) C) D))) (forall ((A tptp.rat) (E tptp.rat) (C tptp.rat) (B2 tptp.rat) (D tptp.rat)) (= (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) E)) C) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat B2) E)) D)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat (tptp.minus_minus_rat A) B2)) E)) C) D))) (forall ((A tptp.int) (E tptp.int) (C tptp.int) (B2 tptp.int) (D tptp.int)) (= (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) E)) C) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B2) E)) D)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) B2)) E)) C) D))) (forall ((A tptp.complex) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.power_power_complex A))) (= (tptp.aa_nat_complex _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) N)) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_nat_complex _let_1 M)) (tptp.aa_nat_complex _let_1 N))))) (forall ((A tptp.real) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_real_fun_nat_real tptp.power_power_real A))) (= (tptp.aa_nat_real _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) N)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real _let_1 M)) (tptp.aa_nat_real _let_1 N))))) (forall ((A tptp.rat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.power_power_rat A))) (= (tptp.aa_nat_rat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) N)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat _let_1 M)) (tptp.aa_nat_rat _let_1 N))))) (forall ((A tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A))) (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) N)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat _let_1 M)) (tptp.aa_nat_nat _let_1 N))))) (forall ((A tptp.int) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.power_power_int A))) (= (tptp.aa_nat_int _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) N)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int _let_1 M)) (tptp.aa_nat_int _let_1 N))))) (forall ((M tptp.nat) (I tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat I) N))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat M) N)) I)))) (forall ((N tptp.nat) (M tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat N) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat M) N))) M))) (forall ((M tptp.nat) (N tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat M) N)) N)) M))) (forall ((A tptp.real) (E tptp.real) (C tptp.real) (B2 tptp.real) (D tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) E)) C)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real B2) E)) D))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A) B2)) E)) C)) D)))) (forall ((A tptp.rat) (E tptp.rat) (C tptp.rat) (B2 tptp.rat) (D tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) E)) C)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat B2) E)) D))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat (tptp.minus_minus_rat A) B2)) E)) C)) D)))) (forall ((A tptp.int) (E tptp.int) (C tptp.int) (B2 tptp.int) (D tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) E)) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B2) E)) D))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) B2)) E)) C)) D)))) (forall ((A tptp.real) (E tptp.real) (C tptp.real) (B2 tptp.real) (D tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) E)) C)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real B2) E)) D))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real C) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real B2) A)) E)) D))))) (forall ((A tptp.rat) (E tptp.rat) (C tptp.rat) (B2 tptp.rat) (D tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) E)) C)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat B2) E)) D))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat C) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat (tptp.minus_minus_rat B2) A)) E)) D))))) (forall ((A tptp.int) (E tptp.int) (C tptp.int) (B2 tptp.int) (D tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) E)) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B2) E)) D))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int C) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int B2) A)) E)) D))))) (forall ((A tptp.real) (E tptp.real) (C tptp.real) (B2 tptp.real) (D tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) E)) C)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real B2) E)) D))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A) B2)) E)) C)) D)))) (forall ((A tptp.rat) (E tptp.rat) (C tptp.rat) (B2 tptp.rat) (D tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) E)) C)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat B2) E)) D))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat (tptp.minus_minus_rat A) B2)) E)) C)) D)))) (forall ((A tptp.int) (E tptp.int) (C tptp.int) (B2 tptp.int) (D tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) E)) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B2) E)) D))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) B2)) E)) C)) D)))) (forall ((A tptp.real) (E tptp.real) (C tptp.real) (B2 tptp.real) (D tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) E)) C)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real B2) E)) D))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real C) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real B2) A)) E)) D))))) (forall ((A tptp.rat) (E tptp.rat) (C tptp.rat) (B2 tptp.rat) (D tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) E)) C)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat B2) E)) D))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat C) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat (tptp.minus_minus_rat B2) A)) E)) D))))) (forall ((A tptp.int) (E tptp.int) (C tptp.int) (B2 tptp.int) (D tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) E)) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B2) E)) D))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int C) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int B2) A)) E)) D))))) (forall ((J tptp.nat) (I tptp.nat) (U tptp.nat) (M tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat J) I)) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat I) U)) M) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat J) U)) N)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat I) J)) U)) M) N)))) (forall ((I tptp.nat) (J tptp.nat) (U tptp.nat) (M tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I) J)) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat I) U)) M) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat J) U)) N)) (= M (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat J) I)) U)) N))))) (forall ((J tptp.nat) (I tptp.nat) (U tptp.nat) (M tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat J) I)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat I) U)) M)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat J) U)) N))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat I) J)) U)) M)) N))))) (forall ((I tptp.nat) (J tptp.nat) (U tptp.nat) (M tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I) J)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat I) U)) M)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat J) U)) N))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat J) I)) U)) N)))))) (forall ((J tptp.nat) (I tptp.nat) (U tptp.nat) (M tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat J) I)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat I) U)) M)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat J) U)) N)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat I) J)) U)) M)) N)))) (forall ((I tptp.nat) (J tptp.nat) (U tptp.nat) (M tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I) J)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat I) U)) M)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat J) U)) N)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat J) I)) U)) N))))) (forall ((Z tptp.complex)) (= (tptp.aa_complex_complex (tptp.times_times_complex (tptp.numera6690914467698888265omplex (tptp.aa_num_num tptp.bit0 tptp.one))) Z) (tptp.aa_complex_complex (tptp.plus_plus_complex Z) Z))) (forall ((Z tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))) Z) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real Z) Z))) (forall ((Z tptp.rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_num_rat tptp.numeral_numeral_rat (tptp.aa_num_num tptp.bit0 tptp.one))) Z) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat Z) Z))) (forall ((Z tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) Z) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Z) Z))) (forall ((Z tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) Z) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int Z) Z))) (forall ((Z tptp.complex)) (= (tptp.aa_complex_complex (tptp.times_times_complex Z) (tptp.numera6690914467698888265omplex (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_complex_complex (tptp.plus_plus_complex Z) Z))) (forall ((Z tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real Z) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real Z) Z))) (forall ((Z tptp.rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat Z) (tptp.aa_num_rat tptp.numeral_numeral_rat (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat Z) Z))) (forall ((Z tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat Z) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Z) Z))) (forall ((Z tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int Z) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int Z) Z))) (forall ((A tptp.complex) (B2 tptp.complex)) (let ((_let_1 (tptp.plus_plus_complex A))) (= (tptp.aa_complex_complex _let_1 (tptp.aa_complex_complex _let_1 B2)) (tptp.aa_complex_complex (tptp.plus_plus_complex (tptp.aa_complex_complex (tptp.times_times_complex (tptp.numera6690914467698888265omplex (tptp.aa_num_num tptp.bit0 tptp.one))) A)) B2)))) (forall ((A tptp.real) (B2 tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A))) (= (tptp.aa_real_real _let_1 (tptp.aa_real_real _let_1 B2)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))) A)) B2)))) (forall ((A tptp.rat) (B2 tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A))) (= (tptp.aa_rat_rat _let_1 (tptp.aa_rat_rat _let_1 B2)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_num_rat tptp.numeral_numeral_rat (tptp.aa_num_num tptp.bit0 tptp.one))) A)) B2)))) (forall ((A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A))) (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat _let_1 B2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) A)) B2)))) (forall ((A tptp.int) (B2 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.plus_plus_int A))) (= (tptp.aa_int_int _let_1 (tptp.aa_int_int _let_1 B2)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) A)) B2)))) (forall ((X tptp.complex)) (= (tptp.aa_nat_complex (tptp.power_power_complex X) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit0 tptp.one)))) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_complex_complex (tptp.times_times_complex X) X)) X)) X))) (forall ((X tptp.real)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit0 tptp.one)))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real X) X)) X)) X))) (forall ((X tptp.rat)) (= (tptp.aa_nat_rat (tptp.power_power_rat X) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit0 tptp.one)))) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat X) X)) X)) X))) (forall ((X tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat X) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit0 tptp.one)))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat X) X)) X)) X))) (forall ((X tptp.int)) (= (tptp.aa_nat_int (tptp.power_power_int X) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit0 tptp.one)))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int X) X)) X)) X))) (forall ((A tptp.complex)) (= (tptp.aa_nat_complex (tptp.power_power_complex A) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_complex_complex (tptp.times_times_complex A) A))) (forall ((A tptp.real)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real A) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) A))) (forall ((A tptp.rat)) (= (tptp.aa_nat_rat (tptp.power_power_rat A) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) A))) (forall ((A tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) A))) (forall ((A tptp.int)) (= (tptp.aa_nat_int (tptp.power_power_int A) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) A))) (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A))) (= (tptp.aa_nat_nat _let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat _let_1) N)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_nat_nat _let_2 N)) _let_1))))) (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_real_fun_nat_real tptp.power_power_real A))) (= (tptp.aa_nat_real _let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat _let_1) N)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_nat_real _let_2 N)) _let_1))))) (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.power_power_int A))) (= (tptp.aa_nat_int _let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat _let_1) N)) (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_nat_int _let_2 N)) _let_1))))) (forall ((A tptp.complex) (N tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.power_power_complex A))) (= (tptp.aa_nat_complex _let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat _let_1) N)) (tptp.aa_nat_complex (tptp.power_power_complex (tptp.aa_nat_complex _let_2 N)) _let_1))))) (forall ((I tptp.nat) (J tptp.nat) (U tptp.nat) (M tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I) J)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat I) U)) M)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat J) U)) N))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat J) I)) U)) N)))))) (forall ((J tptp.nat) (I tptp.nat) (U tptp.nat) (M tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat J) I)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat I) U)) M)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat J) U)) N))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat I) J)) U)) M)) N))))) (forall ((Xs tptp.set_nat) (X tptp.nat) (Y tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool (tptp.vEBT_is_pred_in_set Xs) X) Y)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat Y) Xs)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Y) X)) (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) Xs)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X3) X)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X3) Y)))))))) (forall ((X tptp.complex) (Y tptp.complex)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (let ((_let_2 (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1))) (= (tptp.aa_nat_complex (tptp.power_power_complex (tptp.aa_complex_complex (tptp.plus_plus_complex X) Y)) _let_2) (tptp.aa_complex_complex (tptp.plus_plus_complex (tptp.aa_complex_complex (tptp.plus_plus_complex (tptp.aa_nat_complex (tptp.power_power_complex X) _let_2)) (tptp.aa_nat_complex (tptp.power_power_complex Y) _let_2))) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_complex_complex (tptp.times_times_complex (tptp.numera6690914467698888265omplex _let_1)) X)) Y)))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (let ((_let_2 (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1))) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) Y)) _let_2) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) _let_2)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Y) _let_2))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_num_real tptp.numeral_numeral_real _let_1)) X)) Y)))))) (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (let ((_let_2 (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1))) (= (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat X) Y)) _let_2) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_nat_rat (tptp.power_power_rat X) _let_2)) (tptp.aa_nat_rat (tptp.power_power_rat Y) _let_2))) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_num_rat tptp.numeral_numeral_rat _let_1)) X)) Y)))))) (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat X) Y)) _let_1) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat X) _let_1)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat Y) _let_1))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat _let_1) X)) Y))))) (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (let ((_let_2 (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1))) (= (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int X) Y)) _let_2) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_nat_int (tptp.power_power_int X) _let_2)) (tptp.aa_nat_int (tptp.power_power_int Y) _let_2))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_num_int tptp.numeral_numeral_int _let_1)) X)) Y)))))) (forall ((X tptp.complex) (Y tptp.complex)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (let ((_let_2 (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1))) (= (tptp.aa_nat_complex (tptp.power_power_complex (tptp.aa_complex_complex (tptp.minus_minus_complex X) Y)) _let_2) (tptp.aa_complex_complex (tptp.minus_minus_complex (tptp.aa_complex_complex (tptp.plus_plus_complex (tptp.aa_nat_complex (tptp.power_power_complex X) _let_2)) (tptp.aa_nat_complex (tptp.power_power_complex Y) _let_2))) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_complex_complex (tptp.times_times_complex (tptp.numera6690914467698888265omplex _let_1)) X)) Y)))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (let ((_let_2 (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1))) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real X) Y)) _let_2) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) _let_2)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Y) _let_2))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_num_real tptp.numeral_numeral_real _let_1)) X)) Y)))))) (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (let ((_let_2 (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1))) (= (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_rat_rat (tptp.minus_minus_rat X) Y)) _let_2) (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_nat_rat (tptp.power_power_rat X) _let_2)) (tptp.aa_nat_rat (tptp.power_power_rat Y) _let_2))) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_num_rat tptp.numeral_numeral_rat _let_1)) X)) Y)))))) (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (let ((_let_2 (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1))) (= (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int X) Y)) _let_2) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_nat_int (tptp.power_power_int X) _let_2)) (tptp.aa_nat_int (tptp.power_power_int Y) _let_2))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_num_int tptp.numeral_numeral_int _let_1)) X)) Y)))))) (= tptp.vEBT_VEBT_mul (tptp.vEBT_V4262088993061758097ft_nat tptp.times_times_nat)) (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat X) Y) Z) (= (tptp.aa_opt1882420858203594238on_nat (tptp.aa_opt7711074727033721499on_nat tptp.vEBT_VEBT_mul (tptp.some_nat X)) (tptp.some_nat Y)) (tptp.some_nat Z)))) (forall ((Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat Deg) _let_1))) (let ((_let_3 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high X) _let_2))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_vebt_member (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Mi) Ma)) Deg TreeList Summary)) X)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat _let_1) Deg)) (or (= X Mi) (= X Ma) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Ma)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Mi) X)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_3) (tptp.size_s6755466524823107622T_VEBT TreeList))) (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_vebt_member (tptp.nth_VEBT_VEBT TreeList _let_3)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low X) _let_2))))))))))) (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt _let_175) tptp.deg)) (forall ((Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Mi) Ma)) Deg TreeList Summary)) N)) (=> (not (= Mi Ma)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Mi) Ma)) (exists ((M3 tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (and (= (tptp.some_nat M3) (tptp.vEBT_vebt_mint Summary)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M3) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat _let_1) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat N) _let_1)))))))))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (let ((_let_2 (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_num_real tptp.numeral_numeral_real _let_1)) X)) Y)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) _let_2)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Y) _let_2))))))) (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (let ((_let_2 (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_num_rat tptp.numeral_numeral_rat _let_1)) X)) Y)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_nat_rat (tptp.power_power_rat X) _let_2)) (tptp.aa_nat_rat (tptp.power_power_rat Y) _let_2))))))) (forall ((X tptp.nat) (Px tptp.nat)) (= (= (tptp.vEBT_vebt_pred tptp.summary X) (tptp.some_nat Px)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool (tptp.vEBT_is_pred_in_set (tptp.vEBT_VEBT_set_vebt tptp.summary)) X) Px)))) (forall ((Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Mi) Ma)) Deg TreeList Summary)) N)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Mi) Ma)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Ma) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) Deg)))))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.pp (tptp.aa_Ext2772979874139974381t_bool (tptp.ord_le2932123472753598470d_enat (tptp.numera1916890842035813515d_enat M)) (tptp.numera1916890842035813515d_enat N))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_num_nat tptp.numeral_numeral_nat M)) (tptp.aa_num_nat tptp.numeral_numeral_nat N))))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.pp (tptp.aa_Ext2772979874139974381t_bool (tptp.ord_le72135733267957522d_enat (tptp.numera1916890842035813515d_enat M)) (tptp.numera1916890842035813515d_enat N))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_num_nat tptp.numeral_numeral_nat M)) (tptp.aa_num_nat tptp.numeral_numeral_nat N))))) (forall ((A tptp.complex) (B2 tptp.complex)) (= (tptp.aa_complex_complex (tptp.minus_minus_complex (tptp.aa_complex_complex (tptp.plus_plus_complex A) B2)) B2) A)) (forall ((A tptp.real) (B2 tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) B2)) B2) A)) (forall ((A tptp.rat) (B2 tptp.rat)) (= (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) B2)) B2) A)) (forall ((A tptp.nat) (B2 tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) B2)) B2) A)) (forall ((A tptp.int) (B2 tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) B2)) B2) A)) (forall ((Xs tptp.list_real) (P tptp.fun_real_bool) (N tptp.nat)) (=> (forall ((X4 tptp.real)) (=> (tptp.member_real X4 (tptp.set_real2 Xs)) (tptp.pp (tptp.aa_real_bool P X4)))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N) (tptp.size_size_list_real Xs))) (tptp.pp (tptp.aa_real_bool P (tptp.aa_nat_real (tptp.nth_real Xs) N)))))) (forall ((Xs tptp.list_complex) (P tptp.fun_complex_bool) (N tptp.nat)) (=> (forall ((X4 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex X4) (tptp.set_complex2 Xs))) (tptp.pp (tptp.aa_complex_bool P X4)))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N) (tptp.size_s3451745648224563538omplex Xs))) (tptp.pp (tptp.aa_complex_bool P (tptp.aa_nat_complex (tptp.nth_complex Xs) N)))))) (forall ((Xs tptp.list_int) (P tptp.fun_int_bool) (N tptp.nat)) (=> (forall ((X4 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X4) (tptp.set_int2 Xs))) (tptp.pp (tptp.aa_int_bool P X4)))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N) (tptp.size_size_list_int Xs))) (tptp.pp (tptp.aa_int_bool P (tptp.aa_nat_int (tptp.nth_int Xs) N)))))) (forall ((Xs tptp.list_VEBT_VEBT) (P tptp.fun_VEBT_VEBT_bool) (N tptp.nat)) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (tptp.pp (tptp.aa_set8260762808118238015T_bool (tptp.aa_VEB289770264548726718T_bool tptp.member_VEBT_VEBT X4) (tptp.set_VEBT_VEBT2 Xs))) (tptp.pp (tptp.aa_VEBT_VEBT_bool P X4)))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N) (tptp.size_s6755466524823107622T_VEBT Xs))) (tptp.pp (tptp.aa_VEBT_VEBT_bool P (tptp.nth_VEBT_VEBT Xs N)))))) (forall ((Xs tptp.list_bool) (P tptp.fun_bool_bool) (N tptp.nat)) (=> (forall ((X4 tptp.bool)) (=> (tptp.member_bool X4 (tptp.set_bool2 Xs)) (tptp.pp (tptp.aa_bool_bool P X4)))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N) (tptp.size_size_list_bool Xs))) (tptp.pp (tptp.aa_bool_bool P (tptp.aa_nat_bool (tptp.nth_bool Xs) N)))))) (forall ((Xs tptp.list_nat) (P tptp.fun_nat_bool) (N tptp.nat)) (=> (forall ((X4 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X4) (tptp.set_nat2 Xs))) (tptp.pp (tptp.aa_nat_bool P X4)))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N) (tptp.size_size_list_nat Xs))) (tptp.pp (tptp.aa_nat_bool P (tptp.aa_nat_nat (tptp.nth_nat Xs) N)))))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A))) (= (= (tptp.aa_real_real _let_1 B2) (tptp.aa_real_real _let_1 C)) (= B2 C)))) (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A))) (= (= (tptp.aa_rat_rat _let_1 B2) (tptp.aa_rat_rat _let_1 C)) (= B2 C)))) (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A))) (= (= (tptp.aa_nat_nat _let_1 B2) (tptp.aa_nat_nat _let_1 C)) (= B2 C)))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.plus_plus_int A))) (= (= (tptp.aa_int_int _let_1 B2) (tptp.aa_int_int _let_1 C)) (= B2 C)))) (forall ((B2 tptp.real) (A tptp.real) (C tptp.real)) (= (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real B2) A) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real C) A)) (= B2 C))) (forall ((B2 tptp.rat) (A tptp.rat) (C tptp.rat)) (= (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat B2) A) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat C) A)) (= B2 C))) (forall ((B2 tptp.nat) (A tptp.nat) (C tptp.nat)) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat B2) A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat C) A)) (= B2 C))) (forall ((B2 tptp.int) (A tptp.int) (C tptp.int)) (= (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int B2) A) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int C) A)) (= B2 C))) (forall ((X5 tptp.vEBT_VEBT)) (=> (tptp.pp (tptp.aa_set8260762808118238015T_bool (tptp.aa_VEB289770264548726718T_bool tptp.member_VEBT_VEBT X5) (tptp.set_VEBT_VEBT2 tptp.treeList))) (and (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt X5) tptp.na)) (forall ((Xa tptp.nat) (Xb tptp.nat)) (= (= (tptp.vEBT_vebt_pred X5 Xa) (tptp.some_nat Xb)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool (tptp.vEBT_is_pred_in_set (tptp.vEBT_VEBT_set_vebt X5)) Xa) Xb))))))) (forall ((Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Mi) Ma)) Deg TreeList Summary)) Deg)) (=> (= Mi Ma) (and (forall ((X5 tptp.vEBT_VEBT)) (=> (tptp.pp (tptp.aa_set8260762808118238015T_bool (tptp.aa_VEB289770264548726718T_bool tptp.member_VEBT_VEBT X5) (tptp.set_VEBT_VEBT2 TreeList))) (not (exists ((X_13 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions X5) X_13)))))) (not (exists ((X_13 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions Summary) X_13)))))))) (forall ((C tptp.real) (A tptp.real) (B2 tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real C))) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real _let_1 A)) (tptp.aa_real_real _let_1 B2))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) B2))))) (forall ((C tptp.rat) (A tptp.rat) (B2 tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat C))) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat _let_1 A)) (tptp.aa_rat_rat _let_1 B2))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B2))))) (forall ((C tptp.nat) (A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat C))) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat _let_1 A)) (tptp.aa_nat_nat _let_1 B2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B2))))) (forall ((C tptp.int) (A tptp.int) (B2 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.plus_plus_int C))) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int _let_1 A)) (tptp.aa_int_int _let_1 B2))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B2))))) (forall ((A tptp.real) (C tptp.real) (B2 tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) C)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real B2) C))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) B2)))) (forall ((A tptp.rat) (C tptp.rat) (B2 tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) C)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat B2) C))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B2)))) (forall ((A tptp.nat) (C tptp.nat) (B2 tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) C)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat B2) C))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B2)))) (forall ((A tptp.int) (C tptp.int) (B2 tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int B2) C))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B2)))) (forall ((C tptp.real) (A tptp.real) (B2 tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real C))) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real _let_1 A)) (tptp.aa_real_real _let_1 B2))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B2))))) (forall ((C tptp.rat) (A tptp.rat) (B2 tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat C))) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat _let_1 A)) (tptp.aa_rat_rat _let_1 B2))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B2))))) (forall ((C tptp.nat) (A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat C))) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat _let_1 A)) (tptp.aa_nat_nat _let_1 B2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) B2))))) (forall ((C tptp.int) (A tptp.int) (B2 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.plus_plus_int C))) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int _let_1 A)) (tptp.aa_int_int _let_1 B2))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B2))))) (forall ((A tptp.real) (C tptp.real) (B2 tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) C)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real B2) C))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B2)))) (forall ((A tptp.rat) (C tptp.rat) (B2 tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) C)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat B2) C))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B2)))) (forall ((A tptp.nat) (C tptp.nat) (B2 tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) C)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat B2) C))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) B2)))) (forall ((A tptp.int) (C tptp.int) (B2 tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int B2) C))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B2)))) (forall ((A tptp.complex) (B2 tptp.complex)) (= (tptp.aa_complex_complex (tptp.minus_minus_complex (tptp.aa_complex_complex (tptp.plus_plus_complex A) B2)) B2) A)) (forall ((A tptp.real) (B2 tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) B2)) B2) A)) (forall ((A tptp.rat) (B2 tptp.rat)) (= (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) B2)) B2) A)) (forall ((A tptp.int) (B2 tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) B2)) B2) A)) (forall ((A tptp.complex) (B2 tptp.complex)) (= (tptp.aa_complex_complex (tptp.plus_plus_complex (tptp.aa_complex_complex (tptp.minus_minus_complex A) B2)) B2) A)) (forall ((A tptp.real) (B2 tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A) B2)) B2) A)) (forall ((A tptp.rat) (B2 tptp.rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.minus_minus_rat A) B2)) B2) A)) (forall ((A tptp.int) (B2 tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) B2)) B2) A)) (forall ((C tptp.complex) (A tptp.complex) (B2 tptp.complex)) (let ((_let_1 (tptp.plus_plus_complex C))) (= (tptp.aa_complex_complex (tptp.minus_minus_complex (tptp.aa_complex_complex _let_1 A)) (tptp.aa_complex_complex _let_1 B2)) (tptp.aa_complex_complex (tptp.minus_minus_complex A) B2)))) (forall ((C tptp.real) (A tptp.real) (B2 tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real C))) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real _let_1 A)) (tptp.aa_real_real _let_1 B2)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A) B2)))) (forall ((C tptp.rat) (A tptp.rat) (B2 tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat C))) (= (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_rat_rat _let_1 A)) (tptp.aa_rat_rat _let_1 B2)) (tptp.aa_rat_rat (tptp.minus_minus_rat A) B2)))) (forall ((C tptp.nat) (A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat C))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat _let_1 A)) (tptp.aa_nat_nat _let_1 B2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat A) B2)))) (forall ((C tptp.int) (A tptp.int) (B2 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.plus_plus_int C))) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_int_int _let_1 A)) (tptp.aa_int_int _let_1 B2)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) B2)))) (forall ((A tptp.complex) (B2 tptp.complex)) (= (tptp.aa_complex_complex (tptp.minus_minus_complex (tptp.aa_complex_complex (tptp.plus_plus_complex A) B2)) A) B2)) (forall ((A tptp.real) (B2 tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) B2)) A) B2)) (forall ((A tptp.rat) (B2 tptp.rat)) (= (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) B2)) A) B2)) (forall ((A tptp.nat) (B2 tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) B2)) A) B2)) (forall ((A tptp.int) (B2 tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) B2)) A) B2)) (forall ((A tptp.complex) (C tptp.complex) (B2 tptp.complex)) (= (tptp.aa_complex_complex (tptp.minus_minus_complex (tptp.aa_complex_complex (tptp.plus_plus_complex A) C)) (tptp.aa_complex_complex (tptp.plus_plus_complex B2) C)) (tptp.aa_complex_complex (tptp.minus_minus_complex A) B2))) (forall ((A tptp.real) (C tptp.real) (B2 tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) C)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real B2) C)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A) B2))) (forall ((A tptp.rat) (C tptp.rat) (B2 tptp.rat)) (= (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) C)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat B2) C)) (tptp.aa_rat_rat (tptp.minus_minus_rat A) B2))) (forall ((A tptp.nat) (C tptp.nat) (B2 tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) C)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat B2) C)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat A) B2))) (forall ((A tptp.int) (C tptp.int) (B2 tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int B2) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) B2))) (forall ((X tptp.nat) (Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Mi) Ma)) Deg TreeList Summary))) (=> (or (= X Mi) (= X Ma)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) Deg)) (= (tptp.vEBT_vebt_insert _let_1 X) _let_1))))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.times_times_num (tptp.aa_num_num tptp.bit0 M)) (tptp.aa_num_num tptp.bit0 N)) (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.times_times_num M) N))))) (forall ((M tptp.num)) (= (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.times_times_num M) tptp.one) M)) (forall ((N tptp.num)) (= (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.times_times_num tptp.one) N) N)) (forall ((Deg tptp.nat) (Ma tptp.nat) (X tptp.nat) (Mi tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) Deg)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Ma) X)) (= (tptp.vEBT_vebt_pred (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Mi) Ma)) Deg TreeList Summary) X) (tptp.some_nat Ma))))) (forall ((N tptp.num)) (= (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.times_times_num (tptp.aa_num_num tptp.bit0 tptp.one)) N) (tptp.aa_num_num tptp.bit0 N))) (forall ((A tptp.nat) (M tptp.num) (N tptp.num)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_nat_nat _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat M))) (tptp.aa_num_nat tptp.numeral_numeral_nat N)) (tptp.aa_nat_nat _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.times_times_num M) N)))))) (forall ((A tptp.real) (M tptp.num) (N tptp.num)) (let ((_let_1 (tptp.aa_real_fun_nat_real tptp.power_power_real A))) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_nat_real _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat M))) (tptp.aa_num_nat tptp.numeral_numeral_nat N)) (tptp.aa_nat_real _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.times_times_num M) N)))))) (forall ((A tptp.int) (M tptp.num) (N tptp.num)) (let ((_let_1 (tptp.power_power_int A))) (= (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_nat_int _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat M))) (tptp.aa_num_nat tptp.numeral_numeral_nat N)) (tptp.aa_nat_int _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.times_times_num M) N)))))) (forall ((A tptp.complex) (M tptp.num) (N tptp.num)) (let ((_let_1 (tptp.power_power_complex A))) (= (tptp.aa_nat_complex (tptp.power_power_complex (tptp.aa_nat_complex _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat M))) (tptp.aa_num_nat tptp.numeral_numeral_nat N)) (tptp.aa_nat_complex _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.times_times_num M) N)))))) (forall ((Deg tptp.nat) (X tptp.nat) (Ma tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Mi tptp.nat) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat _let_1) Deg)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X) Ma)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.size_s6755466524823107622T_VEBT TreeList)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high X) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat Deg) _let_1)))) (= (tptp.vEBT_vebt_pred (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Mi) Ma)) Deg TreeList Summary) X) tptp.none_nat)))))) (forall ((P tptp.fun_Ex8563670519792538868t_bool) (N tptp.extended_enat)) (=> (forall ((N2 tptp.extended_enat)) (=> (forall ((M2 tptp.extended_enat)) (=> (tptp.pp (tptp.aa_Ext2772979874139974381t_bool (tptp.ord_le72135733267957522d_enat M2) N2)) (tptp.pp (tptp.aa_Ext2772979874139974381t_bool P M2)))) (tptp.pp (tptp.aa_Ext2772979874139974381t_bool P N2)))) (tptp.pp (tptp.aa_Ext2772979874139974381t_bool P N)))) (forall ((Z tptp.extended_enat) (Y tptp.extended_enat) (X tptp.extended_enat)) (=> (tptp.pp (tptp.aa_Ext2772979874139974381t_bool (tptp.ord_le2932123472753598470d_enat Z) Y)) (= (tptp.plus_p3455044024723400733d_enat X (tptp.minus_3235023915231533773d_enat Y Z)) (tptp.minus_3235023915231533773d_enat (tptp.plus_p3455044024723400733d_enat X Y) Z)))) (forall ((A tptp.real) (C tptp.real) (B2 tptp.real) (D tptp.real)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (let ((_let_2 (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_num_real tptp.numeral_numeral_real _let_1)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) C))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real B2) D))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real A) _let_2)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real D) _let_2))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real B2) _let_2)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real C) _let_2)))))))) (forall ((X tptp.real)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (let ((_let_2 (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1))) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 _let_1))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) _let_2)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_num_real tptp.numeral_numeral_real _let_1)) X)) _let_2))))) (forall ((A tptp.nat) (K tptp.num) (L tptp.num)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat K))) (tptp.aa_num_nat tptp.numeral_numeral_nat L)) (tptp.aa_nat_nat _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.times_times_num K) L)))))) (forall ((A tptp.int) (K tptp.num) (L tptp.num)) (let ((_let_1 (tptp.divide_divide_int A))) (= (tptp.aa_int_int (tptp.divide_divide_int (tptp.aa_int_int _let_1 (tptp.aa_num_int tptp.numeral_numeral_int K))) (tptp.aa_num_int tptp.numeral_numeral_int L)) (tptp.aa_int_int _let_1 (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.times_times_num K) L)))))) (forall ((Uy tptp.nat) (Uz tptp.list_VEBT_VEBT) (Va tptp.vEBT_VEBT) (Vb tptp.nat)) (= (tptp.vEBT_vebt_pred (tptp.vEBT_Node tptp.none_P5556105721700978146at_nat Uy Uz Va) Vb) tptp.none_nat)) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A))) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real _let_1 B2)) C) (tptp.aa_real_real _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real B2) C))))) (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A))) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat _let_1 B2)) C) (tptp.aa_rat_rat _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat B2) C))))) (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat _let_1 B2)) C) (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B2) C))))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.times_times_int A))) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int _let_1 B2)) C) (tptp.aa_int_int _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B2) C))))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A))) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real _let_1 B2)) C) (tptp.aa_real_real _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real B2) C))))) (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A))) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat _let_1 B2)) C) (tptp.aa_rat_rat _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat B2) C))))) (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat _let_1 B2)) C) (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B2) C))))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.times_times_int A))) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int _let_1 B2)) C) (tptp.aa_int_int _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B2) C))))) (forall ((A tptp.real) (B2 tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) B2) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real B2) A))) (forall ((A tptp.rat) (B2 tptp.rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) B2) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat B2) A))) (forall ((A tptp.nat) (B2 tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) B2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B2) A))) (forall ((A tptp.int) (B2 tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) B2) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B2) A))) (forall ((B2 tptp.real) (A tptp.real) (C tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.times_times_real B2))) (let ((_let_2 (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A))) (= (tptp.aa_real_real _let_1 (tptp.aa_real_real _let_2 C)) (tptp.aa_real_real _let_2 (tptp.aa_real_real _let_1 C)))))) (forall ((B2 tptp.rat) (A tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_rat tptp.times_times_rat B2))) (let ((_let_2 (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A))) (= (tptp.aa_rat_rat _let_1 (tptp.aa_rat_rat _let_2 C)) (tptp.aa_rat_rat _let_2 (tptp.aa_rat_rat _let_1 C)))))) (forall ((B2 tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B2))) (let ((_let_2 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A))) (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat _let_2 C)) (tptp.aa_nat_nat _let_2 (tptp.aa_nat_nat _let_1 C)))))) (forall ((B2 tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.times_times_int B2))) (let ((_let_2 (tptp.aa_int_fun_int_int tptp.times_times_int A))) (= (tptp.aa_int_int _let_1 (tptp.aa_int_int _let_2 C)) (tptp.aa_int_int _let_2 (tptp.aa_int_int _let_1 C)))))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A))) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real _let_1 B2)) C) (tptp.aa_real_real _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real B2) C))))) (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A))) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat _let_1 B2)) C) (tptp.aa_rat_rat _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat B2) C))))) (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat _let_1 B2)) C) (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat B2) C))))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.plus_plus_int A))) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int _let_1 B2)) C) (tptp.aa_int_int _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int B2) C))))) (forall ((I tptp.real) (J tptp.real) (K tptp.real) (L tptp.real)) (=> (and (= I J) (= K L)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real I) K) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real J) L)))) (forall ((I tptp.rat) (J tptp.rat) (K tptp.rat) (L tptp.rat)) (=> (and (= I J) (= K L)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat I) K) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat J) L)))) (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (= I J) (= K L)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat I) K) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat J) L)))) (forall ((I tptp.int) (J tptp.int) (K tptp.int) (L tptp.int)) (=> (and (= I J) (= K L)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int I) K) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int J) L)))) (forall ((A4 tptp.real) (K tptp.real) (A tptp.real) (B2 tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real K))) (=> (= A4 (tptp.aa_real_real _let_1 A)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A4) B2) (tptp.aa_real_real _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) B2)))))) (forall ((A4 tptp.rat) (K tptp.rat) (A tptp.rat) (B2 tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat K))) (=> (= A4 (tptp.aa_rat_rat _let_1 A)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A4) B2) (tptp.aa_rat_rat _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) B2)))))) (forall ((A4 tptp.nat) (K tptp.nat) (A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat K))) (=> (= A4 (tptp.aa_nat_nat _let_1 A)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A4) B2) (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) B2)))))) (forall ((A4 tptp.int) (K tptp.int) (A tptp.int) (B2 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.plus_plus_int K))) (=> (= A4 (tptp.aa_int_int _let_1 A)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A4) B2) (tptp.aa_int_int _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) B2)))))) (forall ((B4 tptp.real) (K tptp.real) (B2 tptp.real) (A tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A))) (let ((_let_2 (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real K))) (=> (= B4 (tptp.aa_real_real _let_2 B2)) (= (tptp.aa_real_real _let_1 B4) (tptp.aa_real_real _let_2 (tptp.aa_real_real _let_1 B2))))))) (forall ((B4 tptp.rat) (K tptp.rat) (B2 tptp.rat) (A tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A))) (let ((_let_2 (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat K))) (=> (= B4 (tptp.aa_rat_rat _let_2 B2)) (= (tptp.aa_rat_rat _let_1 B4) (tptp.aa_rat_rat _let_2 (tptp.aa_rat_rat _let_1 B2))))))) (forall ((B4 tptp.nat) (K tptp.nat) (B2 tptp.nat) (A tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A))) (let ((_let_2 (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat K))) (=> (= B4 (tptp.aa_nat_nat _let_2 B2)) (= (tptp.aa_nat_nat _let_1 B4) (tptp.aa_nat_nat _let_2 (tptp.aa_nat_nat _let_1 B2))))))) (forall ((B4 tptp.int) (K tptp.int) (B2 tptp.int) (A tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.plus_plus_int A))) (let ((_let_2 (tptp.aa_int_fun_int_int tptp.plus_plus_int K))) (=> (= B4 (tptp.aa_int_int _let_2 B2)) (= (tptp.aa_int_int _let_1 B4) (tptp.aa_int_int _let_2 (tptp.aa_int_int _let_1 B2))))))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A))) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real _let_1 B2)) C) (tptp.aa_real_real _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real B2) C))))) (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A))) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat _let_1 B2)) C) (tptp.aa_rat_rat _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat B2) C))))) (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat _let_1 B2)) C) (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat B2) C))))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.plus_plus_int A))) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int _let_1 B2)) C) (tptp.aa_int_int _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int B2) C))))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A))) (= (= (tptp.aa_real_real _let_1 B2) (tptp.aa_real_real _let_1 C)) (= B2 C)))) (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A))) (= (= (tptp.aa_rat_rat _let_1 B2) (tptp.aa_rat_rat _let_1 C)) (= B2 C)))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.plus_plus_int A))) (= (= (tptp.aa_int_int _let_1 B2) (tptp.aa_int_int _let_1 C)) (= B2 C)))) (forall ((B2 tptp.real) (A tptp.real) (C tptp.real)) (= (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real B2) A) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real C) A)) (= B2 C))) (forall ((B2 tptp.rat) (A tptp.rat) (C tptp.rat)) (= (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat B2) A) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat C) A)) (= B2 C))) (forall ((B2 tptp.int) (A tptp.int) (C tptp.int)) (= (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int B2) A) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int C) A)) (= B2 C))) (forall ((A tptp.real) (B2 tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) B2) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real B2) A))) (forall ((A tptp.rat) (B2 tptp.rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) B2) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat B2) A))) (forall ((A tptp.nat) (B2 tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) B2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat B2) A))) (forall ((A tptp.int) (B2 tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) B2) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int B2) A))) (forall ((B2 tptp.real) (A tptp.real) (C tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real B2))) (let ((_let_2 (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A))) (= (tptp.aa_real_real _let_1 (tptp.aa_real_real _let_2 C)) (tptp.aa_real_real _let_2 (tptp.aa_real_real _let_1 C)))))) (forall ((B2 tptp.rat) (A tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat B2))) (let ((_let_2 (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A))) (= (tptp.aa_rat_rat _let_1 (tptp.aa_rat_rat _let_2 C)) (tptp.aa_rat_rat _let_2 (tptp.aa_rat_rat _let_1 C)))))) (forall ((B2 tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat B2))) (let ((_let_2 (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A))) (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat _let_2 C)) (tptp.aa_nat_nat _let_2 (tptp.aa_nat_nat _let_1 C)))))) (forall ((B2 tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.plus_plus_int B2))) (let ((_let_2 (tptp.aa_int_fun_int_int tptp.plus_plus_int A))) (= (tptp.aa_int_int _let_1 (tptp.aa_int_int _let_2 C)) (tptp.aa_int_int _let_2 (tptp.aa_int_int _let_1 C)))))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A))) (=> (= (tptp.aa_real_real _let_1 B2) (tptp.aa_real_real _let_1 C)) (= B2 C)))) (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A))) (=> (= (tptp.aa_rat_rat _let_1 B2) (tptp.aa_rat_rat _let_1 C)) (= B2 C)))) (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A))) (=> (= (tptp.aa_nat_nat _let_1 B2) (tptp.aa_nat_nat _let_1 C)) (= B2 C)))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.plus_plus_int A))) (=> (= (tptp.aa_int_int _let_1 B2) (tptp.aa_int_int _let_1 C)) (= B2 C)))) (forall ((B2 tptp.real) (A tptp.real) (C tptp.real)) (=> (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real B2) A) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real C) A)) (= B2 C))) (forall ((B2 tptp.rat) (A tptp.rat) (C tptp.rat)) (=> (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat B2) A) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat C) A)) (= B2 C))) (forall ((B2 tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat B2) A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat C) A)) (= B2 C))) (forall ((B2 tptp.int) (A tptp.int) (C tptp.int)) (=> (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int B2) A) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int C) A)) (= B2 C))) (forall ((A tptp.complex) (B2 tptp.complex) (C tptp.complex) (D tptp.complex)) (=> (= (tptp.aa_complex_complex (tptp.minus_minus_complex A) B2) (tptp.aa_complex_complex (tptp.minus_minus_complex C) D)) (= (= A B2) (= C D)))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real) (D tptp.real)) (=> (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A) B2) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real C) D)) (= (= A B2) (= C D)))) (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat) (D tptp.rat)) (=> (= (tptp.aa_rat_rat (tptp.minus_minus_rat A) B2) (tptp.aa_rat_rat (tptp.minus_minus_rat C) D)) (= (= A B2) (= C D)))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int) (D tptp.int)) (=> (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) B2) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int C) D)) (= (= A B2) (= C D)))) (forall ((A tptp.complex) (C tptp.complex) (B2 tptp.complex)) (let ((_let_1 (tptp.minus_minus_complex A))) (= (tptp.aa_complex_complex (tptp.minus_minus_complex (tptp.aa_complex_complex _let_1 C)) B2) (tptp.aa_complex_complex (tptp.minus_minus_complex (tptp.aa_complex_complex _let_1 B2)) C)))) (forall ((A tptp.real) (C tptp.real) (B2 tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A))) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real _let_1 C)) B2) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real _let_1 B2)) C)))) (forall ((A tptp.rat) (C tptp.rat) (B2 tptp.rat)) (let ((_let_1 (tptp.minus_minus_rat A))) (= (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_rat_rat _let_1 C)) B2) (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_rat_rat _let_1 B2)) C)))) (forall ((A tptp.nat) (C tptp.nat) (B2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat A))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat _let_1 C)) B2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat _let_1 B2)) C)))) (forall ((A tptp.int) (C tptp.int) (B2 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.minus_minus_int A))) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_int_int _let_1 C)) B2) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_int_int _let_1 B2)) C)))) (forall ((I tptp.real) (J tptp.real) (K tptp.real) (L tptp.real)) (=> (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real I) J)) (= K L)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real I) K)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real J) L))))) (forall ((I tptp.rat) (J tptp.rat) (K tptp.rat) (L tptp.rat)) (=> (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat I) J)) (= K L)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat I) K)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat J) L))))) (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I) J)) (= K L)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat I) K)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat J) L))))) (forall ((I tptp.int) (J tptp.int) (K tptp.int) (L tptp.int)) (=> (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int I) J)) (= K L)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int I) K)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int J) L))))) (forall ((I tptp.real) (J tptp.real) (K tptp.real) (L tptp.real)) (=> (and (= I J) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real K) L))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real I) K)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real J) L))))) (forall ((I tptp.rat) (J tptp.rat) (K tptp.rat) (L tptp.rat)) (=> (and (= I J) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat K) L))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat I) K)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat J) L))))) (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (= I J) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) L))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat I) K)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat J) L))))) (forall ((I tptp.int) (J tptp.int) (K tptp.int) (L tptp.int)) (=> (and (= I J) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int K) L))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int I) K)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int J) L))))) (forall ((I tptp.real) (J tptp.real) (K tptp.real) (L tptp.real)) (=> (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real I) J)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real K) L))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real I) K)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real J) L))))) (forall ((I tptp.rat) (J tptp.rat) (K tptp.rat) (L tptp.rat)) (=> (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat I) J)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat K) L))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat I) K)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat J) L))))) (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I) J)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) L))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat I) K)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat J) L))))) (forall ((I tptp.int) (J tptp.int) (K tptp.int) (L tptp.int)) (=> (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int I) J)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int K) L))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int I) K)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int J) L))))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real) (D tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) B2)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real C) D)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) C)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real B2) D)))))) (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat) (D tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B2)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat C) D)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) C)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat B2) D)))))) (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat) (D tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat C) D)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) C)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat B2) D)))))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int) (D tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B2)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int C) D)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int B2) D)))))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real C))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) B2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real _let_1 A)) (tptp.aa_real_real _let_1 B2)))))) (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat C))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B2)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat _let_1 A)) (tptp.aa_rat_rat _let_1 B2)))))) (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat C))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat _let_1 A)) (tptp.aa_nat_nat _let_1 B2)))))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.plus_plus_int C))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B2)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int _let_1 A)) (tptp.aa_int_int _let_1 B2)))))) (forall ((A tptp.nat) (B2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B2)) (not (forall ((C2 tptp.nat)) (not (= B2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) C2))))))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) B2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) C)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real B2) C))))) (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B2)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) C)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat B2) C))))) (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) C)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat B2) C))))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B2)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int B2) C))))) (forall ((A tptp.nat) (B2 tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B2)) (exists ((C3 tptp.nat)) (= B2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) C3))))) (forall ((C tptp.real) (A tptp.real) (B2 tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real C))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real _let_1 A)) (tptp.aa_real_real _let_1 B2))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) B2))))) (forall ((C tptp.rat) (A tptp.rat) (B2 tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat C))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat _let_1 A)) (tptp.aa_rat_rat _let_1 B2))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B2))))) (forall ((C tptp.nat) (A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat C))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat _let_1 A)) (tptp.aa_nat_nat _let_1 B2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B2))))) (forall ((C tptp.int) (A tptp.int) (B2 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.plus_plus_int C))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int _let_1 A)) (tptp.aa_int_int _let_1 B2))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B2))))) (forall ((A tptp.real) (C tptp.real) (B2 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) C)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real B2) C))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) B2)))) (forall ((A tptp.rat) (C tptp.rat) (B2 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) C)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat B2) C))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B2)))) (forall ((A tptp.nat) (C tptp.nat) (B2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) C)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat B2) C))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B2)))) (forall ((A tptp.int) (C tptp.int) (B2 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int B2) C))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B2)))) (forall ((A tptp.real) (B2 tptp.real) (D tptp.real) (C tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) B2)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real D) C)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A) C)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real B2) D)))))) (forall ((A tptp.rat) (B2 tptp.rat) (D tptp.rat) (C tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B2)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat D) C)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.minus_minus_rat A) C)) (tptp.aa_rat_rat (tptp.minus_minus_rat B2) D)))))) (forall ((A tptp.int) (B2 tptp.int) (D tptp.int) (C tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B2)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int D) C)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int B2) D)))))) (forall ((B2 tptp.real) (A tptp.real) (C tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real C))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real B2) A)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real _let_1 A)) (tptp.aa_real_real _let_1 B2)))))) (forall ((B2 tptp.rat) (A tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.minus_minus_rat C))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B2) A)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat _let_1 A)) (tptp.aa_rat_rat _let_1 B2)))))) (forall ((B2 tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.minus_minus_int C))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B2) A)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int _let_1 A)) (tptp.aa_int_int _let_1 B2)))))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) B2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A) C)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real B2) C))))) (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B2)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.minus_minus_rat A) C)) (tptp.aa_rat_rat (tptp.minus_minus_rat B2) C))))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B2)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int B2) C))))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real) (D tptp.real)) (=> (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A) B2) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real C) D)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) B2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real C) D))))) (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat) (D tptp.rat)) (=> (= (tptp.aa_rat_rat (tptp.minus_minus_rat A) B2) (tptp.aa_rat_rat (tptp.minus_minus_rat C) D)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B2)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat C) D))))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int) (D tptp.int)) (=> (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) B2) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int C) D)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B2)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int C) D))))) (forall ((I tptp.real) (J tptp.real) (K tptp.real) (L tptp.real)) (=> (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real I) J)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real K) L))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real I) K)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real J) L))))) (forall ((I tptp.rat) (J tptp.rat) (K tptp.rat) (L tptp.rat)) (=> (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat I) J)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat K) L))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat I) K)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat J) L))))) (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I) J)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat K) L))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat I) K)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat J) L))))) (forall ((I tptp.int) (J tptp.int) (K tptp.int) (L tptp.int)) (=> (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int I) J)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int K) L))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int I) K)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int J) L))))) (forall ((I tptp.real) (J tptp.real) (K tptp.real) (L tptp.real)) (=> (and (= I J) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real K) L))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real I) K)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real J) L))))) (forall ((I tptp.rat) (J tptp.rat) (K tptp.rat) (L tptp.rat)) (=> (and (= I J) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat K) L))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat I) K)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat J) L))))) (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (= I J) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat K) L))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat I) K)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat J) L))))) (forall ((I tptp.int) (J tptp.int) (K tptp.int) (L tptp.int)) (=> (and (= I J) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int K) L))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int I) K)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int J) L))))) (forall ((I tptp.real) (J tptp.real) (K tptp.real) (L tptp.real)) (=> (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real I) J)) (= K L)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real I) K)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real J) L))))) (forall ((I tptp.rat) (J tptp.rat) (K tptp.rat) (L tptp.rat)) (=> (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat I) J)) (= K L)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat I) K)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat J) L))))) (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I) J)) (= K L)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat I) K)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat J) L))))) (forall ((I tptp.int) (J tptp.int) (K tptp.int) (L tptp.int)) (=> (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int I) J)) (= K L)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int I) K)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int J) L))))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real) (D tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B2)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real C) D)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) C)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real B2) D)))))) (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat) (D tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B2)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat C) D)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) C)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat B2) D)))))) (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat) (D tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) B2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat C) D)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) C)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat B2) D)))))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int) (D tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B2)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int C) D)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int B2) D)))))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real C))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real _let_1 A)) (tptp.aa_real_real _let_1 B2)))))) (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat C))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B2)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat _let_1 A)) (tptp.aa_rat_rat _let_1 B2)))))) (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat C))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) B2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat _let_1 A)) (tptp.aa_nat_nat _let_1 B2)))))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.plus_plus_int C))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B2)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int _let_1 A)) (tptp.aa_int_int _let_1 B2)))))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) C)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real B2) C))))) (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B2)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) C)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat B2) C))))) (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) B2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) C)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat B2) C))))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B2)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int B2) C))))) (forall ((C tptp.real) (A tptp.real) (B2 tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real C))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real _let_1 A)) (tptp.aa_real_real _let_1 B2))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B2))))) (forall ((C tptp.rat) (A tptp.rat) (B2 tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat C))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat _let_1 A)) (tptp.aa_rat_rat _let_1 B2))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B2))))) (forall ((C tptp.nat) (A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat C))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat _let_1 A)) (tptp.aa_nat_nat _let_1 B2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) B2))))) (forall ((C tptp.int) (A tptp.int) (B2 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.plus_plus_int C))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int _let_1 A)) (tptp.aa_int_int _let_1 B2))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B2))))) (forall ((A tptp.real) (C tptp.real) (B2 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) C)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real B2) C))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B2)))) (forall ((A tptp.rat) (C tptp.rat) (B2 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) C)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat B2) C))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B2)))) (forall ((A tptp.nat) (C tptp.nat) (B2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) C)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat B2) C))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) B2)))) (forall ((A tptp.int) (C tptp.int) (B2 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int B2) C))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B2)))) (forall ((A tptp.real) (B2 tptp.real) (D tptp.real) (C tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B2)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real D) C)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A) C)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real B2) D)))))) (forall ((A tptp.rat) (B2 tptp.rat) (D tptp.rat) (C tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B2)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat D) C)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.minus_minus_rat A) C)) (tptp.aa_rat_rat (tptp.minus_minus_rat B2) D)))))) (forall ((A tptp.int) (B2 tptp.int) (D tptp.int) (C tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B2)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int D) C)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int B2) D)))))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real) (D tptp.real)) (=> (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A) B2) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real C) D)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real C) D))))) (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat) (D tptp.rat)) (=> (= (tptp.aa_rat_rat (tptp.minus_minus_rat A) B2) (tptp.aa_rat_rat (tptp.minus_minus_rat C) D)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B2)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat C) D))))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int) (D tptp.int)) (=> (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) B2) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int C) D)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B2)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int C) D))))) (forall ((B2 tptp.real) (A tptp.real) (C tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real C))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B2) A)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real _let_1 A)) (tptp.aa_real_real _let_1 B2)))))) (forall ((B2 tptp.rat) (A tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.minus_minus_rat C))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B2) A)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat _let_1 A)) (tptp.aa_rat_rat _let_1 B2)))))) (forall ((B2 tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.minus_minus_int C))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B2) A)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int _let_1 A)) (tptp.aa_int_int _let_1 B2)))))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A) C)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real B2) C))))) (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B2)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.minus_minus_rat A) C)) (tptp.aa_rat_rat (tptp.minus_minus_rat B2) C))))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B2)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int B2) C))))) (forall ((A4 tptp.complex) (K tptp.complex) (A tptp.complex) (B2 tptp.complex)) (let ((_let_1 (tptp.plus_plus_complex K))) (=> (= A4 (tptp.aa_complex_complex _let_1 A)) (= (tptp.aa_complex_complex (tptp.minus_minus_complex A4) B2) (tptp.aa_complex_complex _let_1 (tptp.aa_complex_complex (tptp.minus_minus_complex A) B2)))))) (forall ((A4 tptp.real) (K tptp.real) (A tptp.real) (B2 tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real K))) (=> (= A4 (tptp.aa_real_real _let_1 A)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A4) B2) (tptp.aa_real_real _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A) B2)))))) (forall ((A4 tptp.rat) (K tptp.rat) (A tptp.rat) (B2 tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat K))) (=> (= A4 (tptp.aa_rat_rat _let_1 A)) (= (tptp.aa_rat_rat (tptp.minus_minus_rat A4) B2) (tptp.aa_rat_rat _let_1 (tptp.aa_rat_rat (tptp.minus_minus_rat A) B2)))))) (forall ((A4 tptp.int) (K tptp.int) (A tptp.int) (B2 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.plus_plus_int K))) (=> (= A4 (tptp.aa_int_int _let_1 A)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A4) B2) (tptp.aa_int_int _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) B2)))))) (forall ((A tptp.complex) (B2 tptp.complex) (C tptp.complex)) (= (= (tptp.aa_complex_complex (tptp.minus_minus_complex A) B2) C) (= A (tptp.aa_complex_complex (tptp.plus_plus_complex C) B2)))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (= (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A) B2) C) (= A (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real C) B2)))) (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat)) (= (= (tptp.aa_rat_rat (tptp.minus_minus_rat A) B2) C) (= A (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat C) B2)))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (= (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) B2) C) (= A (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int C) B2)))) (forall ((A tptp.complex) (C tptp.complex) (B2 tptp.complex)) (= (= A (tptp.aa_complex_complex (tptp.minus_minus_complex C) B2)) (= (tptp.aa_complex_complex (tptp.plus_plus_complex A) B2) C))) (forall ((A tptp.real) (C tptp.real) (B2 tptp.real)) (= (= A (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real C) B2)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) B2) C))) (forall ((A tptp.rat) (C tptp.rat) (B2 tptp.rat)) (= (= A (tptp.aa_rat_rat (tptp.minus_minus_rat C) B2)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) B2) C))) (forall ((A tptp.int) (C tptp.int) (B2 tptp.int)) (= (= A (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int C) B2)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) B2) C))) (forall ((A tptp.complex) (B2 tptp.complex) (C tptp.complex)) (let ((_let_1 (tptp.plus_plus_complex A))) (= (tptp.aa_complex_complex _let_1 (tptp.aa_complex_complex (tptp.minus_minus_complex B2) C)) (tptp.aa_complex_complex (tptp.minus_minus_complex (tptp.aa_complex_complex _let_1 B2)) C)))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A))) (= (tptp.aa_real_real _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real B2) C)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real _let_1 B2)) C)))) (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A))) (= (tptp.aa_rat_rat _let_1 (tptp.aa_rat_rat (tptp.minus_minus_rat B2) C)) (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_rat_rat _let_1 B2)) C)))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.plus_plus_int A))) (= (tptp.aa_int_int _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int B2) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_int_int _let_1 B2)) C)))) (forall ((A tptp.complex) (B2 tptp.complex) (C tptp.complex)) (= (tptp.aa_complex_complex (tptp.minus_minus_complex A) (tptp.aa_complex_complex (tptp.minus_minus_complex B2) C)) (tptp.aa_complex_complex (tptp.minus_minus_complex (tptp.aa_complex_complex (tptp.plus_plus_complex A) C)) B2))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real B2) C)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) C)) B2))) (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat)) (= (tptp.aa_rat_rat (tptp.minus_minus_rat A) (tptp.aa_rat_rat (tptp.minus_minus_rat B2) C)) (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) C)) B2))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int B2) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) C)) B2))) (forall ((A tptp.complex) (B2 tptp.complex) (C tptp.complex)) (= (tptp.aa_complex_complex (tptp.plus_plus_complex (tptp.aa_complex_complex (tptp.minus_minus_complex A) B2)) C) (tptp.aa_complex_complex (tptp.minus_minus_complex (tptp.aa_complex_complex (tptp.plus_plus_complex A) C)) B2))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A) B2)) C) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) C)) B2))) (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.minus_minus_rat A) B2)) C) (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) C)) B2))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) B2)) C) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) C)) B2))) (forall ((A tptp.complex) (B2 tptp.complex) (C tptp.complex)) (let ((_let_1 (tptp.minus_minus_complex A))) (= (tptp.aa_complex_complex _let_1 (tptp.aa_complex_complex (tptp.plus_plus_complex B2) C)) (tptp.aa_complex_complex (tptp.minus_minus_complex (tptp.aa_complex_complex _let_1 C)) B2)))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A))) (= (tptp.aa_real_real _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real B2) C)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real _let_1 C)) B2)))) (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.minus_minus_rat A))) (= (tptp.aa_rat_rat _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat B2) C)) (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_rat_rat _let_1 C)) B2)))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.minus_minus_int A))) (= (tptp.aa_int_int _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int B2) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_int_int _let_1 C)) B2)))) (forall ((C tptp.complex) (B2 tptp.complex) (A tptp.complex)) (=> (= (tptp.aa_complex_complex (tptp.plus_plus_complex C) B2) A) (= C (tptp.aa_complex_complex (tptp.minus_minus_complex A) B2)))) (forall ((C tptp.real) (B2 tptp.real) (A tptp.real)) (=> (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real C) B2) A) (= C (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A) B2)))) (forall ((C tptp.rat) (B2 tptp.rat) (A tptp.rat)) (=> (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat C) B2) A) (= C (tptp.aa_rat_rat (tptp.minus_minus_rat A) B2)))) (forall ((C tptp.nat) (B2 tptp.nat) (A tptp.nat)) (=> (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat C) B2) A) (= C (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat A) B2)))) (forall ((C tptp.int) (B2 tptp.int) (A tptp.int)) (=> (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int C) B2) A) (= C (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) B2)))) (forall ((A tptp.complex) (B2 tptp.complex) (C tptp.complex)) (let ((_let_1 (tptp.minus_minus_complex A))) (= (tptp.aa_complex_complex (tptp.minus_minus_complex (tptp.aa_complex_complex _let_1 B2)) C) (tptp.aa_complex_complex _let_1 (tptp.aa_complex_complex (tptp.plus_plus_complex B2) C))))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A))) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real _let_1 B2)) C) (tptp.aa_real_real _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real B2) C))))) (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.minus_minus_rat A))) (= (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_rat_rat _let_1 B2)) C) (tptp.aa_rat_rat _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat B2) C))))) (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat A))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat _let_1 B2)) C) (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat B2) C))))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.minus_minus_int A))) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_int_int _let_1 B2)) C) (tptp.aa_int_int _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int B2) C))))) (forall ((I tptp.real) (J tptp.real) (K tptp.real) (L tptp.real)) (=> (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real I) J)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real K) L))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real I) K)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real J) L))))) (forall ((I tptp.rat) (J tptp.rat) (K tptp.rat) (L tptp.rat)) (=> (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat I) J)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat K) L))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat I) K)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat J) L))))) (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I) J)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat K) L))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat I) K)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat J) L))))) (forall ((I tptp.int) (J tptp.int) (K tptp.int) (L tptp.int)) (=> (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int I) J)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int K) L))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int I) K)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int J) L))))) (forall ((I tptp.real) (J tptp.real) (K tptp.real) (L tptp.real)) (=> (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real I) J)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real K) L))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real I) K)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real J) L))))) (forall ((I tptp.rat) (J tptp.rat) (K tptp.rat) (L tptp.rat)) (=> (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat I) J)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat K) L))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat I) K)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat J) L))))) (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I) J)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) L))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat I) K)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat J) L))))) (forall ((I tptp.int) (J tptp.int) (K tptp.int) (L tptp.int)) (=> (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int I) J)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int K) L))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int I) K)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int J) L))))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real) (D tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) B2)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real C) D)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) C)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real B2) D)))))) (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat) (D tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B2)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat C) D)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) C)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat B2) D)))))) (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat) (D tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat C) D)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) C)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat B2) D)))))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int) (D tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B2)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int C) D)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int B2) D)))))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real) (D tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B2)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real C) D)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) C)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real B2) D)))))) (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat) (D tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B2)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat C) D)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) C)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat B2) D)))))) (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat) (D tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) B2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat C) D)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) C)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat B2) D)))))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int) (D tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B2)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int C) D)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int B2) D)))))) (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B2)))) (=> _let_1 (=> _let_1 (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat B2) A) C) (= B2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat C) A))))))) (forall ((A tptp.nat) (B2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B2)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat B2) A)) B2))) (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B2)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat C) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat B2) A)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat C) A)) B2)))) (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B2)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat B2) C)) A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat B2) A)) C)))) (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B2)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat B2) A)) C) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat B2) C)) A)))) (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat C))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B2)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat _let_1 B2)) A) (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat B2) A)))))) (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat C))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B2)) (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat B2) A)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat _let_1 B2)) A))))) (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B2)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat C) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat B2) A))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat C) A)) B2))))) (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat C) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat B2) C)) A))))) (forall ((A tptp.nat) (B2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B2)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat B2) A)) A) B2))) (forall ((A tptp.real) (C tptp.real) (B2 tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real C) B2))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) B2)) C)))) (forall ((A tptp.rat) (C tptp.rat) (B2 tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) (tptp.aa_rat_rat (tptp.minus_minus_rat C) B2))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) B2)) C)))) (forall ((A tptp.int) (C tptp.int) (B2 tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int C) B2))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) B2)) C)))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A) B2)) C)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real C) B2))))) (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.minus_minus_rat A) B2)) C)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat C) B2))))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) B2)) C)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int C) B2))))) (forall ((A tptp.real) (C tptp.real) (B2 tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real C) B2))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) B2)) C)))) (forall ((A tptp.rat) (C tptp.rat) (B2 tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) (tptp.aa_rat_rat (tptp.minus_minus_rat C) B2))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) B2)) C)))) (forall ((A tptp.int) (C tptp.int) (B2 tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int C) B2))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) B2)) C)))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A) B2)) C)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real C) B2))))) (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.minus_minus_rat A) B2)) C)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat C) B2))))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) B2)) C)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int C) B2))))) (and (=> _let_188 (and (=> _let_189 (= _let_176 _let_173)) (=> (not _let_189) (= _let_176 tptp.none_nat)))) (=> (not _let_188) (= _let_176 _let_172))) (forall ((TreeList tptp.list_VEBT_VEBT) (N tptp.nat) (Summary tptp.vEBT_VEBT) (M tptp.nat) (Deg tptp.nat) (Mi tptp.nat) (Ma tptp.nat)) (let ((_let_1 (= Mi Ma))) (let ((_let_2 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (tptp.pp (tptp.aa_set8260762808118238015T_bool (tptp.aa_VEB289770264548726718T_bool tptp.member_VEBT_VEBT X4) (tptp.set_VEBT_VEBT2 TreeList))) (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt X4) N)))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt Summary) M)) (=> (= (tptp.size_s6755466524823107622T_VEBT TreeList) (tptp.aa_nat_nat _let_2 M)) (=> (= M N) (=> (= Deg (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N) M)) (=> (forall ((I3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I3) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) M))) (= (exists ((X_1 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions (tptp.nth_VEBT_VEBT TreeList I3)) X_1))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions Summary) I3))))) (=> (=> _let_1 (forall ((X4 tptp.vEBT_VEBT)) (=> (tptp.pp (tptp.aa_set8260762808118238015T_bool (tptp.aa_VEB289770264548726718T_bool tptp.member_VEBT_VEBT X4) (tptp.set_VEBT_VEBT2 TreeList))) (not (exists ((X_12 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions X4) X_12))))))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Mi) Ma)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Ma) (tptp.aa_nat_nat _let_2 Deg))) (=> (=> (not _let_1) (forall ((I3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I3) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) M))) (and (=> (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high Ma) N) I3) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions (tptp.nth_VEBT_VEBT TreeList I3)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low Ma) N)))) (forall ((X4 tptp.nat)) (=> (and (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high X4) N) I3) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions (tptp.nth_VEBT_VEBT TreeList I3)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low X4) N)))) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Mi) X4)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X4) Ma))))))))) (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Mi) Ma)) Deg TreeList Summary)) Deg))))))))))))))) (forall ((X tptp.nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Mi tptp.nat) (Ma tptp.nat) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat Deg) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high X) _let_1))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_2) (tptp.size_s6755466524823107622T_VEBT TreeList))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.one_one_nat) Deg)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions (tptp.nth_VEBT_VEBT TreeList _let_2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low X) _let_1))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Mi) Ma)) Deg TreeList Summary)) X)))))))) (forall ((Deg tptp.nat) (Mi tptp.nat) (Ma tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat Deg) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.one_one_nat) Deg)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Mi) Ma)) Deg TreeList Summary)) X)) (or (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions (tptp.nth_VEBT_VEBT TreeList (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high X) _let_1))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low X) _let_1))) (= X Mi) (= X Ma)))))) (forall ((TreeList tptp.list_VEBT_VEBT) (N tptp.nat) (Summary tptp.vEBT_VEBT) (M tptp.nat) (Deg tptp.nat)) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (tptp.pp (tptp.aa_set8260762808118238015T_bool (tptp.aa_VEB289770264548726718T_bool tptp.member_VEBT_VEBT X4) (tptp.set_VEBT_VEBT2 TreeList))) (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt X4) N)))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt Summary) M)) (=> (= (tptp.size_s6755466524823107622T_VEBT TreeList) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) M)) (=> (= M N) (=> (= Deg (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N) M)) (=> (not (exists ((X_12 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions Summary) X_12)))) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (tptp.pp (tptp.aa_set8260762808118238015T_bool (tptp.aa_VEB289770264548726718T_bool tptp.member_VEBT_VEBT X4) (tptp.set_VEBT_VEBT2 TreeList))) (not (exists ((X_12 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions X4) X_12)))))) (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt (tptp.vEBT_Node tptp.none_P5556105721700978146at_nat Deg TreeList Summary)) Deg)))))))))) (forall ((Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Mi) Ma)) Deg TreeList Summary)) Deg)) (=> (not (= Mi Ma)) (= (tptp.the_nat (tptp.vEBT_vebt_maxt Summary)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high Ma) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat Deg) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))))))) (forall ((TreeList tptp.list_VEBT_VEBT) (N tptp.nat) (M tptp.nat)) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (tptp.pp (tptp.aa_set8260762808118238015T_bool (tptp.aa_VEB289770264548726718T_bool tptp.member_VEBT_VEBT X4) (tptp.set_VEBT_VEBT2 TreeList))) (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt X4) N)))) (=> (= (tptp.size_s6755466524823107622T_VEBT TreeList) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) M)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.one_one_nat) N))))) (forall ((Mi tptp.nat) (Ma tptp.nat) (Ux tptp.nat) (Uy tptp.list_VEBT_VEBT) (Uz tptp.vEBT_VEBT)) (= (tptp.vEBT_vebt_maxt (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Mi) Ma)) Ux Uy Uz)) (tptp.some_nat Ma))) (forall ((Mi tptp.nat) (Ma tptp.nat) (Ux tptp.nat) (Uy tptp.list_VEBT_VEBT) (Uz tptp.vEBT_VEBT)) (= (tptp.vEBT_vebt_mint (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Mi) Ma)) Ux Uy Uz)) (tptp.some_nat Mi))) (forall ((A tptp.complex) (B2 tptp.complex) (C tptp.complex)) (let ((_let_1 (tptp.times_times_complex A))) (= (tptp.aa_complex_complex _let_1 (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex B2) C)) (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex (tptp.aa_complex_complex _let_1 B2)) C)))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A))) (= (tptp.aa_real_real _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real B2) C)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real _let_1 B2)) C)))) (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A))) (= (tptp.aa_rat_rat _let_1 (tptp.aa_rat_rat (tptp.divide_divide_rat B2) C)) (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_rat_rat _let_1 B2)) C)))) (forall ((A tptp.complex) (B2 tptp.complex) (C tptp.complex)) (= (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex A) (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex B2) C)) (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex (tptp.aa_complex_complex (tptp.times_times_complex A) C)) B2))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real A) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real B2) C)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) C)) B2))) (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat)) (= (tptp.aa_rat_rat (tptp.divide_divide_rat A) (tptp.aa_rat_rat (tptp.divide_divide_rat B2) C)) (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) C)) B2))) (tptp.pp (tptp.aa_nat_bool _let_161 tptp.na)) (forall ((R tptp.real) (A tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.times_times_real R))) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real _let_1 A)) (tptp.aa_real_real _let_1 R)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real A) R)))) (forall ((X11 tptp.option4927543243414619207at_nat) (X12 tptp.nat) (X13 tptp.list_VEBT_VEBT) (X14 tptp.vEBT_VEBT) (Y11 tptp.option4927543243414619207at_nat) (Y12 tptp.nat) (Y13 tptp.list_VEBT_VEBT) (Y14 tptp.vEBT_VEBT)) (= (= (tptp.vEBT_Node X11 X12 X13 X14) (tptp.vEBT_Node Y11 Y12 Y13 Y14)) (and (= X11 Y11) (= X12 Y12) (= X13 Y13) (= X14 Y14)))) (forall ((A tptp.complex)) (= (tptp.aa_complex_complex (tptp.times_times_complex tptp.one_one_complex) A) A)) (forall ((A tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real tptp.one_one_real) A) A)) (forall ((A tptp.rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat tptp.one_one_rat) A) A)) (forall ((A tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat tptp.one_one_nat) A) A)) (forall ((A tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int tptp.one_one_int) A) A)) (forall ((A tptp.complex)) (= (tptp.aa_complex_complex (tptp.times_times_complex A) tptp.one_one_complex) A)) (forall ((A tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) tptp.one_one_real) A)) (forall ((A tptp.rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) tptp.one_one_rat) A)) (forall ((A tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) tptp.one_one_nat) A)) (forall ((A tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) tptp.one_one_int) A)) (forall ((B2 tptp.complex) (C tptp.complex) (A tptp.complex)) (= (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex B2) C)) A) (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex (tptp.aa_complex_complex (tptp.times_times_complex B2) A)) C))) (forall ((B2 tptp.real) (C tptp.real) (A tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real B2) C)) A) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real B2) A)) C))) (forall ((B2 tptp.rat) (C tptp.rat) (A tptp.rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat (tptp.divide_divide_rat B2) C)) A) (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat B2) A)) C))) (forall ((A tptp.complex) (B2 tptp.complex) (C tptp.complex)) (let ((_let_1 (tptp.divide1717551699836669952omplex A))) (= (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex (tptp.aa_complex_complex _let_1 B2)) C) (tptp.aa_complex_complex _let_1 (tptp.aa_complex_complex (tptp.times_times_complex B2) C))))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real A))) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real _let_1 B2)) C) (tptp.aa_real_real _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real B2) C))))) (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.divide_divide_rat A))) (= (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_rat_rat _let_1 B2)) C) (tptp.aa_rat_rat _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat B2) C))))) (forall ((A tptp.complex)) (= (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex A) tptp.one_one_complex) A)) (forall ((A tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real A) tptp.one_one_real) A)) (forall ((A tptp.rat)) (= (tptp.aa_rat_rat (tptp.divide_divide_rat A) tptp.one_one_rat) A)) (forall ((A tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) tptp.one_one_nat) A)) (forall ((A tptp.int)) (= (tptp.aa_int_int (tptp.divide_divide_int A) tptp.one_one_int) A)) (forall ((A tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) tptp.one_one_nat) A)) (forall ((A tptp.int)) (= (tptp.aa_int_int (tptp.divide_divide_int A) tptp.one_one_int) A)) (forall ((N tptp.nat)) (= (tptp.aa_nat_rat (tptp.power_power_rat tptp.one_one_rat) N) tptp.one_one_rat)) (forall ((N tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat tptp.one_one_nat) N) tptp.one_one_nat)) (forall ((N tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real tptp.one_one_real) N) tptp.one_one_real)) (forall ((N tptp.nat)) (= (tptp.aa_nat_int (tptp.power_power_int tptp.one_one_int) N) tptp.one_one_int)) (forall ((N tptp.nat)) (= (tptp.aa_nat_complex (tptp.power_power_complex tptp.one_one_complex) N) tptp.one_one_complex)) (forall ((A tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A) tptp.one_one_nat) A)) (forall ((A tptp.real)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real A) tptp.one_one_nat) A)) (forall ((A tptp.int)) (= (tptp.aa_nat_int (tptp.power_power_int A) tptp.one_one_nat) A)) (forall ((A tptp.complex)) (= (tptp.aa_nat_complex (tptp.power_power_complex A) tptp.one_one_nat) A)) (forall ((M tptp.nat) (N tptp.nat)) (= (= tptp.one_one_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat M) N)) (and (= M tptp.one_one_nat) (= N tptp.one_one_nat)))) (forall ((M tptp.nat) (N tptp.nat)) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat M) N) tptp.one_one_nat) (and (= M tptp.one_one_nat) (= N tptp.one_one_nat)))) (forall ((N tptp.num)) (= (= (tptp.numera6690914467698888265omplex N) tptp.one_one_complex) (= N tptp.one))) (forall ((N tptp.num)) (= (= (tptp.aa_num_real tptp.numeral_numeral_real N) tptp.one_one_real) (= N tptp.one))) (forall ((N tptp.num)) (= (= (tptp.aa_num_rat tptp.numeral_numeral_rat N) tptp.one_one_rat) (= N tptp.one))) (forall ((N tptp.num)) (= (= (tptp.aa_num_nat tptp.numeral_numeral_nat N) tptp.one_one_nat) (= N tptp.one))) (forall ((N tptp.num)) (= (= (tptp.aa_num_int tptp.numeral_numeral_int N) tptp.one_one_int) (= N tptp.one))) (forall ((N tptp.num)) (= (= tptp.one_one_complex (tptp.numera6690914467698888265omplex N)) (= tptp.one N))) (forall ((N tptp.num)) (= (= tptp.one_one_real (tptp.aa_num_real tptp.numeral_numeral_real N)) (= tptp.one N))) (forall ((N tptp.num)) (= (= tptp.one_one_rat (tptp.aa_num_rat tptp.numeral_numeral_rat N)) (= tptp.one N))) (forall ((N tptp.num)) (= (= tptp.one_one_nat (tptp.aa_num_nat tptp.numeral_numeral_nat N)) (= tptp.one N))) (forall ((N tptp.num)) (= (= tptp.one_one_int (tptp.aa_num_int tptp.numeral_numeral_int N)) (= tptp.one N))) (forall ((A tptp.real) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_real_fun_nat_real tptp.power_power_real A))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real) A)) (= (= (tptp.aa_nat_real _let_1 M) (tptp.aa_nat_real _let_1 N)) (= M N))))) (forall ((A tptp.rat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.power_power_rat A))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.one_one_rat) A)) (= (= (tptp.aa_nat_rat _let_1 M) (tptp.aa_nat_rat _let_1 N)) (= M N))))) (forall ((A tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.one_one_nat) A)) (= (= (tptp.aa_nat_nat _let_1 M) (tptp.aa_nat_nat _let_1 N)) (= M N))))) (forall ((A tptp.int) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.power_power_int A))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.one_one_int) A)) (= (= (tptp.aa_nat_int _let_1 M) (tptp.aa_nat_int _let_1 N)) (= M N))))) (forall ((Option tptp.option_nat)) (=> (not (= Option tptp.none_nat)) (= (tptp.some_nat (tptp.the_nat Option)) Option))) (forall ((Option tptp.option4927543243414619207at_nat)) (=> (not (= Option tptp.none_P5556105721700978146at_nat)) (= (tptp.some_P7363390416028606310at_nat (tptp.the_Pr8591224930841456533at_nat Option)) Option))) (forall ((Option tptp.option_num)) (=> (not (= Option tptp.none_num)) (= (tptp.some_num (tptp.the_num Option)) Option))) (forall ((B2 tptp.real) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (tptp.aa_real_fun_nat_real tptp.power_power_real B2))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real) B2)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_nat_real _let_1 X)) (tptp.aa_nat_real _let_1 Y))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Y)))))) (forall ((B2 tptp.rat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (tptp.power_power_rat B2))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.one_one_rat) B2)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_nat_rat _let_1 X)) (tptp.aa_nat_rat _let_1 Y))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Y)))))) (forall ((B2 tptp.nat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat B2))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.one_one_nat) B2)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat _let_1 X)) (tptp.aa_nat_nat _let_1 Y))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Y)))))) (forall ((B2 tptp.int) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (tptp.power_power_int B2))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.one_one_int) B2)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_nat_int _let_1 X)) (tptp.aa_nat_int _let_1 Y))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Y)))))) (= (tptp.aa_complex_complex _let_49 tptp.one_one_complex) _let_50) (= _let_150 _let_28) (= _let_149 _let_69) _let_186 (= _let_146 _let_44) (forall ((B2 tptp.real) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (tptp.aa_real_fun_nat_real tptp.power_power_real B2))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real) B2)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_nat_real _let_1 X)) (tptp.aa_nat_real _let_1 Y))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X) Y)))))) (forall ((B2 tptp.rat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (tptp.power_power_rat B2))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.one_one_rat) B2)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat _let_1 X)) (tptp.aa_nat_rat _let_1 Y))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X) Y)))))) (forall ((B2 tptp.nat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat B2))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.one_one_nat) B2)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat _let_1 X)) (tptp.aa_nat_nat _let_1 Y))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X) Y)))))) (forall ((B2 tptp.int) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (tptp.power_power_int B2))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.one_one_int) B2)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int _let_1 X)) (tptp.aa_nat_int _let_1 Y))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X) Y)))))) (forall ((N tptp.num)) (= (tptp.aa_complex_complex (tptp.plus_plus_complex (tptp.numera6690914467698888265omplex N)) tptp.one_one_complex) (tptp.numera6690914467698888265omplex (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num N) tptp.one)))) (forall ((N tptp.num)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_num_real tptp.numeral_numeral_real N)) tptp.one_one_real) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num N) tptp.one)))) (forall ((N tptp.num)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat N)) tptp.one_one_rat) (tptp.aa_num_rat tptp.numeral_numeral_rat (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num N) tptp.one)))) (forall ((N tptp.num)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_num_nat tptp.numeral_numeral_nat N)) tptp.one_one_nat) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num N) tptp.one)))) (forall ((N tptp.num)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_num_int tptp.numeral_numeral_int N)) tptp.one_one_int) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num N) tptp.one)))) (forall ((N tptp.num)) (= (tptp.aa_complex_complex (tptp.plus_plus_complex tptp.one_one_complex) (tptp.numera6690914467698888265omplex N)) (tptp.numera6690914467698888265omplex (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num tptp.one) N)))) (forall ((N tptp.num)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real tptp.one_one_real) (tptp.aa_num_real tptp.numeral_numeral_real N)) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num tptp.one) N)))) (forall ((N tptp.num)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat tptp.one_one_rat) (tptp.aa_num_rat tptp.numeral_numeral_rat N)) (tptp.aa_num_rat tptp.numeral_numeral_rat (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num tptp.one) N)))) (forall ((N tptp.num)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat tptp.one_one_nat) (tptp.aa_num_nat tptp.numeral_numeral_nat N)) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num tptp.one) N)))) (forall ((N tptp.num)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int tptp.one_one_int) (tptp.aa_num_int tptp.numeral_numeral_int N)) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num tptp.one) N)))) (forall ((N tptp.num)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_num_real tptp.numeral_numeral_real N)) tptp.one_one_real)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num N) tptp.one)))) (forall ((N tptp.num)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_num_rat tptp.numeral_numeral_rat N)) tptp.one_one_rat)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num N) tptp.one)))) (forall ((N tptp.num)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_num_nat tptp.numeral_numeral_nat N)) tptp.one_one_nat)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num N) tptp.one)))) (forall ((N tptp.num)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_num_int tptp.numeral_numeral_int N)) tptp.one_one_int)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num N) tptp.one)))) (forall ((N tptp.num)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real) (tptp.aa_num_real tptp.numeral_numeral_real N))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num tptp.one) N)))) (forall ((N tptp.num)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.one_one_rat) (tptp.aa_num_rat tptp.numeral_numeral_rat N))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num tptp.one) N)))) (forall ((N tptp.num)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.one_one_nat) (tptp.aa_num_nat tptp.numeral_numeral_nat N))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num tptp.one) N)))) (forall ((N tptp.num)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.one_one_int) (tptp.aa_num_int tptp.numeral_numeral_int N))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num tptp.one) N)))) (forall ((X tptp.complex)) (= (= tptp.one_one_complex X) (= X tptp.one_one_complex))) (forall ((X tptp.real)) (= (= tptp.one_one_real X) (= X tptp.one_one_real))) (forall ((X tptp.rat)) (= (= tptp.one_one_rat X) (= X tptp.one_one_rat))) (forall ((X tptp.nat)) (= (= tptp.one_one_nat X) (= X tptp.one_one_nat))) (forall ((X tptp.int)) (= (= tptp.one_one_int X) (= X tptp.one_one_int))) (forall ((X tptp.real) (Y tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) Y)) (or (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Y)) (= X Y)))) (forall ((S2 tptp.set_real)) (=> (exists ((X5 tptp.real)) (tptp.member_real X5 S2)) (=> (exists ((Z3 tptp.real)) (forall ((X4 tptp.real)) (=> (tptp.member_real X4 S2) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X4) Z3))))) (exists ((Y4 tptp.real)) (and (forall ((X5 tptp.real)) (=> (tptp.member_real X5 S2) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X5) Y4)))) (forall ((Z3 tptp.real)) (=> (forall ((X4 tptp.real)) (=> (tptp.member_real X4 S2) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X4) Z3)))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y4) Z3))))))))) (tptp.pp (tptp.aa_real_bool _let_116 tptp.one_one_real)) (tptp.pp (tptp.aa_rat_bool _let_115 tptp.one_one_rat)) (tptp.pp (tptp.aa_nat_bool _let_161 tptp.one_one_nat)) (tptp.pp (tptp.aa_int_bool _let_114 tptp.one_one_int)) (not (tptp.pp (tptp.aa_real_bool _let_113 tptp.one_one_real))) (not (tptp.pp (tptp.aa_rat_bool _let_111 tptp.one_one_rat))) (not (tptp.pp (tptp.aa_nat_bool _let_155 tptp.one_one_nat))) (not (tptp.pp (tptp.aa_int_bool _let_112 tptp.one_one_int))) (forall ((A tptp.complex)) (= (tptp.aa_complex_complex (tptp.times_times_complex A) tptp.one_one_complex) A)) (forall ((A tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) tptp.one_one_real) A)) (forall ((A tptp.rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) tptp.one_one_rat) A)) (forall ((A tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) tptp.one_one_nat) A)) (forall ((A tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) tptp.one_one_int) A)) (forall ((A tptp.complex)) (= (tptp.aa_complex_complex (tptp.times_times_complex tptp.one_one_complex) A) A)) (forall ((A tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real tptp.one_one_real) A) A)) (forall ((A tptp.rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat tptp.one_one_rat) A) A)) (forall ((A tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat tptp.one_one_nat) A) A)) (forall ((A tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int tptp.one_one_int) A) A)) (forall ((N tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat tptp.one_one_nat) N) N)) (forall ((N tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat N) tptp.one_one_nat) N)) (forall ((X2 tptp.nat)) (= (tptp.the_nat (tptp.some_nat X2)) X2)) (forall ((X2 tptp.product_prod_nat_nat)) (= (tptp.the_Pr8591224930841456533at_nat (tptp.some_P7363390416028606310at_nat X2)) X2)) (forall ((X2 tptp.num)) (= (tptp.the_num (tptp.some_num X2)) X2)) (forall ((Option tptp.option_nat) (Option2 tptp.option_nat)) (let ((_let_1 (= Option2 tptp.none_nat))) (let ((_let_2 (= Option tptp.none_nat))) (=> (= _let_2 _let_1) (=> (=> (not _let_2) (=> (not _let_1) (= (tptp.the_nat Option) (tptp.the_nat Option2)))) (= Option Option2)))))) (forall ((Option tptp.option4927543243414619207at_nat) (Option2 tptp.option4927543243414619207at_nat)) (let ((_let_1 (= Option2 tptp.none_P5556105721700978146at_nat))) (let ((_let_2 (= Option tptp.none_P5556105721700978146at_nat))) (=> (= _let_2 _let_1) (=> (=> (not _let_2) (=> (not _let_1) (= (tptp.the_Pr8591224930841456533at_nat Option) (tptp.the_Pr8591224930841456533at_nat Option2)))) (= Option Option2)))))) (forall ((Option tptp.option_num) (Option2 tptp.option_num)) (let ((_let_1 (= Option2 tptp.none_num))) (let ((_let_2 (= Option tptp.none_num))) (=> (= _let_2 _let_1) (=> (=> (not _let_2) (=> (not _let_1) (= (tptp.the_num Option) (tptp.the_num Option2)))) (= Option Option2)))))) (forall ((A tptp.real) (B2 tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A))) (=> (tptp.pp (tptp.aa_real_bool _let_1 B2)) (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) B2)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real tptp.one_one_real) tptp.one_one_real))))))) (forall ((A tptp.rat) (B2 tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 B2)) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) B2)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat tptp.one_one_rat) tptp.one_one_rat))))))) (forall ((A tptp.real) (B2 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) B2)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real tptp.one_one_real) tptp.one_one_real))) B2)))) (forall ((A tptp.rat) (B2 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B2)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) B2)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat tptp.one_one_rat) tptp.one_one_rat))) B2)))) (forall ((N tptp.num)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.one_one_real) (tptp.aa_num_real tptp.numeral_numeral_real N)))) (forall ((N tptp.num)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.one_one_rat) (tptp.aa_num_rat tptp.numeral_numeral_rat N)))) (forall ((N tptp.num)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.one_one_nat) (tptp.aa_num_nat tptp.numeral_numeral_nat N)))) (forall ((N tptp.num)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.one_one_int) (tptp.aa_num_int tptp.numeral_numeral_int N)))) (forall ((N tptp.num)) (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_num_real tptp.numeral_numeral_real N)) tptp.one_one_real)))) (forall ((N tptp.num)) (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_num_rat tptp.numeral_numeral_rat N)) tptp.one_one_rat)))) (forall ((N tptp.num)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_num_nat tptp.numeral_numeral_nat N)) tptp.one_one_nat)))) (forall ((N tptp.num)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_num_int tptp.numeral_numeral_int N)) tptp.one_one_int)))) (forall ((M tptp.real) (N tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real))) (=> (tptp.pp (tptp.aa_real_bool _let_1 M)) (=> (tptp.pp (tptp.aa_real_bool _let_1 N)) (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real M) N))))))) (forall ((M tptp.rat) (N tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.one_one_rat))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 M)) (=> (tptp.pp (tptp.aa_rat_bool _let_1 N)) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat M) N))))))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.one_one_nat))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 M)) (=> (tptp.pp (tptp.aa_nat_bool _let_1 N)) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat M) N))))))) (forall ((M tptp.int) (N tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.one_one_int))) (=> (tptp.pp (tptp.aa_int_bool _let_1 M)) (=> (tptp.pp (tptp.aa_int_bool _let_1 N)) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int M) N))))))) (forall ((A tptp.real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) tptp.one_one_real)))) (forall ((A tptp.rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) tptp.one_one_rat)))) (forall ((A tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) tptp.one_one_nat)))) (forall ((A tptp.int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) tptp.one_one_int)))) (forall ((A tptp.real) (B2 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) tptp.one_one_real)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real B2) tptp.one_one_real))))) (forall ((A tptp.rat) (B2 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B2)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) tptp.one_one_rat)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat B2) tptp.one_one_rat))))) (forall ((A tptp.nat) (B2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) B2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) tptp.one_one_nat)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat B2) tptp.one_one_nat))))) (forall ((A tptp.int) (B2 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B2)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) tptp.one_one_int)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int B2) tptp.one_one_int))))) (forall ((X tptp.num)) (let ((_let_1 (tptp.numera6690914467698888265omplex X))) (= (tptp.aa_complex_complex (tptp.plus_plus_complex tptp.one_one_complex) _let_1) (tptp.aa_complex_complex (tptp.plus_plus_complex _let_1) tptp.one_one_complex)))) (forall ((X tptp.num)) (let ((_let_1 (tptp.aa_num_real tptp.numeral_numeral_real X))) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real tptp.one_one_real) _let_1) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real _let_1) tptp.one_one_real)))) (forall ((X tptp.num)) (let ((_let_1 (tptp.aa_num_rat tptp.numeral_numeral_rat X))) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat tptp.one_one_rat) _let_1) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat _let_1) tptp.one_one_rat)))) (forall ((X tptp.num)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat X))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat tptp.one_one_nat) _let_1) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat _let_1) tptp.one_one_nat)))) (forall ((X tptp.num)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int X))) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int tptp.one_one_int) _let_1) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int _let_1) tptp.one_one_int)))) (= _let_96 tptp.one_one_complex) (= _let_98 tptp.one_one_real) (= _let_95 tptp.one_one_rat) _let_187 (= _let_97 tptp.one_one_int) (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.one_one_real))) (=> (tptp.pp (tptp.aa_real_bool _let_1 A)) (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real A) N)))))) (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.one_one_rat))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 A)) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_nat_rat (tptp.power_power_rat A) N)))))) (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.one_one_nat))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 A)) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A) N)))))) (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.one_one_int))) (=> (tptp.pp (tptp.aa_int_bool _let_1 A)) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_nat_int (tptp.power_power_int A) N)))))) (forall ((X tptp.complex) (Y tptp.complex) (N tptp.nat)) (=> (= (tptp.aa_complex_complex (tptp.times_times_complex X) Y) tptp.one_one_complex) (= (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_nat_complex (tptp.power_power_complex X) N)) (tptp.aa_nat_complex (tptp.power_power_complex Y) N)) tptp.one_one_complex))) (forall ((X tptp.real) (Y tptp.real) (N tptp.nat)) (=> (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real X) Y) tptp.one_one_real) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) N)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Y) N)) tptp.one_one_real))) (forall ((X tptp.rat) (Y tptp.rat) (N tptp.nat)) (=> (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat X) Y) tptp.one_one_rat) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat (tptp.power_power_rat X) N)) (tptp.aa_nat_rat (tptp.power_power_rat Y) N)) tptp.one_one_rat))) (forall ((X tptp.nat) (Y tptp.nat) (N tptp.nat)) (=> (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat X) Y) tptp.one_one_nat) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat X) N)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat Y) N)) tptp.one_one_nat))) (forall ((X tptp.int) (Y tptp.int) (N tptp.nat)) (=> (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int X) Y) tptp.one_one_int) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int (tptp.power_power_int X) N)) (tptp.aa_nat_int (tptp.power_power_int Y) N)) tptp.one_one_int))) (forall ((A tptp.complex) (N tptp.nat)) (let ((_let_1 (tptp.divide1717551699836669952omplex tptp.one_one_complex))) (= (tptp.aa_nat_complex (tptp.power_power_complex (tptp.aa_complex_complex _let_1 A)) N) (tptp.aa_complex_complex _let_1 (tptp.aa_nat_complex (tptp.power_power_complex A) N))))) (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.one_one_real))) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real _let_1 A)) N) (tptp.aa_real_real _let_1 (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real A) N))))) (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (tptp.divide_divide_rat tptp.one_one_rat))) (= (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_rat_rat _let_1 A)) N) (tptp.aa_rat_rat _let_1 (tptp.aa_nat_rat (tptp.power_power_rat A) N))))) _let_187 (forall ((Option tptp.option_nat)) (=> (not (= Option tptp.none_nat)) (= Option (tptp.some_nat (tptp.the_nat Option))))) (forall ((Option tptp.option4927543243414619207at_nat)) (=> (not (= Option tptp.none_P5556105721700978146at_nat)) (= Option (tptp.some_P7363390416028606310at_nat (tptp.the_Pr8591224930841456533at_nat Option))))) (forall ((Option tptp.option_num)) (=> (not (= Option tptp.none_num)) (= Option (tptp.some_num (tptp.the_num Option))))) (forall ((X5 tptp.real)) (exists ((X_12 tptp.real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X5) X_12)))) (forall ((X5 tptp.rat)) (exists ((X_12 tptp.rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X5) X_12)))) (forall ((X5 tptp.real)) (exists ((Y4 tptp.real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y4) X5)))) (forall ((X5 tptp.rat)) (exists ((Y4 tptp.rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Y4) X5)))) (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real A) N))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real) A)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real _let_1) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) _let_1)))))) (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_rat (tptp.power_power_rat A) N))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.one_one_rat) A)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat _let_1) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) _let_1)))))) (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A) N))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.one_one_nat) A)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_1) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) _let_1)))))) (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_int (tptp.power_power_int A) N))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.one_one_int) A)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int _let_1) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) _let_1)))))) (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real))) (=> (tptp.pp (tptp.aa_real_bool _let_1 A)) (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real A) N))))))) (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.one_one_rat))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 A)) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) (tptp.aa_nat_rat (tptp.power_power_rat A) N))))))) (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.one_one_nat))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 A)) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A) N))))))) (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.one_one_int))) (=> (tptp.pp (tptp.aa_int_bool _let_1 A)) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) (tptp.aa_nat_int (tptp.power_power_int A) N))))))) (forall ((X tptp.complex)) (= (tptp.aa_complex_complex (tptp.minus_minus_complex (tptp.aa_complex_complex (tptp.times_times_complex X) X)) tptp.one_one_complex) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_complex_complex (tptp.plus_plus_complex X) tptp.one_one_complex)) (tptp.aa_complex_complex (tptp.minus_minus_complex X) tptp.one_one_complex)))) (forall ((X tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real X) X)) tptp.one_one_real) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) tptp.one_one_real)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real X) tptp.one_one_real)))) (forall ((X tptp.rat)) (= (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat X) X)) tptp.one_one_rat) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat X) tptp.one_one_rat)) (tptp.aa_rat_rat (tptp.minus_minus_rat X) tptp.one_one_rat)))) (forall ((X tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int X) X)) tptp.one_one_int) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int X) tptp.one_one_int)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int X) tptp.one_one_int)))) (forall ((N tptp.nat) (N3 tptp.nat) (A tptp.real)) (let ((_let_1 (tptp.aa_real_fun_nat_real tptp.power_power_real A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N) N3)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real) A)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_nat_real _let_1 N)) (tptp.aa_nat_real _let_1 N3))))))) (forall ((N tptp.nat) (N3 tptp.nat) (A tptp.rat)) (let ((_let_1 (tptp.power_power_rat A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N) N3)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.one_one_rat) A)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_nat_rat _let_1 N)) (tptp.aa_nat_rat _let_1 N3))))))) (forall ((N tptp.nat) (N3 tptp.nat) (A tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N) N3)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.one_one_nat) A)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat _let_1 N)) (tptp.aa_nat_nat _let_1 N3))))))) (forall ((N tptp.nat) (N3 tptp.nat) (A tptp.int)) (let ((_let_1 (tptp.power_power_int A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N) N3)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.one_one_int) A)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_nat_int _let_1 N)) (tptp.aa_nat_int _let_1 N3))))))) (forall ((A tptp.real) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_real_fun_nat_real tptp.power_power_real A))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real) A)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_nat_real _let_1 M)) (tptp.aa_nat_real _let_1 N))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N)))))) (forall ((A tptp.rat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.power_power_rat A))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.one_one_rat) A)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_nat_rat _let_1 M)) (tptp.aa_nat_rat _let_1 N))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N)))))) (forall ((A tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.one_one_nat) A)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat _let_1 M)) (tptp.aa_nat_nat _let_1 N))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N)))))) (forall ((A tptp.int) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.power_power_int A))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.one_one_int) A)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_nat_int _let_1 M)) (tptp.aa_nat_int _let_1 N))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N)))))) (forall ((N tptp.nat) (N3 tptp.nat) (A tptp.real)) (let ((_let_1 (tptp.aa_real_fun_nat_real tptp.power_power_real A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N) N3)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.one_one_real) A)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_nat_real _let_1 N)) (tptp.aa_nat_real _let_1 N3))))))) (forall ((N tptp.nat) (N3 tptp.nat) (A tptp.rat)) (let ((_let_1 (tptp.power_power_rat A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N) N3)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.one_one_rat) A)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat _let_1 N)) (tptp.aa_nat_rat _let_1 N3))))))) (forall ((N tptp.nat) (N3 tptp.nat) (A tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N) N3)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.one_one_nat) A)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat _let_1 N)) (tptp.aa_nat_nat _let_1 N3))))))) (forall ((N tptp.nat) (N3 tptp.nat) (A tptp.int)) (let ((_let_1 (tptp.power_power_int A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N) N3)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.one_one_int) A)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int _let_1 N)) (tptp.aa_nat_int _let_1 N3))))))) (forall ((A tptp.real) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_real_fun_nat_real tptp.power_power_real A))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real) A)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_nat_real _let_1 M)) (tptp.aa_nat_real _let_1 N))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)))))) (forall ((A tptp.rat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.power_power_rat A))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.one_one_rat) A)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat _let_1 M)) (tptp.aa_nat_rat _let_1 N))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)))))) (forall ((A tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.one_one_nat) A)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat _let_1 M)) (tptp.aa_nat_nat _let_1 N))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)))))) (forall ((A tptp.int) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.power_power_int A))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.one_one_int) A)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int _let_1 M)) (tptp.aa_nat_int _let_1 N))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)))))) (= (tptp.aa_nat_rat (tptp.power_power_rat tptp.one_one_rat) _let_33) tptp.one_one_rat) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat tptp.one_one_nat) _let_33) tptp.one_one_nat) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real tptp.one_one_real) _let_33) tptp.one_one_real) (= (tptp.aa_nat_int (tptp.power_power_int tptp.one_one_int) _let_33) tptp.one_one_int) (= (tptp.aa_nat_complex (tptp.power_power_complex tptp.one_one_complex) _let_33) tptp.one_one_complex) _let_186 (forall ((X tptp.complex) (Y tptp.complex) (Z tptp.complex) (W tptp.complex)) (= (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex X) Y)) (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex Z) W)) (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex (tptp.aa_complex_complex (tptp.times_times_complex X) Z)) (tptp.aa_complex_complex (tptp.times_times_complex Y) W)))) (forall ((X tptp.real) (Y tptp.real) (Z tptp.real) (W tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real X) Y)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real Z) W)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real X) Z)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real Y) W)))) (forall ((X tptp.rat) (Y tptp.rat) (Z tptp.rat) (W tptp.rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat (tptp.divide_divide_rat X) Y)) (tptp.aa_rat_rat (tptp.divide_divide_rat Z) W)) (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat X) Z)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat Y) W)))) (forall ((X tptp.complex) (Y tptp.complex) (Z tptp.complex) (W tptp.complex)) (= (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex X) Y)) (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex Z) W)) (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex (tptp.aa_complex_complex (tptp.times_times_complex X) W)) (tptp.aa_complex_complex (tptp.times_times_complex Y) Z)))) (forall ((X tptp.real) (Y tptp.real) (Z tptp.real) (W tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real X) Y)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real Z) W)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real X) W)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real Y) Z)))) (forall ((X tptp.rat) (Y tptp.rat) (Z tptp.rat) (W tptp.rat)) (= (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_rat_rat (tptp.divide_divide_rat X) Y)) (tptp.aa_rat_rat (tptp.divide_divide_rat Z) W)) (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat X) W)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat Y) Z)))) (forall ((A tptp.complex) (B2 tptp.complex) (C tptp.complex)) (let ((_let_1 (tptp.divide1717551699836669952omplex A))) (= (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex (tptp.aa_complex_complex _let_1 B2)) C) (tptp.aa_complex_complex _let_1 (tptp.aa_complex_complex (tptp.times_times_complex C) B2))))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real A))) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real _let_1 B2)) C) (tptp.aa_real_real _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real C) B2))))) (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.divide_divide_rat A))) (= (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_rat_rat _let_1 B2)) C) (tptp.aa_rat_rat _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat C) B2))))) (forall ((A tptp.complex) (B2 tptp.complex) (C tptp.complex)) (= (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex (tptp.aa_complex_complex (tptp.plus_plus_complex A) B2)) C) (tptp.aa_complex_complex (tptp.plus_plus_complex (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex A) C)) (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex B2) C)))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) B2)) C) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real A) C)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real B2) C)))) (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat)) (= (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) B2)) C) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.divide_divide_rat A) C)) (tptp.aa_rat_rat (tptp.divide_divide_rat B2) C)))) (forall ((A tptp.complex) (B2 tptp.complex) (C tptp.complex)) (= (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex (tptp.aa_complex_complex (tptp.minus_minus_complex A) B2)) C) (tptp.aa_complex_complex (tptp.minus_minus_complex (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex A) C)) (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex B2) C)))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A) B2)) C) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real A) C)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real B2) C)))) (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat)) (= (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_rat_rat (tptp.minus_minus_rat A) B2)) C) (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_rat_rat (tptp.divide_divide_rat A) C)) (tptp.aa_rat_rat (tptp.divide_divide_rat B2) C)))) (forall ((B2 tptp.nat) (K tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) B2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.one_one_nat) K)) (exists ((N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat B2))) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat _let_1 N2)) K)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat K) (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N2) tptp.one_one_nat)))))))))) (forall ((B2 tptp.nat) (K tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 B2)) (=> (tptp.pp (tptp.aa_nat_bool _let_1 K)) (exists ((N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat B2))) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat _let_1 N2)) K)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N2) tptp.one_one_nat))))))))))) (forall ((F tptp.fun_Pr2477239776880934807at_nat) (A tptp.product_prod_nat_nat) (B2 tptp.product_prod_nat_nat)) (= (tptp.vEBT_V1502963449132264192at_nat F (tptp.some_P7363390416028606310at_nat A) (tptp.some_P7363390416028606310at_nat B2)) (tptp.some_P7363390416028606310at_nat (tptp.aa_Pro262675715343573244at_nat (tptp.aa_Pro8023792847356852296at_nat F A) B2)))) (forall ((F tptp.fun_num_fun_num_num) (A tptp.num) (B2 tptp.num)) (= (tptp.vEBT_V819420779217536731ft_num F (tptp.some_num A) (tptp.some_num B2)) (tptp.some_num (tptp.aa_num_num (tptp.aa_num_fun_num_num F A) B2)))) (forall ((F tptp.fun_nat_fun_nat_nat) (A tptp.nat) (B2 tptp.nat)) (= (tptp.aa_opt1882420858203594238on_nat (tptp.aa_opt7711074727033721499on_nat (tptp.vEBT_V4262088993061758097ft_nat F) (tptp.some_nat A)) (tptp.some_nat B2)) (tptp.some_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat F A) B2)))) (forall ((Uu tptp.fun_Pr2477239776880934807at_nat) (Uv tptp.option4927543243414619207at_nat)) (= (tptp.vEBT_V1502963449132264192at_nat Uu tptp.none_P5556105721700978146at_nat Uv) tptp.none_P5556105721700978146at_nat)) (forall ((Uu tptp.fun_num_fun_num_num) (Uv tptp.option_num)) (= (tptp.vEBT_V819420779217536731ft_num Uu tptp.none_num Uv) tptp.none_num)) (forall ((Uu tptp.fun_nat_fun_nat_nat) (Uv tptp.option_nat)) (= (tptp.aa_opt1882420858203594238on_nat (tptp.aa_opt7711074727033721499on_nat (tptp.vEBT_V4262088993061758097ft_nat Uu) tptp.none_nat) Uv) tptp.none_nat)) (forall ((Uu tptp.nat) (Uv tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT)) (= (tptp.vEBT_vebt_mint (tptp.vEBT_Node tptp.none_P5556105721700978146at_nat Uu Uv Uw)) tptp.none_nat)) (forall ((Uu tptp.nat) (Uv tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT)) (= (tptp.vEBT_vebt_maxt (tptp.vEBT_Node tptp.none_P5556105721700978146at_nat Uu Uv Uw)) tptp.none_nat)) (forall ((Uw tptp.fun_Pr2477239776880934807at_nat) (V tptp.product_prod_nat_nat)) (= (tptp.vEBT_V1502963449132264192at_nat Uw (tptp.some_P7363390416028606310at_nat V) tptp.none_P5556105721700978146at_nat) tptp.none_P5556105721700978146at_nat)) (forall ((Uw tptp.fun_num_fun_num_num) (V tptp.num)) (= (tptp.vEBT_V819420779217536731ft_num Uw (tptp.some_num V) tptp.none_num) tptp.none_num)) (forall ((Uw tptp.fun_nat_fun_nat_nat) (V tptp.nat)) (= (tptp.aa_opt1882420858203594238on_nat (tptp.aa_opt7711074727033721499on_nat (tptp.vEBT_V4262088993061758097ft_nat Uw) (tptp.some_nat V)) tptp.none_nat) tptp.none_nat)) (forall ((X tptp.fun_Pr2477239776880934807at_nat) (Xa2 tptp.option4927543243414619207at_nat) (Xb2 tptp.option4927543243414619207at_nat) (Y tptp.option4927543243414619207at_nat)) (let ((_let_1 (not (= Y tptp.none_P5556105721700978146at_nat)))) (=> (= (tptp.vEBT_V1502963449132264192at_nat X Xa2 Xb2) Y) (=> (=> (= Xa2 tptp.none_P5556105721700978146at_nat) _let_1) (=> (=> (exists ((V2 tptp.product_prod_nat_nat)) (= Xa2 (tptp.some_P7363390416028606310at_nat V2))) (=> (= Xb2 tptp.none_P5556105721700978146at_nat) _let_1)) (not (forall ((A3 tptp.product_prod_nat_nat)) (=> (= Xa2 (tptp.some_P7363390416028606310at_nat A3)) (forall ((B3 tptp.product_prod_nat_nat)) (=> (= Xb2 (tptp.some_P7363390416028606310at_nat B3)) (not (= Y (tptp.some_P7363390416028606310at_nat (tptp.aa_Pro262675715343573244at_nat (tptp.aa_Pro8023792847356852296at_nat X A3) B3)))))))))))))) (forall ((X tptp.fun_num_fun_num_num) (Xa2 tptp.option_num) (Xb2 tptp.option_num) (Y tptp.option_num)) (let ((_let_1 (not (= Y tptp.none_num)))) (=> (= (tptp.vEBT_V819420779217536731ft_num X Xa2 Xb2) Y) (=> (=> (= Xa2 tptp.none_num) _let_1) (=> (=> (exists ((V2 tptp.num)) (= Xa2 (tptp.some_num V2))) (=> (= Xb2 tptp.none_num) _let_1)) (not (forall ((A3 tptp.num)) (=> (= Xa2 (tptp.some_num A3)) (forall ((B3 tptp.num)) (=> (= Xb2 (tptp.some_num B3)) (not (= Y (tptp.some_num (tptp.aa_num_num (tptp.aa_num_fun_num_num X A3) B3)))))))))))))) (forall ((X tptp.fun_nat_fun_nat_nat) (Xa2 tptp.option_nat) (Xb2 tptp.option_nat) (Y tptp.option_nat)) (let ((_let_1 (not (= Y tptp.none_nat)))) (=> (= (tptp.aa_opt1882420858203594238on_nat (tptp.aa_opt7711074727033721499on_nat (tptp.vEBT_V4262088993061758097ft_nat X) Xa2) Xb2) Y) (=> (=> (= Xa2 tptp.none_nat) _let_1) (=> (=> (exists ((V2 tptp.nat)) (= Xa2 (tptp.some_nat V2))) (=> (= Xb2 tptp.none_nat) _let_1)) (not (forall ((A3 tptp.nat)) (=> (= Xa2 (tptp.some_nat A3)) (forall ((B3 tptp.nat)) (=> (= Xb2 (tptp.some_nat B3)) (not (= Y (tptp.some_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat X A3) B3)))))))))))))) (forall ((Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (N tptp.nat) (Va tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat Va) _let_1))) (let ((_let_3 (tptp.the_nat (tptp.vEBT_vebt_mint Summary)))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Mi) Ma)) Deg TreeList Summary)) N)) (=> (= N (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat tptp.suc Va))) (=> (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Ma) Mi))) (=> (not (= Ma Mi)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat _let_3) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat _let_1) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat _let_1) _let_2)))) (tptp.the_nat (tptp.vEBT_vebt_mint (tptp.nth_VEBT_VEBT TreeList _let_3))))) (tptp.aa_nat_nat tptp.suc _let_2))) (tptp.size_s6755466524823107622T_VEBT TreeList))))))))))) (forall ((B2 tptp.real) (A tptp.real)) (let ((_let_1 (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real B2) A)) _let_1)) A) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real B2) A)) _let_1)))) (forall ((A tptp.real) (B2 tptp.real)) (let ((_let_1 (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) B2)) _let_1)) A) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real B2) A)) _let_1)))) (and (=> _let_185 (= _let_176 (tptp.aa_opt1882420858203594238on_nat (tptp.aa_opt7711074727033721499on_nat tptp.vEBT_VEBT_add (tptp.aa_opt1882420858203594238on_nat _let_171 (tptp.some_nat _let_169))) (tptp.vEBT_vebt_pred _let_177 _let_180)))) (=> (not _let_185) (= _let_176 (tptp.if_option_nat (tptp.aa_option_nat_bool (tptp.aa_opt7943525813896274546t_bool tptp.fequal_option_nat _let_170) tptp.none_nat) (tptp.if_option_nat _let_174 _let_173 tptp.none_nat) _let_172)))) (forall ((TreeList tptp.list_VEBT_VEBT) (N tptp.nat) (Summary tptp.vEBT_VEBT) (M tptp.nat) (Deg tptp.nat) (Mi tptp.nat) (Ma tptp.nat)) (let ((_let_1 (= Mi Ma))) (let ((_let_2 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (tptp.pp (tptp.aa_set8260762808118238015T_bool (tptp.aa_VEB289770264548726718T_bool tptp.member_VEBT_VEBT X4) (tptp.set_VEBT_VEBT2 TreeList))) (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt X4) N)))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt Summary) M)) (=> (= (tptp.size_s6755466524823107622T_VEBT TreeList) (tptp.aa_nat_nat _let_2 M)) (=> (= M (tptp.aa_nat_nat tptp.suc N)) (=> (= Deg (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N) M)) (=> (forall ((I3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I3) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) M))) (= (exists ((X_1 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions (tptp.nth_VEBT_VEBT TreeList I3)) X_1))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions Summary) I3))))) (=> (=> _let_1 (forall ((X4 tptp.vEBT_VEBT)) (=> (tptp.pp (tptp.aa_set8260762808118238015T_bool (tptp.aa_VEB289770264548726718T_bool tptp.member_VEBT_VEBT X4) (tptp.set_VEBT_VEBT2 TreeList))) (not (exists ((X_12 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions X4) X_12))))))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Mi) Ma)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Ma) (tptp.aa_nat_nat _let_2 Deg))) (=> (=> (not _let_1) (forall ((I3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I3) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) M))) (and (=> (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high Ma) N) I3) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions (tptp.nth_VEBT_VEBT TreeList I3)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low Ma) N)))) (forall ((X4 tptp.nat)) (=> (and (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high X4) N) I3) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions (tptp.nth_VEBT_VEBT TreeList I3)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low X4) N)))) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Mi) X4)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X4) Ma))))))))) (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Mi) Ma)) Deg TreeList Summary)) Deg))))))))))))))) (forall ((Deg tptp.nat) (X tptp.nat) (Ma tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Mi tptp.nat) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat Deg) _let_1))) (let ((_let_3 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high X) _let_2))) (let ((_let_4 (tptp.vEBT_vebt_pred Summary _let_3))) (let ((_let_5 (tptp.aa_opt7711074727033721499on_nat tptp.vEBT_VEBT_mul (tptp.some_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat _let_1) _let_2))))) (let ((_let_6 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low X) _let_2))) (let ((_let_7 (tptp.nth_VEBT_VEBT TreeList _let_3))) (let ((_let_8 (tptp.vEBT_vebt_mint _let_7))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat _let_1) Deg)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X) Ma)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_3) (tptp.size_s6755466524823107622T_VEBT TreeList))) (= (tptp.vEBT_vebt_pred (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Mi) Ma)) Deg TreeList Summary) X) (tptp.if_option_nat (tptp.aa_bool_bool (tptp.fconj (tptp.aa_bool_bool tptp.fNot (tptp.aa_option_nat_bool (tptp.aa_opt7943525813896274546t_bool tptp.fequal_option_nat _let_8) tptp.none_nat))) (tptp.aa_option_nat_bool (tptp.aa_opt7943525813896274546t_bool tptp.vEBT_VEBT_greater (tptp.some_nat _let_6)) _let_8)) (tptp.aa_opt1882420858203594238on_nat (tptp.aa_opt7711074727033721499on_nat tptp.vEBT_VEBT_add (tptp.aa_opt1882420858203594238on_nat _let_5 (tptp.some_nat _let_3))) (tptp.vEBT_vebt_pred _let_7 _let_6)) (tptp.if_option_nat (tptp.aa_option_nat_bool (tptp.aa_opt7943525813896274546t_bool tptp.fequal_option_nat _let_4) tptp.none_nat) (tptp.if_option_nat (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Mi) X) (tptp.some_nat Mi) tptp.none_nat) (tptp.aa_opt1882420858203594238on_nat (tptp.aa_opt7711074727033721499on_nat tptp.vEBT_VEBT_add (tptp.aa_opt1882420858203594238on_nat _let_5 _let_4)) (tptp.vEBT_vebt_maxt (tptp.nth_VEBT_VEBT TreeList (tptp.the_nat _let_4))))))))))))))))))) (forall ((Deg tptp.nat) (X tptp.nat) (Ma tptp.nat) (Mi tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat Deg) _let_1))) (let ((_let_3 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high X) _let_2))) (let ((_let_4 (tptp.vEBT_vebt_pred Summary _let_3))) (let ((_let_5 (tptp.aa_opt7711074727033721499on_nat tptp.vEBT_VEBT_mul (tptp.some_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat _let_1) _let_2))))) (let ((_let_6 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low X) _let_2))) (let ((_let_7 (tptp.nth_VEBT_VEBT TreeList _let_3))) (let ((_let_8 (tptp.vEBT_vebt_mint _let_7))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat _let_1) Deg)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X) Ma)) (= (tptp.vEBT_vebt_pred (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Mi) Ma)) Deg TreeList Summary) X) (tptp.if_option_nat (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_3) (tptp.size_s6755466524823107622T_VEBT TreeList)) (tptp.if_option_nat (tptp.aa_bool_bool (tptp.fconj (tptp.aa_bool_bool tptp.fNot (tptp.aa_option_nat_bool (tptp.aa_opt7943525813896274546t_bool tptp.fequal_option_nat _let_8) tptp.none_nat))) (tptp.aa_option_nat_bool (tptp.aa_opt7943525813896274546t_bool tptp.vEBT_VEBT_greater (tptp.some_nat _let_6)) _let_8)) (tptp.aa_opt1882420858203594238on_nat (tptp.aa_opt7711074727033721499on_nat tptp.vEBT_VEBT_add (tptp.aa_opt1882420858203594238on_nat _let_5 (tptp.some_nat _let_3))) (tptp.vEBT_vebt_pred _let_7 _let_6)) (tptp.if_option_nat (tptp.aa_option_nat_bool (tptp.aa_opt7943525813896274546t_bool tptp.fequal_option_nat _let_4) tptp.none_nat) (tptp.if_option_nat (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Mi) X) (tptp.some_nat Mi) tptp.none_nat) (tptp.aa_opt1882420858203594238on_nat (tptp.aa_opt7711074727033721499on_nat tptp.vEBT_VEBT_add (tptp.aa_opt1882420858203594238on_nat _let_5 _let_4)) (tptp.vEBT_vebt_maxt (tptp.nth_VEBT_VEBT TreeList (tptp.the_nat _let_4)))))) tptp.none_nat))))))))))))) (forall ((L tptp.num) (R tptp.nat) (Q2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) Q2))) (let ((_let_2 (tptp.unique5026877609467782581ep_nat L (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Q2) R)))) (let ((_let_3 (tptp.aa_num_nat tptp.numeral_numeral_nat L))) (let ((_let_4 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat _let_3) R)))) (and (=> _let_4 (= _let_2 (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat _let_1) tptp.one_one_nat)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat R) _let_3)))) (=> (not _let_4) (= _let_2 (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat _let_1) R))))))))) (forall ((L tptp.num) (R tptp.int) (Q2 tptp.int)) (let ((_let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) Q2))) (let ((_let_2 (tptp.aa_Pro6970504127699319548nt_int (tptp.unique5024387138958732305ep_int L) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int Q2) R)))) (let ((_let_3 (tptp.aa_num_int tptp.numeral_numeral_int L))) (let ((_let_4 (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int _let_3) R)))) (and (=> _let_4 (= _let_2 (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int _let_1) tptp.one_one_int)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int R) _let_3)))) (=> (not _let_4) (= _let_2 (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int _let_1) R))))))))) (forall ((L tptp.num) (R tptp.code_integer) (Q2 tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))) Q2))) (let ((_let_2 (tptp.unique4921790084139445826nteger L (tptp.produc1086072967326762835nteger Q2 R)))) (let ((_let_3 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger L))) (let ((_let_4 (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger _let_3) R)))) (and (=> _let_4 (= _let_2 (tptp.produc1086072967326762835nteger (tptp.plus_p5714425477246183910nteger _let_1 tptp.one_one_Code_integer) (tptp.minus_8373710615458151222nteger R _let_3)))) (=> (not _let_4) (= _let_2 (tptp.produc1086072967326762835nteger _let_1 R))))))))) (forall ((T tptp.vEBT_VEBT) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt T) N)) (=> (= (tptp.vEBT_vebt_maxt T) tptp.none_nat) (= (tptp.vEBT_VEBT_set_vebt T) tptp.bot_bot_set_nat)))) (forall ((T tptp.vEBT_VEBT) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt T) N)) (=> (= (tptp.vEBT_vebt_mint T) tptp.none_nat) (= (tptp.vEBT_VEBT_set_vebt T) tptp.bot_bot_set_nat)))) (forall ((Xs tptp.list_int) (P tptp.fun_int_bool)) (= (forall ((X3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X3) (tptp.set_int2 Xs))) (tptp.pp (tptp.aa_int_bool P X3)))) (forall ((I4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I4) (tptp.size_size_list_int Xs))) (tptp.pp (tptp.aa_int_bool P (tptp.aa_nat_int (tptp.nth_int Xs) I4))))))) (forall ((Xs tptp.list_VEBT_VEBT) (P tptp.fun_VEBT_VEBT_bool)) (= (forall ((X3 tptp.vEBT_VEBT)) (=> (tptp.pp (tptp.aa_set8260762808118238015T_bool (tptp.aa_VEB289770264548726718T_bool tptp.member_VEBT_VEBT X3) (tptp.set_VEBT_VEBT2 Xs))) (tptp.pp (tptp.aa_VEBT_VEBT_bool P X3)))) (forall ((I4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I4) (tptp.size_s6755466524823107622T_VEBT Xs))) (tptp.pp (tptp.aa_VEBT_VEBT_bool P (tptp.nth_VEBT_VEBT Xs I4))))))) (forall ((Xs tptp.list_bool) (P tptp.fun_bool_bool)) (= (forall ((X3 tptp.bool)) (=> (tptp.member_bool X3 (tptp.set_bool2 Xs)) (tptp.pp (tptp.aa_bool_bool P X3)))) (forall ((I4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I4) (tptp.size_size_list_bool Xs))) (tptp.pp (tptp.aa_bool_bool P (tptp.aa_nat_bool (tptp.nth_bool Xs) I4))))))) (forall ((Xs tptp.list_nat) (P tptp.fun_nat_bool)) (= (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) (tptp.set_nat2 Xs))) (tptp.pp (tptp.aa_nat_bool P X3)))) (forall ((I4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I4) (tptp.size_size_list_nat Xs))) (tptp.pp (tptp.aa_nat_bool P (tptp.aa_nat_nat (tptp.nth_nat Xs) I4))))))) (forall ((X tptp.nat)) (=> (forall ((N2 tptp.nat)) (not (= X (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N2) N2)))) (not (forall ((N2 tptp.nat)) (not (= X (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N2) (tptp.aa_nat_nat tptp.suc N2)))))))) (forall ((T tptp.vEBT_VEBT)) (= (tptp.vEBT_VEBT_set_vebt T) (tptp.collect_nat (tptp.vEBT_vebt_member T)))) (forall ((Tree tptp.vEBT_VEBT) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt Tree) (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat tptp.suc N)))) (exists ((Info2 tptp.option4927543243414619207at_nat) (TreeList2 tptp.list_VEBT_VEBT) (S3 tptp.vEBT_VEBT)) (= Tree (tptp.vEBT_Node Info2 (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat tptp.suc N)) TreeList2 S3))))) (forall ((V tptp.num) (W tptp.num)) (= (tptp.aa_int_int (tptp.divide_divide_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 V))) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 W))) (tptp.aa_int_int (tptp.divide_divide_int (tptp.aa_num_int tptp.numeral_numeral_int V)) (tptp.aa_num_int tptp.numeral_numeral_int W)))) (forall ((Nat tptp.nat) (Nat2 tptp.nat)) (= (= (tptp.aa_nat_nat tptp.suc Nat) (tptp.aa_nat_nat tptp.suc Nat2)) (= Nat Nat2))) (forall ((X2 tptp.nat) (Y2 tptp.nat)) (= (= (tptp.aa_nat_nat tptp.suc X2) (tptp.aa_nat_nat tptp.suc Y2)) (= X2 Y2))) (forall ((N tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N) (tptp.aa_nat_nat tptp.suc N)))) (forall ((M tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat tptp.suc M)) (tptp.aa_nat_nat tptp.suc N))))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat tptp.suc M)) (tptp.aa_nat_nat tptp.suc N))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N)))) (forall ((N tptp.nat) (M tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat tptp.suc N)) (tptp.aa_nat_nat tptp.suc M))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N) M)))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M))) (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat tptp.suc N)) (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat _let_1 N))))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat tptp.suc M)) (tptp.aa_nat_nat tptp.suc N)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) N))) (forall ((M tptp.nat) (N tptp.nat) (K tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat tptp.suc M)) N)) (tptp.aa_nat_nat tptp.suc K)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) N)) K))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat M))) (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat tptp.suc N)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) (tptp.aa_nat_nat _let_1 N))))) (forall ((N tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat tptp.suc N)) tptp.one_one_nat) N)) (forall ((K tptp.nat) (J tptp.nat) (I tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) J)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat J) K))) I) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat tptp.suc J)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat K) I))))) (forall ((K tptp.nat) (J tptp.nat) (I tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) J)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat I) (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat J) K))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat I) K)) (tptp.aa_nat_nat tptp.suc J))))) (forall ((N tptp.num)) (= (tptp.aa_nat_nat tptp.suc (tptp.aa_num_nat tptp.numeral_numeral_nat N)) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num N) tptp.one)))) (forall ((N tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat tptp.suc N)))) (forall ((N tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N) (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat tptp.suc N)))) (forall ((M tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat tptp.suc M))) _let_1) (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat M) _let_1))))) (= (tptp.aa_nat_nat tptp.suc tptp.one_one_nat) _let_33) (forall ((C tptp.real)) (= (tptp.aa_rea7340605660300375871l_real tptp.aTP_Lamm_ae C) (tptp.aa_rea7340605660300375871l_real tptp.times_times_real C))) (forall ((C tptp.rat)) (= (tptp.aTP_Lamm_af C) (tptp.aa_rat_fun_rat_rat tptp.times_times_rat C))) (forall ((C tptp.nat)) (= (tptp.aa_nat_fun_nat_nat tptp.aTP_Lamm_ag C) (tptp.aa_nat_fun_nat_nat tptp.times_times_nat C))) (forall ((C tptp.int)) (= (tptp.aTP_Lamm_ah C) (tptp.aa_int_fun_int_int tptp.times_times_int C))) (forall ((N tptp.nat)) (not (= N (tptp.aa_nat_nat tptp.suc N)))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (= (tptp.aa_nat_nat tptp.suc X) (tptp.aa_nat_nat tptp.suc Y)) (= X Y))) (= tptp.aTP_Lamm_ai (tptp.times_times_complex tptp.one_one_complex)) (= tptp.aTP_Lamm_aj (tptp.aa_rea7340605660300375871l_real tptp.times_times_real tptp.one_one_real)) (= tptp.aTP_Lamm_ak (tptp.aa_rat_fun_rat_rat tptp.times_times_rat tptp.one_one_rat)) (= tptp.aTP_Lamm_al (tptp.aa_nat_fun_nat_nat tptp.times_times_nat tptp.one_one_nat)) (= tptp.aTP_Lamm_am (tptp.aa_int_fun_int_int tptp.times_times_int tptp.one_one_int)) (forall ((X tptp.produc7004362771917097900on_nat)) (=> (forall ((Uu2 tptp.fun_nat_fun_nat_nat) (Uv2 tptp.option_nat)) (not (= X (tptp.produc6699827698519632094on_nat Uu2 (tptp.produc5098337634421038937on_nat tptp.none_nat Uv2))))) (=> (forall ((Uw2 tptp.fun_nat_fun_nat_nat) (V2 tptp.nat)) (not (= X (tptp.produc6699827698519632094on_nat Uw2 (tptp.produc5098337634421038937on_nat (tptp.some_nat V2) tptp.none_nat))))) (not (forall ((F2 tptp.fun_nat_fun_nat_nat) (A3 tptp.nat) (B3 tptp.nat)) (not (= X (tptp.produc6699827698519632094on_nat F2 (tptp.produc5098337634421038937on_nat (tptp.some_nat A3) (tptp.some_nat B3)))))))))) (forall ((X tptp.produc1260151622200656695at_nat)) (=> (forall ((Uu2 tptp.fun_Pr2477239776880934807at_nat) (Uv2 tptp.option4927543243414619207at_nat)) (not (= X (tptp.produc7814092408141220007at_nat Uu2 (tptp.produc488173922507101015at_nat tptp.none_P5556105721700978146at_nat Uv2))))) (=> (forall ((Uw2 tptp.fun_Pr2477239776880934807at_nat) (V2 tptp.product_prod_nat_nat)) (not (= X (tptp.produc7814092408141220007at_nat Uw2 (tptp.produc488173922507101015at_nat (tptp.some_P7363390416028606310at_nat V2) tptp.none_P5556105721700978146at_nat))))) (not (forall ((F2 tptp.fun_Pr2477239776880934807at_nat) (A3 tptp.product_prod_nat_nat) (B3 tptp.product_prod_nat_nat)) (not (= X (tptp.produc7814092408141220007at_nat F2 (tptp.produc488173922507101015at_nat (tptp.some_P7363390416028606310at_nat A3) (tptp.some_P7363390416028606310at_nat B3)))))))))) (forall ((X tptp.produc2703417854250991842on_num)) (=> (forall ((Uu2 tptp.fun_num_fun_num_num) (Uv2 tptp.option_num)) (not (= X (tptp.produc6360833703471310868on_num Uu2 (tptp.produc8585076106096196333on_num tptp.none_num Uv2))))) (=> (forall ((Uw2 tptp.fun_num_fun_num_num) (V2 tptp.num)) (not (= X (tptp.produc6360833703471310868on_num Uw2 (tptp.produc8585076106096196333on_num (tptp.some_num V2) tptp.none_num))))) (not (forall ((F2 tptp.fun_num_fun_num_num) (A3 tptp.num) (B3 tptp.num)) (not (= X (tptp.produc6360833703471310868on_num F2 (tptp.produc8585076106096196333on_num (tptp.some_num A3) (tptp.some_num B3)))))))))) (forall ((X tptp.produc3700678068921409119on_nat)) (=> (forall ((Uu2 tptp.fun_nat_fun_nat_bool) (Uv2 tptp.option_nat)) (not (= X (tptp.produc2004789812759622991on_nat Uu2 (tptp.produc5098337634421038937on_nat tptp.none_nat Uv2))))) (=> (forall ((Uw2 tptp.fun_nat_fun_nat_bool) (V2 tptp.nat)) (not (= X (tptp.produc2004789812759622991on_nat Uw2 (tptp.produc5098337634421038937on_nat (tptp.some_nat V2) tptp.none_nat))))) (not (forall ((F2 tptp.fun_nat_fun_nat_bool) (X4 tptp.nat) (Y4 tptp.nat)) (not (= X (tptp.produc2004789812759622991on_nat F2 (tptp.produc5098337634421038937on_nat (tptp.some_nat X4) (tptp.some_nat Y4)))))))))) (forall ((X tptp.produc533602882674032673at_nat)) (=> (forall ((Uu2 tptp.fun_Pr248683899324676269t_bool) (Uv2 tptp.option4927543243414619207at_nat)) (not (= X (tptp.produc5961576194287291153at_nat Uu2 (tptp.produc488173922507101015at_nat tptp.none_P5556105721700978146at_nat Uv2))))) (=> (forall ((Uw2 tptp.fun_Pr248683899324676269t_bool) (V2 tptp.product_prod_nat_nat)) (not (= X (tptp.produc5961576194287291153at_nat Uw2 (tptp.produc488173922507101015at_nat (tptp.some_P7363390416028606310at_nat V2) tptp.none_P5556105721700978146at_nat))))) (not (forall ((F2 tptp.fun_Pr248683899324676269t_bool) (X4 tptp.product_prod_nat_nat) (Y4 tptp.product_prod_nat_nat)) (not (= X (tptp.produc5961576194287291153at_nat F2 (tptp.produc488173922507101015at_nat (tptp.some_P7363390416028606310at_nat X4) (tptp.some_P7363390416028606310at_nat Y4)))))))))) (forall ((X tptp.produc6167219322466932359on_num)) (=> (forall ((Uu2 tptp.fun_num_fun_num_bool) (Uv2 tptp.option_num)) (not (= X (tptp.produc8433281988922931063on_num Uu2 (tptp.produc8585076106096196333on_num tptp.none_num Uv2))))) (=> (forall ((Uw2 tptp.fun_num_fun_num_bool) (V2 tptp.num)) (not (= X (tptp.produc8433281988922931063on_num Uw2 (tptp.produc8585076106096196333on_num (tptp.some_num V2) tptp.none_num))))) (not (forall ((F2 tptp.fun_num_fun_num_bool) (X4 tptp.num) (Y4 tptp.num)) (not (= X (tptp.produc8433281988922931063on_num F2 (tptp.produc8585076106096196333on_num (tptp.some_num X4) (tptp.some_num Y4)))))))))) (forall ((I tptp.nat) (K tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I) K)) (=> (not (= K (tptp.aa_nat_nat tptp.suc I))) (not (forall ((J2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I) J2)) (not (= K (tptp.aa_nat_nat tptp.suc J2))))))))) (forall ((M tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat tptp.suc M)) N)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N)))) (forall ((I tptp.nat) (K tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat tptp.suc I)) K)) (not (forall ((J2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I) J2)) (not (= K (tptp.aa_nat_nat tptp.suc J2)))))))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc M))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N)) (=> (not (= _let_1 N)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_1) N)))))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat tptp.suc N))) (=> (not (tptp.pp (tptp.aa_nat_bool _let_1 N))) (= M N))))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 N)) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat tptp.suc N)))))) (forall ((N tptp.nat) (P tptp.fun_nat_bool)) (= (exists ((I4 tptp.nat)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I4) (tptp.aa_nat_nat tptp.suc N))) (tptp.pp (tptp.aa_nat_bool P I4)))) (or (tptp.pp (tptp.aa_nat_bool P N)) (exists ((I4 tptp.nat)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I4) N)) (tptp.pp (tptp.aa_nat_bool P I4))))))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M))) (= (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat tptp.suc N))) (or (tptp.pp (tptp.aa_nat_bool _let_1 N)) (= M N))))) (forall ((M tptp.nat) (N tptp.nat)) (= (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N) (tptp.aa_nat_nat tptp.suc M))))) (forall ((N tptp.nat) (P tptp.fun_nat_bool)) (= (forall ((I4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I4) (tptp.aa_nat_nat tptp.suc N))) (tptp.pp (tptp.aa_nat_bool P I4)))) (and (tptp.pp (tptp.aa_nat_bool P N)) (forall ((I4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I4) N)) (tptp.pp (tptp.aa_nat_bool P I4))))))) (forall ((N tptp.nat) (M tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat tptp.suc N)) M)) (exists ((M4 tptp.nat)) (and (= M (tptp.aa_nat_nat tptp.suc M4)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N) M4)))))) (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N))) (=> (not (tptp.pp (tptp.aa_nat_bool _let_1 M))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat tptp.suc M))) (= M N))))) (forall ((M tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat tptp.suc M)) (tptp.aa_nat_nat tptp.suc N))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N)))) (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I) J)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat J) K)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat tptp.suc I)) K))))) (forall ((I tptp.nat) (J tptp.nat) (P tptp.fun_nat_fun_nat_bool)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I) J)) (=> (forall ((I3 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool P I3) (tptp.aa_nat_nat tptp.suc I3)))) (=> (forall ((I3 tptp.nat) (J2 tptp.nat) (K3 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool P I3))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I3) J2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat J2) K3)) (=> (tptp.pp (tptp.aa_nat_bool _let_1 J2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool P J2) K3)) (tptp.pp (tptp.aa_nat_bool _let_1 K3)))))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool P I) J)))))) (forall ((I tptp.nat) (J tptp.nat) (P tptp.fun_nat_bool)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I) J)) (=> (forall ((I3 tptp.nat)) (=> (= J (tptp.aa_nat_nat tptp.suc I3)) (tptp.pp (tptp.aa_nat_bool P I3)))) (=> (forall ((I3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I3) J)) (=> (tptp.pp (tptp.aa_nat_bool P (tptp.aa_nat_nat tptp.suc I3))) (tptp.pp (tptp.aa_nat_bool P I3))))) (tptp.pp (tptp.aa_nat_bool P I)))))) (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N))) (=> (not (tptp.pp (tptp.aa_nat_bool _let_1 M))) (= (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat tptp.suc M))) (= N M))))) (forall ((M tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat tptp.suc M)) N)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N))) (let ((_let_2 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M))) (=> (tptp.pp (tptp.aa_nat_bool _let_2 _let_1)) (=> (not (tptp.pp (tptp.aa_nat_bool _let_2 N))) (= M _let_1)))))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 N)) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat tptp.suc N)))))) (forall ((N tptp.nat) (M5 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat tptp.suc N)) M5)) (exists ((M3 tptp.nat)) (= M5 (tptp.aa_nat_nat tptp.suc M3))))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N))) (let ((_let_2 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M))) (= (tptp.pp (tptp.aa_nat_bool _let_2 _let_1)) (or (tptp.pp (tptp.aa_nat_bool _let_2 N)) (= M _let_1)))))) (forall ((N tptp.nat)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat tptp.suc N)) N)))) (forall ((M tptp.nat) (N tptp.nat)) (= (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat tptp.suc N)) M)))) (forall ((P tptp.fun_nat_bool) (N tptp.nat)) (=> (forall ((N2 tptp.nat)) (=> (forall ((M2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat tptp.suc M2)) N2)) (tptp.pp (tptp.aa_nat_bool P M2)))) (tptp.pp (tptp.aa_nat_bool P N2)))) (tptp.pp (tptp.aa_nat_bool P N)))) (forall ((M tptp.nat) (N tptp.nat) (P tptp.fun_nat_bool)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)) (=> (tptp.pp (tptp.aa_nat_bool P M)) (=> (forall ((N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (=> (tptp.pp (tptp.aa_nat_bool P N2)) (tptp.pp (tptp.aa_nat_bool P (tptp.aa_nat_nat tptp.suc N2)))))) (tptp.pp (tptp.aa_nat_bool P N)))))) (forall ((M tptp.nat) (N tptp.nat) (R2 tptp.fun_nat_fun_nat_bool)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)) (=> (forall ((X4 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool R2 X4) X4))) (=> (forall ((X4 tptp.nat) (Y4 tptp.nat) (Z4 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool R2 X4))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 Y4)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool R2 Y4) Z4)) (tptp.pp (tptp.aa_nat_bool _let_1 Z4)))))) (=> (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool R2 N2) (tptp.aa_nat_nat tptp.suc N2)))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool R2 M) N))))))) (forall ((A4 tptp.nat) (K tptp.nat) (A tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat K))) (=> (= A4 (tptp.aa_nat_nat _let_1 A)) (= (tptp.aa_nat_nat tptp.suc A4) (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat tptp.suc A)))))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat tptp.suc M)) N) (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) N)))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat tptp.suc M)) N) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) (tptp.aa_nat_nat tptp.suc N)))) (forall ((P tptp.fun_nat_bool) (K tptp.nat) (I tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool P K)) (=> (forall ((N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool P (tptp.aa_nat_nat tptp.suc N2))) (tptp.pp (tptp.aa_nat_bool P N2)))) (tptp.pp (tptp.aa_nat_bool P (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat K) I)))))) (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat tptp.suc K)))) (= (= (tptp.aa_nat_nat _let_1 M) (tptp.aa_nat_nat _let_1 N)) (= M N)))) (forall ((N tptp.num)) (let ((_let_1 (tptp.numera6690914467698888265omplex N))) (= (tptp.numera6690914467698888265omplex (tptp.aa_num_num tptp.bit0 N)) (tptp.aa_complex_complex (tptp.plus_plus_complex _let_1) _let_1)))) (forall ((N tptp.num)) (let ((_let_1 (tptp.aa_num_real tptp.numeral_numeral_real N))) (= (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 N)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real _let_1) _let_1)))) (forall ((N tptp.num)) (let ((_let_1 (tptp.aa_num_rat tptp.numeral_numeral_rat N))) (= (tptp.aa_num_rat tptp.numeral_numeral_rat (tptp.aa_num_num tptp.bit0 N)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat _let_1) _let_1)))) (forall ((N tptp.num)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat N))) (= (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 N)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat _let_1) _let_1)))) (forall ((N tptp.num)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int N))) (= (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 N)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int _let_1) _let_1)))) (forall ((T tptp.vEBT_VEBT)) (= (tptp.vEBT_set_vebt T) (tptp.collect_nat (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions T)))) (forall ((X tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real) X)) (exists ((N2 tptp.nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) N2)))))) (forall ((Z tptp.complex) (W tptp.num)) (let ((_let_1 (tptp.power_power_complex Z))) (let ((_let_2 (tptp.aa_nat_complex _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat W)))) (= (tptp.aa_nat_complex _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 W))) (tptp.aa_complex_complex (tptp.times_times_complex _let_2) _let_2))))) (forall ((Z tptp.real) (W tptp.num)) (let ((_let_1 (tptp.aa_real_fun_nat_real tptp.power_power_real Z))) (let ((_let_2 (tptp.aa_nat_real _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat W)))) (= (tptp.aa_nat_real _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 W))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real _let_2) _let_2))))) (forall ((Z tptp.rat) (W tptp.num)) (let ((_let_1 (tptp.power_power_rat Z))) (let ((_let_2 (tptp.aa_nat_rat _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat W)))) (= (tptp.aa_nat_rat _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 W))) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat _let_2) _let_2))))) (forall ((Z tptp.nat) (W tptp.num)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat Z))) (let ((_let_2 (tptp.aa_nat_nat _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat W)))) (= (tptp.aa_nat_nat _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 W))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat _let_2) _let_2))))) (forall ((Z tptp.int) (W tptp.num)) (let ((_let_1 (tptp.power_power_int Z))) (let ((_let_2 (tptp.aa_nat_int _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat W)))) (= (tptp.aa_nat_int _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 W))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int _let_2) _let_2))))) (forall ((Xs tptp.list_complex)) (= (tptp.set_complex2 Xs) (tptp.collect_complex (tptp.aTP_Lamm_an Xs)))) (forall ((Xs tptp.list_real)) (= (tptp.set_real2 Xs) (tptp.collect_real (tptp.aTP_Lamm_ao Xs)))) (forall ((Xs tptp.list_list_nat)) (= (tptp.set_list_nat2 Xs) (tptp.collect_list_nat (tptp.aTP_Lamm_ap Xs)))) (forall ((Xs tptp.list_int)) (= (tptp.set_int2 Xs) (tptp.collect_int (tptp.aTP_Lamm_aq Xs)))) (forall ((Xs tptp.list_VEBT_VEBT)) (= (tptp.set_VEBT_VEBT2 Xs) (tptp.collect_VEBT_VEBT (tptp.aTP_Lamm_ar Xs)))) (forall ((Xs tptp.list_bool)) (= (tptp.set_bool2 Xs) (tptp.collect_bool (tptp.aTP_Lamm_as Xs)))) (forall ((Xs tptp.list_nat)) (= (tptp.set_nat2 Xs) (tptp.collect_nat (tptp.aTP_Lamm_at Xs)))) (forall ((F tptp.fun_nat_real) (N tptp.nat) (N4 tptp.nat)) (=> (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_nat_real F N2)) (tptp.aa_nat_real F (tptp.aa_nat_nat tptp.suc N2))))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N) N4)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_nat_real F N)) (tptp.aa_nat_real F N4)))))) (forall ((F tptp.fun_nat_rat) (N tptp.nat) (N4 tptp.nat)) (=> (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_nat_rat F N2)) (tptp.aa_nat_rat F (tptp.aa_nat_nat tptp.suc N2))))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N) N4)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_nat_rat F N)) (tptp.aa_nat_rat F N4)))))) (forall ((F tptp.fun_nat_num) (N tptp.nat) (N4 tptp.nat)) (=> (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num (tptp.aa_nat_num F N2)) (tptp.aa_nat_num F (tptp.aa_nat_nat tptp.suc N2))))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N) N4)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num (tptp.aa_nat_num F N)) (tptp.aa_nat_num F N4)))))) (forall ((F tptp.fun_nat_nat) (N tptp.nat) (N4 tptp.nat)) (=> (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat F N2)) (tptp.aa_nat_nat F (tptp.aa_nat_nat tptp.suc N2))))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N) N4)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat F N)) (tptp.aa_nat_nat F N4)))))) (forall ((F tptp.fun_nat_int) (N tptp.nat) (N4 tptp.nat)) (=> (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_nat_int F N2)) (tptp.aa_nat_int F (tptp.aa_nat_nat tptp.suc N2))))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N) N4)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_nat_int F N)) (tptp.aa_nat_int F N4)))))) (forall ((F tptp.fun_nat_real) (N tptp.nat) (M tptp.nat)) (=> (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_nat_real F N2)) (tptp.aa_nat_real F (tptp.aa_nat_nat tptp.suc N2))))) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_nat_real F N)) (tptp.aa_nat_real F M))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N) M))))) (forall ((F tptp.fun_nat_rat) (N tptp.nat) (M tptp.nat)) (=> (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_nat_rat F N2)) (tptp.aa_nat_rat F (tptp.aa_nat_nat tptp.suc N2))))) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_nat_rat F N)) (tptp.aa_nat_rat F M))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N) M))))) (forall ((F tptp.fun_nat_num) (N tptp.nat) (M tptp.nat)) (=> (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num (tptp.aa_nat_num F N2)) (tptp.aa_nat_num F (tptp.aa_nat_nat tptp.suc N2))))) (= (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num (tptp.aa_nat_num F N)) (tptp.aa_nat_num F M))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N) M))))) (forall ((F tptp.fun_nat_nat) (N tptp.nat) (M tptp.nat)) (=> (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat F N2)) (tptp.aa_nat_nat F (tptp.aa_nat_nat tptp.suc N2))))) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat F N)) (tptp.aa_nat_nat F M))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N) M))))) (forall ((F tptp.fun_nat_int) (N tptp.nat) (M tptp.nat)) (=> (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_nat_int F N2)) (tptp.aa_nat_int F (tptp.aa_nat_nat tptp.suc N2))))) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_nat_int F N)) (tptp.aa_nat_int F M))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N) M))))) (forall ((A tptp.complex) (N tptp.nat)) (let ((_let_1 (tptp.power_power_complex A))) (= (tptp.aa_nat_complex _let_1 (tptp.aa_nat_nat tptp.suc N)) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_nat_complex _let_1 N)) A)))) (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (tptp.aa_real_fun_nat_real tptp.power_power_real A))) (= (tptp.aa_nat_real _let_1 (tptp.aa_nat_nat tptp.suc N)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real _let_1 N)) A)))) (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (tptp.power_power_rat A))) (= (tptp.aa_nat_rat _let_1 (tptp.aa_nat_nat tptp.suc N)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat _let_1 N)) A)))) (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A))) (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat tptp.suc N)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat _let_1 N)) A)))) (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (tptp.power_power_int A))) (= (tptp.aa_nat_int _let_1 (tptp.aa_nat_nat tptp.suc N)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int _let_1 N)) A)))) (forall ((A tptp.complex) (N tptp.nat)) (let ((_let_1 (tptp.power_power_complex A))) (= (tptp.aa_nat_complex _let_1 (tptp.aa_nat_nat tptp.suc N)) (tptp.aa_complex_complex (tptp.times_times_complex A) (tptp.aa_nat_complex _let_1 N))))) (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (tptp.aa_real_fun_nat_real tptp.power_power_real A))) (= (tptp.aa_nat_real _let_1 (tptp.aa_nat_nat tptp.suc N)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) (tptp.aa_nat_real _let_1 N))))) (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (tptp.power_power_rat A))) (= (tptp.aa_nat_rat _let_1 (tptp.aa_nat_nat tptp.suc N)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) (tptp.aa_nat_rat _let_1 N))))) (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A))) (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat tptp.suc N)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) (tptp.aa_nat_nat _let_1 N))))) (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (tptp.power_power_int A))) (= (tptp.aa_nat_int _let_1 (tptp.aa_nat_nat tptp.suc N)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) (tptp.aa_nat_int _let_1 N))))) (forall ((F tptp.fun_nat_set_int) (N tptp.nat) (N4 tptp.nat)) (=> (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int (tptp.aa_nat_set_int F N2)) (tptp.aa_nat_set_int F (tptp.aa_nat_nat tptp.suc N2))))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N) N4)) (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int (tptp.aa_nat_set_int F N)) (tptp.aa_nat_set_int F N4)))))) (forall ((F tptp.fun_nat_rat) (N tptp.nat) (N4 tptp.nat)) (=> (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat F N2)) (tptp.aa_nat_rat F (tptp.aa_nat_nat tptp.suc N2))))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N) N4)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat F N)) (tptp.aa_nat_rat F N4)))))) (forall ((F tptp.fun_nat_num) (N tptp.nat) (N4 tptp.nat)) (=> (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_nat_num F N2)) (tptp.aa_nat_num F (tptp.aa_nat_nat tptp.suc N2))))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N) N4)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_nat_num F N)) (tptp.aa_nat_num F N4)))))) (forall ((F tptp.fun_nat_nat) (N tptp.nat) (N4 tptp.nat)) (=> (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat F N2)) (tptp.aa_nat_nat F (tptp.aa_nat_nat tptp.suc N2))))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N) N4)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat F N)) (tptp.aa_nat_nat F N4)))))) (forall ((F tptp.fun_nat_int) (N tptp.nat) (N4 tptp.nat)) (=> (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int F N2)) (tptp.aa_nat_int F (tptp.aa_nat_nat tptp.suc N2))))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N) N4)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int F N)) (tptp.aa_nat_int F N4)))))) (forall ((F tptp.fun_nat_set_int) (N tptp.nat) (N4 tptp.nat)) (=> (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int (tptp.aa_nat_set_int F (tptp.aa_nat_nat tptp.suc N2))) (tptp.aa_nat_set_int F N2)))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N) N4)) (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int (tptp.aa_nat_set_int F N4)) (tptp.aa_nat_set_int F N)))))) (forall ((F tptp.fun_nat_rat) (N tptp.nat) (N4 tptp.nat)) (=> (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat F (tptp.aa_nat_nat tptp.suc N2))) (tptp.aa_nat_rat F N2)))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N) N4)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat F N4)) (tptp.aa_nat_rat F N)))))) (forall ((F tptp.fun_nat_num) (N tptp.nat) (N4 tptp.nat)) (=> (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_nat_num F (tptp.aa_nat_nat tptp.suc N2))) (tptp.aa_nat_num F N2)))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N) N4)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_nat_num F N4)) (tptp.aa_nat_num F N)))))) (forall ((F tptp.fun_nat_nat) (N tptp.nat) (N4 tptp.nat)) (=> (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat F (tptp.aa_nat_nat tptp.suc N2))) (tptp.aa_nat_nat F N2)))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N) N4)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat F N4)) (tptp.aa_nat_nat F N)))))) (forall ((F tptp.fun_nat_int) (N tptp.nat) (N4 tptp.nat)) (=> (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int F (tptp.aa_nat_nat tptp.suc N2))) (tptp.aa_nat_int F N2)))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N) N4)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int F N4)) (tptp.aa_nat_int F N)))))) (forall ((M tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat tptp.suc M)) N)))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat tptp.suc M)) N)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N)))) (forall ((I tptp.nat) (J tptp.nat) (P tptp.fun_nat_bool)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I) J)) (=> (tptp.pp (tptp.aa_nat_bool P I)) (=> (forall ((N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I) N2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) J)) (=> (tptp.pp (tptp.aa_nat_bool P N2)) (tptp.pp (tptp.aa_nat_bool P (tptp.aa_nat_nat tptp.suc N2))))))) (tptp.pp (tptp.aa_nat_bool P J)))))) (forall ((I tptp.nat) (J tptp.nat) (P tptp.fun_nat_bool)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I) J)) (=> (tptp.pp (tptp.aa_nat_bool P J)) (=> (forall ((N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I) N2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) J)) (=> (tptp.pp (tptp.aa_nat_bool P (tptp.aa_nat_nat tptp.suc N2))) (tptp.pp (tptp.aa_nat_bool P N2)))))) (tptp.pp (tptp.aa_nat_bool P I)))))) (forall ((M tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat tptp.suc M)) N)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N)))) (forall ((M tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N) (tptp.aa_nat_nat tptp.suc M))) (= N M)))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) (tptp.aa_nat_nat tptp.suc N))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)))) (forall ((N tptp.nat) (M tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N) M)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat tptp.suc N)) M)))) (forall ((M tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) (tptp.aa_nat_nat tptp.suc N))))) (forall ((M tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N)) (exists ((K3 tptp.nat)) (= N (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) K3)))))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N)) (exists ((K2 tptp.nat)) (= N (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) K2)))))) (forall ((I tptp.nat) (M tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I) (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) I))))) (forall ((I tptp.nat) (M tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I) (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat I) M))))) (forall ((M tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N)) (not (forall ((Q3 tptp.nat)) (not (= N (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) Q3)))))))) (forall ((M tptp.nat) (N tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) N)) (tptp.aa_nat_nat tptp.suc M)))) (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N) M)) (= (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat tptp.suc N))) (tptp.aa_nat_nat _let_1 N))))) (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat tptp.suc K)))) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat _let_1 M)) (tptp.aa_nat_nat _let_1 N))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N))))) (forall ((N tptp.nat) (M tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N) M)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat tptp.suc M)) N) (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) N))))) (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat tptp.suc K)))) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat _let_1 M)) (tptp.aa_nat_nat _let_1 N))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N))))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat tptp.suc M)) N) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat M) N)))) (forall ((M tptp.nat) (N tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat M) N)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat tptp.suc M)) N)))) (forall ((N tptp.nat)) (= (tptp.aa_nat_nat tptp.suc N) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat tptp.one_one_nat) N))) (= _let_147 tptp.suc) (forall ((N tptp.nat)) (= (tptp.aa_nat_nat tptp.suc N) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N) tptp.one_one_nat))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M))) (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat tptp.suc N)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat _let_1 tptp.one_one_nat)) N)))) (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real))) (=> (tptp.pp (tptp.aa_real_bool _let_1 A)) (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real A) (tptp.aa_nat_nat tptp.suc N))))))) (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.one_one_rat))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 A)) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_nat_rat (tptp.power_power_rat A) (tptp.aa_nat_nat tptp.suc N))))))) (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.one_one_nat))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 A)) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A) (tptp.aa_nat_nat tptp.suc N))))))) (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.one_one_int))) (=> (tptp.pp (tptp.aa_int_bool _let_1 A)) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_nat_int (tptp.power_power_int A) (tptp.aa_nat_nat tptp.suc N))))))) (forall ((Xs tptp.list_real) (B4 tptp.set_real)) (= (tptp.ord_less_eq_set_real (tptp.set_real2 Xs) B4) (forall ((X3 tptp.real)) (=> (tptp.member_real X3 (tptp.set_real2 Xs)) (tptp.member_real X3 B4))))) (forall ((Xs tptp.list_complex) (B4 tptp.set_complex)) (= (tptp.pp (tptp.aa_set_complex_bool (tptp.ord_le211207098394363844omplex (tptp.set_complex2 Xs)) B4)) (forall ((X3 tptp.complex)) (let ((_let_1 (tptp.member_complex X3))) (=> (tptp.pp (tptp.aa_set_complex_bool _let_1 (tptp.set_complex2 Xs))) (tptp.pp (tptp.aa_set_complex_bool _let_1 B4))))))) (forall ((Xs tptp.list_VEBT_VEBT) (B4 tptp.set_VEBT_VEBT)) (= (tptp.ord_le4337996190870823476T_VEBT (tptp.set_VEBT_VEBT2 Xs) B4) (forall ((X3 tptp.vEBT_VEBT)) (let ((_let_1 (tptp.aa_VEB289770264548726718T_bool tptp.member_VEBT_VEBT X3))) (=> (tptp.pp (tptp.aa_set8260762808118238015T_bool _let_1 (tptp.set_VEBT_VEBT2 Xs))) (tptp.pp (tptp.aa_set8260762808118238015T_bool _let_1 B4))))))) (forall ((Xs tptp.list_nat) (B4 tptp.set_nat)) (= (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat (tptp.set_nat2 Xs)) B4)) (forall ((X3 tptp.nat)) (let ((_let_1 (tptp.member_nat X3))) (=> (tptp.pp (tptp.aa_set_nat_bool _let_1 (tptp.set_nat2 Xs))) (tptp.pp (tptp.aa_set_nat_bool _let_1 B4))))))) (forall ((Xs tptp.list_int) (B4 tptp.set_int)) (= (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int (tptp.set_int2 Xs)) B4)) (forall ((X3 tptp.int)) (let ((_let_1 (tptp.member_int X3))) (=> (tptp.pp (tptp.aa_set_int_bool _let_1 (tptp.set_int2 Xs))) (tptp.pp (tptp.aa_set_int_bool _let_1 B4))))))) (forall ((N tptp.nat)) (exists ((Xs2 tptp.list_VEBT_VEBT)) (= (tptp.size_s6755466524823107622T_VEBT Xs2) N))) (forall ((N tptp.nat)) (exists ((Xs2 tptp.list_bool)) (= (tptp.size_size_list_bool Xs2) N))) (forall ((N tptp.nat)) (exists ((Xs2 tptp.list_nat)) (= (tptp.size_size_list_nat Xs2) N))) (forall ((Xs tptp.list_VEBT_VEBT) (Ys tptp.list_VEBT_VEBT)) (=> (not (= (tptp.size_s6755466524823107622T_VEBT Xs) (tptp.size_s6755466524823107622T_VEBT Ys))) (not (= Xs Ys)))) (forall ((Xs tptp.list_bool) (Ys tptp.list_bool)) (=> (not (= (tptp.size_size_list_bool Xs) (tptp.size_size_list_bool Ys))) (not (= Xs Ys)))) (forall ((Xs tptp.list_nat) (Ys tptp.list_nat)) (=> (not (= (tptp.size_size_list_nat Xs) (tptp.size_size_list_nat Ys))) (not (= Xs Ys)))) (forall ((N tptp.nat) (Q2 tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat N))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat _let_1 Q2)) M)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat tptp.suc Q2)))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat M) N) Q2))))) (forall ((V tptp.num) (N tptp.nat)) (= (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_num_nat tptp.numeral_numeral_nat V)) N)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num V) tptp.one))) N))) (forall ((N tptp.nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.one_one_real) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))) N)))) (forall ((A tptp.complex) (N tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.power_power_complex A))) (= (tptp.aa_nat_complex _let_2 (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat _let_1) N))) (tptp.aa_complex_complex (tptp.times_times_complex A) (tptp.aa_nat_complex (tptp.power_power_complex (tptp.aa_nat_complex _let_2 N)) _let_1)))))) (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_real_fun_nat_real tptp.power_power_real A))) (= (tptp.aa_nat_real _let_2 (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat _let_1) N))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_nat_real _let_2 N)) _let_1)))))) (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.power_power_rat A))) (= (tptp.aa_nat_rat _let_2 (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat _let_1) N))) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_nat_rat _let_2 N)) _let_1)))))) (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A))) (= (tptp.aa_nat_nat _let_2 (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat _let_1) N))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_nat_nat _let_2 N)) _let_1)))))) (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.power_power_int A))) (= (tptp.aa_nat_int _let_2 (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat _let_1) N))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_nat_int _let_2 N)) _let_1)))))) (forall ((P tptp.fun_li6006399982103069984T_bool) (Xs tptp.list_VEBT_VEBT)) (=> (forall ((Xs2 tptp.list_VEBT_VEBT)) (=> (forall ((Ys2 tptp.list_VEBT_VEBT)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.size_s6755466524823107622T_VEBT Ys2)) (tptp.size_s6755466524823107622T_VEBT Xs2))) (tptp.pp (tptp.aa_lis2822252094023462681T_bool P Ys2)))) (tptp.pp (tptp.aa_lis2822252094023462681T_bool P Xs2)))) (tptp.pp (tptp.aa_lis2822252094023462681T_bool P Xs)))) (forall ((P tptp.fun_list_bool_bool) (Xs tptp.list_bool)) (=> (forall ((Xs2 tptp.list_bool)) (=> (forall ((Ys2 tptp.list_bool)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.size_size_list_bool Ys2)) (tptp.size_size_list_bool Xs2))) (tptp.pp (tptp.aa_list_bool_bool P Ys2)))) (tptp.pp (tptp.aa_list_bool_bool P Xs2)))) (tptp.pp (tptp.aa_list_bool_bool P Xs)))) (forall ((P tptp.fun_list_nat_bool) (Xs tptp.list_nat)) (=> (forall ((Xs2 tptp.list_nat)) (=> (forall ((Ys2 tptp.list_nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.size_size_list_nat Ys2)) (tptp.size_size_list_nat Xs2))) (tptp.pp (tptp.aa_list_nat_bool P Ys2)))) (tptp.pp (tptp.aa_list_nat_bool P Xs2)))) (tptp.pp (tptp.aa_list_nat_bool P Xs)))) (forall ((Ma tptp.nat) (X tptp.nat) (Mi tptp.nat) (Va tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat tptp.suc Va)))) (let ((_let_3 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat _let_2) _let_1))) (let ((_let_4 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high X) _let_3))) (let ((_let_5 (tptp.vEBT_vebt_pred Summary _let_4))) (let ((_let_6 (tptp.aa_opt7711074727033721499on_nat tptp.vEBT_VEBT_mul (tptp.some_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat _let_1) _let_3))))) (let ((_let_7 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low X) _let_3))) (let ((_let_8 (tptp.nth_VEBT_VEBT TreeList _let_4))) (let ((_let_9 (tptp.vEBT_vebt_mint _let_8))) (let ((_let_10 (tptp.vEBT_vebt_pred (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Mi) Ma)) _let_2 TreeList Summary) X))) (let ((_let_11 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Ma) X)))) (and (=> _let_11 (= _let_10 (tptp.some_nat Ma))) (=> (not _let_11) (= _let_10 (tptp.if_option_nat (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_4) (tptp.size_s6755466524823107622T_VEBT TreeList)) (tptp.if_option_nat (tptp.aa_bool_bool (tptp.fconj (tptp.aa_bool_bool tptp.fNot (tptp.aa_option_nat_bool (tptp.aa_opt7943525813896274546t_bool tptp.fequal_option_nat _let_9) tptp.none_nat))) (tptp.aa_option_nat_bool (tptp.aa_opt7943525813896274546t_bool tptp.vEBT_VEBT_greater (tptp.some_nat _let_7)) _let_9)) (tptp.aa_opt1882420858203594238on_nat (tptp.aa_opt7711074727033721499on_nat tptp.vEBT_VEBT_add (tptp.aa_opt1882420858203594238on_nat _let_6 (tptp.some_nat _let_4))) (tptp.vEBT_vebt_pred _let_8 _let_7)) (tptp.if_option_nat (tptp.aa_option_nat_bool (tptp.aa_opt7943525813896274546t_bool tptp.fequal_option_nat _let_5) tptp.none_nat) (tptp.if_option_nat (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Mi) X) (tptp.some_nat Mi) tptp.none_nat) (tptp.aa_opt1882420858203594238on_nat (tptp.aa_opt7711074727033721499on_nat tptp.vEBT_VEBT_add (tptp.aa_opt1882420858203594238on_nat _let_6 _let_5)) (tptp.vEBT_vebt_maxt (tptp.nth_VEBT_VEBT TreeList (tptp.the_nat _let_5)))))) tptp.none_nat)))))))))))))))) (forall ((Xs tptp.list_int) (Ys tptp.list_int)) (=> (= (tptp.size_size_list_int Xs) (tptp.size_size_list_int Ys)) (=> (forall ((I3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I3) (tptp.size_size_list_int Xs))) (= (tptp.aa_nat_int (tptp.nth_int Xs) I3) (tptp.aa_nat_int (tptp.nth_int Ys) I3)))) (= Xs Ys)))) (forall ((Xs tptp.list_VEBT_VEBT) (Ys tptp.list_VEBT_VEBT)) (=> (= (tptp.size_s6755466524823107622T_VEBT Xs) (tptp.size_s6755466524823107622T_VEBT Ys)) (=> (forall ((I3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I3) (tptp.size_s6755466524823107622T_VEBT Xs))) (= (tptp.nth_VEBT_VEBT Xs I3) (tptp.nth_VEBT_VEBT Ys I3)))) (= Xs Ys)))) (forall ((Xs tptp.list_bool) (Ys tptp.list_bool)) (=> (= (tptp.size_size_list_bool Xs) (tptp.size_size_list_bool Ys)) (=> (forall ((I3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I3) (tptp.size_size_list_bool Xs))) (= (tptp.pp (tptp.aa_nat_bool (tptp.nth_bool Xs) I3)) (tptp.pp (tptp.aa_nat_bool (tptp.nth_bool Ys) I3))))) (= Xs Ys)))) (forall ((Xs tptp.list_nat) (Ys tptp.list_nat)) (=> (= (tptp.size_size_list_nat Xs) (tptp.size_size_list_nat Ys)) (=> (forall ((I3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I3) (tptp.size_size_list_nat Xs))) (= (tptp.aa_nat_nat (tptp.nth_nat Xs) I3) (tptp.aa_nat_nat (tptp.nth_nat Ys) I3)))) (= Xs Ys)))) (forall ((K tptp.nat) (P tptp.fun_nat_fun_int_bool)) (= (forall ((I4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I4) K)) (exists ((X_1 tptp.int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_nat_fun_int_bool P I4) X_1))))) (exists ((Xs3 tptp.list_int)) (and (= (tptp.size_size_list_int Xs3) K) (forall ((I4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I4) K)) (tptp.pp (tptp.aa_int_bool (tptp.aa_nat_fun_int_bool P I4) (tptp.aa_nat_int (tptp.nth_int Xs3) I4))))))))) (forall ((K tptp.nat) (P tptp.fun_na2351039247863542899T_bool)) (= (forall ((I4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I4) K)) (exists ((X_1 tptp.vEBT_VEBT)) (tptp.pp (tptp.aa_VEBT_VEBT_bool (tptp.aa_nat8029987864780243636T_bool P I4) X_1))))) (exists ((Xs3 tptp.list_VEBT_VEBT)) (and (= (tptp.size_s6755466524823107622T_VEBT Xs3) K) (forall ((I4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I4) K)) (tptp.pp (tptp.aa_VEBT_VEBT_bool (tptp.aa_nat8029987864780243636T_bool P I4) (tptp.nth_VEBT_VEBT Xs3 I4))))))))) (forall ((K tptp.nat) (P tptp.fun_na9137082442855928016l_bool)) (= (forall ((I4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I4) K)) (exists ((X_1 tptp.bool)) (tptp.pp (tptp.aa_bool_bool (tptp.aa_nat_fun_bool_bool P I4) X_1))))) (exists ((Xs3 tptp.list_bool)) (and (= (tptp.size_size_list_bool Xs3) K) (forall ((I4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I4) K)) (tptp.pp (tptp.aa_bool_bool (tptp.aa_nat_fun_bool_bool P I4) (tptp.aa_nat_bool (tptp.nth_bool Xs3) I4))))))))) (forall ((K tptp.nat) (P tptp.fun_nat_fun_nat_bool)) (= (forall ((I4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I4) K)) (exists ((X_1 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool P I4) X_1))))) (exists ((Xs3 tptp.list_nat)) (and (= (tptp.size_size_list_nat Xs3) K) (forall ((I4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I4) K)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool P I4) (tptp.aa_nat_nat (tptp.nth_nat Xs3) I4))))))))) (forall ((Xs tptp.list_int) (Ys tptp.list_int)) (= (= Xs Ys) (and (= (tptp.size_size_list_int Xs) (tptp.size_size_list_int Ys)) (forall ((I4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I4) (tptp.size_size_list_int Xs))) (= (tptp.aa_nat_int (tptp.nth_int Xs) I4) (tptp.aa_nat_int (tptp.nth_int Ys) I4))))))) (forall ((Xs tptp.list_VEBT_VEBT) (Ys tptp.list_VEBT_VEBT)) (= (= Xs Ys) (and (= (tptp.size_s6755466524823107622T_VEBT Xs) (tptp.size_s6755466524823107622T_VEBT Ys)) (forall ((I4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I4) (tptp.size_s6755466524823107622T_VEBT Xs))) (= (tptp.nth_VEBT_VEBT Xs I4) (tptp.nth_VEBT_VEBT Ys I4))))))) (forall ((Xs tptp.list_bool) (Ys tptp.list_bool)) (= (= Xs Ys) (and (= (tptp.size_size_list_bool Xs) (tptp.size_size_list_bool Ys)) (forall ((I4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I4) (tptp.size_size_list_bool Xs))) (= (tptp.pp (tptp.aa_nat_bool (tptp.nth_bool Xs) I4)) (tptp.pp (tptp.aa_nat_bool (tptp.nth_bool Ys) I4)))))))) (forall ((Xs tptp.list_nat) (Ys tptp.list_nat)) (= (= Xs Ys) (and (= (tptp.size_size_list_nat Xs) (tptp.size_size_list_nat Ys)) (forall ((I4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I4) (tptp.size_size_list_nat Xs))) (= (tptp.aa_nat_nat (tptp.nth_nat Xs) I4) (tptp.aa_nat_nat (tptp.nth_nat Ys) I4))))))) (forall ((TreeList tptp.list_VEBT_VEBT) (N tptp.nat) (Summary tptp.vEBT_VEBT) (M tptp.nat) (Deg tptp.nat)) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (tptp.pp (tptp.aa_set8260762808118238015T_bool (tptp.aa_VEB289770264548726718T_bool tptp.member_VEBT_VEBT X4) (tptp.set_VEBT_VEBT2 TreeList))) (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt X4) N)))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt Summary) M)) (=> (= (tptp.size_s6755466524823107622T_VEBT TreeList) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) M)) (=> (= M (tptp.aa_nat_nat tptp.suc N)) (=> (= Deg (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N) M)) (=> (not (exists ((X_12 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions Summary) X_12)))) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (tptp.pp (tptp.aa_set8260762808118238015T_bool (tptp.aa_VEB289770264548726718T_bool tptp.member_VEBT_VEBT X4) (tptp.set_VEBT_VEBT2 TreeList))) (not (exists ((X_12 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions X4) X_12)))))) (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt (tptp.vEBT_Node tptp.none_P5556105721700978146at_nat Deg TreeList Summary)) Deg)))))))))) (forall ((A tptp.nat) (B2 tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) B2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) tptp.one_one_nat)) B2)))) (forall ((A tptp.int) (B2 tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B2)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) tptp.one_one_int)) B2)))) (forall ((N tptp.nat) (Xs tptp.list_real)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N) (tptp.size_size_list_real Xs))) (tptp.member_real (tptp.aa_nat_real (tptp.nth_real Xs) N) (tptp.set_real2 Xs)))) (forall ((N tptp.nat) (Xs tptp.list_complex)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N) (tptp.size_s3451745648224563538omplex Xs))) (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex (tptp.aa_nat_complex (tptp.nth_complex Xs) N)) (tptp.set_complex2 Xs))))) (forall ((N tptp.nat) (Xs tptp.list_int)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N) (tptp.size_size_list_int Xs))) (tptp.pp (tptp.aa_set_int_bool (tptp.member_int (tptp.aa_nat_int (tptp.nth_int Xs) N)) (tptp.set_int2 Xs))))) (forall ((N tptp.nat) (Xs tptp.list_VEBT_VEBT)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N) (tptp.size_s6755466524823107622T_VEBT Xs))) (tptp.pp (tptp.aa_set8260762808118238015T_bool (tptp.aa_VEB289770264548726718T_bool tptp.member_VEBT_VEBT (tptp.nth_VEBT_VEBT Xs N)) (tptp.set_VEBT_VEBT2 Xs))))) (forall ((N tptp.nat) (Xs tptp.list_bool)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N) (tptp.size_size_list_bool Xs))) (tptp.member_bool (tptp.aa_nat_bool (tptp.nth_bool Xs) N) (tptp.set_bool2 Xs)))) (forall ((N tptp.nat) (Xs tptp.list_nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N) (tptp.size_size_list_nat Xs))) (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat (tptp.aa_nat_nat (tptp.nth_nat Xs) N)) (tptp.set_nat2 Xs))))) (forall ((N tptp.nat) (Xs tptp.list_int) (P tptp.fun_int_bool)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N) (tptp.size_size_list_int Xs))) (=> (forall ((X4 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X4) (tptp.set_int2 Xs))) (tptp.pp (tptp.aa_int_bool P X4)))) (tptp.pp (tptp.aa_int_bool P (tptp.aa_nat_int (tptp.nth_int Xs) N)))))) (forall ((N tptp.nat) (Xs tptp.list_VEBT_VEBT) (P tptp.fun_VEBT_VEBT_bool)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N) (tptp.size_s6755466524823107622T_VEBT Xs))) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (tptp.pp (tptp.aa_set8260762808118238015T_bool (tptp.aa_VEB289770264548726718T_bool tptp.member_VEBT_VEBT X4) (tptp.set_VEBT_VEBT2 Xs))) (tptp.pp (tptp.aa_VEBT_VEBT_bool P X4)))) (tptp.pp (tptp.aa_VEBT_VEBT_bool P (tptp.nth_VEBT_VEBT Xs N)))))) (forall ((N tptp.nat) (Xs tptp.list_bool) (P tptp.fun_bool_bool)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N) (tptp.size_size_list_bool Xs))) (=> (forall ((X4 tptp.bool)) (=> (tptp.member_bool X4 (tptp.set_bool2 Xs)) (tptp.pp (tptp.aa_bool_bool P X4)))) (tptp.pp (tptp.aa_bool_bool P (tptp.aa_nat_bool (tptp.nth_bool Xs) N)))))) (forall ((N tptp.nat) (Xs tptp.list_nat) (P tptp.fun_nat_bool)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N) (tptp.size_size_list_nat Xs))) (=> (forall ((X4 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X4) (tptp.set_nat2 Xs))) (tptp.pp (tptp.aa_nat_bool P X4)))) (tptp.pp (tptp.aa_nat_bool P (tptp.aa_nat_nat (tptp.nth_nat Xs) N)))))) (forall ((X tptp.real) (Xs tptp.list_real)) (= (tptp.member_real X (tptp.set_real2 Xs)) (exists ((I4 tptp.nat)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I4) (tptp.size_size_list_real Xs))) (= (tptp.aa_nat_real (tptp.nth_real Xs) I4) X))))) (forall ((X tptp.complex) (Xs tptp.list_complex)) (= (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex X) (tptp.set_complex2 Xs))) (exists ((I4 tptp.nat)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I4) (tptp.size_s3451745648224563538omplex Xs))) (= (tptp.aa_nat_complex (tptp.nth_complex Xs) I4) X))))) (forall ((X tptp.int) (Xs tptp.list_int)) (= (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X) (tptp.set_int2 Xs))) (exists ((I4 tptp.nat)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I4) (tptp.size_size_list_int Xs))) (= (tptp.aa_nat_int (tptp.nth_int Xs) I4) X))))) (forall ((X tptp.vEBT_VEBT) (Xs tptp.list_VEBT_VEBT)) (= (tptp.pp (tptp.aa_set8260762808118238015T_bool (tptp.aa_VEB289770264548726718T_bool tptp.member_VEBT_VEBT X) (tptp.set_VEBT_VEBT2 Xs))) (exists ((I4 tptp.nat)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I4) (tptp.size_s6755466524823107622T_VEBT Xs))) (= (tptp.nth_VEBT_VEBT Xs I4) X))))) (forall ((X tptp.bool) (Xs tptp.list_bool)) (= (tptp.member_bool X (tptp.set_bool2 Xs)) (exists ((I4 tptp.nat)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I4) (tptp.size_size_list_bool Xs))) (= (tptp.pp (tptp.aa_nat_bool (tptp.nth_bool Xs) I4)) (tptp.pp X)))))) (forall ((X tptp.nat) (Xs tptp.list_nat)) (= (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X) (tptp.set_nat2 Xs))) (exists ((I4 tptp.nat)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I4) (tptp.size_size_list_nat Xs))) (= (tptp.aa_nat_nat (tptp.nth_nat Xs) I4) X))))) (forall ((Xs tptp.list_real) (P tptp.fun_real_bool) (X tptp.real)) (=> (forall ((I3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I3) (tptp.size_size_list_real Xs))) (tptp.pp (tptp.aa_real_bool P (tptp.aa_nat_real (tptp.nth_real Xs) I3))))) (=> (tptp.member_real X (tptp.set_real2 Xs)) (tptp.pp (tptp.aa_real_bool P X))))) (forall ((Xs tptp.list_complex) (P tptp.fun_complex_bool) (X tptp.complex)) (=> (forall ((I3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I3) (tptp.size_s3451745648224563538omplex Xs))) (tptp.pp (tptp.aa_complex_bool P (tptp.aa_nat_complex (tptp.nth_complex Xs) I3))))) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex X) (tptp.set_complex2 Xs))) (tptp.pp (tptp.aa_complex_bool P X))))) (forall ((Xs tptp.list_int) (P tptp.fun_int_bool) (X tptp.int)) (=> (forall ((I3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I3) (tptp.size_size_list_int Xs))) (tptp.pp (tptp.aa_int_bool P (tptp.aa_nat_int (tptp.nth_int Xs) I3))))) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X) (tptp.set_int2 Xs))) (tptp.pp (tptp.aa_int_bool P X))))) (forall ((Xs tptp.list_VEBT_VEBT) (P tptp.fun_VEBT_VEBT_bool) (X tptp.vEBT_VEBT)) (=> (forall ((I3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I3) (tptp.size_s6755466524823107622T_VEBT Xs))) (tptp.pp (tptp.aa_VEBT_VEBT_bool P (tptp.nth_VEBT_VEBT Xs I3))))) (=> (tptp.pp (tptp.aa_set8260762808118238015T_bool (tptp.aa_VEB289770264548726718T_bool tptp.member_VEBT_VEBT X) (tptp.set_VEBT_VEBT2 Xs))) (tptp.pp (tptp.aa_VEBT_VEBT_bool P X))))) (forall ((Xs tptp.list_bool) (P tptp.fun_bool_bool) (X tptp.bool)) (=> (forall ((I3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I3) (tptp.size_size_list_bool Xs))) (tptp.pp (tptp.aa_bool_bool P (tptp.aa_nat_bool (tptp.nth_bool Xs) I3))))) (=> (tptp.member_bool X (tptp.set_bool2 Xs)) (tptp.pp (tptp.aa_bool_bool P X))))) (forall ((Xs tptp.list_nat) (P tptp.fun_nat_bool) (X tptp.nat)) (=> (forall ((I3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I3) (tptp.size_size_list_nat Xs))) (tptp.pp (tptp.aa_nat_bool P (tptp.aa_nat_nat (tptp.nth_nat Xs) I3))))) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X) (tptp.set_nat2 Xs))) (tptp.pp (tptp.aa_nat_bool P X))))) (forall ((Mi tptp.nat) (Ma tptp.nat) (Va tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat tptp.suc Va)))) (let ((_let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat _let_1) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_3 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high X) _let_2))) (let ((_let_4 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_3) (tptp.size_s6755466524823107622T_VEBT TreeList))))) (let ((_let_5 (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Ma) X))))) (let ((_let_6 (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Mi))))) (= (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_vebt_member (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Mi) Ma)) _let_1 TreeList Summary)) X)) (=> (not (= X Mi)) (=> (not (= X Ma)) (and _let_6 (=> _let_6 (and _let_5 (=> _let_5 (and (=> _let_4 (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_vebt_member (tptp.nth_VEBT_VEBT TreeList _let_3)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low X) _let_2)))) _let_4))))))))))))))) (forall ((V tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat tptp.suc V)))) (= (tptp.vEBT_vebt_insert (tptp.vEBT_Node tptp.none_P5556105721700978146at_nat _let_1 TreeList Summary) X) (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat X) X)) _let_1 TreeList Summary)))) (forall ((N tptp.nat)) (= (tptp.vEBT_VEBT_set_vebt (tptp.vEBT_vebt_buildup N)) tptp.bot_bot_set_nat)) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (not (= (tptp.aa_nat_nat _let_1 M) (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat _let_1 N)))))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (not (= (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat _let_1 M)) (tptp.aa_nat_nat _let_1 N))))) (forall ((Mi tptp.nat) (Ma tptp.nat) (V tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Vc tptp.vEBT_VEBT) (X tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc V))) (let ((_let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat _let_1) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_3 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high X) _let_2))) (let ((_let_4 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_3) (tptp.size_s6755466524823107622T_VEBT TreeList))))) (= (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_VEBT_membermima (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Mi) Ma)) _let_1 TreeList Vc)) X)) (or (= X Mi) (= X Ma) (and (=> _let_4 (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_VEBT_membermima (tptp.nth_VEBT_VEBT TreeList _let_3)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low X) _let_2)))) _let_4)))))))) (forall ((Uy tptp.option4927543243414619207at_nat) (V tptp.nat) (TreeList tptp.list_VEBT_VEBT) (S tptp.vEBT_VEBT) (X tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc V))) (let ((_let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat _let_1) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_3 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high X) _let_2))) (let ((_let_4 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_3) (tptp.size_s6755466524823107622T_VEBT TreeList))))) (= (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_V5719532721284313246member (tptp.vEBT_Node Uy _let_1 TreeList S)) X)) (and (=> _let_4 (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_V5719532721284313246member (tptp.nth_VEBT_VEBT TreeList _let_3)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low X) _let_2)))) _let_4))))))) (forall ((V tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Vd tptp.vEBT_VEBT) (X tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc V))) (let ((_let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat _let_1) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_3 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high X) _let_2))) (let ((_let_4 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_3) (tptp.size_s6755466524823107622T_VEBT TreeList))))) (= (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_VEBT_membermima (tptp.vEBT_Node tptp.none_P5556105721700978146at_nat _let_1 TreeList Vd)) X)) (and (=> _let_4 (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_VEBT_membermima (tptp.nth_VEBT_VEBT TreeList _let_3)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low X) _let_2)))) _let_4))))))) (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y tptp.option_nat)) (let ((_let_1 (not (= Y tptp.none_nat)))) (=> (= (tptp.vEBT_vebt_pred X Xa2) Y) (=> (=> (exists ((Uu2 tptp.bool) (Uv2 tptp.bool)) (= X (tptp.vEBT_Leaf Uu2 Uv2))) (=> (= Xa2 tptp.zero_zero_nat) _let_1)) (=> (forall ((A3 tptp.bool)) (let ((_let_1 (tptp.pp A3))) (=> (exists ((Uw2 tptp.bool)) (= X (tptp.vEBT_Leaf A3 Uw2))) (=> (= Xa2 (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)) (not (and (=> _let_1 (= Y (tptp.some_nat tptp.zero_zero_nat))) (=> (not _let_1) (= Y tptp.none_nat)))))))) (=> (forall ((A3 tptp.bool) (B3 tptp.bool)) (let ((_let_1 (tptp.pp A3))) (let ((_let_2 (tptp.pp B3))) (=> (= X (tptp.vEBT_Leaf A3 B3)) (=> (exists ((Va2 tptp.nat)) (= Xa2 (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat tptp.suc Va2)))) (not (and (=> _let_2 (= Y (tptp.some_nat tptp.one_one_nat))) (=> (not _let_2) (and (=> _let_1 (= Y (tptp.some_nat tptp.zero_zero_nat))) (=> (not _let_1) (= Y tptp.none_nat))))))))))) (=> (=> (exists ((Uy2 tptp.nat) (Uz2 tptp.list_VEBT_VEBT) (Va3 tptp.vEBT_VEBT)) (= X (tptp.vEBT_Node tptp.none_P5556105721700978146at_nat Uy2 Uz2 Va3))) _let_1) (=> (=> (exists ((V2 tptp.product_prod_nat_nat) (Vd2 tptp.list_VEBT_VEBT) (Ve tptp.vEBT_VEBT)) (= X (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat V2) tptp.zero_zero_nat Vd2 Ve))) _let_1) (=> (=> (exists ((V2 tptp.product_prod_nat_nat) (Vh tptp.list_VEBT_VEBT) (Vi tptp.vEBT_VEBT)) (= X (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat V2) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat) Vh Vi))) _let_1) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat tptp.suc Va2)))) (let ((_let_3 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat _let_2) _let_1))) (let ((_let_4 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high Xa2) _let_3))) (let ((_let_5 (tptp.vEBT_vebt_pred Summary2 _let_4))) (let ((_let_6 (tptp.aa_opt7711074727033721499on_nat tptp.vEBT_VEBT_mul (tptp.some_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat _let_1) _let_3))))) (let ((_let_7 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low Xa2) _let_3))) (let ((_let_8 (tptp.nth_VEBT_VEBT TreeList2 _let_4))) (let ((_let_9 (tptp.vEBT_vebt_mint _let_8))) (let ((_let_10 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Ma2) Xa2)))) (=> (= X (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Mi2) Ma2)) _let_2 TreeList2 Summary2)) (not (and (=> _let_10 (= Y (tptp.some_nat Ma2))) (=> (not _let_10) (= Y (tptp.if_option_nat (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_4) (tptp.size_s6755466524823107622T_VEBT TreeList2)) (tptp.if_option_nat (tptp.aa_bool_bool (tptp.fconj (tptp.aa_bool_bool tptp.fNot (tptp.aa_option_nat_bool (tptp.aa_opt7943525813896274546t_bool tptp.fequal_option_nat _let_9) tptp.none_nat))) (tptp.aa_option_nat_bool (tptp.aa_opt7943525813896274546t_bool tptp.vEBT_VEBT_greater (tptp.some_nat _let_7)) _let_9)) (tptp.aa_opt1882420858203594238on_nat (tptp.aa_opt7711074727033721499on_nat tptp.vEBT_VEBT_add (tptp.aa_opt1882420858203594238on_nat _let_6 (tptp.some_nat _let_4))) (tptp.vEBT_vebt_pred _let_8 _let_7)) (tptp.if_option_nat (tptp.aa_option_nat_bool (tptp.aa_opt7943525813896274546t_bool tptp.fequal_option_nat _let_5) tptp.none_nat) (tptp.if_option_nat (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Mi2) Xa2) (tptp.some_nat Mi2) tptp.none_nat) (tptp.aa_opt1882420858203594238on_nat (tptp.aa_opt7711074727033721499on_nat tptp.vEBT_VEBT_add (tptp.aa_opt1882420858203594238on_nat _let_6 _let_5)) (tptp.vEBT_vebt_maxt (tptp.nth_VEBT_VEBT TreeList2 (tptp.the_nat _let_5)))))) tptp.none_nat))))))))))))))))))))))))))) (forall ((X tptp.nat) (N tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low X) N) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat X) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N)))) (forall ((Uw tptp.nat) (Ux tptp.list_VEBT_VEBT) (Uy tptp.vEBT_VEBT)) (tptp.pp (tptp.aa_VEBT_VEBT_bool tptp.vEBT_VEBT_minNull (tptp.vEBT_Node tptp.none_P5556105721700978146at_nat Uw Ux Uy)))) (forall ((T tptp.vEBT_VEBT)) (not (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt T) tptp.zero_zero_nat)))) (forall ((T tptp.vEBT_VEBT)) (not (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt T) tptp.zero_zero_nat)))) (forall ((N tptp.nat) (X tptp.nat)) (not (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_VEBT_membermima (tptp.vEBT_vebt_buildup N)) X)))) (forall ((N tptp.nat) (X tptp.nat)) (not (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_V5719532721284313246member (tptp.vEBT_vebt_buildup N)) X)))) (forall ((T tptp.vEBT_VEBT) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt T) N)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)))) (forall ((A tptp.bool) (B2 tptp.bool)) (not (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt (tptp.vEBT_Leaf A B2)) tptp.zero_zero_nat)))) (forall ((T tptp.vEBT_VEBT) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt T) N)) (=> (= N tptp.one_one_nat) (exists ((A3 tptp.bool) (B3 tptp.bool)) (= T (tptp.vEBT_Leaf A3 B3)))))) (forall ((T tptp.vEBT_VEBT)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt T) tptp.one_one_nat)) (exists ((A3 tptp.bool) (B3 tptp.bool)) (= T (tptp.vEBT_Leaf A3 B3))))) (forall ((T tptp.vEBT_VEBT)) (= (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt T) tptp.one_one_nat)) (exists ((A5 tptp.bool) (B5 tptp.bool)) (= T (tptp.vEBT_Leaf A5 B5))))) (forall ((T tptp.vEBT_VEBT) (X tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions T) X)) (or (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_V5719532721284313246member T) X)) (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_VEBT_membermima T) X))))) (forall ((N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt (tptp.vEBT_vebt_buildup N)) N)))) (forall ((A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A) B2))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat _let_1) B2) _let_1))) (forall ((A tptp.int) (B2 tptp.int)) (let ((_let_1 (tptp.aa_int_int (tptp.modulo_modulo_int A) B2))) (= (tptp.aa_int_int (tptp.modulo_modulo_int _let_1) B2) _let_1))) (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (let ((_let_1 (tptp.modulo364778990260209775nteger A B2))) (= (tptp.modulo364778990260209775nteger _let_1 B2) _let_1))) (forall ((Tree tptp.vEBT_VEBT) (N tptp.nat) (X tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt Tree) N)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_vebt_member Tree) X)) (or (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_V5719532721284313246member Tree) X)) (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_VEBT_membermima Tree) X)))))) (forall ((N tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N) tptp.zero_zero_nat)) (= N tptp.zero_zero_nat))) (forall ((N tptp.nat)) (= (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N))) (= N tptp.zero_zero_nat))) (forall ((A tptp.complex)) (= (tptp.aa_complex_complex (tptp.times_times_complex tptp.zero_zero_complex) A) tptp.zero_zero_complex)) (forall ((A tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real tptp.zero_zero_real) A) tptp.zero_zero_real)) (forall ((A tptp.rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat tptp.zero_zero_rat) A) tptp.zero_zero_rat)) (forall ((A tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)) (forall ((A tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int tptp.zero_zero_int) A) tptp.zero_zero_int)) (forall ((A tptp.complex)) (= (tptp.aa_complex_complex (tptp.times_times_complex A) tptp.zero_zero_complex) tptp.zero_zero_complex)) (forall ((A tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) tptp.zero_zero_real) tptp.zero_zero_real)) (forall ((A tptp.rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) tptp.zero_zero_rat) tptp.zero_zero_rat)) (forall ((A tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) tptp.zero_zero_nat) tptp.zero_zero_nat)) (forall ((A tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) tptp.zero_zero_int) tptp.zero_zero_int)) (forall ((A tptp.complex) (B2 tptp.complex)) (= (= (tptp.aa_complex_complex (tptp.times_times_complex A) B2) tptp.zero_zero_complex) (or (= A tptp.zero_zero_complex) (= B2 tptp.zero_zero_complex)))) (forall ((A tptp.real) (B2 tptp.real)) (= (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) B2) tptp.zero_zero_real) (or (= A tptp.zero_zero_real) (= B2 tptp.zero_zero_real)))) (forall ((A tptp.rat) (B2 tptp.rat)) (= (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) B2) tptp.zero_zero_rat) (or (= A tptp.zero_zero_rat) (= B2 tptp.zero_zero_rat)))) (forall ((A tptp.nat) (B2 tptp.nat)) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) B2) tptp.zero_zero_nat) (or (= A tptp.zero_zero_nat) (= B2 tptp.zero_zero_nat)))) (forall ((A tptp.int) (B2 tptp.int)) (= (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) B2) tptp.zero_zero_int) (or (= A tptp.zero_zero_int) (= B2 tptp.zero_zero_int)))) (forall ((C tptp.complex) (A tptp.complex) (B2 tptp.complex)) (let ((_let_1 (tptp.times_times_complex C))) (= (= (tptp.aa_complex_complex _let_1 A) (tptp.aa_complex_complex _let_1 B2)) (or (= C tptp.zero_zero_complex) (= A B2))))) (forall ((C tptp.real) (A tptp.real) (B2 tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.times_times_real C))) (= (= (tptp.aa_real_real _let_1 A) (tptp.aa_real_real _let_1 B2)) (or (= C tptp.zero_zero_real) (= A B2))))) (forall ((C tptp.rat) (A tptp.rat) (B2 tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_rat tptp.times_times_rat C))) (= (= (tptp.aa_rat_rat _let_1 A) (tptp.aa_rat_rat _let_1 B2)) (or (= C tptp.zero_zero_rat) (= A B2))))) (forall ((C tptp.nat) (A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat C))) (= (= (tptp.aa_nat_nat _let_1 A) (tptp.aa_nat_nat _let_1 B2)) (or (= C tptp.zero_zero_nat) (= A B2))))) (forall ((C tptp.int) (A tptp.int) (B2 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.times_times_int C))) (= (= (tptp.aa_int_int _let_1 A) (tptp.aa_int_int _let_1 B2)) (or (= C tptp.zero_zero_int) (= A B2))))) (forall ((A tptp.complex) (C tptp.complex) (B2 tptp.complex)) (= (= (tptp.aa_complex_complex (tptp.times_times_complex A) C) (tptp.aa_complex_complex (tptp.times_times_complex B2) C)) (or (= C tptp.zero_zero_complex) (= A B2)))) (forall ((A tptp.real) (C tptp.real) (B2 tptp.real)) (= (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) C) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real B2) C)) (or (= C tptp.zero_zero_real) (= A B2)))) (forall ((A tptp.rat) (C tptp.rat) (B2 tptp.rat)) (= (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) C) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat B2) C)) (or (= C tptp.zero_zero_rat) (= A B2)))) (forall ((A tptp.nat) (C tptp.nat) (B2 tptp.nat)) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) C) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B2) C)) (or (= C tptp.zero_zero_nat) (= A B2)))) (forall ((A tptp.int) (C tptp.int) (B2 tptp.int)) (= (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) C) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B2) C)) (or (= C tptp.zero_zero_int) (= A B2)))) (forall ((A tptp.complex)) (= (tptp.aa_complex_complex (tptp.plus_plus_complex tptp.zero_zero_complex) A) A)) (forall ((A tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real tptp.zero_zero_real) A) A)) (forall ((A tptp.rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat tptp.zero_zero_rat) A) A)) (forall ((A tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat tptp.zero_zero_nat) A) A)) (forall ((A tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int tptp.zero_zero_int) A) A)) (forall ((X tptp.nat) (Y tptp.nat)) (= (= tptp.zero_zero_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat X) Y)) (and (= X tptp.zero_zero_nat) (= Y tptp.zero_zero_nat)))) (forall ((X tptp.nat) (Y tptp.nat)) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat X) Y) tptp.zero_zero_nat) (and (= X tptp.zero_zero_nat) (= Y tptp.zero_zero_nat)))) (forall ((A tptp.complex) (B2 tptp.complex)) (= (= A (tptp.aa_complex_complex (tptp.plus_plus_complex A) B2)) (= B2 tptp.zero_zero_complex))) (forall ((A tptp.real) (B2 tptp.real)) (= (= A (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) B2)) (= B2 tptp.zero_zero_real))) (forall ((A tptp.rat) (B2 tptp.rat)) (= (= A (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) B2)) (= B2 tptp.zero_zero_rat))) (forall ((A tptp.nat) (B2 tptp.nat)) (= (= A (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) B2)) (= B2 tptp.zero_zero_nat))) (forall ((A tptp.int) (B2 tptp.int)) (= (= A (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) B2)) (= B2 tptp.zero_zero_int))) (forall ((A tptp.complex) (B2 tptp.complex)) (= (= A (tptp.aa_complex_complex (tptp.plus_plus_complex B2) A)) (= B2 tptp.zero_zero_complex))) (forall ((A tptp.real) (B2 tptp.real)) (= (= A (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real B2) A)) (= B2 tptp.zero_zero_real))) (forall ((A tptp.rat) (B2 tptp.rat)) (= (= A (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat B2) A)) (= B2 tptp.zero_zero_rat))) (forall ((A tptp.nat) (B2 tptp.nat)) (= (= A (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat B2) A)) (= B2 tptp.zero_zero_nat))) (forall ((A tptp.int) (B2 tptp.int)) (= (= A (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int B2) A)) (= B2 tptp.zero_zero_int))) (forall ((A tptp.complex) (B2 tptp.complex)) (= (= (tptp.aa_complex_complex (tptp.plus_plus_complex A) B2) A) (= B2 tptp.zero_zero_complex))) (forall ((A tptp.real) (B2 tptp.real)) (= (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) B2) A) (= B2 tptp.zero_zero_real))) (forall ((A tptp.rat) (B2 tptp.rat)) (= (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) B2) A) (= B2 tptp.zero_zero_rat))) (forall ((A tptp.nat) (B2 tptp.nat)) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) B2) A) (= B2 tptp.zero_zero_nat))) (forall ((A tptp.int) (B2 tptp.int)) (= (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) B2) A) (= B2 tptp.zero_zero_int))) (forall ((B2 tptp.complex) (A tptp.complex)) (= (= (tptp.aa_complex_complex (tptp.plus_plus_complex B2) A) A) (= B2 tptp.zero_zero_complex))) (forall ((B2 tptp.real) (A tptp.real)) (= (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real B2) A) A) (= B2 tptp.zero_zero_real))) (forall ((B2 tptp.rat) (A tptp.rat)) (= (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat B2) A) A) (= B2 tptp.zero_zero_rat))) (forall ((B2 tptp.nat) (A tptp.nat)) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat B2) A) A) (= B2 tptp.zero_zero_nat))) (forall ((B2 tptp.int) (A tptp.int)) (= (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int B2) A) A) (= B2 tptp.zero_zero_int))) (forall ((A tptp.real)) (= (= tptp.zero_zero_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) A)) (= A tptp.zero_zero_real))) (forall ((A tptp.rat)) (= (= tptp.zero_zero_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) A)) (= A tptp.zero_zero_rat))) (forall ((A tptp.int)) (= (= tptp.zero_zero_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) A)) (= A tptp.zero_zero_int))) (forall ((A tptp.complex)) (= (tptp.aa_complex_complex (tptp.plus_plus_complex A) tptp.zero_zero_complex) A)) (forall ((A tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) tptp.zero_zero_real) A)) (forall ((A tptp.rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) tptp.zero_zero_rat) A)) (forall ((A tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) tptp.zero_zero_nat) A)) (forall ((A tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) tptp.zero_zero_int) A)) (forall ((A tptp.complex)) (= (tptp.aa_complex_complex (tptp.minus_minus_complex A) A) tptp.zero_zero_complex)) (forall ((A tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A) A) tptp.zero_zero_real)) (forall ((A tptp.rat)) (= (tptp.aa_rat_rat (tptp.minus_minus_rat A) A) tptp.zero_zero_rat)) (forall ((A tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat A) A) tptp.zero_zero_nat)) (forall ((A tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) A) tptp.zero_zero_int)) (forall ((A tptp.complex)) (= (tptp.aa_complex_complex (tptp.minus_minus_complex A) tptp.zero_zero_complex) A)) (forall ((A tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A) tptp.zero_zero_real) A)) (forall ((A tptp.rat)) (= (tptp.aa_rat_rat (tptp.minus_minus_rat A) tptp.zero_zero_rat) A)) (forall ((A tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat A) tptp.zero_zero_nat) A)) (forall ((A tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) tptp.zero_zero_int) A)) (forall ((A tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)) (forall ((A tptp.complex)) (= (tptp.aa_complex_complex (tptp.minus_minus_complex A) tptp.zero_zero_complex) A)) (forall ((A tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A) tptp.zero_zero_real) A)) (forall ((A tptp.rat)) (= (tptp.aa_rat_rat (tptp.minus_minus_rat A) tptp.zero_zero_rat) A)) (forall ((A tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) tptp.zero_zero_int) A)) (forall ((A tptp.complex)) (= (tptp.aa_complex_complex (tptp.minus_minus_complex A) A) tptp.zero_zero_complex)) (forall ((A tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A) A) tptp.zero_zero_real)) (forall ((A tptp.rat)) (= (tptp.aa_rat_rat (tptp.minus_minus_rat A) A) tptp.zero_zero_rat)) (forall ((A tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) A) tptp.zero_zero_int)) (forall ((A tptp.complex) (B2 tptp.complex)) (= (= (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex A) B2) tptp.zero_zero_complex) (or (= A tptp.zero_zero_complex) (= B2 tptp.zero_zero_complex)))) (forall ((A tptp.real) (B2 tptp.real)) (= (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real A) B2) tptp.zero_zero_real) (or (= A tptp.zero_zero_real) (= B2 tptp.zero_zero_real)))) (forall ((A tptp.rat) (B2 tptp.rat)) (= (= (tptp.aa_rat_rat (tptp.divide_divide_rat A) B2) tptp.zero_zero_rat) (or (= A tptp.zero_zero_rat) (= B2 tptp.zero_zero_rat)))) (forall ((C tptp.complex) (A tptp.complex) (B2 tptp.complex)) (let ((_let_1 (tptp.divide1717551699836669952omplex C))) (= (= (tptp.aa_complex_complex _let_1 A) (tptp.aa_complex_complex _let_1 B2)) (or (= C tptp.zero_zero_complex) (= A B2))))) (forall ((C tptp.real) (A tptp.real) (B2 tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real C))) (= (= (tptp.aa_real_real _let_1 A) (tptp.aa_real_real _let_1 B2)) (or (= C tptp.zero_zero_real) (= A B2))))) (forall ((C tptp.rat) (A tptp.rat) (B2 tptp.rat)) (let ((_let_1 (tptp.divide_divide_rat C))) (= (= (tptp.aa_rat_rat _let_1 A) (tptp.aa_rat_rat _let_1 B2)) (or (= C tptp.zero_zero_rat) (= A B2))))) (forall ((A tptp.complex) (C tptp.complex) (B2 tptp.complex)) (= (= (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex A) C) (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex B2) C)) (or (= C tptp.zero_zero_complex) (= A B2)))) (forall ((A tptp.real) (C tptp.real) (B2 tptp.real)) (= (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real A) C) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real B2) C)) (or (= C tptp.zero_zero_real) (= A B2)))) (forall ((A tptp.rat) (C tptp.rat) (B2 tptp.rat)) (= (= (tptp.aa_rat_rat (tptp.divide_divide_rat A) C) (tptp.aa_rat_rat (tptp.divide_divide_rat B2) C)) (or (= C tptp.zero_zero_rat) (= A B2)))) (forall ((A tptp.complex)) (= (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex A) tptp.zero_zero_complex) tptp.zero_zero_complex)) (forall ((A tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real A) tptp.zero_zero_real) tptp.zero_zero_real)) (forall ((A tptp.rat)) (= (tptp.aa_rat_rat (tptp.divide_divide_rat A) tptp.zero_zero_rat) tptp.zero_zero_rat)) (forall ((A tptp.complex)) (= (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex tptp.zero_zero_complex) A) tptp.zero_zero_complex)) (forall ((A tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.zero_zero_real) A) tptp.zero_zero_real)) (forall ((A tptp.rat)) (= (tptp.aa_rat_rat (tptp.divide_divide_rat tptp.zero_zero_rat) A) tptp.zero_zero_rat)) (forall ((A tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)) (forall ((A tptp.int)) (= (tptp.aa_int_int (tptp.divide_divide_int tptp.zero_zero_int) A) tptp.zero_zero_int)) (forall ((A tptp.complex)) (= (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex A) tptp.zero_zero_complex) tptp.zero_zero_complex)) (forall ((A tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real A) tptp.zero_zero_real) tptp.zero_zero_real)) (forall ((A tptp.rat)) (= (tptp.aa_rat_rat (tptp.divide_divide_rat A) tptp.zero_zero_rat) tptp.zero_zero_rat)) (forall ((A tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) tptp.zero_zero_nat) tptp.zero_zero_nat)) (forall ((A tptp.int)) (= (tptp.aa_int_int (tptp.divide_divide_int A) tptp.zero_zero_int) tptp.zero_zero_int)) (forall ((A tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)) (forall ((A tptp.int)) (= (tptp.aa_int_int (tptp.divide_divide_int tptp.zero_zero_int) A) tptp.zero_zero_int)) (forall ((A tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) tptp.zero_zero_nat) tptp.zero_zero_nat)) (forall ((A tptp.int)) (= (tptp.aa_int_int (tptp.divide_divide_int A) tptp.zero_zero_int) tptp.zero_zero_int)) (forall ((A tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)) (forall ((A tptp.int)) (= (tptp.aa_int_int (tptp.modulo_modulo_int tptp.zero_zero_int) A) tptp.zero_zero_int)) (forall ((A tptp.code_integer)) (= (tptp.modulo364778990260209775nteger tptp.zero_z3403309356797280102nteger A) tptp.zero_z3403309356797280102nteger)) (forall ((A tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A) tptp.zero_zero_nat) A)) (forall ((A tptp.int)) (= (tptp.aa_int_int (tptp.modulo_modulo_int A) tptp.zero_zero_int) A)) (forall ((A tptp.code_integer)) (= (tptp.modulo364778990260209775nteger A tptp.zero_z3403309356797280102nteger) A)) (forall ((A tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A) A) tptp.zero_zero_nat)) (forall ((A tptp.int)) (= (tptp.aa_int_int (tptp.modulo_modulo_int A) A) tptp.zero_zero_int)) (forall ((A tptp.code_integer)) (= (tptp.modulo364778990260209775nteger A A) tptp.zero_z3403309356797280102nteger)) (forall ((A tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)) (forall ((A tptp.int)) (= (tptp.aa_int_int (tptp.modulo_modulo_int tptp.zero_zero_int) A) tptp.zero_zero_int)) (forall ((A tptp.code_integer)) (= (tptp.modulo364778990260209775nteger tptp.zero_z3403309356797280102nteger A) tptp.zero_z3403309356797280102nteger)) (forall ((N tptp.nat)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N) tptp.zero_zero_nat)))) (forall ((N tptp.nat)) (= (not (= N tptp.zero_zero_nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)))) (forall ((A tptp.nat)) (= (not (= A tptp.zero_zero_nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) A)))) (forall ((N tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) N))) (forall ((A tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) A))) (forall ((B2 tptp.nat) (A tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat B2) A)) B2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A) B2))) (forall ((B2 tptp.int) (A tptp.int)) (= (tptp.aa_int_int (tptp.modulo_modulo_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int B2) A)) B2) (tptp.aa_int_int (tptp.modulo_modulo_int A) B2))) (forall ((B2 tptp.code_integer) (A tptp.code_integer)) (= (tptp.modulo364778990260209775nteger (tptp.plus_p5714425477246183910nteger B2 A) B2) (tptp.modulo364778990260209775nteger A B2))) (forall ((A tptp.nat) (B2 tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) B2)) B2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A) B2))) (forall ((A tptp.int) (B2 tptp.int)) (= (tptp.aa_int_int (tptp.modulo_modulo_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) B2)) B2) (tptp.aa_int_int (tptp.modulo_modulo_int A) B2))) (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (= (tptp.modulo364778990260209775nteger (tptp.plus_p5714425477246183910nteger A B2) B2) (tptp.modulo364778990260209775nteger A B2))) (forall ((A tptp.int) (B2 tptp.int)) (= (tptp.aa_int_int (tptp.modulo_modulo_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) B2)) B2) (tptp.aa_int_int (tptp.modulo_modulo_int A) B2))) (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (= (tptp.modulo364778990260209775nteger (tptp.minus_8373710615458151222nteger A B2) B2) (tptp.modulo364778990260209775nteger A B2))) (forall ((M tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) tptp.zero_zero_nat) M)) (forall ((M tptp.nat) (N tptp.nat)) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) N) tptp.zero_zero_nat) (and (= M tptp.zero_zero_nat) (= N tptp.zero_zero_nat)))) (forall ((M tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) M) tptp.zero_zero_nat)) (forall ((N tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat tptp.zero_zero_nat) N) tptp.zero_zero_nat)) (forall ((M tptp.nat) (N tptp.nat)) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat M) N) tptp.zero_zero_nat) (or (= M tptp.zero_zero_nat) (= N tptp.zero_zero_nat)))) (forall ((M tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat M) tptp.zero_zero_nat) tptp.zero_zero_nat)) (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat K))) (= (= (tptp.aa_nat_nat _let_1 M) (tptp.aa_nat_nat _let_1 N)) (or (= M N) (= K tptp.zero_zero_nat))))) (forall ((M tptp.nat) (K tptp.nat) (N tptp.nat)) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat M) K) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat N) K)) (or (= M N) (= K tptp.zero_zero_nat)))) (forall ((M tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat M) N) M))) (forall ((B2 tptp.real) (A tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real B2) A)) B2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) tptp.zero_zero_real)))) (forall ((B2 tptp.rat) (A tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat B2) A)) B2)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) tptp.zero_zero_rat)))) (forall ((B2 tptp.nat) (A tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat B2) A)) B2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) tptp.zero_zero_nat)))) (forall ((B2 tptp.int) (A tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int B2) A)) B2)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) tptp.zero_zero_int)))) (forall ((A tptp.real) (B2 tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) B2)) B2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) tptp.zero_zero_real)))) (forall ((A tptp.rat) (B2 tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) B2)) B2)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) tptp.zero_zero_rat)))) (forall ((A tptp.nat) (B2 tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) B2)) B2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) tptp.zero_zero_nat)))) (forall ((A tptp.int) (B2 tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) B2)) B2)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) tptp.zero_zero_int)))) (forall ((A tptp.real) (B2 tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) B2))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) B2)))) (forall ((A tptp.rat) (B2 tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) B2))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) B2)))) (forall ((A tptp.nat) (B2 tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) B2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) B2)))) (forall ((A tptp.int) (B2 tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) B2))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) B2)))) (forall ((A tptp.real) (B2 tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real B2) A))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) B2)))) (forall ((A tptp.rat) (B2 tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat B2) A))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) B2)))) (forall ((A tptp.nat) (B2 tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat B2) A))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) B2)))) (forall ((A tptp.int) (B2 tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int B2) A))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) B2)))) (forall ((A tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) A)) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) tptp.zero_zero_real)))) (forall ((A tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) A)) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) tptp.zero_zero_rat)))) (forall ((A tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) A)) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) tptp.zero_zero_int)))) (forall ((A tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (= (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) A))) (tptp.pp (tptp.aa_real_bool _let_1 A))))) (forall ((A tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat))) (= (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) A))) (tptp.pp (tptp.aa_rat_bool _let_1 A))))) (forall ((A tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) A))) (tptp.pp (tptp.aa_int_bool _let_1 A))))) (forall ((A tptp.real) (B2 tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A) B2))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real B2) A)))) (forall ((A tptp.rat) (B2 tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_rat_rat (tptp.minus_minus_rat A) B2))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B2) A)))) (forall ((A tptp.int) (B2 tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) B2))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B2) A)))) (forall ((B2 tptp.real) (A tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real B2) A)) B2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) tptp.zero_zero_real)))) (forall ((B2 tptp.rat) (A tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat B2) A)) B2)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) tptp.zero_zero_rat)))) (forall ((B2 tptp.nat) (A tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat B2) A)) B2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) tptp.zero_zero_nat)))) (forall ((B2 tptp.int) (A tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int B2) A)) B2)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) tptp.zero_zero_int)))) (forall ((A tptp.real) (B2 tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) B2)) B2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) tptp.zero_zero_real)))) (forall ((A tptp.rat) (B2 tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) B2)) B2)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) tptp.zero_zero_rat)))) (forall ((A tptp.nat) (B2 tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) B2)) B2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) tptp.zero_zero_nat)))) (forall ((A tptp.int) (B2 tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) B2)) B2)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) tptp.zero_zero_int)))) (forall ((A tptp.real) (B2 tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) B2))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) B2)))) (forall ((A tptp.rat) (B2 tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) B2))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) B2)))) (forall ((A tptp.nat) (B2 tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) B2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) B2)))) (forall ((A tptp.int) (B2 tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) B2))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) B2)))) (forall ((A tptp.real) (B2 tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real B2) A))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) B2)))) (forall ((A tptp.rat) (B2 tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat B2) A))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) B2)))) (forall ((A tptp.nat) (B2 tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat B2) A))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) B2)))) (forall ((A tptp.int) (B2 tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int B2) A))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) B2)))) (forall ((A tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) A)) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) tptp.zero_zero_real)))) (forall ((A tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) A)) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) tptp.zero_zero_rat)))) (forall ((A tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) A)) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) tptp.zero_zero_int)))) (forall ((A tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real))) (= (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) A))) (tptp.pp (tptp.aa_real_bool _let_1 A))))) (forall ((A tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat))) (= (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) A))) (tptp.pp (tptp.aa_rat_bool _let_1 A))))) (forall ((A tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int))) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) A))) (tptp.pp (tptp.aa_int_bool _let_1 A))))) (forall ((A tptp.real) (B2 tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A) B2))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B2) A)))) (forall ((A tptp.rat) (B2 tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) (tptp.aa_rat_rat (tptp.minus_minus_rat A) B2))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B2) A)))) (forall ((A tptp.int) (B2 tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) B2))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B2) A)))) (forall ((C tptp.complex) (B2 tptp.complex)) (= (= C (tptp.aa_complex_complex (tptp.times_times_complex C) B2)) (or (= C tptp.zero_zero_complex) (= B2 tptp.one_one_complex)))) (forall ((C tptp.real) (B2 tptp.real)) (= (= C (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real C) B2)) (or (= C tptp.zero_zero_real) (= B2 tptp.one_one_real)))) (forall ((C tptp.rat) (B2 tptp.rat)) (= (= C (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat C) B2)) (or (= C tptp.zero_zero_rat) (= B2 tptp.one_one_rat)))) (forall ((C tptp.int) (B2 tptp.int)) (= (= C (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int C) B2)) (or (= C tptp.zero_zero_int) (= B2 tptp.one_one_int)))) (forall ((C tptp.complex) (A tptp.complex)) (= (= (tptp.aa_complex_complex (tptp.times_times_complex C) A) C) (or (= C tptp.zero_zero_complex) (= A tptp.one_one_complex)))) (forall ((C tptp.real) (A tptp.real)) (= (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real C) A) C) (or (= C tptp.zero_zero_real) (= A tptp.one_one_real)))) (forall ((C tptp.rat) (A tptp.rat)) (= (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat C) A) C) (or (= C tptp.zero_zero_rat) (= A tptp.one_one_rat)))) (forall ((C tptp.int) (A tptp.int)) (= (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int C) A) C) (or (= C tptp.zero_zero_int) (= A tptp.one_one_int)))) (forall ((C tptp.complex) (B2 tptp.complex)) (= (= C (tptp.aa_complex_complex (tptp.times_times_complex B2) C)) (or (= C tptp.zero_zero_complex) (= B2 tptp.one_one_complex)))) (forall ((C tptp.real) (B2 tptp.real)) (= (= C (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real B2) C)) (or (= C tptp.zero_zero_real) (= B2 tptp.one_one_real)))) (forall ((C tptp.rat) (B2 tptp.rat)) (= (= C (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat B2) C)) (or (= C tptp.zero_zero_rat) (= B2 tptp.one_one_rat)))) (forall ((C tptp.int) (B2 tptp.int)) (= (= C (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B2) C)) (or (= C tptp.zero_zero_int) (= B2 tptp.one_one_int)))) (forall ((A tptp.complex) (C tptp.complex)) (= (= (tptp.aa_complex_complex (tptp.times_times_complex A) C) C) (or (= C tptp.zero_zero_complex) (= A tptp.one_one_complex)))) (forall ((A tptp.real) (C tptp.real)) (= (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) C) C) (or (= C tptp.zero_zero_real) (= A tptp.one_one_real)))) (forall ((A tptp.rat) (C tptp.rat)) (= (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) C) C) (or (= C tptp.zero_zero_rat) (= A tptp.one_one_rat)))) (forall ((A tptp.int) (C tptp.int)) (= (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) C) C) (or (= C tptp.zero_zero_int) (= A tptp.one_one_int)))) (forall ((X tptp.real) (Y tptp.real)) (= (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real X) X)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real Y) Y)) tptp.zero_zero_real) (and (= X tptp.zero_zero_real) (= Y tptp.zero_zero_real)))) (forall ((X tptp.rat) (Y tptp.rat)) (= (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat X) X)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat Y) Y)) tptp.zero_zero_rat) (and (= X tptp.zero_zero_rat) (= Y tptp.zero_zero_rat)))) (forall ((X tptp.int) (Y tptp.int)) (= (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int X) X)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int Y) Y)) tptp.zero_zero_int) (and (= X tptp.zero_zero_int) (= Y tptp.zero_zero_int)))) (= (tptp.aa_complex_complex _let_129 tptp.one_one_complex) tptp.zero_zero_complex) (= (tptp.aa_real_real _let_131 tptp.one_one_real) tptp.zero_zero_real) (= (tptp.aa_rat_rat _let_128 tptp.one_one_rat) tptp.zero_zero_rat) (= (tptp.aa_int_int _let_130 tptp.one_one_int) tptp.zero_zero_int) (forall ((C tptp.complex) (A tptp.complex) (B2 tptp.complex)) (let ((_let_1 (tptp.times_times_complex C))) (let ((_let_2 (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex (tptp.aa_complex_complex _let_1 A)) (tptp.aa_complex_complex _let_1 B2)))) (let ((_let_3 (= C tptp.zero_zero_complex))) (and (=> _let_3 (= _let_2 tptp.zero_zero_complex)) (=> (not _let_3) (= _let_2 (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex A) B2)))))))) (forall ((C tptp.real) (A tptp.real) (B2 tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.times_times_real C))) (let ((_let_2 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real _let_1 A)) (tptp.aa_real_real _let_1 B2)))) (let ((_let_3 (= C tptp.zero_zero_real))) (and (=> _let_3 (= _let_2 tptp.zero_zero_real)) (=> (not _let_3) (= _let_2 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real A) B2)))))))) (forall ((C tptp.rat) (A tptp.rat) (B2 tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_rat tptp.times_times_rat C))) (let ((_let_2 (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_rat_rat _let_1 A)) (tptp.aa_rat_rat _let_1 B2)))) (let ((_let_3 (= C tptp.zero_zero_rat))) (and (=> _let_3 (= _let_2 tptp.zero_zero_rat)) (=> (not _let_3) (= _let_2 (tptp.aa_rat_rat (tptp.divide_divide_rat A) B2)))))))) (forall ((C tptp.complex) (A tptp.complex) (B2 tptp.complex)) (let ((_let_1 (tptp.times_times_complex C))) (=> (not (= C tptp.zero_zero_complex)) (= (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex (tptp.aa_complex_complex _let_1 A)) (tptp.aa_complex_complex _let_1 B2)) (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex A) B2))))) (forall ((C tptp.real) (A tptp.real) (B2 tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.times_times_real C))) (=> (not (= C tptp.zero_zero_real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real _let_1 A)) (tptp.aa_real_real _let_1 B2)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real A) B2))))) (forall ((C tptp.rat) (A tptp.rat) (B2 tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_rat tptp.times_times_rat C))) (=> (not (= C tptp.zero_zero_rat)) (= (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_rat_rat _let_1 A)) (tptp.aa_rat_rat _let_1 B2)) (tptp.aa_rat_rat (tptp.divide_divide_rat A) B2))))) (forall ((C tptp.complex) (A tptp.complex) (B2 tptp.complex)) (=> (not (= C tptp.zero_zero_complex)) (= (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex (tptp.aa_complex_complex (tptp.times_times_complex C) A)) (tptp.aa_complex_complex (tptp.times_times_complex B2) C)) (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex A) B2)))) (forall ((C tptp.real) (A tptp.real) (B2 tptp.real)) (=> (not (= C tptp.zero_zero_real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real C) A)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real B2) C)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real A) B2)))) (forall ((C tptp.rat) (A tptp.rat) (B2 tptp.rat)) (=> (not (= C tptp.zero_zero_rat)) (= (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat C) A)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat B2) C)) (tptp.aa_rat_rat (tptp.divide_divide_rat A) B2)))) (forall ((C tptp.complex) (A tptp.complex) (B2 tptp.complex)) (=> (not (= C tptp.zero_zero_complex)) (= (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex (tptp.aa_complex_complex (tptp.times_times_complex A) C)) (tptp.aa_complex_complex (tptp.times_times_complex B2) C)) (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex A) B2)))) (forall ((C tptp.real) (A tptp.real) (B2 tptp.real)) (=> (not (= C tptp.zero_zero_real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) C)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real B2) C)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real A) B2)))) (forall ((C tptp.rat) (A tptp.rat) (B2 tptp.rat)) (=> (not (= C tptp.zero_zero_rat)) (= (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) C)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat B2) C)) (tptp.aa_rat_rat (tptp.divide_divide_rat A) B2)))) (forall ((C tptp.complex) (A tptp.complex) (B2 tptp.complex)) (=> (not (= C tptp.zero_zero_complex)) (= (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex (tptp.aa_complex_complex (tptp.times_times_complex A) C)) (tptp.aa_complex_complex (tptp.times_times_complex C) B2)) (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex A) B2)))) (forall ((C tptp.real) (A tptp.real) (B2 tptp.real)) (=> (not (= C tptp.zero_zero_real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) C)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real C) B2)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real A) B2)))) (forall ((C tptp.rat) (A tptp.rat) (B2 tptp.rat)) (=> (not (= C tptp.zero_zero_rat)) (= (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) C)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat C) B2)) (tptp.aa_rat_rat (tptp.divide_divide_rat A) B2)))) (forall ((C tptp.nat) (A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat C))) (let ((_let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat _let_1 A)) (tptp.aa_nat_nat _let_1 B2)))) (let ((_let_3 (= C tptp.zero_zero_nat))) (and (=> _let_3 (= _let_2 tptp.zero_zero_nat)) (=> (not _let_3) (= _let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) B2)))))))) (forall ((C tptp.int) (A tptp.int) (B2 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.times_times_int C))) (let ((_let_2 (tptp.aa_int_int (tptp.divide_divide_int (tptp.aa_int_int _let_1 A)) (tptp.aa_int_int _let_1 B2)))) (let ((_let_3 (= C tptp.zero_zero_int))) (and (=> _let_3 (= _let_2 tptp.zero_zero_int)) (=> (not _let_3) (= _let_2 (tptp.aa_int_int (tptp.divide_divide_int A) B2)))))))) (forall ((C tptp.nat) (A tptp.nat) (B2 tptp.nat)) (=> (not (= C tptp.zero_zero_nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) C)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B2) C)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) B2)))) (forall ((C tptp.int) (A tptp.int) (B2 tptp.int)) (=> (not (= C tptp.zero_zero_int)) (= (tptp.aa_int_int (tptp.divide_divide_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B2) C)) (tptp.aa_int_int (tptp.divide_divide_int A) B2)))) (forall ((C tptp.nat) (A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat C))) (=> (not (= C tptp.zero_zero_nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat _let_1 A)) (tptp.aa_nat_nat _let_1 B2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) B2))))) (forall ((C tptp.int) (A tptp.int) (B2 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.times_times_int C))) (=> (not (= C tptp.zero_zero_int)) (= (tptp.aa_int_int (tptp.divide_divide_int (tptp.aa_int_int _let_1 A)) (tptp.aa_int_int _let_1 B2)) (tptp.aa_int_int (tptp.divide_divide_int A) B2))))) (forall ((A tptp.complex) (B2 tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex (tptp.aa_complex_complex (tptp.times_times_complex A) B2)) A) B2))) (forall ((A tptp.real) (B2 tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) B2)) A) B2))) (forall ((A tptp.rat) (B2 tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (= (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) B2)) A) B2))) (forall ((A tptp.nat) (B2 tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) B2)) A) B2))) (forall ((A tptp.int) (B2 tptp.int)) (=> (not (= A tptp.zero_zero_int)) (= (tptp.aa_int_int (tptp.divide_divide_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) B2)) A) B2))) (forall ((B2 tptp.complex) (A tptp.complex)) (=> (not (= B2 tptp.zero_zero_complex)) (= (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex (tptp.aa_complex_complex (tptp.times_times_complex A) B2)) B2) A))) (forall ((B2 tptp.real) (A tptp.real)) (=> (not (= B2 tptp.zero_zero_real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) B2)) B2) A))) (forall ((B2 tptp.rat) (A tptp.rat)) (=> (not (= B2 tptp.zero_zero_rat)) (= (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) B2)) B2) A))) (forall ((B2 tptp.nat) (A tptp.nat)) (=> (not (= B2 tptp.zero_zero_nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) B2)) B2) A))) (forall ((B2 tptp.int) (A tptp.int)) (=> (not (= B2 tptp.zero_zero_int)) (= (tptp.aa_int_int (tptp.divide_divide_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) B2)) B2) A))) (forall ((A tptp.nat) (B2 tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) B2)) tptp.zero_zero_nat)) (forall ((A tptp.complex) (B2 tptp.complex)) (= (= (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex A) B2) tptp.one_one_complex) (and (not (= B2 tptp.zero_zero_complex)) (= A B2)))) (forall ((A tptp.real) (B2 tptp.real)) (= (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real A) B2) tptp.one_one_real) (and (not (= B2 tptp.zero_zero_real)) (= A B2)))) (forall ((A tptp.rat) (B2 tptp.rat)) (= (= (tptp.aa_rat_rat (tptp.divide_divide_rat A) B2) tptp.one_one_rat) (and (not (= B2 tptp.zero_zero_rat)) (= A B2)))) (forall ((A tptp.complex) (B2 tptp.complex)) (= (= tptp.one_one_complex (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex A) B2)) (and (not (= B2 tptp.zero_zero_complex)) (= A B2)))) (forall ((A tptp.real) (B2 tptp.real)) (= (= tptp.one_one_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real A) B2)) (and (not (= B2 tptp.zero_zero_real)) (= A B2)))) (forall ((A tptp.rat) (B2 tptp.rat)) (= (= tptp.one_one_rat (tptp.aa_rat_rat (tptp.divide_divide_rat A) B2)) (and (not (= B2 tptp.zero_zero_rat)) (= A B2)))) (forall ((A tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex A) A) tptp.one_one_complex))) (forall ((A tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real A) A) tptp.one_one_real))) (forall ((A tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (= (tptp.aa_rat_rat (tptp.divide_divide_rat A) A) tptp.one_one_rat))) (forall ((A tptp.complex)) (let ((_let_1 (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex A) A))) (let ((_let_2 (= A tptp.zero_zero_complex))) (and (=> _let_2 (= _let_1 tptp.zero_zero_complex)) (=> (not _let_2) (= _let_1 tptp.one_one_complex)))))) (forall ((A tptp.real)) (let ((_let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real A) A))) (let ((_let_2 (= A tptp.zero_zero_real))) (and (=> _let_2 (= _let_1 tptp.zero_zero_real)) (=> (not _let_2) (= _let_1 tptp.one_one_real)))))) (forall ((A tptp.rat)) (let ((_let_1 (tptp.aa_rat_rat (tptp.divide_divide_rat A) A))) (let ((_let_2 (= A tptp.zero_zero_rat))) (and (=> _let_2 (= _let_1 tptp.zero_zero_rat)) (=> (not _let_2) (= _let_1 tptp.one_one_rat)))))) (forall ((B2 tptp.real) (A tptp.real)) (= (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real B2) A) tptp.one_one_real) (and (not (= A tptp.zero_zero_real)) (= A B2)))) (forall ((B2 tptp.rat) (A tptp.rat)) (= (= (tptp.aa_rat_rat (tptp.divide_divide_rat B2) A) tptp.one_one_rat) (and (not (= A tptp.zero_zero_rat)) (= A B2)))) (forall ((B2 tptp.real) (A tptp.real)) (= (= tptp.one_one_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real B2) A)) (and (not (= A tptp.zero_zero_real)) (= A B2)))) (forall ((B2 tptp.rat) (A tptp.rat)) (= (= tptp.one_one_rat (tptp.aa_rat_rat (tptp.divide_divide_rat B2) A)) (and (not (= A tptp.zero_zero_rat)) (= A B2)))) (forall ((A tptp.real)) (= (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.one_one_real) A) tptp.zero_zero_real) (= A tptp.zero_zero_real))) (forall ((A tptp.rat)) (= (= (tptp.aa_rat_rat (tptp.divide_divide_rat tptp.one_one_rat) A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))) (forall ((A tptp.real)) (= (= tptp.zero_zero_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.one_one_real) A)) (= A tptp.zero_zero_real))) (forall ((A tptp.rat)) (= (= tptp.zero_zero_rat (tptp.aa_rat_rat (tptp.divide_divide_rat tptp.one_one_rat) A)) (= A tptp.zero_zero_rat))) (forall ((A tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex A) A) tptp.one_one_complex))) (forall ((A tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real A) A) tptp.one_one_real))) (forall ((A tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (= (tptp.aa_rat_rat (tptp.divide_divide_rat A) A) tptp.one_one_rat))) (forall ((A tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) A) tptp.one_one_nat))) (forall ((A tptp.int)) (=> (not (= A tptp.zero_zero_int)) (= (tptp.aa_int_int (tptp.divide_divide_int A) A) tptp.one_one_int))) (forall ((N tptp.nat)) (= (tptp.aa_nat_rat (tptp.power_power_rat tptp.zero_zero_rat) (tptp.aa_nat_nat tptp.suc N)) tptp.zero_zero_rat)) (forall ((N tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat tptp.zero_zero_nat) (tptp.aa_nat_nat tptp.suc N)) tptp.zero_zero_nat)) (forall ((N tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real tptp.zero_zero_real) (tptp.aa_nat_nat tptp.suc N)) tptp.zero_zero_real)) (forall ((N tptp.nat)) (= (tptp.aa_nat_int (tptp.power_power_int tptp.zero_zero_int) (tptp.aa_nat_nat tptp.suc N)) tptp.zero_zero_int)) (forall ((N tptp.nat)) (= (tptp.aa_nat_complex (tptp.power_power_complex tptp.zero_zero_complex) (tptp.aa_nat_nat tptp.suc N)) tptp.zero_zero_complex)) (forall ((K tptp.num)) (= (tptp.aa_nat_rat (tptp.power_power_rat tptp.zero_zero_rat) (tptp.aa_num_nat tptp.numeral_numeral_nat K)) tptp.zero_zero_rat)) (forall ((K tptp.num)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat tptp.zero_zero_nat) (tptp.aa_num_nat tptp.numeral_numeral_nat K)) tptp.zero_zero_nat)) (forall ((K tptp.num)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real tptp.zero_zero_real) (tptp.aa_num_nat tptp.numeral_numeral_nat K)) tptp.zero_zero_real)) (forall ((K tptp.num)) (= (tptp.aa_nat_int (tptp.power_power_int tptp.zero_zero_int) (tptp.aa_num_nat tptp.numeral_numeral_nat K)) tptp.zero_zero_int)) (forall ((K tptp.num)) (= (tptp.aa_nat_complex (tptp.power_power_complex tptp.zero_zero_complex) (tptp.aa_num_nat tptp.numeral_numeral_nat K)) tptp.zero_zero_complex)) (forall ((B2 tptp.nat) (A tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B2) A)) B2) tptp.zero_zero_nat)) (forall ((B2 tptp.int) (A tptp.int)) (= (tptp.aa_int_int (tptp.modulo_modulo_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B2) A)) B2) tptp.zero_zero_int)) (forall ((B2 tptp.code_integer) (A tptp.code_integer)) (= (tptp.modulo364778990260209775nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B2) A) B2) tptp.zero_z3403309356797280102nteger)) (forall ((A tptp.nat) (B2 tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) B2)) B2) tptp.zero_zero_nat)) (forall ((A tptp.int) (B2 tptp.int)) (= (tptp.aa_int_int (tptp.modulo_modulo_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) B2)) B2) tptp.zero_zero_int)) (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (= (tptp.modulo364778990260209775nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) B2) B2) tptp.zero_z3403309356797280102nteger)) (forall ((A tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A) tptp.one_one_nat) tptp.zero_zero_nat)) (forall ((A tptp.int)) (= (tptp.aa_int_int (tptp.modulo_modulo_int A) tptp.one_one_int) tptp.zero_zero_int)) (forall ((A tptp.code_integer)) (= (tptp.modulo364778990260209775nteger A tptp.one_one_Code_integer) tptp.zero_z3403309356797280102nteger)) (forall ((A tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A) tptp.one_one_nat) tptp.zero_zero_nat)) (forall ((A tptp.int)) (= (tptp.aa_int_int (tptp.modulo_modulo_int A) tptp.one_one_int) tptp.zero_zero_int)) (forall ((A tptp.code_integer)) (= (tptp.modulo364778990260209775nteger A tptp.one_one_Code_integer) tptp.zero_z3403309356797280102nteger)) (forall ((A tptp.nat) (B2 tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A) B2)) B2) tptp.zero_zero_nat)) (forall ((A tptp.int) (B2 tptp.int)) (= (tptp.aa_int_int (tptp.divide_divide_int (tptp.aa_int_int (tptp.modulo_modulo_int A) B2)) B2) tptp.zero_zero_int)) (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (= (tptp.divide6298287555418463151nteger (tptp.modulo364778990260209775nteger A B2) B2) tptp.zero_z3403309356797280102nteger)) (forall ((A tptp.nat) (B2 tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A) B2)) B2) tptp.zero_zero_nat)) (forall ((A tptp.int) (B2 tptp.int)) (= (tptp.aa_int_int (tptp.divide_divide_int (tptp.aa_int_int (tptp.modulo_modulo_int A) B2)) B2) tptp.zero_zero_int)) (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (= (tptp.divide6298287555418463151nteger (tptp.modulo364778990260209775nteger A B2) B2) tptp.zero_z3403309356797280102nteger)) (forall ((A tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)) A)) (forall ((A tptp.real)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real A) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)) A)) (forall ((A tptp.int)) (= (tptp.aa_nat_int (tptp.power_power_int A) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)) A)) (forall ((A tptp.complex)) (= (tptp.aa_nat_complex (tptp.power_power_complex A) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)) A)) (forall ((A tptp.nat) (C tptp.nat) (B2 tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat C) B2))) B2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A) B2))) (forall ((A tptp.int) (C tptp.int) (B2 tptp.int)) (= (tptp.aa_int_int (tptp.modulo_modulo_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int C) B2))) B2) (tptp.aa_int_int (tptp.modulo_modulo_int A) B2))) (forall ((A tptp.code_integer) (C tptp.code_integer) (B2 tptp.code_integer)) (= (tptp.modulo364778990260209775nteger (tptp.plus_p5714425477246183910nteger A (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger C) B2)) B2) (tptp.modulo364778990260209775nteger A B2))) (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B2) C))) B2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A) B2))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (= (tptp.aa_int_int (tptp.modulo_modulo_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B2) C))) B2) (tptp.aa_int_int (tptp.modulo_modulo_int A) B2))) (forall ((A tptp.code_integer) (B2 tptp.code_integer) (C tptp.code_integer)) (= (tptp.modulo364778990260209775nteger (tptp.plus_p5714425477246183910nteger A (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B2) C)) B2) (tptp.modulo364778990260209775nteger A B2))) (forall ((C tptp.nat) (B2 tptp.nat) (A tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat C) B2)) A)) B2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A) B2))) (forall ((C tptp.int) (B2 tptp.int) (A tptp.int)) (= (tptp.aa_int_int (tptp.modulo_modulo_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int C) B2)) A)) B2) (tptp.aa_int_int (tptp.modulo_modulo_int A) B2))) (forall ((C tptp.code_integer) (B2 tptp.code_integer) (A tptp.code_integer)) (= (tptp.modulo364778990260209775nteger (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger C) B2) A) B2) (tptp.modulo364778990260209775nteger A B2))) (forall ((B2 tptp.nat) (C tptp.nat) (A tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B2) C)) A)) B2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A) B2))) (forall ((B2 tptp.int) (C tptp.int) (A tptp.int)) (= (tptp.aa_int_int (tptp.modulo_modulo_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B2) C)) A)) B2) (tptp.aa_int_int (tptp.modulo_modulo_int A) B2))) (forall ((B2 tptp.code_integer) (C tptp.code_integer) (A tptp.code_integer)) (= (tptp.modulo364778990260209775nteger (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B2) C) A) B2) (tptp.modulo364778990260209775nteger A B2))) (forall ((N tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.aa_nat_nat tptp.suc N)))) (forall ((N tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat))) (= N tptp.zero_zero_nat))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat))) (= (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) N))) (or (tptp.pp (tptp.aa_nat_bool _let_1 M)) (tptp.pp (tptp.aa_nat_bool _let_1 N)))))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat))) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat M) N) _let_1) (and (= M _let_1) (= N _let_1))))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat))) (= (= _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat M) N)) (and (= M _let_1) (= N _let_1))))) (forall ((N tptp.nat) (M tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) M))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N)))) (forall ((M tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat M) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)) M)) (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat K))) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat _let_1 M)) (tptp.aa_nat_nat _let_1 N))) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) K)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N)))))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat))) (= (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat M) N))) (and (tptp.pp (tptp.aa_nat_bool _let_1 M)) (tptp.pp (tptp.aa_nat_bool _let_1 N)))))) (forall ((M tptp.nat) (K tptp.nat) (N tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat M) K)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat N) K))) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) K)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N))))) (forall ((M tptp.nat) (N tptp.nat)) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) N) tptp.zero_zero_nat) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)))) (forall ((M tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) N) tptp.zero_zero_nat))) (forall ((M tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat M) N) tptp.zero_zero_nat))) (forall ((N tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N) tptp.one_one_nat)) (= N tptp.zero_zero_nat))) (forall ((N tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat _let_1) N) _let_1))) (forall ((X tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat))) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat X) M) _let_1) (or (= M tptp.zero_zero_nat) (= X _let_1))))) (forall ((X tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat))) (= (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat X) N))) (or (tptp.pp (tptp.aa_nat_bool _let_1 X)) (= N tptp.zero_zero_nat))))) (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat K))) (let ((_let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat _let_1 M)) (tptp.aa_nat_nat _let_1 N)))) (let ((_let_3 (= K tptp.zero_zero_nat))) (and (=> _let_3 (= _let_2 tptp.zero_zero_nat)) (=> (not _let_3) (= _let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat M) N)))))))) (forall ((M tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat M) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)) tptp.zero_zero_nat)) (forall ((A tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (= (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.one_one_real) A))) (tptp.pp (tptp.aa_real_bool _let_1 A))))) (forall ((A tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat))) (= (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat (tptp.divide_divide_rat tptp.one_one_rat) A))) (tptp.pp (tptp.aa_rat_bool _let_1 A))))) (forall ((A tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.one_one_real) A)) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) tptp.zero_zero_real)))) (forall ((A tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.divide_divide_rat tptp.one_one_rat) A)) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) tptp.zero_zero_rat)))) (forall ((A tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real))) (= (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.one_one_real) A))) (tptp.pp (tptp.aa_real_bool _let_1 A))))) (forall ((A tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat))) (= (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat (tptp.divide_divide_rat tptp.one_one_rat) A))) (tptp.pp (tptp.aa_rat_bool _let_1 A))))) (forall ((A tptp.real) (B2 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) A)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real B2) A))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B2))))) (forall ((A tptp.rat) (B2 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) A)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.one_one_rat) (tptp.aa_rat_rat (tptp.divide_divide_rat B2) A))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B2))))) (forall ((A tptp.real) (B2 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) tptp.zero_zero_real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real B2) A))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B2) A))))) (forall ((A tptp.rat) (B2 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) tptp.zero_zero_rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.one_one_rat) (tptp.aa_rat_rat (tptp.divide_divide_rat B2) A))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B2) A))))) (forall ((A tptp.real) (B2 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) A)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real B2) A)) tptp.one_one_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B2) A))))) (forall ((A tptp.rat) (B2 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) A)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.divide_divide_rat B2) A)) tptp.one_one_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B2) A))))) (forall ((A tptp.real) (B2 tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A))) (=> (tptp.pp (tptp.aa_real_bool _let_1 tptp.zero_zero_real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real B2) A)) tptp.one_one_real)) (tptp.pp (tptp.aa_real_bool _let_1 B2)))))) (forall ((A tptp.rat) (B2 tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 tptp.zero_zero_rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.divide_divide_rat B2) A)) tptp.one_one_rat)) (tptp.pp (tptp.aa_rat_bool _let_1 B2)))))) (forall ((A tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.one_one_real) A)) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) tptp.zero_zero_real)))) (forall ((A tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.divide_divide_rat tptp.one_one_rat) A)) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) tptp.zero_zero_rat)))) (forall ((B2 tptp.complex) (W tptp.num) (A tptp.complex)) (let ((_let_1 (tptp.numera6690914467698888265omplex W))) (let ((_let_2 (= _let_1 tptp.zero_zero_complex))) (= (= (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex B2) _let_1) A) (and (=> (not _let_2) (= B2 (tptp.aa_complex_complex (tptp.times_times_complex A) _let_1))) (=> _let_2 (= A tptp.zero_zero_complex))))))) (forall ((B2 tptp.real) (W tptp.num) (A tptp.real)) (let ((_let_1 (tptp.aa_num_real tptp.numeral_numeral_real W))) (let ((_let_2 (= _let_1 tptp.zero_zero_real))) (= (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real B2) _let_1) A) (and (=> (not _let_2) (= B2 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) _let_1))) (=> _let_2 (= A tptp.zero_zero_real))))))) (forall ((B2 tptp.rat) (W tptp.num) (A tptp.rat)) (let ((_let_1 (tptp.aa_num_rat tptp.numeral_numeral_rat W))) (let ((_let_2 (= _let_1 tptp.zero_zero_rat))) (= (= (tptp.aa_rat_rat (tptp.divide_divide_rat B2) _let_1) A) (and (=> (not _let_2) (= B2 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) _let_1))) (=> _let_2 (= A tptp.zero_zero_rat))))))) (forall ((A tptp.complex) (B2 tptp.complex) (W tptp.num)) (let ((_let_1 (tptp.numera6690914467698888265omplex W))) (let ((_let_2 (= _let_1 tptp.zero_zero_complex))) (= (= A (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex B2) _let_1)) (and (=> (not _let_2) (= (tptp.aa_complex_complex (tptp.times_times_complex A) _let_1) B2)) (=> _let_2 (= A tptp.zero_zero_complex))))))) (forall ((A tptp.real) (B2 tptp.real) (W tptp.num)) (let ((_let_1 (tptp.aa_num_real tptp.numeral_numeral_real W))) (let ((_let_2 (= _let_1 tptp.zero_zero_real))) (= (= A (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real B2) _let_1)) (and (=> (not _let_2) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) _let_1) B2)) (=> _let_2 (= A tptp.zero_zero_real))))))) (forall ((A tptp.rat) (B2 tptp.rat) (W tptp.num)) (let ((_let_1 (tptp.aa_num_rat tptp.numeral_numeral_rat W))) (let ((_let_2 (= _let_1 tptp.zero_zero_rat))) (= (= A (tptp.aa_rat_rat (tptp.divide_divide_rat B2) _let_1)) (and (=> (not _let_2) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) _let_1) B2)) (=> _let_2 (= A tptp.zero_zero_rat))))))) (forall ((A tptp.complex) (B2 tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex A) (tptp.aa_complex_complex (tptp.times_times_complex A) B2)) (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex tptp.one_one_complex) B2)))) (forall ((A tptp.real) (B2 tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real A) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) B2)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.one_one_real) B2)))) (forall ((A tptp.rat) (B2 tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (= (tptp.aa_rat_rat (tptp.divide_divide_rat A) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) B2)) (tptp.aa_rat_rat (tptp.divide_divide_rat tptp.one_one_rat) B2)))) (forall ((B2 tptp.complex) (A tptp.complex)) (=> (not (= B2 tptp.zero_zero_complex)) (= (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex B2) (tptp.aa_complex_complex (tptp.times_times_complex A) B2)) (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex tptp.one_one_complex) A)))) (forall ((B2 tptp.real) (A tptp.real)) (=> (not (= B2 tptp.zero_zero_real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real B2) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) B2)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.one_one_real) A)))) (forall ((B2 tptp.rat) (A tptp.rat)) (=> (not (= B2 tptp.zero_zero_rat)) (= (tptp.aa_rat_rat (tptp.divide_divide_rat B2) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) B2)) (tptp.aa_rat_rat (tptp.divide_divide_rat tptp.one_one_rat) A)))) (forall ((B2 tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (not (= B2 tptp.zero_zero_nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat C) B2))) B2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat C) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) B2))))) (forall ((B2 tptp.int) (A tptp.int) (C tptp.int)) (=> (not (= B2 tptp.zero_zero_int)) (= (tptp.aa_int_int (tptp.divide_divide_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int C) B2))) B2) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int C) (tptp.aa_int_int (tptp.divide_divide_int A) B2))))) (forall ((B2 tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (not (= B2 tptp.zero_zero_nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B2) C))) B2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat C) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) B2))))) (forall ((B2 tptp.int) (A tptp.int) (C tptp.int)) (=> (not (= B2 tptp.zero_zero_int)) (= (tptp.aa_int_int (tptp.divide_divide_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B2) C))) B2) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int C) (tptp.aa_int_int (tptp.divide_divide_int A) B2))))) (forall ((B2 tptp.nat) (C tptp.nat) (A tptp.nat)) (=> (not (= B2 tptp.zero_zero_nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat C) B2)) A)) B2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat C) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) B2))))) (forall ((B2 tptp.int) (C tptp.int) (A tptp.int)) (=> (not (= B2 tptp.zero_zero_int)) (= (tptp.aa_int_int (tptp.divide_divide_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int C) B2)) A)) B2) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int C) (tptp.aa_int_int (tptp.divide_divide_int A) B2))))) (forall ((B2 tptp.nat) (C tptp.nat) (A tptp.nat)) (=> (not (= B2 tptp.zero_zero_nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B2) C)) A)) B2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat C) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) B2))))) (forall ((B2 tptp.int) (C tptp.int) (A tptp.int)) (=> (not (= B2 tptp.zero_zero_int)) (= (tptp.aa_int_int (tptp.divide_divide_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B2) C)) A)) B2) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int C) (tptp.aa_int_int (tptp.divide_divide_int A) B2))))) (forall ((A tptp.rat) (N tptp.nat)) (= (= (tptp.aa_nat_rat (tptp.power_power_rat A) N) tptp.zero_zero_rat) (and (= A tptp.zero_zero_rat) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N))))) (forall ((A tptp.nat) (N tptp.nat)) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A) N) tptp.zero_zero_nat) (and (= A tptp.zero_zero_nat) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N))))) (forall ((A tptp.real) (N tptp.nat)) (= (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real A) N) tptp.zero_zero_real) (and (= A tptp.zero_zero_real) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N))))) (forall ((A tptp.int) (N tptp.nat)) (= (= (tptp.aa_nat_int (tptp.power_power_int A) N) tptp.zero_zero_int) (and (= A tptp.zero_zero_int) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N))))) (forall ((A tptp.complex) (N tptp.nat)) (= (= (tptp.aa_nat_complex (tptp.power_power_complex A) N) tptp.zero_zero_complex) (and (= A tptp.zero_zero_complex) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N))))) (forall ((N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (= (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat))) N))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)))) (= (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat M) N))) (and (tptp.pp (tptp.aa_nat_bool _let_1 M)) (tptp.pp (tptp.aa_nat_bool _let_1 N)))))) (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat K))) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat _let_1 M)) (tptp.aa_nat_nat _let_1 N))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) K)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)))))) (forall ((M tptp.nat) (K tptp.nat) (N tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat M) K)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat N) K))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) K)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N))))) (forall ((N tptp.nat) (M tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat N) M)) N) M))) (forall ((N tptp.nat) (M tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat M) N)) N) M))) (forall ((M tptp.nat) (K tptp.nat) (N tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat K) N)))) N) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat tptp.suc M)) N))) (forall ((M tptp.nat) (N tptp.nat) (K tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat N) K)))) N) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat tptp.suc M)) N))) (forall ((K tptp.nat) (N tptp.nat) (M tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat K) N)) M))) N) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat tptp.suc M)) N))) (forall ((N tptp.nat) (K tptp.nat) (M tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat N) K)) M))) N) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat tptp.suc M)) N))) (forall ((A tptp.real) (B2 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) A)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.one_one_real) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real B2) A))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) B2))))) (forall ((A tptp.rat) (B2 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) A)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.one_one_rat) (tptp.aa_rat_rat (tptp.divide_divide_rat B2) A))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B2))))) (forall ((A tptp.real) (B2 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) tptp.zero_zero_real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.one_one_real) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real B2) A))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real B2) A))))) (forall ((A tptp.rat) (B2 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) tptp.zero_zero_rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.one_one_rat) (tptp.aa_rat_rat (tptp.divide_divide_rat B2) A))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B2) A))))) (forall ((A tptp.real) (B2 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) A)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real B2) A)) tptp.one_one_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real B2) A))))) (forall ((A tptp.rat) (B2 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) A)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.divide_divide_rat B2) A)) tptp.one_one_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B2) A))))) (forall ((A tptp.real) (B2 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) tptp.zero_zero_real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real B2) A)) tptp.one_one_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) B2))))) (forall ((A tptp.rat) (B2 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) tptp.zero_zero_rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.divide_divide_rat B2) A)) tptp.one_one_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B2))))) (forall ((B2 tptp.real) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_real_fun_nat_real tptp.power_power_real B2))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) B2)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B2) tptp.one_one_real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_nat_real _let_1 M)) (tptp.aa_nat_real _let_1 N))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N) M))))))) (forall ((B2 tptp.rat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.power_power_rat B2))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) B2)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B2) tptp.one_one_rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_nat_rat _let_1 M)) (tptp.aa_nat_rat _let_1 N))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N) M))))))) (forall ((B2 tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat B2))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) B2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat B2) tptp.one_one_nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat _let_1 M)) (tptp.aa_nat_nat _let_1 N))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N) M))))))) (forall ((B2 tptp.int) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.power_power_int B2))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) B2)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B2) tptp.one_one_int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_nat_int _let_1 M)) (tptp.aa_nat_int _let_1 N))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N) M))))))) (forall ((A tptp.real) (B2 tptp.real) (N tptp.nat)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool _let_1 A)) (=> (tptp.pp (tptp.aa_real_bool _let_1 B2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real A) N)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real B2) N))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) B2)))))))) (forall ((A tptp.rat) (B2 tptp.rat) (N tptp.nat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 A)) (=> (tptp.pp (tptp.aa_rat_bool _let_1 B2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat (tptp.power_power_rat A) N)) (tptp.aa_nat_rat (tptp.power_power_rat B2) N))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B2)))))))) (forall ((A tptp.nat) (B2 tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 A)) (=> (tptp.pp (tptp.aa_nat_bool _let_1 B2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A) N)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat B2) N))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B2)))))))) (forall ((A tptp.int) (B2 tptp.int) (N tptp.nat)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.pp (tptp.aa_int_bool _let_1 A)) (=> (tptp.pp (tptp.aa_int_bool _let_1 B2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int (tptp.power_power_int A) N)) (tptp.aa_nat_int (tptp.power_power_int B2) N))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B2)))))))) (forall ((A tptp.rat)) (= (= (tptp.aa_nat_rat (tptp.power_power_rat A) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))) (forall ((A tptp.nat)) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) tptp.zero_zero_nat) (= A tptp.zero_zero_nat))) (forall ((A tptp.real)) (= (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real A) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) tptp.zero_zero_real) (= A tptp.zero_zero_real))) (forall ((A tptp.int)) (= (= (tptp.aa_nat_int (tptp.power_power_int A) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) tptp.zero_zero_int) (= A tptp.zero_zero_int))) (forall ((A tptp.complex)) (= (= (tptp.aa_nat_complex (tptp.power_power_complex A) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) tptp.zero_zero_complex) (= A tptp.zero_zero_complex))) _let_166 _let_165 _let_164 _let_166 _let_165 _let_164 (forall ((M tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat tptp.suc M))) _let_1) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat M) _let_1)))) (forall ((N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (= (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) tptp.one_one_nat)) N))) (forall ((K tptp.num) (N tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat K))) (=> (not (= _let_1 tptp.one_one_nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat _let_1) N))) _let_1) tptp.one_one_nat)))) _let_163 _let_162 _let_163 _let_162 (forall ((B2 tptp.real) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_real_fun_nat_real tptp.power_power_real B2))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) B2)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B2) tptp.one_one_real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_nat_real _let_1 M)) (tptp.aa_nat_real _let_1 N))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N) M))))))) (forall ((B2 tptp.rat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.power_power_rat B2))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) B2)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B2) tptp.one_one_rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat _let_1 M)) (tptp.aa_nat_rat _let_1 N))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N) M))))))) (forall ((B2 tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat B2))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) B2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat B2) tptp.one_one_nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat _let_1 M)) (tptp.aa_nat_nat _let_1 N))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N) M))))))) (forall ((B2 tptp.int) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.power_power_int B2))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) B2)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B2) tptp.one_one_int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int _let_1 M)) (tptp.aa_nat_int _let_1 N))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N) M))))))) (forall ((A tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real A) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) tptp.zero_zero_real)) (= A tptp.zero_zero_real))) (forall ((A tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat (tptp.power_power_rat A) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) tptp.zero_zero_rat)) (= A tptp.zero_zero_rat))) (forall ((A tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int (tptp.power_power_int A) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) tptp.zero_zero_int)) (= A tptp.zero_zero_int))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool _let_2 X)) (=> (tptp.pp (tptp.aa_real_bool _let_2 Y)) (= (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) _let_1) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Y) _let_1)) (= X Y))))))) (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (tptp.pp (tptp.aa_rat_bool _let_2 X)) (=> (tptp.pp (tptp.aa_rat_bool _let_2 Y)) (= (= (tptp.aa_nat_rat (tptp.power_power_rat X) _let_1) (tptp.aa_nat_rat (tptp.power_power_rat Y) _let_1)) (= X Y))))))) (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (tptp.pp (tptp.aa_nat_bool _let_2 X)) (=> (tptp.pp (tptp.aa_nat_bool _let_2 Y)) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat X) _let_1) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat Y) _let_1)) (= X Y))))))) (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.pp (tptp.aa_int_bool _let_2 X)) (=> (tptp.pp (tptp.aa_int_bool _let_2 Y)) (= (= (tptp.aa_nat_int (tptp.power_power_int X) _let_1) (tptp.aa_nat_int (tptp.power_power_int Y) _let_1)) (= X Y))))))) (forall ((A tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real A) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (not (= A tptp.zero_zero_real)))) (forall ((A tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) (tptp.aa_nat_rat (tptp.power_power_rat A) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (not (= A tptp.zero_zero_rat)))) (forall ((A tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) (tptp.aa_nat_int (tptp.power_power_int A) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (not (= A tptp.zero_zero_int)))) (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_nat_rat (tptp.power_power_rat X) _let_1)) (tptp.aa_nat_rat (tptp.power_power_rat Y) _let_1)) tptp.zero_zero_rat) (and (= X tptp.zero_zero_rat) (= Y tptp.zero_zero_rat))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) _let_1)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Y) _let_1)) tptp.zero_zero_real) (and (= X tptp.zero_zero_real) (= Y tptp.zero_zero_real))))) (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_nat_int (tptp.power_power_int X) _let_1)) (tptp.aa_nat_int (tptp.power_power_int Y) _let_1)) tptp.zero_zero_int) (and (= X tptp.zero_zero_int) (= Y tptp.zero_zero_int))))) (forall ((A tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (not (= _let_1 tptp.zero_zero_nat)) (= _let_1 tptp.one_one_nat)))) (forall ((A tptp.int)) (let ((_let_1 (tptp.aa_int_int (tptp.modulo_modulo_int A) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (not (= _let_1 tptp.zero_zero_int)) (= _let_1 tptp.one_one_int)))) (forall ((A tptp.code_integer)) (let ((_let_1 (tptp.modulo364778990260209775nteger A (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (not (= _let_1 tptp.zero_z3403309356797280102nteger)) (= _let_1 tptp.one_one_Code_integer)))) (forall ((A tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (not (= _let_1 tptp.one_one_nat)) (= _let_1 tptp.zero_zero_nat)))) (forall ((A tptp.int)) (let ((_let_1 (tptp.aa_int_int (tptp.modulo_modulo_int A) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (not (= _let_1 tptp.one_one_int)) (= _let_1 tptp.zero_zero_int)))) (forall ((A tptp.code_integer)) (let ((_let_1 (tptp.modulo364778990260209775nteger A (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (not (= _let_1 tptp.one_one_Code_integer)) (= _let_1 tptp.zero_z3403309356797280102nteger)))) (forall ((N tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat N) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (not (= _let_1 (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat))) (= _let_1 tptp.zero_zero_nat)))) (forall ((M tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) M)) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) tptp.zero_zero_nat)) (forall ((M tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat M) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) _let_1)) (= _let_1 tptp.one_one_nat)))) (forall ((X tptp.complex)) (= (= tptp.zero_zero_complex X) (= X tptp.zero_zero_complex))) (forall ((X tptp.real)) (= (= tptp.zero_zero_real X) (= X tptp.zero_zero_real))) (forall ((X tptp.rat)) (= (= tptp.zero_zero_rat X) (= X tptp.zero_zero_rat))) (forall ((X tptp.nat)) (= (= tptp.zero_zero_nat X) (= X tptp.zero_zero_nat))) (forall ((X tptp.int)) (= (= tptp.zero_zero_int X) (= X tptp.zero_zero_int))) (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.modulo364778990260209775nteger A B2)) A)))) (forall ((A tptp.nat) (B2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) A)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A) B2)) A)))) (forall ((A tptp.int) (B2 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) A)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.modulo_modulo_int A) B2)) A)))) (forall ((B2 tptp.nat) (A tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) B2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A) B2)) B2)))) (forall ((B2 tptp.int) (A tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) B2)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.modulo_modulo_int A) B2)) B2)))) (forall ((B2 tptp.code_integer) (A tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) B2)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.modulo364778990260209775nteger A B2)) B2)))) (forall ((A tptp.nat) (B2 tptp.nat)) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A) B2) A) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) B2) tptp.zero_zero_nat))) (forall ((A tptp.int) (B2 tptp.int)) (= (= (tptp.aa_int_int (tptp.modulo_modulo_int A) B2) A) (= (tptp.aa_int_int (tptp.divide_divide_int A) B2) tptp.zero_zero_int))) (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (= (= (tptp.modulo364778990260209775nteger A B2) A) (= (tptp.divide6298287555418463151nteger A B2) tptp.zero_z3403309356797280102nteger))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat M) N)))) (let ((_let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_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 ((N tptp.nat) (M tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat M) N)) N)))) (forall ((M tptp.nat) (D tptp.nat)) (=> (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat M) D) tptp.zero_zero_nat) (exists ((Q3 tptp.nat)) (= M (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat D) Q3))))) (forall ((Uu tptp.option4927543243414619207at_nat) (Uv tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT) (Ux tptp.nat)) (not (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_V5719532721284313246member (tptp.vEBT_Node Uu tptp.zero_zero_nat Uv Uw)) Ux)))) (tptp.pp (tptp.aa_VEBT_VEBT_bool tptp.vEBT_VEBT_minNull (tptp.vEBT_Leaf tptp.fFalse tptp.fFalse))) (forall ((Uv tptp.bool)) (not (tptp.pp (tptp.aa_VEBT_VEBT_bool tptp.vEBT_VEBT_minNull (tptp.vEBT_Leaf tptp.fTrue Uv))))) (forall ((Uu tptp.bool)) (not (tptp.pp (tptp.aa_VEBT_VEBT_bool tptp.vEBT_VEBT_minNull (tptp.vEBT_Leaf Uu tptp.fTrue))))) (forall ((A tptp.bool) (B2 tptp.bool) (X tptp.nat)) (let ((_let_1 (= X tptp.one_one_nat))) (let ((_let_2 (= X tptp.zero_zero_nat))) (= (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_vebt_member (tptp.vEBT_Leaf A B2)) X)) (and (=> _let_2 (tptp.pp A)) (=> (not _let_2) (and (=> _let_1 (tptp.pp B2)) _let_1))))))) (forall ((X tptp.nat) (A tptp.bool) (B2 tptp.bool)) (let ((_let_1 (tptp.vEBT_Leaf A B2))) (let ((_let_2 (tptp.vEBT_vebt_insert _let_1 X))) (let ((_let_3 (= X tptp.one_one_nat))) (let ((_let_4 (= X tptp.zero_zero_nat))) (and (=> _let_4 (= _let_2 (tptp.vEBT_Leaf tptp.fTrue B2))) (=> (not _let_4) (and (=> _let_3 (= _let_2 (tptp.vEBT_Leaf A tptp.fTrue))) (=> (not _let_3) (= _let_2 _let_1)))))))))) (forall ((B2 tptp.code_integer) (A tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) B2)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (tptp.modulo364778990260209775nteger A B2))))) (forall ((B2 tptp.nat) (A tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) B2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A) B2))))) (forall ((B2 tptp.int) (A tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) B2)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.aa_int_int (tptp.modulo_modulo_int A) B2))))) (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger A) B2)) (= (tptp.modulo364778990260209775nteger A B2) A)))) (forall ((A tptp.nat) (B2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) A)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) B2)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A) B2) A)))) (forall ((A tptp.int) (B2 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) A)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B2)) (= (tptp.aa_int_int (tptp.modulo_modulo_int A) B2) A)))) (forall ((N tptp.num) (Q2 tptp.num)) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 N))) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 Q2))) tptp.zero_zero_nat) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_num_nat tptp.numeral_numeral_nat N)) (tptp.aa_num_nat tptp.numeral_numeral_nat Q2)) tptp.zero_zero_nat))) (forall ((N tptp.num) (Q2 tptp.num)) (= (= (tptp.aa_int_int (tptp.modulo_modulo_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 N))) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 Q2))) tptp.zero_zero_int) (= (tptp.aa_int_int (tptp.modulo_modulo_int (tptp.aa_num_int tptp.numeral_numeral_int N)) (tptp.aa_num_int tptp.numeral_numeral_int Q2)) tptp.zero_zero_int))) (forall ((N tptp.num) (Q2 tptp.num)) (= (= (tptp.modulo364778990260209775nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 N)) (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 Q2))) tptp.zero_z3403309356797280102nteger) (= (tptp.modulo364778990260209775nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger N) (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger Q2)) tptp.zero_z3403309356797280102nteger))) (forall ((N tptp.num)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_num_nat tptp.numeral_numeral_nat N)) (tptp.aa_num_nat tptp.numeral_numeral_nat tptp.one)) tptp.zero_zero_nat)) (forall ((N tptp.num)) (= (tptp.aa_int_int (tptp.modulo_modulo_int (tptp.aa_num_int tptp.numeral_numeral_int N)) (tptp.aa_num_int tptp.numeral_numeral_int tptp.one)) tptp.zero_zero_int)) (forall ((N tptp.num)) (= (tptp.modulo364778990260209775nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger N) (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger tptp.one)) tptp.zero_z3403309356797280102nteger)) (forall ((X tptp.produc9072475918466114483BT_nat)) (=> (forall ((A3 tptp.bool) (B3 tptp.bool) (X4 tptp.nat)) (not (= X (tptp.produc738532404422230701BT_nat (tptp.vEBT_Leaf A3 B3) X4)))) (=> (forall ((Uu2 tptp.option4927543243414619207at_nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT) (Ux2 tptp.nat)) (not (= X (tptp.produc738532404422230701BT_nat (tptp.vEBT_Node Uu2 tptp.zero_zero_nat Uv2 Uw2) Ux2)))) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (S3 tptp.vEBT_VEBT) (X4 tptp.nat)) (not (= X (tptp.produc738532404422230701BT_nat (tptp.vEBT_Node Uy2 (tptp.aa_nat_nat tptp.suc V2) TreeList2 S3) X4)))))))) (forall ((N tptp.nat) (M tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat M) N)) N)))) (forall ((A4 tptp.nat) (B4 tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A4) B4)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (=> (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A4) N) tptp.zero_zero_nat) (=> (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat B4) N) tptp.zero_zero_nat) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A4) N)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat B4) N)))))))) (forall ((A tptp.bool) (B2 tptp.bool)) (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt (tptp.vEBT_Leaf A B2)) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)))) (forall ((N tptp.nat)) (let ((_let_1 (tptp.aa_nat_rat (tptp.power_power_rat tptp.zero_zero_rat) N))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_rat)) (=> (not _let_2) (= _let_1 tptp.zero_zero_rat)))))) (forall ((N tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat tptp.zero_zero_nat) N))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_nat)) (=> (not _let_2) (= _let_1 tptp.zero_zero_nat)))))) (forall ((N tptp.nat)) (let ((_let_1 (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real tptp.zero_zero_real) N))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_real)) (=> (not _let_2) (= _let_1 tptp.zero_zero_real)))))) (forall ((N tptp.nat)) (let ((_let_1 (tptp.aa_nat_int (tptp.power_power_int tptp.zero_zero_int) N))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_int)) (=> (not _let_2) (= _let_1 tptp.zero_zero_int)))))) (forall ((N tptp.nat)) (let ((_let_1 (tptp.aa_nat_complex (tptp.power_power_complex tptp.zero_zero_complex) N))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_complex)) (=> (not _let_2) (= _let_1 tptp.zero_zero_complex)))))) (forall ((N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (= (tptp.aa_nat_rat (tptp.power_power_rat tptp.zero_zero_rat) N) tptp.zero_zero_rat))) (forall ((N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat tptp.zero_zero_nat) N) tptp.zero_zero_nat))) (forall ((N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real tptp.zero_zero_real) N) tptp.zero_zero_real))) (forall ((N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (= (tptp.aa_nat_int (tptp.power_power_int tptp.zero_zero_int) N) tptp.zero_zero_int))) (forall ((N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (= (tptp.aa_nat_complex (tptp.power_power_complex tptp.zero_zero_complex) N) tptp.zero_zero_complex))) (forall ((A tptp.nat) (C tptp.nat) (B2 tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A) C)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat B2) C))) C) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) B2)) C))) (forall ((A tptp.int) (C tptp.int) (B2 tptp.int)) (= (tptp.aa_int_int (tptp.modulo_modulo_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.modulo_modulo_int A) C)) (tptp.aa_int_int (tptp.modulo_modulo_int B2) C))) C) (tptp.aa_int_int (tptp.modulo_modulo_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) B2)) C))) (forall ((A tptp.code_integer) (C tptp.code_integer) (B2 tptp.code_integer)) (= (tptp.modulo364778990260209775nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.modulo364778990260209775nteger A C)) (tptp.modulo364778990260209775nteger B2 C)) C) (tptp.modulo364778990260209775nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) B2) C))) (forall ((A tptp.nat) (C tptp.nat) (A2 tptp.nat) (B2 tptp.nat) (B tptp.nat)) (=> (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A) C) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A2) C)) (=> (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat B2) C) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat B) C)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) B2)) C) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A2) B)) C))))) (forall ((A tptp.int) (C tptp.int) (A2 tptp.int) (B2 tptp.int) (B tptp.int)) (=> (= (tptp.aa_int_int (tptp.modulo_modulo_int A) C) (tptp.aa_int_int (tptp.modulo_modulo_int A2) C)) (=> (= (tptp.aa_int_int (tptp.modulo_modulo_int B2) C) (tptp.aa_int_int (tptp.modulo_modulo_int B) C)) (= (tptp.aa_int_int (tptp.modulo_modulo_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) B2)) C) (tptp.aa_int_int (tptp.modulo_modulo_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A2) B)) C))))) (forall ((A tptp.code_integer) (C tptp.code_integer) (A2 tptp.code_integer) (B2 tptp.code_integer) (B tptp.code_integer)) (=> (= (tptp.modulo364778990260209775nteger A C) (tptp.modulo364778990260209775nteger A2 C)) (=> (= (tptp.modulo364778990260209775nteger B2 C) (tptp.modulo364778990260209775nteger B C)) (= (tptp.modulo364778990260209775nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) B2) C) (tptp.modulo364778990260209775nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A2) B) C))))) (forall ((A tptp.nat) (C tptp.nat) (B2 tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) C)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B2) C)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A) B2)) C))) (forall ((A tptp.int) (C tptp.int) (B2 tptp.int)) (= (tptp.aa_int_int (tptp.modulo_modulo_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B2) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.modulo_modulo_int A) B2)) C))) (forall ((A tptp.code_integer) (C tptp.code_integer) (B2 tptp.code_integer)) (= (tptp.modulo364778990260209775nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) C) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B2) C)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.modulo364778990260209775nteger A B2)) C))) (forall ((C tptp.nat) (A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat C))) (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A) B2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat _let_1 A)) (tptp.aa_nat_nat _let_1 B2))))) (forall ((C tptp.int) (A tptp.int) (B2 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.times_times_int C))) (= (tptp.aa_int_int _let_1 (tptp.aa_int_int (tptp.modulo_modulo_int A) B2)) (tptp.aa_int_int (tptp.modulo_modulo_int (tptp.aa_int_int _let_1 A)) (tptp.aa_int_int _let_1 B2))))) (forall ((C tptp.code_integer) (A tptp.code_integer) (B2 tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger C))) (= (tptp.aa_Cod1783974652533396728nteger _let_1 (tptp.modulo364778990260209775nteger A B2)) (tptp.modulo364778990260209775nteger (tptp.aa_Cod1783974652533396728nteger _let_1 A) (tptp.aa_Cod1783974652533396728nteger _let_1 B2))))) (forall ((A tptp.nat) (C tptp.nat) (B2 tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A) C)) B2)) C) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) B2)) C))) (forall ((A tptp.int) (C tptp.int) (B2 tptp.int)) (= (tptp.aa_int_int (tptp.modulo_modulo_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.modulo_modulo_int A) C)) B2)) C) (tptp.aa_int_int (tptp.modulo_modulo_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) B2)) C))) (forall ((A tptp.code_integer) (C tptp.code_integer) (B2 tptp.code_integer)) (= (tptp.modulo364778990260209775nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.modulo364778990260209775nteger A C)) B2) C) (tptp.modulo364778990260209775nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) B2) C))) (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat B2) C))) C) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat _let_1 B2)) C)))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.times_times_int A))) (= (tptp.aa_int_int (tptp.modulo_modulo_int (tptp.aa_int_int _let_1 (tptp.aa_int_int (tptp.modulo_modulo_int B2) C))) C) (tptp.aa_int_int (tptp.modulo_modulo_int (tptp.aa_int_int _let_1 B2)) C)))) (forall ((A tptp.code_integer) (B2 tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A))) (= (tptp.modulo364778990260209775nteger (tptp.aa_Cod1783974652533396728nteger _let_1 (tptp.modulo364778990260209775nteger B2 C)) C) (tptp.modulo364778990260209775nteger (tptp.aa_Cod1783974652533396728nteger _let_1 B2) C)))) (forall ((A tptp.nat) (C tptp.nat) (B2 tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A) C)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat B2) C))) C) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) B2)) C))) (forall ((A tptp.int) (C tptp.int) (B2 tptp.int)) (= (tptp.aa_int_int (tptp.modulo_modulo_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.modulo_modulo_int A) C)) (tptp.aa_int_int (tptp.modulo_modulo_int B2) C))) C) (tptp.aa_int_int (tptp.modulo_modulo_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) B2)) C))) (forall ((A tptp.code_integer) (C tptp.code_integer) (B2 tptp.code_integer)) (= (tptp.modulo364778990260209775nteger (tptp.plus_p5714425477246183910nteger (tptp.modulo364778990260209775nteger A C) (tptp.modulo364778990260209775nteger B2 C)) C) (tptp.modulo364778990260209775nteger (tptp.plus_p5714425477246183910nteger A B2) C))) (forall ((A tptp.nat) (C tptp.nat) (A2 tptp.nat) (B2 tptp.nat) (B tptp.nat)) (=> (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A) C) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A2) C)) (=> (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat B2) C) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat B) C)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) B2)) C) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A2) B)) C))))) (forall ((A tptp.int) (C tptp.int) (A2 tptp.int) (B2 tptp.int) (B tptp.int)) (=> (= (tptp.aa_int_int (tptp.modulo_modulo_int A) C) (tptp.aa_int_int (tptp.modulo_modulo_int A2) C)) (=> (= (tptp.aa_int_int (tptp.modulo_modulo_int B2) C) (tptp.aa_int_int (tptp.modulo_modulo_int B) C)) (= (tptp.aa_int_int (tptp.modulo_modulo_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) B2)) C) (tptp.aa_int_int (tptp.modulo_modulo_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A2) B)) C))))) (forall ((A tptp.code_integer) (C tptp.code_integer) (A2 tptp.code_integer) (B2 tptp.code_integer) (B tptp.code_integer)) (=> (= (tptp.modulo364778990260209775nteger A C) (tptp.modulo364778990260209775nteger A2 C)) (=> (= (tptp.modulo364778990260209775nteger B2 C) (tptp.modulo364778990260209775nteger B C)) (= (tptp.modulo364778990260209775nteger (tptp.plus_p5714425477246183910nteger A B2) C) (tptp.modulo364778990260209775nteger (tptp.plus_p5714425477246183910nteger A2 B) C))))) (forall ((A tptp.nat) (C tptp.nat) (B2 tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A) C)) B2)) C) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) B2)) C))) (forall ((A tptp.int) (C tptp.int) (B2 tptp.int)) (= (tptp.aa_int_int (tptp.modulo_modulo_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.modulo_modulo_int A) C)) B2)) C) (tptp.aa_int_int (tptp.modulo_modulo_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) B2)) C))) (forall ((A tptp.code_integer) (C tptp.code_integer) (B2 tptp.code_integer)) (= (tptp.modulo364778990260209775nteger (tptp.plus_p5714425477246183910nteger (tptp.modulo364778990260209775nteger A C) B2) C) (tptp.modulo364778990260209775nteger (tptp.plus_p5714425477246183910nteger A B2) C))) (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat B2) C))) C) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat _let_1 B2)) C)))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.plus_plus_int A))) (= (tptp.aa_int_int (tptp.modulo_modulo_int (tptp.aa_int_int _let_1 (tptp.aa_int_int (tptp.modulo_modulo_int B2) C))) C) (tptp.aa_int_int (tptp.modulo_modulo_int (tptp.aa_int_int _let_1 B2)) C)))) (forall ((A tptp.code_integer) (B2 tptp.code_integer) (C tptp.code_integer)) (= (tptp.modulo364778990260209775nteger (tptp.plus_p5714425477246183910nteger A (tptp.modulo364778990260209775nteger B2 C)) C) (tptp.modulo364778990260209775nteger (tptp.plus_p5714425477246183910nteger A B2) C))) (forall ((A tptp.int) (C tptp.int) (B2 tptp.int)) (= (tptp.aa_int_int (tptp.modulo_modulo_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_int_int (tptp.modulo_modulo_int A) C)) (tptp.aa_int_int (tptp.modulo_modulo_int B2) C))) C) (tptp.aa_int_int (tptp.modulo_modulo_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) B2)) C))) (forall ((A tptp.code_integer) (C tptp.code_integer) (B2 tptp.code_integer)) (= (tptp.modulo364778990260209775nteger (tptp.minus_8373710615458151222nteger (tptp.modulo364778990260209775nteger A C) (tptp.modulo364778990260209775nteger B2 C)) C) (tptp.modulo364778990260209775nteger (tptp.minus_8373710615458151222nteger A B2) C))) (forall ((A tptp.int) (C tptp.int) (A2 tptp.int) (B2 tptp.int) (B tptp.int)) (=> (= (tptp.aa_int_int (tptp.modulo_modulo_int A) C) (tptp.aa_int_int (tptp.modulo_modulo_int A2) C)) (=> (= (tptp.aa_int_int (tptp.modulo_modulo_int B2) C) (tptp.aa_int_int (tptp.modulo_modulo_int B) C)) (= (tptp.aa_int_int (tptp.modulo_modulo_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) B2)) C) (tptp.aa_int_int (tptp.modulo_modulo_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A2) B)) C))))) (forall ((A tptp.code_integer) (C tptp.code_integer) (A2 tptp.code_integer) (B2 tptp.code_integer) (B tptp.code_integer)) (=> (= (tptp.modulo364778990260209775nteger A C) (tptp.modulo364778990260209775nteger A2 C)) (=> (= (tptp.modulo364778990260209775nteger B2 C) (tptp.modulo364778990260209775nteger B C)) (= (tptp.modulo364778990260209775nteger (tptp.minus_8373710615458151222nteger A B2) C) (tptp.modulo364778990260209775nteger (tptp.minus_8373710615458151222nteger A2 B) C))))) (forall ((A tptp.int) (C tptp.int) (B2 tptp.int)) (= (tptp.aa_int_int (tptp.modulo_modulo_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_int_int (tptp.modulo_modulo_int A) C)) B2)) C) (tptp.aa_int_int (tptp.modulo_modulo_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) B2)) C))) (forall ((A tptp.code_integer) (C tptp.code_integer) (B2 tptp.code_integer)) (= (tptp.modulo364778990260209775nteger (tptp.minus_8373710615458151222nteger (tptp.modulo364778990260209775nteger A C) B2) C) (tptp.modulo364778990260209775nteger (tptp.minus_8373710615458151222nteger A B2) C))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.minus_minus_int A))) (= (tptp.aa_int_int (tptp.modulo_modulo_int (tptp.aa_int_int _let_1 (tptp.aa_int_int (tptp.modulo_modulo_int B2) C))) C) (tptp.aa_int_int (tptp.modulo_modulo_int (tptp.aa_int_int _let_1 B2)) C)))) (forall ((A tptp.code_integer) (B2 tptp.code_integer) (C tptp.code_integer)) (= (tptp.modulo364778990260209775nteger (tptp.minus_8373710615458151222nteger A (tptp.modulo364778990260209775nteger B2 C)) C) (tptp.modulo364778990260209775nteger (tptp.minus_8373710615458151222nteger A B2) C))) (forall ((A tptp.nat) (B2 tptp.nat) (N tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A) B2)) N)) B2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A) N)) B2))) (forall ((A tptp.int) (B2 tptp.int) (N tptp.nat)) (= (tptp.aa_int_int (tptp.modulo_modulo_int (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_int_int (tptp.modulo_modulo_int A) B2)) N)) B2) (tptp.aa_int_int (tptp.modulo_modulo_int (tptp.aa_nat_int (tptp.power_power_int A) N)) B2))) (forall ((A tptp.code_integer) (B2 tptp.code_integer) (N tptp.nat)) (= (tptp.modulo364778990260209775nteger (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger (tptp.modulo364778990260209775nteger A B2)) N) B2) (tptp.modulo364778990260209775nteger (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger A) N) B2))) (forall ((Y tptp.vEBT_VEBT)) (=> (forall ((X112 tptp.option4927543243414619207at_nat) (X122 tptp.nat) (X132 tptp.list_VEBT_VEBT) (X142 tptp.vEBT_VEBT)) (not (= Y (tptp.vEBT_Node X112 X122 X132 X142)))) (not (forall ((X21 tptp.bool) (X222 tptp.bool)) (not (= Y (tptp.vEBT_Leaf X21 X222))))))) (forall ((X11 tptp.option4927543243414619207at_nat) (X12 tptp.nat) (X13 tptp.list_VEBT_VEBT) (X14 tptp.vEBT_VEBT) (X212 tptp.bool) (X223 tptp.bool)) (not (= (tptp.vEBT_Node X11 X12 X13 X14) (tptp.vEBT_Leaf X212 X223)))) (forall ((X tptp.produc9072475918466114483BT_nat)) (=> (forall ((Uu2 tptp.bool) (Uv2 tptp.bool) (D2 tptp.nat)) (not (= X (tptp.produc738532404422230701BT_nat (tptp.vEBT_Leaf Uu2 Uv2) D2)))) (not (forall ((Mima tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (Deg3 tptp.nat)) (not (= X (tptp.produc738532404422230701BT_nat (tptp.vEBT_Node Mima Deg2 TreeList2 Summary2) Deg3))))))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat M) N))) N) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat tptp.suc M)) N))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat M) N)))) N) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat tptp.suc M))) N))) (forall ((M tptp.nat) (N tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat M) N)) M))) (forall ((Uu tptp.bool) (Uv tptp.bool)) (= (tptp.vEBT_vebt_pred (tptp.vEBT_Leaf Uu Uv) tptp.zero_zero_nat) tptp.none_nat)) (tptp.pp (tptp.aa_real_bool _let_75 tptp.zero_zero_real)) (tptp.pp (tptp.aa_rat_bool _let_110 tptp.zero_zero_rat)) (tptp.pp (tptp.aa_nat_bool _let_157 tptp.zero_zero_nat)) _let_142 (forall ((X tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) X))) (not (tptp.pp (tptp.aa_real_bool _let_76 tptp.zero_zero_real))) (not (tptp.pp (tptp.aa_rat_bool _let_103 tptp.zero_zero_rat))) (not (tptp.pp (tptp.aa_nat_bool _let_144 tptp.zero_zero_nat))) _let_143 (forall ((D1 tptp.real) (D22 tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool _let_1 D1)) (=> (tptp.pp (tptp.aa_real_bool _let_1 D22)) (exists ((E2 tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real E2))) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) E2)) (tptp.pp (tptp.aa_real_bool _let_1 D1)) (tptp.pp (tptp.aa_real_bool _let_1 D22))))))))) (forall ((D1 tptp.rat) (D22 tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 D1)) (=> (tptp.pp (tptp.aa_rat_bool _let_1 D22)) (exists ((E2 tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat E2))) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) E2)) (tptp.pp (tptp.aa_rat_bool _let_1 D1)) (tptp.pp (tptp.aa_rat_bool _let_1 D22))))))))) (forall ((N tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (not (= N tptp.zero_zero_nat)))) (forall ((M tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N)) (not (= N tptp.zero_zero_nat)))) (forall ((N tptp.nat)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N) tptp.zero_zero_nat)))) (forall ((N tptp.nat)) (=> (not (= N tptp.zero_zero_nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)))) (forall ((N tptp.num)) (not (= tptp.zero_zero_complex (tptp.numera6690914467698888265omplex N)))) (forall ((N tptp.num)) (not (= tptp.zero_zero_real (tptp.aa_num_real tptp.numeral_numeral_real N)))) (forall ((N tptp.num)) (not (= tptp.zero_zero_rat (tptp.aa_num_rat tptp.numeral_numeral_rat N)))) (forall ((N tptp.num)) (not (= tptp.zero_zero_nat (tptp.aa_num_nat tptp.numeral_numeral_nat N)))) (forall ((N tptp.num)) (not (= tptp.zero_zero_int (tptp.aa_num_int tptp.numeral_numeral_int N)))) (forall ((A tptp.complex) (B2 tptp.complex)) (=> (not (= (tptp.aa_complex_complex (tptp.times_times_complex A) B2) tptp.zero_zero_complex)) (and (not (= A tptp.zero_zero_complex)) (not (= B2 tptp.zero_zero_complex))))) (forall ((A tptp.real) (B2 tptp.real)) (=> (not (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) B2) tptp.zero_zero_real)) (and (not (= A tptp.zero_zero_real)) (not (= B2 tptp.zero_zero_real))))) (forall ((A tptp.rat) (B2 tptp.rat)) (=> (not (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) B2) tptp.zero_zero_rat)) (and (not (= A tptp.zero_zero_rat)) (not (= B2 tptp.zero_zero_rat))))) (forall ((A tptp.nat) (B2 tptp.nat)) (=> (not (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) B2) tptp.zero_zero_nat)) (and (not (= A tptp.zero_zero_nat)) (not (= B2 tptp.zero_zero_nat))))) (forall ((A tptp.int) (B2 tptp.int)) (=> (not (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) B2) tptp.zero_zero_int)) (and (not (= A tptp.zero_zero_int)) (not (= B2 tptp.zero_zero_int))))) (forall ((A tptp.complex) (B2 tptp.complex)) (=> (= (tptp.aa_complex_complex (tptp.times_times_complex A) B2) tptp.zero_zero_complex) (or (= A tptp.zero_zero_complex) (= B2 tptp.zero_zero_complex)))) (forall ((A tptp.real) (B2 tptp.real)) (=> (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) B2) tptp.zero_zero_real) (or (= A tptp.zero_zero_real) (= B2 tptp.zero_zero_real)))) (forall ((A tptp.rat) (B2 tptp.rat)) (=> (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) B2) tptp.zero_zero_rat) (or (= A tptp.zero_zero_rat) (= B2 tptp.zero_zero_rat)))) (forall ((A tptp.nat) (B2 tptp.nat)) (=> (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) B2) tptp.zero_zero_nat) (or (= A tptp.zero_zero_nat) (= B2 tptp.zero_zero_nat)))) (forall ((A tptp.int) (B2 tptp.int)) (=> (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) B2) tptp.zero_zero_int) (or (= A tptp.zero_zero_int) (= B2 tptp.zero_zero_int)))) (forall ((A tptp.complex) (B2 tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (=> (not (= B2 tptp.zero_zero_complex)) (not (= (tptp.aa_complex_complex (tptp.times_times_complex A) B2) tptp.zero_zero_complex))))) (forall ((A tptp.real) (B2 tptp.real)) (=> (not (= A tptp.zero_zero_real)) (=> (not (= B2 tptp.zero_zero_real)) (not (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) B2) tptp.zero_zero_real))))) (forall ((A tptp.rat) (B2 tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (=> (not (= B2 tptp.zero_zero_rat)) (not (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) B2) tptp.zero_zero_rat))))) (forall ((A tptp.nat) (B2 tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (=> (not (= B2 tptp.zero_zero_nat)) (not (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) B2) tptp.zero_zero_nat))))) (forall ((A tptp.int) (B2 tptp.int)) (=> (not (= A tptp.zero_zero_int)) (=> (not (= B2 tptp.zero_zero_int)) (not (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) B2) tptp.zero_zero_int))))) (forall ((C tptp.complex) (A tptp.complex) (B2 tptp.complex)) (let ((_let_1 (tptp.times_times_complex C))) (=> (not (= C tptp.zero_zero_complex)) (= (= (tptp.aa_complex_complex _let_1 A) (tptp.aa_complex_complex _let_1 B2)) (= A B2))))) (forall ((C tptp.real) (A tptp.real) (B2 tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.times_times_real C))) (=> (not (= C tptp.zero_zero_real)) (= (= (tptp.aa_real_real _let_1 A) (tptp.aa_real_real _let_1 B2)) (= A B2))))) (forall ((C tptp.rat) (A tptp.rat) (B2 tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_rat tptp.times_times_rat C))) (=> (not (= C tptp.zero_zero_rat)) (= (= (tptp.aa_rat_rat _let_1 A) (tptp.aa_rat_rat _let_1 B2)) (= A B2))))) (forall ((C tptp.nat) (A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat C))) (=> (not (= C tptp.zero_zero_nat)) (= (= (tptp.aa_nat_nat _let_1 A) (tptp.aa_nat_nat _let_1 B2)) (= A B2))))) (forall ((C tptp.int) (A tptp.int) (B2 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.times_times_int C))) (=> (not (= C tptp.zero_zero_int)) (= (= (tptp.aa_int_int _let_1 A) (tptp.aa_int_int _let_1 B2)) (= A B2))))) (forall ((C tptp.complex) (A tptp.complex) (B2 tptp.complex)) (=> (not (= C tptp.zero_zero_complex)) (= (= (tptp.aa_complex_complex (tptp.times_times_complex A) C) (tptp.aa_complex_complex (tptp.times_times_complex B2) C)) (= A B2)))) (forall ((C tptp.real) (A tptp.real) (B2 tptp.real)) (=> (not (= C tptp.zero_zero_real)) (= (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) C) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real B2) C)) (= A B2)))) (forall ((C tptp.rat) (A tptp.rat) (B2 tptp.rat)) (=> (not (= C tptp.zero_zero_rat)) (= (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) C) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat B2) C)) (= A B2)))) (forall ((C tptp.nat) (A tptp.nat) (B2 tptp.nat)) (=> (not (= C tptp.zero_zero_nat)) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) C) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B2) C)) (= A B2)))) (forall ((C tptp.int) (A tptp.int) (B2 tptp.int)) (=> (not (= C tptp.zero_zero_int)) (= (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) C) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B2) C)) (= A B2)))) (not (= tptp.zero_zero_complex tptp.one_one_complex)) (not (= tptp.zero_zero_real tptp.one_one_real)) (not (= tptp.zero_zero_rat tptp.one_one_rat)) (not (= tptp.zero_zero_nat tptp.one_one_nat)) (not (= tptp.zero_zero_int tptp.one_one_int)) (forall ((A tptp.complex)) (= (tptp.aa_complex_complex (tptp.plus_plus_complex A) tptp.zero_zero_complex) A)) (forall ((A tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) tptp.zero_zero_real) A)) (forall ((A tptp.rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) tptp.zero_zero_rat) A)) (forall ((A tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) tptp.zero_zero_nat) A)) (forall ((A tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) tptp.zero_zero_int) A)) (forall ((A tptp.complex)) (= (tptp.aa_complex_complex (tptp.plus_plus_complex tptp.zero_zero_complex) A) A)) (forall ((A tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real tptp.zero_zero_real) A) A)) (forall ((A tptp.rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat tptp.zero_zero_rat) A) A)) (forall ((A tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int tptp.zero_zero_int) A) A)) (forall ((A tptp.complex)) (= (tptp.aa_complex_complex (tptp.plus_plus_complex A) tptp.zero_zero_complex) A)) (forall ((A tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) tptp.zero_zero_real) A)) (forall ((A tptp.rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) tptp.zero_zero_rat) A)) (forall ((A tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) tptp.zero_zero_nat) A)) (forall ((A tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) tptp.zero_zero_int) A)) (forall ((A tptp.complex)) (= (tptp.aa_complex_complex (tptp.plus_plus_complex tptp.zero_zero_complex) A) A)) (forall ((A tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real tptp.zero_zero_real) A) A)) (forall ((A tptp.rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat tptp.zero_zero_rat) A) A)) (forall ((A tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat tptp.zero_zero_nat) A) A)) (forall ((A tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int tptp.zero_zero_int) A) A)) (forall ((A tptp.complex) (B2 tptp.complex)) (= (= A B2) (= (tptp.aa_complex_complex (tptp.minus_minus_complex A) B2) tptp.zero_zero_complex))) (forall ((A tptp.real) (B2 tptp.real)) (= (= A B2) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A) B2) tptp.zero_zero_real))) (forall ((A tptp.rat) (B2 tptp.rat)) (= (= A B2) (= (tptp.aa_rat_rat (tptp.minus_minus_rat A) B2) tptp.zero_zero_rat))) (forall ((A tptp.int) (B2 tptp.int)) (= (= A B2) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) B2) tptp.zero_zero_int))) (forall ((A tptp.rat) (N tptp.nat)) (=> (not (= A tptp.zero_zero_rat)) (not (= (tptp.aa_nat_rat (tptp.power_power_rat A) N) tptp.zero_zero_rat)))) (forall ((A tptp.nat) (N tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (not (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A) N) tptp.zero_zero_nat)))) (forall ((A tptp.real) (N tptp.nat)) (=> (not (= A tptp.zero_zero_real)) (not (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real A) N) tptp.zero_zero_real)))) (forall ((A tptp.int) (N tptp.nat)) (=> (not (= A tptp.zero_zero_int)) (not (= (tptp.aa_nat_int (tptp.power_power_int A) N) tptp.zero_zero_int)))) (forall ((A tptp.complex) (N tptp.nat)) (=> (not (= A tptp.zero_zero_complex)) (not (= (tptp.aa_nat_complex (tptp.power_power_complex A) N) tptp.zero_zero_complex)))) (forall ((Ux tptp.list_VEBT_VEBT) (Uy tptp.vEBT_VEBT) (Uz tptp.nat)) (not (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_VEBT_membermima (tptp.vEBT_Node tptp.none_P5556105721700978146at_nat tptp.zero_zero_nat Ux Uy)) Uz)))) (= (tptp.aa_num_nat tptp.size_size_num tptp.one) tptp.zero_zero_nat) (forall ((X2 tptp.nat)) (not (= tptp.zero_zero_nat (tptp.aa_nat_nat tptp.suc X2)))) (forall ((Nat2 tptp.nat)) (not (= (tptp.aa_nat_nat tptp.suc Nat2) tptp.zero_zero_nat))) (forall ((Nat2 tptp.nat)) (not (= tptp.zero_zero_nat (tptp.aa_nat_nat tptp.suc Nat2)))) (forall ((Nat tptp.nat) (X2 tptp.nat)) (=> (= Nat (tptp.aa_nat_nat tptp.suc X2)) (not (= Nat tptp.zero_zero_nat)))) (forall ((Y tptp.nat)) (=> (not (= Y tptp.zero_zero_nat)) (not (forall ((Nat3 tptp.nat)) (not (= Y (tptp.aa_nat_nat tptp.suc Nat3))))))) (forall ((P tptp.fun_nat_bool) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool P tptp.zero_zero_nat)) (=> (forall ((N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool P N2)) (tptp.pp (tptp.aa_nat_bool P (tptp.aa_nat_nat tptp.suc N2))))) (tptp.pp (tptp.aa_nat_bool P N))))) (forall ((P tptp.fun_nat_fun_nat_bool) (M tptp.nat) (N tptp.nat)) (=> (forall ((X4 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool P X4) tptp.zero_zero_nat))) (=> (forall ((Y4 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool P tptp.zero_zero_nat) (tptp.aa_nat_nat tptp.suc Y4)))) (=> (forall ((X4 tptp.nat) (Y4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool P X4) Y4)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool P (tptp.aa_nat_nat tptp.suc X4)) (tptp.aa_nat_nat tptp.suc Y4))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool P M) N)))))) (forall ((P tptp.fun_nat_bool) (K tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool P K)) (=> (forall ((N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool P (tptp.aa_nat_nat tptp.suc N2))) (tptp.pp (tptp.aa_nat_bool P N2)))) (tptp.pp (tptp.aa_nat_bool P tptp.zero_zero_nat))))) (forall ((M tptp.nat)) (not (= (tptp.aa_nat_nat tptp.suc M) tptp.zero_zero_nat))) (forall ((M tptp.nat)) (not (= tptp.zero_zero_nat (tptp.aa_nat_nat tptp.suc M)))) (forall ((M tptp.nat)) (not (= tptp.zero_zero_nat (tptp.aa_nat_nat tptp.suc M)))) (forall ((N tptp.nat)) (=> (not (= N tptp.zero_zero_nat)) (exists ((M3 tptp.nat)) (= N (tptp.aa_nat_nat tptp.suc M3))))) (forall ((P tptp.fun_nat_bool) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool P tptp.zero_zero_nat)) (=> (forall ((N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)) (=> (not (tptp.pp (tptp.aa_nat_bool P N2))) (exists ((M2 tptp.nat)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M2) N2)) (not (tptp.pp (tptp.aa_nat_bool P M2)))))))) (tptp.pp (tptp.aa_nat_bool P N))))) (forall ((M tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N)) (not (= N tptp.zero_zero_nat)))) (forall ((N tptp.nat)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N) tptp.zero_zero_nat)))) (forall ((N tptp.nat)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N) tptp.zero_zero_nat)))) (forall ((N tptp.nat)) (= (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N))) (= N tptp.zero_zero_nat))) (forall ((N tptp.nat)) (=> (not (= N tptp.zero_zero_nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)))) (forall ((A tptp.nat)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) tptp.zero_zero_nat)))) (forall ((N tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N) tptp.zero_zero_nat)) (= N tptp.zero_zero_nat))) (forall ((A tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) tptp.zero_zero_nat)) (= A tptp.zero_zero_nat))) (forall ((A tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) tptp.zero_zero_nat)) (= A tptp.zero_zero_nat))) (forall ((N tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) N))) (forall ((M tptp.nat) (N tptp.nat)) (=> (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) N) M) (= N tptp.zero_zero_nat))) (forall ((N tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat tptp.zero_zero_nat) N) N)) (forall ((M tptp.nat) (N tptp.nat)) (=> (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) N) tptp.zero_zero_nat) (=> (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) M) tptp.zero_zero_nat) (= M N)))) (forall ((M tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) tptp.zero_zero_nat) M)) (forall ((N tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat tptp.zero_zero_nat) N) tptp.zero_zero_nat)) (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat K))) (= (= (tptp.aa_nat_nat _let_1 M) (tptp.aa_nat_nat _let_1 N)) (or (= K tptp.zero_zero_nat) (= M N))))) (forall ((P tptp.fun_nat_bool) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (= N tptp.zero_zero_nat))) (= (tptp.pp (tptp.aa_nat_bool P (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat M) N))) (and (=> _let_1 (tptp.pp (tptp.aa_nat_bool P M))) (=> (not _let_1) (forall ((I4 tptp.nat) (J3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat J3) N)) (=> (= M (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat N) I4)) J3)) (tptp.pp (tptp.aa_nat_bool P J3)))))))))) (forall ((A tptp.real) (N tptp.nat) (B2 tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real A) N) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real B2) N)) (=> (tptp.pp (tptp.aa_real_bool _let_1 A)) (=> (tptp.pp (tptp.aa_real_bool _let_1 B2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (= A B2))))))) (forall ((A tptp.rat) (N tptp.nat) (B2 tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (= (tptp.aa_nat_rat (tptp.power_power_rat A) N) (tptp.aa_nat_rat (tptp.power_power_rat B2) N)) (=> (tptp.pp (tptp.aa_rat_bool _let_1 A)) (=> (tptp.pp (tptp.aa_rat_bool _let_1 B2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (= A B2))))))) (forall ((A tptp.nat) (N tptp.nat) (B2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A) N) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat B2) N)) (=> (tptp.pp (tptp.aa_nat_bool _let_1 A)) (=> (tptp.pp (tptp.aa_nat_bool _let_1 B2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (= A B2))))))) (forall ((A tptp.int) (N tptp.nat) (B2 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (= (tptp.aa_nat_int (tptp.power_power_int A) N) (tptp.aa_nat_int (tptp.power_power_int B2) N)) (=> (tptp.pp (tptp.aa_int_bool _let_1 A)) (=> (tptp.pp (tptp.aa_int_bool _let_1 B2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (= A B2))))))) (forall ((N tptp.nat) (A tptp.real) (B2 tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (=> (tptp.pp (tptp.aa_real_bool _let_1 A)) (=> (tptp.pp (tptp.aa_real_bool _let_1 B2)) (= (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real A) N) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real B2) N)) (= A B2))))))) (forall ((N tptp.nat) (A tptp.rat) (B2 tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (=> (tptp.pp (tptp.aa_rat_bool _let_1 A)) (=> (tptp.pp (tptp.aa_rat_bool _let_1 B2)) (= (= (tptp.aa_nat_rat (tptp.power_power_rat A) N) (tptp.aa_nat_rat (tptp.power_power_rat B2) N)) (= A B2))))))) (forall ((N tptp.nat) (A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (=> (tptp.pp (tptp.aa_nat_bool _let_1 A)) (=> (tptp.pp (tptp.aa_nat_bool _let_1 B2)) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A) N) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat B2) N)) (= A B2))))))) (forall ((N tptp.nat) (A tptp.int) (B2 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (=> (tptp.pp (tptp.aa_int_bool _let_1 A)) (=> (tptp.pp (tptp.aa_int_bool _let_1 B2)) (= (= (tptp.aa_nat_int (tptp.power_power_int A) N) (tptp.aa_nat_int (tptp.power_power_int B2) N)) (= A B2))))))) (= tptp.aTP_Lamm_au (tptp.times_times_complex tptp.zero_zero_complex)) (= tptp.aTP_Lamm_av (tptp.aa_rea7340605660300375871l_real tptp.times_times_real tptp.zero_zero_real)) (= tptp.aTP_Lamm_aw (tptp.aa_rat_fun_rat_rat tptp.times_times_rat tptp.zero_zero_rat)) (= tptp.aTP_Lamm_ax (tptp.aa_nat_fun_nat_nat tptp.times_times_nat tptp.zero_zero_nat)) (= tptp.aTP_Lamm_ay (tptp.aa_int_fun_int_int tptp.times_times_int tptp.zero_zero_int)) (forall ((Info tptp.option4927543243414619207at_nat) (Ts tptp.list_VEBT_VEBT) (S tptp.vEBT_VEBT) (X tptp.nat)) (let ((_let_1 (tptp.vEBT_Node Info tptp.zero_zero_nat Ts S))) (= (tptp.vEBT_vebt_insert _let_1 X) _let_1))) (forall ((Mi tptp.nat) (Ma tptp.nat) (Va tptp.list_VEBT_VEBT) (Vb tptp.vEBT_VEBT) (X tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_VEBT_membermima (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Mi) Ma)) tptp.zero_zero_nat Va Vb)) X)) (or (= X Mi) (= X Ma)))) (forall ((C tptp.code_integer) (A tptp.code_integer) (B2 tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B2))) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) C)) (= (tptp.modulo364778990260209775nteger A (tptp.aa_Cod1783974652533396728nteger _let_1 C)) (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger _let_1 (tptp.modulo364778990260209775nteger (tptp.divide6298287555418463151nteger A B2) C)) (tptp.modulo364778990260209775nteger A B2)))))) (forall ((C tptp.nat) (A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A))) (let ((_let_2 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B2))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) C)) (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat _let_2 C)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat _let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) B2)) C))) (tptp.aa_nat_nat _let_1 B2))))))) (forall ((C tptp.int) (A tptp.int) (B2 tptp.int)) (let ((_let_1 (tptp.modulo_modulo_int A))) (let ((_let_2 (tptp.aa_int_fun_int_int tptp.times_times_int B2))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) C)) (= (tptp.aa_int_int _let_1 (tptp.aa_int_int _let_2 C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int _let_2 (tptp.aa_int_int (tptp.modulo_modulo_int (tptp.aa_int_int (tptp.divide_divide_int A) B2)) C))) (tptp.aa_int_int _let_1 B2))))))) (forall ((M tptp.num) (Q2 tptp.num) (N tptp.num)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat Q2))) (let ((_let_2 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 Q2)))) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 M))) _let_2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 N))) _let_2)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_num_nat tptp.numeral_numeral_nat M)) _let_1) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_num_nat tptp.numeral_numeral_nat N)) _let_1)))))) (forall ((M tptp.num) (Q2 tptp.num) (N tptp.num)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int Q2))) (let ((_let_2 (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 Q2)))) (= (= (tptp.aa_int_int (tptp.modulo_modulo_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 M))) _let_2) (tptp.aa_int_int (tptp.modulo_modulo_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 N))) _let_2)) (= (tptp.aa_int_int (tptp.modulo_modulo_int (tptp.aa_num_int tptp.numeral_numeral_int M)) _let_1) (tptp.aa_int_int (tptp.modulo_modulo_int (tptp.aa_num_int tptp.numeral_numeral_int N)) _let_1)))))) (forall ((M tptp.num) (Q2 tptp.num) (N tptp.num)) (let ((_let_1 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger Q2))) (let ((_let_2 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 Q2)))) (= (= (tptp.modulo364778990260209775nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 M)) _let_2) (tptp.modulo364778990260209775nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 N)) _let_2)) (= (tptp.modulo364778990260209775nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger M) _let_1) (tptp.modulo364778990260209775nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger N) _let_1)))))) (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat tptp.one))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_num_nat tptp.numeral_numeral_nat M)) _let_1) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_num_nat tptp.numeral_numeral_nat N)) _let_1)))) (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int tptp.one))) (= (tptp.aa_int_int (tptp.modulo_modulo_int (tptp.aa_num_int tptp.numeral_numeral_int M)) _let_1) (tptp.aa_int_int (tptp.modulo_modulo_int (tptp.aa_num_int tptp.numeral_numeral_int N)) _let_1)))) (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger tptp.one))) (= (tptp.modulo364778990260209775nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger M) _let_1) (tptp.modulo364778990260209775nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger N) _let_1)))) (forall ((A tptp.int) (C tptp.int) (B2 tptp.int)) (=> (= (tptp.aa_int_int (tptp.modulo_modulo_int A) C) (tptp.aa_int_int (tptp.modulo_modulo_int B2) C)) (not (forall ((D2 tptp.int)) (not (= B2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int C) D2)))))))) (forall ((A tptp.code_integer) (C tptp.code_integer) (B2 tptp.code_integer)) (=> (= (tptp.modulo364778990260209775nteger A C) (tptp.modulo364778990260209775nteger B2 C)) (not (forall ((D2 tptp.code_integer)) (not (= B2 (tptp.plus_p5714425477246183910nteger A (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger C) D2)))))))) (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) B2)) C) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) C)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat B2) C))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A) C)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat B2) C))) C)))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (= (tptp.aa_int_int (tptp.divide_divide_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) B2)) C) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.divide_divide_int A) C)) (tptp.aa_int_int (tptp.divide_divide_int B2) C))) (tptp.aa_int_int (tptp.divide_divide_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.modulo_modulo_int A) C)) (tptp.aa_int_int (tptp.modulo_modulo_int B2) C))) C)))) (forall ((A tptp.code_integer) (B2 tptp.code_integer) (C tptp.code_integer)) (= (tptp.divide6298287555418463151nteger (tptp.plus_p5714425477246183910nteger A B2) C) (tptp.plus_p5714425477246183910nteger (tptp.plus_p5714425477246183910nteger (tptp.divide6298287555418463151nteger A C) (tptp.divide6298287555418463151nteger B2 C)) (tptp.divide6298287555418463151nteger (tptp.plus_p5714425477246183910nteger (tptp.modulo364778990260209775nteger A C) (tptp.modulo364778990260209775nteger B2 C)) C)))) (forall ((M tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)) M)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat M) N))) M) tptp.one_one_nat))) (forall ((P tptp.fun_nat_bool) (N tptp.nat) (P2 tptp.nat) (M tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool P N)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N) P2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) P2)) (=> (forall ((N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) P2)) (=> (tptp.pp (tptp.aa_nat_bool P N2)) (tptp.pp (tptp.aa_nat_bool P (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat tptp.suc N2)) P2)))))) (tptp.pp (tptp.aa_nat_bool P M))))))) (forall ((M tptp.nat) (N tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat M) (tptp.aa_nat_nat tptp.suc N))) N))) (forall ((A tptp.real) (B2 tptp.real) (N tptp.nat)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B2)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) A)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real A) N)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real B2) N))))))) (forall ((A tptp.rat) (B2 tptp.rat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B2)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) A)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_nat_rat (tptp.power_power_rat A) N)) (tptp.aa_nat_rat (tptp.power_power_rat B2) N))))))) (forall ((A tptp.nat) (B2 tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) B2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) A)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A) N)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat B2) N))))))) (forall ((A tptp.int) (B2 tptp.int) (N tptp.nat)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B2)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) A)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_nat_int (tptp.power_power_int A) N)) (tptp.aa_nat_int (tptp.power_power_int B2) N))))))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat M) N))) (let ((_let_2 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N)))) (and (=> _let_2 (= _let_1 M)) (=> (not _let_2) (= _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) N)) N))))))) (forall ((M tptp.nat) (N tptp.nat)) (=> (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat M) N) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) N)) N)))) (forall ((X tptp.produc9072475918466114483BT_nat)) (=> (forall ((A3 tptp.bool) (B3 tptp.bool) (X4 tptp.nat)) (not (= X (tptp.produc738532404422230701BT_nat (tptp.vEBT_Leaf A3 B3) X4)))) (=> (forall ((Info2 tptp.option4927543243414619207at_nat) (Ts2 tptp.list_VEBT_VEBT) (S3 tptp.vEBT_VEBT) (X4 tptp.nat)) (not (= X (tptp.produc738532404422230701BT_nat (tptp.vEBT_Node Info2 tptp.zero_zero_nat Ts2 S3) X4)))) (=> (forall ((Info2 tptp.option4927543243414619207at_nat) (Ts2 tptp.list_VEBT_VEBT) (S3 tptp.vEBT_VEBT) (X4 tptp.nat)) (not (= X (tptp.produc738532404422230701BT_nat (tptp.vEBT_Node Info2 (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat) Ts2 S3) X4)))) (=> (forall ((V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (X4 tptp.nat)) (not (= X (tptp.produc738532404422230701BT_nat (tptp.vEBT_Node tptp.none_P5556105721700978146at_nat (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat tptp.suc V2)) TreeList2 Summary2) X4)))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (X4 tptp.nat)) (not (= X (tptp.produc738532404422230701BT_nat (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Mi2) Ma2)) (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat tptp.suc Va2)) TreeList2 Summary2) X4)))))))))) (forall ((X tptp.produc9072475918466114483BT_nat)) (=> (forall ((A3 tptp.bool) (B3 tptp.bool) (X4 tptp.nat)) (not (= X (tptp.produc738532404422230701BT_nat (tptp.vEBT_Leaf A3 B3) X4)))) (=> (forall ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT) (X4 tptp.nat)) (not (= X (tptp.produc738532404422230701BT_nat (tptp.vEBT_Node tptp.none_P5556105721700978146at_nat Uu2 Uv2 Uw2) X4)))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT) (X4 tptp.nat)) (not (= X (tptp.produc738532404422230701BT_nat (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat V2) tptp.zero_zero_nat Uy2 Uz2) X4)))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT) (X4 tptp.nat)) (not (= X (tptp.produc738532404422230701BT_nat (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat V2) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat) Vb2 Vc2) X4)))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (X4 tptp.nat)) (not (= X (tptp.produc738532404422230701BT_nat (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Mi2) Ma2)) (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat tptp.suc Va2)) TreeList2 Summary2) X4)))))))))) (forall ((N tptp.nat) (M tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N) M)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat M) N) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) N)) N)))) (forall ((X tptp.nat) (N tptp.nat) (Y tptp.nat)) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat X) N) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat Y) N)) (exists ((Q1 tptp.nat) (Q22 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat N))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat X) (tptp.aa_nat_nat _let_1 Q1)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Y) (tptp.aa_nat_nat _let_1 Q22))))))) (forall ((X tptp.vEBT_VEBT)) (=> (not (= X (tptp.vEBT_Leaf tptp.fFalse tptp.fFalse))) (=> (forall ((Uv2 tptp.bool)) (not (= X (tptp.vEBT_Leaf tptp.fTrue Uv2)))) (=> (forall ((Uu2 tptp.bool)) (not (= X (tptp.vEBT_Leaf Uu2 tptp.fTrue)))) (=> (forall ((Uw2 tptp.nat) (Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (not (= X (tptp.vEBT_Node tptp.none_P5556105721700978146at_nat Uw2 Ux2 Uy2)))) (not (forall ((Uz2 tptp.product_prod_nat_nat) (Va3 tptp.nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (not (= X (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat Uz2) Va3 Vb2 Vc2)))))))))) (forall ((A tptp.bool) (Uw tptp.bool)) (let ((_let_1 (tptp.vEBT_vebt_pred (tptp.vEBT_Leaf A Uw) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)))) (let ((_let_2 (tptp.pp A))) (and (=> _let_2 (= _let_1 (tptp.some_nat tptp.zero_zero_nat))) (=> (not _let_2) (= _let_1 tptp.none_nat)))))) (forall ((A tptp.bool) (B2 tptp.bool)) (let ((_let_1 (tptp.vEBT_vebt_mint (tptp.vEBT_Leaf A B2)))) (let ((_let_2 (tptp.pp B2))) (let ((_let_3 (tptp.pp A))) (and (=> _let_3 (= _let_1 (tptp.some_nat tptp.zero_zero_nat))) (=> (not _let_3) (and (=> _let_2 (= _let_1 (tptp.some_nat tptp.one_one_nat))) (=> (not _let_2) (= _let_1 tptp.none_nat))))))))) (forall ((N tptp.num)) (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_num_real tptp.numeral_numeral_real N)) tptp.zero_zero_real)))) (forall ((N tptp.num)) (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_num_rat tptp.numeral_numeral_rat N)) tptp.zero_zero_rat)))) (forall ((N tptp.num)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_num_nat tptp.numeral_numeral_nat N)) tptp.zero_zero_nat)))) (forall ((N tptp.num)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_num_int tptp.numeral_numeral_int N)) tptp.zero_zero_int)))) (forall ((N tptp.num)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_num_real tptp.numeral_numeral_real N)))) (forall ((N tptp.num)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_num_rat tptp.numeral_numeral_rat N)))) (forall ((N tptp.num)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) (tptp.aa_num_nat tptp.numeral_numeral_nat N)))) (forall ((N tptp.num)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.aa_num_int tptp.numeral_numeral_int N)))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.times_times_real C))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) B2)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) C)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real _let_1 A)) (tptp.aa_real_real _let_1 B2))))))) (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_rat tptp.times_times_rat C))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B2)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) C)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat _let_1 A)) (tptp.aa_rat_rat _let_1 B2))))))) (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat C))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) C)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat _let_1 A)) (tptp.aa_nat_nat _let_1 B2))))))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.times_times_int C))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B2)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) C)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int _let_1 A)) (tptp.aa_int_int _let_1 B2))))))) (forall ((A tptp.real) (B2 tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (= (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) B2))) (or (and (tptp.pp (tptp.aa_real_bool _let_1 A)) (tptp.pp (tptp.aa_real_bool _let_1 B2))) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real B2) tptp.zero_zero_real))))))) (forall ((A tptp.rat) (B2 tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat))) (= (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) B2))) (or (and (tptp.pp (tptp.aa_rat_bool _let_1 A)) (tptp.pp (tptp.aa_rat_bool _let_1 B2))) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B2) tptp.zero_zero_rat))))))) (forall ((A tptp.int) (B2 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) B2))) (or (and (tptp.pp (tptp.aa_int_bool _let_1 A)) (tptp.pp (tptp.aa_int_bool _let_1 B2))) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B2) tptp.zero_zero_int))))))) (forall ((A tptp.real) (B2 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) A)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real B2) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real B2) A)) tptp.zero_zero_real))))) (forall ((A tptp.rat) (B2 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) A)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B2) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat B2) A)) tptp.zero_zero_rat))))) (forall ((A tptp.nat) (B2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) A)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B2) tptp.zero_zero_nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B2) A)) tptp.zero_zero_nat))))) (forall ((A tptp.int) (B2 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) A)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B2) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B2) A)) tptp.zero_zero_int))))) (forall ((A tptp.real) (B2 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) tptp.zero_zero_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) B2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) B2)) tptp.zero_zero_real))))) (forall ((A tptp.rat) (B2 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) tptp.zero_zero_rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) B2)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) B2)) tptp.zero_zero_rat))))) (forall ((A tptp.nat) (B2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) tptp.zero_zero_nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) B2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) B2)) tptp.zero_zero_nat))))) (forall ((A tptp.int) (B2 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) tptp.zero_zero_int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) B2)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) B2)) tptp.zero_zero_int))))) (forall ((A tptp.real) (B2 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) A)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real B2) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) B2)) tptp.zero_zero_real))))) (forall ((A tptp.rat) (B2 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) A)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B2) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) B2)) tptp.zero_zero_rat))))) (forall ((A tptp.nat) (B2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) A)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B2) tptp.zero_zero_nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) B2)) tptp.zero_zero_nat))))) (forall ((A tptp.int) (B2 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) A)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B2) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) B2)) tptp.zero_zero_int))))) (forall ((A tptp.real) (B2 tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool _let_1 A)) (=> (tptp.pp (tptp.aa_real_bool _let_1 B2)) (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) B2))))))) (forall ((A tptp.rat) (B2 tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 A)) (=> (tptp.pp (tptp.aa_rat_bool _let_1 B2)) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) B2))))))) (forall ((A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 A)) (=> (tptp.pp (tptp.aa_nat_bool _let_1 B2)) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) B2))))))) (forall ((A tptp.int) (B2 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.pp (tptp.aa_int_bool _let_1 A)) (=> (tptp.pp (tptp.aa_int_bool _let_1 B2)) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) B2))))))) (forall ((A tptp.real) (B2 tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (or (and (tptp.pp (tptp.aa_real_bool _let_1 A)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real B2) tptp.zero_zero_real))) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool _let_1 B2)))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) B2)) tptp.zero_zero_real))))) (forall ((A tptp.rat) (B2 tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (or (and (tptp.pp (tptp.aa_rat_bool _let_1 A)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B2) tptp.zero_zero_rat))) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool _let_1 B2)))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) B2)) tptp.zero_zero_rat))))) (forall ((A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (or (and (tptp.pp (tptp.aa_nat_bool _let_1 A)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B2) tptp.zero_zero_nat))) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) tptp.zero_zero_nat)) (tptp.pp (tptp.aa_nat_bool _let_1 B2)))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) B2)) tptp.zero_zero_nat))))) (forall ((A tptp.int) (B2 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (or (and (tptp.pp (tptp.aa_int_bool _let_1 A)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B2) tptp.zero_zero_int))) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool _let_1 B2)))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) B2)) tptp.zero_zero_int))))) (forall ((A tptp.real) (B2 tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) B2)) tptp.zero_zero_real)) (or (and (tptp.pp (tptp.aa_real_bool _let_1 A)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real B2) tptp.zero_zero_real))) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool _let_1 B2))))))) (forall ((A tptp.rat) (B2 tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat))) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) B2)) tptp.zero_zero_rat)) (or (and (tptp.pp (tptp.aa_rat_bool _let_1 A)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B2) tptp.zero_zero_rat))) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool _let_1 B2))))))) (forall ((A tptp.int) (B2 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) B2)) tptp.zero_zero_int)) (or (and (tptp.pp (tptp.aa_int_bool _let_1 A)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B2) tptp.zero_zero_int))) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool _let_1 B2))))))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) B2)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) C)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) C)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real B2) C)))))) (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B2)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) C)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) C)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat B2) C)))))) (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) C)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) C)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B2) C)))))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B2)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) C)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B2) C)))))) (forall ((B2 tptp.real) (A tptp.real) (C tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real B2) A)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real C) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) C)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real B2) C)))))) (forall ((B2 tptp.rat) (A tptp.rat) (C tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B2) A)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat C) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) C)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat B2) C)))))) (forall ((B2 tptp.int) (A tptp.int) (C tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B2) A)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int C) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B2) C)))))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.times_times_real C))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) B2)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) C)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real _let_1 A)) (tptp.aa_real_real _let_1 B2))))))) (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_rat tptp.times_times_rat C))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B2)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) C)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat _let_1 A)) (tptp.aa_rat_rat _let_1 B2))))))) (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat C))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) C)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat _let_1 A)) (tptp.aa_nat_nat _let_1 B2))))))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.times_times_int C))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B2)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) C)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int _let_1 A)) (tptp.aa_int_int _let_1 B2))))))) (forall ((A tptp.real) (B2 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) tptp.zero_zero_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real B2) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) B2)))))) (forall ((A tptp.rat) (B2 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) tptp.zero_zero_rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B2) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) B2)))))) (forall ((A tptp.int) (B2 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) tptp.zero_zero_int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B2) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) B2)))))) (forall ((B2 tptp.real) (A tptp.real) (C tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.times_times_real C))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real B2) A)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real C) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real _let_1 A)) (tptp.aa_real_real _let_1 B2))))))) (forall ((B2 tptp.rat) (A tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_rat tptp.times_times_rat C))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B2) A)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat C) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat _let_1 A)) (tptp.aa_rat_rat _let_1 B2))))))) (forall ((B2 tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.times_times_int C))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B2) A)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int C) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int _let_1 A)) (tptp.aa_int_int _let_1 B2))))))) (forall ((A tptp.real) (B2 tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (or (and (tptp.pp (tptp.aa_real_bool _let_1 A)) (tptp.pp (tptp.aa_real_bool _let_1 B2))) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real B2) tptp.zero_zero_real)))) (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) B2)))))) (forall ((A tptp.rat) (B2 tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (or (and (tptp.pp (tptp.aa_rat_bool _let_1 A)) (tptp.pp (tptp.aa_rat_bool _let_1 B2))) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B2) tptp.zero_zero_rat)))) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) B2)))))) (forall ((A tptp.int) (B2 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (or (and (tptp.pp (tptp.aa_int_bool _let_1 A)) (tptp.pp (tptp.aa_int_bool _let_1 B2))) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B2) tptp.zero_zero_int)))) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) B2)))))) (forall ((A tptp.real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) A)))) (forall ((A tptp.rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) A)))) (forall ((A tptp.int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) A)))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real) (D tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) B2)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real C) D)) (=> (tptp.pp (tptp.aa_real_bool _let_1 A)) (=> (tptp.pp (tptp.aa_real_bool _let_1 C)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) C)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real B2) D))))))))) (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat) (D tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B2)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat C) D)) (=> (tptp.pp (tptp.aa_rat_bool _let_1 A)) (=> (tptp.pp (tptp.aa_rat_bool _let_1 C)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) C)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat B2) D))))))))) (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat) (D tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat C) D)) (=> (tptp.pp (tptp.aa_nat_bool _let_1 A)) (=> (tptp.pp (tptp.aa_nat_bool _let_1 C)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) C)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B2) D))))))))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int) (D tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B2)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int C) D)) (=> (tptp.pp (tptp.aa_int_bool _let_1 A)) (=> (tptp.pp (tptp.aa_int_bool _let_1 C)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B2) D))))))))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real) (D tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) B2)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real C) D)) (=> (tptp.pp (tptp.aa_real_bool _let_1 B2)) (=> (tptp.pp (tptp.aa_real_bool _let_1 C)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) C)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real B2) D))))))))) (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat) (D tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B2)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat C) D)) (=> (tptp.pp (tptp.aa_rat_bool _let_1 B2)) (=> (tptp.pp (tptp.aa_rat_bool _let_1 C)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) C)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat B2) D))))))))) (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat) (D tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat C) D)) (=> (tptp.pp (tptp.aa_nat_bool _let_1 B2)) (=> (tptp.pp (tptp.aa_nat_bool _let_1 C)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) C)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B2) D))))))))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int) (D tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B2)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int C) D)) (=> (tptp.pp (tptp.aa_int_bool _let_1 B2)) (=> (tptp.pp (tptp.aa_int_bool _let_1 C)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B2) D))))))))) (forall ((N tptp.num)) (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_num_real tptp.numeral_numeral_real N)) tptp.zero_zero_real)))) (forall ((N tptp.num)) (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_num_rat tptp.numeral_numeral_rat N)) tptp.zero_zero_rat)))) (forall ((N tptp.num)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_num_nat tptp.numeral_numeral_nat N)) tptp.zero_zero_nat)))) (forall ((N tptp.num)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_num_int tptp.numeral_numeral_int N)) tptp.zero_zero_int)))) (forall ((N tptp.num)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) (tptp.aa_num_real tptp.numeral_numeral_real N)))) (forall ((N tptp.num)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) (tptp.aa_num_rat tptp.numeral_numeral_rat N)))) (forall ((N tptp.num)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.aa_num_nat tptp.numeral_numeral_nat N)))) (forall ((N tptp.num)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) (tptp.aa_num_int tptp.numeral_numeral_int N)))) (not (tptp.pp (tptp.aa_real_bool _let_116 tptp.zero_zero_real))) (not (tptp.pp (tptp.aa_rat_bool _let_115 tptp.zero_zero_rat))) (not (tptp.pp (tptp.aa_nat_bool _let_161 tptp.zero_zero_nat))) (not (tptp.pp (tptp.aa_int_bool _let_114 tptp.zero_zero_int))) _let_160 _let_159 _let_158 _let_156 _let_160 _let_159 _let_158 _let_156 (forall ((A tptp.real) (C tptp.real) (B2 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) tptp.zero_zero_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real C) B2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) C)) B2))))) (forall ((A tptp.rat) (C tptp.rat) (B2 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) tptp.zero_zero_rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat C) B2)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) C)) B2))))) (forall ((A tptp.nat) (C tptp.nat) (B2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) tptp.zero_zero_nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat C) B2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) C)) B2))))) (forall ((A tptp.int) (C tptp.int) (B2 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) tptp.zero_zero_int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int C) B2)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) C)) B2))))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real B2))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) A)) (=> (tptp.pp (tptp.aa_real_bool _let_1 C)) (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) C))))))) (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B2))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) A)) (=> (tptp.pp (tptp.aa_rat_bool _let_1 C)) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) C))))))) (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B2))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) A)) (=> (tptp.pp (tptp.aa_nat_bool _let_1 C)) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) C))))))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B2))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) A)) (=> (tptp.pp (tptp.aa_int_bool _let_1 C)) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) C))))))) (forall ((C tptp.real) (A tptp.real) (B2 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real C) tptp.zero_zero_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) B2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) C)) B2))))) (forall ((C tptp.rat) (A tptp.rat) (B2 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat C) tptp.zero_zero_rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B2)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) C)) B2))))) (forall ((C tptp.nat) (A tptp.nat) (B2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat C) tptp.zero_zero_nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) C)) B2))))) (forall ((C tptp.int) (A tptp.int) (B2 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int C) tptp.zero_zero_int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B2)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) C)) B2))))) (forall ((C tptp.real) (B2 tptp.real) (A tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real B2))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) C)) (=> (tptp.pp (tptp.aa_real_bool _let_1 A)) (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) C))))))) (forall ((C tptp.rat) (B2 tptp.rat) (A tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B2))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) C)) (=> (tptp.pp (tptp.aa_rat_bool _let_1 A)) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) C))))))) (forall ((C tptp.nat) (B2 tptp.nat) (A tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B2))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) C)) (=> (tptp.pp (tptp.aa_nat_bool _let_1 A)) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) C))))))) (forall ((C tptp.int) (B2 tptp.int) (A tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B2))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) C)) (=> (tptp.pp (tptp.aa_int_bool _let_1 A)) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) C))))))) (forall ((A tptp.real) (B2 tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool _let_1 A)) (=> (tptp.pp (tptp.aa_real_bool _let_1 B2)) (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) B2))))))) (forall ((A tptp.rat) (B2 tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 A)) (=> (tptp.pp (tptp.aa_rat_bool _let_1 B2)) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) B2))))))) (forall ((A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 A)) (=> (tptp.pp (tptp.aa_nat_bool _let_1 B2)) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) B2))))))) (forall ((A tptp.int) (B2 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.pp (tptp.aa_int_bool _let_1 A)) (=> (tptp.pp (tptp.aa_int_bool _let_1 B2)) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) B2))))))) (forall ((A tptp.real) (B2 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) tptp.zero_zero_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real B2) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) B2)) tptp.zero_zero_real))))) (forall ((A tptp.rat) (B2 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) tptp.zero_zero_rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B2) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) B2)) tptp.zero_zero_rat))))) (forall ((A tptp.nat) (B2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) tptp.zero_zero_nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B2) tptp.zero_zero_nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) B2)) tptp.zero_zero_nat))))) (forall ((A tptp.int) (B2 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) tptp.zero_zero_int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B2) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) B2)) tptp.zero_zero_int))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool _let_1 X)) (=> (tptp.pp (tptp.aa_real_bool _let_1 Y)) (= (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) Y) tptp.zero_zero_real) (and (= X tptp.zero_zero_real) (= Y tptp.zero_zero_real))))))) (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 X)) (=> (tptp.pp (tptp.aa_rat_bool _let_1 Y)) (= (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat X) Y) tptp.zero_zero_rat) (and (= X tptp.zero_zero_rat) (= Y tptp.zero_zero_rat))))))) (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 X)) (=> (tptp.pp (tptp.aa_nat_bool _let_1 Y)) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat X) Y) tptp.zero_zero_nat) (and (= X tptp.zero_zero_nat) (= Y tptp.zero_zero_nat))))))) (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.pp (tptp.aa_int_bool _let_1 X)) (=> (tptp.pp (tptp.aa_int_bool _let_1 Y)) (= (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int X) Y) tptp.zero_zero_int) (and (= X tptp.zero_zero_int) (= Y tptp.zero_zero_int))))))) (forall ((X tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) tptp.zero_zero_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y) tptp.zero_zero_real)) (= (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) Y) tptp.zero_zero_real) (and (= X tptp.zero_zero_real) (= Y tptp.zero_zero_real)))))) (forall ((X tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) tptp.zero_zero_rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat Y) tptp.zero_zero_rat)) (= (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat X) Y) tptp.zero_zero_rat) (and (= X tptp.zero_zero_rat) (= Y tptp.zero_zero_rat)))))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X) tptp.zero_zero_nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Y) tptp.zero_zero_nat)) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat X) Y) tptp.zero_zero_nat) (and (= X tptp.zero_zero_nat) (= Y tptp.zero_zero_nat)))))) (forall ((X tptp.int) (Y tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X) tptp.zero_zero_int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Y) tptp.zero_zero_int)) (= (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int X) Y) tptp.zero_zero_int) (and (= X tptp.zero_zero_int) (= Y tptp.zero_zero_int)))))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.times_times_real C))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B2)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) C)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real _let_1 A)) (tptp.aa_real_real _let_1 B2))))))) (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_rat tptp.times_times_rat C))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B2)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) C)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat _let_1 A)) (tptp.aa_rat_rat _let_1 B2))))))) (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat C))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) B2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) C)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat _let_1 A)) (tptp.aa_nat_nat _let_1 B2))))))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.times_times_int C))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B2)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) C)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int _let_1 A)) (tptp.aa_int_int _let_1 B2))))))) (forall ((A tptp.real) (C tptp.real) (B2 tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) C)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real B2) C))) (or (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) C)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B2))) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real C) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B2) A)))))) (forall ((A tptp.rat) (C tptp.rat) (B2 tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) C)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat B2) C))) (or (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) C)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B2))) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat C) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B2) A)))))) (forall ((A tptp.int) (C tptp.int) (B2 tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B2) C))) (or (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) C)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B2))) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int C) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B2) A)))))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B2)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) C)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) C)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real B2) C)))))) (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B2)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) C)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) C)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat B2) C)))))) (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) B2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) C)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) C)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B2) C)))))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B2)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) C)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B2) C)))))) (forall ((B2 tptp.real) (A tptp.real) (C tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B2) A)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real C) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) C)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real B2) C)))))) (forall ((B2 tptp.rat) (A tptp.rat) (C tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B2) A)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat C) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) C)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat B2) C)))))) (forall ((B2 tptp.int) (A tptp.int) (C tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B2) A)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int C) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B2) C)))))) (forall ((C tptp.real) (A tptp.real) (B2 tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.times_times_real C))) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real _let_1 A)) (tptp.aa_real_real _let_1 B2))) (or (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) C)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B2))) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real C) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B2) A))))))) (forall ((C tptp.rat) (A tptp.rat) (B2 tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_rat tptp.times_times_rat C))) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat _let_1 A)) (tptp.aa_rat_rat _let_1 B2))) (or (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) C)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B2))) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat C) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B2) A))))))) (forall ((C tptp.int) (A tptp.int) (B2 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.times_times_int C))) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int _let_1 A)) (tptp.aa_int_int _let_1 B2))) (or (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) C)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B2))) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int C) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B2) A))))))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.times_times_real C))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B2)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) C)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real _let_1 A)) (tptp.aa_real_real _let_1 B2))))))) (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_rat tptp.times_times_rat C))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B2)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) C)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat _let_1 A)) (tptp.aa_rat_rat _let_1 B2))))))) (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat C))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) B2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) C)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat _let_1 A)) (tptp.aa_nat_nat _let_1 B2))))))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.times_times_int C))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B2)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) C)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int _let_1 A)) (tptp.aa_int_int _let_1 B2))))))) (forall ((B2 tptp.real) (A tptp.real) (C tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.times_times_real C))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B2) A)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real C) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real _let_1 A)) (tptp.aa_real_real _let_1 B2))))))) (forall ((B2 tptp.rat) (A tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_rat tptp.times_times_rat C))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B2) A)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat C) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat _let_1 A)) (tptp.aa_rat_rat _let_1 B2))))))) (forall ((B2 tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.times_times_int C))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B2) A)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int C) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int _let_1 A)) (tptp.aa_int_int _let_1 B2))))))) (forall ((C tptp.real) (A tptp.real) (B2 tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.times_times_real C))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) C)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real _let_1 A)) (tptp.aa_real_real _let_1 B2))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B2)))))) (forall ((C tptp.rat) (A tptp.rat) (B2 tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_rat tptp.times_times_rat C))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) C)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat _let_1 A)) (tptp.aa_rat_rat _let_1 B2))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B2)))))) (forall ((C tptp.int) (A tptp.int) (B2 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.times_times_int C))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) C)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int _let_1 A)) (tptp.aa_int_int _let_1 B2))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B2)))))) (forall ((C tptp.real) (A tptp.real) (B2 tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.times_times_real C))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real C) tptp.zero_zero_real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real _let_1 A)) (tptp.aa_real_real _let_1 B2))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B2) A)))))) (forall ((C tptp.rat) (A tptp.rat) (B2 tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_rat tptp.times_times_rat C))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat C) tptp.zero_zero_rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat _let_1 A)) (tptp.aa_rat_rat _let_1 B2))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B2) A)))))) (forall ((C tptp.int) (A tptp.int) (B2 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.times_times_int C))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int C) tptp.zero_zero_int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int _let_1 A)) (tptp.aa_int_int _let_1 B2))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B2) A)))))) (forall ((B2 tptp.real) (A tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real B2) A))) (=> (tptp.pp (tptp.aa_real_bool _let_1 A)) (tptp.pp (tptp.aa_real_bool _let_1 B2)))))) (forall ((B2 tptp.rat) (A tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat B2) A))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 A)) (tptp.pp (tptp.aa_rat_bool _let_1 B2)))))) (forall ((B2 tptp.nat) (A tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B2) A))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 A)) (tptp.pp (tptp.aa_nat_bool _let_1 B2)))))) (forall ((B2 tptp.int) (A tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int))) (=> (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B2) A))) (=> (tptp.pp (tptp.aa_int_bool _let_1 A)) (tptp.pp (tptp.aa_int_bool _let_1 B2)))))) (forall ((A tptp.real) (B2 tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) B2))) (=> (tptp.pp (tptp.aa_real_bool _let_1 A)) (tptp.pp (tptp.aa_real_bool _let_1 B2)))))) (forall ((A tptp.rat) (B2 tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) B2))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 A)) (tptp.pp (tptp.aa_rat_bool _let_1 B2)))))) (forall ((A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) B2))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 A)) (tptp.pp (tptp.aa_nat_bool _let_1 B2)))))) (forall ((A tptp.int) (B2 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int))) (=> (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) B2))) (=> (tptp.pp (tptp.aa_int_bool _let_1 A)) (tptp.pp (tptp.aa_int_bool _let_1 B2)))))) (forall ((A tptp.real) (B2 tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real))) (= (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) B2))) (or (and (tptp.pp (tptp.aa_real_bool _let_1 A)) (tptp.pp (tptp.aa_real_bool _let_1 B2))) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B2) tptp.zero_zero_real))))))) (forall ((A tptp.rat) (B2 tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat))) (= (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) B2))) (or (and (tptp.pp (tptp.aa_rat_bool _let_1 A)) (tptp.pp (tptp.aa_rat_bool _let_1 B2))) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B2) tptp.zero_zero_rat))))))) (forall ((A tptp.int) (B2 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int))) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) B2))) (or (and (tptp.pp (tptp.aa_int_bool _let_1 A)) (tptp.pp (tptp.aa_int_bool _let_1 B2))) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B2) tptp.zero_zero_int))))))) (forall ((A tptp.real) (B2 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) A)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B2) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real B2) A)) tptp.zero_zero_real))))) (forall ((A tptp.rat) (B2 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) A)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B2) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat B2) A)) tptp.zero_zero_rat))))) (forall ((A tptp.nat) (B2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) A)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat B2) tptp.zero_zero_nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B2) A)) tptp.zero_zero_nat))))) (forall ((A tptp.int) (B2 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) A)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B2) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B2) A)) tptp.zero_zero_int))))) (forall ((A tptp.real) (B2 tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool _let_1 A)) (=> (tptp.pp (tptp.aa_real_bool _let_1 B2)) (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) B2))))))) (forall ((A tptp.rat) (B2 tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 A)) (=> (tptp.pp (tptp.aa_rat_bool _let_1 B2)) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) B2))))))) (forall ((A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 A)) (=> (tptp.pp (tptp.aa_nat_bool _let_1 B2)) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) B2))))))) (forall ((A tptp.int) (B2 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int))) (=> (tptp.pp (tptp.aa_int_bool _let_1 A)) (=> (tptp.pp (tptp.aa_int_bool _let_1 B2)) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) B2))))))) (forall ((A tptp.real) (B2 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) A)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B2) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) B2)) tptp.zero_zero_real))))) (forall ((A tptp.rat) (B2 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) A)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B2) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) B2)) tptp.zero_zero_rat))))) (forall ((A tptp.nat) (B2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) A)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat B2) tptp.zero_zero_nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) B2)) tptp.zero_zero_nat))))) (forall ((A tptp.int) (B2 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) A)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B2) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) B2)) tptp.zero_zero_int))))) (forall ((A tptp.real) (B2 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) tptp.zero_zero_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) B2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) B2)) tptp.zero_zero_real))))) (forall ((A tptp.rat) (B2 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) tptp.zero_zero_rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) B2)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) B2)) tptp.zero_zero_rat))))) (forall ((A tptp.nat) (B2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) tptp.zero_zero_nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) B2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) B2)) tptp.zero_zero_nat))))) (forall ((A tptp.int) (B2 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) tptp.zero_zero_int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) B2)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) B2)) tptp.zero_zero_int))))) (forall ((A tptp.real) (B2 tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real))) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) B2)) tptp.zero_zero_real)) (or (and (tptp.pp (tptp.aa_real_bool _let_1 A)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B2) tptp.zero_zero_real))) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool _let_1 B2))))))) (forall ((A tptp.rat) (B2 tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat))) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) B2)) tptp.zero_zero_rat)) (or (and (tptp.pp (tptp.aa_rat_bool _let_1 A)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B2) tptp.zero_zero_rat))) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool _let_1 B2))))))) (forall ((A tptp.int) (B2 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int))) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) B2)) tptp.zero_zero_int)) (or (and (tptp.pp (tptp.aa_int_bool _let_1 A)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B2) tptp.zero_zero_int))) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool _let_1 B2))))))) (forall ((A tptp.real)) (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) A)) tptp.zero_zero_real)))) (forall ((A tptp.rat)) (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) A)) tptp.zero_zero_rat)))) (forall ((A tptp.int)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) A)) tptp.zero_zero_int)))) (forall ((A tptp.real) (B2 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) tptp.zero_zero_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B2) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) B2)))))) (forall ((A tptp.rat) (B2 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) tptp.zero_zero_rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B2) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) B2)))))) (forall ((A tptp.int) (B2 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) tptp.zero_zero_int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B2) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) B2)))))) (forall ((B2 tptp.bool) (A tptp.bool)) (let ((_let_1 (tptp.vEBT_vebt_maxt (tptp.vEBT_Leaf A B2)))) (let ((_let_2 (tptp.pp A))) (let ((_let_3 (tptp.pp B2))) (and (=> _let_3 (= _let_1 (tptp.some_nat tptp.one_one_nat))) (=> (not _let_3) (and (=> _let_2 (= _let_1 (tptp.some_nat tptp.zero_zero_nat))) (=> (not _let_2) (= _let_1 tptp.none_nat))))))))) (forall ((A tptp.real) (B2 tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) B2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A) B2)) tptp.zero_zero_real)))) (forall ((A tptp.rat) (B2 tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B2)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.minus_minus_rat A) B2)) tptp.zero_zero_rat)))) (forall ((A tptp.int) (B2 tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B2)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) B2)) tptp.zero_zero_int)))) _let_154 _let_153 _let_152 _let_151 (not (tptp.pp (tptp.aa_real_bool _let_113 tptp.zero_zero_real))) (not (tptp.pp (tptp.aa_rat_bool _let_111 tptp.zero_zero_rat))) (not (tptp.pp (tptp.aa_nat_bool _let_155 tptp.zero_zero_nat))) (not (tptp.pp (tptp.aa_int_bool _let_112 tptp.zero_zero_int))) _let_154 _let_153 _let_152 _let_151 (forall ((X tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) Y)) tptp.zero_zero_real)) (or (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y) tptp.zero_zero_real))))) (forall ((X tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat X) Y)) tptp.zero_zero_rat)) (or (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Y) tptp.zero_zero_rat))))) (forall ((X tptp.int) (Y tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int X) Y)) tptp.zero_zero_int)) (or (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Y) tptp.zero_zero_int))))) (forall ((A tptp.real) (B2 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) tptp.zero_zero_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B2) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) B2)) tptp.zero_zero_real))))) (forall ((A tptp.rat) (B2 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) tptp.zero_zero_rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B2) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) B2)) tptp.zero_zero_rat))))) (forall ((A tptp.nat) (B2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) tptp.zero_zero_nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat B2) tptp.zero_zero_nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) B2)) tptp.zero_zero_nat))))) (forall ((A tptp.int) (B2 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) tptp.zero_zero_int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B2) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) B2)) tptp.zero_zero_int))))) (forall ((A tptp.real) (B2 tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool _let_1 A)) (=> (tptp.pp (tptp.aa_real_bool _let_1 B2)) (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) B2))))))) (forall ((A tptp.rat) (B2 tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 A)) (=> (tptp.pp (tptp.aa_rat_bool _let_1 B2)) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) B2))))))) (forall ((A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 A)) (=> (tptp.pp (tptp.aa_nat_bool _let_1 B2)) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) B2))))))) (forall ((A tptp.int) (B2 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int))) (=> (tptp.pp (tptp.aa_int_bool _let_1 A)) (=> (tptp.pp (tptp.aa_int_bool _let_1 B2)) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) B2))))))) (forall ((A tptp.nat) (B2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) B2)) (not (forall ((C2 tptp.nat)) (=> (= B2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) C2)) (= C2 tptp.zero_zero_nat)))))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B2))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) A)) (=> (tptp.pp (tptp.aa_real_bool _let_1 C)) (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) C))))))) (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B2))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) A)) (=> (tptp.pp (tptp.aa_rat_bool _let_1 C)) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) C))))))) (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat B2))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) A)) (=> (tptp.pp (tptp.aa_nat_bool _let_1 C)) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) C))))))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_int B2))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) A)) (=> (tptp.pp (tptp.aa_int_bool _let_1 C)) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) C))))))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) B2)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real C) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real B2) C)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real A) C)))))) (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B2)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat C) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.divide_divide_rat B2) C)) (tptp.aa_rat_rat (tptp.divide_divide_rat A) C)))))) (forall ((X tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) tptp.zero_zero_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real X) Y)))))) (forall ((X tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) tptp.zero_zero_rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat Y) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_rat_rat (tptp.divide_divide_rat X) Y)))))) (forall ((X tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) tptp.zero_zero_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) Y)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real X) Y)) tptp.zero_zero_real))))) (forall ((X tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) tptp.zero_zero_rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) Y)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.divide_divide_rat X) Y)) tptp.zero_zero_rat))))) (forall ((X tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real X) Y)) tptp.zero_zero_real))))) (forall ((X tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) X)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat Y) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.divide_divide_rat X) Y)) tptp.zero_zero_rat))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool _let_1 X)) (=> (tptp.pp (tptp.aa_real_bool _let_1 Y)) (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real X) Y))))))) (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 X)) (=> (tptp.pp (tptp.aa_rat_bool _let_1 Y)) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat (tptp.divide_divide_rat X) Y))))))) (forall ((A tptp.real) (B2 tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (= (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real A) B2))) (or (and (tptp.pp (tptp.aa_real_bool _let_1 A)) (tptp.pp (tptp.aa_real_bool _let_1 B2))) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real B2) tptp.zero_zero_real))))))) (forall ((A tptp.rat) (B2 tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat))) (= (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat (tptp.divide_divide_rat A) B2))) (or (and (tptp.pp (tptp.aa_rat_bool _let_1 A)) (tptp.pp (tptp.aa_rat_bool _let_1 B2))) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B2) tptp.zero_zero_rat))))))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) B2)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) C)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real A) C)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real B2) C)))))) (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B2)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) C)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.divide_divide_rat A) C)) (tptp.aa_rat_rat (tptp.divide_divide_rat B2) C)))))) (forall ((A tptp.real) (B2 tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real A) B2)) tptp.zero_zero_real)) (or (and (tptp.pp (tptp.aa_real_bool _let_1 A)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real B2) tptp.zero_zero_real))) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool _let_1 B2))))))) (forall ((A tptp.rat) (B2 tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat))) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.divide_divide_rat A) B2)) tptp.zero_zero_rat)) (or (and (tptp.pp (tptp.aa_rat_bool _let_1 A)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B2) tptp.zero_zero_rat))) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool _let_1 B2))))))) (forall ((A tptp.real) (B2 tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A) B2)) tptp.zero_zero_real)))) (forall ((A tptp.rat) (B2 tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B2)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.minus_minus_rat A) B2)) tptp.zero_zero_rat)))) (forall ((A tptp.int) (B2 tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B2)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) B2)) tptp.zero_zero_int)))) (forall ((B2 tptp.real) (A tptp.real) (C tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B2) A)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real C) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real A) C)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real B2) C)))))) (forall ((B2 tptp.rat) (A tptp.rat) (C tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B2) A)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat C) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.divide_divide_rat A) C)) (tptp.aa_rat_rat (tptp.divide_divide_rat B2) C)))))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B2)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) C)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real A) C)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real B2) C)))))) (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B2)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) C)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.divide_divide_rat A) C)) (tptp.aa_rat_rat (tptp.divide_divide_rat B2) C)))))) (forall ((A tptp.real) (B2 tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real))) (= (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real A) B2))) (or (and (tptp.pp (tptp.aa_real_bool _let_1 A)) (tptp.pp (tptp.aa_real_bool _let_1 B2))) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B2) tptp.zero_zero_real))))))) (forall ((A tptp.rat) (B2 tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat))) (= (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat (tptp.divide_divide_rat A) B2))) (or (and (tptp.pp (tptp.aa_rat_bool _let_1 A)) (tptp.pp (tptp.aa_rat_bool _let_1 B2))) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B2) tptp.zero_zero_rat))))))) (forall ((A tptp.real) (C tptp.real) (B2 tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real A) C)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real B2) C))) (and (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) C)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B2))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real C) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B2) A))) (not (= C tptp.zero_zero_real))))) (forall ((A tptp.rat) (C tptp.rat) (B2 tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.divide_divide_rat A) C)) (tptp.aa_rat_rat (tptp.divide_divide_rat B2) C))) (and (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) C)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B2))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat C) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B2) A))) (not (= C tptp.zero_zero_rat))))) (forall ((A tptp.real) (B2 tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real))) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real A) B2)) tptp.zero_zero_real)) (or (and (tptp.pp (tptp.aa_real_bool _let_1 A)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B2) tptp.zero_zero_real))) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool _let_1 B2))))))) (forall ((A tptp.rat) (B2 tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat))) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.divide_divide_rat A) B2)) tptp.zero_zero_rat)) (or (and (tptp.pp (tptp.aa_rat_bool _let_1 A)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B2) tptp.zero_zero_rat))) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool _let_1 B2))))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool _let_1 X)) (=> (tptp.pp (tptp.aa_real_bool _let_1 Y)) (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real X) Y))))))) (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 X)) (=> (tptp.pp (tptp.aa_rat_bool _let_1 Y)) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat (tptp.divide_divide_rat X) Y))))))) (forall ((X tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real X) Y)) tptp.zero_zero_real))))) (forall ((X tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) X)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Y) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.divide_divide_rat X) Y)) tptp.zero_zero_rat))))) (forall ((X tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) tptp.zero_zero_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) Y)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real X) Y)) tptp.zero_zero_real))))) (forall ((X tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) tptp.zero_zero_rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) Y)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.divide_divide_rat X) Y)) tptp.zero_zero_rat))))) (forall ((X tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) tptp.zero_zero_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real X) Y)))))) (forall ((X tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) tptp.zero_zero_rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Y) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) (tptp.aa_rat_rat (tptp.divide_divide_rat X) Y)))))) (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool _let_1 A)) (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real A) N)))))) (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 A)) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_nat_rat (tptp.power_power_rat A) N)))))) (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 A)) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A) N)))))) (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.pp (tptp.aa_int_bool _let_1 A)) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_nat_int (tptp.power_power_int A) N)))))) (forall ((A tptp.real) (B2 tptp.real) (N tptp.nat)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) B2)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) A)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real A) N)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real B2) N)))))) (forall ((A tptp.rat) (B2 tptp.rat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B2)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) A)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat (tptp.power_power_rat A) N)) (tptp.aa_nat_rat (tptp.power_power_rat B2) N)))))) (forall ((A tptp.nat) (B2 tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) A)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A) N)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat B2) N)))))) (forall ((A tptp.int) (B2 tptp.int) (N tptp.nat)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B2)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) A)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int (tptp.power_power_int A) N)) (tptp.aa_nat_int (tptp.power_power_int B2) N)))))) (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool _let_1 A)) (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real A) N)))))) (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 A)) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_nat_rat (tptp.power_power_rat A) N)))))) (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 A)) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A) N)))))) (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int))) (=> (tptp.pp (tptp.aa_int_bool _let_1 A)) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_nat_int (tptp.power_power_int A) N)))))) (forall ((X tptp.vEBT_VEBT)) (=> (not (tptp.pp (tptp.aa_VEBT_VEBT_bool tptp.vEBT_VEBT_minNull X))) (=> (forall ((Uv2 tptp.bool)) (not (= X (tptp.vEBT_Leaf tptp.fTrue Uv2)))) (=> (forall ((Uu2 tptp.bool)) (not (= X (tptp.vEBT_Leaf Uu2 tptp.fTrue)))) (not (forall ((Uz2 tptp.product_prod_nat_nat) (Va3 tptp.nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (not (= X (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat Uz2) Va3 Vb2 Vc2))))))))) (forall ((Y tptp.complex) (Z tptp.complex) (X tptp.complex) (W tptp.complex)) (=> (not (= Y tptp.zero_zero_complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (= (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex X) Y) (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex W) Z)) (= (tptp.aa_complex_complex (tptp.times_times_complex X) Z) (tptp.aa_complex_complex (tptp.times_times_complex W) Y)))))) (forall ((Y tptp.real) (Z tptp.real) (X tptp.real) (W tptp.real)) (=> (not (= Y tptp.zero_zero_real)) (=> (not (= Z tptp.zero_zero_real)) (= (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real X) Y) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real W) Z)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real X) Z) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real W) Y)))))) (forall ((Y tptp.rat) (Z tptp.rat) (X tptp.rat) (W tptp.rat)) (=> (not (= Y tptp.zero_zero_rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (= (tptp.aa_rat_rat (tptp.divide_divide_rat X) Y) (tptp.aa_rat_rat (tptp.divide_divide_rat W) Z)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat X) Z) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat W) Y)))))) (forall ((B2 tptp.complex) (C tptp.complex) (A tptp.complex)) (let ((_let_1 (= C tptp.zero_zero_complex))) (= (= (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex B2) C) A) (and (=> (not _let_1) (= B2 (tptp.aa_complex_complex (tptp.times_times_complex A) C))) (=> _let_1 (= A tptp.zero_zero_complex)))))) (forall ((B2 tptp.real) (C tptp.real) (A tptp.real)) (let ((_let_1 (= C tptp.zero_zero_real))) (= (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real B2) C) A) (and (=> (not _let_1) (= B2 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) C))) (=> _let_1 (= A tptp.zero_zero_real)))))) (forall ((B2 tptp.rat) (C tptp.rat) (A tptp.rat)) (let ((_let_1 (= C tptp.zero_zero_rat))) (= (= (tptp.aa_rat_rat (tptp.divide_divide_rat B2) C) A) (and (=> (not _let_1) (= B2 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) C))) (=> _let_1 (= A tptp.zero_zero_rat)))))) (forall ((A tptp.complex) (B2 tptp.complex) (C tptp.complex)) (let ((_let_1 (= C tptp.zero_zero_complex))) (= (= A (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex B2) C)) (and (=> (not _let_1) (= (tptp.aa_complex_complex (tptp.times_times_complex A) C) B2)) (=> _let_1 (= A tptp.zero_zero_complex)))))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (= C tptp.zero_zero_real))) (= (= A (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real B2) C)) (and (=> (not _let_1) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) C) B2)) (=> _let_1 (= A tptp.zero_zero_real)))))) (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (= C tptp.zero_zero_rat))) (= (= A (tptp.aa_rat_rat (tptp.divide_divide_rat B2) C)) (and (=> (not _let_1) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) C) B2)) (=> _let_1 (= A tptp.zero_zero_rat)))))) (forall ((C tptp.complex) (B2 tptp.complex) (A tptp.complex)) (=> (not (= C tptp.zero_zero_complex)) (=> (= B2 (tptp.aa_complex_complex (tptp.times_times_complex A) C)) (= (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex B2) C) A)))) (forall ((C tptp.real) (B2 tptp.real) (A tptp.real)) (=> (not (= C tptp.zero_zero_real)) (=> (= B2 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) C)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real B2) C) A)))) (forall ((C tptp.rat) (B2 tptp.rat) (A tptp.rat)) (=> (not (= C tptp.zero_zero_rat)) (=> (= B2 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) C)) (= (tptp.aa_rat_rat (tptp.divide_divide_rat B2) C) A)))) (forall ((C tptp.complex) (A tptp.complex) (B2 tptp.complex)) (=> (not (= C tptp.zero_zero_complex)) (=> (= (tptp.aa_complex_complex (tptp.times_times_complex A) C) B2) (= A (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex B2) C))))) (forall ((C tptp.real) (A tptp.real) (B2 tptp.real)) (=> (not (= C tptp.zero_zero_real)) (=> (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) C) B2) (= A (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real B2) C))))) (forall ((C tptp.rat) (A tptp.rat) (B2 tptp.rat)) (=> (not (= C tptp.zero_zero_rat)) (=> (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) C) B2) (= A (tptp.aa_rat_rat (tptp.divide_divide_rat B2) C))))) (forall ((C tptp.complex) (B2 tptp.complex) (A tptp.complex)) (=> (not (= C tptp.zero_zero_complex)) (= (= (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex B2) C) A) (= B2 (tptp.aa_complex_complex (tptp.times_times_complex A) C))))) (forall ((C tptp.real) (B2 tptp.real) (A tptp.real)) (=> (not (= C tptp.zero_zero_real)) (= (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real B2) C) A) (= B2 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) C))))) (forall ((C tptp.rat) (B2 tptp.rat) (A tptp.rat)) (=> (not (= C tptp.zero_zero_rat)) (= (= (tptp.aa_rat_rat (tptp.divide_divide_rat B2) C) A) (= B2 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) C))))) (forall ((C tptp.complex) (A tptp.complex) (B2 tptp.complex)) (=> (not (= C tptp.zero_zero_complex)) (= (= A (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex B2) C)) (= (tptp.aa_complex_complex (tptp.times_times_complex A) C) B2)))) (forall ((C tptp.real) (A tptp.real) (B2 tptp.real)) (=> (not (= C tptp.zero_zero_real)) (= (= A (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real B2) C)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) C) B2)))) (forall ((C tptp.rat) (A tptp.rat) (B2 tptp.rat)) (=> (not (= C tptp.zero_zero_rat)) (= (= A (tptp.aa_rat_rat (tptp.divide_divide_rat B2) C)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) C) B2)))) (forall ((B2 tptp.complex) (A tptp.complex)) (=> (not (= B2 tptp.zero_zero_complex)) (= (= (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex A) B2) tptp.one_one_complex) (= A B2)))) (forall ((B2 tptp.real) (A tptp.real)) (=> (not (= B2 tptp.zero_zero_real)) (= (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real A) B2) tptp.one_one_real) (= A B2)))) (forall ((B2 tptp.rat) (A tptp.rat)) (=> (not (= B2 tptp.zero_zero_rat)) (= (= (tptp.aa_rat_rat (tptp.divide_divide_rat A) B2) tptp.one_one_rat) (= A B2)))) (forall ((X tptp.vEBT_VEBT)) (=> (tptp.pp (tptp.aa_VEBT_VEBT_bool tptp.vEBT_VEBT_minNull X)) (=> (not (= X (tptp.vEBT_Leaf tptp.fFalse tptp.fFalse))) (not (forall ((Uw2 tptp.nat) (Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (not (= X (tptp.vEBT_Node tptp.none_P5556105721700978146at_nat Uw2 Ux2 Uy2)))))))) (forall ((A tptp.rat)) (= (tptp.aa_nat_rat (tptp.power_power_rat A) tptp.zero_zero_nat) tptp.one_one_rat)) (forall ((A tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A) tptp.zero_zero_nat) tptp.one_one_nat)) (forall ((A tptp.real)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real A) tptp.zero_zero_nat) tptp.one_one_real)) (forall ((A tptp.int)) (= (tptp.aa_nat_int (tptp.power_power_int A) tptp.zero_zero_nat) tptp.one_one_int)) (forall ((A tptp.complex)) (= (tptp.aa_nat_complex (tptp.power_power_complex A) tptp.zero_zero_nat) tptp.one_one_complex)) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) (tptp.aa_nat_nat tptp.suc N))) (or (= M tptp.zero_zero_nat) (exists ((J3 tptp.nat)) (and (= M (tptp.aa_nat_nat tptp.suc J3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat J3) N))))))) (forall ((N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (exists ((M3 tptp.nat)) (= N (tptp.aa_nat_nat tptp.suc M3))))) (forall ((N tptp.nat) (P tptp.fun_nat_bool)) (= (forall ((I4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I4) (tptp.aa_nat_nat tptp.suc N))) (tptp.pp (tptp.aa_nat_bool P I4)))) (and (tptp.pp (tptp.aa_nat_bool P tptp.zero_zero_nat)) (forall ((I4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I4) N)) (tptp.pp (tptp.aa_nat_bool P (tptp.aa_nat_nat tptp.suc I4)))))))) (forall ((N tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (exists ((M6 tptp.nat)) (= N (tptp.aa_nat_nat tptp.suc M6))))) (forall ((N tptp.nat) (P tptp.fun_nat_bool)) (= (exists ((I4 tptp.nat)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I4) (tptp.aa_nat_nat tptp.suc N))) (tptp.pp (tptp.aa_nat_bool P I4)))) (or (tptp.pp (tptp.aa_nat_bool P tptp.zero_zero_nat)) (exists ((I4 tptp.nat)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I4) N)) (tptp.pp (tptp.aa_nat_bool P (tptp.aa_nat_nat tptp.suc I4)))))))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat))) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) N) _let_1) (or (and (= M _let_1) (= N tptp.zero_zero_nat)) (and (= M tptp.zero_zero_nat) (= N _let_1)))))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat))) (= (= _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) N)) (or (and (= M _let_1) (= N tptp.zero_zero_nat)) (and (= M tptp.zero_zero_nat) (= N _let_1)))))) (forall ((P tptp.fun_nat_bool) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool P N)) (=> (not (tptp.pp (tptp.aa_nat_bool P tptp.zero_zero_nat))) (exists ((K3 tptp.nat)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K3) N)) (forall ((I2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I2) K3)) (not (tptp.pp (tptp.aa_nat_bool P I2))))) (tptp.pp (tptp.aa_nat_bool P K3))))))) (forall ((X2 tptp.nat)) (= (tptp.size_size_option_nat (tptp.some_nat X2)) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat))) (forall ((X2 tptp.product_prod_nat_nat)) (= (tptp.size_s170228958280169651at_nat (tptp.some_P7363390416028606310at_nat X2)) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat))) (forall ((X2 tptp.num)) (= (tptp.size_size_option_num (tptp.some_num X2)) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat))) (forall ((I tptp.nat) (J tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I) J)) (exists ((K3 tptp.nat)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) K3)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat I) K3) J))))) (= (tptp.size_size_option_nat tptp.none_nat) _let_42) (= (tptp.size_s170228958280169651at_nat tptp.none_P5556105721700978146at_nat) _let_42) (= (tptp.size_size_option_num tptp.none_num) _let_42) (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 N)) (=> (tptp.pp (tptp.aa_nat_bool _let_1 M)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) N)) M)))))) (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat K))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) K)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat _let_1 M)) (tptp.aa_nat_nat _let_1 N))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N)))))) (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat K))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) K)) (= (= (tptp.aa_nat_nat _let_1 M) (tptp.aa_nat_nat _let_1 N)) (= M N))))) (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat K))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I) J)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) K)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat _let_1 I)) (tptp.aa_nat_nat _let_1 J))))))) (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I) J)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) K)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat I) K)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat J) K)))))) (= tptp.one_one_nat _let_42) (forall ((B2 tptp.nat) (A tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A))) (let ((_let_2 (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) B2)))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) B2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_2) B2)) (= _let_2 (tptp.aa_nat_nat _let_1 B2))))))) (forall ((B2 tptp.int) (A tptp.int)) (let ((_let_1 (tptp.modulo_modulo_int A))) (let ((_let_2 (tptp.aa_int_int _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) B2)))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) B2)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int _let_2) B2)) (= _let_2 (tptp.aa_int_int _let_1 B2))))))) (forall ((B2 tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (tptp.modulo364778990260209775nteger A (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))) B2)))) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) B2)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger _let_1) B2)) (= _let_1 (tptp.modulo364778990260209775nteger A B2)))))) (forall ((M tptp.nat) (N tptp.nat)) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat M) N) tptp.zero_zero_nat) (or (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N)) (= N tptp.zero_zero_nat)))) (forall ((N tptp.nat) (M tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N) M)) tptp.zero_zero_nat)) (forall ((A tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) _let_1) A) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A) _let_1)) tptp.zero_zero_nat)))) (forall ((A tptp.int)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (= (tptp.aa_int_int (tptp.divide_divide_int A) _let_1) A) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) (tptp.aa_int_int (tptp.modulo_modulo_int A) _let_1)) tptp.zero_zero_int)))) (forall ((A tptp.code_integer)) (let ((_let_1 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (= (tptp.divide6298287555418463151nteger A _let_1) A) (= (tptp.plus_p5714425477246183910nteger A (tptp.modulo364778990260209775nteger A _let_1)) tptp.zero_z3403309356797280102nteger)))) (forall ((I tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat I))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) I)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat _let_1 M)) (tptp.aa_nat_nat _let_1 N))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N)))))) (forall ((M tptp.nat) (N tptp.nat)) (=> (= M (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat M) N)) (or (= N tptp.one_one_nat) (= M tptp.zero_zero_nat)))) (forall ((Info tptp.option4927543243414619207at_nat) (Ts tptp.list_VEBT_VEBT) (S tptp.vEBT_VEBT) (X tptp.nat)) (let ((_let_1 (tptp.vEBT_Node Info (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat) Ts S))) (= (tptp.vEBT_vebt_insert _let_1 X) _let_1))) (forall ((V tptp.product_prod_nat_nat) (Uy tptp.list_VEBT_VEBT) (Uz tptp.vEBT_VEBT) (X tptp.nat)) (not (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_vebt_member (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat V) tptp.zero_zero_nat Uy Uz)) X)))) (forall ((A4 tptp.nat) (B4 tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A4) B4)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A4) N)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.if_nat (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.fequal_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat B4) N)) tptp.zero_zero_nat)) tptp.one_one_nat) tptp.zero_zero_nat))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat B4) N)))))) (forall ((X tptp.produc9072475918466114483BT_nat)) (=> (forall ((Uu2 tptp.bool) (Uv2 tptp.bool) (Uw2 tptp.nat)) (not (= X (tptp.produc738532404422230701BT_nat (tptp.vEBT_Leaf Uu2 Uv2) Uw2)))) (=> (forall ((Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT) (Uz2 tptp.nat)) (not (= X (tptp.produc738532404422230701BT_nat (tptp.vEBT_Node tptp.none_P5556105721700978146at_nat tptp.zero_zero_nat Ux2 Uy2) Uz2)))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.list_VEBT_VEBT) (Vb2 tptp.vEBT_VEBT) (X4 tptp.nat)) (not (= X (tptp.produc738532404422230701BT_nat (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Mi2) Ma2)) tptp.zero_zero_nat Va3 Vb2) X4)))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT) (X4 tptp.nat)) (not (= X (tptp.produc738532404422230701BT_nat (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Mi2) Ma2)) (tptp.aa_nat_nat tptp.suc V2) TreeList2 Vc2) X4)))) (not (forall ((V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Vd2 tptp.vEBT_VEBT) (X4 tptp.nat)) (not (= X (tptp.produc738532404422230701BT_nat (tptp.vEBT_Node tptp.none_P5556105721700978146at_nat (tptp.aa_nat_nat tptp.suc V2) TreeList2 Vd2) X4)))))))))) (forall ((X tptp.produc9072475918466114483BT_nat)) (=> (forall ((Uu2 tptp.bool) (Uv2 tptp.bool)) (not (= X (tptp.produc738532404422230701BT_nat (tptp.vEBT_Leaf Uu2 Uv2) tptp.zero_zero_nat)))) (=> (forall ((A3 tptp.bool) (Uw2 tptp.bool)) (not (= X (tptp.produc738532404422230701BT_nat (tptp.vEBT_Leaf A3 Uw2) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat))))) (=> (forall ((A3 tptp.bool) (B3 tptp.bool) (Va2 tptp.nat)) (not (= X (tptp.produc738532404422230701BT_nat (tptp.vEBT_Leaf A3 B3) (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat tptp.suc Va2)))))) (=> (forall ((Uy2 tptp.nat) (Uz2 tptp.list_VEBT_VEBT) (Va3 tptp.vEBT_VEBT) (Vb2 tptp.nat)) (not (= X (tptp.produc738532404422230701BT_nat (tptp.vEBT_Node tptp.none_P5556105721700978146at_nat Uy2 Uz2 Va3) Vb2)))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vd2 tptp.list_VEBT_VEBT) (Ve tptp.vEBT_VEBT) (Vf tptp.nat)) (not (= X (tptp.produc738532404422230701BT_nat (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat V2) tptp.zero_zero_nat Vd2 Ve) Vf)))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vh tptp.list_VEBT_VEBT) (Vi tptp.vEBT_VEBT) (Vj tptp.nat)) (not (= X (tptp.produc738532404422230701BT_nat (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat V2) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat) Vh Vi) Vj)))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (X4 tptp.nat)) (not (= X (tptp.produc738532404422230701BT_nat (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Mi2) Ma2)) (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat tptp.suc Va2)) TreeList2 Summary2) X4)))))))))))) (forall ((B2 tptp.bool) (A tptp.bool) (Va tptp.nat)) (let ((_let_1 (tptp.vEBT_vebt_pred (tptp.vEBT_Leaf A B2) (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat tptp.suc Va))))) (let ((_let_2 (tptp.pp A))) (let ((_let_3 (tptp.pp B2))) (and (=> _let_3 (= _let_1 (tptp.some_nat tptp.one_one_nat))) (=> (not _let_3) (and (=> _let_2 (= _let_1 (tptp.some_nat tptp.zero_zero_nat))) (=> (not _let_2) (= _let_1 tptp.none_nat))))))))) (forall ((B2 tptp.nat) (A tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A))) (let ((_let_2 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_3 (tptp.aa_nat_nat _let_2 B2))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) B2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A) _let_3)) B2)) (= (tptp.aa_nat_nat _let_2 (tptp.aa_nat_nat _let_1 _let_3)) (tptp.aa_nat_nat _let_1 B2)))))))) (forall ((B2 tptp.int) (A tptp.int)) (let ((_let_1 (tptp.divide_divide_int A))) (let ((_let_2 (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_3 (tptp.aa_int_int _let_2 B2))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) B2)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.modulo_modulo_int A) _let_3)) B2)) (= (tptp.aa_int_int _let_2 (tptp.aa_int_int _let_1 _let_3)) (tptp.aa_int_int _let_1 B2)))))))) (forall ((B2 tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_2 (tptp.aa_Cod1783974652533396728nteger _let_1 B2))) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) B2)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.modulo364778990260209775nteger A _let_2)) B2)) (= (tptp.aa_Cod1783974652533396728nteger _let_1 (tptp.divide6298287555418463151nteger A _let_2)) (tptp.divide6298287555418463151nteger A B2))))))) (forall ((M tptp.num) (Q2 tptp.num)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 Q2)))) (not (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 M))) _let_1) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_num_nat tptp.numeral_numeral_nat tptp.one)) _let_1))))) (forall ((M tptp.num) (Q2 tptp.num)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 Q2)))) (not (= (tptp.aa_int_int (tptp.modulo_modulo_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 M))) _let_1) (tptp.aa_int_int (tptp.modulo_modulo_int (tptp.aa_num_int tptp.numeral_numeral_int tptp.one)) _let_1))))) (forall ((M tptp.num) (Q2 tptp.num)) (let ((_let_1 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 Q2)))) (not (= (tptp.modulo364778990260209775nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 M)) _let_1) (tptp.modulo364778990260209775nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger tptp.one) _let_1))))) (forall ((Q2 tptp.num) (N tptp.num)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 Q2)))) (not (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_num_nat tptp.numeral_numeral_nat tptp.one)) _let_1) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 N))) _let_1))))) (forall ((Q2 tptp.num) (N tptp.num)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 Q2)))) (not (= (tptp.aa_int_int (tptp.modulo_modulo_int (tptp.aa_num_int tptp.numeral_numeral_int tptp.one)) _let_1) (tptp.aa_int_int (tptp.modulo_modulo_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 N))) _let_1))))) (forall ((Q2 tptp.num) (N tptp.num)) (let ((_let_1 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 Q2)))) (not (= (tptp.modulo364778990260209775nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger tptp.one) _let_1) (tptp.modulo364778990260209775nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 N)) _let_1))))) (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat _let_1 B2)) C) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat B2) C))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat B2) C))) C))))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.times_times_int A))) (= (tptp.aa_int_int (tptp.divide_divide_int (tptp.aa_int_int _let_1 B2)) C) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int _let_1 (tptp.aa_int_int (tptp.divide_divide_int B2) C))) (tptp.aa_int_int (tptp.divide_divide_int (tptp.aa_int_int _let_1 (tptp.aa_int_int (tptp.modulo_modulo_int B2) C))) C))))) (forall ((A tptp.code_integer) (B2 tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A))) (= (tptp.divide6298287555418463151nteger (tptp.aa_Cod1783974652533396728nteger _let_1 B2) C) (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger _let_1 (tptp.divide6298287555418463151nteger B2 C)) (tptp.divide6298287555418463151nteger (tptp.aa_Cod1783974652533396728nteger _let_1 (tptp.modulo364778990260209775nteger B2 C)) C))))) (forall ((B2 tptp.nat) (A tptp.nat) (C tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) B2))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A) B2))) C) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) C))) (forall ((B2 tptp.int) (A tptp.int) (C tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B2) (tptp.aa_int_int (tptp.divide_divide_int A) B2))) (tptp.aa_int_int (tptp.modulo_modulo_int A) B2))) C) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) C))) (forall ((B2 tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (= (tptp.plus_p5714425477246183910nteger (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B2) (tptp.divide6298287555418463151nteger A B2)) (tptp.modulo364778990260209775nteger A B2)) C) (tptp.plus_p5714425477246183910nteger A C))) (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) B2)) B2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A) B2))) C) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) C))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.divide_divide_int A) B2)) B2)) (tptp.aa_int_int (tptp.modulo_modulo_int A) B2))) C) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) C))) (forall ((A tptp.code_integer) (B2 tptp.code_integer) (C tptp.code_integer)) (= (tptp.plus_p5714425477246183910nteger (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.divide6298287555418463151nteger A B2)) B2) (tptp.modulo364778990260209775nteger A B2)) C) (tptp.plus_p5714425477246183910nteger A C))) (forall ((A tptp.nat) (B2 tptp.nat)) (= A (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) B2)) B2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A) B2)))) (forall ((A tptp.int) (B2 tptp.int)) (= A (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.divide_divide_int A) B2)) B2)) (tptp.aa_int_int (tptp.modulo_modulo_int A) B2)))) (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (= A (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.divide6298287555418463151nteger A B2)) B2) (tptp.modulo364778990260209775nteger A B2)))) (forall ((A tptp.nat) (B2 tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) B2)) B2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A) B2)) A)) (forall ((A tptp.int) (B2 tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.divide_divide_int A) B2)) B2)) (tptp.aa_int_int (tptp.modulo_modulo_int A) B2)) A)) (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (= (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.divide6298287555418463151nteger A B2)) B2) (tptp.modulo364778990260209775nteger A B2)) A)) (forall ((A tptp.nat) (B2 tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A) B2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) B2)) B2)) A)) (forall ((A tptp.int) (B2 tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.modulo_modulo_int A) B2)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.divide_divide_int A) B2)) B2)) A)) (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (= (tptp.plus_p5714425477246183910nteger (tptp.modulo364778990260209775nteger A B2) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.divide6298287555418463151nteger A B2)) B2)) A)) (forall ((A tptp.nat) (B2 tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A) B2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) B2))) A)) (forall ((A tptp.int) (B2 tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.modulo_modulo_int A) B2)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B2) (tptp.aa_int_int (tptp.divide_divide_int A) B2))) A)) (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (= (tptp.plus_p5714425477246183910nteger (tptp.modulo364778990260209775nteger A B2) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B2) (tptp.divide6298287555418463151nteger A B2))) A)) (forall ((B2 tptp.nat) (A tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) B2))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A) B2)) A)) (forall ((B2 tptp.int) (A tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B2) (tptp.aa_int_int (tptp.divide_divide_int A) B2))) (tptp.aa_int_int (tptp.modulo_modulo_int A) B2)) A)) (forall ((B2 tptp.code_integer) (A tptp.code_integer)) (= (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B2) (tptp.divide6298287555418463151nteger A B2)) (tptp.modulo364778990260209775nteger A B2)) A)) (forall ((A tptp.nat) (B2 tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) B2)) B2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A) B2))) (forall ((A tptp.int) (B2 tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.divide_divide_int A) B2)) B2)) (tptp.aa_int_int (tptp.modulo_modulo_int A) B2))) (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (= (tptp.minus_8373710615458151222nteger A (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.divide6298287555418463151nteger A B2)) B2)) (tptp.modulo364778990260209775nteger A B2))) (forall ((A tptp.nat) (B2 tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A) B2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) B2)) B2))) (forall ((A tptp.int) (B2 tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) (tptp.aa_int_int (tptp.modulo_modulo_int A) B2)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.divide_divide_int A) B2)) B2))) (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (= (tptp.minus_8373710615458151222nteger A (tptp.modulo364778990260209775nteger A B2)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.divide6298287555418463151nteger A B2)) B2))) (forall ((A tptp.nat) (B2 tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A) B2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) B2)))) (forall ((A tptp.int) (B2 tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) (tptp.aa_int_int (tptp.modulo_modulo_int A) B2)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B2) (tptp.aa_int_int (tptp.divide_divide_int A) B2)))) (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (= (tptp.minus_8373710615458151222nteger A (tptp.modulo364778990260209775nteger A B2)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B2) (tptp.divide6298287555418463151nteger A B2)))) (forall ((A tptp.nat) (B2 tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) B2))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A) B2))) (forall ((A tptp.int) (B2 tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B2) (tptp.aa_int_int (tptp.divide_divide_int A) B2))) (tptp.aa_int_int (tptp.modulo_modulo_int A) B2))) (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (= (tptp.minus_8373710615458151222nteger A (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B2) (tptp.divide6298287555418463151nteger A B2))) (tptp.modulo364778990260209775nteger A B2))) (forall ((M tptp.nat) (Q2 tptp.nat) (N tptp.nat)) (=> (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat M) Q2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat N) Q2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N) M)) (not (forall ((S3 tptp.nat)) (not (= M (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat Q2) S3))))))))) (forall ((M tptp.nat) (Q2 tptp.nat) (N tptp.nat)) (=> (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat M) Q2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat N) Q2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)) (not (forall ((S3 tptp.nat)) (not (= N (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat Q2) S3))))))))) (forall ((X tptp.nat) (N tptp.nat) (Y tptp.nat)) (=> (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat X) N) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat Y) N)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Y) X)) (exists ((Q3 tptp.nat)) (= X (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Y) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat N) Q3))))))) (forall ((X tptp.vEBT_VEBT) (Y tptp.bool)) (let ((_let_1 (tptp.pp Y))) (let ((_let_2 (not _let_1))) (=> (= (tptp.pp (tptp.aa_VEBT_VEBT_bool tptp.vEBT_VEBT_minNull X)) _let_1) (=> (=> (= X (tptp.vEBT_Leaf tptp.fFalse tptp.fFalse)) _let_2) (=> (=> (exists ((Uv2 tptp.bool)) (= X (tptp.vEBT_Leaf tptp.fTrue Uv2))) _let_1) (=> (=> (exists ((Uu2 tptp.bool)) (= X (tptp.vEBT_Leaf Uu2 tptp.fTrue))) _let_1) (=> (=> (exists ((Uw2 tptp.nat) (Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (= X (tptp.vEBT_Node tptp.none_P5556105721700978146at_nat Uw2 Ux2 Uy2))) _let_2) (not (=> (exists ((Uz2 tptp.product_prod_nat_nat) (Va3 tptp.nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (= X (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat Uz2) Va3 Vb2 Vc2))) _let_1)))))))))) (forall ((A4 tptp.nat) (N tptp.nat)) (= A4 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A4) N)) N)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A4) N)))) (forall ((M tptp.nat) (N tptp.nat) (Q2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat M))) (let ((_let_2 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat N))) (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat _let_2 Q2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat _let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat M) N)) Q2))) (tptp.aa_nat_nat _let_1 N)))))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat M) N) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat M) N)) N)))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real) (D tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B2)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real C) D)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) A)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) C)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) C)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real B2) D)))))))) (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat) (D tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B2)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat C) D)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) A)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) C)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) C)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat B2) D)))))))) (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat) (D tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) B2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat C) D)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) A)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) C)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) C)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B2) D)))))))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int) (D tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B2)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int C) D)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) A)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) C)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B2) D)))))))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real) (D tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) B2)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real C) D)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) A)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) C)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) C)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real B2) D)))))))) (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat) (D tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B2)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat C) D)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) A)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) C)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) C)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat B2) D)))))))) (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat) (D tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat C) D)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) A)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) C)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) C)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B2) D)))))))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int) (D tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B2)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int C) D)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) A)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) C)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B2) D)))))))) (forall ((A tptp.real) (C tptp.real) (B2 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) C)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real B2) C))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) C)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) B2))))) (forall ((A tptp.rat) (C tptp.rat) (B2 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) C)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat B2) C))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) C)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B2))))) (forall ((A tptp.nat) (C tptp.nat) (B2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) C)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B2) C))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) C)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B2))))) (forall ((A tptp.int) (C tptp.int) (B2 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B2) C))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) C)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B2))))) (forall ((C tptp.real) (A tptp.real) (B2 tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.times_times_real C))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real _let_1 A)) (tptp.aa_real_real _let_1 B2))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) C)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) B2)))))) (forall ((C tptp.rat) (A tptp.rat) (B2 tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_rat tptp.times_times_rat C))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat _let_1 A)) (tptp.aa_rat_rat _let_1 B2))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) C)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B2)))))) (forall ((C tptp.nat) (A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat C))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat _let_1 A)) (tptp.aa_nat_nat _let_1 B2))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) C)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B2)))))) (forall ((C tptp.int) (A tptp.int) (B2 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.times_times_int C))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int _let_1 A)) (tptp.aa_int_int _let_1 B2))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) C)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B2)))))) (forall ((C tptp.real) (A tptp.real) (B2 tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.times_times_real C))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) C)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real _let_1 A)) (tptp.aa_real_real _let_1 B2))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) B2)))))) (forall ((C tptp.rat) (A tptp.rat) (B2 tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_rat tptp.times_times_rat C))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) C)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat _let_1 A)) (tptp.aa_rat_rat _let_1 B2))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B2)))))) (forall ((C tptp.int) (A tptp.int) (B2 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.times_times_int C))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) C)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int _let_1 A)) (tptp.aa_int_int _let_1 B2))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B2)))))) (forall ((C tptp.real) (A tptp.real) (B2 tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.times_times_real C))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real C) tptp.zero_zero_real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real _let_1 A)) (tptp.aa_real_real _let_1 B2))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real B2) A)))))) (forall ((C tptp.rat) (A tptp.rat) (B2 tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_rat tptp.times_times_rat C))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat C) tptp.zero_zero_rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat _let_1 A)) (tptp.aa_rat_rat _let_1 B2))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B2) A)))))) (forall ((C tptp.int) (A tptp.int) (B2 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.times_times_int C))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int C) tptp.zero_zero_int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int _let_1 A)) (tptp.aa_int_int _let_1 B2))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B2) A)))))) (forall ((A tptp.real) (C tptp.real) (B2 tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) C)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real B2) C))) (and (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) C)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B2))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real C) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B2) A)))))) (forall ((A tptp.rat) (C tptp.rat) (B2 tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) C)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat B2) C))) (and (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) C)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B2))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat C) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B2) A)))))) (forall ((A tptp.int) (C tptp.int) (B2 tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B2) C))) (and (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) C)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B2))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int C) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B2) A)))))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real) (D tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B2)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real C) D)) (=> (tptp.pp (tptp.aa_real_bool _let_1 A)) (=> (tptp.pp (tptp.aa_real_bool _let_1 C)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) C)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real B2) D))))))))) (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat) (D tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B2)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat C) D)) (=> (tptp.pp (tptp.aa_rat_bool _let_1 A)) (=> (tptp.pp (tptp.aa_rat_bool _let_1 C)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) C)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat B2) D))))))))) (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat) (D tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) B2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat C) D)) (=> (tptp.pp (tptp.aa_nat_bool _let_1 A)) (=> (tptp.pp (tptp.aa_nat_bool _let_1 C)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) C)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B2) D))))))))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int) (D tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B2)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int C) D)) (=> (tptp.pp (tptp.aa_int_bool _let_1 A)) (=> (tptp.pp (tptp.aa_int_bool _let_1 C)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B2) D))))))))) (forall ((A tptp.real) (C tptp.real) (B2 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) C)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real B2) C))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) C)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B2))))) (forall ((A tptp.rat) (C tptp.rat) (B2 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) C)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat B2) C))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) C)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B2))))) (forall ((A tptp.nat) (C tptp.nat) (B2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) C)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B2) C))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) C)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) B2))))) (forall ((A tptp.int) (C tptp.int) (B2 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B2) C))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) C)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B2))))) (forall ((C tptp.real) (A tptp.real) (B2 tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.times_times_real C))) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real _let_1 A)) (tptp.aa_real_real _let_1 B2))) (and (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) C)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B2))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real C) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B2) A))))))) (forall ((C tptp.rat) (A tptp.rat) (B2 tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_rat tptp.times_times_rat C))) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat _let_1 A)) (tptp.aa_rat_rat _let_1 B2))) (and (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) C)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B2))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat C) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B2) A))))))) (forall ((C tptp.int) (A tptp.int) (B2 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.times_times_int C))) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int _let_1 A)) (tptp.aa_int_int _let_1 B2))) (and (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) C)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B2))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int C) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B2) A))))))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real) (D tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B2)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real C) D)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) B2)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) C)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) C)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real B2) D)))))))) (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat) (D tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B2)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat C) D)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) B2)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) C)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) C)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat B2) D)))))))) (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat) (D tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) B2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat C) D)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) B2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) C)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) C)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B2) D)))))))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int) (D tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B2)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int C) D)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) B2)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) C)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B2) D)))))))) (forall ((C tptp.real) (A tptp.real) (B2 tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.times_times_real C))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real _let_1 A)) (tptp.aa_real_real _let_1 B2))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) C)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B2)))))) (forall ((C tptp.rat) (A tptp.rat) (B2 tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_rat tptp.times_times_rat C))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat _let_1 A)) (tptp.aa_rat_rat _let_1 B2))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) C)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B2)))))) (forall ((C tptp.nat) (A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat C))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat _let_1 A)) (tptp.aa_nat_nat _let_1 B2))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) C)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) B2)))))) (forall ((C tptp.int) (A tptp.int) (B2 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.times_times_int C))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int _let_1 A)) (tptp.aa_int_int _let_1 B2))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) C)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B2)))))) (forall ((A tptp.real) (C tptp.real) (B2 tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) C)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real B2) C))) (and (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) C)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) B2))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real C) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real B2) A)))))) (forall ((A tptp.rat) (C tptp.rat) (B2 tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) C)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat B2) C))) (and (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) C)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B2))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat C) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B2) A)))))) (forall ((A tptp.int) (C tptp.int) (B2 tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B2) C))) (and (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) C)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B2))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int C) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B2) A)))))) (forall ((C tptp.real) (A tptp.real) (B2 tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.times_times_real C))) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real _let_1 A)) (tptp.aa_real_real _let_1 B2))) (and (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) C)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) B2))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real C) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real B2) A))))))) (forall ((C tptp.rat) (A tptp.rat) (B2 tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_rat tptp.times_times_rat C))) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat _let_1 A)) (tptp.aa_rat_rat _let_1 B2))) (and (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) C)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B2))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat C) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B2) A))))))) (forall ((C tptp.int) (A tptp.int) (B2 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.times_times_int C))) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int _let_1 A)) (tptp.aa_int_int _let_1 B2))) (and (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) C)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B2))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int C) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B2) A))))))) (forall ((X tptp.real) (Y tptp.real)) (=> (forall ((E2 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) E2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real Y) E2))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) Y)))) (forall ((X tptp.rat) (Y tptp.rat)) (=> (forall ((E2 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) E2)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat Y) E2))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) Y)))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B2))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) A)) (=> (tptp.pp (tptp.aa_real_bool _let_1 C)) (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) C))))))) (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B2))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) A)) (=> (tptp.pp (tptp.aa_rat_bool _let_1 C)) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) C))))))) (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat B2))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) A)) (=> (tptp.pp (tptp.aa_nat_bool _let_1 C)) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) C))))))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_int B2))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) A)) (=> (tptp.pp (tptp.aa_int_bool _let_1 C)) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) C))))))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) A)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real B2) C)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B2) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) C)))))) (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) A)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B2) C)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B2) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) C)))))) (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) A)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B2) C)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat B2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) C)))))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) A)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B2) C)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B2) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) C)))))) (forall ((A tptp.real) (B2 tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool _let_1 A)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) B2)) (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) B2))))))) (forall ((A tptp.rat) (B2 tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 A)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) B2)) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) B2))))))) (forall ((A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 A)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) B2)) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) B2))))))) (forall ((A tptp.int) (B2 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int))) (=> (tptp.pp (tptp.aa_int_bool _let_1 A)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) B2)) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) B2))))))) (forall ((A tptp.real) (B2 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) tptp.zero_zero_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B2) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) B2)) tptp.zero_zero_real))))) (forall ((A tptp.rat) (B2 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) tptp.zero_zero_rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B2) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) B2)) tptp.zero_zero_rat))))) (forall ((A tptp.nat) (B2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) tptp.zero_zero_nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat B2) tptp.zero_zero_nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) B2)) tptp.zero_zero_nat))))) (forall ((A tptp.int) (B2 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) tptp.zero_zero_int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B2) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) B2)) tptp.zero_zero_int))))) (forall ((A tptp.real) (B2 tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) A)) (=> (tptp.pp (tptp.aa_real_bool _let_1 B2)) (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) B2))))))) (forall ((A tptp.rat) (B2 tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) A)) (=> (tptp.pp (tptp.aa_rat_bool _let_1 B2)) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) B2))))))) (forall ((A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) A)) (=> (tptp.pp (tptp.aa_nat_bool _let_1 B2)) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) B2))))))) (forall ((A tptp.int) (B2 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) A)) (=> (tptp.pp (tptp.aa_int_bool _let_1 B2)) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) B2))))))) (forall ((A tptp.real) (B2 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) tptp.zero_zero_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real B2) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) B2)) tptp.zero_zero_real))))) (forall ((A tptp.rat) (B2 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) tptp.zero_zero_rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B2) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) B2)) tptp.zero_zero_rat))))) (forall ((A tptp.nat) (B2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) tptp.zero_zero_nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B2) tptp.zero_zero_nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) B2)) tptp.zero_zero_nat))))) (forall ((A tptp.int) (B2 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) tptp.zero_zero_int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B2) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) B2)) tptp.zero_zero_int))))) (forall ((X tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) tptp.zero_zero_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) Y)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real X) Y)) tptp.zero_zero_real))))) (forall ((X tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) tptp.zero_zero_rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) Y)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.divide_divide_rat X) Y)) tptp.zero_zero_rat))))) (forall ((X tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) tptp.zero_zero_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real X) Y)))))) (forall ((X tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) tptp.zero_zero_rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Y) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_rat_rat (tptp.divide_divide_rat X) Y)))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool _let_1 X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) Y)) (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real X) Y))))))) (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 X)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) Y)) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat (tptp.divide_divide_rat X) Y))))))) (forall ((X tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real X) Y)) tptp.zero_zero_real))))) (forall ((X tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) X)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Y) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.divide_divide_rat X) Y)) tptp.zero_zero_rat))))) (forall ((A tptp.real) (C tptp.real) (B2 tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real A) C)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real B2) C))) (and (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) C)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) B2))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real C) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real B2) A)))))) (forall ((A tptp.rat) (C tptp.rat) (B2 tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.divide_divide_rat A) C)) (tptp.aa_rat_rat (tptp.divide_divide_rat B2) C))) (and (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) C)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B2))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat C) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B2) A)))))) (forall ((X tptp.real) (Y tptp.real) (W tptp.real) (Z tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool _let_1 X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) Y)) (=> (tptp.pp (tptp.aa_real_bool _let_1 W)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real W) Z)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real X) Z)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real Y) W))))))))) (forall ((X tptp.rat) (Y tptp.rat) (W tptp.rat) (Z tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 X)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) Y)) (=> (tptp.pp (tptp.aa_rat_bool _let_1 W)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat W) Z)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.divide_divide_rat X) Z)) (tptp.aa_rat_rat (tptp.divide_divide_rat Y) W))))))))) (forall ((X tptp.real) (Y tptp.real) (W tptp.real) (Z tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Y)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) W)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real W) Z)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real X) Z)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real Y) W)))))))) (forall ((X tptp.rat) (Y tptp.rat) (W tptp.rat) (Z tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) X)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) Y)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) W)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat W) Z)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.divide_divide_rat X) Z)) (tptp.aa_rat_rat (tptp.divide_divide_rat Y) W)))))))) (forall ((Y tptp.real) (X tptp.real) (W tptp.real) (Z tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) Y)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) Y)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) W)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real W) Z)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real X) Z)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real Y) W)))))))) (forall ((Y tptp.rat) (X tptp.rat) (W tptp.rat) (Z tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) Y)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) Y)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) W)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat W) Z)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.divide_divide_rat X) Z)) (tptp.aa_rat_rat (tptp.divide_divide_rat Y) W)))))))) (forall ((B2 tptp.nat) (A tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 B2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B2) A)) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) B2))))))) (forall ((B2 tptp.int) (A tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int))) (=> (tptp.pp (tptp.aa_int_bool _let_1 B2)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B2) A)) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.divide_divide_int A) B2))))))) (forall ((A tptp.nat) (B2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) A)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) B2)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) B2) tptp.zero_zero_nat)))) (forall ((A tptp.int) (B2 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) A)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B2)) (= (tptp.aa_int_int (tptp.divide_divide_int A) B2) tptp.zero_zero_int)))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool _let_1 X)) (=> (tptp.pp (tptp.aa_real_bool _let_1 Y)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y) tptp.one_one_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real Y) X)) X))))))) (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 X)) (=> (tptp.pp (tptp.aa_rat_bool _let_1 Y)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat Y) tptp.one_one_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat Y) X)) X))))))) (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.pp (tptp.aa_int_bool _let_1 X)) (=> (tptp.pp (tptp.aa_int_bool _let_1 Y)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Y) tptp.one_one_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int Y) X)) X))))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool _let_1 X)) (=> (tptp.pp (tptp.aa_real_bool _let_1 Y)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y) tptp.one_one_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real X) Y)) X))))))) (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 X)) (=> (tptp.pp (tptp.aa_rat_bool _let_1 Y)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat Y) tptp.one_one_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat X) Y)) X))))))) (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.pp (tptp.aa_int_bool _let_1 X)) (=> (tptp.pp (tptp.aa_int_bool _let_1 Y)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Y) tptp.one_one_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int X) Y)) X))))))) (forall ((A tptp.real) (B2 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) tptp.one_one_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) B2)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real B2) tptp.one_one_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) B2)) tptp.one_one_real)))))) (forall ((A tptp.rat) (B2 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) tptp.one_one_rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) B2)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B2) tptp.one_one_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) B2)) tptp.one_one_rat)))))) (forall ((A tptp.nat) (B2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) tptp.one_one_nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) B2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B2) tptp.one_one_nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) B2)) tptp.one_one_nat)))))) (forall ((A tptp.int) (B2 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) tptp.one_one_int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) B2)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B2) tptp.one_one_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) B2)) tptp.one_one_int)))))) (forall ((C tptp.real) (A tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real C) tptp.one_one_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) A)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) C)) A))))) (forall ((C tptp.rat) (A tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat C) tptp.one_one_rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) A)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) C)) A))))) (forall ((C tptp.nat) (A tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat C) tptp.one_one_nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) A)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) C)) A))))) (forall ((C tptp.int) (A tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int C) tptp.one_one_int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) A)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) C)) A))))) (forall ((X tptp.real) (Y tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real X) X)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real Y) Y))) tptp.zero_zero_real)) (and (= X tptp.zero_zero_real) (= Y tptp.zero_zero_real)))) (forall ((X tptp.rat) (Y tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat X) X)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat Y) Y))) tptp.zero_zero_rat)) (and (= X tptp.zero_zero_rat) (= Y tptp.zero_zero_rat)))) (forall ((X tptp.int) (Y tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int X) X)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int Y) Y))) tptp.zero_zero_int)) (and (= X tptp.zero_zero_int) (= Y tptp.zero_zero_int)))) (forall ((X tptp.real) (Y tptp.real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real X) X)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real Y) Y))))) (forall ((X tptp.rat) (Y tptp.rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat X) X)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat Y) Y))))) (forall ((X tptp.int) (Y tptp.int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int X) X)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int Y) Y))))) (forall ((A tptp.real) (N tptp.nat) (B2 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real A) N)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real B2) N))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) B2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B2))))) (forall ((A tptp.rat) (N tptp.nat) (B2 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_nat_rat (tptp.power_power_rat A) N)) (tptp.aa_nat_rat (tptp.power_power_rat B2) N))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) B2)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B2))))) (forall ((A tptp.nat) (N tptp.nat) (B2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A) N)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat B2) N))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) B2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) B2))))) (forall ((A tptp.int) (N tptp.nat) (B2 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_nat_int (tptp.power_power_int A) N)) (tptp.aa_nat_int (tptp.power_power_int B2) N))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) B2)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B2))))) (forall ((X tptp.real) (Y tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real X) X)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real Y) Y)))) (or (not (= X tptp.zero_zero_real)) (not (= Y tptp.zero_zero_real))))) (forall ((X tptp.rat) (Y tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat X) X)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat Y) Y)))) (or (not (= X tptp.zero_zero_rat)) (not (= Y tptp.zero_zero_rat))))) (forall ((X tptp.int) (Y tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int X) X)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int Y) Y)))) (or (not (= X tptp.zero_zero_int)) (not (= Y tptp.zero_zero_int))))) (forall ((X tptp.real) (Y tptp.real)) (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real X) X)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real Y) Y))) tptp.zero_zero_real)))) (forall ((X tptp.rat) (Y tptp.rat)) (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat X) X)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat Y) Y))) tptp.zero_zero_rat)))) (forall ((X tptp.int) (Y tptp.int)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int X) X)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int Y) Y))) tptp.zero_zero_int)))) (forall ((C tptp.nat) (A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) C)) (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B2) C)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat _let_1 B2)) C))))) (forall ((C tptp.int) (A tptp.int) (B2 tptp.int)) (let ((_let_1 (tptp.divide_divide_int A))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) C)) (= (tptp.aa_int_int _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B2) C)) (tptp.aa_int_int (tptp.divide_divide_int (tptp.aa_int_int _let_1 B2)) C))))) (tptp.pp (tptp.aa_real_bool _let_76 _let_150)) (tptp.pp (tptp.aa_rat_bool _let_103 _let_149)) (tptp.pp (tptp.aa_nat_bool _let_144 _let_148)) (tptp.pp (tptp.aa_int_bool _let_104 _let_146)) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real C))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B2)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real C) tptp.zero_zero_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) B2))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real _let_1 A)) (tptp.aa_real_real _let_1 B2)))))))) (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.divide_divide_rat C))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B2)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat C) tptp.zero_zero_rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) B2))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat _let_1 A)) (tptp.aa_rat_rat _let_1 B2)))))))) (forall ((B2 tptp.real) (A tptp.real) (C tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real C))) (let ((_let_2 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B2) A)) (=> (tptp.pp (tptp.aa_real_bool _let_2 C)) (=> (tptp.pp (tptp.aa_real_bool _let_2 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) B2))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real _let_1 A)) (tptp.aa_real_real _let_1 B2))))))))) (forall ((B2 tptp.rat) (A tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.divide_divide_rat C))) (let ((_let_2 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B2) A)) (=> (tptp.pp (tptp.aa_rat_bool _let_2 C)) (=> (tptp.pp (tptp.aa_rat_bool _let_2 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) B2))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat _let_1 A)) (tptp.aa_rat_rat _let_1 B2))))))))) (forall ((Y tptp.real) (Z tptp.real) (X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) Y)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real Z) Y)) X)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Z) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real X) Y)))))) (forall ((Y tptp.rat) (Z tptp.rat) (X tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) Y)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat Z) Y)) X)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Z) (tptp.aa_rat_rat (tptp.divide_divide_rat X) Y)))))) (forall ((Y tptp.real) (X tptp.real) (Z tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) Y)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real Z) Y))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real X) Y)) Z))))) (forall ((Y tptp.rat) (X tptp.rat) (Z tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) Y)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat Z) Y))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.divide_divide_rat X) Y)) Z))))) (forall ((C tptp.real) (A tptp.real) (B2 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) C)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real B2) C))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) C)) B2))))) (forall ((C tptp.rat) (A tptp.rat) (B2 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) C)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) (tptp.aa_rat_rat (tptp.divide_divide_rat B2) C))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) C)) B2))))) (forall ((C tptp.real) (B2 tptp.real) (A tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) C)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real B2) C)) A)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B2) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) C)))))) (forall ((C tptp.rat) (B2 tptp.rat) (A tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) C)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.divide_divide_rat B2) C)) A)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B2) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) C)))))) (forall ((C tptp.real) (A tptp.real) (B2 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real C) tptp.zero_zero_real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real B2) C))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B2) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) C)))))) (forall ((C tptp.rat) (A tptp.rat) (B2 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat C) tptp.zero_zero_rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) (tptp.aa_rat_rat (tptp.divide_divide_rat B2) C))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B2) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) C)))))) (forall ((C tptp.real) (B2 tptp.real) (A tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real C) tptp.zero_zero_real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real B2) C)) A)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) C)) B2))))) (forall ((C tptp.rat) (B2 tptp.rat) (A tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat C) tptp.zero_zero_rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.divide_divide_rat B2) C)) A)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) C)) B2))))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A))) (let ((_let_2 (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real C) tptp.zero_zero_real)))) (let ((_let_3 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) C))) (let ((_let_4 (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) C)))) (= (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real B2) C))) (and (=> _let_4 (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real _let_3) B2))) (=> (not _let_4) (and (=> _let_2 (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B2) _let_3))) (=> (not _let_2) (tptp.pp (tptp.aa_real_bool _let_1 tptp.zero_zero_real)))))))))))) (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A))) (let ((_let_2 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat C) tptp.zero_zero_rat)))) (let ((_let_3 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) C))) (let ((_let_4 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) C)))) (= (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat (tptp.divide_divide_rat B2) C))) (and (=> _let_4 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat _let_3) B2))) (=> (not _let_4) (and (=> _let_2 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B2) _let_3))) (=> (not _let_2) (tptp.pp (tptp.aa_rat_bool _let_1 tptp.zero_zero_rat)))))))))))) (forall ((B2 tptp.real) (C tptp.real) (A tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real))) (let ((_let_2 (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real C) tptp.zero_zero_real)))) (let ((_let_3 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) C))) (let ((_let_4 (tptp.pp (tptp.aa_real_bool _let_1 C)))) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real B2) C)) A)) (and (=> _let_4 (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B2) _let_3))) (=> (not _let_4) (and (=> _let_2 (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real _let_3) B2))) (=> (not _let_2) (tptp.pp (tptp.aa_real_bool _let_1 A)))))))))))) (forall ((B2 tptp.rat) (C tptp.rat) (A tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat))) (let ((_let_2 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat C) tptp.zero_zero_rat)))) (let ((_let_3 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) C))) (let ((_let_4 (tptp.pp (tptp.aa_rat_bool _let_1 C)))) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.divide_divide_rat B2) C)) A)) (and (=> _let_4 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B2) _let_3))) (=> (not _let_4) (and (=> _let_2 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat _let_3) B2))) (=> (not _let_2) (tptp.pp (tptp.aa_rat_bool _let_1 A)))))))))))) (forall ((B2 tptp.real) (A tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A))) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real B2) A))) (or (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) A)) (tptp.pp (tptp.aa_real_bool _let_1 B2))) (and (tptp.pp (tptp.aa_real_bool _let_1 tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B2) A))))))) (forall ((B2 tptp.rat) (A tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A))) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.one_one_rat) (tptp.aa_rat_rat (tptp.divide_divide_rat B2) A))) (or (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) A)) (tptp.pp (tptp.aa_rat_bool _let_1 B2))) (and (tptp.pp (tptp.aa_rat_bool _let_1 tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B2) A))))))) (forall ((B2 tptp.real) (A tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A))) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real B2) A)) tptp.one_one_real)) (or (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) A)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B2) A))) (and (tptp.pp (tptp.aa_real_bool _let_1 tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool _let_1 B2))) (= A tptp.zero_zero_real))))) (forall ((B2 tptp.rat) (A tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A))) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.divide_divide_rat B2) A)) tptp.one_one_rat)) (or (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) A)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B2) A))) (and (tptp.pp (tptp.aa_rat_bool _let_1 tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool _let_1 B2))) (= A tptp.zero_zero_rat))))) (forall ((A tptp.real) (N tptp.nat)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) A)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) tptp.one_one_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real A) N)) tptp.one_one_real))))) (forall ((A tptp.rat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) A)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) tptp.one_one_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat (tptp.power_power_rat A) N)) tptp.one_one_rat))))) (forall ((A tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) A)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) tptp.one_one_nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A) N)) tptp.one_one_nat))))) (forall ((A tptp.int) (N tptp.nat)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) A)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) tptp.one_one_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int (tptp.power_power_int A) N)) tptp.one_one_int))))) (forall ((B2 tptp.complex) (C tptp.complex) (W tptp.num)) (let ((_let_1 (tptp.numera6690914467698888265omplex W))) (let ((_let_2 (= C tptp.zero_zero_complex))) (= (= (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex B2) C) _let_1) (and (=> (not _let_2) (= B2 (tptp.aa_complex_complex (tptp.times_times_complex _let_1) C))) (=> _let_2 (= _let_1 tptp.zero_zero_complex))))))) (forall ((B2 tptp.real) (C tptp.real) (W tptp.num)) (let ((_let_1 (tptp.aa_num_real tptp.numeral_numeral_real W))) (let ((_let_2 (= C tptp.zero_zero_real))) (= (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real B2) C) _let_1) (and (=> (not _let_2) (= B2 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real _let_1) C))) (=> _let_2 (= _let_1 tptp.zero_zero_real))))))) (forall ((B2 tptp.rat) (C tptp.rat) (W tptp.num)) (let ((_let_1 (tptp.aa_num_rat tptp.numeral_numeral_rat W))) (let ((_let_2 (= C tptp.zero_zero_rat))) (= (= (tptp.aa_rat_rat (tptp.divide_divide_rat B2) C) _let_1) (and (=> (not _let_2) (= B2 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat _let_1) C))) (=> _let_2 (= _let_1 tptp.zero_zero_rat))))))) (forall ((W tptp.num) (B2 tptp.complex) (C tptp.complex)) (let ((_let_1 (tptp.numera6690914467698888265omplex W))) (let ((_let_2 (= C tptp.zero_zero_complex))) (= (= _let_1 (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex B2) C)) (and (=> (not _let_2) (= (tptp.aa_complex_complex (tptp.times_times_complex _let_1) C) B2)) (=> _let_2 (= _let_1 tptp.zero_zero_complex))))))) (forall ((W tptp.num) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (tptp.aa_num_real tptp.numeral_numeral_real W))) (let ((_let_2 (= C tptp.zero_zero_real))) (= (= _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real B2) C)) (and (=> (not _let_2) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real _let_1) C) B2)) (=> _let_2 (= _let_1 tptp.zero_zero_real))))))) (forall ((W tptp.num) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_num_rat tptp.numeral_numeral_rat W))) (let ((_let_2 (= C tptp.zero_zero_rat))) (= (= _let_1 (tptp.aa_rat_rat (tptp.divide_divide_rat B2) C)) (and (=> (not _let_2) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat _let_1) C) B2)) (=> _let_2 (= _let_1 tptp.zero_zero_rat))))))) (forall ((Z tptp.complex) (A tptp.complex) (B2 tptp.complex)) (let ((_let_1 (tptp.aa_complex_complex (tptp.plus_plus_complex (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex A) Z)) B2))) (let ((_let_2 (= Z tptp.zero_zero_complex))) (and (=> _let_2 (= _let_1 B2)) (=> (not _let_2) (= _let_1 (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex (tptp.aa_complex_complex (tptp.plus_plus_complex A) (tptp.aa_complex_complex (tptp.times_times_complex B2) Z))) Z))))))) (forall ((Z tptp.real) (A tptp.real) (B2 tptp.real)) (let ((_let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real A) Z)) B2))) (let ((_let_2 (= Z tptp.zero_zero_real))) (and (=> _let_2 (= _let_1 B2)) (=> (not _let_2) (= _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real B2) Z))) Z))))))) (forall ((Z tptp.rat) (A tptp.rat) (B2 tptp.rat)) (let ((_let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.divide_divide_rat A) Z)) B2))) (let ((_let_2 (= Z tptp.zero_zero_rat))) (and (=> _let_2 (= _let_1 B2)) (=> (not _let_2) (= _let_1 (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat B2) Z))) Z))))))) (forall ((Z tptp.complex) (A tptp.complex) (B2 tptp.complex)) (let ((_let_1 (tptp.aa_complex_complex (tptp.plus_plus_complex A) (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex B2) Z)))) (let ((_let_2 (= Z tptp.zero_zero_complex))) (and (=> _let_2 (= _let_1 A)) (=> (not _let_2) (= _let_1 (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex (tptp.aa_complex_complex (tptp.plus_plus_complex (tptp.aa_complex_complex (tptp.times_times_complex A) Z)) B2)) Z))))))) (forall ((Z tptp.real) (A tptp.real) (B2 tptp.real)) (let ((_let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real B2) Z)))) (let ((_let_2 (= Z tptp.zero_zero_real))) (and (=> _let_2 (= _let_1 A)) (=> (not _let_2) (= _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) Z)) B2)) Z))))))) (forall ((Z tptp.rat) (A tptp.rat) (B2 tptp.rat)) (let ((_let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) (tptp.aa_rat_rat (tptp.divide_divide_rat B2) Z)))) (let ((_let_2 (= Z tptp.zero_zero_rat))) (and (=> _let_2 (= _let_1 A)) (=> (not _let_2) (= _let_1 (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) Z)) B2)) Z))))))) (forall ((Y tptp.complex) (Z tptp.complex) (X tptp.complex) (W tptp.complex)) (=> (not (= Y tptp.zero_zero_complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (tptp.aa_complex_complex (tptp.plus_plus_complex (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex X) Y)) (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex W) Z)) (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex (tptp.aa_complex_complex (tptp.plus_plus_complex (tptp.aa_complex_complex (tptp.times_times_complex X) Z)) (tptp.aa_complex_complex (tptp.times_times_complex W) Y))) (tptp.aa_complex_complex (tptp.times_times_complex Y) Z)))))) (forall ((Y tptp.real) (Z tptp.real) (X tptp.real) (W tptp.real)) (=> (not (= Y tptp.zero_zero_real)) (=> (not (= Z tptp.zero_zero_real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real X) Y)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real W) Z)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real X) Z)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real W) Y))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real Y) Z)))))) (forall ((Y tptp.rat) (Z tptp.rat) (X tptp.rat) (W tptp.rat)) (=> (not (= Y tptp.zero_zero_rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.divide_divide_rat X) Y)) (tptp.aa_rat_rat (tptp.divide_divide_rat W) Z)) (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat X) Z)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat W) Y))) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat Y) Z)))))) (forall ((Y tptp.complex) (X tptp.complex) (Z tptp.complex)) (=> (not (= Y tptp.zero_zero_complex)) (= (tptp.aa_complex_complex (tptp.plus_plus_complex (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex X) Y)) Z) (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex (tptp.aa_complex_complex (tptp.plus_plus_complex X) (tptp.aa_complex_complex (tptp.times_times_complex Z) Y))) Y)))) (forall ((Y tptp.real) (X tptp.real) (Z tptp.real)) (=> (not (= Y tptp.zero_zero_real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real X) Y)) Z) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real Z) Y))) Y)))) (forall ((Y tptp.rat) (X tptp.rat) (Z tptp.rat)) (=> (not (= Y tptp.zero_zero_rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.divide_divide_rat X) Y)) Z) (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat X) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat Z) Y))) Y)))) (forall ((Y tptp.complex) (Z tptp.complex) (X tptp.complex)) (=> (not (= Y tptp.zero_zero_complex)) (= (tptp.aa_complex_complex (tptp.plus_plus_complex Z) (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex X) Y)) (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex (tptp.aa_complex_complex (tptp.plus_plus_complex X) (tptp.aa_complex_complex (tptp.times_times_complex Z) Y))) Y)))) (forall ((Y tptp.real) (Z tptp.real) (X tptp.real)) (=> (not (= Y tptp.zero_zero_real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real Z) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real X) Y)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real Z) Y))) Y)))) (forall ((Y tptp.rat) (Z tptp.rat) (X tptp.rat)) (=> (not (= Y tptp.zero_zero_rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat Z) (tptp.aa_rat_rat (tptp.divide_divide_rat X) Y)) (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat X) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat Z) Y))) Y)))) (forall ((Z tptp.complex) (X tptp.complex) (Y tptp.complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (tptp.aa_complex_complex (tptp.plus_plus_complex X) (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex Y) Z)) (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex (tptp.aa_complex_complex (tptp.plus_plus_complex (tptp.aa_complex_complex (tptp.times_times_complex X) Z)) Y)) Z)))) (forall ((Z tptp.real) (X tptp.real) (Y tptp.real)) (=> (not (= Z tptp.zero_zero_real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real Y) Z)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real X) Z)) Y)) Z)))) (forall ((Z tptp.rat) (X tptp.rat) (Y tptp.rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat X) (tptp.aa_rat_rat (tptp.divide_divide_rat Y) Z)) (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat X) Z)) Y)) Z)))) (forall ((Z tptp.complex) (X tptp.complex) (Y tptp.complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (tptp.aa_complex_complex (tptp.plus_plus_complex (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex X) Z)) Y) (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex (tptp.aa_complex_complex (tptp.plus_plus_complex X) (tptp.aa_complex_complex (tptp.times_times_complex Y) Z))) Z)))) (forall ((Z tptp.real) (X tptp.real) (Y tptp.real)) (=> (not (= Z tptp.zero_zero_real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real X) Z)) Y) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real Y) Z))) Z)))) (forall ((Z tptp.rat) (X tptp.rat) (Y tptp.rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.divide_divide_rat X) Z)) Y) (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat X) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat Y) Z))) Z)))) (forall ((A tptp.real) (N tptp.nat) (B2 tptp.real)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real A) _let_1)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real B2) _let_1))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) B2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) B2)))))) (forall ((A tptp.rat) (N tptp.nat) (B2 tptp.rat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat (tptp.power_power_rat A) _let_1)) (tptp.aa_nat_rat (tptp.power_power_rat B2) _let_1))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) B2)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B2)))))) (forall ((A tptp.nat) (N tptp.nat) (B2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A) _let_1)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat B2) _let_1))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) B2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B2)))))) (forall ((A tptp.int) (N tptp.nat) (B2 tptp.int)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int (tptp.power_power_int A) _let_1)) (tptp.aa_nat_int (tptp.power_power_int B2) _let_1))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) B2)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B2)))))) (forall ((A tptp.real) (N tptp.nat) (B2 tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (let ((_let_2 (tptp.aa_nat_nat tptp.suc N))) (=> (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real A) _let_2) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real B2) _let_2)) (=> (tptp.pp (tptp.aa_real_bool _let_1 A)) (=> (tptp.pp (tptp.aa_real_bool _let_1 B2)) (= A B2))))))) (forall ((A tptp.rat) (N tptp.nat) (B2 tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat))) (let ((_let_2 (tptp.aa_nat_nat tptp.suc N))) (=> (= (tptp.aa_nat_rat (tptp.power_power_rat A) _let_2) (tptp.aa_nat_rat (tptp.power_power_rat B2) _let_2)) (=> (tptp.pp (tptp.aa_rat_bool _let_1 A)) (=> (tptp.pp (tptp.aa_rat_bool _let_1 B2)) (= A B2))))))) (forall ((A tptp.nat) (N tptp.nat) (B2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat))) (let ((_let_2 (tptp.aa_nat_nat tptp.suc N))) (=> (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A) _let_2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat B2) _let_2)) (=> (tptp.pp (tptp.aa_nat_bool _let_1 A)) (=> (tptp.pp (tptp.aa_nat_bool _let_1 B2)) (= A B2))))))) (forall ((A tptp.int) (N tptp.nat) (B2 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_2 (tptp.aa_nat_nat tptp.suc N))) (=> (= (tptp.aa_nat_int (tptp.power_power_int A) _let_2) (tptp.aa_nat_int (tptp.power_power_int B2) _let_2)) (=> (tptp.pp (tptp.aa_int_bool _let_1 A)) (=> (tptp.pp (tptp.aa_int_bool _let_1 B2)) (= A B2))))))) (forall ((B2 tptp.nat) (A tptp.nat)) (=> (not (= B2 tptp.zero_zero_nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat B2) A)) B2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) B2)) tptp.one_one_nat)))) (forall ((B2 tptp.int) (A tptp.int)) (=> (not (= B2 tptp.zero_zero_int)) (= (tptp.aa_int_int (tptp.divide_divide_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int B2) A)) B2) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.divide_divide_int A) B2)) tptp.one_one_int)))) (forall ((B2 tptp.nat) (A tptp.nat)) (=> (not (= B2 tptp.zero_zero_nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) B2)) B2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) B2)) tptp.one_one_nat)))) (forall ((B2 tptp.int) (A tptp.int)) (=> (not (= B2 tptp.zero_zero_int)) (= (tptp.aa_int_int (tptp.divide_divide_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) B2)) B2) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.divide_divide_int A) B2)) tptp.one_one_int)))) (forall ((Z tptp.complex) (A tptp.complex) (B2 tptp.complex)) (let ((_let_1 (tptp.aa_complex_complex (tptp.minus_minus_complex A) (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex B2) Z)))) (let ((_let_2 (= Z tptp.zero_zero_complex))) (and (=> _let_2 (= _let_1 A)) (=> (not _let_2) (= _let_1 (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex (tptp.aa_complex_complex (tptp.minus_minus_complex (tptp.aa_complex_complex (tptp.times_times_complex A) Z)) B2)) Z))))))) (forall ((Z tptp.real) (A tptp.real) (B2 tptp.real)) (let ((_let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real B2) Z)))) (let ((_let_2 (= Z tptp.zero_zero_real))) (and (=> _let_2 (= _let_1 A)) (=> (not _let_2) (= _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) Z)) B2)) Z))))))) (forall ((Z tptp.rat) (A tptp.rat) (B2 tptp.rat)) (let ((_let_1 (tptp.aa_rat_rat (tptp.minus_minus_rat A) (tptp.aa_rat_rat (tptp.divide_divide_rat B2) Z)))) (let ((_let_2 (= Z tptp.zero_zero_rat))) (and (=> _let_2 (= _let_1 A)) (=> (not _let_2) (= _let_1 (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) Z)) B2)) Z))))))) (forall ((Y tptp.complex) (Z tptp.complex) (X tptp.complex) (W tptp.complex)) (=> (not (= Y tptp.zero_zero_complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (tptp.aa_complex_complex (tptp.minus_minus_complex (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex X) Y)) (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex W) Z)) (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex (tptp.aa_complex_complex (tptp.minus_minus_complex (tptp.aa_complex_complex (tptp.times_times_complex X) Z)) (tptp.aa_complex_complex (tptp.times_times_complex W) Y))) (tptp.aa_complex_complex (tptp.times_times_complex Y) Z)))))) (forall ((Y tptp.real) (Z tptp.real) (X tptp.real) (W tptp.real)) (=> (not (= Y tptp.zero_zero_real)) (=> (not (= Z tptp.zero_zero_real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real X) Y)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real W) Z)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real X) Z)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real W) Y))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real Y) Z)))))) (forall ((Y tptp.rat) (Z tptp.rat) (X tptp.rat) (W tptp.rat)) (=> (not (= Y tptp.zero_zero_rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_rat_rat (tptp.divide_divide_rat X) Y)) (tptp.aa_rat_rat (tptp.divide_divide_rat W) Z)) (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat X) Z)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat W) Y))) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat Y) Z)))))) (forall ((Z tptp.complex) (X tptp.complex) (Y tptp.complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (tptp.aa_complex_complex (tptp.minus_minus_complex X) (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex Y) Z)) (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex (tptp.aa_complex_complex (tptp.minus_minus_complex (tptp.aa_complex_complex (tptp.times_times_complex X) Z)) Y)) Z)))) (forall ((Z tptp.real) (X tptp.real) (Y tptp.real)) (=> (not (= Z tptp.zero_zero_real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real Y) Z)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real X) Z)) Y)) Z)))) (forall ((Z tptp.rat) (X tptp.rat) (Y tptp.rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (tptp.aa_rat_rat (tptp.minus_minus_rat X) (tptp.aa_rat_rat (tptp.divide_divide_rat Y) Z)) (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat X) Z)) Y)) Z)))) (forall ((Z tptp.complex) (X tptp.complex) (Y tptp.complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (tptp.aa_complex_complex (tptp.minus_minus_complex (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex X) Z)) Y) (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex (tptp.aa_complex_complex (tptp.minus_minus_complex X) (tptp.aa_complex_complex (tptp.times_times_complex Y) Z))) Z)))) (forall ((Z tptp.real) (X tptp.real) (Y tptp.real)) (=> (not (= Z tptp.zero_zero_real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real X) Z)) Y) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real Y) Z))) Z)))) (forall ((Z tptp.rat) (X tptp.rat) (Y tptp.rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_rat_rat (tptp.divide_divide_rat X) Z)) Y) (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_rat_rat (tptp.minus_minus_rat X) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat Y) Z))) Z)))) (forall ((M tptp.code_integer) (X tptp.code_integer)) (let ((_let_1 (tptp.modulo364778990260209775nteger X M))) (let ((_let_2 (tptp.modulo364778990260209775nteger X (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))) M)))) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) M)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) X)) (or (= _let_2 _let_1) (= _let_2 (tptp.plus_p5714425477246183910nteger _let_1 M)))))))) (forall ((M tptp.nat) (X tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat X))) (let ((_let_2 (tptp.aa_nat_nat _let_1 M))) (let ((_let_3 (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) M)))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) M)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) X)) (or (= _let_3 _let_2) (= _let_3 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat _let_2) M))))))))) (forall ((M tptp.int) (X tptp.int)) (let ((_let_1 (tptp.modulo_modulo_int X))) (let ((_let_2 (tptp.aa_int_int _let_1 M))) (let ((_let_3 (tptp.aa_int_int _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) M)))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) M)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) X)) (or (= _let_3 _let_2) (= _let_3 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int _let_2) M))))))))) (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (let ((_let_1 (tptp.modulo364778990260209775nteger A (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))) B2)))) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) B2)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger B2) _let_1)) (= (tptp.minus_8373710615458151222nteger _let_1 B2) (tptp.modulo364778990260209775nteger A B2))))))) (forall ((A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A))) (let ((_let_2 (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) B2)))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) A)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) B2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B2) _let_2)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat _let_2) B2) (tptp.aa_nat_nat _let_1 B2)))))))) (forall ((A tptp.int) (B2 tptp.int)) (let ((_let_1 (tptp.modulo_modulo_int A))) (let ((_let_2 (tptp.aa_int_int _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) B2)))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) A)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) B2)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B2) _let_2)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int _let_2) B2) (tptp.aa_int_int _let_1 B2)))))))) (forall ((V tptp.product_prod_nat_nat) (Vb tptp.list_VEBT_VEBT) (Vc tptp.vEBT_VEBT) (X tptp.nat)) (not (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_vebt_member (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat V) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat) Vb Vc)) X)))) (= _let_145 _let_42) (forall ((X2 tptp.num)) (= (tptp.aa_num_nat tptp.size_size_num (tptp.aa_num_num tptp.bit0 X2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_num_nat tptp.size_size_num X2)) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)))) (forall ((P tptp.fun_nat_bool) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool P N)) (=> (not (tptp.pp (tptp.aa_nat_bool P tptp.zero_zero_nat))) (exists ((K3 tptp.nat)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat K3) N)) (forall ((I2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I2) K3)) (not (tptp.pp (tptp.aa_nat_bool P I2))))) (tptp.pp (tptp.aa_nat_bool P (tptp.aa_nat_nat tptp.suc K3)))))))) (forall ((N tptp.nat) (I tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) (tptp.aa_nat_nat tptp.suc I))) N)))) (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 N)) (=> (tptp.pp (tptp.aa_nat_bool _let_1 M)) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat M) N))))))) (forall ((N tptp.nat) (M tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)) M)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat M) N)))))) (forall ((N tptp.nat) (M tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)) M)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat N) M)))))) (forall ((X tptp.real) (Xs tptp.list_real)) (=> (tptp.member_real X (tptp.set_real2 Xs)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.size_size_list_real Xs))))) (forall ((X tptp.complex) (Xs tptp.list_complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex X) (tptp.set_complex2 Xs))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.size_s3451745648224563538omplex Xs))))) (forall ((X tptp.int) (Xs tptp.list_int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X) (tptp.set_int2 Xs))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.size_size_list_int Xs))))) (forall ((X tptp.vEBT_VEBT) (Xs tptp.list_VEBT_VEBT)) (=> (tptp.pp (tptp.aa_set8260762808118238015T_bool (tptp.aa_VEB289770264548726718T_bool tptp.member_VEBT_VEBT X) (tptp.set_VEBT_VEBT2 Xs))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.size_s6755466524823107622T_VEBT Xs))))) (forall ((X tptp.bool) (Xs tptp.list_bool)) (=> (tptp.member_bool X (tptp.set_bool2 Xs)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.size_size_list_bool Xs))))) (forall ((X tptp.nat) (Xs tptp.list_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X) (tptp.set_nat2 Xs))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.size_size_list_nat Xs))))) (forall ((N tptp.nat) (P tptp.fun_nat_bool)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (=> (tptp.pp (tptp.aa_nat_bool P tptp.one_one_nat)) (=> (forall ((N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)) (=> (tptp.pp (tptp.aa_nat_bool P N2)) (tptp.pp (tptp.aa_nat_bool P (tptp.aa_nat_nat tptp.suc N2)))))) (tptp.pp (tptp.aa_nat_bool P N)))))) (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat K))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) K)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat _let_1 M)) (tptp.aa_nat_nat _let_1 N))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)))))) (forall ((P tptp.fun_nat_bool) (A tptp.nat) (B2 tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool P (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat A) B2))) (and (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) B2)) (tptp.pp (tptp.aa_nat_bool P tptp.zero_zero_nat))) (forall ((D3 tptp.nat)) (=> (= A (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat B2) D3)) (tptp.pp (tptp.aa_nat_bool P D3))))))) (forall ((P tptp.fun_nat_bool) (A tptp.nat) (B2 tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool P (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat A) B2))) (not (or (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) B2)) (not (tptp.pp (tptp.aa_nat_bool P tptp.zero_zero_nat)))) (exists ((D3 tptp.nat)) (and (= A (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat B2) D3)) (not (tptp.pp (tptp.aa_nat_bool P D3))))))))) (forall ((N tptp.nat) (K tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)) N)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat K) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat N) K))))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat))) (= (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat M) N))) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N) M)) (tptp.pp (tptp.aa_nat_bool _let_1 N)))))) (forall ((M tptp.nat) (N tptp.nat) (K tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat K))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) M)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat _let_1 N)) (tptp.aa_nat_nat _let_1 M))))))) (forall ((I tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 I)) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat I) N)))))) (forall ((Q2 tptp.nat) (M tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) Q2)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat M) Q2)) N)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat N) Q2)))))) (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat K))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) K)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat _let_1 M)) (tptp.aa_nat_nat _let_1 N)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat M) N))))) (forall ((M tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) M)) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat M) N) M) (= N tptp.one_one_nat)))) (forall ((N tptp.nat) (M tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.one_one_nat) N)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) M)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat M) N)) M))))) (forall ((P tptp.fun_nat_bool) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool P tptp.zero_zero_nat)) (=> (tptp.pp (tptp.aa_nat_bool P tptp.one_one_nat)) (=> (forall ((N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool P N2)) (tptp.pp (tptp.aa_nat_bool P (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N2) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))))) (tptp.pp (tptp.aa_nat_bool P N)))))) (forall ((X tptp.vEBT_VEBT)) (=> (forall ((A3 tptp.bool) (B3 tptp.bool)) (not (= X (tptp.vEBT_Leaf A3 B3)))) (=> (forall ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (not (= X (tptp.vEBT_Node tptp.none_P5556105721700978146at_nat Uu2 Uv2 Uw2)))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Ux2 tptp.nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (not (= X (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Mi2) Ma2)) Ux2 Uy2 Uz2)))))))) (forall ((X tptp.real) (Y tptp.real)) (=> (forall ((Z4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) Z4)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Z4) tptp.one_one_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real Z4) X)) Y))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) Y)))) (forall ((X tptp.rat) (Y tptp.rat)) (=> (forall ((Z4 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) Z4)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Z4) tptp.one_one_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat Z4) X)) Y))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) Y)))) (forall ((A tptp.real) (C tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) C)) C)) (and (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) C)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) tptp.one_one_real))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real C) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real) A)))))) (forall ((A tptp.rat) (C tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) C)) C)) (and (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) C)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) tptp.one_one_rat))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat C) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.one_one_rat) A)))))) (forall ((A tptp.int) (C tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) C)) C)) (and (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) C)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) tptp.one_one_int))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int C) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.one_one_int) A)))))) (forall ((C tptp.real) (B2 tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real C) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real B2) C))) (and (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) C)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real) B2))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real C) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B2) tptp.one_one_real)))))) (forall ((C tptp.rat) (B2 tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat C) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat B2) C))) (and (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) C)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.one_one_rat) B2))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat C) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B2) tptp.one_one_rat)))))) (forall ((C tptp.int) (B2 tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int C) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B2) C))) (and (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) C)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.one_one_int) B2))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int C) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B2) tptp.one_one_int)))))) (forall ((C tptp.real) (A tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real C) A)) C)) (and (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) C)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) tptp.one_one_real))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real C) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real) A)))))) (forall ((C tptp.rat) (A tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat C) A)) C)) (and (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) C)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) tptp.one_one_rat))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat C) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.one_one_rat) A)))))) (forall ((C tptp.int) (A tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int C) A)) C)) (and (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) C)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) tptp.one_one_int))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int C) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.one_one_int) A)))))) (forall ((C tptp.real) (B2 tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real C) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real C) B2))) (and (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) C)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real) B2))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real C) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B2) tptp.one_one_real)))))) (forall ((C tptp.rat) (B2 tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat C) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat C) B2))) (and (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) C)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.one_one_rat) B2))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat C) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B2) tptp.one_one_rat)))))) (forall ((C tptp.int) (B2 tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int C) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int C) B2))) (and (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) C)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.one_one_int) B2))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int C) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B2) tptp.one_one_int)))))) (forall ((A tptp.real) (C tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) C)) C)) (and (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) C)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) tptp.one_one_real))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real C) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.one_one_real) A)))))) (forall ((A tptp.rat) (C tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) C)) C)) (and (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) C)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) tptp.one_one_rat))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat C) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.one_one_rat) A)))))) (forall ((A tptp.int) (C tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) C)) C)) (and (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) C)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) tptp.one_one_int))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int C) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.one_one_int) A)))))) (forall ((C tptp.real) (B2 tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real C) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real B2) C))) (and (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) C)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.one_one_real) B2))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real C) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real B2) tptp.one_one_real)))))) (forall ((C tptp.rat) (B2 tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat C) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat B2) C))) (and (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) C)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.one_one_rat) B2))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat C) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B2) tptp.one_one_rat)))))) (forall ((C tptp.int) (B2 tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int C) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B2) C))) (and (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) C)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.one_one_int) B2))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int C) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B2) tptp.one_one_int)))))) (forall ((C tptp.real) (A tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real C) A)) C)) (and (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) C)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) tptp.one_one_real))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real C) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.one_one_real) A)))))) (forall ((C tptp.rat) (A tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat C) A)) C)) (and (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) C)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) tptp.one_one_rat))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat C) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.one_one_rat) A)))))) (forall ((C tptp.int) (A tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int C) A)) C)) (and (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) C)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) tptp.one_one_int))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int C) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.one_one_int) A)))))) (forall ((C tptp.real) (B2 tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real C) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real C) B2))) (and (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) C)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.one_one_real) B2))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real C) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real B2) tptp.one_one_real)))))) (forall ((C tptp.rat) (B2 tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat C) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat C) B2))) (and (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) C)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.one_one_rat) B2))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat C) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B2) tptp.one_one_rat)))))) (forall ((C tptp.int) (B2 tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int C) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int C) B2))) (and (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) C)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.one_one_int) B2))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int C) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B2) tptp.one_one_int)))))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real C))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) B2)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real C) tptp.zero_zero_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) B2))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real _let_1 A)) (tptp.aa_real_real _let_1 B2)))))))) (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.divide_divide_rat C))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B2)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat C) tptp.zero_zero_rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) B2))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat _let_1 A)) (tptp.aa_rat_rat _let_1 B2)))))))) (forall ((Y tptp.real) (Z tptp.real) (X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) Y)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real Z) Y)) X)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Z) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real X) Y)))))) (forall ((Y tptp.rat) (Z tptp.rat) (X tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) Y)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat Z) Y)) X)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat Z) (tptp.aa_rat_rat (tptp.divide_divide_rat X) Y)))))) (forall ((Y tptp.real) (X tptp.real) (Z tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) Y)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real Z) Y))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real X) Y)) Z))))) (forall ((Y tptp.rat) (X tptp.rat) (Z tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) Y)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat Z) Y))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.divide_divide_rat X) Y)) Z))))) (forall ((C tptp.real) (A tptp.real) (B2 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) C)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real B2) C))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) C)) B2))))) (forall ((C tptp.rat) (A tptp.rat) (B2 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) C)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) (tptp.aa_rat_rat (tptp.divide_divide_rat B2) C))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) C)) B2))))) (forall ((C tptp.real) (B2 tptp.real) (A tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) C)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real B2) C)) A)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real B2) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) C)))))) (forall ((C tptp.rat) (B2 tptp.rat) (A tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) C)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.divide_divide_rat B2) C)) A)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B2) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) C)))))) (forall ((C tptp.real) (A tptp.real) (B2 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real C) tptp.zero_zero_real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real B2) C))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real B2) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) C)))))) (forall ((C tptp.rat) (A tptp.rat) (B2 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat C) tptp.zero_zero_rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) (tptp.aa_rat_rat (tptp.divide_divide_rat B2) C))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B2) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) C)))))) (forall ((C tptp.real) (B2 tptp.real) (A tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real C) tptp.zero_zero_real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real B2) C)) A)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) C)) B2))))) (forall ((C tptp.rat) (B2 tptp.rat) (A tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat C) tptp.zero_zero_rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.divide_divide_rat B2) C)) A)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) C)) B2))))) (forall ((B2 tptp.real) (A tptp.real) (C tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real C))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real B2) A)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) C)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) B2))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real _let_1 A)) (tptp.aa_real_real _let_1 B2)))))))) (forall ((B2 tptp.rat) (A tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.divide_divide_rat C))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B2) A)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) C)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) B2))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat _let_1 A)) (tptp.aa_rat_rat _let_1 B2)))))))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A))) (let ((_let_2 (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real C) tptp.zero_zero_real)))) (let ((_let_3 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) C))) (let ((_let_4 (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) C)))) (= (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real B2) C))) (and (=> _let_4 (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real _let_3) B2))) (=> (not _let_4) (and (=> _let_2 (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real B2) _let_3))) (=> (not _let_2) (tptp.pp (tptp.aa_real_bool _let_1 tptp.zero_zero_real)))))))))))) (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A))) (let ((_let_2 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat C) tptp.zero_zero_rat)))) (let ((_let_3 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) C))) (let ((_let_4 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) C)))) (= (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat (tptp.divide_divide_rat B2) C))) (and (=> _let_4 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat _let_3) B2))) (=> (not _let_4) (and (=> _let_2 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B2) _let_3))) (=> (not _let_2) (tptp.pp (tptp.aa_rat_bool _let_1 tptp.zero_zero_rat)))))))))))) (forall ((B2 tptp.real) (C tptp.real) (A tptp.real)) (let ((_let_1 (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real C) tptp.zero_zero_real)))) (let ((_let_2 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) C))) (let ((_let_3 (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) C)))) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real B2) C)) A)) (and (=> _let_3 (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real B2) _let_2))) (=> (not _let_3) (and (=> _let_1 (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real _let_2) B2))) (=> (not _let_1) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) A))))))))))) (forall ((B2 tptp.rat) (C tptp.rat) (A tptp.rat)) (let ((_let_1 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat C) tptp.zero_zero_rat)))) (let ((_let_2 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) C))) (let ((_let_3 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) C)))) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.divide_divide_rat B2) C)) A)) (and (=> _let_3 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B2) _let_2))) (=> (not _let_3) (and (=> _let_1 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat _let_2) B2))) (=> (not _let_1) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) A))))))))))) (forall ((B2 tptp.real) (A tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.one_one_real) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real B2) A))) (or (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) A)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) B2))) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real B2) A)))))) (forall ((B2 tptp.rat) (A tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.one_one_rat) (tptp.aa_rat_rat (tptp.divide_divide_rat B2) A))) (or (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) A)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B2))) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B2) A)))))) (forall ((B2 tptp.real) (A tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real B2) A)) tptp.one_one_real)) (or (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) A)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real B2) A))) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) B2))) (= A tptp.zero_zero_real)))) (forall ((B2 tptp.rat) (A tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.divide_divide_rat B2) A)) tptp.one_one_rat)) (or (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) A)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B2) A))) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B2))) (= A tptp.zero_zero_rat)))) (forall ((X tptp.real) (A tptp.real) (Y tptp.real) (U tptp.real) (V tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) A)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y) A)) (=> (tptp.pp (tptp.aa_real_bool _let_1 U)) (=> (tptp.pp (tptp.aa_real_bool _let_1 V)) (=> (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real U) V) tptp.one_one_real) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real U) X)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real V) Y))) A))))))))) (forall ((X tptp.rat) (A tptp.rat) (Y tptp.rat) (U tptp.rat) (V tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) A)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat Y) A)) (=> (tptp.pp (tptp.aa_rat_bool _let_1 U)) (=> (tptp.pp (tptp.aa_rat_bool _let_1 V)) (=> (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat U) V) tptp.one_one_rat) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat U) X)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat V) Y))) A))))))))) (forall ((X tptp.int) (A tptp.int) (Y tptp.int) (U tptp.int) (V tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X) A)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Y) A)) (=> (tptp.pp (tptp.aa_int_bool _let_1 U)) (=> (tptp.pp (tptp.aa_int_bool _let_1 V)) (=> (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int U) V) tptp.one_one_int) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int U) X)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int V) Y))) A))))))))) (forall ((B2 tptp.real) (C tptp.real) (W tptp.num)) (let ((_let_1 (tptp.aa_num_real tptp.numeral_numeral_real W))) (let ((_let_2 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real))) (let ((_let_3 (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real C) tptp.zero_zero_real)))) (let ((_let_4 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real _let_1) C))) (let ((_let_5 (tptp.pp (tptp.aa_real_bool _let_2 C)))) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real B2) C)) _let_1)) (and (=> _let_5 (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B2) _let_4))) (=> (not _let_5) (and (=> _let_3 (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real _let_4) B2))) (=> (not _let_3) (tptp.pp (tptp.aa_real_bool _let_2 _let_1))))))))))))) (forall ((B2 tptp.rat) (C tptp.rat) (W tptp.num)) (let ((_let_1 (tptp.aa_num_rat tptp.numeral_numeral_rat W))) (let ((_let_2 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat))) (let ((_let_3 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat C) tptp.zero_zero_rat)))) (let ((_let_4 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat _let_1) C))) (let ((_let_5 (tptp.pp (tptp.aa_rat_bool _let_2 C)))) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.divide_divide_rat B2) C)) _let_1)) (and (=> _let_5 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B2) _let_4))) (=> (not _let_5) (and (=> _let_3 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat _let_4) B2))) (=> (not _let_3) (tptp.pp (tptp.aa_rat_bool _let_2 _let_1))))))))))))) (forall ((W tptp.num) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (tptp.aa_num_real tptp.numeral_numeral_real W))) (let ((_let_2 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real _let_1))) (let ((_let_3 (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real C) tptp.zero_zero_real)))) (let ((_let_4 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real _let_1) C))) (let ((_let_5 (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) C)))) (= (tptp.pp (tptp.aa_real_bool _let_2 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real B2) C))) (and (=> _let_5 (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real _let_4) B2))) (=> (not _let_5) (and (=> _let_3 (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B2) _let_4))) (=> (not _let_3) (tptp.pp (tptp.aa_real_bool _let_2 tptp.zero_zero_real))))))))))))) (forall ((W tptp.num) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_num_rat tptp.numeral_numeral_rat W))) (let ((_let_2 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat _let_1))) (let ((_let_3 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat C) tptp.zero_zero_rat)))) (let ((_let_4 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat _let_1) C))) (let ((_let_5 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) C)))) (= (tptp.pp (tptp.aa_rat_bool _let_2 (tptp.aa_rat_rat (tptp.divide_divide_rat B2) C))) (and (=> _let_5 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat _let_4) B2))) (=> (not _let_5) (and (=> _let_3 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B2) _let_4))) (=> (not _let_3) (tptp.pp (tptp.aa_rat_bool _let_2 tptp.zero_zero_rat))))))))))))) (forall ((Y tptp.real) (Z tptp.real) (X tptp.real) (W tptp.real)) (=> (not (= Y tptp.zero_zero_real)) (=> (not (= Z tptp.zero_zero_real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real X) Y)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real W) Z))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real X) Z)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real W) Y))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real Y) Z))) tptp.zero_zero_real)))))) (forall ((Y tptp.rat) (Z tptp.rat) (X tptp.rat) (W tptp.rat)) (=> (not (= Y tptp.zero_zero_rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.divide_divide_rat X) Y)) (tptp.aa_rat_rat (tptp.divide_divide_rat W) Z))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat X) Z)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat W) Y))) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat Y) Z))) tptp.zero_zero_rat)))))) (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_2 (tptp.aa_Cod1783974652533396728nteger _let_1 B2))) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) B2)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger B2) (tptp.modulo364778990260209775nteger A _let_2))) (= (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger _let_1 (tptp.divide6298287555418463151nteger A _let_2)) tptp.one_one_Code_integer) (tptp.divide6298287555418463151nteger A B2)))))))) (forall ((A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A))) (let ((_let_2 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_3 (tptp.aa_nat_nat _let_2 B2))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) A)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) B2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A) _let_3))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat _let_2 (tptp.aa_nat_nat _let_1 _let_3))) tptp.one_one_nat) (tptp.aa_nat_nat _let_1 B2))))))))) (forall ((A tptp.int) (B2 tptp.int)) (let ((_let_1 (tptp.divide_divide_int A))) (let ((_let_2 (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_3 (tptp.aa_int_int _let_2 B2))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) A)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) B2)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B2) (tptp.aa_int_int (tptp.modulo_modulo_int A) _let_3))) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int _let_2 (tptp.aa_int_int _let_1 _let_3))) tptp.one_one_int) (tptp.aa_int_int _let_1 B2))))))))) (forall ((Y tptp.real) (Z tptp.real) (X tptp.real) (W tptp.real)) (=> (not (= Y tptp.zero_zero_real)) (=> (not (= Z tptp.zero_zero_real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real X) Y)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real W) Z))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real X) Z)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real W) Y))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real Y) Z))) tptp.zero_zero_real)))))) (forall ((Y tptp.rat) (Z tptp.rat) (X tptp.rat) (W tptp.rat)) (=> (not (= Y tptp.zero_zero_rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.divide_divide_rat X) Y)) (tptp.aa_rat_rat (tptp.divide_divide_rat W) Z))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat X) Z)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat W) Y))) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat Y) Z))) tptp.zero_zero_rat)))))) (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real A) N))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) A)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) tptp.one_one_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) _let_1)) _let_1)))))) (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_rat (tptp.power_power_rat A) N))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) A)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) tptp.one_one_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) _let_1)) _let_1)))))) (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A) N))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) A)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) tptp.one_one_nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) _let_1)) _let_1)))))) (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_int (tptp.power_power_int A) N))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) A)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) tptp.one_one_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) _let_1)) _let_1)))))) (forall ((A tptp.real) (N tptp.nat)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) A)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) tptp.one_one_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real A) (tptp.aa_nat_nat tptp.suc N))) A))))) (forall ((A tptp.rat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) A)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) tptp.one_one_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat (tptp.power_power_rat A) (tptp.aa_nat_nat tptp.suc N))) A))))) (forall ((A tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) A)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) tptp.one_one_nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A) (tptp.aa_nat_nat tptp.suc N))) A))))) (forall ((A tptp.int) (N tptp.nat)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) A)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) tptp.one_one_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int (tptp.power_power_int A) (tptp.aa_nat_nat tptp.suc N))) A))))) (forall ((A tptp.real) (N tptp.nat)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) A)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) tptp.one_one_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real A) (tptp.aa_nat_nat tptp.suc N))) tptp.one_one_real))))) (forall ((A tptp.rat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) A)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) tptp.one_one_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_nat_rat (tptp.power_power_rat A) (tptp.aa_nat_nat tptp.suc N))) tptp.one_one_rat))))) (forall ((A tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) A)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) tptp.one_one_nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A) (tptp.aa_nat_nat tptp.suc N))) tptp.one_one_nat))))) (forall ((A tptp.int) (N tptp.nat)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) A)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) tptp.one_one_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_nat_int (tptp.power_power_int A) (tptp.aa_nat_nat tptp.suc N))) tptp.one_one_int))))) (forall ((N tptp.nat) (N3 tptp.nat) (A tptp.real)) (let ((_let_1 (tptp.aa_real_fun_nat_real tptp.power_power_real A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N) N3)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) A)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) tptp.one_one_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_nat_real _let_1 N3)) (tptp.aa_nat_real _let_1 N)))))))) (forall ((N tptp.nat) (N3 tptp.nat) (A tptp.rat)) (let ((_let_1 (tptp.power_power_rat A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N) N3)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) A)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) tptp.one_one_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_nat_rat _let_1 N3)) (tptp.aa_nat_rat _let_1 N)))))))) (forall ((N tptp.nat) (N3 tptp.nat) (A tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N) N3)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) A)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) tptp.one_one_nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat _let_1 N3)) (tptp.aa_nat_nat _let_1 N)))))))) (forall ((N tptp.nat) (N3 tptp.nat) (A tptp.int)) (let ((_let_1 (tptp.power_power_int A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N) N3)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) A)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) tptp.one_one_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_nat_int _let_1 N3)) (tptp.aa_nat_int _let_1 N)))))))) (forall ((N tptp.nat) (N3 tptp.nat) (A tptp.real)) (let ((_let_1 (tptp.aa_real_fun_nat_real tptp.power_power_real A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N) N3)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) A)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) tptp.one_one_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_nat_real _let_1 N3)) (tptp.aa_nat_real _let_1 N)))))))) (forall ((N tptp.nat) (N3 tptp.nat) (A tptp.rat)) (let ((_let_1 (tptp.power_power_rat A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N) N3)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) A)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) tptp.one_one_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat _let_1 N3)) (tptp.aa_nat_rat _let_1 N)))))))) (forall ((N tptp.nat) (N3 tptp.nat) (A tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N) N3)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) A)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) tptp.one_one_nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat _let_1 N3)) (tptp.aa_nat_nat _let_1 N)))))))) (forall ((N tptp.nat) (N3 tptp.nat) (A tptp.int)) (let ((_let_1 (tptp.power_power_int A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N) N3)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) A)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) tptp.one_one_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int _let_1 N3)) (tptp.aa_nat_int _let_1 N)))))))) (forall ((X tptp.vEBT_VEBT) (Y tptp.option_nat)) (=> (= (tptp.vEBT_vebt_mint X) Y) (=> (forall ((A3 tptp.bool) (B3 tptp.bool)) (let ((_let_1 (tptp.pp B3))) (let ((_let_2 (tptp.pp A3))) (=> (= X (tptp.vEBT_Leaf A3 B3)) (not (and (=> _let_2 (= Y (tptp.some_nat tptp.zero_zero_nat))) (=> (not _let_2) (and (=> _let_1 (= Y (tptp.some_nat tptp.one_one_nat))) (=> (not _let_1) (= Y tptp.none_nat)))))))))) (=> (=> (exists ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (= X (tptp.vEBT_Node tptp.none_P5556105721700978146at_nat Uu2 Uv2 Uw2))) (not (= Y tptp.none_nat))) (not (forall ((Mi2 tptp.nat)) (=> (exists ((Ma2 tptp.nat) (Ux2 tptp.nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (= X (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Mi2) Ma2)) Ux2 Uy2 Uz2))) (not (= Y (tptp.some_nat Mi2)))))))))) (= (tptp.aa_nat_rat (tptp.power_power_rat tptp.zero_zero_rat) _let_33) tptp.zero_zero_rat) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat tptp.zero_zero_nat) _let_33) tptp.zero_zero_nat) (= (tptp.aa_nat_real _let_80 _let_33) tptp.zero_zero_real) (= (tptp.aa_nat_int _let_79 _let_33) tptp.zero_zero_int) (= (tptp.aa_nat_complex _let_78 _let_33) tptp.zero_zero_complex) (forall ((X tptp.vEBT_VEBT) (Y tptp.option_nat)) (=> (= (tptp.vEBT_vebt_maxt X) Y) (=> (forall ((A3 tptp.bool) (B3 tptp.bool)) (let ((_let_1 (tptp.pp A3))) (let ((_let_2 (tptp.pp B3))) (=> (= X (tptp.vEBT_Leaf A3 B3)) (not (and (=> _let_2 (= Y (tptp.some_nat tptp.one_one_nat))) (=> (not _let_2) (and (=> _let_1 (= Y (tptp.some_nat tptp.zero_zero_nat))) (=> (not _let_1) (= Y tptp.none_nat)))))))))) (=> (=> (exists ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (= X (tptp.vEBT_Node tptp.none_P5556105721700978146at_nat Uu2 Uv2 Uw2))) (not (= Y tptp.none_nat))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat)) (=> (exists ((Ux2 tptp.nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (= X (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Mi2) Ma2)) Ux2 Uy2 Uz2))) (not (= Y (tptp.some_nat Ma2)))))))))) (forall ((A tptp.real) (N tptp.nat)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.one_one_real) A)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real A) N)))))) (forall ((A tptp.rat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.one_one_rat) A)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) (tptp.aa_nat_rat (tptp.power_power_rat A) N)))))) (forall ((A tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.one_one_nat) A)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A) N)))))) (forall ((A tptp.int) (N tptp.nat)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.one_one_int) A)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) (tptp.aa_nat_int (tptp.power_power_int A) N)))))) (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real))) (=> (tptp.pp (tptp.aa_real_bool _let_1 A)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real A) N))))))) (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.one_one_rat))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 A)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_nat_rat (tptp.power_power_rat A) N))))))) (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.one_one_nat))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 A)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A) N))))))) (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.one_one_int))) (=> (tptp.pp (tptp.aa_int_bool _let_1 A)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_nat_int (tptp.power_power_int A) N))))))) (= _let_33 _let_43) (tptp.pp (tptp.aa_nat_bool _let_144 _let_33)) (forall ((A tptp.complex) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.power_power_complex A))) (=> (not (= A tptp.zero_zero_complex)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N) M)) (= (tptp.aa_nat_complex _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) N)) (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex (tptp.aa_nat_complex _let_1 M)) (tptp.aa_nat_complex _let_1 N))))))) (forall ((A tptp.real) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.aa_real_fun_nat_real tptp.power_power_real A))) (=> (not (= A tptp.zero_zero_real)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N) M)) (= (tptp.aa_nat_real _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) N)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_nat_real _let_1 M)) (tptp.aa_nat_real _let_1 N))))))) (forall ((A tptp.rat) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.power_power_rat A))) (=> (not (= A tptp.zero_zero_rat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N) M)) (= (tptp.aa_nat_rat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) N)) (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_nat_rat _let_1 M)) (tptp.aa_nat_rat _let_1 N))))))) (forall ((A tptp.nat) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A))) (=> (not (= A tptp.zero_zero_nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N) M)) (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) N)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat _let_1 M)) (tptp.aa_nat_nat _let_1 N))))))) (forall ((A tptp.int) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.power_power_int A))) (=> (not (= A tptp.zero_zero_int)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N) M)) (= (tptp.aa_nat_int _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) N)) (tptp.aa_int_int (tptp.divide_divide_int (tptp.aa_nat_int _let_1 M)) (tptp.aa_nat_int _let_1 N))))))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat M) N))) (let ((_let_2 (or (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N)) (= N tptp.zero_zero_nat)))) (and (=> _let_2 (= _let_1 tptp.zero_zero_nat)) (=> (not _let_2) (= _let_1 (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) N)) N)))))))) (forall ((N tptp.nat) (M tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (=> (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat M) N) (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) N)) N)))))) (forall ((N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (= N (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) tptp.one_one_nat))))) (forall ((N tptp.nat) (M tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat tptp.suc M)) N) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) tptp.one_one_nat))))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_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.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) tptp.one_one_nat)) N)))))))) (forall ((Q2 tptp.nat) (M tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) Q2)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat N) Q2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat M) Q2)) N))))) (forall ((N tptp.nat) (M tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat N) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat M) N))))))) (forall ((N tptp.nat) (M tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat M) N)) N)))))) (forall ((P tptp.fun_nat_bool) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (= N tptp.zero_zero_nat))) (= (tptp.pp (tptp.aa_nat_bool P (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat M) N))) (and (=> _let_1 (tptp.pp (tptp.aa_nat_bool P tptp.zero_zero_nat))) (=> (not _let_1) (forall ((I4 tptp.nat) (J3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat J3) N)) (=> (= M (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat N) I4)) J3)) (tptp.pp (tptp.aa_nat_bool P I4)))))))))) (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y tptp.bool)) (let ((_let_1 (tptp.pp Y))) (=> (= (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_V5719532721284313246member X) Xa2)) _let_1) (=> (forall ((A3 tptp.bool) (B3 tptp.bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (=> (= X (tptp.vEBT_Leaf A3 B3)) (= (tptp.pp Y) (not (and (=> _let_2 (tptp.pp A3)) (=> (not _let_2) (and (=> _let_1 (tptp.pp B3)) _let_1))))))))) (=> (=> (exists ((Uu2 tptp.option4927543243414619207at_nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (= X (tptp.vEBT_Node Uu2 tptp.zero_zero_nat Uv2 Uw2))) _let_1) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat tptp.suc V2)) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_2) (tptp.size_s6755466524823107622T_VEBT TreeList2))))) (=> (exists ((S3 tptp.vEBT_VEBT)) (= X (tptp.vEBT_Node Uy2 (tptp.aa_nat_nat tptp.suc V2) TreeList2 S3))) (= (tptp.pp Y) (not (and (=> _let_3 (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_V5719532721284313246member (tptp.nth_VEBT_VEBT TreeList2 _let_2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low Xa2) _let_1)))) _let_3)))))))))))))) (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_V5719532721284313246member X) Xa2)) (=> (forall ((A3 tptp.bool) (B3 tptp.bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (=> (= X (tptp.vEBT_Leaf A3 B3)) (not (and (=> _let_2 (tptp.pp A3)) (=> (not _let_2) (and (=> _let_1 (tptp.pp B3)) _let_1)))))))) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat tptp.suc V2)) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_2) (tptp.size_s6755466524823107622T_VEBT TreeList2))))) (=> (exists ((S3 tptp.vEBT_VEBT)) (= X (tptp.vEBT_Node Uy2 (tptp.aa_nat_nat tptp.suc V2) TreeList2 S3))) (not (and (=> _let_3 (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_V5719532721284313246member (tptp.nth_VEBT_VEBT TreeList2 _let_2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low Xa2) _let_1)))) _let_3))))))))))) (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_V5719532721284313246member X) Xa2))) (=> (forall ((A3 tptp.bool) (B3 tptp.bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (=> (= X (tptp.vEBT_Leaf A3 B3)) (and (=> _let_2 (tptp.pp A3)) (=> (not _let_2) (and (=> _let_1 (tptp.pp B3)) _let_1))))))) (=> (forall ((Uu2 tptp.option4927543243414619207at_nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (not (= X (tptp.vEBT_Node Uu2 tptp.zero_zero_nat Uv2 Uw2)))) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat tptp.suc V2)) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_2) (tptp.size_s6755466524823107622T_VEBT TreeList2))))) (=> (exists ((S3 tptp.vEBT_VEBT)) (= X (tptp.vEBT_Node Uy2 (tptp.aa_nat_nat tptp.suc V2) TreeList2 S3))) (and (=> _let_3 (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_V5719532721284313246member (tptp.nth_VEBT_VEBT TreeList2 _let_2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low Xa2) _let_1)))) _let_3))))))))))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_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.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) tptp.one_one_nat)) N)))))))) (forall ((V tptp.product_prod_nat_nat) (Vd tptp.list_VEBT_VEBT) (Ve2 tptp.vEBT_VEBT) (Vf2 tptp.nat)) (= (tptp.vEBT_vebt_pred (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat V) tptp.zero_zero_nat Vd Ve2) Vf2) tptp.none_nat)) (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y tptp.bool)) (let ((_let_1 (tptp.pp Y))) (=> (= (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_VEBT_membermima X) Xa2)) _let_1) (=> (=> (exists ((Uu2 tptp.bool) (Uv2 tptp.bool)) (= X (tptp.vEBT_Leaf Uu2 Uv2))) _let_1) (=> (=> (exists ((Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (= X (tptp.vEBT_Node tptp.none_P5556105721700978146at_nat tptp.zero_zero_nat Ux2 Uy2))) _let_1) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat)) (=> (exists ((Va3 tptp.list_VEBT_VEBT) (Vb2 tptp.vEBT_VEBT)) (= X (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Mi2) Ma2)) tptp.zero_zero_nat Va3 Vb2))) (= (tptp.pp Y) (not (or (= Xa2 Mi2) (= Xa2 Ma2)))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat tptp.suc V2)) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_2) (tptp.size_s6755466524823107622T_VEBT TreeList2))))) (=> (exists ((Vc2 tptp.vEBT_VEBT)) (= X (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Mi2) Ma2)) (tptp.aa_nat_nat tptp.suc V2) TreeList2 Vc2))) (= (tptp.pp Y) (not (or (= Xa2 Mi2) (= Xa2 Ma2) (and (=> _let_3 (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_VEBT_membermima (tptp.nth_VEBT_VEBT TreeList2 _let_2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low Xa2) _let_1)))) _let_3))))))))) (not (forall ((V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat tptp.suc V2)) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_2) (tptp.size_s6755466524823107622T_VEBT TreeList2))))) (=> (exists ((Vd2 tptp.vEBT_VEBT)) (= X (tptp.vEBT_Node tptp.none_P5556105721700978146at_nat (tptp.aa_nat_nat tptp.suc V2) TreeList2 Vd2))) (= (tptp.pp Y) (not (and (=> _let_3 (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_VEBT_membermima (tptp.nth_VEBT_VEBT TreeList2 _let_2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low Xa2) _let_1)))) _let_3)))))))))))))))) (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_VEBT_membermima X) Xa2))) (=> (forall ((Uu2 tptp.bool) (Uv2 tptp.bool)) (not (= X (tptp.vEBT_Leaf Uu2 Uv2)))) (=> (forall ((Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (not (= X (tptp.vEBT_Node tptp.none_P5556105721700978146at_nat tptp.zero_zero_nat Ux2 Uy2)))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat)) (=> (exists ((Va3 tptp.list_VEBT_VEBT) (Vb2 tptp.vEBT_VEBT)) (= X (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Mi2) Ma2)) tptp.zero_zero_nat Va3 Vb2))) (or (= Xa2 Mi2) (= Xa2 Ma2)))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat tptp.suc V2)) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_2) (tptp.size_s6755466524823107622T_VEBT TreeList2))))) (=> (exists ((Vc2 tptp.vEBT_VEBT)) (= X (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Mi2) Ma2)) (tptp.aa_nat_nat tptp.suc V2) TreeList2 Vc2))) (or (= Xa2 Mi2) (= Xa2 Ma2) (and (=> _let_3 (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_VEBT_membermima (tptp.nth_VEBT_VEBT TreeList2 _let_2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low Xa2) _let_1)))) _let_3))))))) (not (forall ((V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat tptp.suc V2)) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_2) (tptp.size_s6755466524823107622T_VEBT TreeList2))))) (=> (exists ((Vd2 tptp.vEBT_VEBT)) (= X (tptp.vEBT_Node tptp.none_P5556105721700978146at_nat (tptp.aa_nat_nat tptp.suc V2) TreeList2 Vd2))) (and (=> _let_3 (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_VEBT_membermima (tptp.nth_VEBT_VEBT TreeList2 _let_2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low Xa2) _let_1)))) _let_3))))))))))))) (forall ((X tptp.real) (A tptp.real) (Y tptp.real) (U tptp.real) (V tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) A)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y) A)) (=> (tptp.pp (tptp.aa_real_bool _let_1 U)) (=> (tptp.pp (tptp.aa_real_bool _let_1 V)) (=> (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real U) V) tptp.one_one_real) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real U) X)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real V) Y))) A))))))))) (forall ((X tptp.rat) (A tptp.rat) (Y tptp.rat) (U tptp.rat) (V tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) A)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Y) A)) (=> (tptp.pp (tptp.aa_rat_bool _let_1 U)) (=> (tptp.pp (tptp.aa_rat_bool _let_1 V)) (=> (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat U) V) tptp.one_one_rat) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat U) X)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat V) Y))) A))))))))) (forall ((X tptp.int) (A tptp.int) (Y tptp.int) (U tptp.int) (V tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) A)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Y) A)) (=> (tptp.pp (tptp.aa_int_bool _let_1 U)) (=> (tptp.pp (tptp.aa_int_bool _let_1 V)) (=> (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int U) V) tptp.one_one_int) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int U) X)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int V) Y))) A))))))))) (forall ((W tptp.num) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (tptp.aa_num_real tptp.numeral_numeral_real W))) (let ((_let_2 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real _let_1))) (let ((_let_3 (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real C) tptp.zero_zero_real)))) (let ((_let_4 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real _let_1) C))) (let ((_let_5 (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) C)))) (= (tptp.pp (tptp.aa_real_bool _let_2 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real B2) C))) (and (=> _let_5 (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real _let_4) B2))) (=> (not _let_5) (and (=> _let_3 (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real B2) _let_4))) (=> (not _let_3) (tptp.pp (tptp.aa_real_bool _let_2 tptp.zero_zero_real))))))))))))) (forall ((W tptp.num) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_num_rat tptp.numeral_numeral_rat W))) (let ((_let_2 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat _let_1))) (let ((_let_3 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat C) tptp.zero_zero_rat)))) (let ((_let_4 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat _let_1) C))) (let ((_let_5 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) C)))) (= (tptp.pp (tptp.aa_rat_bool _let_2 (tptp.aa_rat_rat (tptp.divide_divide_rat B2) C))) (and (=> _let_5 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat _let_4) B2))) (=> (not _let_5) (and (=> _let_3 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B2) _let_4))) (=> (not _let_3) (tptp.pp (tptp.aa_rat_bool _let_2 tptp.zero_zero_rat))))))))))))) (forall ((B2 tptp.real) (C tptp.real) (W tptp.num)) (let ((_let_1 (tptp.aa_num_real tptp.numeral_numeral_real W))) (let ((_let_2 (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real C) tptp.zero_zero_real)))) (let ((_let_3 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real _let_1) C))) (let ((_let_4 (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) C)))) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real B2) C)) _let_1)) (and (=> _let_4 (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real B2) _let_3))) (=> (not _let_4) (and (=> _let_2 (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real _let_3) B2))) (=> (not _let_2) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) _let_1)))))))))))) (forall ((B2 tptp.rat) (C tptp.rat) (W tptp.num)) (let ((_let_1 (tptp.aa_num_rat tptp.numeral_numeral_rat W))) (let ((_let_2 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat C) tptp.zero_zero_rat)))) (let ((_let_3 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat _let_1) C))) (let ((_let_4 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) C)))) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.divide_divide_rat B2) C)) _let_1)) (and (=> _let_4 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B2) _let_3))) (=> (not _let_4) (and (=> _let_2 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat _let_3) B2))) (=> (not _let_2) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1)))))))))))) (forall ((A tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool _let_1 A)) (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real A) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))))))) (forall ((A tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 A)) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat (tptp.divide_divide_rat A) (tptp.aa_num_rat tptp.numeral_numeral_rat (tptp.aa_num_num tptp.bit0 tptp.one)))))))) (forall ((A tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real))) (= (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real A) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))))) (tptp.pp (tptp.aa_real_bool _let_1 A))))) (forall ((A tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat))) (= (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat (tptp.divide_divide_rat A) (tptp.aa_num_rat tptp.numeral_numeral_rat (tptp.aa_num_num tptp.bit0 tptp.one))))) (tptp.pp (tptp.aa_rat_bool _let_1 A))))) (forall ((U tptp.real) (V tptp.real) (R tptp.real) (S tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real U) V)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) R)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real R) S)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real U) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real R) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real V) U))) S))) V)))))) (forall ((U tptp.rat) (V tptp.rat) (R tptp.rat) (S tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat U) V)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) R)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat R) S)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat U) (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat R) (tptp.aa_rat_rat (tptp.minus_minus_rat V) U))) S))) V)))))) (forall ((A tptp.real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real A) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))))) (forall ((A tptp.rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_nat_rat (tptp.power_power_rat A) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))))) (forall ((A tptp.int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.aa_nat_int (tptp.power_power_int A) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (let ((_let_2 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) _let_2) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Y) _let_2)) (=> (tptp.pp (tptp.aa_real_bool _let_1 X)) (=> (tptp.pp (tptp.aa_real_bool _let_1 Y)) (= X Y))))))) (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat))) (let ((_let_2 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (= (tptp.aa_nat_rat (tptp.power_power_rat X) _let_2) (tptp.aa_nat_rat (tptp.power_power_rat Y) _let_2)) (=> (tptp.pp (tptp.aa_rat_bool _let_1 X)) (=> (tptp.pp (tptp.aa_rat_bool _let_1 Y)) (= X Y))))))) (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat))) (let ((_let_2 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat X) _let_2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat Y) _let_2)) (=> (tptp.pp (tptp.aa_nat_bool _let_1 X)) (=> (tptp.pp (tptp.aa_nat_bool _let_1 Y)) (= X Y))))))) (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_2 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (= (tptp.aa_nat_int (tptp.power_power_int X) _let_2) (tptp.aa_nat_int (tptp.power_power_int Y) _let_2)) (=> (tptp.pp (tptp.aa_int_bool _let_1 X)) (=> (tptp.pp (tptp.aa_int_bool _let_1 Y)) (= X Y))))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) _let_1)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Y) _let_1))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) Y)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) Y)))))) (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat (tptp.power_power_rat X) _let_1)) (tptp.aa_nat_rat (tptp.power_power_rat Y) _let_1))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) Y)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) Y)))))) (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat X) _let_1)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat Y) _let_1))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) Y)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X) Y)))))) (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int (tptp.power_power_int X) _let_1)) (tptp.aa_nat_int (tptp.power_power_int Y) _let_1))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) Y)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X) Y)))))) (forall ((A tptp.real)) (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real A) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) tptp.zero_zero_real)))) (forall ((A tptp.rat)) (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_nat_rat (tptp.power_power_rat A) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) tptp.zero_zero_rat)))) (forall ((A tptp.int)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_nat_int (tptp.power_power_int A) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) tptp.zero_zero_int)))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (=> (not (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) N)) tptp.zero_zero_nat)) (not (= (tptp.aa_nat_nat _let_1 M) tptp.zero_zero_nat))))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))))) (=> (not (= (tptp.aa_nat_int _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) N)) tptp.zero_zero_int)) (not (= (tptp.aa_nat_int _let_1 M) tptp.zero_zero_int))))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (=> (not (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) N)) tptp.zero_zero_nat)) (not (= (tptp.aa_nat_nat _let_1 N) tptp.zero_zero_nat))))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))))) (=> (not (= (tptp.aa_nat_int _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) N)) tptp.zero_zero_int)) (not (= (tptp.aa_nat_int _let_1 N) tptp.zero_zero_int))))) (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (=> (not (= (tptp.aa_nat_nat _let_1 N) tptp.zero_zero_nat)) (not (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) M)) tptp.zero_zero_nat))))) (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))))) (=> (not (= (tptp.aa_nat_int _let_1 N) tptp.zero_zero_int)) (not (= (tptp.aa_nat_int _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) M)) tptp.zero_zero_int))))) (forall ((A tptp.nat) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A))) (let ((_let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat _let_1 M)) (tptp.aa_nat_nat _let_1 N)))) (let ((_let_3 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N) M)))) (=> (not (= A tptp.zero_zero_nat)) (and (=> _let_3 (= _let_2 (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) N)))) (=> (not _let_3) (= _let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat tptp.one_one_nat) (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) M))))))))))) (forall ((A tptp.int) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.power_power_int A))) (let ((_let_2 (tptp.aa_int_int (tptp.divide_divide_int (tptp.aa_nat_int _let_1 M)) (tptp.aa_nat_int _let_1 N)))) (let ((_let_3 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N) M)))) (=> (not (= A tptp.zero_zero_int)) (and (=> _let_3 (= _let_2 (tptp.aa_nat_int _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) N)))) (=> (not _let_3) (= _let_2 (tptp.aa_int_int (tptp.divide_divide_int tptp.one_one_int) (tptp.aa_nat_int _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) M))))))))))) (forall ((N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (or (= N tptp.zero_zero_nat) (= N (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat))))) (forall ((N tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (or (= N tptp.zero_zero_nat) (= N (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat))))) (forall ((M tptp.nat) (P2 tptp.complex)) (let ((_let_1 (tptp.power_power_complex P2))) (let ((_let_2 (tptp.aa_nat_complex _let_1 M))) (let ((_let_3 (= M tptp.zero_zero_nat))) (and (=> _let_3 (= _let_2 tptp.one_one_complex)) (=> (not _let_3) (= _let_2 (tptp.aa_complex_complex (tptp.times_times_complex P2) (tptp.aa_nat_complex _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) tptp.one_one_nat)))))))))) (forall ((M tptp.nat) (P2 tptp.real)) (let ((_let_1 (tptp.aa_real_fun_nat_real tptp.power_power_real P2))) (let ((_let_2 (tptp.aa_nat_real _let_1 M))) (let ((_let_3 (= M tptp.zero_zero_nat))) (and (=> _let_3 (= _let_2 tptp.one_one_real)) (=> (not _let_3) (= _let_2 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real P2) (tptp.aa_nat_real _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) tptp.one_one_nat)))))))))) (forall ((M tptp.nat) (P2 tptp.rat)) (let ((_let_1 (tptp.power_power_rat P2))) (let ((_let_2 (tptp.aa_nat_rat _let_1 M))) (let ((_let_3 (= M tptp.zero_zero_nat))) (and (=> _let_3 (= _let_2 tptp.one_one_rat)) (=> (not _let_3) (= _let_2 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat P2) (tptp.aa_nat_rat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) tptp.one_one_nat)))))))))) (forall ((M tptp.nat) (P2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat P2))) (let ((_let_2 (tptp.aa_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.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat P2) (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) tptp.one_one_nat)))))))))) (forall ((M tptp.nat) (P2 tptp.int)) (let ((_let_1 (tptp.power_power_int P2))) (let ((_let_2 (tptp.aa_nat_int _let_1 M))) (let ((_let_3 (= M tptp.zero_zero_nat))) (and (=> _let_3 (= _let_2 tptp.one_one_int)) (=> (not _let_3) (= _let_2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int P2) (tptp.aa_nat_int _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) tptp.one_one_nat)))))))))) (forall ((N tptp.nat) (A tptp.complex)) (let ((_let_1 (tptp.power_power_complex A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (= (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_nat_complex _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) tptp.one_one_nat))) A) (tptp.aa_nat_complex _let_1 N))))) (forall ((N tptp.nat) (A tptp.real)) (let ((_let_1 (tptp.aa_real_fun_nat_real tptp.power_power_real A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) tptp.one_one_nat))) A) (tptp.aa_nat_real _let_1 N))))) (forall ((N tptp.nat) (A tptp.rat)) (let ((_let_1 (tptp.power_power_rat A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) tptp.one_one_nat))) A) (tptp.aa_nat_rat _let_1 N))))) (forall ((N tptp.nat) (A tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) tptp.one_one_nat))) A) (tptp.aa_nat_nat _let_1 N))))) (forall ((N tptp.nat) (A tptp.int)) (let ((_let_1 (tptp.power_power_int A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) tptp.one_one_nat))) A) (tptp.aa_nat_int _let_1 N))))) (forall ((N tptp.nat) (M tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N) M)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat M) N) (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) N)) N)))))) (forall ((P tptp.fun_nat_bool) (M tptp.nat) (N tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool P (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat M) N))) (or (and (= N tptp.zero_zero_nat) (tptp.pp (tptp.aa_nat_bool P tptp.zero_zero_nat))) (exists ((Q4 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat N))) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat _let_1 Q4)) M)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat tptp.suc Q4)))) (tptp.pp (tptp.aa_nat_bool P Q4)))))))) (forall ((A tptp.nat) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_2 (tptp.aa_nat_nat _let_1 N))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) _let_2)) (tptp.aa_nat_nat _let_1 M)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A) (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N) M)))) _let_2))))) (forall ((A tptp.int) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_2 (tptp.aa_nat_int _let_1 N))) (= (tptp.aa_int_int (tptp.modulo_modulo_int (tptp.aa_int_int (tptp.divide_divide_int A) _let_2)) (tptp.aa_nat_int _let_1 M)) (tptp.aa_int_int (tptp.divide_divide_int (tptp.aa_int_int (tptp.modulo_modulo_int A) (tptp.aa_nat_int _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N) M)))) _let_2))))) (forall ((A tptp.code_integer) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.power_8256067586552552935nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_2 (tptp.aa_nat_Code_integer _let_1 N))) (= (tptp.modulo364778990260209775nteger (tptp.divide6298287555418463151nteger A _let_2) (tptp.aa_nat_Code_integer _let_1 M)) (tptp.divide6298287555418463151nteger (tptp.modulo364778990260209775nteger A (tptp.aa_nat_Code_integer _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N) M))) _let_2))))) (forall ((V tptp.product_prod_nat_nat) (Vh2 tptp.list_VEBT_VEBT) (Vi2 tptp.vEBT_VEBT) (Vj2 tptp.nat)) (= (tptp.vEBT_vebt_pred (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat V) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat) Vh2 Vi2) Vj2) tptp.none_nat)) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) _let_1)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Y) _let_1))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) Y)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Y)))))) (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_nat_rat (tptp.power_power_rat X) _let_1)) (tptp.aa_nat_rat (tptp.power_power_rat Y) _let_1))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) Y)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) Y)))))) (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat X) _let_1)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat Y) _let_1))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) Y)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Y)))))) (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_nat_int (tptp.power_power_int X) _let_1)) (tptp.aa_nat_int (tptp.power_power_int Y) _let_1))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) Y)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) Y)))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) _let_1)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Y) _let_1)))))) (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_nat_rat (tptp.power_power_rat X) _let_1)) (tptp.aa_nat_rat (tptp.power_power_rat Y) _let_1)))))) (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_nat_int (tptp.power_power_int X) _let_1)) (tptp.aa_nat_int (tptp.power_power_int Y) _let_1)))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) _let_1)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Y) _let_1))) tptp.zero_zero_real)) (and (= X tptp.zero_zero_real) (= Y tptp.zero_zero_real))))) (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_nat_rat (tptp.power_power_rat X) _let_1)) (tptp.aa_nat_rat (tptp.power_power_rat Y) _let_1))) tptp.zero_zero_rat)) (and (= X tptp.zero_zero_rat) (= Y tptp.zero_zero_rat))))) (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_nat_int (tptp.power_power_int X) _let_1)) (tptp.aa_nat_int (tptp.power_power_int Y) _let_1))) tptp.zero_zero_int)) (and (= X tptp.zero_zero_int) (= Y tptp.zero_zero_int))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) _let_1)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Y) _let_1))) tptp.zero_zero_real))))) (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_nat_rat (tptp.power_power_rat X) _let_1)) (tptp.aa_nat_rat (tptp.power_power_rat Y) _let_1))) tptp.zero_zero_rat))))) (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_nat_int (tptp.power_power_int X) _let_1)) (tptp.aa_nat_int (tptp.power_power_int Y) _let_1))) tptp.zero_zero_int))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) _let_1)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Y) _let_1)))) (or (not (= X tptp.zero_zero_real)) (not (= Y tptp.zero_zero_real)))))) (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_nat_rat (tptp.power_power_rat X) _let_1)) (tptp.aa_nat_rat (tptp.power_power_rat Y) _let_1)))) (or (not (= X tptp.zero_zero_rat)) (not (= Y tptp.zero_zero_rat)))))) (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_nat_int (tptp.power_power_int X) _let_1)) (tptp.aa_nat_int (tptp.power_power_int Y) _let_1)))) (or (not (= X tptp.zero_zero_int)) (not (= Y tptp.zero_zero_int)))))) (forall ((A tptp.real) (N tptp.nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N))))) (forall ((A tptp.rat) (N tptp.nat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_nat_rat (tptp.power_power_rat A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N))))) (forall ((A tptp.int) (N tptp.nat)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.aa_nat_int (tptp.power_power_int A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N))))) (forall ((P tptp.fun_nat_bool) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool P tptp.zero_zero_nat)) (=> (forall ((N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool P N2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)) (tptp.pp (tptp.aa_nat_bool P (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N2)))))) (=> (forall ((N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool P N2)) (tptp.pp (tptp.aa_nat_bool P (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N2)))))) (tptp.pp (tptp.aa_nat_bool P N)))))) (forall ((N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)) N)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat N) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))))) (forall ((N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 N)) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat tptp.suc N)) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))))))) (forall ((M tptp.nat) (N tptp.nat) (A tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_2 (tptp.aa_nat_nat _let_1 M))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) _let_2)) (tptp.aa_nat_nat _let_1 N)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A) (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) M)))) _let_2)))))) (forall ((M tptp.nat) (N tptp.nat) (A tptp.int)) (let ((_let_1 (tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_2 (tptp.aa_nat_int _let_1 M))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)) (= (tptp.aa_int_int (tptp.modulo_modulo_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) _let_2)) (tptp.aa_nat_int _let_1 N)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.modulo_modulo_int A) (tptp.aa_nat_int _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) M)))) _let_2)))))) (forall ((M tptp.nat) (N tptp.nat) (A tptp.code_integer)) (let ((_let_1 (tptp.power_8256067586552552935nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_2 (tptp.aa_nat_Code_integer _let_1 M))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)) (= (tptp.modulo364778990260209775nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) _let_2) (tptp.aa_nat_Code_integer _let_1 N)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.modulo364778990260209775nteger A (tptp.aa_nat_Code_integer _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) M)))) _let_2)))))) (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_vebt_member X) Xa2)) (=> (forall ((A3 tptp.bool) (B3 tptp.bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (=> (= X (tptp.vEBT_Leaf A3 B3)) (not (and (=> _let_2 (tptp.pp A3)) (=> (not _let_2) (and (=> _let_1 (tptp.pp B3)) _let_1)))))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat tptp.suc Va2))) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_2) (tptp.size_s6755466524823107622T_VEBT TreeList2))))) (let ((_let_4 (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Ma2) Xa2))))) (let ((_let_5 (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Xa2) Mi2))))) (=> (exists ((Summary2 tptp.vEBT_VEBT)) (= X (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Mi2) Ma2)) (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat tptp.suc Va2)) TreeList2 Summary2))) (not (=> (not (= Xa2 Mi2)) (=> (not (= Xa2 Ma2)) (and _let_5 (=> _let_5 (and _let_4 (=> _let_4 (and (=> _let_3 (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_vebt_member (tptp.nth_VEBT_VEBT TreeList2 _let_2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low Xa2) _let_1)))) _let_3))))))))))))))))))) (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y tptp.bool)) (let ((_let_1 (tptp.pp Y))) (=> (= (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_vebt_member X) Xa2)) _let_1) (=> (forall ((A3 tptp.bool) (B3 tptp.bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (=> (= X (tptp.vEBT_Leaf A3 B3)) (= (tptp.pp Y) (not (and (=> _let_2 (tptp.pp A3)) (=> (not _let_2) (and (=> _let_1 (tptp.pp B3)) _let_1))))))))) (=> (=> (exists ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (= X (tptp.vEBT_Node tptp.none_P5556105721700978146at_nat Uu2 Uv2 Uw2))) _let_1) (=> (=> (exists ((V2 tptp.product_prod_nat_nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (= X (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat V2) tptp.zero_zero_nat Uy2 Uz2))) _let_1) (=> (=> (exists ((V2 tptp.product_prod_nat_nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (= X (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat V2) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat) Vb2 Vc2))) _let_1) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat tptp.suc Va2))) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_2) (tptp.size_s6755466524823107622T_VEBT TreeList2))))) (let ((_let_4 (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Ma2) Xa2))))) (let ((_let_5 (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Xa2) Mi2))))) (=> (exists ((Summary2 tptp.vEBT_VEBT)) (= X (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Mi2) Ma2)) (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat tptp.suc Va2)) TreeList2 Summary2))) (= (tptp.pp Y) (not (=> (not (= Xa2 Mi2)) (=> (not (= Xa2 Ma2)) (and _let_5 (=> _let_5 (and _let_4 (=> _let_4 (and (=> _let_3 (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_vebt_member (tptp.nth_VEBT_VEBT TreeList2 _let_2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low Xa2) _let_1)))) _let_3)))))))))))))))))))))))) (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_vebt_member X) Xa2))) (=> (forall ((A3 tptp.bool) (B3 tptp.bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (=> (= X (tptp.vEBT_Leaf A3 B3)) (and (=> _let_2 (tptp.pp A3)) (=> (not _let_2) (and (=> _let_1 (tptp.pp B3)) _let_1))))))) (=> (forall ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (not (= X (tptp.vEBT_Node tptp.none_P5556105721700978146at_nat Uu2 Uv2 Uw2)))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (not (= X (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat V2) tptp.zero_zero_nat Uy2 Uz2)))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (not (= X (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat V2) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat) Vb2 Vc2)))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat tptp.suc Va2))) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_2) (tptp.size_s6755466524823107622T_VEBT TreeList2))))) (let ((_let_4 (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Ma2) Xa2))))) (let ((_let_5 (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Xa2) Mi2))))) (=> (exists ((Summary2 tptp.vEBT_VEBT)) (= X (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Mi2) Ma2)) (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat tptp.suc Va2)) TreeList2 Summary2))) (=> (not (= Xa2 Mi2)) (=> (not (= Xa2 Ma2)) (and _let_5 (=> _let_5 (and _let_4 (=> _let_4 (and (=> _let_3 (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_vebt_member (tptp.nth_VEBT_VEBT TreeList2 _let_2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low Xa2) _let_1)))) _let_3))))))))))))))))))))) (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real A) (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N))))) (tptp.pp (tptp.aa_real_bool _let_1 A))))) (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_nat_rat (tptp.power_power_rat A) (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N))))) (tptp.pp (tptp.aa_rat_bool _let_1 A))))) (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_nat_int (tptp.power_power_int A) (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N))))) (tptp.pp (tptp.aa_int_bool _let_1 A))))) (forall ((A tptp.real) (N tptp.nat)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real A) (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N)))) tptp.zero_zero_real)))) (forall ((A tptp.rat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_nat_rat (tptp.power_power_rat A) (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N)))) tptp.zero_zero_rat)))) (forall ((A tptp.int) (N tptp.nat)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_nat_int (tptp.power_power_int A) (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N)))) tptp.zero_zero_int)))) (forall ((X tptp.nat) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_2 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N) M)))) (=> (tptp.pp (tptp.aa_nat_bool _let_2 N)) (=> (tptp.pp (tptp.aa_nat_bool _let_2 M)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high X) N)) (tptp.aa_nat_nat _let_1 M))))))))) (forall ((X tptp.nat) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_2 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N) M)))) (=> (tptp.pp (tptp.aa_nat_bool _let_2 N)) (=> (tptp.pp (tptp.aa_nat_bool _let_2 M)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low X) N)) (tptp.aa_nat_nat _let_1 N))))))))) (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_VEBT_membermima X) Xa2)) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat)) (=> (exists ((Va3 tptp.list_VEBT_VEBT) (Vb2 tptp.vEBT_VEBT)) (= X (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Mi2) Ma2)) tptp.zero_zero_nat Va3 Vb2))) (not (or (= Xa2 Mi2) (= Xa2 Ma2))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat tptp.suc V2)) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_2) (tptp.size_s6755466524823107622T_VEBT TreeList2))))) (=> (exists ((Vc2 tptp.vEBT_VEBT)) (= X (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Mi2) Ma2)) (tptp.aa_nat_nat tptp.suc V2) TreeList2 Vc2))) (not (or (= Xa2 Mi2) (= Xa2 Ma2) (and (=> _let_3 (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_VEBT_membermima (tptp.nth_VEBT_VEBT TreeList2 _let_2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low Xa2) _let_1)))) _let_3)))))))) (not (forall ((V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat tptp.suc V2)) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_2) (tptp.size_s6755466524823107622T_VEBT TreeList2))))) (=> (exists ((Vd2 tptp.vEBT_VEBT)) (= X (tptp.vEBT_Node tptp.none_P5556105721700978146at_nat (tptp.aa_nat_nat tptp.suc V2) TreeList2 Vd2))) (not (and (=> _let_3 (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_VEBT_membermima (tptp.nth_VEBT_VEBT TreeList2 _let_2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low Xa2) _let_1)))) _let_3)))))))))))) (forall ((U tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (let ((_let_2 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real U) (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real X) Y)) (=> (tptp.pp (tptp.aa_real_bool _let_2 X)) (=> (tptp.pp (tptp.aa_real_bool _let_2 Y)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real U) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) Y)) (tptp.aa_num_real tptp.numeral_numeral_real _let_1)))))))))) (forall ((U tptp.rat) (X tptp.rat) (Y tptp.rat)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (let ((_let_2 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (= (tptp.aa_nat_rat (tptp.power_power_rat U) (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat X) Y)) (=> (tptp.pp (tptp.aa_rat_bool _let_2 X)) (=> (tptp.pp (tptp.aa_rat_bool _let_2 Y)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat U) (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat X) Y)) (tptp.aa_num_rat tptp.numeral_numeral_rat _let_1)))))))))) (forall ((A1 tptp.vEBT_VEBT) (A22 tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt A1) A22)) (or (and (exists ((A5 tptp.bool) (B5 tptp.bool)) (= A1 (tptp.vEBT_Leaf A5 B5))) (= A22 (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat))) (exists ((TreeList3 tptp.list_VEBT_VEBT) (N5 tptp.nat) (Summary3 tptp.vEBT_VEBT)) (and (= A1 (tptp.vEBT_Node tptp.none_P5556105721700978146at_nat A22 TreeList3 Summary3)) (forall ((X3 tptp.vEBT_VEBT)) (=> (tptp.pp (tptp.aa_set8260762808118238015T_bool (tptp.aa_VEB289770264548726718T_bool tptp.member_VEBT_VEBT X3) (tptp.set_VEBT_VEBT2 TreeList3))) (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt X3) N5)))) (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt Summary3) N5)) (= (tptp.size_s6755466524823107622T_VEBT TreeList3) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N5)) (= A22 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N5) N5)) (not (exists ((X_1 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions Summary3) X_1)))) (forall ((X3 tptp.vEBT_VEBT)) (=> (tptp.pp (tptp.aa_set8260762808118238015T_bool (tptp.aa_VEB289770264548726718T_bool tptp.member_VEBT_VEBT X3) (tptp.set_VEBT_VEBT2 TreeList3))) (not (exists ((X_1 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions X3) X_1)))))))) (exists ((TreeList3 tptp.list_VEBT_VEBT) (N5 tptp.nat) (Summary3 tptp.vEBT_VEBT)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N5))) (and (= A1 (tptp.vEBT_Node tptp.none_P5556105721700978146at_nat A22 TreeList3 Summary3)) (forall ((X3 tptp.vEBT_VEBT)) (=> (tptp.pp (tptp.aa_set8260762808118238015T_bool (tptp.aa_VEB289770264548726718T_bool tptp.member_VEBT_VEBT X3) (tptp.set_VEBT_VEBT2 TreeList3))) (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt X3) N5)))) (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt Summary3) _let_1)) (= (tptp.size_s6755466524823107622T_VEBT TreeList3) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) _let_1)) (= A22 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N5) _let_1)) (not (exists ((X_1 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions Summary3) X_1)))) (forall ((X3 tptp.vEBT_VEBT)) (=> (tptp.pp (tptp.aa_set8260762808118238015T_bool (tptp.aa_VEB289770264548726718T_bool tptp.member_VEBT_VEBT X3) (tptp.set_VEBT_VEBT2 TreeList3))) (not (exists ((X_1 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions X3) X_1))))))))) (exists ((TreeList3 tptp.list_VEBT_VEBT) (N5 tptp.nat) (Summary3 tptp.vEBT_VEBT) (Mi3 tptp.nat) (Ma3 tptp.nat)) (let ((_let_1 (= Mi3 Ma3))) (let ((_let_2 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (and (= A1 (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Mi3) Ma3)) A22 TreeList3 Summary3)) (forall ((X3 tptp.vEBT_VEBT)) (=> (tptp.pp (tptp.aa_set8260762808118238015T_bool (tptp.aa_VEB289770264548726718T_bool tptp.member_VEBT_VEBT X3) (tptp.set_VEBT_VEBT2 TreeList3))) (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt X3) N5)))) (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt Summary3) N5)) (= (tptp.size_s6755466524823107622T_VEBT TreeList3) (tptp.aa_nat_nat _let_2 N5)) (= A22 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N5) N5)) (forall ((I4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I4) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N5))) (= (exists ((X_1 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions (tptp.nth_VEBT_VEBT TreeList3 I4)) X_1))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions Summary3) I4))))) (=> _let_1 (forall ((X3 tptp.vEBT_VEBT)) (=> (tptp.pp (tptp.aa_set8260762808118238015T_bool (tptp.aa_VEB289770264548726718T_bool tptp.member_VEBT_VEBT X3) (tptp.set_VEBT_VEBT2 TreeList3))) (not (exists ((X_1 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions X3) X_1))))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Mi3) Ma3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Ma3) (tptp.aa_nat_nat _let_2 A22))) (=> (not _let_1) (forall ((I4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I4) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N5))) (and (=> (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high Ma3) N5) I4) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions (tptp.nth_VEBT_VEBT TreeList3 I4)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low Ma3) N5)))) (forall ((X3 tptp.nat)) (=> (and (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high X3) N5) I4) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions (tptp.nth_VEBT_VEBT TreeList3 I4)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low X3) N5)))) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Mi3) X3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X3) Ma3))))))))))))) (exists ((TreeList3 tptp.list_VEBT_VEBT) (N5 tptp.nat) (Summary3 tptp.vEBT_VEBT) (Mi3 tptp.nat) (Ma3 tptp.nat)) (let ((_let_1 (= Mi3 Ma3))) (let ((_let_2 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_3 (tptp.aa_nat_nat tptp.suc N5))) (and (= A1 (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Mi3) Ma3)) A22 TreeList3 Summary3)) (forall ((X3 tptp.vEBT_VEBT)) (=> (tptp.pp (tptp.aa_set8260762808118238015T_bool (tptp.aa_VEB289770264548726718T_bool tptp.member_VEBT_VEBT X3) (tptp.set_VEBT_VEBT2 TreeList3))) (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt X3) N5)))) (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt Summary3) _let_3)) (= (tptp.size_s6755466524823107622T_VEBT TreeList3) (tptp.aa_nat_nat _let_2 _let_3)) (= A22 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N5) _let_3)) (forall ((I4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I4) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_nat_nat tptp.suc N5)))) (= (exists ((X_1 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions (tptp.nth_VEBT_VEBT TreeList3 I4)) X_1))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions Summary3) I4))))) (=> _let_1 (forall ((X3 tptp.vEBT_VEBT)) (=> (tptp.pp (tptp.aa_set8260762808118238015T_bool (tptp.aa_VEB289770264548726718T_bool tptp.member_VEBT_VEBT X3) (tptp.set_VEBT_VEBT2 TreeList3))) (not (exists ((X_1 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions X3) X_1))))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Mi3) Ma3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Ma3) (tptp.aa_nat_nat _let_2 A22))) (=> (not _let_1) (forall ((I4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I4) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_nat_nat tptp.suc N5)))) (and (=> (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high Ma3) N5) I4) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions (tptp.nth_VEBT_VEBT TreeList3 I4)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low Ma3) N5)))) (forall ((X3 tptp.nat)) (=> (and (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high X3) N5) I4) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions (tptp.nth_VEBT_VEBT TreeList3 I4)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low X3) N5)))) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Mi3) X3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X3) Ma3))))))))))))))))) (forall ((A1 tptp.vEBT_VEBT) (A22 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt A1) A22)) (=> (=> (exists ((A3 tptp.bool) (B3 tptp.bool)) (= A1 (tptp.vEBT_Leaf A3 B3))) (not (= A22 (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)))) (=> (forall ((TreeList2 tptp.list_VEBT_VEBT) (N2 tptp.nat) (Summary2 tptp.vEBT_VEBT) (M3 tptp.nat) (Deg2 tptp.nat)) (=> (= A1 (tptp.vEBT_Node tptp.none_P5556105721700978146at_nat Deg2 TreeList2 Summary2)) (=> (= A22 Deg2) (=> (forall ((X5 tptp.vEBT_VEBT)) (=> (tptp.pp (tptp.aa_set8260762808118238015T_bool (tptp.aa_VEB289770264548726718T_bool tptp.member_VEBT_VEBT X5) (tptp.set_VEBT_VEBT2 TreeList2))) (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt X5) N2)))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt Summary2) M3)) (=> (= (tptp.size_s6755466524823107622T_VEBT TreeList2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) M3)) (=> (= M3 N2) (=> (= Deg2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N2) M3)) (=> (not (exists ((X_13 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions Summary2) X_13)))) (not (forall ((X5 tptp.vEBT_VEBT)) (=> (tptp.pp (tptp.aa_set8260762808118238015T_bool (tptp.aa_VEB289770264548726718T_bool tptp.member_VEBT_VEBT X5) (tptp.set_VEBT_VEBT2 TreeList2))) (not (exists ((X_13 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions X5) X_13)))))))))))))))) (=> (forall ((TreeList2 tptp.list_VEBT_VEBT) (N2 tptp.nat) (Summary2 tptp.vEBT_VEBT) (M3 tptp.nat) (Deg2 tptp.nat)) (=> (= A1 (tptp.vEBT_Node tptp.none_P5556105721700978146at_nat Deg2 TreeList2 Summary2)) (=> (= A22 Deg2) (=> (forall ((X5 tptp.vEBT_VEBT)) (=> (tptp.pp (tptp.aa_set8260762808118238015T_bool (tptp.aa_VEB289770264548726718T_bool tptp.member_VEBT_VEBT X5) (tptp.set_VEBT_VEBT2 TreeList2))) (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt X5) N2)))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt Summary2) M3)) (=> (= (tptp.size_s6755466524823107622T_VEBT TreeList2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) M3)) (=> (= M3 (tptp.aa_nat_nat tptp.suc N2)) (=> (= Deg2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N2) M3)) (=> (not (exists ((X_13 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions Summary2) X_13)))) (not (forall ((X5 tptp.vEBT_VEBT)) (=> (tptp.pp (tptp.aa_set8260762808118238015T_bool (tptp.aa_VEB289770264548726718T_bool tptp.member_VEBT_VEBT X5) (tptp.set_VEBT_VEBT2 TreeList2))) (not (exists ((X_13 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions X5) X_13)))))))))))))))) (=> (forall ((TreeList2 tptp.list_VEBT_VEBT) (N2 tptp.nat) (Summary2 tptp.vEBT_VEBT) (M3 tptp.nat) (Deg2 tptp.nat) (Mi2 tptp.nat) (Ma2 tptp.nat)) (let ((_let_1 (= Mi2 Ma2))) (let ((_let_2 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (=> (= A1 (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Mi2) Ma2)) Deg2 TreeList2 Summary2)) (=> (= A22 Deg2) (=> (forall ((X5 tptp.vEBT_VEBT)) (=> (tptp.pp (tptp.aa_set8260762808118238015T_bool (tptp.aa_VEB289770264548726718T_bool tptp.member_VEBT_VEBT X5) (tptp.set_VEBT_VEBT2 TreeList2))) (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt X5) N2)))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt Summary2) M3)) (=> (= (tptp.size_s6755466524823107622T_VEBT TreeList2) (tptp.aa_nat_nat _let_2 M3)) (=> (= M3 N2) (=> (= Deg2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N2) M3)) (=> (forall ((I2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) M3))) (= (exists ((X_1 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions (tptp.nth_VEBT_VEBT TreeList2 I2)) X_1))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions Summary2) I2))))) (=> (=> _let_1 (forall ((X5 tptp.vEBT_VEBT)) (=> (tptp.pp (tptp.aa_set8260762808118238015T_bool (tptp.aa_VEB289770264548726718T_bool tptp.member_VEBT_VEBT X5) (tptp.set_VEBT_VEBT2 TreeList2))) (not (exists ((X_13 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions X5) X_13))))))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Mi2) Ma2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Ma2) (tptp.aa_nat_nat _let_2 Deg2))) (not (=> (not _let_1) (forall ((I2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) M3))) (and (=> (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high Ma2) N2) I2) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions (tptp.nth_VEBT_VEBT TreeList2 I2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low Ma2) N2)))) (forall ((X5 tptp.nat)) (=> (and (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high X5) N2) I2) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions (tptp.nth_VEBT_VEBT TreeList2 I2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low X5) N2)))) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Mi2) X5)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X5) Ma2)))))))))))))))))))))))) (not (forall ((TreeList2 tptp.list_VEBT_VEBT) (N2 tptp.nat) (Summary2 tptp.vEBT_VEBT) (M3 tptp.nat) (Deg2 tptp.nat) (Mi2 tptp.nat) (Ma2 tptp.nat)) (let ((_let_1 (= Mi2 Ma2))) (let ((_let_2 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (=> (= A1 (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Mi2) Ma2)) Deg2 TreeList2 Summary2)) (=> (= A22 Deg2) (=> (forall ((X5 tptp.vEBT_VEBT)) (=> (tptp.pp (tptp.aa_set8260762808118238015T_bool (tptp.aa_VEB289770264548726718T_bool tptp.member_VEBT_VEBT X5) (tptp.set_VEBT_VEBT2 TreeList2))) (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt X5) N2)))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt Summary2) M3)) (=> (= (tptp.size_s6755466524823107622T_VEBT TreeList2) (tptp.aa_nat_nat _let_2 M3)) (=> (= M3 (tptp.aa_nat_nat tptp.suc N2)) (=> (= Deg2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N2) M3)) (=> (forall ((I2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) M3))) (= (exists ((X_1 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions (tptp.nth_VEBT_VEBT TreeList2 I2)) X_1))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions Summary2) I2))))) (=> (=> _let_1 (forall ((X5 tptp.vEBT_VEBT)) (=> (tptp.pp (tptp.aa_set8260762808118238015T_bool (tptp.aa_VEB289770264548726718T_bool tptp.member_VEBT_VEBT X5) (tptp.set_VEBT_VEBT2 TreeList2))) (not (exists ((X_13 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions X5) X_13))))))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Mi2) Ma2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Ma2) (tptp.aa_nat_nat _let_2 Deg2))) (not (=> (not _let_1) (forall ((I2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) M3))) (and (=> (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high Ma2) N2) I2) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions (tptp.nth_VEBT_VEBT TreeList2 I2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low Ma2) N2)))) (forall ((X5 tptp.nat)) (=> (and (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high X5) N2) I2) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions (tptp.nth_VEBT_VEBT TreeList2 I2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low X5) N2)))) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Mi2) X5)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X5) Ma2))))))))))))))))))))))))))))))) (forall ((Uu tptp.nat) (Uv tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT) (X tptp.nat)) (not (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_vebt_member (tptp.vEBT_Node tptp.none_P5556105721700978146at_nat Uu Uv Uw)) X)))) (forall ((Uz tptp.product_prod_nat_nat) (Va tptp.nat) (Vb tptp.list_VEBT_VEBT) (Vc tptp.vEBT_VEBT)) (not (tptp.pp (tptp.aa_VEBT_VEBT_bool tptp.vEBT_VEBT_minNull (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat Uz) Va Vb Vc))))) (forall ((T tptp.vEBT_VEBT) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt T) N)) (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat (tptp.vEBT_VEBT_set_vebt T)) (tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N)) tptp.one_one_nat)))))) (forall ((A tptp.int)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.aa_int_int (tptp.bit_se7879613467334960850it_int tptp.zero_zero_nat) A) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int tptp.one_one_int) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int _let_1) (tptp.aa_int_int (tptp.divide_divide_int A) _let_1)))))) (forall ((A tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se7882103937844011126it_nat tptp.zero_zero_nat) A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat tptp.one_one_nat) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat _let_1) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) _let_1)))))) (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y tptp.option_nat)) (=> (= (tptp.vEBT_vebt_pred X Xa2) Y) (=> (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_pred_rel (tptp.produc738532404422230701BT_nat X Xa2)) (=> (forall ((Uu2 tptp.bool) (Uv2 tptp.bool)) (let ((_let_1 (tptp.vEBT_Leaf Uu2 Uv2))) (=> (= X _let_1) (=> (= Xa2 tptp.zero_zero_nat) (=> (= Y tptp.none_nat) (not (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_pred_rel (tptp.produc738532404422230701BT_nat _let_1 tptp.zero_zero_nat)))))))) (=> (forall ((A3 tptp.bool) (Uw2 tptp.bool)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat))) (let ((_let_2 (tptp.vEBT_Leaf A3 Uw2))) (let ((_let_3 (tptp.pp A3))) (=> (= X _let_2) (=> (= Xa2 _let_1) (=> (and (=> _let_3 (= Y (tptp.some_nat tptp.zero_zero_nat))) (=> (not _let_3) (= Y tptp.none_nat))) (not (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_pred_rel (tptp.produc738532404422230701BT_nat _let_2 _let_1)))))))))) (=> (forall ((A3 tptp.bool) (B3 tptp.bool)) (=> (= X (tptp.vEBT_Leaf A3 B3)) (forall ((Va2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat tptp.suc Va2)))) (let ((_let_2 (tptp.pp A3))) (let ((_let_3 (tptp.pp B3))) (=> (= Xa2 _let_1) (=> (and (=> _let_3 (= Y (tptp.some_nat tptp.one_one_nat))) (=> (not _let_3) (and (=> _let_2 (= Y (tptp.some_nat tptp.zero_zero_nat))) (=> (not _let_2) (= Y tptp.none_nat))))) (not (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_pred_rel (tptp.produc738532404422230701BT_nat (tptp.vEBT_Leaf A3 B3) _let_1))))))))))) (=> (forall ((Uy2 tptp.nat) (Uz2 tptp.list_VEBT_VEBT) (Va3 tptp.vEBT_VEBT)) (let ((_let_1 (tptp.vEBT_Node tptp.none_P5556105721700978146at_nat Uy2 Uz2 Va3))) (=> (= X _let_1) (=> (= Y tptp.none_nat) (not (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_pred_rel (tptp.produc738532404422230701BT_nat _let_1 Xa2))))))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vd2 tptp.list_VEBT_VEBT) (Ve tptp.vEBT_VEBT)) (let ((_let_1 (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat V2) tptp.zero_zero_nat Vd2 Ve))) (=> (= X _let_1) (=> (= Y tptp.none_nat) (not (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_pred_rel (tptp.produc738532404422230701BT_nat _let_1 Xa2))))))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vh tptp.list_VEBT_VEBT) (Vi tptp.vEBT_VEBT)) (let ((_let_1 (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat V2) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat) Vh Vi))) (=> (= X _let_1) (=> (= Y tptp.none_nat) (not (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_pred_rel (tptp.produc738532404422230701BT_nat _let_1 Xa2))))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat tptp.suc Va2)))) (let ((_let_2 (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Mi2) Ma2)) _let_1 TreeList2 Summary2))) (let ((_let_3 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_4 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat _let_1) _let_3))) (let ((_let_5 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high Xa2) _let_4))) (let ((_let_6 (tptp.vEBT_vebt_pred Summary2 _let_5))) (let ((_let_7 (tptp.aa_opt7711074727033721499on_nat tptp.vEBT_VEBT_mul (tptp.some_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat _let_3) _let_4))))) (let ((_let_8 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low Xa2) _let_4))) (let ((_let_9 (tptp.nth_VEBT_VEBT TreeList2 _let_5))) (let ((_let_10 (tptp.vEBT_vebt_mint _let_9))) (let ((_let_11 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Ma2) Xa2)))) (=> (= X _let_2) (=> (and (=> _let_11 (= Y (tptp.some_nat Ma2))) (=> (not _let_11) (= Y (tptp.if_option_nat (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_5) (tptp.size_s6755466524823107622T_VEBT TreeList2)) (tptp.if_option_nat (tptp.aa_bool_bool (tptp.fconj (tptp.aa_bool_bool tptp.fNot (tptp.aa_option_nat_bool (tptp.aa_opt7943525813896274546t_bool tptp.fequal_option_nat _let_10) tptp.none_nat))) (tptp.aa_option_nat_bool (tptp.aa_opt7943525813896274546t_bool tptp.vEBT_VEBT_greater (tptp.some_nat _let_8)) _let_10)) (tptp.aa_opt1882420858203594238on_nat (tptp.aa_opt7711074727033721499on_nat tptp.vEBT_VEBT_add (tptp.aa_opt1882420858203594238on_nat _let_7 (tptp.some_nat _let_5))) (tptp.vEBT_vebt_pred _let_9 _let_8)) (tptp.if_option_nat (tptp.aa_option_nat_bool (tptp.aa_opt7943525813896274546t_bool tptp.fequal_option_nat _let_6) tptp.none_nat) (tptp.if_option_nat (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Mi2) Xa2) (tptp.some_nat Mi2) tptp.none_nat) (tptp.aa_opt1882420858203594238on_nat (tptp.aa_opt7711074727033721499on_nat tptp.vEBT_VEBT_add (tptp.aa_opt1882420858203594238on_nat _let_7 _let_6)) (tptp.vEBT_vebt_maxt (tptp.nth_VEBT_VEBT TreeList2 (tptp.the_nat _let_6)))))) tptp.none_nat)))) (not (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_pred_rel (tptp.produc738532404422230701BT_nat _let_2 Xa2))))))))))))))))))))))))))) (forall ((A4 tptp.set_nat) (B4 tptp.set_nat)) (= (= (tptp.minus_minus_set_nat A4 B4) tptp.bot_bot_set_nat) (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat A4) B4)))) (forall ((A4 tptp.set_real) (B4 tptp.set_real)) (= (= (tptp.minus_minus_set_real A4 B4) tptp.bot_bot_set_real) (tptp.ord_less_eq_set_real A4 B4))) (forall ((A4 tptp.set_int) (B4 tptp.set_int)) (= (= (tptp.minus_minus_set_int A4 B4) tptp.bot_bot_set_int) (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int A4) B4)))) (forall ((A4 tptp.set_nat)) (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat tptp.bot_bot_set_nat) A4))) (forall ((A4 tptp.set_real)) (tptp.ord_less_eq_set_real tptp.bot_bot_set_real A4)) (forall ((A4 tptp.set_int)) (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int tptp.bot_bot_set_int) A4))) (forall ((A4 tptp.set_nat)) (= (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat A4) tptp.bot_bot_set_nat)) (= A4 tptp.bot_bot_set_nat))) (forall ((A4 tptp.set_real)) (= (tptp.ord_less_eq_set_real A4 tptp.bot_bot_set_real) (= A4 tptp.bot_bot_set_real))) (forall ((A4 tptp.set_int)) (= (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int A4) tptp.bot_bot_set_int)) (= A4 tptp.bot_bot_set_int))) (forall ((A tptp.real)) (= (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) A) tptp.zero_zero_real) (= A tptp.zero_zero_real))) (forall ((A tptp.rat)) (= (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))) (forall ((A tptp.int)) (= (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) A) tptp.zero_zero_int) (= A tptp.zero_zero_int))) (forall ((A tptp.int)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.aa_int_int (tptp.bit_se4203085406695923979it_int tptp.zero_zero_nat) A) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int _let_1) (tptp.aa_int_int (tptp.divide_divide_int A) _let_1))))) (forall ((A tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se4205575877204974255it_nat tptp.zero_zero_nat) A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat _let_1) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) _let_1))))) (forall ((N tptp.nat) (A tptp.code_integer)) (let ((_let_1 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.bit_se2793503036327961859nteger (tptp.aa_nat_nat tptp.suc N) A) (tptp.plus_p5714425477246183910nteger (tptp.modulo364778990260209775nteger A _let_1) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger _let_1) (tptp.bit_se2793503036327961859nteger N (tptp.divide6298287555418463151nteger A _let_1))))))) (forall ((N tptp.nat) (A tptp.int)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.aa_int_int (tptp.bit_se7879613467334960850it_int (tptp.aa_nat_nat tptp.suc N)) A) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.modulo_modulo_int A) _let_1)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int _let_1) (tptp.aa_int_int (tptp.bit_se7879613467334960850it_int N) (tptp.aa_int_int (tptp.divide_divide_int A) _let_1))))))) (forall ((N tptp.nat) (A tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se7882103937844011126it_nat (tptp.aa_nat_nat tptp.suc N)) A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A) _let_1)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat _let_1) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se7882103937844011126it_nat N) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) _let_1))))))) (forall ((N tptp.nat) (A tptp.code_integer)) (let ((_let_1 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.bit_se1345352211410354436nteger (tptp.aa_nat_nat tptp.suc N) A) (tptp.plus_p5714425477246183910nteger (tptp.modulo364778990260209775nteger A _let_1) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger _let_1) (tptp.bit_se1345352211410354436nteger N (tptp.divide6298287555418463151nteger A _let_1))))))) (forall ((N tptp.nat) (A tptp.int)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.aa_int_int (tptp.bit_se2159334234014336723it_int (tptp.aa_nat_nat tptp.suc N)) A) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.modulo_modulo_int A) _let_1)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int _let_1) (tptp.aa_int_int (tptp.bit_se2159334234014336723it_int N) (tptp.aa_int_int (tptp.divide_divide_int A) _let_1))))))) (forall ((N tptp.nat) (A tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se2161824704523386999it_nat (tptp.aa_nat_nat tptp.suc N)) A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A) _let_1)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat _let_1) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se2161824704523386999it_nat N) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) _let_1))))))) (forall ((A4 tptp.set_nat) (B4 tptp.set_nat)) (=> (forall ((X4 tptp.nat)) (let ((_let_1 (tptp.member_nat X4))) (=> (tptp.pp (tptp.aa_set_nat_bool _let_1 A4)) (tptp.pp (tptp.aa_set_nat_bool _let_1 B4))))) (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat A4) B4)))) (forall ((A4 tptp.set_real) (B4 tptp.set_real)) (=> (forall ((X4 tptp.real)) (=> (tptp.member_real X4 A4) (tptp.member_real X4 B4))) (tptp.ord_less_eq_set_real A4 B4))) (forall ((A4 tptp.set_complex) (B4 tptp.set_complex)) (=> (forall ((X4 tptp.complex)) (let ((_let_1 (tptp.member_complex X4))) (=> (tptp.pp (tptp.aa_set_complex_bool _let_1 A4)) (tptp.pp (tptp.aa_set_complex_bool _let_1 B4))))) (tptp.pp (tptp.aa_set_complex_bool (tptp.ord_le211207098394363844omplex A4) B4)))) (forall ((A4 tptp.set_int) (B4 tptp.set_int)) (=> (forall ((X4 tptp.int)) (let ((_let_1 (tptp.member_int X4))) (=> (tptp.pp (tptp.aa_set_int_bool _let_1 A4)) (tptp.pp (tptp.aa_set_int_bool _let_1 B4))))) (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int A4) B4)))) (forall ((A4 tptp.set_int) (B4 tptp.set_int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int A4) B4)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int B4) A4)) (= A4 B4)))) (forall ((A4 tptp.set_int) (B4 tptp.set_int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int A4) B4)) (=> (not (= A4 B4)) (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_set_int A4) B4))))) (forall ((K tptp.int) (L tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) K)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int K) L)) (= (tptp.aa_int_int (tptp.divide_divide_int K) L) tptp.zero_zero_int)))) (forall ((K tptp.int) (L tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int K) tptp.zero_zero_int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int L) K)) (= (tptp.aa_int_int (tptp.divide_divide_int K) L) tptp.zero_zero_int)))) (forall ((N tptp.extended_enat)) (= (tptp.pp (tptp.aa_Ext2772979874139974381t_bool (tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat) N)) (not (= N tptp.zero_z5237406670263579293d_enat)))) (forall ((N tptp.extended_enat)) (= (tptp.minus_3235023915231533773d_enat N tptp.zero_z5237406670263579293d_enat) N)) (forall ((N tptp.extended_enat)) (= (tptp.minus_3235023915231533773d_enat tptp.zero_z5237406670263579293d_enat N) tptp.zero_z5237406670263579293d_enat)) (forall ((X tptp.real)) (= (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real X) X)))) (= X tptp.zero_zero_real))) (forall ((V tptp.num) (W tptp.num)) (= (tptp.aa_int_int (tptp.modulo_modulo_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 V))) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 W))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_int_int (tptp.modulo_modulo_int (tptp.aa_num_int tptp.numeral_numeral_int V)) (tptp.aa_num_int tptp.numeral_numeral_int W))))) (forall ((K tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.divide_divide_int K) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))))) (tptp.pp (tptp.aa_int_bool _let_1 K))))) (forall ((K tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.divide_divide_int K) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one)))) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int K) tptp.zero_zero_int)))) (forall ((A4 tptp.set_nat) (B4 tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_set_nat A4) B4)) (exists ((B3 tptp.nat)) (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat B3) (tptp.minus_minus_set_nat B4 A4)))))) (forall ((A4 tptp.set_real) (B4 tptp.set_real)) (=> (tptp.ord_less_set_real A4 B4) (exists ((B3 tptp.real)) (tptp.member_real B3 (tptp.minus_minus_set_real B4 A4))))) (forall ((A4 tptp.set_int) (B4 tptp.set_int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_set_int A4) B4)) (exists ((B3 tptp.int)) (tptp.pp (tptp.aa_set_int_bool (tptp.member_int B3) (tptp.minus_minus_set_int B4 A4)))))) (forall ((A4 tptp.set_complex) (B4 tptp.set_complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.ord_less_set_complex A4) B4)) (exists ((B3 tptp.complex)) (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex B3) (tptp.minus_811609699411566653omplex B4 A4)))))) (forall ((A4 tptp.int) (B4 tptp.int) (N tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A4) B4)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) N)) (=> (= (tptp.aa_int_int (tptp.modulo_modulo_int A4) N) tptp.zero_zero_int) (=> (= (tptp.aa_int_int (tptp.modulo_modulo_int B4) N) tptp.zero_zero_int) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.divide_divide_int A4) N)) (tptp.aa_int_int (tptp.divide_divide_int B4) N)))))))) (forall ((A4 tptp.int) (B4 tptp.int) (N tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A4) B4)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) N)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.divide_divide_int A4) N)) (tptp.aa_int_int (tptp.if_int (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.fequal_int (tptp.aa_int_int (tptp.modulo_modulo_int B4) N)) tptp.zero_zero_int) tptp.one_one_int) tptp.zero_zero_int))) (tptp.aa_int_int (tptp.divide_divide_int B4) N)))))) (forall ((C tptp.int) (A tptp.int) (B2 tptp.int)) (let ((_let_1 (tptp.modulo_modulo_int A))) (let ((_let_2 (tptp.aa_int_fun_int_int tptp.times_times_int B2))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) C)) (= (tptp.aa_int_int _let_1 (tptp.aa_int_int _let_2 C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int _let_2 (tptp.aa_int_int (tptp.modulo_modulo_int (tptp.aa_int_int (tptp.divide_divide_int A) B2)) C))) (tptp.aa_int_int _let_1 B2))))))) (forall ((K tptp.int) (P tptp.fun_int_fun_int_bool) (N tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) K)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool P (tptp.aa_int_int (tptp.divide_divide_int N) K)) (tptp.aa_int_int (tptp.modulo_modulo_int N) K))) (forall ((I4 tptp.int) (J3 tptp.int)) (=> (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) J3)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int J3) K)) (= N (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int K) I4)) J3))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool P I4) J3))))))) (forall ((K tptp.int) (P tptp.fun_int_fun_int_bool) (N tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int K) tptp.zero_zero_int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool P (tptp.aa_int_int (tptp.divide_divide_int N) K)) (tptp.aa_int_int (tptp.modulo_modulo_int N) K))) (forall ((I4 tptp.int) (J3 tptp.int)) (=> (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int K) J3)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int J3) tptp.zero_zero_int)) (= N (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int K) I4)) J3))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool P I4) J3))))))) (forall ((A4 tptp.int) (N tptp.int)) (= A4 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.divide_divide_int A4) N)) N)) (tptp.aa_int_int (tptp.modulo_modulo_int A4) N)))) (forall ((A tptp.int) (B2 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) tptp.zero_zero_int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) B2)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.divide_divide_int A) B2)) tptp.zero_zero_int))))) (forall ((B2 tptp.int) (A tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B2) tptp.zero_zero_int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.divide_divide_int A) B2)) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) A))))) (forall ((B2 tptp.int) (A tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) B2)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.divide_divide_int A) B2)) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) tptp.zero_zero_int))))) (forall ((L tptp.int) (K tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) L)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int L) K)) (= (tptp.aa_int_int (tptp.divide_divide_int K) L) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.divide_divide_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int K) L)) L)) tptp.one_one_int))))) (forall ((A tptp.int) (B2 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) A)) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.divide_divide_int A) B2))) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B2) A)) (tptp.pp (tptp.aa_int_bool _let_1 B2))))))) (forall ((B2 tptp.int) (A tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) B2)) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.divide_divide_int A) B2))) (tptp.pp (tptp.aa_int_bool _let_1 A)))))) (forall ((B2 tptp.int) (A tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B2) tptp.zero_zero_int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.aa_int_int (tptp.divide_divide_int A) B2))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) tptp.zero_zero_int))))) (forall ((K tptp.int) (I tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int))) (=> (tptp.pp (tptp.aa_int_bool _let_1 K)) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.divide_divide_int I) K))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int K) I)))))) (forall ((A tptp.int) (B2 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) tptp.zero_zero_int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) B2)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.divide_divide_int A) B2)) tptp.zero_zero_int))))) (forall ((A tptp.int) (B2 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) A)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B2) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.divide_divide_int A) B2)) tptp.zero_zero_int))))) (forall ((X tptp.int) (K tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) X)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.one_one_int) K)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.divide_divide_int X) K)) X))))) (forall ((L tptp.int) (K tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int L) K)) (=> (tptp.pp (tptp.aa_int_bool _let_1 L)) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.divide_divide_int K) L))))))) (forall ((K tptp.int) (L tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.divide_divide_int K) L))) (or (= K tptp.zero_zero_int) (= L tptp.zero_zero_int) (and (tptp.pp (tptp.aa_int_bool _let_1 K)) (tptp.pp (tptp.aa_int_bool _let_1 L))) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int K) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int L) tptp.zero_zero_int))))))) (forall ((A tptp.int) (B tptp.int) (B2 tptp.int)) (let ((_let_1 (tptp.divide_divide_int A))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) tptp.zero_zero_int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) B)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B) B2)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int _let_1 B)) (tptp.aa_int_int _let_1 B2)))))))) (forall ((A tptp.int) (A2 tptp.int) (B2 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) A2)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B2) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.divide_divide_int A2) B2)) (tptp.aa_int_int (tptp.divide_divide_int A) B2)))))) (forall ((I tptp.int) (K tptp.int)) (= (= (tptp.aa_int_int (tptp.divide_divide_int I) K) tptp.zero_zero_int) (or (= K tptp.zero_zero_int) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) I)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int I) K))) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int I) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int K) I)))))) (forall ((A tptp.int) (B tptp.int) (B2 tptp.int)) (let ((_let_1 (tptp.divide_divide_int A))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) A)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) B)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B) B2)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int _let_1 B2)) (tptp.aa_int_int _let_1 B)))))))) (forall ((A tptp.int) (A2 tptp.int) (B2 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) A2)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) B2)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.divide_divide_int A) B2)) (tptp.aa_int_int (tptp.divide_divide_int A2) B2)))))) (forall ((C tptp.int) (A tptp.int) (B2 tptp.int)) (let ((_let_1 (tptp.divide_divide_int A))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) C)) (= (tptp.aa_int_int _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B2) C)) (tptp.aa_int_int (tptp.divide_divide_int (tptp.aa_int_int _let_1 B2)) C))))) (forall ((A tptp.int) (B2 tptp.int) (Q2 tptp.int) (R tptp.int)) (=> (= A (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B2) Q2)) R)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) R)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int R) B2)) (= (tptp.aa_int_int (tptp.divide_divide_int A) B2) Q2))))) (forall ((A tptp.int) (B2 tptp.int) (Q2 tptp.int) (R tptp.int)) (=> (= A (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B2) Q2)) R)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int R) tptp.zero_zero_int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B2) R)) (= (tptp.aa_int_int (tptp.divide_divide_int A) B2) Q2))))) (forall ((P tptp.fun_int_bool) (N tptp.int) (K tptp.int)) (= (tptp.pp (tptp.aa_int_bool P (tptp.aa_int_int (tptp.divide_divide_int N) K))) (and (=> (= K tptp.zero_zero_int) (tptp.pp (tptp.aa_int_bool P tptp.zero_zero_int))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) K)) (forall ((I4 tptp.int) (J3 tptp.int)) (=> (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) J3)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int J3) K)) (= N (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int K) I4)) J3))) (tptp.pp (tptp.aa_int_bool P I4))))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int K) tptp.zero_zero_int)) (forall ((I4 tptp.int) (J3 tptp.int)) (=> (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int K) J3)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int J3) tptp.zero_zero_int)) (= N (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int K) I4)) J3))) (tptp.pp (tptp.aa_int_bool P I4)))))))) (forall ((A tptp.int) (B2 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) tptp.zero_zero_int)) (= (tptp.aa_int_int (tptp.modulo_modulo_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int tptp.one_one_int) (tptp.aa_int_int _let_1 B2))) (tptp.aa_int_int _let_1 A)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_int_int _let_1 (tptp.aa_int_int (tptp.modulo_modulo_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int B2) tptp.one_one_int)) A))) tptp.one_one_int))))) (forall ((A tptp.int) (B2 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_2 (tptp.aa_int_fun_int_int tptp.plus_plus_int tptp.one_one_int))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) A)) (= (tptp.aa_int_int (tptp.modulo_modulo_int (tptp.aa_int_int _let_2 (tptp.aa_int_int _let_1 B2))) (tptp.aa_int_int _let_1 A)) (tptp.aa_int_int _let_2 (tptp.aa_int_int _let_1 (tptp.aa_int_int (tptp.modulo_modulo_int B2) A)))))))) (forall ((M tptp.extended_enat) (N tptp.extended_enat)) (let ((_let_1 (tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat))) (= (tptp.pp (tptp.aa_Ext2772979874139974381t_bool _let_1 (tptp.times_7803423173614009249d_enat M N))) (and (tptp.pp (tptp.aa_Ext2772979874139974381t_bool _let_1 M)) (tptp.pp (tptp.aa_Ext2772979874139974381t_bool _let_1 N)))))) (forall ((N tptp.extended_enat)) (not (tptp.pp (tptp.aa_Ext2772979874139974381t_bool (tptp.ord_le72135733267957522d_enat N) tptp.zero_z5237406670263579293d_enat)))) (forall ((M tptp.extended_enat) (N tptp.extended_enat)) (= (= (tptp.plus_p3455044024723400733d_enat M N) tptp.zero_z5237406670263579293d_enat) (and (= M tptp.zero_z5237406670263579293d_enat) (= N tptp.zero_z5237406670263579293d_enat)))) (forall ((N tptp.extended_enat)) (tptp.pp (tptp.aa_Ext2772979874139974381t_bool (tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) N))) (forall ((N tptp.extended_enat)) (= (tptp.pp (tptp.aa_Ext2772979874139974381t_bool (tptp.ord_le2932123472753598470d_enat N) tptp.zero_z5237406670263579293d_enat)) (= N tptp.zero_z5237406670263579293d_enat))) (forall ((N tptp.nat) (P tptp.fun_nat_bool)) (= (exists ((M6 tptp.nat)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M6) N)) (tptp.pp (tptp.aa_nat_bool P M6)))) (exists ((X3 tptp.nat)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) (tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat N))) (tptp.pp (tptp.aa_nat_bool P X3)))))) (forall ((N tptp.nat) (P tptp.fun_nat_bool)) (= (forall ((M6 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M6) N)) (tptp.pp (tptp.aa_nat_bool P M6)))) (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) (tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat N))) (tptp.pp (tptp.aa_nat_bool P X3)))))) (forall ((A4 tptp.set_nat)) (not (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_set_nat A4) tptp.bot_bot_set_nat)))) (forall ((A4 tptp.set_int)) (not (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_set_int A4) tptp.bot_bot_set_int)))) (forall ((A4 tptp.set_real)) (not (tptp.ord_less_set_real A4 tptp.bot_bot_set_real))) (forall ((A4 tptp.set_nat) (B4 tptp.set_nat) (X tptp.nat)) (let ((_let_1 (tptp.member_nat X))) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat A4) B4)) (=> (tptp.pp (tptp.aa_set_nat_bool _let_1 A4)) (tptp.pp (tptp.aa_set_nat_bool _let_1 B4)))))) (forall ((A4 tptp.set_real) (B4 tptp.set_real) (X tptp.real)) (=> (tptp.ord_less_eq_set_real A4 B4) (=> (tptp.member_real X A4) (tptp.member_real X B4)))) (forall ((A4 tptp.set_complex) (B4 tptp.set_complex) (X tptp.complex)) (let ((_let_1 (tptp.member_complex X))) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.ord_le211207098394363844omplex A4) B4)) (=> (tptp.pp (tptp.aa_set_complex_bool _let_1 A4)) (tptp.pp (tptp.aa_set_complex_bool _let_1 B4)))))) (forall ((A4 tptp.set_int) (B4 tptp.set_int) (X tptp.int)) (let ((_let_1 (tptp.member_int X))) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int A4) B4)) (=> (tptp.pp (tptp.aa_set_int_bool _let_1 A4)) (tptp.pp (tptp.aa_set_int_bool _let_1 B4)))))) (forall ((A4 tptp.set_nat) (B4 tptp.set_nat) (C tptp.nat)) (let ((_let_1 (tptp.member_nat C))) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat A4) B4)) (=> (tptp.pp (tptp.aa_set_nat_bool _let_1 A4)) (tptp.pp (tptp.aa_set_nat_bool _let_1 B4)))))) (forall ((A4 tptp.set_real) (B4 tptp.set_real) (C tptp.real)) (=> (tptp.ord_less_eq_set_real A4 B4) (=> (tptp.member_real C A4) (tptp.member_real C B4)))) (forall ((A4 tptp.set_complex) (B4 tptp.set_complex) (C tptp.complex)) (let ((_let_1 (tptp.member_complex C))) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.ord_le211207098394363844omplex A4) B4)) (=> (tptp.pp (tptp.aa_set_complex_bool _let_1 A4)) (tptp.pp (tptp.aa_set_complex_bool _let_1 B4)))))) (forall ((A4 tptp.set_int) (B4 tptp.set_int) (C tptp.int)) (let ((_let_1 (tptp.member_int C))) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int A4) B4)) (=> (tptp.pp (tptp.aa_set_int_bool _let_1 A4)) (tptp.pp (tptp.aa_set_int_bool _let_1 B4)))))) (forall ((A4 tptp.set_int) (B4 tptp.set_int)) (=> (= A4 B4) (not (=> (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int A4) B4)) (not (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int B4) A4))))))) (forall ((A4 tptp.set_nat) (B4 tptp.set_nat)) (= (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat A4) B4)) (forall ((X3 tptp.nat)) (let ((_let_1 (tptp.member_nat X3))) (=> (tptp.pp (tptp.aa_set_nat_bool _let_1 A4)) (tptp.pp (tptp.aa_set_nat_bool _let_1 B4))))))) (forall ((A4 tptp.set_real) (B4 tptp.set_real)) (= (tptp.ord_less_eq_set_real A4 B4) (forall ((X3 tptp.real)) (=> (tptp.member_real X3 A4) (tptp.member_real X3 B4))))) (forall ((A4 tptp.set_complex) (B4 tptp.set_complex)) (= (tptp.pp (tptp.aa_set_complex_bool (tptp.ord_le211207098394363844omplex A4) B4)) (forall ((X3 tptp.complex)) (let ((_let_1 (tptp.member_complex X3))) (=> (tptp.pp (tptp.aa_set_complex_bool _let_1 A4)) (tptp.pp (tptp.aa_set_complex_bool _let_1 B4))))))) (forall ((A4 tptp.set_int) (B4 tptp.set_int)) (= (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int A4) B4)) (forall ((X3 tptp.int)) (let ((_let_1 (tptp.member_int X3))) (=> (tptp.pp (tptp.aa_set_int_bool _let_1 A4)) (tptp.pp (tptp.aa_set_int_bool _let_1 B4))))))) (forall ((A4 tptp.set_int) (B4 tptp.set_int)) (=> (= A4 B4) (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int A4) B4)))) (forall ((A4 tptp.set_int) (B4 tptp.set_int)) (=> (= A4 B4) (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int B4) A4)))) (forall ((A4 tptp.set_nat) (B4 tptp.set_nat)) (= (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat A4) B4)) (forall ((T2 tptp.nat)) (let ((_let_1 (tptp.member_nat T2))) (=> (tptp.pp (tptp.aa_set_nat_bool _let_1 A4)) (tptp.pp (tptp.aa_set_nat_bool _let_1 B4))))))) (forall ((A4 tptp.set_real) (B4 tptp.set_real)) (= (tptp.ord_less_eq_set_real A4 B4) (forall ((T2 tptp.real)) (=> (tptp.member_real T2 A4) (tptp.member_real T2 B4))))) (forall ((A4 tptp.set_complex) (B4 tptp.set_complex)) (= (tptp.pp (tptp.aa_set_complex_bool (tptp.ord_le211207098394363844omplex A4) B4)) (forall ((T2 tptp.complex)) (let ((_let_1 (tptp.member_complex T2))) (=> (tptp.pp (tptp.aa_set_complex_bool _let_1 A4)) (tptp.pp (tptp.aa_set_complex_bool _let_1 B4))))))) (forall ((A4 tptp.set_int) (B4 tptp.set_int)) (= (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int A4) B4)) (forall ((T2 tptp.int)) (let ((_let_1 (tptp.member_int T2))) (=> (tptp.pp (tptp.aa_set_int_bool _let_1 A4)) (tptp.pp (tptp.aa_set_int_bool _let_1 B4))))))) (forall ((A4 tptp.set_int)) (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int A4) A4))) (forall ((P tptp.fun_complex_bool) (Q tptp.fun_complex_bool)) (=> (forall ((X4 tptp.complex)) (=> (tptp.pp (tptp.aa_complex_bool P X4)) (tptp.pp (tptp.aa_complex_bool Q X4)))) (tptp.pp (tptp.aa_set_complex_bool (tptp.ord_le211207098394363844omplex (tptp.collect_complex P)) (tptp.collect_complex Q))))) (forall ((P tptp.fun_real_bool) (Q tptp.fun_real_bool)) (=> (forall ((X4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool P X4)) (tptp.pp (tptp.aa_real_bool Q X4)))) (tptp.ord_less_eq_set_real (tptp.collect_real P) (tptp.collect_real Q)))) (forall ((P tptp.fun_list_nat_bool) (Q tptp.fun_list_nat_bool)) (=> (forall ((X4 tptp.list_nat)) (=> (tptp.pp (tptp.aa_list_nat_bool P X4)) (tptp.pp (tptp.aa_list_nat_bool Q X4)))) (tptp.ord_le6045566169113846134st_nat (tptp.collect_list_nat P) (tptp.collect_list_nat Q)))) (forall ((P tptp.fun_nat_bool) (Q tptp.fun_nat_bool)) (=> (forall ((X4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool P X4)) (tptp.pp (tptp.aa_nat_bool Q X4)))) (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat (tptp.collect_nat P)) (tptp.collect_nat Q))))) (forall ((P tptp.fun_int_bool) (Q tptp.fun_int_bool)) (=> (forall ((X4 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool P X4)) (tptp.pp (tptp.aa_int_bool Q X4)))) (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int (tptp.collect_int P)) (tptp.collect_int Q))))) (forall ((A4 tptp.set_int) (B4 tptp.set_int) (C4 tptp.set_int)) (let ((_let_1 (tptp.ord_less_eq_set_int A4))) (=> (tptp.pp (tptp.aa_set_int_bool _let_1 B4)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int B4) C4)) (tptp.pp (tptp.aa_set_int_bool _let_1 C4)))))) (forall ((A4 tptp.set_int) (B4 tptp.set_int)) (= (= A4 B4) (and (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int A4) B4)) (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int B4) A4))))) (forall ((P tptp.fun_complex_bool) (Q tptp.fun_complex_bool)) (= (tptp.pp (tptp.aa_set_complex_bool (tptp.ord_le211207098394363844omplex (tptp.collect_complex P)) (tptp.collect_complex Q))) (forall ((X3 tptp.complex)) (=> (tptp.pp (tptp.aa_complex_bool P X3)) (tptp.pp (tptp.aa_complex_bool Q X3)))))) (forall ((P tptp.fun_real_bool) (Q tptp.fun_real_bool)) (= (tptp.ord_less_eq_set_real (tptp.collect_real P) (tptp.collect_real Q)) (forall ((X3 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool P X3)) (tptp.pp (tptp.aa_real_bool Q X3)))))) (forall ((P tptp.fun_list_nat_bool) (Q tptp.fun_list_nat_bool)) (= (tptp.ord_le6045566169113846134st_nat (tptp.collect_list_nat P) (tptp.collect_list_nat Q)) (forall ((X3 tptp.list_nat)) (=> (tptp.pp (tptp.aa_list_nat_bool P X3)) (tptp.pp (tptp.aa_list_nat_bool Q X3)))))) (forall ((P tptp.fun_nat_bool) (Q tptp.fun_nat_bool)) (= (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat (tptp.collect_nat P)) (tptp.collect_nat Q))) (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool P X3)) (tptp.pp (tptp.aa_nat_bool Q X3)))))) (forall ((P tptp.fun_int_bool) (Q tptp.fun_int_bool)) (= (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int (tptp.collect_int P)) (tptp.collect_int Q))) (forall ((X3 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool P X3)) (tptp.pp (tptp.aa_int_bool Q X3)))))) (forall ((A4 tptp.set_int) (C4 tptp.set_int) (D4 tptp.set_int) (B4 tptp.set_int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int A4) C4)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int D4) B4)) (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int (tptp.minus_minus_set_int A4 B4)) (tptp.minus_minus_set_int C4 D4)))))) (forall ((A4 tptp.set_int) (B4 tptp.set_int)) (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int (tptp.minus_minus_set_int A4 B4)) A4))) (forall ((A4 tptp.set_int) (B4 tptp.set_int) (C4 tptp.set_int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int A4) B4)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int B4) C4)) (= (tptp.minus_minus_set_int B4 (tptp.minus_minus_set_int C4 A4)) A4)))) (forall ((A4 tptp.set_int) (B4 tptp.set_int)) (= (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int A4) B4)) (or (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_set_int A4) B4)) (= A4 B4)))) (forall ((A4 tptp.set_int) (B4 tptp.set_int) (C4 tptp.set_int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int A4) B4)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_set_int B4) C4)) (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_set_int A4) C4))))) (forall ((A4 tptp.set_int) (B4 tptp.set_int)) (= (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_set_int A4) B4)) (and (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int A4) B4)) (not (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int B4) A4)))))) (forall ((A4 tptp.set_int) (B4 tptp.set_int) (C4 tptp.set_int)) (let ((_let_1 (tptp.ord_less_set_int A4))) (=> (tptp.pp (tptp.aa_set_int_bool _let_1 B4)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int B4) C4)) (tptp.pp (tptp.aa_set_int_bool _let_1 C4)))))) (forall ((A4 tptp.set_int) (B4 tptp.set_int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_set_int A4) B4)) (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int A4) B4)))) (forall ((A4 tptp.set_int) (B4 tptp.set_int)) (= (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_set_int A4) B4)) (and (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int A4) B4)) (not (= A4 B4))))) (forall ((A4 tptp.set_int) (B4 tptp.set_int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_set_int A4) B4)) (not (=> (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int A4) B4)) (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int B4) A4)))))) (forall ((N tptp.nat)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) N)) tptp.zero_zero_int)))) (forall ((A tptp.real) (N tptp.nat)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) A)) (exists ((R3 tptp.real)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) R3)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real R3) (tptp.aa_nat_nat tptp.suc N)) A))))) (forall ((Y tptp.real) (X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) Y)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) tptp.one_one_real)) (exists ((N2 tptp.nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) N2)) Y)))))) (forall ((N tptp.nat) (A tptp.real)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) A)) (exists ((X4 tptp.real)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) X4)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X4) N) A) (forall ((Y5 tptp.real)) (=> (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) Y5)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Y5) N) A)) (= Y5 X4)))))))) (forall ((N tptp.nat) (A tptp.real)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) A)) (exists ((R3 tptp.real)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) R3)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real R3) N) A)))))) (forall ((A tptp.int) (B2 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) tptp.zero_zero_int)) (= (tptp.aa_int_int (tptp.divide_divide_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int tptp.one_one_int) (tptp.aa_int_int _let_1 B2))) (tptp.aa_int_int _let_1 A)) (tptp.aa_int_int (tptp.divide_divide_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int B2) tptp.one_one_int)) A))))) (forall ((A tptp.int) (B2 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) A)) (= (tptp.aa_int_int (tptp.divide_divide_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int tptp.one_one_int) (tptp.aa_int_int _let_1 B2))) (tptp.aa_int_int _let_1 A)) (tptp.aa_int_int (tptp.divide_divide_int B2) A))))) (forall ((A4 tptp.set_nat) (B4 tptp.set_nat)) (= (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat A4) B4)) (tptp.ord_le8840051076831633728t_bool (tptp.aTP_Lamm_ac A4) (tptp.aTP_Lamm_ac B4)))) (forall ((A4 tptp.set_real) (B4 tptp.set_real)) (= (tptp.ord_less_eq_set_real A4 B4) (tptp.ord_le5573776112191778788l_bool (tptp.aTP_Lamm_aa A4) (tptp.aTP_Lamm_aa B4)))) (forall ((A4 tptp.set_complex) (B4 tptp.set_complex)) (= (tptp.pp (tptp.aa_set_complex_bool (tptp.ord_le211207098394363844omplex A4) B4)) (tptp.ord_le4633831435867229666x_bool (tptp.aTP_Lamm_a A4) (tptp.aTP_Lamm_a B4)))) (forall ((A4 tptp.set_int) (B4 tptp.set_int)) (= (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int A4) B4)) (tptp.ord_le5715760110363009508t_bool (tptp.aTP_Lamm_ad A4) (tptp.aTP_Lamm_ad B4)))) (forall ((A4 tptp.set_complex) (P tptp.fun_complex_bool)) (tptp.pp (tptp.aa_set_complex_bool (tptp.ord_le211207098394363844omplex (tptp.collect_complex (tptp.aa_fun1096865461735438652x_bool (tptp.aTP_Lamm_az A4) P))) A4))) (forall ((A4 tptp.set_real) (P tptp.fun_real_bool)) (tptp.ord_less_eq_set_real (tptp.collect_real (tptp.aa_fun6476784834714468668l_bool (tptp.aTP_Lamm_ba A4) P)) A4)) (forall ((A4 tptp.set_list_nat) (P tptp.fun_list_nat_bool)) (tptp.ord_le6045566169113846134st_nat (tptp.collect_list_nat (tptp.aa_fun6009467934925565500t_bool (tptp.aTP_Lamm_bb A4) P)) A4)) (forall ((A4 tptp.set_nat) (P tptp.fun_nat_bool)) (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat (tptp.collect_nat (tptp.aa_fun3878383735219268284t_bool (tptp.aTP_Lamm_bc A4) P))) A4))) (forall ((A4 tptp.set_int) (P tptp.fun_int_bool)) (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int (tptp.collect_int (tptp.aa_fun5146555767781538748t_bool (tptp.aTP_Lamm_bd A4) P))) A4))) (forall ((M tptp.nat) (K tptp.int)) (let ((_let_1 (tptp.power_power_int K))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) M)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) K)) (= (tptp.aa_int_int (tptp.divide_divide_int (tptp.aa_nat_int _let_1 M)) K) (tptp.aa_nat_int _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)))))))) (forall ((N tptp.nat) (A tptp.code_integer)) (let ((_let_1 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.bit_se8260200283734997820nteger (tptp.aa_nat_nat tptp.suc N) A) (tptp.plus_p5714425477246183910nteger (tptp.modulo364778990260209775nteger A _let_1) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger _let_1) (tptp.bit_se8260200283734997820nteger N (tptp.divide6298287555418463151nteger A _let_1))))))) (forall ((N tptp.nat) (A tptp.int)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.aa_int_int (tptp.bit_se4203085406695923979it_int (tptp.aa_nat_nat tptp.suc N)) A) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.modulo_modulo_int A) _let_1)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int _let_1) (tptp.aa_int_int (tptp.bit_se4203085406695923979it_int N) (tptp.aa_int_int (tptp.divide_divide_int A) _let_1))))))) (forall ((N tptp.nat) (A tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se4205575877204974255it_nat (tptp.aa_nat_nat tptp.suc N)) A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A) _let_1)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat _let_1) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se4205575877204974255it_nat N) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) _let_1))))))) (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_vebt_member X) Xa2))) (=> (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel (tptp.produc738532404422230701BT_nat X Xa2)) (=> (forall ((A3 tptp.bool) (B3 tptp.bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (let ((_let_3 (tptp.vEBT_Leaf A3 B3))) (=> (= X _let_3) (=> (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel (tptp.produc738532404422230701BT_nat _let_3 Xa2)) (and (=> _let_2 (tptp.pp A3)) (=> (not _let_2) (and (=> _let_1 (tptp.pp B3)) _let_1))))))))) (=> (forall ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (let ((_let_1 (tptp.vEBT_Node tptp.none_P5556105721700978146at_nat Uu2 Uv2 Uw2))) (=> (= X _let_1) (not (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel (tptp.produc738532404422230701BT_nat _let_1 Xa2)))))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (let ((_let_1 (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat V2) tptp.zero_zero_nat Uy2 Uz2))) (=> (= X _let_1) (not (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel (tptp.produc738532404422230701BT_nat _let_1 Xa2)))))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (let ((_let_1 (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat V2) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat) Vb2 Vc2))) (=> (= X _let_1) (not (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel (tptp.produc738532404422230701BT_nat _let_1 Xa2)))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat tptp.suc Va2)))) (let ((_let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat _let_1) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_3 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high Xa2) _let_2))) (let ((_let_4 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_3) (tptp.size_s6755466524823107622T_VEBT TreeList2))))) (let ((_let_5 (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Ma2) Xa2))))) (let ((_let_6 (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Xa2) Mi2))))) (let ((_let_7 (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Mi2) Ma2)) _let_1 TreeList2 Summary2))) (=> (= X _let_7) (=> (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel (tptp.produc738532404422230701BT_nat _let_7 Xa2)) (=> (not (= Xa2 Mi2)) (=> (not (= Xa2 Ma2)) (and _let_6 (=> _let_6 (and _let_5 (=> _let_5 (and (=> _let_4 (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_vebt_member (tptp.nth_VEBT_VEBT TreeList2 _let_3)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low Xa2) _let_2)))) _let_4))))))))))))))))))))))))) (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y tptp.bool)) (=> (= (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_vebt_member X) Xa2)) (tptp.pp Y)) (=> (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel (tptp.produc738532404422230701BT_nat X Xa2)) (=> (forall ((A3 tptp.bool) (B3 tptp.bool)) (let ((_let_1 (tptp.vEBT_Leaf A3 B3))) (let ((_let_2 (= Xa2 tptp.one_one_nat))) (let ((_let_3 (= Xa2 tptp.zero_zero_nat))) (=> (= X _let_1) (=> (= (tptp.pp Y) (and (=> _let_3 (tptp.pp A3)) (=> (not _let_3) (and (=> _let_2 (tptp.pp B3)) _let_2)))) (not (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel (tptp.produc738532404422230701BT_nat _let_1 Xa2))))))))) (=> (forall ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (let ((_let_1 (tptp.vEBT_Node tptp.none_P5556105721700978146at_nat Uu2 Uv2 Uw2))) (=> (= X _let_1) (=> (not (tptp.pp Y)) (not (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel (tptp.produc738532404422230701BT_nat _let_1 Xa2))))))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (let ((_let_1 (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat V2) tptp.zero_zero_nat Uy2 Uz2))) (=> (= X _let_1) (=> (not (tptp.pp Y)) (not (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel (tptp.produc738532404422230701BT_nat _let_1 Xa2))))))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (let ((_let_1 (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat V2) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat) Vb2 Vc2))) (=> (= X _let_1) (=> (not (tptp.pp Y)) (not (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel (tptp.produc738532404422230701BT_nat _let_1 Xa2))))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat tptp.suc Va2)))) (let ((_let_2 (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Mi2) Ma2)) _let_1 TreeList2 Summary2))) (let ((_let_3 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat _let_1) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_4 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high Xa2) _let_3))) (let ((_let_5 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_4) (tptp.size_s6755466524823107622T_VEBT TreeList2))))) (let ((_let_6 (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Ma2) Xa2))))) (let ((_let_7 (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Xa2) Mi2))))) (=> (= X _let_2) (=> (= (tptp.pp Y) (=> (not (= Xa2 Mi2)) (=> (not (= Xa2 Ma2)) (and _let_7 (=> _let_7 (and _let_6 (=> _let_6 (and (=> _let_5 (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_vebt_member (tptp.nth_VEBT_VEBT TreeList2 _let_4)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low Xa2) _let_3)))) _let_5)))))))) (not (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel (tptp.produc738532404422230701BT_nat _let_2 Xa2))))))))))))))))))))) (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_V5719532721284313246member X) Xa2))) (=> (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel (tptp.produc738532404422230701BT_nat X Xa2)) (=> (forall ((A3 tptp.bool) (B3 tptp.bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (let ((_let_3 (tptp.vEBT_Leaf A3 B3))) (=> (= X _let_3) (=> (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel (tptp.produc738532404422230701BT_nat _let_3 Xa2)) (and (=> _let_2 (tptp.pp A3)) (=> (not _let_2) (and (=> _let_1 (tptp.pp B3)) _let_1))))))))) (=> (forall ((Uu2 tptp.option4927543243414619207at_nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (let ((_let_1 (tptp.vEBT_Node Uu2 tptp.zero_zero_nat Uv2 Uw2))) (=> (= X _let_1) (not (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel (tptp.produc738532404422230701BT_nat _let_1 Xa2)))))) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (S3 tptp.vEBT_VEBT)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc V2))) (let ((_let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat _let_1) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_3 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high Xa2) _let_2))) (let ((_let_4 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_3) (tptp.size_s6755466524823107622T_VEBT TreeList2))))) (let ((_let_5 (tptp.vEBT_Node Uy2 _let_1 TreeList2 S3))) (=> (= X _let_5) (=> (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel (tptp.produc738532404422230701BT_nat _let_5 Xa2)) (and (=> _let_4 (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_V5719532721284313246member (tptp.nth_VEBT_VEBT TreeList2 _let_3)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low Xa2) _let_2)))) _let_4))))))))))))))) (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_V5719532721284313246member X) Xa2)) (=> (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel (tptp.produc738532404422230701BT_nat X Xa2)) (=> (forall ((A3 tptp.bool) (B3 tptp.bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (let ((_let_3 (tptp.vEBT_Leaf A3 B3))) (=> (= X _let_3) (=> (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel (tptp.produc738532404422230701BT_nat _let_3 Xa2)) (not (and (=> _let_2 (tptp.pp A3)) (=> (not _let_2) (and (=> _let_1 (tptp.pp B3)) _let_1)))))))))) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (S3 tptp.vEBT_VEBT)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc V2))) (let ((_let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat _let_1) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_3 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high Xa2) _let_2))) (let ((_let_4 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_3) (tptp.size_s6755466524823107622T_VEBT TreeList2))))) (let ((_let_5 (tptp.vEBT_Node Uy2 _let_1 TreeList2 S3))) (=> (= X _let_5) (=> (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel (tptp.produc738532404422230701BT_nat _let_5 Xa2)) (not (and (=> _let_4 (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_V5719532721284313246member (tptp.nth_VEBT_VEBT TreeList2 _let_3)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low Xa2) _let_2)))) _let_4))))))))))))))) (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y tptp.bool)) (=> (= (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_V5719532721284313246member X) Xa2)) (tptp.pp Y)) (=> (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel (tptp.produc738532404422230701BT_nat X Xa2)) (=> (forall ((A3 tptp.bool) (B3 tptp.bool)) (let ((_let_1 (tptp.vEBT_Leaf A3 B3))) (let ((_let_2 (= Xa2 tptp.one_one_nat))) (let ((_let_3 (= Xa2 tptp.zero_zero_nat))) (=> (= X _let_1) (=> (= (tptp.pp Y) (and (=> _let_3 (tptp.pp A3)) (=> (not _let_3) (and (=> _let_2 (tptp.pp B3)) _let_2)))) (not (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel (tptp.produc738532404422230701BT_nat _let_1 Xa2))))))))) (=> (forall ((Uu2 tptp.option4927543243414619207at_nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (let ((_let_1 (tptp.vEBT_Node Uu2 tptp.zero_zero_nat Uv2 Uw2))) (=> (= X _let_1) (=> (not (tptp.pp Y)) (not (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel (tptp.produc738532404422230701BT_nat _let_1 Xa2))))))) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (S3 tptp.vEBT_VEBT)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc V2))) (let ((_let_2 (tptp.vEBT_Node Uy2 _let_1 TreeList2 S3))) (let ((_let_3 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat _let_1) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_4 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high Xa2) _let_3))) (let ((_let_5 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_4) (tptp.size_s6755466524823107622T_VEBT TreeList2))))) (=> (= X _let_2) (=> (= (tptp.pp Y) (and (=> _let_5 (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_V5719532721284313246member (tptp.nth_VEBT_VEBT TreeList2 _let_4)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low Xa2) _let_3)))) _let_5)) (not (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel (tptp.produc738532404422230701BT_nat _let_2 Xa2))))))))))))))))) (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_vebt_member X) Xa2)) (=> (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel (tptp.produc738532404422230701BT_nat X Xa2)) (=> (forall ((A3 tptp.bool) (B3 tptp.bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (let ((_let_3 (tptp.vEBT_Leaf A3 B3))) (=> (= X _let_3) (=> (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel (tptp.produc738532404422230701BT_nat _let_3 Xa2)) (not (and (=> _let_2 (tptp.pp A3)) (=> (not _let_2) (and (=> _let_1 (tptp.pp B3)) _let_1)))))))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat tptp.suc Va2)))) (let ((_let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat _let_1) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_3 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high Xa2) _let_2))) (let ((_let_4 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_3) (tptp.size_s6755466524823107622T_VEBT TreeList2))))) (let ((_let_5 (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Ma2) Xa2))))) (let ((_let_6 (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Xa2) Mi2))))) (let ((_let_7 (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Mi2) Ma2)) _let_1 TreeList2 Summary2))) (=> (= X _let_7) (=> (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel (tptp.produc738532404422230701BT_nat _let_7 Xa2)) (not (=> (not (= Xa2 Mi2)) (=> (not (= Xa2 Ma2)) (and _let_6 (=> _let_6 (and _let_5 (=> _let_5 (and (=> _let_4 (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_vebt_member (tptp.nth_VEBT_VEBT TreeList2 _let_3)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low Xa2) _let_2)))) _let_4))))))))))))))))))))))) (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_VEBT_membermima X) Xa2))) (=> (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel (tptp.produc738532404422230701BT_nat X Xa2)) (=> (forall ((Uu2 tptp.bool) (Uv2 tptp.bool)) (let ((_let_1 (tptp.vEBT_Leaf Uu2 Uv2))) (=> (= X _let_1) (not (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel (tptp.produc738532404422230701BT_nat _let_1 Xa2)))))) (=> (forall ((Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (let ((_let_1 (tptp.vEBT_Node tptp.none_P5556105721700978146at_nat tptp.zero_zero_nat Ux2 Uy2))) (=> (= X _let_1) (not (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel (tptp.produc738532404422230701BT_nat _let_1 Xa2)))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.list_VEBT_VEBT) (Vb2 tptp.vEBT_VEBT)) (let ((_let_1 (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Mi2) Ma2)) tptp.zero_zero_nat Va3 Vb2))) (=> (= X _let_1) (=> (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel (tptp.produc738532404422230701BT_nat _let_1 Xa2)) (or (= Xa2 Mi2) (= Xa2 Ma2)))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc V2))) (let ((_let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat _let_1) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_3 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high Xa2) _let_2))) (let ((_let_4 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_3) (tptp.size_s6755466524823107622T_VEBT TreeList2))))) (let ((_let_5 (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Mi2) Ma2)) _let_1 TreeList2 Vc2))) (=> (= X _let_5) (=> (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel (tptp.produc738532404422230701BT_nat _let_5 Xa2)) (or (= Xa2 Mi2) (= Xa2 Ma2) (and (=> _let_4 (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_VEBT_membermima (tptp.nth_VEBT_VEBT TreeList2 _let_3)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low Xa2) _let_2)))) _let_4)))))))))) (not (forall ((V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Vd2 tptp.vEBT_VEBT)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc V2))) (let ((_let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat _let_1) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_3 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high Xa2) _let_2))) (let ((_let_4 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_3) (tptp.size_s6755466524823107622T_VEBT TreeList2))))) (let ((_let_5 (tptp.vEBT_Node tptp.none_P5556105721700978146at_nat _let_1 TreeList2 Vd2))) (=> (= X _let_5) (=> (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel (tptp.produc738532404422230701BT_nat _let_5 Xa2)) (and (=> _let_4 (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_VEBT_membermima (tptp.nth_VEBT_VEBT TreeList2 _let_3)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low Xa2) _let_2)))) _let_4))))))))))))))))) (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y tptp.bool)) (=> (= (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_VEBT_membermima X) Xa2)) (tptp.pp Y)) (=> (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel (tptp.produc738532404422230701BT_nat X Xa2)) (=> (forall ((Uu2 tptp.bool) (Uv2 tptp.bool)) (let ((_let_1 (tptp.vEBT_Leaf Uu2 Uv2))) (=> (= X _let_1) (=> (not (tptp.pp Y)) (not (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel (tptp.produc738532404422230701BT_nat _let_1 Xa2))))))) (=> (forall ((Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (let ((_let_1 (tptp.vEBT_Node tptp.none_P5556105721700978146at_nat tptp.zero_zero_nat Ux2 Uy2))) (=> (= X _let_1) (=> (not (tptp.pp Y)) (not (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel (tptp.produc738532404422230701BT_nat _let_1 Xa2))))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.list_VEBT_VEBT) (Vb2 tptp.vEBT_VEBT)) (let ((_let_1 (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Mi2) Ma2)) tptp.zero_zero_nat Va3 Vb2))) (=> (= X _let_1) (=> (= (tptp.pp Y) (or (= Xa2 Mi2) (= Xa2 Ma2))) (not (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel (tptp.produc738532404422230701BT_nat _let_1 Xa2))))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc V2))) (let ((_let_2 (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Mi2) Ma2)) _let_1 TreeList2 Vc2))) (let ((_let_3 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat _let_1) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_4 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high Xa2) _let_3))) (let ((_let_5 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_4) (tptp.size_s6755466524823107622T_VEBT TreeList2))))) (=> (= X _let_2) (=> (= (tptp.pp Y) (or (= Xa2 Mi2) (= Xa2 Ma2) (and (=> _let_5 (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_VEBT_membermima (tptp.nth_VEBT_VEBT TreeList2 _let_4)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low Xa2) _let_3)))) _let_5))) (not (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel (tptp.produc738532404422230701BT_nat _let_2 Xa2))))))))))) (not (forall ((V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Vd2 tptp.vEBT_VEBT)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc V2))) (let ((_let_2 (tptp.vEBT_Node tptp.none_P5556105721700978146at_nat _let_1 TreeList2 Vd2))) (let ((_let_3 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat _let_1) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_4 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high Xa2) _let_3))) (let ((_let_5 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_4) (tptp.size_s6755466524823107622T_VEBT TreeList2))))) (=> (= X _let_2) (=> (= (tptp.pp Y) (and (=> _let_5 (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_VEBT_membermima (tptp.nth_VEBT_VEBT TreeList2 _let_4)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low Xa2) _let_3)))) _let_5)) (not (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel (tptp.produc738532404422230701BT_nat _let_2 Xa2))))))))))))))))))) (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.bit_se7879613467334960850it_int N) K))) (tptp.pp (tptp.aa_int_bool _let_1 K))))) (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.bit_se2159334234014336723it_int N) K))) (tptp.pp (tptp.aa_int_bool _let_1 K))))) (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.bit_se4203085406695923979it_int N) K))) (tptp.pp (tptp.aa_int_bool _let_1 K))))) (forall ((N tptp.nat) (K tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.bit_se7879613467334960850it_int N) K)) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int K) tptp.zero_zero_int)))) (forall ((N tptp.nat) (K tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.bit_se2159334234014336723it_int N) K)) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int K) tptp.zero_zero_int)))) (forall ((N tptp.nat) (K tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.bit_se4203085406695923979it_int N) K)) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int K) tptp.zero_zero_int)))) (forall ((W tptp.int) (Z tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int W) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int Z) tptp.one_one_int))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int W) Z)))) (forall ((W tptp.int) (Z tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int W) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int Z) tptp.one_one_int))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int W) Z)))) (forall ((K tptp.int) (L tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int K) tptp.zero_zero_int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int L) K)) (= (tptp.aa_int_int (tptp.modulo_modulo_int K) L) K)))) (forall ((K tptp.int) (L tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) K)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int K) L)) (= (tptp.aa_int_int (tptp.modulo_modulo_int K) L) K)))) (forall ((P tptp.fun_int_bool) (N tptp.int) (K tptp.int)) (= (tptp.pp (tptp.aa_int_bool P (tptp.aa_int_int (tptp.modulo_modulo_int N) K))) (and (=> (= K tptp.zero_zero_int) (tptp.pp (tptp.aa_int_bool P N))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) K)) (forall ((I4 tptp.int) (J3 tptp.int)) (=> (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) J3)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int J3) K)) (= N (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int K) I4)) J3))) (tptp.pp (tptp.aa_int_bool P J3))))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int K) tptp.zero_zero_int)) (forall ((I4 tptp.int) (J3 tptp.int)) (=> (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int K) J3)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int J3) tptp.zero_zero_int)) (= N (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int K) I4)) J3))) (tptp.pp (tptp.aa_int_bool P J3)))))))) (forall ((B tptp.int) (Q5 tptp.int) (R4 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B) Q5)) R4))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int R4) B)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) B)) (tptp.pp (tptp.aa_int_bool _let_1 Q5))))))) (forall ((A tptp.int) (B2 tptp.int) (Q2 tptp.int) (R tptp.int)) (=> (= A (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B2) Q2)) R)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int R) tptp.zero_zero_int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B2) R)) (= (tptp.aa_int_int (tptp.modulo_modulo_int A) B2) R))))) (forall ((A tptp.int) (B2 tptp.int) (Q2 tptp.int) (R tptp.int)) (=> (= A (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B2) Q2)) R)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) R)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int R) B2)) (= (tptp.aa_int_int (tptp.modulo_modulo_int A) B2) R))))) (forall ((B2 tptp.int) (Q2 tptp.int) (R tptp.int) (B tptp.int) (Q5 tptp.int) (R4 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B) Q5)) R4))) (=> (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B2) Q2)) R) _let_2) (=> (tptp.pp (tptp.aa_int_bool _let_1 _let_2)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int R4) B)) (=> (tptp.pp (tptp.aa_int_bool _let_1 R)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) B)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B) B2)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Q2) Q5))))))))))) (forall ((B2 tptp.int) (Q2 tptp.int) (R tptp.int) (B tptp.int) (Q5 tptp.int) (R4 tptp.int)) (let ((_let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B) Q5)) R4))) (=> (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B2) Q2)) R) _let_1) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int _let_1) tptp.zero_zero_int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int R) B2)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) R4)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) B)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B) B2)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Q5) Q2)))))))))) (forall ((B2 tptp.int) (Q5 tptp.int) (R4 tptp.int) (Q2 tptp.int) (R tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.times_times_int B2))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int _let_1 Q5)) R4)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int _let_1 Q2)) R))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) R4)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int R4) B2)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int R) B2)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Q5) Q2)))))))) (forall ((B2 tptp.int) (Q5 tptp.int) (R4 tptp.int) (Q2 tptp.int) (R tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_int B2))) (let ((_let_2 (tptp.aa_int_fun_int_int tptp.times_times_int B2))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int _let_2 Q5)) R4)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int _let_2 Q2)) R))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int R) tptp.zero_zero_int)) (=> (tptp.pp (tptp.aa_int_bool _let_1 R)) (=> (tptp.pp (tptp.aa_int_bool _let_1 R4)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Q2) Q5))))))))) (forall ((M tptp.int) (D tptp.int)) (= (= (tptp.aa_int_int (tptp.modulo_modulo_int M) D) tptp.zero_zero_int) (exists ((Q4 tptp.int)) (= M (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int D) Q4))))) (forall ((M tptp.int) (D tptp.int)) (=> (= (tptp.aa_int_int (tptp.modulo_modulo_int M) D) tptp.zero_zero_int) (exists ((Q3 tptp.int)) (= M (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int D) Q3))))) (forall ((M tptp.int) (N tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) M)) (= (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int M) N) tptp.one_one_int) (and (= M tptp.one_one_int) (= N tptp.one_one_int))))) (forall ((I tptp.int) (J tptp.int) (K tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.times_times_int K))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int I) J)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) K)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int _let_1 I)) (tptp.aa_int_int _let_1 J))))))) (forall ((B2 tptp.int) (A tptp.int)) (let ((_let_1 (tptp.aa_int_int (tptp.modulo_modulo_int A) B2))) (let ((_let_2 (tptp.aa_int_fun_int_bool tptp.ord_less_int B2))) (=> (tptp.pp (tptp.aa_int_bool _let_2 tptp.zero_zero_int)) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int _let_1) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool _let_2 _let_1))))))) (forall ((B2 tptp.int) (A tptp.int)) (let ((_let_1 (tptp.aa_int_int (tptp.modulo_modulo_int A) B2))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) B2)) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) _let_1)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int _let_1) B2)))))) (forall ((I tptp.int) (K tptp.int)) (= (= (tptp.aa_int_int (tptp.modulo_modulo_int I) K) I) (or (= K tptp.zero_zero_int) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) I)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int I) K))) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int I) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int K) I)))))) (forall ((Z tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.one_one_int) Z)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) Z)))) (forall ((M tptp.int) (K tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) M)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.modulo_modulo_int M) K)) M)))) (forall ((L tptp.int) (K tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int L) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.modulo_modulo_int K) L)) tptp.zero_zero_int)))) (forall ((L tptp.int) (K tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) L)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.aa_int_int (tptp.modulo_modulo_int K) L))))) (not (= tptp.zero_z5237406670263579293d_enat tptp.one_on7984719198319812577d_enat)) (forall ((K tptp.int) (L tptp.int)) (let ((_let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int K) L))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) K)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int _let_1) tptp.zero_zero_int)) (= (tptp.aa_int_int (tptp.modulo_modulo_int K) L) _let_1))))) (forall ((W tptp.int) (Z tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int W) Z)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int W) tptp.one_one_int)) Z)))) (forall ((I tptp.int) (K tptp.int) (P tptp.fun_int_bool)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int I) K)) (=> (tptp.pp (tptp.aa_int_bool P (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int K) tptp.one_one_int))) (=> (forall ((I3 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int I3) K)) (=> (tptp.pp (tptp.aa_int_bool P I3)) (tptp.pp (tptp.aa_int_bool P (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int I3) tptp.one_one_int)))))) (tptp.pp (tptp.aa_int_bool P I)))))) (forall ((L tptp.int) (K tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) L)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int L) K)) (= (tptp.aa_int_int (tptp.modulo_modulo_int K) L) (tptp.aa_int_int (tptp.modulo_modulo_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int K) L)) L))))) (forall ((Z tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int tptp.one_one_int) Z)) Z)) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Z) tptp.zero_zero_int)))) (forall ((W tptp.int) (Z tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_int W))) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int Z) tptp.one_one_int))) (or (tptp.pp (tptp.aa_int_bool _let_1 Z)) (= W Z))))) (forall ((Z tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) Z)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int tptp.one_one_int) Z))))) (forall ((I tptp.int) (K tptp.int) (P tptp.fun_int_bool)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int I) K)) (=> (tptp.pp (tptp.aa_int_bool P K)) (=> (forall ((I3 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int I3) K)) (=> (tptp.pp (tptp.aa_int_bool P I3)) (tptp.pp (tptp.aa_int_bool P (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int I3) tptp.one_one_int)))))) (tptp.pp (tptp.aa_int_bool P I)))))) (forall ((K tptp.int) (I tptp.int) (P tptp.fun_int_bool)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int K) I)) (=> (tptp.pp (tptp.aa_int_bool P (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int K) tptp.one_one_int))) (=> (forall ((I3 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int K) I3)) (=> (tptp.pp (tptp.aa_int_bool P I3)) (tptp.pp (tptp.aa_int_bool P (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int I3) tptp.one_one_int)))))) (tptp.pp (tptp.aa_int_bool P I)))))) (forall ((K tptp.int) (I tptp.int) (P tptp.fun_int_bool)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int K) I)) (=> (tptp.pp (tptp.aa_int_bool P K)) (=> (forall ((I3 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int K) I3)) (=> (tptp.pp (tptp.aa_int_bool P I3)) (tptp.pp (tptp.aa_int_bool P (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int I3) tptp.one_one_int)))))) (tptp.pp (tptp.aa_int_bool P I)))))) (forall ((W tptp.int) (Z tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int W) tptp.one_one_int)) Z)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int W) Z)))) (forall ((P tptp.fun_int_bool) (K tptp.int) (I tptp.int)) (=> (tptp.pp (tptp.aa_int_bool P K)) (=> (forall ((I3 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int K) I3)) (=> (tptp.pp (tptp.aa_int_bool P I3)) (tptp.pp (tptp.aa_int_bool P (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int I3) tptp.one_one_int)))))) (=> (forall ((I3 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int I3) K)) (=> (tptp.pp (tptp.aa_int_bool P I3)) (tptp.pp (tptp.aa_int_bool P (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int I3) tptp.one_one_int)))))) (tptp.pp (tptp.aa_int_bool P I)))))) (forall ((L tptp.int) (K tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) L)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.modulo_modulo_int K) L)) L)))) (forall ((L tptp.int) (K tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_int L))) (=> (tptp.pp (tptp.aa_int_bool _let_1 tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.modulo_modulo_int K) L)))))) _let_143 (forall ((N tptp.nat) (K tptp.int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.bit_se4203085406695923979it_int N) K)) K))) (forall ((K tptp.int) (N tptp.nat)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int K) (tptp.aa_int_int (tptp.bit_se7879613467334960850it_int N) K)))) (forall ((A tptp.int) (X tptp.int)) (or (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) X)) (= A X) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X) A)))) _let_142 (forall ((L tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int tptp.zero_zero_int) L) tptp.zero_zero_int)) (forall ((K tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int K) tptp.zero_zero_int) tptp.zero_zero_int)) (forall ((M tptp.extended_enat) (N tptp.extended_enat)) (= (= (tptp.times_7803423173614009249d_enat M N) tptp.zero_z5237406670263579293d_enat) (or (= M tptp.zero_z5237406670263579293d_enat) (= N tptp.zero_z5237406670263579293d_enat)))) (forall ((Z1 tptp.int) (Z22 tptp.int) (W tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int Z1) Z22)) W) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int Z1) W)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int Z22) W)))) (forall ((W tptp.int) (Z1 tptp.int) (Z22 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.times_times_int W))) (= (tptp.aa_int_int _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int Z1) Z22)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int _let_1 Z1)) (tptp.aa_int_int _let_1 Z22))))) (forall ((A4 tptp.set_nat) (B4 tptp.set_nat) (C tptp.nat)) (let ((_let_1 (tptp.member_nat C))) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_set_nat A4) B4)) (=> (tptp.pp (tptp.aa_set_nat_bool _let_1 A4)) (tptp.pp (tptp.aa_set_nat_bool _let_1 B4)))))) (forall ((A4 tptp.set_real) (B4 tptp.set_real) (C tptp.real)) (=> (tptp.ord_less_set_real A4 B4) (=> (tptp.member_real C A4) (tptp.member_real C B4)))) (forall ((A4 tptp.set_int) (B4 tptp.set_int) (C tptp.int)) (let ((_let_1 (tptp.member_int C))) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_set_int A4) B4)) (=> (tptp.pp (tptp.aa_set_int_bool _let_1 A4)) (tptp.pp (tptp.aa_set_int_bool _let_1 B4)))))) (forall ((A4 tptp.set_complex) (B4 tptp.set_complex) (C tptp.complex)) (let ((_let_1 (tptp.member_complex C))) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.ord_less_set_complex A4) B4)) (=> (tptp.pp (tptp.aa_set_complex_bool _let_1 A4)) (tptp.pp (tptp.aa_set_complex_bool _let_1 B4)))))) (forall ((A4 tptp.set_nat) (B4 tptp.set_nat)) (= (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_set_nat A4) B4)) (tptp.ord_le6841235830588351564t_bool (tptp.aTP_Lamm_ac A4) (tptp.aTP_Lamm_ac B4)))) (forall ((A4 tptp.set_real) (B4 tptp.set_real)) (= (tptp.ord_less_set_real A4 B4) (tptp.ord_le7519368973566061808l_bool (tptp.aTP_Lamm_aa A4) (tptp.aTP_Lamm_aa B4)))) (forall ((A4 tptp.set_int) (B4 tptp.set_int)) (= (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_set_int A4) B4)) (tptp.ord_le3716944864119727344t_bool (tptp.aTP_Lamm_ad A4) (tptp.aTP_Lamm_ad B4)))) (forall ((A4 tptp.set_complex) (B4 tptp.set_complex)) (= (tptp.pp (tptp.aa_set_complex_bool (tptp.ord_less_set_complex A4) B4)) (tptp.ord_le3776645642988763374x_bool (tptp.aTP_Lamm_a A4) (tptp.aTP_Lamm_a B4)))) (forall ((W tptp.int) (Z1 tptp.int) (Z22 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.times_times_int W))) (= (tptp.aa_int_int _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int Z1) Z22)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_int_int _let_1 Z1)) (tptp.aa_int_int _let_1 Z22))))) (forall ((Z1 tptp.int) (Z22 tptp.int) (W tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int Z1) Z22)) W) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int Z1) W)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int Z22) W)))) (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_VEBT_membermima X) Xa2)) (=> (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel (tptp.produc738532404422230701BT_nat X Xa2)) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.list_VEBT_VEBT) (Vb2 tptp.vEBT_VEBT)) (let ((_let_1 (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Mi2) Ma2)) tptp.zero_zero_nat Va3 Vb2))) (=> (= X _let_1) (=> (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel (tptp.produc738532404422230701BT_nat _let_1 Xa2)) (not (or (= Xa2 Mi2) (= Xa2 Ma2))))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc V2))) (let ((_let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat _let_1) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_3 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high Xa2) _let_2))) (let ((_let_4 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_3) (tptp.size_s6755466524823107622T_VEBT TreeList2))))) (let ((_let_5 (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Mi2) Ma2)) _let_1 TreeList2 Vc2))) (=> (= X _let_5) (=> (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel (tptp.produc738532404422230701BT_nat _let_5 Xa2)) (not (or (= Xa2 Mi2) (= Xa2 Ma2) (and (=> _let_4 (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_VEBT_membermima (tptp.nth_VEBT_VEBT TreeList2 _let_3)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low Xa2) _let_2)))) _let_4))))))))))) (not (forall ((V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Vd2 tptp.vEBT_VEBT)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc V2))) (let ((_let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat _let_1) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_3 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high Xa2) _let_2))) (let ((_let_4 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_3) (tptp.size_s6755466524823107622T_VEBT TreeList2))))) (let ((_let_5 (tptp.vEBT_Node tptp.none_P5556105721700978146at_nat _let_1 TreeList2 Vd2))) (=> (= X _let_5) (=> (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel (tptp.produc738532404422230701BT_nat _let_5 Xa2)) (not (and (=> _let_4 (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_VEBT_membermima (tptp.nth_VEBT_VEBT TreeList2 _let_3)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low Xa2) _let_2)))) _let_4)))))))))))))))) (forall ((B2 tptp.rat) (A tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B2) A)) (= (tptp.set_or633870826150836451st_rat A B2) tptp.bot_bot_set_rat))) (forall ((B2 tptp.num) (A tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num B2) A)) (= (tptp.set_or7049704709247886629st_num A B2) tptp.bot_bot_set_num))) (forall ((B2 tptp.nat) (A tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat B2) A)) (= (tptp.set_or1269000886237332187st_nat A B2) tptp.bot_bot_set_nat))) (forall ((B2 tptp.int) (A tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B2) A)) (= (tptp.aa_int_set_int (tptp.aa_int8639817059373041269et_int tptp.set_or1266510415728281911st_int A) B2) tptp.bot_bot_set_int))) (forall ((B2 tptp.real) (A tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B2) A)) (= (tptp.set_or1222579329274155063t_real A B2) tptp.bot_bot_set_real))) (forall ((A tptp.set_int) (B2 tptp.set_int) (C tptp.set_int) (D tptp.set_int)) (= (tptp.ord_le4403425263959731960et_int (tptp.set_or370866239135849197et_int A B2) (tptp.set_or370866239135849197et_int C D)) (or (not (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int A) B2))) (and (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int C) A)) (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int B2) D)))))) (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat) (D tptp.rat)) (= (tptp.ord_less_eq_set_rat (tptp.set_or633870826150836451st_rat A B2) (tptp.set_or633870826150836451st_rat C D)) (or (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B2))) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat C) A)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B2) D)))))) (forall ((A tptp.num) (B2 tptp.num) (C tptp.num) (D tptp.num)) (= (tptp.ord_less_eq_set_num (tptp.set_or7049704709247886629st_num A B2) (tptp.set_or7049704709247886629st_num C D)) (or (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A) B2))) (and (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num C) A)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num B2) D)))))) (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat) (D tptp.nat)) (= (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat (tptp.set_or1269000886237332187st_nat A B2)) (tptp.set_or1269000886237332187st_nat C D))) (or (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B2))) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat C) A)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B2) D)))))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int) (D tptp.int)) (= (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int (tptp.aa_int_set_int (tptp.aa_int8639817059373041269et_int tptp.set_or1266510415728281911st_int A) B2)) (tptp.aa_int_set_int (tptp.aa_int8639817059373041269et_int tptp.set_or1266510415728281911st_int C) D))) (or (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B2))) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int C) A)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B2) D)))))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real) (D tptp.real)) (= (tptp.ord_less_eq_set_real (tptp.set_or1222579329274155063t_real A B2) (tptp.set_or1222579329274155063t_real C D)) (or (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) B2))) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real C) A)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real B2) D)))))) (forall ((A tptp.set_int) (B2 tptp.set_int)) (= (= tptp.bot_bot_set_set_int (tptp.set_or370866239135849197et_int A B2)) (not (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int A) B2))))) (forall ((A tptp.rat) (B2 tptp.rat)) (= (= tptp.bot_bot_set_rat (tptp.set_or633870826150836451st_rat A B2)) (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B2))))) (forall ((A tptp.num) (B2 tptp.num)) (= (= tptp.bot_bot_set_num (tptp.set_or7049704709247886629st_num A B2)) (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A) B2))))) (forall ((A tptp.nat) (B2 tptp.nat)) (= (= tptp.bot_bot_set_nat (tptp.set_or1269000886237332187st_nat A B2)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B2))))) (forall ((A tptp.int) (B2 tptp.int)) (= (= tptp.bot_bot_set_int (tptp.aa_int_set_int (tptp.aa_int8639817059373041269et_int tptp.set_or1266510415728281911st_int A) B2)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B2))))) (forall ((A tptp.real) (B2 tptp.real)) (= (= tptp.bot_bot_set_real (tptp.set_or1222579329274155063t_real A B2)) (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) B2))))) (forall ((A tptp.set_int) (B2 tptp.set_int)) (= (= (tptp.set_or370866239135849197et_int A B2) tptp.bot_bot_set_set_int) (not (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int A) B2))))) (forall ((A tptp.rat) (B2 tptp.rat)) (= (= (tptp.set_or633870826150836451st_rat A B2) tptp.bot_bot_set_rat) (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B2))))) (forall ((A tptp.num) (B2 tptp.num)) (= (= (tptp.set_or7049704709247886629st_num A B2) tptp.bot_bot_set_num) (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A) B2))))) (forall ((A tptp.nat) (B2 tptp.nat)) (= (= (tptp.set_or1269000886237332187st_nat A B2) tptp.bot_bot_set_nat) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B2))))) (forall ((A tptp.int) (B2 tptp.int)) (= (= (tptp.aa_int_set_int (tptp.aa_int8639817059373041269et_int tptp.set_or1266510415728281911st_int A) B2) tptp.bot_bot_set_int) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B2))))) (forall ((A tptp.real) (B2 tptp.real)) (= (= (tptp.set_or1222579329274155063t_real A B2) tptp.bot_bot_set_real) (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) B2))))) (forall ((D tptp.int) (P tptp.fun_int_bool) (K tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) D)) (=> (forall ((X4 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool P X4)) (tptp.pp (tptp.aa_int_bool P (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int X4) D))))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) K)) (forall ((X5 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool P X5)) (tptp.pp (tptp.aa_int_bool P (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int X5) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int K) D)))))))))) (forall ((D tptp.int) (P tptp.fun_int_bool) (K tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) D)) (=> (forall ((X4 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool P X4)) (tptp.pp (tptp.aa_int_bool P (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int X4) D))))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) K)) (forall ((X5 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool P X5)) (tptp.pp (tptp.aa_int_bool P (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int X5) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int K) D)))))))))) (forall ((I tptp.set_int) (L tptp.set_int) (U tptp.set_int)) (= (tptp.member_set_int I (tptp.set_or370866239135849197et_int L U)) (and (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int L) I)) (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int I) U))))) (forall ((I tptp.rat) (L tptp.rat) (U tptp.rat)) (= (tptp.member_rat I (tptp.set_or633870826150836451st_rat L U)) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat L) I)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat I) U))))) (forall ((I tptp.num) (L tptp.num) (U tptp.num)) (= (tptp.member_num I (tptp.set_or7049704709247886629st_num L U)) (and (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num L) I)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num I) U))))) (forall ((I tptp.nat) (L tptp.nat) (U tptp.nat)) (= (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat I) (tptp.set_or1269000886237332187st_nat L U))) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat L) I)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I) U))))) (forall ((I tptp.int) (L tptp.int) (U tptp.int)) (= (tptp.pp (tptp.aa_set_int_bool (tptp.member_int I) (tptp.aa_int_set_int (tptp.aa_int8639817059373041269et_int tptp.set_or1266510415728281911st_int L) U))) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int L) I)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int I) U))))) (forall ((I tptp.real) (L tptp.real) (U tptp.real)) (= (tptp.member_real I (tptp.set_or1222579329274155063t_real L U)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real L) I)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real I) U))))) (forall ((L tptp.set_int) (H tptp.set_int) (L2 tptp.set_int) (H2 tptp.set_int)) (= (= (tptp.set_or370866239135849197et_int L H) (tptp.set_or370866239135849197et_int L2 H2)) (or (and (= L L2) (= H H2)) (and (not (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int L) H))) (not (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int L2) H2))))))) (forall ((L tptp.rat) (H tptp.rat) (L2 tptp.rat) (H2 tptp.rat)) (= (= (tptp.set_or633870826150836451st_rat L H) (tptp.set_or633870826150836451st_rat L2 H2)) (or (and (= L L2) (= H H2)) (and (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat L) H))) (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat L2) H2))))))) (forall ((L tptp.num) (H tptp.num) (L2 tptp.num) (H2 tptp.num)) (= (= (tptp.set_or7049704709247886629st_num L H) (tptp.set_or7049704709247886629st_num L2 H2)) (or (and (= L L2) (= H H2)) (and (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num L) H))) (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num L2) H2))))))) (forall ((L tptp.nat) (H tptp.nat) (L2 tptp.nat) (H2 tptp.nat)) (= (= (tptp.set_or1269000886237332187st_nat L H) (tptp.set_or1269000886237332187st_nat L2 H2)) (or (and (= L L2) (= H H2)) (and (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat L) H))) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat L2) H2))))))) (forall ((L tptp.int) (H tptp.int) (L2 tptp.int) (H2 tptp.int)) (= (= (tptp.aa_int_set_int (tptp.aa_int8639817059373041269et_int tptp.set_or1266510415728281911st_int L) H) (tptp.aa_int_set_int (tptp.aa_int8639817059373041269et_int tptp.set_or1266510415728281911st_int L2) H2)) (or (and (= L L2) (= H H2)) (and (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int L) H))) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int L2) H2))))))) (forall ((L tptp.real) (H tptp.real) (L2 tptp.real) (H2 tptp.real)) (= (= (tptp.set_or1222579329274155063t_real L H) (tptp.set_or1222579329274155063t_real L2 H2)) (or (and (= L L2) (= H H2)) (and (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real L) H))) (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real L2) H2))))))) (forall ((T tptp.real)) (exists ((Z4 tptp.real)) (forall ((X5 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X5) Z4)) (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real T) X5))))))) (forall ((T tptp.rat)) (exists ((Z4 tptp.rat)) (forall ((X5 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X5) Z4)) (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat T) X5))))))) (forall ((T tptp.num)) (exists ((Z4 tptp.num)) (forall ((X5 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X5) Z4)) (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num T) X5))))))) (forall ((T tptp.nat)) (exists ((Z4 tptp.nat)) (forall ((X5 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X5) Z4)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat T) X5))))))) (forall ((T tptp.int)) (exists ((Z4 tptp.int)) (forall ((X5 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X5) Z4)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int T) X5))))))) (forall ((T tptp.real)) (exists ((Z4 tptp.real)) (forall ((X5 tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X5))) (=> (tptp.pp (tptp.aa_real_bool _let_1 Z4)) (tptp.pp (tptp.aa_real_bool _let_1 T))))))) (forall ((T tptp.rat)) (exists ((Z4 tptp.rat)) (forall ((X5 tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X5))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 Z4)) (tptp.pp (tptp.aa_rat_bool _let_1 T))))))) (forall ((T tptp.num)) (exists ((Z4 tptp.num)) (forall ((X5 tptp.num)) (let ((_let_1 (tptp.aa_num_fun_num_bool tptp.ord_less_num X5))) (=> (tptp.pp (tptp.aa_num_bool _let_1 Z4)) (tptp.pp (tptp.aa_num_bool _let_1 T))))))) (forall ((T tptp.nat)) (exists ((Z4 tptp.nat)) (forall ((X5 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X5))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 Z4)) (tptp.pp (tptp.aa_nat_bool _let_1 T))))))) (forall ((T tptp.int)) (exists ((Z4 tptp.int)) (forall ((X5 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_int X5))) (=> (tptp.pp (tptp.aa_int_bool _let_1 Z4)) (tptp.pp (tptp.aa_int_bool _let_1 T))))))) (forall ((T tptp.real)) (exists ((Z4 tptp.real)) (forall ((X5 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X5) Z4)) (not (= X5 T)))))) (forall ((T tptp.rat)) (exists ((Z4 tptp.rat)) (forall ((X5 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X5) Z4)) (not (= X5 T)))))) (forall ((T tptp.num)) (exists ((Z4 tptp.num)) (forall ((X5 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X5) Z4)) (not (= X5 T)))))) (forall ((T tptp.nat)) (exists ((Z4 tptp.nat)) (forall ((X5 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X5) Z4)) (not (= X5 T)))))) (forall ((T tptp.int)) (exists ((Z4 tptp.int)) (forall ((X5 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X5) Z4)) (not (= X5 T)))))) (forall ((T tptp.real)) (exists ((Z4 tptp.real)) (forall ((X5 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X5) Z4)) (not (= X5 T)))))) (forall ((T tptp.rat)) (exists ((Z4 tptp.rat)) (forall ((X5 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X5) Z4)) (not (= X5 T)))))) (forall ((T tptp.num)) (exists ((Z4 tptp.num)) (forall ((X5 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X5) Z4)) (not (= X5 T)))))) (forall ((T tptp.nat)) (exists ((Z4 tptp.nat)) (forall ((X5 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X5) Z4)) (not (= X5 T)))))) (forall ((T tptp.int)) (exists ((Z4 tptp.int)) (forall ((X5 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X5) Z4)) (not (= X5 T)))))) (forall ((P tptp.fun_real_bool) (P3 tptp.fun_real_bool) (Q tptp.fun_real_bool) (Q6 tptp.fun_real_bool)) (=> (exists ((Z3 tptp.real)) (forall ((X4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X4) Z3)) (= (tptp.pp (tptp.aa_real_bool P X4)) (tptp.pp (tptp.aa_real_bool P3 X4)))))) (=> (exists ((Z3 tptp.real)) (forall ((X4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X4) Z3)) (= (tptp.pp (tptp.aa_real_bool Q X4)) (tptp.pp (tptp.aa_real_bool Q6 X4)))))) (exists ((Z4 tptp.real)) (forall ((X5 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X5) Z4)) (= (or (tptp.pp (tptp.aa_real_bool P X5)) (tptp.pp (tptp.aa_real_bool Q X5))) (or (tptp.pp (tptp.aa_real_bool P3 X5)) (tptp.pp (tptp.aa_real_bool Q6 X5)))))))))) (forall ((P tptp.fun_rat_bool) (P3 tptp.fun_rat_bool) (Q tptp.fun_rat_bool) (Q6 tptp.fun_rat_bool)) (=> (exists ((Z3 tptp.rat)) (forall ((X4 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X4) Z3)) (= (tptp.pp (tptp.aa_rat_bool P X4)) (tptp.pp (tptp.aa_rat_bool P3 X4)))))) (=> (exists ((Z3 tptp.rat)) (forall ((X4 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X4) Z3)) (= (tptp.pp (tptp.aa_rat_bool Q X4)) (tptp.pp (tptp.aa_rat_bool Q6 X4)))))) (exists ((Z4 tptp.rat)) (forall ((X5 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X5) Z4)) (= (or (tptp.pp (tptp.aa_rat_bool P X5)) (tptp.pp (tptp.aa_rat_bool Q X5))) (or (tptp.pp (tptp.aa_rat_bool P3 X5)) (tptp.pp (tptp.aa_rat_bool Q6 X5)))))))))) (forall ((P tptp.fun_num_bool) (P3 tptp.fun_num_bool) (Q tptp.fun_num_bool) (Q6 tptp.fun_num_bool)) (=> (exists ((Z3 tptp.num)) (forall ((X4 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X4) Z3)) (= (tptp.pp (tptp.aa_num_bool P X4)) (tptp.pp (tptp.aa_num_bool P3 X4)))))) (=> (exists ((Z3 tptp.num)) (forall ((X4 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X4) Z3)) (= (tptp.pp (tptp.aa_num_bool Q X4)) (tptp.pp (tptp.aa_num_bool Q6 X4)))))) (exists ((Z4 tptp.num)) (forall ((X5 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X5) Z4)) (= (or (tptp.pp (tptp.aa_num_bool P X5)) (tptp.pp (tptp.aa_num_bool Q X5))) (or (tptp.pp (tptp.aa_num_bool P3 X5)) (tptp.pp (tptp.aa_num_bool Q6 X5)))))))))) (forall ((P tptp.fun_nat_bool) (P3 tptp.fun_nat_bool) (Q tptp.fun_nat_bool) (Q6 tptp.fun_nat_bool)) (=> (exists ((Z3 tptp.nat)) (forall ((X4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X4) Z3)) (= (tptp.pp (tptp.aa_nat_bool P X4)) (tptp.pp (tptp.aa_nat_bool P3 X4)))))) (=> (exists ((Z3 tptp.nat)) (forall ((X4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X4) Z3)) (= (tptp.pp (tptp.aa_nat_bool Q X4)) (tptp.pp (tptp.aa_nat_bool Q6 X4)))))) (exists ((Z4 tptp.nat)) (forall ((X5 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X5) Z4)) (= (or (tptp.pp (tptp.aa_nat_bool P X5)) (tptp.pp (tptp.aa_nat_bool Q X5))) (or (tptp.pp (tptp.aa_nat_bool P3 X5)) (tptp.pp (tptp.aa_nat_bool Q6 X5)))))))))) (forall ((P tptp.fun_int_bool) (P3 tptp.fun_int_bool) (Q tptp.fun_int_bool) (Q6 tptp.fun_int_bool)) (=> (exists ((Z3 tptp.int)) (forall ((X4 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X4) Z3)) (= (tptp.pp (tptp.aa_int_bool P X4)) (tptp.pp (tptp.aa_int_bool P3 X4)))))) (=> (exists ((Z3 tptp.int)) (forall ((X4 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X4) Z3)) (= (tptp.pp (tptp.aa_int_bool Q X4)) (tptp.pp (tptp.aa_int_bool Q6 X4)))))) (exists ((Z4 tptp.int)) (forall ((X5 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X5) Z4)) (= (or (tptp.pp (tptp.aa_int_bool P X5)) (tptp.pp (tptp.aa_int_bool Q X5))) (or (tptp.pp (tptp.aa_int_bool P3 X5)) (tptp.pp (tptp.aa_int_bool Q6 X5)))))))))) (forall ((P tptp.fun_real_bool) (P3 tptp.fun_real_bool) (Q tptp.fun_real_bool) (Q6 tptp.fun_real_bool)) (=> (exists ((Z3 tptp.real)) (forall ((X4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X4) Z3)) (= (tptp.pp (tptp.aa_real_bool P X4)) (tptp.pp (tptp.aa_real_bool P3 X4)))))) (=> (exists ((Z3 tptp.real)) (forall ((X4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X4) Z3)) (= (tptp.pp (tptp.aa_real_bool Q X4)) (tptp.pp (tptp.aa_real_bool Q6 X4)))))) (exists ((Z4 tptp.real)) (forall ((X5 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X5) Z4)) (= (and (tptp.pp (tptp.aa_real_bool P X5)) (tptp.pp (tptp.aa_real_bool Q X5))) (and (tptp.pp (tptp.aa_real_bool P3 X5)) (tptp.pp (tptp.aa_real_bool Q6 X5)))))))))) (forall ((P tptp.fun_rat_bool) (P3 tptp.fun_rat_bool) (Q tptp.fun_rat_bool) (Q6 tptp.fun_rat_bool)) (=> (exists ((Z3 tptp.rat)) (forall ((X4 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X4) Z3)) (= (tptp.pp (tptp.aa_rat_bool P X4)) (tptp.pp (tptp.aa_rat_bool P3 X4)))))) (=> (exists ((Z3 tptp.rat)) (forall ((X4 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X4) Z3)) (= (tptp.pp (tptp.aa_rat_bool Q X4)) (tptp.pp (tptp.aa_rat_bool Q6 X4)))))) (exists ((Z4 tptp.rat)) (forall ((X5 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X5) Z4)) (= (and (tptp.pp (tptp.aa_rat_bool P X5)) (tptp.pp (tptp.aa_rat_bool Q X5))) (and (tptp.pp (tptp.aa_rat_bool P3 X5)) (tptp.pp (tptp.aa_rat_bool Q6 X5)))))))))) (forall ((P tptp.fun_num_bool) (P3 tptp.fun_num_bool) (Q tptp.fun_num_bool) (Q6 tptp.fun_num_bool)) (=> (exists ((Z3 tptp.num)) (forall ((X4 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X4) Z3)) (= (tptp.pp (tptp.aa_num_bool P X4)) (tptp.pp (tptp.aa_num_bool P3 X4)))))) (=> (exists ((Z3 tptp.num)) (forall ((X4 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X4) Z3)) (= (tptp.pp (tptp.aa_num_bool Q X4)) (tptp.pp (tptp.aa_num_bool Q6 X4)))))) (exists ((Z4 tptp.num)) (forall ((X5 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X5) Z4)) (= (and (tptp.pp (tptp.aa_num_bool P X5)) (tptp.pp (tptp.aa_num_bool Q X5))) (and (tptp.pp (tptp.aa_num_bool P3 X5)) (tptp.pp (tptp.aa_num_bool Q6 X5)))))))))) (forall ((P tptp.fun_nat_bool) (P3 tptp.fun_nat_bool) (Q tptp.fun_nat_bool) (Q6 tptp.fun_nat_bool)) (=> (exists ((Z3 tptp.nat)) (forall ((X4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X4) Z3)) (= (tptp.pp (tptp.aa_nat_bool P X4)) (tptp.pp (tptp.aa_nat_bool P3 X4)))))) (=> (exists ((Z3 tptp.nat)) (forall ((X4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X4) Z3)) (= (tptp.pp (tptp.aa_nat_bool Q X4)) (tptp.pp (tptp.aa_nat_bool Q6 X4)))))) (exists ((Z4 tptp.nat)) (forall ((X5 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X5) Z4)) (= (and (tptp.pp (tptp.aa_nat_bool P X5)) (tptp.pp (tptp.aa_nat_bool Q X5))) (and (tptp.pp (tptp.aa_nat_bool P3 X5)) (tptp.pp (tptp.aa_nat_bool Q6 X5)))))))))) (forall ((P tptp.fun_int_bool) (P3 tptp.fun_int_bool) (Q tptp.fun_int_bool) (Q6 tptp.fun_int_bool)) (=> (exists ((Z3 tptp.int)) (forall ((X4 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X4) Z3)) (= (tptp.pp (tptp.aa_int_bool P X4)) (tptp.pp (tptp.aa_int_bool P3 X4)))))) (=> (exists ((Z3 tptp.int)) (forall ((X4 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X4) Z3)) (= (tptp.pp (tptp.aa_int_bool Q X4)) (tptp.pp (tptp.aa_int_bool Q6 X4)))))) (exists ((Z4 tptp.int)) (forall ((X5 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X5) Z4)) (= (and (tptp.pp (tptp.aa_int_bool P X5)) (tptp.pp (tptp.aa_int_bool Q X5))) (and (tptp.pp (tptp.aa_int_bool P3 X5)) (tptp.pp (tptp.aa_int_bool Q6 X5)))))))))) (forall ((T tptp.real)) (exists ((Z4 tptp.real)) (forall ((X5 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Z4) X5)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real T) X5)))))) (forall ((T tptp.rat)) (exists ((Z4 tptp.rat)) (forall ((X5 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Z4) X5)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat T) X5)))))) (forall ((T tptp.num)) (exists ((Z4 tptp.num)) (forall ((X5 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num Z4) X5)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num T) X5)))))) (forall ((T tptp.nat)) (exists ((Z4 tptp.nat)) (forall ((X5 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Z4) X5)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat T) X5)))))) (forall ((T tptp.int)) (exists ((Z4 tptp.int)) (forall ((X5 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Z4) X5)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int T) X5)))))) (forall ((T tptp.real)) (exists ((Z4 tptp.real)) (forall ((X5 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Z4) X5)) (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X5) T))))))) (forall ((T tptp.rat)) (exists ((Z4 tptp.rat)) (forall ((X5 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Z4) X5)) (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X5) T))))))) (forall ((T tptp.num)) (exists ((Z4 tptp.num)) (forall ((X5 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num Z4) X5)) (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X5) T))))))) (forall ((T tptp.nat)) (exists ((Z4 tptp.nat)) (forall ((X5 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Z4) X5)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X5) T))))))) (forall ((T tptp.int)) (exists ((Z4 tptp.int)) (forall ((X5 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Z4) X5)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X5) T))))))) (forall ((T tptp.real)) (exists ((Z4 tptp.real)) (forall ((X5 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Z4) X5)) (not (= X5 T)))))) (forall ((T tptp.rat)) (exists ((Z4 tptp.rat)) (forall ((X5 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Z4) X5)) (not (= X5 T)))))) (forall ((T tptp.num)) (exists ((Z4 tptp.num)) (forall ((X5 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num Z4) X5)) (not (= X5 T)))))) (forall ((T tptp.nat)) (exists ((Z4 tptp.nat)) (forall ((X5 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Z4) X5)) (not (= X5 T)))))) (forall ((T tptp.int)) (exists ((Z4 tptp.int)) (forall ((X5 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Z4) X5)) (not (= X5 T)))))) (forall ((T tptp.real)) (exists ((Z4 tptp.real)) (forall ((X5 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Z4) X5)) (not (= X5 T)))))) (forall ((T tptp.rat)) (exists ((Z4 tptp.rat)) (forall ((X5 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Z4) X5)) (not (= X5 T)))))) (forall ((T tptp.num)) (exists ((Z4 tptp.num)) (forall ((X5 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num Z4) X5)) (not (= X5 T)))))) (forall ((T tptp.nat)) (exists ((Z4 tptp.nat)) (forall ((X5 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Z4) X5)) (not (= X5 T)))))) (forall ((T tptp.int)) (exists ((Z4 tptp.int)) (forall ((X5 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Z4) X5)) (not (= X5 T)))))) (forall ((P tptp.fun_real_bool) (P3 tptp.fun_real_bool) (Q tptp.fun_real_bool) (Q6 tptp.fun_real_bool)) (=> (exists ((Z3 tptp.real)) (forall ((X4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Z3) X4)) (= (tptp.pp (tptp.aa_real_bool P X4)) (tptp.pp (tptp.aa_real_bool P3 X4)))))) (=> (exists ((Z3 tptp.real)) (forall ((X4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Z3) X4)) (= (tptp.pp (tptp.aa_real_bool Q X4)) (tptp.pp (tptp.aa_real_bool Q6 X4)))))) (exists ((Z4 tptp.real)) (forall ((X5 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Z4) X5)) (= (or (tptp.pp (tptp.aa_real_bool P X5)) (tptp.pp (tptp.aa_real_bool Q X5))) (or (tptp.pp (tptp.aa_real_bool P3 X5)) (tptp.pp (tptp.aa_real_bool Q6 X5)))))))))) (forall ((P tptp.fun_rat_bool) (P3 tptp.fun_rat_bool) (Q tptp.fun_rat_bool) (Q6 tptp.fun_rat_bool)) (=> (exists ((Z3 tptp.rat)) (forall ((X4 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Z3) X4)) (= (tptp.pp (tptp.aa_rat_bool P X4)) (tptp.pp (tptp.aa_rat_bool P3 X4)))))) (=> (exists ((Z3 tptp.rat)) (forall ((X4 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Z3) X4)) (= (tptp.pp (tptp.aa_rat_bool Q X4)) (tptp.pp (tptp.aa_rat_bool Q6 X4)))))) (exists ((Z4 tptp.rat)) (forall ((X5 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Z4) X5)) (= (or (tptp.pp (tptp.aa_rat_bool P X5)) (tptp.pp (tptp.aa_rat_bool Q X5))) (or (tptp.pp (tptp.aa_rat_bool P3 X5)) (tptp.pp (tptp.aa_rat_bool Q6 X5)))))))))) (forall ((P tptp.fun_num_bool) (P3 tptp.fun_num_bool) (Q tptp.fun_num_bool) (Q6 tptp.fun_num_bool)) (=> (exists ((Z3 tptp.num)) (forall ((X4 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num Z3) X4)) (= (tptp.pp (tptp.aa_num_bool P X4)) (tptp.pp (tptp.aa_num_bool P3 X4)))))) (=> (exists ((Z3 tptp.num)) (forall ((X4 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num Z3) X4)) (= (tptp.pp (tptp.aa_num_bool Q X4)) (tptp.pp (tptp.aa_num_bool Q6 X4)))))) (exists ((Z4 tptp.num)) (forall ((X5 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num Z4) X5)) (= (or (tptp.pp (tptp.aa_num_bool P X5)) (tptp.pp (tptp.aa_num_bool Q X5))) (or (tptp.pp (tptp.aa_num_bool P3 X5)) (tptp.pp (tptp.aa_num_bool Q6 X5)))))))))) (forall ((P tptp.fun_nat_bool) (P3 tptp.fun_nat_bool) (Q tptp.fun_nat_bool) (Q6 tptp.fun_nat_bool)) (=> (exists ((Z3 tptp.nat)) (forall ((X4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Z3) X4)) (= (tptp.pp (tptp.aa_nat_bool P X4)) (tptp.pp (tptp.aa_nat_bool P3 X4)))))) (=> (exists ((Z3 tptp.nat)) (forall ((X4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Z3) X4)) (= (tptp.pp (tptp.aa_nat_bool Q X4)) (tptp.pp (tptp.aa_nat_bool Q6 X4)))))) (exists ((Z4 tptp.nat)) (forall ((X5 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Z4) X5)) (= (or (tptp.pp (tptp.aa_nat_bool P X5)) (tptp.pp (tptp.aa_nat_bool Q X5))) (or (tptp.pp (tptp.aa_nat_bool P3 X5)) (tptp.pp (tptp.aa_nat_bool Q6 X5)))))))))) (forall ((P tptp.fun_int_bool) (P3 tptp.fun_int_bool) (Q tptp.fun_int_bool) (Q6 tptp.fun_int_bool)) (=> (exists ((Z3 tptp.int)) (forall ((X4 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Z3) X4)) (= (tptp.pp (tptp.aa_int_bool P X4)) (tptp.pp (tptp.aa_int_bool P3 X4)))))) (=> (exists ((Z3 tptp.int)) (forall ((X4 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Z3) X4)) (= (tptp.pp (tptp.aa_int_bool Q X4)) (tptp.pp (tptp.aa_int_bool Q6 X4)))))) (exists ((Z4 tptp.int)) (forall ((X5 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Z4) X5)) (= (or (tptp.pp (tptp.aa_int_bool P X5)) (tptp.pp (tptp.aa_int_bool Q X5))) (or (tptp.pp (tptp.aa_int_bool P3 X5)) (tptp.pp (tptp.aa_int_bool Q6 X5)))))))))) (forall ((P tptp.fun_real_bool) (P3 tptp.fun_real_bool) (Q tptp.fun_real_bool) (Q6 tptp.fun_real_bool)) (=> (exists ((Z3 tptp.real)) (forall ((X4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Z3) X4)) (= (tptp.pp (tptp.aa_real_bool P X4)) (tptp.pp (tptp.aa_real_bool P3 X4)))))) (=> (exists ((Z3 tptp.real)) (forall ((X4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Z3) X4)) (= (tptp.pp (tptp.aa_real_bool Q X4)) (tptp.pp (tptp.aa_real_bool Q6 X4)))))) (exists ((Z4 tptp.real)) (forall ((X5 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Z4) X5)) (= (and (tptp.pp (tptp.aa_real_bool P X5)) (tptp.pp (tptp.aa_real_bool Q X5))) (and (tptp.pp (tptp.aa_real_bool P3 X5)) (tptp.pp (tptp.aa_real_bool Q6 X5)))))))))) (forall ((P tptp.fun_rat_bool) (P3 tptp.fun_rat_bool) (Q tptp.fun_rat_bool) (Q6 tptp.fun_rat_bool)) (=> (exists ((Z3 tptp.rat)) (forall ((X4 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Z3) X4)) (= (tptp.pp (tptp.aa_rat_bool P X4)) (tptp.pp (tptp.aa_rat_bool P3 X4)))))) (=> (exists ((Z3 tptp.rat)) (forall ((X4 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Z3) X4)) (= (tptp.pp (tptp.aa_rat_bool Q X4)) (tptp.pp (tptp.aa_rat_bool Q6 X4)))))) (exists ((Z4 tptp.rat)) (forall ((X5 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Z4) X5)) (= (and (tptp.pp (tptp.aa_rat_bool P X5)) (tptp.pp (tptp.aa_rat_bool Q X5))) (and (tptp.pp (tptp.aa_rat_bool P3 X5)) (tptp.pp (tptp.aa_rat_bool Q6 X5)))))))))) (forall ((P tptp.fun_num_bool) (P3 tptp.fun_num_bool) (Q tptp.fun_num_bool) (Q6 tptp.fun_num_bool)) (=> (exists ((Z3 tptp.num)) (forall ((X4 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num Z3) X4)) (= (tptp.pp (tptp.aa_num_bool P X4)) (tptp.pp (tptp.aa_num_bool P3 X4)))))) (=> (exists ((Z3 tptp.num)) (forall ((X4 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num Z3) X4)) (= (tptp.pp (tptp.aa_num_bool Q X4)) (tptp.pp (tptp.aa_num_bool Q6 X4)))))) (exists ((Z4 tptp.num)) (forall ((X5 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num Z4) X5)) (= (and (tptp.pp (tptp.aa_num_bool P X5)) (tptp.pp (tptp.aa_num_bool Q X5))) (and (tptp.pp (tptp.aa_num_bool P3 X5)) (tptp.pp (tptp.aa_num_bool Q6 X5)))))))))) (forall ((P tptp.fun_nat_bool) (P3 tptp.fun_nat_bool) (Q tptp.fun_nat_bool) (Q6 tptp.fun_nat_bool)) (=> (exists ((Z3 tptp.nat)) (forall ((X4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Z3) X4)) (= (tptp.pp (tptp.aa_nat_bool P X4)) (tptp.pp (tptp.aa_nat_bool P3 X4)))))) (=> (exists ((Z3 tptp.nat)) (forall ((X4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Z3) X4)) (= (tptp.pp (tptp.aa_nat_bool Q X4)) (tptp.pp (tptp.aa_nat_bool Q6 X4)))))) (exists ((Z4 tptp.nat)) (forall ((X5 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Z4) X5)) (= (and (tptp.pp (tptp.aa_nat_bool P X5)) (tptp.pp (tptp.aa_nat_bool Q X5))) (and (tptp.pp (tptp.aa_nat_bool P3 X5)) (tptp.pp (tptp.aa_nat_bool Q6 X5)))))))))) (forall ((P tptp.fun_int_bool) (P3 tptp.fun_int_bool) (Q tptp.fun_int_bool) (Q6 tptp.fun_int_bool)) (=> (exists ((Z3 tptp.int)) (forall ((X4 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Z3) X4)) (= (tptp.pp (tptp.aa_int_bool P X4)) (tptp.pp (tptp.aa_int_bool P3 X4)))))) (=> (exists ((Z3 tptp.int)) (forall ((X4 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Z3) X4)) (= (tptp.pp (tptp.aa_int_bool Q X4)) (tptp.pp (tptp.aa_int_bool Q6 X4)))))) (exists ((Z4 tptp.int)) (forall ((X5 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Z4) X5)) (= (and (tptp.pp (tptp.aa_int_bool P X5)) (tptp.pp (tptp.aa_int_bool Q X5))) (and (tptp.pp (tptp.aa_int_bool P3 X5)) (tptp.pp (tptp.aa_int_bool Q6 X5)))))))))) (forall ((P tptp.fun_nat_bool) (X tptp.nat) (M7 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool P X)) (=> (forall ((X4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool P X4)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X4) M7)))) (not (forall ((M3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool P M3)) (not (forall ((X5 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool P X5)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X5) M3))))))))))) (forall ((D tptp.int) (P tptp.fun_int_bool)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) D)) (=> (forall ((X4 tptp.int) (K3 tptp.int)) (= (tptp.pp (tptp.aa_int_bool P X4)) (tptp.pp (tptp.aa_int_bool P (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int X4) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int K3) D)))))) (= (exists ((X_1 tptp.int)) (tptp.pp (tptp.aa_int_bool P X_1))) (exists ((X3 tptp.int)) (and (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X3) (tptp.aa_int_set_int (tptp.aa_int8639817059373041269et_int tptp.set_or1266510415728281911st_int tptp.one_one_int) D))) (tptp.pp (tptp.aa_int_bool P X3)))))))) (forall ((D4 tptp.int) (A4 tptp.set_int) (T tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) D4)) (forall ((X5 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_int T))) (=> (forall ((Xa3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Xa3) (tptp.aa_int_set_int (tptp.aa_int8639817059373041269et_int tptp.set_or1266510415728281911st_int tptp.one_one_int) D4))) (forall ((Xb3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Xb3) A4)) (not (= X5 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int Xb3) Xa3))))))) (=> (tptp.pp (tptp.aa_int_bool _let_1 X5)) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int X5) D4))))))))) (forall ((D4 tptp.int) (T tptp.int) (A4 tptp.set_int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) D4)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int T) A4)) (forall ((X5 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Xa3) (tptp.aa_int_set_int (tptp.aa_int8639817059373041269et_int tptp.set_or1266510415728281911st_int tptp.one_one_int) D4))) (forall ((Xb3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Xb3) A4)) (not (= X5 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int Xb3) Xa3))))))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X5) T)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int X5) D4)) T)))))))) (forall ((D4 tptp.int) (T tptp.int) (A4 tptp.set_int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) D4)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int T) A4)) (forall ((X5 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Xa3) (tptp.aa_int_set_int (tptp.aa_int8639817059373041269et_int tptp.set_or1266510415728281911st_int tptp.one_one_int) D4))) (forall ((Xb3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Xb3) A4)) (not (= X5 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int Xb3) Xa3))))))) (=> (not (= X5 T)) (not (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int X5) D4) T)))))))) (forall ((D4 tptp.int) (T tptp.int) (A4 tptp.set_int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) D4)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int T) tptp.one_one_int)) A4)) (forall ((X5 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Xa3) (tptp.aa_int_set_int (tptp.aa_int8639817059373041269et_int tptp.set_or1266510415728281911st_int tptp.one_one_int) D4))) (forall ((Xb3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Xb3) A4)) (not (= X5 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int Xb3) Xa3))))))) (=> (= X5 T) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int X5) D4) T))))))) (forall ((D4 tptp.int) (T tptp.int) (B4 tptp.set_int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) D4)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int T) B4)) (forall ((X5 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_int T))) (=> (forall ((Xa3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Xa3) (tptp.aa_int_set_int (tptp.aa_int8639817059373041269et_int tptp.set_or1266510415728281911st_int tptp.one_one_int) D4))) (forall ((Xb3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Xb3) B4)) (not (= X5 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int Xb3) Xa3))))))) (=> (tptp.pp (tptp.aa_int_bool _let_1 X5)) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int X5) D4)))))))))) (forall ((D4 tptp.int) (B4 tptp.set_int) (T tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) D4)) (forall ((X5 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Xa3) (tptp.aa_int_set_int (tptp.aa_int8639817059373041269et_int tptp.set_or1266510415728281911st_int tptp.one_one_int) D4))) (forall ((Xb3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Xb3) B4)) (not (= X5 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int Xb3) Xa3))))))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X5) T)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int X5) D4)) T))))))) (forall ((D4 tptp.int) (T tptp.int) (B4 tptp.set_int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) D4)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int T) B4)) (forall ((X5 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Xa3) (tptp.aa_int_set_int (tptp.aa_int8639817059373041269et_int tptp.set_or1266510415728281911st_int tptp.one_one_int) D4))) (forall ((Xb3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Xb3) B4)) (not (= X5 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int Xb3) Xa3))))))) (=> (not (= X5 T)) (not (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int X5) D4) T)))))))) (forall ((D4 tptp.int) (T tptp.int) (B4 tptp.set_int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) D4)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int T) tptp.one_one_int)) B4)) (forall ((X5 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Xa3) (tptp.aa_int_set_int (tptp.aa_int8639817059373041269et_int tptp.set_or1266510415728281911st_int tptp.one_one_int) D4))) (forall ((Xb3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Xb3) B4)) (not (= X5 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int Xb3) Xa3))))))) (=> (= X5 T) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int X5) D4) T))))))) (forall ((D4 tptp.int) (A4 tptp.set_int) (T tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) D4)) (forall ((X5 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int T))) (=> (forall ((Xa3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Xa3) (tptp.aa_int_set_int (tptp.aa_int8639817059373041269et_int tptp.set_or1266510415728281911st_int tptp.one_one_int) D4))) (forall ((Xb3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Xb3) A4)) (not (= X5 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int Xb3) Xa3))))))) (=> (tptp.pp (tptp.aa_int_bool _let_1 X5)) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int X5) D4))))))))) (forall ((D4 tptp.int) (T tptp.int) (A4 tptp.set_int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) D4)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int T) tptp.one_one_int)) A4)) (forall ((X5 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Xa3) (tptp.aa_int_set_int (tptp.aa_int8639817059373041269et_int tptp.set_or1266510415728281911st_int tptp.one_one_int) D4))) (forall ((Xb3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Xb3) A4)) (not (= X5 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int Xb3) Xa3))))))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X5) T)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int X5) D4)) T)))))))) (forall ((D4 tptp.int) (T tptp.int) (B4 tptp.set_int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) D4)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int T) tptp.one_one_int)) B4)) (forall ((X5 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int T))) (=> (forall ((Xa3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Xa3) (tptp.aa_int_set_int (tptp.aa_int8639817059373041269et_int tptp.set_or1266510415728281911st_int tptp.one_one_int) D4))) (forall ((Xb3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Xb3) B4)) (not (= X5 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int Xb3) Xa3))))))) (=> (tptp.pp (tptp.aa_int_bool _let_1 X5)) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int X5) D4)))))))))) (forall ((D4 tptp.int) (B4 tptp.set_int) (T tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) D4)) (forall ((X5 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Xa3) (tptp.aa_int_set_int (tptp.aa_int8639817059373041269et_int tptp.set_or1266510415728281911st_int tptp.one_one_int) D4))) (forall ((Xb3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Xb3) B4)) (not (= X5 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int Xb3) Xa3))))))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X5) T)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int X5) D4)) T))))))) (forall ((D4 tptp.int) (P tptp.fun_int_bool) (P3 tptp.fun_int_bool) (A4 tptp.set_int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) D4)) (=> (exists ((Z3 tptp.int)) (forall ((X4 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Z3) X4)) (= (tptp.pp (tptp.aa_int_bool P X4)) (tptp.pp (tptp.aa_int_bool P3 X4)))))) (=> (forall ((X4 tptp.int)) (=> (forall ((Xa tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Xa) (tptp.aa_int_set_int (tptp.aa_int8639817059373041269et_int tptp.set_or1266510415728281911st_int tptp.one_one_int) D4))) (forall ((Xb tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Xb) A4)) (not (= X4 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int Xb) Xa))))))) (=> (tptp.pp (tptp.aa_int_bool P X4)) (tptp.pp (tptp.aa_int_bool P (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int X4) D4)))))) (=> (forall ((X4 tptp.int) (K3 tptp.int)) (= (tptp.pp (tptp.aa_int_bool P3 X4)) (tptp.pp (tptp.aa_int_bool P3 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int X4) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int K3) D4)))))) (= (exists ((X_1 tptp.int)) (tptp.pp (tptp.aa_int_bool P X_1))) (or (exists ((X3 tptp.int)) (and (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X3) (tptp.aa_int_set_int (tptp.aa_int8639817059373041269et_int tptp.set_or1266510415728281911st_int tptp.one_one_int) D4))) (tptp.pp (tptp.aa_int_bool P3 X3)))) (exists ((X3 tptp.int)) (and (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X3) (tptp.aa_int_set_int (tptp.aa_int8639817059373041269et_int tptp.set_or1266510415728281911st_int tptp.one_one_int) D4))) (exists ((Xa4 tptp.int)) (and (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Xa4) A4)) (tptp.pp (tptp.aa_int_bool P (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int Xa4) X3)))))))))))))) (forall ((D4 tptp.int) (P tptp.fun_int_bool) (P3 tptp.fun_int_bool) (B4 tptp.set_int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) D4)) (=> (exists ((Z3 tptp.int)) (forall ((X4 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X4) Z3)) (= (tptp.pp (tptp.aa_int_bool P X4)) (tptp.pp (tptp.aa_int_bool P3 X4)))))) (=> (forall ((X4 tptp.int)) (=> (forall ((Xa tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Xa) (tptp.aa_int_set_int (tptp.aa_int8639817059373041269et_int tptp.set_or1266510415728281911st_int tptp.one_one_int) D4))) (forall ((Xb tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Xb) B4)) (not (= X4 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int Xb) Xa))))))) (=> (tptp.pp (tptp.aa_int_bool P X4)) (tptp.pp (tptp.aa_int_bool P (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int X4) D4)))))) (=> (forall ((X4 tptp.int) (K3 tptp.int)) (= (tptp.pp (tptp.aa_int_bool P3 X4)) (tptp.pp (tptp.aa_int_bool P3 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int X4) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int K3) D4)))))) (= (exists ((X_1 tptp.int)) (tptp.pp (tptp.aa_int_bool P X_1))) (or (exists ((X3 tptp.int)) (and (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X3) (tptp.aa_int_set_int (tptp.aa_int8639817059373041269et_int tptp.set_or1266510415728281911st_int tptp.one_one_int) D4))) (tptp.pp (tptp.aa_int_bool P3 X3)))) (exists ((X3 tptp.int)) (and (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X3) (tptp.aa_int_set_int (tptp.aa_int8639817059373041269et_int tptp.set_or1266510415728281911st_int tptp.one_one_int) D4))) (exists ((Xa4 tptp.int)) (and (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Xa4) B4)) (tptp.pp (tptp.aa_int_bool P (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int Xa4) X3)))))))))))))) (forall ((T tptp.real)) (exists ((Z4 tptp.real)) (forall ((X5 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X5) Z4)) (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real T) X5))))))) (forall ((T tptp.rat)) (exists ((Z4 tptp.rat)) (forall ((X5 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X5) Z4)) (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat T) X5))))))) (forall ((T tptp.num)) (exists ((Z4 tptp.num)) (forall ((X5 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X5) Z4)) (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num T) X5))))))) (forall ((T tptp.nat)) (exists ((Z4 tptp.nat)) (forall ((X5 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X5) Z4)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat T) X5))))))) (forall ((T tptp.int)) (exists ((Z4 tptp.int)) (forall ((X5 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X5) Z4)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int T) X5))))))) (forall ((T tptp.real)) (exists ((Z4 tptp.real)) (forall ((X5 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X5) Z4)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X5) T)))))) (forall ((T tptp.rat)) (exists ((Z4 tptp.rat)) (forall ((X5 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X5) Z4)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X5) T)))))) (forall ((T tptp.num)) (exists ((Z4 tptp.num)) (forall ((X5 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X5) Z4)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X5) T)))))) (forall ((T tptp.nat)) (exists ((Z4 tptp.nat)) (forall ((X5 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X5) Z4)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X5) T)))))) (forall ((T tptp.int)) (exists ((Z4 tptp.int)) (forall ((X5 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X5) Z4)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X5) T)))))) (forall ((T tptp.real)) (exists ((Z4 tptp.real)) (forall ((X5 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Z4) X5)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real T) X5)))))) (forall ((T tptp.rat)) (exists ((Z4 tptp.rat)) (forall ((X5 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Z4) X5)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat T) X5)))))) (forall ((T tptp.num)) (exists ((Z4 tptp.num)) (forall ((X5 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num Z4) X5)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num T) X5)))))) (forall ((T tptp.nat)) (exists ((Z4 tptp.nat)) (forall ((X5 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Z4) X5)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat T) X5)))))) (forall ((T tptp.int)) (exists ((Z4 tptp.int)) (forall ((X5 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Z4) X5)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int T) X5)))))) (forall ((T tptp.real)) (exists ((Z4 tptp.real)) (forall ((X5 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Z4) X5)) (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X5) T))))))) (forall ((T tptp.rat)) (exists ((Z4 tptp.rat)) (forall ((X5 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Z4) X5)) (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X5) T))))))) (forall ((T tptp.num)) (exists ((Z4 tptp.num)) (forall ((X5 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num Z4) X5)) (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X5) T))))))) (forall ((T tptp.nat)) (exists ((Z4 tptp.nat)) (forall ((X5 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Z4) X5)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X5) T))))))) (forall ((T tptp.int)) (exists ((Z4 tptp.int)) (forall ((X5 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Z4) X5)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X5) T))))))) (forall ((P tptp.fun_complex_bool) (D4 tptp.complex) (Q tptp.fun_complex_bool)) (=> (forall ((X4 tptp.complex) (K3 tptp.complex)) (= (tptp.pp (tptp.aa_complex_bool P X4)) (tptp.pp (tptp.aa_complex_bool P (tptp.aa_complex_complex (tptp.minus_minus_complex X4) (tptp.aa_complex_complex (tptp.times_times_complex K3) D4)))))) (=> (forall ((X4 tptp.complex) (K3 tptp.complex)) (= (tptp.pp (tptp.aa_complex_bool Q X4)) (tptp.pp (tptp.aa_complex_bool Q (tptp.aa_complex_complex (tptp.minus_minus_complex X4) (tptp.aa_complex_complex (tptp.times_times_complex K3) D4)))))) (forall ((X5 tptp.complex) (K4 tptp.complex)) (let ((_let_1 (tptp.aa_complex_complex (tptp.minus_minus_complex X5) (tptp.aa_complex_complex (tptp.times_times_complex K4) D4)))) (= (or (tptp.pp (tptp.aa_complex_bool P X5)) (tptp.pp (tptp.aa_complex_bool Q X5))) (or (tptp.pp (tptp.aa_complex_bool P _let_1)) (tptp.pp (tptp.aa_complex_bool Q _let_1))))))))) (forall ((P tptp.fun_real_bool) (D4 tptp.real) (Q tptp.fun_real_bool)) (=> (forall ((X4 tptp.real) (K3 tptp.real)) (= (tptp.pp (tptp.aa_real_bool P X4)) (tptp.pp (tptp.aa_real_bool P (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real X4) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real K3) D4)))))) (=> (forall ((X4 tptp.real) (K3 tptp.real)) (= (tptp.pp (tptp.aa_real_bool Q X4)) (tptp.pp (tptp.aa_real_bool Q (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real X4) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real K3) D4)))))) (forall ((X5 tptp.real) (K4 tptp.real)) (let ((_let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real X5) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real K4) D4)))) (= (or (tptp.pp (tptp.aa_real_bool P X5)) (tptp.pp (tptp.aa_real_bool Q X5))) (or (tptp.pp (tptp.aa_real_bool P _let_1)) (tptp.pp (tptp.aa_real_bool Q _let_1))))))))) (forall ((P tptp.fun_rat_bool) (D4 tptp.rat) (Q tptp.fun_rat_bool)) (=> (forall ((X4 tptp.rat) (K3 tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool P X4)) (tptp.pp (tptp.aa_rat_bool P (tptp.aa_rat_rat (tptp.minus_minus_rat X4) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat K3) D4)))))) (=> (forall ((X4 tptp.rat) (K3 tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool Q X4)) (tptp.pp (tptp.aa_rat_bool Q (tptp.aa_rat_rat (tptp.minus_minus_rat X4) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat K3) D4)))))) (forall ((X5 tptp.rat) (K4 tptp.rat)) (let ((_let_1 (tptp.aa_rat_rat (tptp.minus_minus_rat X5) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat K4) D4)))) (= (or (tptp.pp (tptp.aa_rat_bool P X5)) (tptp.pp (tptp.aa_rat_bool Q X5))) (or (tptp.pp (tptp.aa_rat_bool P _let_1)) (tptp.pp (tptp.aa_rat_bool Q _let_1))))))))) (forall ((P tptp.fun_int_bool) (D4 tptp.int) (Q tptp.fun_int_bool)) (=> (forall ((X4 tptp.int) (K3 tptp.int)) (= (tptp.pp (tptp.aa_int_bool P X4)) (tptp.pp (tptp.aa_int_bool P (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int X4) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int K3) D4)))))) (=> (forall ((X4 tptp.int) (K3 tptp.int)) (= (tptp.pp (tptp.aa_int_bool Q X4)) (tptp.pp (tptp.aa_int_bool Q (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int X4) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int K3) D4)))))) (forall ((X5 tptp.int) (K4 tptp.int)) (let ((_let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int X5) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int K4) D4)))) (= (or (tptp.pp (tptp.aa_int_bool P X5)) (tptp.pp (tptp.aa_int_bool Q X5))) (or (tptp.pp (tptp.aa_int_bool P _let_1)) (tptp.pp (tptp.aa_int_bool Q _let_1))))))))) (forall ((P tptp.fun_complex_bool) (D4 tptp.complex) (Q tptp.fun_complex_bool)) (=> (forall ((X4 tptp.complex) (K3 tptp.complex)) (= (tptp.pp (tptp.aa_complex_bool P X4)) (tptp.pp (tptp.aa_complex_bool P (tptp.aa_complex_complex (tptp.minus_minus_complex X4) (tptp.aa_complex_complex (tptp.times_times_complex K3) D4)))))) (=> (forall ((X4 tptp.complex) (K3 tptp.complex)) (= (tptp.pp (tptp.aa_complex_bool Q X4)) (tptp.pp (tptp.aa_complex_bool Q (tptp.aa_complex_complex (tptp.minus_minus_complex X4) (tptp.aa_complex_complex (tptp.times_times_complex K3) D4)))))) (forall ((X5 tptp.complex) (K4 tptp.complex)) (let ((_let_1 (tptp.aa_complex_complex (tptp.minus_minus_complex X5) (tptp.aa_complex_complex (tptp.times_times_complex K4) D4)))) (= (and (tptp.pp (tptp.aa_complex_bool P X5)) (tptp.pp (tptp.aa_complex_bool Q X5))) (and (tptp.pp (tptp.aa_complex_bool P _let_1)) (tptp.pp (tptp.aa_complex_bool Q _let_1))))))))) (forall ((P tptp.fun_real_bool) (D4 tptp.real) (Q tptp.fun_real_bool)) (=> (forall ((X4 tptp.real) (K3 tptp.real)) (= (tptp.pp (tptp.aa_real_bool P X4)) (tptp.pp (tptp.aa_real_bool P (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real X4) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real K3) D4)))))) (=> (forall ((X4 tptp.real) (K3 tptp.real)) (= (tptp.pp (tptp.aa_real_bool Q X4)) (tptp.pp (tptp.aa_real_bool Q (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real X4) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real K3) D4)))))) (forall ((X5 tptp.real) (K4 tptp.real)) (let ((_let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real X5) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real K4) D4)))) (= (and (tptp.pp (tptp.aa_real_bool P X5)) (tptp.pp (tptp.aa_real_bool Q X5))) (and (tptp.pp (tptp.aa_real_bool P _let_1)) (tptp.pp (tptp.aa_real_bool Q _let_1))))))))) (forall ((P tptp.fun_rat_bool) (D4 tptp.rat) (Q tptp.fun_rat_bool)) (=> (forall ((X4 tptp.rat) (K3 tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool P X4)) (tptp.pp (tptp.aa_rat_bool P (tptp.aa_rat_rat (tptp.minus_minus_rat X4) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat K3) D4)))))) (=> (forall ((X4 tptp.rat) (K3 tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool Q X4)) (tptp.pp (tptp.aa_rat_bool Q (tptp.aa_rat_rat (tptp.minus_minus_rat X4) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat K3) D4)))))) (forall ((X5 tptp.rat) (K4 tptp.rat)) (let ((_let_1 (tptp.aa_rat_rat (tptp.minus_minus_rat X5) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat K4) D4)))) (= (and (tptp.pp (tptp.aa_rat_bool P X5)) (tptp.pp (tptp.aa_rat_bool Q X5))) (and (tptp.pp (tptp.aa_rat_bool P _let_1)) (tptp.pp (tptp.aa_rat_bool Q _let_1))))))))) (forall ((P tptp.fun_int_bool) (D4 tptp.int) (Q tptp.fun_int_bool)) (=> (forall ((X4 tptp.int) (K3 tptp.int)) (= (tptp.pp (tptp.aa_int_bool P X4)) (tptp.pp (tptp.aa_int_bool P (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int X4) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int K3) D4)))))) (=> (forall ((X4 tptp.int) (K3 tptp.int)) (= (tptp.pp (tptp.aa_int_bool Q X4)) (tptp.pp (tptp.aa_int_bool Q (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int X4) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int K3) D4)))))) (forall ((X5 tptp.int) (K4 tptp.int)) (let ((_let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int X5) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int K4) D4)))) (= (and (tptp.pp (tptp.aa_int_bool P X5)) (tptp.pp (tptp.aa_int_bool Q X5))) (and (tptp.pp (tptp.aa_int_bool P _let_1)) (tptp.pp (tptp.aa_int_bool Q _let_1))))))))) (forall ((X tptp.int) (X6 tptp.int) (P tptp.bool) (P3 tptp.bool)) (let ((_let_1 (tptp.pp P3))) (let ((_let_2 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_3 (tptp.pp (tptp.aa_int_bool _let_2 X6)))) (let ((_let_4 (tptp.pp P))) (=> (= X X6) (=> (=> _let_3 (= _let_4 _let_1)) (= (=> (tptp.pp (tptp.aa_int_bool _let_2 X)) _let_4) (=> _let_3 _let_1))))))))) (forall ((X tptp.int) (X6 tptp.int) (P tptp.bool) (P3 tptp.bool)) (let ((_let_1 (tptp.pp P3))) (let ((_let_2 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_3 (tptp.pp (tptp.aa_int_bool _let_2 X6)))) (let ((_let_4 (tptp.pp P))) (=> (= X X6) (=> (=> _let_3 (= _let_4 _let_1)) (= (and (tptp.pp (tptp.aa_int_bool _let_2 X)) _let_4) (and _let_3 _let_1))))))))) (forall ((A tptp.set_int) (B2 tptp.set_int) (C tptp.set_int) (D tptp.set_int)) (let ((_let_1 (tptp.ord_less_eq_set_int C))) (= (tptp.ord_less_set_set_int (tptp.set_or370866239135849197et_int A B2) (tptp.set_or370866239135849197et_int C D)) (and (or (not (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int A) B2))) (and (tptp.pp (tptp.aa_set_int_bool _let_1 A)) (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int B2) D)) (or (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_set_int C) A)) (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_set_int B2) D))))) (tptp.pp (tptp.aa_set_int_bool _let_1 D)))))) (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat) (D tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat C))) (= (tptp.ord_less_set_rat (tptp.set_or633870826150836451st_rat A B2) (tptp.set_or633870826150836451st_rat C D)) (and (or (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B2))) (and (tptp.pp (tptp.aa_rat_bool _let_1 A)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B2) D)) (or (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat C) A)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B2) D))))) (tptp.pp (tptp.aa_rat_bool _let_1 D)))))) (forall ((A tptp.num) (B2 tptp.num) (C tptp.num) (D tptp.num)) (let ((_let_1 (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num C))) (= (tptp.ord_less_set_num (tptp.set_or7049704709247886629st_num A B2) (tptp.set_or7049704709247886629st_num C D)) (and (or (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A) B2))) (and (tptp.pp (tptp.aa_num_bool _let_1 A)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num B2) D)) (or (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num C) A)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num B2) D))))) (tptp.pp (tptp.aa_num_bool _let_1 D)))))) (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat) (D tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat C))) (= (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_set_nat (tptp.set_or1269000886237332187st_nat A B2)) (tptp.set_or1269000886237332187st_nat C D))) (and (or (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B2))) (and (tptp.pp (tptp.aa_nat_bool _let_1 A)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B2) D)) (or (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat C) A)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat B2) D))))) (tptp.pp (tptp.aa_nat_bool _let_1 D)))))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int) (D tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int C))) (= (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_set_int (tptp.aa_int_set_int (tptp.aa_int8639817059373041269et_int tptp.set_or1266510415728281911st_int A) B2)) (tptp.aa_int_set_int (tptp.aa_int8639817059373041269et_int tptp.set_or1266510415728281911st_int C) D))) (and (or (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B2))) (and (tptp.pp (tptp.aa_int_bool _let_1 A)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B2) D)) (or (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int C) A)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B2) D))))) (tptp.pp (tptp.aa_int_bool _let_1 D)))))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real) (D tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real C))) (= (tptp.ord_less_set_real (tptp.set_or1222579329274155063t_real A B2) (tptp.set_or1222579329274155063t_real C D)) (and (or (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) B2))) (and (tptp.pp (tptp.aa_real_bool _let_1 A)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real B2) D)) (or (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real C) A)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B2) D))))) (tptp.pp (tptp.aa_real_bool _let_1 D)))))) (forall ((D tptp.int) (P1 tptp.fun_int_bool) (P tptp.fun_int_bool)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) D)) (=> (forall ((X4 tptp.int) (K3 tptp.int)) (= (tptp.pp (tptp.aa_int_bool P1 X4)) (tptp.pp (tptp.aa_int_bool P1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int X4) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int K3) D)))))) (=> (exists ((Z3 tptp.int)) (forall ((X4 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X4) Z3)) (= (tptp.pp (tptp.aa_int_bool P X4)) (tptp.pp (tptp.aa_int_bool P1 X4)))))) (=> (exists ((X_13 tptp.int)) (tptp.pp (tptp.aa_int_bool P1 X_13))) (exists ((X_12 tptp.int)) (tptp.pp (tptp.aa_int_bool P X_12)))))))) (forall ((D tptp.int) (P3 tptp.fun_int_bool) (P tptp.fun_int_bool)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) D)) (=> (forall ((X4 tptp.int) (K3 tptp.int)) (= (tptp.pp (tptp.aa_int_bool P3 X4)) (tptp.pp (tptp.aa_int_bool P3 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int X4) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int K3) D)))))) (=> (exists ((Z3 tptp.int)) (forall ((X4 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Z3) X4)) (= (tptp.pp (tptp.aa_int_bool P X4)) (tptp.pp (tptp.aa_int_bool P3 X4)))))) (=> (exists ((X_13 tptp.int)) (tptp.pp (tptp.aa_int_bool P3 X_13))) (exists ((X_12 tptp.int)) (tptp.pp (tptp.aa_int_bool P X_12)))))))) (forall ((A tptp.real) (B2 tptp.real) (P tptp.fun_re1255401033344146673l_bool)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) B2)) (=> (forall ((A3 tptp.real) (B3 tptp.real) (C2 tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool P A3))) (=> (tptp.pp (tptp.aa_real_bool _let_1 B3)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool P B3) C2)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A3) B3)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real B3) C2)) (tptp.pp (tptp.aa_real_bool _let_1 C2)))))))) (=> (forall ((X4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) X4)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X4) B2)) (exists ((D5 tptp.real)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) D5)) (forall ((A3 tptp.real) (B3 tptp.real)) (=> (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A3) X4)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X4) B3)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real B3) A3)) D5))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool P A3) B3))))))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool P A) B2)))))) (forall ((Z tptp.real) (X tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) Z)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real X) Z)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real Y) Z))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) Y))))) (forall ((Z tptp.rat) (X tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) Z)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat X) Z)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat Y) Z))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) Y))))) (forall ((Z tptp.int) (X tptp.int) (Y tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) Z)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int X) Z)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int Y) Z))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X) Y))))) (forall ((Z tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.times_times_real Z))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) Z)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real _let_1 X)) (tptp.aa_real_real _let_1 Y))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) Y)))))) (forall ((Z tptp.rat) (X tptp.rat) (Y tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_rat tptp.times_times_rat Z))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) Z)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat _let_1 X)) (tptp.aa_rat_rat _let_1 Y))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) Y)))))) (forall ((Z tptp.int) (X tptp.int) (Y tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.times_times_int Z))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) Z)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int _let_1 X)) (tptp.aa_int_int _let_1 Y))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X) Y)))))) (forall ((Q2 tptp.nat) (R tptp.nat)) (= (tptp.pp (tptp.aa_Pro2232559814647311250t_bool tptp.unique6322359934112328802ux_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Q2) R))) (= R tptp.zero_zero_nat))) (forall ((Q2 tptp.int) (R tptp.int)) (= (tptp.pp (tptp.aa_Pro4501881432599481050t_bool tptp.unique6319869463603278526ux_int (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int Q2) R))) (= R tptp.zero_zero_int))) (forall ((N tptp.nat) (Xs tptp.list_int) (Ys tptp.list_int)) (let ((_let_1 (tptp.size_size_list_int Ys))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.size_size_list_int Xs)) _let_1))) (= (tptp.nth_Pr4439495888332055232nt_int (tptp.product_int_int Xs Ys) N) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int (tptp.aa_nat_int (tptp.nth_int Xs) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat N) _let_1))) (tptp.aa_nat_int (tptp.nth_int Ys) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat N) _let_1))))))) (forall ((N tptp.nat) (Xs tptp.list_int) (Ys tptp.list_VEBT_VEBT)) (let ((_let_1 (tptp.size_s6755466524823107622T_VEBT Ys))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.size_size_list_int Xs)) _let_1))) (= (tptp.nth_Pr3474266648193625910T_VEBT (tptp.produc662631939642741121T_VEBT Xs Ys) N) (tptp.produc3329399203697025711T_VEBT (tptp.aa_nat_int (tptp.nth_int Xs) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat N) _let_1)) (tptp.nth_VEBT_VEBT Ys (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat N) _let_1))))))) (forall ((N tptp.nat) (Xs tptp.list_int) (Ys tptp.list_bool)) (let ((_let_1 (tptp.size_size_list_bool Ys))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.size_size_list_int Xs)) _let_1))) (= (tptp.nth_Pr6495399312670224281t_bool (tptp.product_int_bool Xs Ys) N) (tptp.produc788913908665201810t_bool (tptp.aa_nat_int (tptp.nth_int Xs) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat N) _let_1)) (tptp.aa_nat_bool (tptp.nth_bool Ys) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat N) _let_1))))))) (forall ((N tptp.nat) (Xs tptp.list_int) (Ys tptp.list_nat)) (let ((_let_1 (tptp.size_size_list_nat Ys))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.size_size_list_int Xs)) _let_1))) (= (tptp.nth_Pr8617346907841251940nt_nat (tptp.product_int_nat Xs Ys) N) (tptp.product_Pair_int_nat (tptp.aa_nat_int (tptp.nth_int Xs) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat N) _let_1)) (tptp.aa_nat_nat (tptp.nth_nat Ys) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat N) _let_1))))))) (forall ((N tptp.nat) (Xs tptp.list_VEBT_VEBT) (Ys tptp.list_int)) (let ((_let_1 (tptp.size_size_list_int Ys))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.size_s6755466524823107622T_VEBT Xs)) _let_1))) (= (tptp.nth_Pr6837108013167703752BT_int (tptp.produc7292646706713671643BT_int Xs Ys) N) (tptp.produc736041933913180425BT_int (tptp.nth_VEBT_VEBT Xs (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat N) _let_1)) (tptp.aa_nat_int (tptp.nth_int Ys) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat N) _let_1))))))) (forall ((N tptp.nat) (Xs tptp.list_VEBT_VEBT) (Ys tptp.list_VEBT_VEBT)) (let ((_let_1 (tptp.size_s6755466524823107622T_VEBT Ys))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.size_s6755466524823107622T_VEBT Xs)) _let_1))) (= (tptp.nth_Pr4953567300277697838T_VEBT (tptp.produc4743750530478302277T_VEBT Xs Ys) N) (tptp.produc537772716801021591T_VEBT (tptp.nth_VEBT_VEBT Xs (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat N) _let_1)) (tptp.nth_VEBT_VEBT Ys (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat N) _let_1))))))) (forall ((N tptp.nat) (Xs tptp.list_VEBT_VEBT) (Ys tptp.list_bool)) (let ((_let_1 (tptp.size_size_list_bool Ys))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.size_s6755466524823107622T_VEBT Xs)) _let_1))) (= (tptp.nth_Pr1289831921885633937T_bool (tptp.produc5466675335756156456T_bool Xs Ys) N) (tptp.produc3035007008238225530T_bool (tptp.nth_VEBT_VEBT Xs (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat N) _let_1)) (tptp.aa_nat_bool (tptp.nth_bool Ys) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat N) _let_1))))))) (forall ((N tptp.nat) (Xs tptp.list_VEBT_VEBT) (Ys tptp.list_nat)) (let ((_let_1 (tptp.size_size_list_nat Ys))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.size_s6755466524823107622T_VEBT Xs)) _let_1))) (= (tptp.nth_Pr1791586995822124652BT_nat (tptp.produc7295137177222721919BT_nat Xs Ys) N) (tptp.produc738532404422230701BT_nat (tptp.nth_VEBT_VEBT Xs (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat N) _let_1)) (tptp.aa_nat_nat (tptp.nth_nat Ys) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat N) _let_1))))))) (forall ((N tptp.nat) (Xs tptp.list_bool) (Ys tptp.list_int)) (let ((_let_1 (tptp.size_size_list_int Ys))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.size_size_list_bool Xs)) _let_1))) (= (tptp.nth_Pr7231943226834047147ol_int (tptp.product_bool_int Xs Ys) N) (tptp.produc8871513391732212460ol_int (tptp.aa_nat_bool (tptp.nth_bool Xs) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat N) _let_1)) (tptp.aa_nat_int (tptp.nth_int Ys) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat N) _let_1))))))) (forall ((N tptp.nat) (Xs tptp.list_bool) (Ys tptp.list_VEBT_VEBT)) (let ((_let_1 (tptp.size_s6755466524823107622T_VEBT Ys))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.size_size_list_bool Xs)) _let_1))) (= (tptp.nth_Pr3250499561091541003T_VEBT (tptp.produc2282853104913622818T_VEBT Xs Ys) N) (tptp.produc9074556814250467700T_VEBT (tptp.aa_nat_bool (tptp.nth_bool Xs) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat N) _let_1)) (tptp.nth_VEBT_VEBT Ys (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat N) _let_1))))))) (forall ((B2 tptp.int) (A tptp.int) (Q2 tptp.int) (R tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_2 (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int Q2))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B2) tptp.zero_zero_int)) (=> (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.eucl_rel_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) tptp.one_one_int) B2) (tptp.aa_int7462565939943104719nt_int _let_2 R))) (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.eucl_rel_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int tptp.one_one_int) (tptp.aa_int_int _let_1 A)) (tptp.aa_int_int _let_1 B2)) (tptp.aa_int7462565939943104719nt_int _let_2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_int_int _let_1 R)) tptp.one_one_int))))))))) (forall ((Xs tptp.list_VEBT_VEBT) (Ys tptp.list_VEBT_VEBT)) (= (tptp.size_s7466405169056248089T_VEBT (tptp.produc4743750530478302277T_VEBT Xs Ys)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.size_s6755466524823107622T_VEBT Xs)) (tptp.size_s6755466524823107622T_VEBT Ys)))) (forall ((Xs tptp.list_VEBT_VEBT) (Ys tptp.list_bool)) (= (tptp.size_s1343096544515248124T_bool (tptp.produc5466675335756156456T_bool Xs Ys)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.size_s6755466524823107622T_VEBT Xs)) (tptp.size_size_list_bool Ys)))) (forall ((Xs tptp.list_VEBT_VEBT) (Ys tptp.list_nat)) (= (tptp.size_s6152045936467909847BT_nat (tptp.produc7295137177222721919BT_nat Xs Ys)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.size_s6755466524823107622T_VEBT Xs)) (tptp.size_size_list_nat Ys)))) (forall ((Xs tptp.list_bool) (Ys tptp.list_VEBT_VEBT)) (= (tptp.size_s7211631430880329078T_VEBT (tptp.produc2282853104913622818T_VEBT Xs Ys)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.size_size_list_bool Xs)) (tptp.size_s6755466524823107622T_VEBT Ys)))) (forall ((Xs tptp.list_bool) (Ys tptp.list_bool)) (= (tptp.size_s6988337448923680857l_bool (tptp.product_bool_bool Xs Ys)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.size_size_list_bool Xs)) (tptp.size_size_list_bool Ys)))) (forall ((Xs tptp.list_bool) (Ys tptp.list_nat)) (= (tptp.size_s3243772863075988794ol_nat (tptp.product_bool_nat Xs Ys)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.size_size_list_bool Xs)) (tptp.size_size_list_nat Ys)))) (forall ((Xs tptp.list_nat) (Ys tptp.list_VEBT_VEBT)) (= (tptp.size_s4762443039079500285T_VEBT (tptp.produc7156399406898700509T_VEBT Xs Ys)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.size_size_list_nat Xs)) (tptp.size_s6755466524823107622T_VEBT Ys)))) (forall ((Xs tptp.list_nat) (Ys tptp.list_bool)) (= (tptp.size_s783543119881238752t_bool (tptp.product_nat_bool Xs Ys)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.size_size_list_nat Xs)) (tptp.size_size_list_bool Ys)))) (forall ((Xs tptp.list_nat) (Ys tptp.list_nat)) (= (tptp.size_s5460976970255530739at_nat (tptp.product_nat_nat Xs Ys)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.size_size_list_nat Xs)) (tptp.size_size_list_nat Ys)))) (forall ((A tptp.int) (B2 tptp.int) (Q2 tptp.int) (R tptp.int) (Q5 tptp.int) (R4 tptp.int)) (let ((_let_1 (tptp.eucl_rel_int A B2))) (=> (tptp.pp (tptp.aa_Pro4501881432599481050t_bool _let_1 (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int Q2) R))) (=> (tptp.pp (tptp.aa_Pro4501881432599481050t_bool _let_1 (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int Q5) R4))) (= R R4))))) (forall ((A tptp.int) (B2 tptp.int) (Q2 tptp.int) (R tptp.int) (Q5 tptp.int) (R4 tptp.int)) (let ((_let_1 (tptp.eucl_rel_int A B2))) (=> (tptp.pp (tptp.aa_Pro4501881432599481050t_bool _let_1 (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int Q2) R))) (=> (tptp.pp (tptp.aa_Pro4501881432599481050t_bool _let_1 (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int Q5) R4))) (= Q2 Q5))))) (forall ((K tptp.int)) (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.eucl_rel_int K tptp.zero_zero_int) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int tptp.zero_zero_int) K)))) (forall ((K tptp.int) (L tptp.int) (Q2 tptp.int) (R tptp.int)) (=> (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.eucl_rel_int K L) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int Q2) R))) (= (tptp.aa_int_int (tptp.divide_divide_int K) L) Q2))) (forall ((K tptp.int) (L tptp.int) (Q2 tptp.int) (R tptp.int)) (=> (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.eucl_rel_int K L) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int Q2) R))) (= (tptp.aa_int_int (tptp.modulo_modulo_int K) L) R))) (forall ((L tptp.int) (K tptp.int) (Q2 tptp.int)) (=> (not (= L tptp.zero_zero_int)) (=> (= K (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int Q2) L)) (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.eucl_rel_int K L) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int Q2) tptp.zero_zero_int)))))) (forall ((K tptp.int) (L tptp.int)) (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.eucl_rel_int K L) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int (tptp.aa_int_int (tptp.divide_divide_int K) L)) (tptp.aa_int_int (tptp.modulo_modulo_int K) L))))) (forall ((K tptp.int) (L tptp.int) (Q2 tptp.int) (R tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_int L))) (let ((_let_2 (tptp.pp (tptp.aa_int_bool _let_1 tptp.zero_zero_int)))) (let ((_let_3 (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) L)))) (= (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.eucl_rel_int K L) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int Q2) R))) (and (= K (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int L) Q2)) R)) (=> _let_3 (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) R)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int R) L)))) (=> (not _let_3) (and (=> _let_2 (and (tptp.pp (tptp.aa_int_bool _let_1 R)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int R) tptp.zero_zero_int)))) (=> (not _let_2) (= Q2 tptp.zero_zero_int)))))))))) (forall ((Z tptp.real) (X tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) Z)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real X) Z)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real Y) Z))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Y))))) (forall ((Z tptp.rat) (X tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) Z)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat X) Z)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat Y) Z))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) Y))))) (forall ((Z tptp.int) (X tptp.int) (Y tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) Z)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int X) Z)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int Y) Z))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) Y))))) (forall ((B2 tptp.int) (A tptp.int) (Q2 tptp.int) (R tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_2 (tptp.aa_int_fun_int_int tptp.plus_plus_int tptp.one_one_int))) (let ((_let_3 (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int Q2))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) B2)) (=> (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.eucl_rel_int A B2) (tptp.aa_int7462565939943104719nt_int _let_3 R))) (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.eucl_rel_int (tptp.aa_int_int _let_2 (tptp.aa_int_int _let_1 A)) (tptp.aa_int_int _let_1 B2)) (tptp.aa_int7462565939943104719nt_int _let_3 (tptp.aa_int_int _let_2 (tptp.aa_int_int _let_1 R))))))))))) (forall ((Z tptp.nat) (X tptp.nat) (A4 tptp.set_nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Z) X)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_VEBT_min_in_set A4) Z)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A4)) (exists ((X_12 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool (tptp.vEBT_is_pred_in_set A4) X) X_12))))))) (forall ((T tptp.vEBT_VEBT) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt T) N)) (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat (tptp.vEBT_VEBT_set_vebt T))))) (forall ((Xs tptp.set_nat) (A tptp.nat)) (=> (not (exists ((X_12 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool (tptp.vEBT_is_pred_in_set Xs) A) X_12)))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat Xs)) (not (exists ((X5 tptp.nat)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X5) Xs)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X5) A)))))))) (forall ((X1 tptp.int) (X2 tptp.int) (Y1 tptp.int) (Y2 tptp.int)) (= (= (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int X1) X2) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int Y1) Y2)) (and (= X1 Y1) (= X2 Y2)))) (forall ((X1 tptp.fun_Co6545587727236015215e_term) (X2 tptp.produc8923325533196201883nteger) (Y1 tptp.fun_Co6545587727236015215e_term) (Y2 tptp.produc8923325533196201883nteger)) (= (= (tptp.produc4282985567423050387nteger X1 X2) (tptp.produc4282985567423050387nteger Y1 Y2)) (and (= X1 Y1) (= X2 Y2)))) (forall ((X1 tptp.fun_Pr272337284026993017e_term) (X2 tptp.produc8923325533196201883nteger) (Y1 tptp.fun_Pr272337284026993017e_term) (Y2 tptp.produc8923325533196201883nteger)) (= (= (tptp.produc7384524951051686153nteger X1 X2) (tptp.produc7384524951051686153nteger Y1 Y2)) (and (= X1 Y1) (= X2 Y2)))) (forall ((X1 tptp.fun_Pr9164807099015279978e_term) (X2 tptp.product_prod_int_int) (Y1 tptp.fun_Pr9164807099015279978e_term) (Y2 tptp.product_prod_int_int)) (= (= (tptp.produc1560874099174258678nt_int X1 X2) (tptp.produc1560874099174258678nt_int Y1 Y2)) (and (= X1 Y1) (= X2 Y2)))) (forall ((X1 tptp.fun_in6429348457993719614e_term) (X2 tptp.product_prod_int_int) (Y1 tptp.fun_in6429348457993719614e_term) (Y2 tptp.product_prod_int_int)) (= (= (tptp.produc4852315488734385442nt_int X1 X2) (tptp.produc4852315488734385442nt_int Y1 Y2)) (and (= X1 Y1) (= X2 Y2)))) (forall ((A tptp.int) (B2 tptp.int) (A2 tptp.int) (B tptp.int)) (= (= (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int A) B2) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int A2) B)) (and (= A A2) (= B2 B)))) (forall ((A tptp.fun_Co6545587727236015215e_term) (B2 tptp.produc8923325533196201883nteger) (A2 tptp.fun_Co6545587727236015215e_term) (B tptp.produc8923325533196201883nteger)) (= (= (tptp.produc4282985567423050387nteger A B2) (tptp.produc4282985567423050387nteger A2 B)) (and (= A A2) (= B2 B)))) (forall ((A tptp.fun_Pr272337284026993017e_term) (B2 tptp.produc8923325533196201883nteger) (A2 tptp.fun_Pr272337284026993017e_term) (B tptp.produc8923325533196201883nteger)) (= (= (tptp.produc7384524951051686153nteger A B2) (tptp.produc7384524951051686153nteger A2 B)) (and (= A A2) (= B2 B)))) (forall ((A tptp.fun_Pr9164807099015279978e_term) (B2 tptp.product_prod_int_int) (A2 tptp.fun_Pr9164807099015279978e_term) (B tptp.product_prod_int_int)) (= (= (tptp.produc1560874099174258678nt_int A B2) (tptp.produc1560874099174258678nt_int A2 B)) (and (= A A2) (= B2 B)))) (forall ((A tptp.fun_in6429348457993719614e_term) (B2 tptp.product_prod_int_int) (A2 tptp.fun_in6429348457993719614e_term) (B tptp.product_prod_int_int)) (= (= (tptp.produc4852315488734385442nt_int A B2) (tptp.produc4852315488734385442nt_int A2 B)) (and (= A A2) (= B2 B)))) (forall ((Xs tptp.list_VEBT_VEBT)) (tptp.finite5795047828879050333T_VEBT (tptp.set_VEBT_VEBT2 Xs))) (forall ((Xs tptp.list_nat)) (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat (tptp.set_nat2 Xs)))) (forall ((Xs tptp.list_int)) (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int (tptp.set_int2 Xs)))) (forall ((Xs tptp.list_complex)) (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex (tptp.set_complex2 Xs)))) (forall ((A tptp.rat) (B2 tptp.rat)) (= (not (tptp.finite_finite_rat (tptp.set_or633870826150836451st_rat A B2))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B2)))) (forall ((A tptp.real) (B2 tptp.real)) (= (not (tptp.finite_finite_real (tptp.set_or1222579329274155063t_real A B2))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B2)))) (forall ((N3 tptp.set_nat) (N tptp.nat)) (=> (forall ((X4 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X4) N3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X4) N)))) (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat N3)))) (forall ((N3 tptp.set_nat)) (= (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat N3)) (exists ((M6 tptp.nat)) (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) N3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X3) M6))))))) (forall ((N3 tptp.set_nat)) (= (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat N3)) (exists ((M6 tptp.nat)) (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) N3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X3) M6))))))) (forall ((A4 tptp.set_VEBT_VEBT)) (=> (tptp.finite5795047828879050333T_VEBT A4) (exists ((Xs2 tptp.list_VEBT_VEBT)) (= (tptp.set_VEBT_VEBT2 Xs2) A4)))) (forall ((A4 tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A4)) (exists ((Xs2 tptp.list_nat)) (= (tptp.set_nat2 Xs2) A4)))) (forall ((A4 tptp.set_int)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A4)) (exists ((Xs2 tptp.list_int)) (= (tptp.set_int2 Xs2) A4)))) (forall ((A4 tptp.set_complex)) (=> (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex A4)) (exists ((Xs2 tptp.list_complex)) (= (tptp.set_complex2 Xs2) A4)))) (forall ((P tptp.fun_nat_bool) (I tptp.nat)) (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat (tptp.collect_nat (tptp.aa_nat_fun_nat_bool (tptp.aTP_Lamm_be P) I))))) (forall ((F tptp.fun_nat_nat) (U tptp.nat)) (=> (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) (tptp.aa_nat_nat F N2)))) (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat (tptp.collect_nat (tptp.aa_nat_fun_nat_bool (tptp.aTP_Lamm_bf F) U)))))) (forall ((A4 tptp.set_complex) (N tptp.nat)) (=> (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex A4)) (tptp.finite8712137658972009173omplex (tptp.collect_list_complex (tptp.aa_nat8039161444313734436x_bool (tptp.aTP_Lamm_bg A4) N))))) (forall ((A4 tptp.set_VEBT_VEBT) (N tptp.nat)) (=> (tptp.finite5795047828879050333T_VEBT A4) (tptp.finite3004134309566078307T_VEBT (tptp.collec5608196760682091941T_VEBT (tptp.aa_nat1297483763028037422T_bool (tptp.aTP_Lamm_bh A4) N))))) (forall ((A4 tptp.set_bool) (N tptp.nat)) (=> (tptp.finite_finite_bool A4) (tptp.finite7866827932528546246t_bool (tptp.collect_list_bool (tptp.aa_nat4862889769322786699l_bool (tptp.aTP_Lamm_bi A4) N))))) (forall ((A4 tptp.set_nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A4)) (tptp.finite8100373058378681591st_nat (tptp.collect_list_nat (tptp.aa_nat2079453845469346690t_bool (tptp.aTP_Lamm_bj A4) N))))) (forall ((A4 tptp.set_int) (N tptp.nat)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A4)) (tptp.finite3922522038869484883st_int (tptp.collect_list_int (tptp.aa_nat1619170893822700070t_bool (tptp.aTP_Lamm_bk A4) N))))) (forall ((A tptp.rat) (B2 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B2)) (not (tptp.finite_finite_rat (tptp.set_or633870826150836451st_rat A B2))))) (forall ((A tptp.real) (B2 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B2)) (not (tptp.finite_finite_real (tptp.set_or1222579329274155063t_real A B2))))) (forall ((A4 tptp.set_complex) (N tptp.nat)) (=> (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex A4)) (tptp.finite8712137658972009173omplex (tptp.collect_list_complex (tptp.aa_nat8039161444313734436x_bool (tptp.aTP_Lamm_bl A4) N))))) (forall ((A4 tptp.set_VEBT_VEBT) (N tptp.nat)) (=> (tptp.finite5795047828879050333T_VEBT A4) (tptp.finite3004134309566078307T_VEBT (tptp.collec5608196760682091941T_VEBT (tptp.aa_nat1297483763028037422T_bool (tptp.aTP_Lamm_bm A4) N))))) (forall ((A4 tptp.set_bool) (N tptp.nat)) (=> (tptp.finite_finite_bool A4) (tptp.finite7866827932528546246t_bool (tptp.collect_list_bool (tptp.aa_nat4862889769322786699l_bool (tptp.aTP_Lamm_bn A4) N))))) (forall ((A4 tptp.set_nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A4)) (tptp.finite8100373058378681591st_nat (tptp.collect_list_nat (tptp.aa_nat2079453845469346690t_bool (tptp.aTP_Lamm_bo A4) N))))) (forall ((A4 tptp.set_int) (N tptp.nat)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A4)) (tptp.finite3922522038869484883st_int (tptp.collect_list_int (tptp.aa_nat1619170893822700070t_bool (tptp.aTP_Lamm_bp A4) N))))) (forall ((Y tptp.product_prod_int_int)) (not (forall ((A3 tptp.int) (B3 tptp.int)) (not (= Y (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int A3) B3)))))) (forall ((Y tptp.produc5207004643709237345nteger)) (not (forall ((A3 tptp.fun_Co6545587727236015215e_term) (B3 tptp.produc8923325533196201883nteger)) (not (= Y (tptp.produc4282985567423050387nteger A3 B3)))))) (forall ((Y tptp.produc1616345218596728535nteger)) (not (forall ((A3 tptp.fun_Pr272337284026993017e_term) (B3 tptp.produc8923325533196201883nteger)) (not (= Y (tptp.produc7384524951051686153nteger A3 B3)))))) (forall ((Y tptp.produc4441460161354545860nt_int)) (not (forall ((A3 tptp.fun_Pr9164807099015279978e_term) (B3 tptp.product_prod_int_int)) (not (= Y (tptp.produc1560874099174258678nt_int A3 B3)))))) (forall ((Y tptp.produc6768802789813714928nt_int)) (not (forall ((A3 tptp.fun_in6429348457993719614e_term) (B3 tptp.product_prod_int_int)) (not (= Y (tptp.produc4852315488734385442nt_int A3 B3)))))) (forall ((P2 tptp.product_prod_int_int)) (exists ((X4 tptp.int) (Y4 tptp.int)) (= P2 (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int X4) Y4)))) (forall ((P2 tptp.produc5207004643709237345nteger)) (exists ((X4 tptp.fun_Co6545587727236015215e_term) (Y4 tptp.produc8923325533196201883nteger)) (= P2 (tptp.produc4282985567423050387nteger X4 Y4)))) (forall ((P2 tptp.produc1616345218596728535nteger)) (exists ((X4 tptp.fun_Pr272337284026993017e_term) (Y4 tptp.produc8923325533196201883nteger)) (= P2 (tptp.produc7384524951051686153nteger X4 Y4)))) (forall ((P2 tptp.produc4441460161354545860nt_int)) (exists ((X4 tptp.fun_Pr9164807099015279978e_term) (Y4 tptp.product_prod_int_int)) (= P2 (tptp.produc1560874099174258678nt_int X4 Y4)))) (forall ((P2 tptp.produc6768802789813714928nt_int)) (exists ((X4 tptp.fun_in6429348457993719614e_term) (Y4 tptp.product_prod_int_int)) (= P2 (tptp.produc4852315488734385442nt_int X4 Y4)))) (forall ((P tptp.fun_Pr803113274115125473t_bool) (P2 tptp.product_prod_int_int)) (=> (forall ((A3 tptp.int) (B3 tptp.int)) (tptp.pp (tptp.aa_Pro4501881432599481050t_bool P (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int A3) B3)))) (tptp.pp (tptp.aa_Pro4501881432599481050t_bool P P2)))) (forall ((P tptp.fun_Pr5900652808213522383r_bool) (P2 tptp.produc5207004643709237345nteger)) (=> (forall ((A3 tptp.fun_Co6545587727236015215e_term) (B3 tptp.produc8923325533196201883nteger)) (tptp.pp (tptp.aa_Pro7150874649148492216r_bool P (tptp.produc4282985567423050387nteger A3 B3)))) (tptp.pp (tptp.aa_Pro7150874649148492216r_bool P P2)))) (forall ((P tptp.fun_Pr5991498150630465241r_bool) (P2 tptp.produc1616345218596728535nteger)) (=> (forall ((A3 tptp.fun_Pr272337284026993017e_term) (B3 tptp.produc8923325533196201883nteger)) (tptp.pp (tptp.aa_Pro3640759179027349698r_bool P (tptp.produc7384524951051686153nteger A3 B3)))) (tptp.pp (tptp.aa_Pro3640759179027349698r_bool P P2)))) (forall ((P tptp.fun_Pr6019674992625747500t_bool) (P2 tptp.produc4441460161354545860nt_int)) (=> (forall ((A3 tptp.fun_Pr9164807099015279978e_term) (B3 tptp.product_prod_int_int)) (tptp.pp (tptp.aa_Pro5031108791230793749t_bool P (tptp.produc1560874099174258678nt_int A3 B3)))) (tptp.pp (tptp.aa_Pro5031108791230793749t_bool P P2)))) (forall ((P tptp.fun_Pr5504123824928244736t_bool) (P2 tptp.produc6768802789813714928nt_int)) (=> (forall ((A3 tptp.fun_in6429348457993719614e_term) (B3 tptp.product_prod_int_int)) (tptp.pp (tptp.aa_Pro7591400126937138665t_bool P (tptp.produc4852315488734385442nt_int A3 B3)))) (tptp.pp (tptp.aa_Pro7591400126937138665t_bool P P2)))) (forall ((A tptp.int) (B2 tptp.int) (A2 tptp.int) (B tptp.int)) (=> (= (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int A) B2) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int A2) B)) (not (=> (= A A2) (not (= B2 B)))))) (forall ((A tptp.fun_Co6545587727236015215e_term) (B2 tptp.produc8923325533196201883nteger) (A2 tptp.fun_Co6545587727236015215e_term) (B tptp.produc8923325533196201883nteger)) (=> (= (tptp.produc4282985567423050387nteger A B2) (tptp.produc4282985567423050387nteger A2 B)) (not (=> (= A A2) (not (= B2 B)))))) (forall ((A tptp.fun_Pr272337284026993017e_term) (B2 tptp.produc8923325533196201883nteger) (A2 tptp.fun_Pr272337284026993017e_term) (B tptp.produc8923325533196201883nteger)) (=> (= (tptp.produc7384524951051686153nteger A B2) (tptp.produc7384524951051686153nteger A2 B)) (not (=> (= A A2) (not (= B2 B)))))) (forall ((A tptp.fun_Pr9164807099015279978e_term) (B2 tptp.product_prod_int_int) (A2 tptp.fun_Pr9164807099015279978e_term) (B tptp.product_prod_int_int)) (=> (= (tptp.produc1560874099174258678nt_int A B2) (tptp.produc1560874099174258678nt_int A2 B)) (not (=> (= A A2) (not (= B2 B)))))) (forall ((A tptp.fun_in6429348457993719614e_term) (B2 tptp.product_prod_int_int) (A2 tptp.fun_in6429348457993719614e_term) (B tptp.product_prod_int_int)) (=> (= (tptp.produc4852315488734385442nt_int A B2) (tptp.produc4852315488734385442nt_int A2 B)) (not (=> (= A A2) (not (= B2 B)))))) (forall ((N3 tptp.set_nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat N3) (tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat N))) (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat N3)))) (forall ((Y tptp.produc5207004643709237345nteger)) (not (forall ((A3 tptp.fun_Co6545587727236015215e_term) (B3 tptp.code_integer) (C2 tptp.code_integer)) (not (= Y (tptp.produc4282985567423050387nteger A3 (tptp.produc1086072967326762835nteger B3 C2))))))) (forall ((Y tptp.produc1616345218596728535nteger)) (not (forall ((A3 tptp.fun_Pr272337284026993017e_term) (B3 tptp.code_integer) (C2 tptp.code_integer)) (not (= Y (tptp.produc7384524951051686153nteger A3 (tptp.produc1086072967326762835nteger B3 C2))))))) (forall ((Y tptp.produc4441460161354545860nt_int)) (not (forall ((A3 tptp.fun_Pr9164807099015279978e_term) (B3 tptp.int) (C2 tptp.int)) (not (= Y (tptp.produc1560874099174258678nt_int A3 (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int B3) C2))))))) (forall ((Y tptp.produc6768802789813714928nt_int)) (not (forall ((A3 tptp.fun_in6429348457993719614e_term) (B3 tptp.int) (C2 tptp.int)) (not (= Y (tptp.produc4852315488734385442nt_int A3 (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int B3) C2))))))) (forall ((P tptp.fun_Pr5900652808213522383r_bool) (X tptp.produc5207004643709237345nteger)) (=> (forall ((A3 tptp.fun_Co6545587727236015215e_term) (B3 tptp.code_integer) (C2 tptp.code_integer)) (tptp.pp (tptp.aa_Pro7150874649148492216r_bool P (tptp.produc4282985567423050387nteger A3 (tptp.produc1086072967326762835nteger B3 C2))))) (tptp.pp (tptp.aa_Pro7150874649148492216r_bool P X)))) (forall ((P tptp.fun_Pr5991498150630465241r_bool) (X tptp.produc1616345218596728535nteger)) (=> (forall ((A3 tptp.fun_Pr272337284026993017e_term) (B3 tptp.code_integer) (C2 tptp.code_integer)) (tptp.pp (tptp.aa_Pro3640759179027349698r_bool P (tptp.produc7384524951051686153nteger A3 (tptp.produc1086072967326762835nteger B3 C2))))) (tptp.pp (tptp.aa_Pro3640759179027349698r_bool P X)))) (forall ((P tptp.fun_Pr6019674992625747500t_bool) (X tptp.produc4441460161354545860nt_int)) (=> (forall ((A3 tptp.fun_Pr9164807099015279978e_term) (B3 tptp.int) (C2 tptp.int)) (tptp.pp (tptp.aa_Pro5031108791230793749t_bool P (tptp.produc1560874099174258678nt_int A3 (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int B3) C2))))) (tptp.pp (tptp.aa_Pro5031108791230793749t_bool P X)))) (forall ((P tptp.fun_Pr5504123824928244736t_bool) (X tptp.produc6768802789813714928nt_int)) (=> (forall ((A3 tptp.fun_in6429348457993719614e_term) (B3 tptp.int) (C2 tptp.int)) (tptp.pp (tptp.aa_Pro7591400126937138665t_bool P (tptp.produc4852315488734385442nt_int A3 (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int B3) C2))))) (tptp.pp (tptp.aa_Pro7591400126937138665t_bool P X)))) (forall ((K tptp.nat)) (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat (tptp.collect_nat (tptp.aa_nat_fun_nat_bool tptp.aTP_Lamm_bq K))))) (forall ((K tptp.nat)) (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat (tptp.collect_nat (tptp.aa_nat_fun_nat_bool tptp.aTP_Lamm_br K))))) (forall ((A4 tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A4)) (tptp.finite1152437895449049373et_nat (tptp.collect_set_nat (tptp.aTP_Lamm_bs A4))))) (forall ((A4 tptp.set_complex)) (=> (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex A4)) (tptp.finite6551019134538273531omplex (tptp.collect_set_complex (tptp.aTP_Lamm_bt A4))))) (forall ((A4 tptp.set_int)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A4)) (tptp.finite6197958912794628473et_int (tptp.collect_set_int (tptp.aTP_Lamm_bu A4))))) (forall ((P tptp.fun_real_bool) (Q tptp.fun_re1255401033344146673l_bool)) (=> (tptp.finite_finite_real (tptp.collect_real P)) (= (tptp.finite_finite_real (tptp.collect_real (tptp.aa_fun4964148113266127823l_bool (tptp.aTP_Lamm_bv P) Q))) (forall ((Y3 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool P Y3)) (tptp.finite_finite_real (tptp.collect_real (tptp.aa_rea7809428808904475482l_bool (tptp.aTP_Lamm_bw Q) Y3)))))))) (forall ((P tptp.fun_real_bool) (Q tptp.fun_na6801867027684862029l_bool)) (=> (tptp.finite_finite_real (tptp.collect_real P)) (= (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat (tptp.collect_nat (tptp.aa_fun7391232120346184911t_bool (tptp.aTP_Lamm_bx P) Q)))) (forall ((Y3 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool P Y3)) (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat (tptp.collect_nat (tptp.aa_real_fun_nat_bool (tptp.aTP_Lamm_by Q) Y3))))))))) (forall ((P tptp.fun_real_bool) (Q tptp.fun_in3970322703178350321l_bool)) (=> (tptp.finite_finite_real (tptp.collect_real P)) (= (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int (tptp.collect_int (tptp.aa_fun69789402421856207t_bool (tptp.aTP_Lamm_bz P) Q)))) (forall ((Y3 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool P Y3)) (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int (tptp.collect_int (tptp.aa_real_fun_int_bool (tptp.aTP_Lamm_ca Q) Y3))))))))) (forall ((P tptp.fun_real_bool) (Q tptp.fun_co2286642472385812463l_bool)) (=> (tptp.finite_finite_real (tptp.collect_real P)) (= (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex (tptp.collect_complex (tptp.aa_fun6039685132559610447x_bool (tptp.aTP_Lamm_cb P) Q)))) (forall ((Y3 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool P Y3)) (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex (tptp.collect_complex (tptp.aa_rea5887071448072802392x_bool (tptp.aTP_Lamm_cc Q) Y3))))))))) (forall ((P tptp.fun_nat_bool) (Q tptp.fun_re9121486324101951821t_bool)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat (tptp.collect_nat P))) (= (tptp.finite_finite_real (tptp.collect_real (tptp.aa_fun4927090880566115059l_bool (tptp.aTP_Lamm_cd P) Q))) (forall ((Y3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool P Y3)) (tptp.finite_finite_real (tptp.collect_real (tptp.aa_nat_fun_real_bool (tptp.aTP_Lamm_ce Q) Y3)))))))) (forall ((P tptp.fun_nat_bool) (Q tptp.fun_nat_fun_nat_bool)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat (tptp.collect_nat P))) (= (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat (tptp.collect_nat (tptp.aa_fun8399658544460314611t_bool (tptp.aTP_Lamm_cf P) Q)))) (forall ((Y3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool P Y3)) (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat (tptp.collect_nat (tptp.aa_nat_fun_nat_bool (tptp.aTP_Lamm_cg Q) Y3))))))))) (forall ((P tptp.fun_nat_bool) (Q tptp.fun_int_fun_nat_bool)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat (tptp.collect_nat P))) (= (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int (tptp.collect_int (tptp.aa_fun6484551404966387955t_bool (tptp.aTP_Lamm_ch P) Q)))) (forall ((Y3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool P Y3)) (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int (tptp.collect_int (tptp.aa_nat_fun_int_bool (tptp.aTP_Lamm_ci Q) Y3))))))))) (forall ((P tptp.fun_nat_bool) (Q tptp.fun_co2841405903858895691t_bool)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat (tptp.collect_nat P))) (= (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex (tptp.collect_complex (tptp.aa_fun6682930621474858099x_bool (tptp.aTP_Lamm_cj P) Q)))) (forall ((Y3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool P Y3)) (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex (tptp.collect_complex (tptp.aa_nat5545486172511849908x_bool (tptp.aTP_Lamm_ck Q) Y3))))))))) (forall ((P tptp.fun_int_bool) (Q tptp.fun_re8661203372455305201t_bool)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int (tptp.collect_int P))) (= (tptp.finite_finite_real (tptp.collect_real (tptp.aa_fun7352647192720469839l_bool (tptp.aTP_Lamm_cl P) Q))) (forall ((Y3 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool P Y3)) (tptp.finite_finite_real (tptp.collect_real (tptp.aa_int_fun_real_bool (tptp.aTP_Lamm_cm Q) Y3)))))))) (forall ((P tptp.fun_int_bool) (Q tptp.fun_nat_fun_int_bool)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int (tptp.collect_int P))) (= (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat (tptp.collect_nat (tptp.aa_fun7626329022887090767t_bool (tptp.aTP_Lamm_cn P) Q)))) (forall ((Y3 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool P Y3)) (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat (tptp.collect_nat (tptp.aa_int_fun_nat_bool (tptp.aTP_Lamm_co Q) Y3))))))))) (forall ((N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.one_one_nat) N)) (tptp.finite_finite_real (tptp.collect_real (tptp.aa_nat_fun_real_bool tptp.aTP_Lamm_cp N))))) (forall ((N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.one_one_nat) N)) (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex (tptp.collect_complex (tptp.aTP_Lamm_cq N)))))) (forall ((I5 tptp.set_real) (X tptp.fun_real_complex) (Y tptp.fun_real_complex)) (let ((_let_1 (tptp.aTP_Lamm_cr I5))) (=> (tptp.finite_finite_real (tptp.collect_real (tptp.aa_fun3813300650643916655l_bool _let_1 X))) (=> (tptp.finite_finite_real (tptp.collect_real (tptp.aa_fun3813300650643916655l_bool _let_1 Y))) (tptp.finite_finite_real (tptp.collect_real (tptp.aa_fun3813300650643916655l_bool (tptp.aa_fun5520078544946397361l_bool (tptp.aTP_Lamm_cs I5) X) Y))))))) (forall ((I5 tptp.set_nat) (X tptp.fun_nat_complex) (Y tptp.fun_nat_complex)) (let ((_let_1 (tptp.aTP_Lamm_ct I5))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat (tptp.collect_nat (tptp.aa_fun8004580481347240231t_bool _let_1 X)))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat (tptp.collect_nat (tptp.aa_fun8004580481347240231t_bool _let_1 Y)))) (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat (tptp.collect_nat (tptp.aa_fun8004580481347240231t_bool (tptp.aa_fun5430245816583273541t_bool (tptp.aTP_Lamm_cu I5) X) Y)))))))) (forall ((I5 tptp.set_int) (X tptp.fun_int_complex) (Y tptp.fun_int_complex)) (let ((_let_1 (tptp.aTP_Lamm_cv I5))) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int (tptp.collect_int (tptp.aa_fun8146511558608327279t_bool _let_1 X)))) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int (tptp.collect_int (tptp.aa_fun8146511558608327279t_bool _let_1 Y)))) (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int (tptp.collect_int (tptp.aa_fun8146511558608327279t_bool (tptp.aa_fun3850298374753145905t_bool (tptp.aTP_Lamm_cw I5) X) Y)))))))) (forall ((I5 tptp.set_complex) (X tptp.fun_complex_complex) (Y tptp.fun_complex_complex)) (let ((_let_1 (tptp.aTP_Lamm_cx I5))) (=> (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex (tptp.collect_complex (tptp.aa_fun9073502203726719595x_bool _let_1 X)))) (=> (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex (tptp.collect_complex (tptp.aa_fun9073502203726719595x_bool _let_1 Y)))) (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex (tptp.collect_complex (tptp.aa_fun9073502203726719595x_bool (tptp.aa_fun6641798613628721963x_bool (tptp.aTP_Lamm_cy I5) X) Y)))))))) (forall ((I5 tptp.set_real) (X tptp.fun_real_real) (Y tptp.fun_real_real)) (let ((_let_1 (tptp.aTP_Lamm_cz I5))) (=> (tptp.finite_finite_real (tptp.collect_real (tptp.aa_fun9137271176455094897l_bool _let_1 X))) (=> (tptp.finite_finite_real (tptp.collect_real (tptp.aa_fun9137271176455094897l_bool _let_1 Y))) (tptp.finite_finite_real (tptp.collect_real (tptp.aa_fun9137271176455094897l_bool (tptp.aa_fun334843040499603765l_bool (tptp.aTP_Lamm_da I5) X) Y))))))) (forall ((I5 tptp.set_nat) (X tptp.fun_nat_real) (Y tptp.fun_nat_real)) (let ((_let_1 (tptp.aTP_Lamm_db I5))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat (tptp.collect_nat (tptp.aa_fun1349230436907296553t_bool _let_1 X)))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat (tptp.collect_nat (tptp.aa_fun1349230436907296553t_bool _let_1 Y)))) (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat (tptp.collect_nat (tptp.aa_fun1349230436907296553t_bool (tptp.aa_fun849216055071118793t_bool (tptp.aTP_Lamm_dc I5) X) Y)))))))) (forall ((I5 tptp.set_int) (X tptp.fun_int_real) (Y tptp.fun_int_real)) (let ((_let_1 (tptp.aTP_Lamm_dd I5))) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int (tptp.collect_int (tptp.aa_fun1262781554902806129t_bool _let_1 X)))) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int (tptp.collect_int (tptp.aa_fun1262781554902806129t_bool _let_1 Y)))) (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int (tptp.collect_int (tptp.aa_fun1262781554902806129t_bool (tptp.aa_fun6205147705862377397t_bool (tptp.aTP_Lamm_de I5) X) Y)))))))) (forall ((I5 tptp.set_complex) (X tptp.fun_complex_real) (Y tptp.fun_complex_real)) (let ((_let_1 (tptp.aTP_Lamm_df I5))) (=> (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex (tptp.collect_complex (tptp.aa_fun2898354424061222765x_bool _let_1 X)))) (=> (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex (tptp.collect_complex (tptp.aa_fun2898354424061222765x_bool _let_1 Y)))) (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex (tptp.collect_complex (tptp.aa_fun2898354424061222765x_bool (tptp.aa_fun2094807616088678831x_bool (tptp.aTP_Lamm_dg I5) X) Y)))))))) (forall ((I5 tptp.set_real) (X tptp.fun_real_rat) (Y tptp.fun_real_rat)) (let ((_let_1 (tptp.aTP_Lamm_dh I5))) (=> (tptp.finite_finite_real (tptp.collect_real (tptp.aa_fun8987621170725249221l_bool _let_1 X))) (=> (tptp.finite_finite_real (tptp.collect_real (tptp.aa_fun8987621170725249221l_bool _let_1 Y))) (tptp.finite_finite_real (tptp.collect_real (tptp.aa_fun8987621170725249221l_bool (tptp.aa_fun8530242357055030877l_bool (tptp.aTP_Lamm_di I5) X) Y))))))) (forall ((I5 tptp.set_nat) (X tptp.fun_nat_rat) (Y tptp.fun_nat_rat)) (let ((_let_1 (tptp.aTP_Lamm_dj I5))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat (tptp.collect_nat (tptp.aa_fun5637262893798792573t_bool _let_1 X)))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat (tptp.collect_nat (tptp.aa_fun5637262893798792573t_bool _let_1 Y)))) (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat (tptp.collect_nat (tptp.aa_fun5637262893798792573t_bool (tptp.aa_fun2107527232086395633t_bool (tptp.aTP_Lamm_dk I5) X) Y)))))))) (forall ((I5 tptp.set_real) (X tptp.fun_real_complex) (Y tptp.fun_real_complex)) (let ((_let_1 (tptp.aTP_Lamm_dl I5))) (=> (tptp.finite_finite_real (tptp.collect_real (tptp.aa_fun3813300650643916655l_bool _let_1 X))) (=> (tptp.finite_finite_real (tptp.collect_real (tptp.aa_fun3813300650643916655l_bool _let_1 Y))) (tptp.finite_finite_real (tptp.collect_real (tptp.aa_fun3813300650643916655l_bool (tptp.aa_fun5520078544946397361l_bool (tptp.aTP_Lamm_dm I5) X) Y))))))) (forall ((I5 tptp.set_nat) (X tptp.fun_nat_complex) (Y tptp.fun_nat_complex)) (let ((_let_1 (tptp.aTP_Lamm_dn I5))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat (tptp.collect_nat (tptp.aa_fun8004580481347240231t_bool _let_1 X)))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat (tptp.collect_nat (tptp.aa_fun8004580481347240231t_bool _let_1 Y)))) (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat (tptp.collect_nat (tptp.aa_fun8004580481347240231t_bool (tptp.aa_fun5430245816583273541t_bool (tptp.aTP_Lamm_do I5) X) Y)))))))) (forall ((I5 tptp.set_int) (X tptp.fun_int_complex) (Y tptp.fun_int_complex)) (let ((_let_1 (tptp.aTP_Lamm_dp I5))) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int (tptp.collect_int (tptp.aa_fun8146511558608327279t_bool _let_1 X)))) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int (tptp.collect_int (tptp.aa_fun8146511558608327279t_bool _let_1 Y)))) (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int (tptp.collect_int (tptp.aa_fun8146511558608327279t_bool (tptp.aa_fun3850298374753145905t_bool (tptp.aTP_Lamm_dq I5) X) Y)))))))) (forall ((I5 tptp.set_complex) (X tptp.fun_complex_complex) (Y tptp.fun_complex_complex)) (let ((_let_1 (tptp.aTP_Lamm_dr I5))) (=> (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex (tptp.collect_complex (tptp.aa_fun9073502203726719595x_bool _let_1 X)))) (=> (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex (tptp.collect_complex (tptp.aa_fun9073502203726719595x_bool _let_1 Y)))) (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex (tptp.collect_complex (tptp.aa_fun9073502203726719595x_bool (tptp.aa_fun6641798613628721963x_bool (tptp.aTP_Lamm_ds I5) X) Y)))))))) (forall ((I5 tptp.set_real) (X tptp.fun_real_real) (Y tptp.fun_real_real)) (let ((_let_1 (tptp.aTP_Lamm_dt I5))) (=> (tptp.finite_finite_real (tptp.collect_real (tptp.aa_fun9137271176455094897l_bool _let_1 X))) (=> (tptp.finite_finite_real (tptp.collect_real (tptp.aa_fun9137271176455094897l_bool _let_1 Y))) (tptp.finite_finite_real (tptp.collect_real (tptp.aa_fun9137271176455094897l_bool (tptp.aa_fun334843040499603765l_bool (tptp.aTP_Lamm_du I5) X) Y))))))) (forall ((I5 tptp.set_nat) (X tptp.fun_nat_real) (Y tptp.fun_nat_real)) (let ((_let_1 (tptp.aTP_Lamm_dv I5))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat (tptp.collect_nat (tptp.aa_fun1349230436907296553t_bool _let_1 X)))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat (tptp.collect_nat (tptp.aa_fun1349230436907296553t_bool _let_1 Y)))) (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat (tptp.collect_nat (tptp.aa_fun1349230436907296553t_bool (tptp.aa_fun849216055071118793t_bool (tptp.aTP_Lamm_dw I5) X) Y)))))))) (forall ((I5 tptp.set_int) (X tptp.fun_int_real) (Y tptp.fun_int_real)) (let ((_let_1 (tptp.aTP_Lamm_dx I5))) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int (tptp.collect_int (tptp.aa_fun1262781554902806129t_bool _let_1 X)))) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int (tptp.collect_int (tptp.aa_fun1262781554902806129t_bool _let_1 Y)))) (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int (tptp.collect_int (tptp.aa_fun1262781554902806129t_bool (tptp.aa_fun6205147705862377397t_bool (tptp.aTP_Lamm_dy I5) X) Y)))))))) (forall ((I5 tptp.set_complex) (X tptp.fun_complex_real) (Y tptp.fun_complex_real)) (let ((_let_1 (tptp.aTP_Lamm_dz I5))) (=> (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex (tptp.collect_complex (tptp.aa_fun2898354424061222765x_bool _let_1 X)))) (=> (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex (tptp.collect_complex (tptp.aa_fun2898354424061222765x_bool _let_1 Y)))) (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex (tptp.collect_complex (tptp.aa_fun2898354424061222765x_bool (tptp.aa_fun2094807616088678831x_bool (tptp.aTP_Lamm_ea I5) X) Y)))))))) (forall ((I5 tptp.set_real) (X tptp.fun_real_rat) (Y tptp.fun_real_rat)) (let ((_let_1 (tptp.aTP_Lamm_eb I5))) (=> (tptp.finite_finite_real (tptp.collect_real (tptp.aa_fun8987621170725249221l_bool _let_1 X))) (=> (tptp.finite_finite_real (tptp.collect_real (tptp.aa_fun8987621170725249221l_bool _let_1 Y))) (tptp.finite_finite_real (tptp.collect_real (tptp.aa_fun8987621170725249221l_bool (tptp.aa_fun8530242357055030877l_bool (tptp.aTP_Lamm_ec I5) X) Y))))))) (forall ((I5 tptp.set_nat) (X tptp.fun_nat_rat) (Y tptp.fun_nat_rat)) (let ((_let_1 (tptp.aTP_Lamm_ed I5))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat (tptp.collect_nat (tptp.aa_fun5637262893798792573t_bool _let_1 X)))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat (tptp.collect_nat (tptp.aa_fun5637262893798792573t_bool _let_1 Y)))) (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat (tptp.collect_nat (tptp.aa_fun5637262893798792573t_bool (tptp.aa_fun2107527232086395633t_bool (tptp.aTP_Lamm_ee I5) X) Y)))))))) (forall ((A tptp.int) (B2 tptp.int)) (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int (tptp.collect_int (tptp.aa_int_fun_int_bool (tptp.aTP_Lamm_ef A) B2))))) (forall ((A tptp.int) (B2 tptp.int)) (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int (tptp.collect_int (tptp.aa_int_fun_int_bool (tptp.aTP_Lamm_eg A) B2))))) (forall ((A tptp.int) (B2 tptp.int)) (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int (tptp.collect_int (tptp.aa_int_fun_int_bool (tptp.aTP_Lamm_eh A) B2))))) (forall ((A tptp.int) (B2 tptp.int)) (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int (tptp.collect_int (tptp.aa_int_fun_int_bool (tptp.aTP_Lamm_ei A) B2))))) (forall ((M7 tptp.set_list_VEBT_VEBT)) (=> (tptp.finite3004134309566078307T_VEBT M7) (exists ((N2 tptp.nat)) (forall ((X5 tptp.list_VEBT_VEBT)) (=> (tptp.member2936631157270082147T_VEBT X5 M7) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.size_s6755466524823107622T_VEBT X5)) N2))))))) (forall ((M7 tptp.set_list_bool)) (=> (tptp.finite7866827932528546246t_bool M7) (exists ((N2 tptp.nat)) (forall ((X5 tptp.list_bool)) (=> (tptp.member_list_bool X5 M7) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.size_size_list_bool X5)) N2))))))) (forall ((M7 tptp.set_list_nat)) (=> (tptp.finite8100373058378681591st_nat M7) (exists ((N2 tptp.nat)) (forall ((X5 tptp.list_nat)) (=> (tptp.member_list_nat X5 M7) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.size_size_list_nat X5)) N2))))))) (forall ((A4 tptp.set_real) (A tptp.real)) (=> (tptp.finite_finite_real A4) (=> (tptp.member_real A A4) (exists ((X4 tptp.real)) (and (tptp.member_real X4 A4) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X4) A)) (forall ((Xa tptp.real)) (=> (tptp.member_real Xa A4) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Xa) X4)) (= X4 Xa))))))))) (forall ((A4 tptp.set_set_int) (A tptp.set_int)) (=> (tptp.finite6197958912794628473et_int A4) (=> (tptp.member_set_int A A4) (exists ((X4 tptp.set_int)) (and (tptp.member_set_int X4 A4) (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int X4) A)) (forall ((Xa tptp.set_int)) (=> (tptp.member_set_int Xa A4) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int Xa) X4)) (= X4 Xa))))))))) (forall ((A4 tptp.set_rat) (A tptp.rat)) (=> (tptp.finite_finite_rat A4) (=> (tptp.member_rat A A4) (exists ((X4 tptp.rat)) (and (tptp.member_rat X4 A4) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X4) A)) (forall ((Xa tptp.rat)) (=> (tptp.member_rat Xa A4) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat Xa) X4)) (= X4 Xa))))))))) (forall ((A4 tptp.set_num) (A tptp.num)) (=> (tptp.finite_finite_num A4) (=> (tptp.member_num A A4) (exists ((X4 tptp.num)) (and (tptp.member_num X4 A4) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X4) A)) (forall ((Xa tptp.num)) (=> (tptp.member_num Xa A4) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num Xa) X4)) (= X4 Xa))))))))) (forall ((A4 tptp.set_nat) (A tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A4)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat A) A4)) (exists ((X4 tptp.nat)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X4) A4)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X4) A)) (forall ((Xa tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat Xa) A4)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Xa) X4)) (= X4 Xa))))))))) (forall ((A4 tptp.set_int) (A tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A4)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int A) A4)) (exists ((X4 tptp.int)) (and (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X4) A4)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X4) A)) (forall ((Xa tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Xa) A4)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Xa) X4)) (= X4 Xa))))))))) (forall ((A4 tptp.set_real) (A tptp.real)) (=> (tptp.finite_finite_real A4) (=> (tptp.member_real A A4) (exists ((X4 tptp.real)) (and (tptp.member_real X4 A4) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) X4)) (forall ((Xa tptp.real)) (=> (tptp.member_real Xa A4) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X4) Xa)) (= X4 Xa))))))))) (forall ((A4 tptp.set_set_int) (A tptp.set_int)) (=> (tptp.finite6197958912794628473et_int A4) (=> (tptp.member_set_int A A4) (exists ((X4 tptp.set_int)) (and (tptp.member_set_int X4 A4) (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int A) X4)) (forall ((Xa tptp.set_int)) (=> (tptp.member_set_int Xa A4) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int X4) Xa)) (= X4 Xa))))))))) (forall ((A4 tptp.set_rat) (A tptp.rat)) (=> (tptp.finite_finite_rat A4) (=> (tptp.member_rat A A4) (exists ((X4 tptp.rat)) (and (tptp.member_rat X4 A4) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) X4)) (forall ((Xa tptp.rat)) (=> (tptp.member_rat Xa A4) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X4) Xa)) (= X4 Xa))))))))) (forall ((A4 tptp.set_num) (A tptp.num)) (=> (tptp.finite_finite_num A4) (=> (tptp.member_num A A4) (exists ((X4 tptp.num)) (and (tptp.member_num X4 A4) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A) X4)) (forall ((Xa tptp.num)) (=> (tptp.member_num Xa A4) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X4) Xa)) (= X4 Xa))))))))) (forall ((A4 tptp.set_nat) (A tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A4)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat A) A4)) (exists ((X4 tptp.nat)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X4) A4)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) X4)) (forall ((Xa tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat Xa) A4)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X4) Xa)) (= X4 Xa))))))))) (forall ((A4 tptp.set_int) (A tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A4)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int A) A4)) (exists ((X4 tptp.int)) (and (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X4) A4)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) X4)) (forall ((Xa tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Xa) A4)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X4) Xa)) (= X4 Xa))))))))) (forall ((B4 tptp.set_nat) (A4 tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat B4)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat A4) B4)) (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A4))))) (forall ((B4 tptp.set_complex) (A4 tptp.set_complex)) (=> (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex B4)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.ord_le211207098394363844omplex A4) B4)) (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex A4))))) (forall ((B4 tptp.set_int) (A4 tptp.set_int)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int B4)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int A4) B4)) (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A4))))) (forall ((S2 tptp.set_nat) (T3 tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat S2) T3)) (=> (not (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat S2))) (not (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat T3)))))) (forall ((S2 tptp.set_complex) (T3 tptp.set_complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.ord_le211207098394363844omplex S2) T3)) (=> (not (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex S2))) (not (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex T3)))))) (forall ((S2 tptp.set_int) (T3 tptp.set_int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int S2) T3)) (=> (not (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int S2))) (not (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int T3)))))) (forall ((A4 tptp.set_nat) (B4 tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat A4) B4)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat B4)) (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A4))))) (forall ((A4 tptp.set_complex) (B4 tptp.set_complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.ord_le211207098394363844omplex A4) B4)) (=> (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex B4)) (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex A4))))) (forall ((A4 tptp.set_int) (B4 tptp.set_int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int A4) B4)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int B4)) (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A4))))) (forall ((A4 tptp.set_nat) (P tptp.fun_set_nat_bool)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A4)) (=> (forall ((A6 tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A6)) (=> (forall ((B6 tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_set_nat B6) A6)) (tptp.pp (tptp.aa_set_nat_bool P B6)))) (tptp.pp (tptp.aa_set_nat_bool P A6))))) (tptp.pp (tptp.aa_set_nat_bool P A4))))) (forall ((A4 tptp.set_int) (P tptp.fun_set_int_bool)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A4)) (=> (forall ((A6 tptp.set_int)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A6)) (=> (forall ((B6 tptp.set_int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_set_int B6) A6)) (tptp.pp (tptp.aa_set_int_bool P B6)))) (tptp.pp (tptp.aa_set_int_bool P A6))))) (tptp.pp (tptp.aa_set_int_bool P A4))))) (forall ((A4 tptp.set_complex) (P tptp.fun_set_complex_bool)) (=> (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex A4)) (=> (forall ((A6 tptp.set_complex)) (=> (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex A6)) (=> (forall ((B6 tptp.set_complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.ord_less_set_complex B6) A6)) (tptp.pp (tptp.aa_set_complex_bool P B6)))) (tptp.pp (tptp.aa_set_complex_bool P A6))))) (tptp.pp (tptp.aa_set_complex_bool P A4))))) (forall ((P tptp.fun_real_bool) (F tptp.fun_real_real)) (=> (tptp.finite_finite_real (tptp.collect_real P)) (tptp.finite_finite_real (tptp.collect_real (tptp.aa_fun9137271176455094897l_bool (tptp.aTP_Lamm_ej P) F))))) (forall ((P tptp.fun_real_bool) (F tptp.fun_real_nat)) (=> (tptp.finite_finite_real (tptp.collect_real P)) (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat (tptp.collect_nat (tptp.aa_fun3670751239728173737t_bool (tptp.aTP_Lamm_ek P) F)))))) (forall ((P tptp.fun_real_bool) (F tptp.fun_real_int)) (=> (tptp.finite_finite_real (tptp.collect_real P)) (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int (tptp.collect_int (tptp.aa_fun6938287985607813617t_bool (tptp.aTP_Lamm_el P) F)))))) (forall ((P tptp.fun_real_bool) (F tptp.fun_real_complex)) (=> (tptp.finite_finite_real (tptp.collect_real P)) (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex (tptp.collect_complex (tptp.aa_fun6713666175893136621x_bool (tptp.aTP_Lamm_em P) F)))))) (forall ((P tptp.fun_nat_bool) (F tptp.fun_nat_real)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat (tptp.collect_nat P))) (tptp.finite_finite_real (tptp.collect_real (tptp.aa_fun2369234836118212941l_bool (tptp.aTP_Lamm_en P) F))))) (forall ((P tptp.fun_nat_bool) (F tptp.fun_nat_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat (tptp.collect_nat P))) (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat (tptp.collect_nat (tptp.aa_fun1783405840085286277t_bool (tptp.aTP_Lamm_eo P) F)))))) (forall ((P tptp.fun_nat_bool) (F tptp.fun_nat_int)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat (tptp.collect_nat P))) (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int (tptp.collect_int (tptp.aa_fun5050942585964926157t_bool (tptp.aTP_Lamm_ep P) F)))))) (forall ((P tptp.fun_nat_bool) (F tptp.fun_nat_complex)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat (tptp.collect_nat P))) (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex (tptp.collect_complex (tptp.aa_fun678042768005816265x_bool (tptp.aTP_Lamm_eq P) F)))))) (forall ((P tptp.fun_int_bool) (F tptp.fun_int_real)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int (tptp.collect_int P))) (tptp.finite_finite_real (tptp.collect_real (tptp.aa_fun1272151855474214385l_bool (tptp.aTP_Lamm_er P) F))))) (forall ((P tptp.fun_int_bool) (F tptp.fun_int_nat)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int (tptp.collect_int P))) (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat (tptp.collect_nat (tptp.aa_fun8751864718750488105t_bool (tptp.aTP_Lamm_es P) F)))))) (forall ((P tptp.fun_real_bool) (Q tptp.fun_real_bool) (F tptp.fun_re7681423839302404990l_real)) (=> (tptp.finite_finite_real (tptp.collect_real P)) (=> (tptp.finite_finite_real (tptp.collect_real Q)) (tptp.finite_finite_real (tptp.collect_real (tptp.aa_fun955784922888763656l_bool (tptp.aa_fun2902298374912565143l_bool (tptp.aTP_Lamm_et P) Q) F)))))) (forall ((P tptp.fun_real_bool) (Q tptp.fun_real_bool) (F tptp.fun_re7428432522468557474al_nat)) (=> (tptp.finite_finite_real (tptp.collect_real P)) (=> (tptp.finite_finite_real (tptp.collect_real Q)) (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat (tptp.collect_nat (tptp.aa_fun528418799539591104t_bool (tptp.aa_fun8259732966411813455t_bool (tptp.aTP_Lamm_eu P) Q) F))))))) (forall ((P tptp.fun_real_bool) (Q tptp.fun_real_bool) (F tptp.fun_re4938349377536830718al_int)) (=> (tptp.finite_finite_real (tptp.collect_real P)) (=> (tptp.finite_finite_real (tptp.collect_real Q)) (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int (tptp.collect_int (tptp.aa_fun1238366933954993416t_bool (tptp.aa_fun2410317078794417559t_bool (tptp.aTP_Lamm_ev P) Q) F))))))) (forall ((P tptp.fun_real_bool) (Q tptp.fun_real_bool) (F tptp.fun_re7812779276277946752omplex)) (=> (tptp.finite_finite_real (tptp.collect_real P)) (=> (tptp.finite_finite_real (tptp.collect_real Q)) (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex (tptp.collect_complex (tptp.aa_fun8363404835654190852x_bool (tptp.aa_fun7464652376466389139x_bool (tptp.aTP_Lamm_ew P) Q) F))))))) (forall ((P tptp.fun_real_bool) (Q tptp.fun_nat_bool) (F tptp.fun_re4238438383274954274t_real)) (=> (tptp.finite_finite_real (tptp.collect_real P)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat (tptp.collect_nat Q))) (tptp.finite_finite_real (tptp.collect_real (tptp.aa_fun5008594764412271332l_bool (tptp.aa_fun7835077198776561559l_bool (tptp.aTP_Lamm_ex P) Q) F)))))) (forall ((P tptp.fun_real_bool) (Q tptp.fun_nat_bool) (F tptp.fun_real_fun_nat_nat)) (=> (tptp.finite_finite_real (tptp.collect_real P)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat (tptp.collect_nat Q))) (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat (tptp.collect_nat (tptp.aa_fun3685766209695167900t_bool (tptp.aa_fun2965812958138651215t_bool (tptp.aTP_Lamm_ey P) Q) F))))))) (forall ((P tptp.fun_real_bool) (Q tptp.fun_nat_bool) (F tptp.fun_real_fun_nat_int)) (=> (tptp.finite_finite_real (tptp.collect_real P)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat (tptp.collect_nat Q))) (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int (tptp.collect_int (tptp.aa_fun4395714344110570212t_bool (tptp.aa_fun6339769107376031127t_bool (tptp.aTP_Lamm_ez P) Q) F))))))) (forall ((P tptp.fun_real_bool) (Q tptp.fun_nat_bool) (F tptp.fun_re2084383175013312036omplex)) (=> (tptp.finite_finite_real (tptp.collect_real P)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat (tptp.collect_nat Q))) (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex (tptp.collect_complex (tptp.aa_fun9170867047750497504x_bool (tptp.aa_fun2493215948360222867x_bool (tptp.aTP_Lamm_fa P) Q) F))))))) (forall ((P tptp.fun_real_bool) (Q tptp.fun_int_bool) (F tptp.fun_re7457141977439324286t_real)) (=> (tptp.finite_finite_real (tptp.collect_real P)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int (tptp.collect_int Q))) (tptp.finite_finite_real (tptp.collect_real (tptp.aa_fun6686107996194020744l_bool (tptp.aa_fun7698435294645330071l_bool (tptp.aTP_Lamm_fb P) Q) F)))))) (forall ((P tptp.fun_real_bool) (Q tptp.fun_int_bool) (F tptp.fun_real_fun_int_nat)) (=> (tptp.finite_finite_real (tptp.collect_real P)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int (tptp.collect_int Q))) (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat (tptp.collect_nat (tptp.aa_fun6723608294159301696t_bool (tptp.aa_fun543251173574902607t_bool (tptp.aTP_Lamm_fc P) Q) F))))))) (forall ((A4 tptp.set_real)) (=> (tptp.finite_finite_real A4) (=> (not (= A4 tptp.bot_bot_set_real)) (exists ((X4 tptp.real)) (and (tptp.member_real X4 A4) (forall ((Xa tptp.real)) (=> (tptp.member_real Xa A4) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Xa) X4)) (= X4 Xa))))))))) (forall ((A4 tptp.set_set_int)) (=> (tptp.finite6197958912794628473et_int A4) (=> (not (= A4 tptp.bot_bot_set_set_int)) (exists ((X4 tptp.set_int)) (and (tptp.member_set_int X4 A4) (forall ((Xa tptp.set_int)) (=> (tptp.member_set_int Xa A4) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int Xa) X4)) (= X4 Xa))))))))) (forall ((A4 tptp.set_rat)) (=> (tptp.finite_finite_rat A4) (=> (not (= A4 tptp.bot_bot_set_rat)) (exists ((X4 tptp.rat)) (and (tptp.member_rat X4 A4) (forall ((Xa tptp.rat)) (=> (tptp.member_rat Xa A4) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat Xa) X4)) (= X4 Xa))))))))) (forall ((A4 tptp.set_num)) (=> (tptp.finite_finite_num A4) (=> (not (= A4 tptp.bot_bot_set_num)) (exists ((X4 tptp.num)) (and (tptp.member_num X4 A4) (forall ((Xa tptp.num)) (=> (tptp.member_num Xa A4) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num Xa) X4)) (= X4 Xa))))))))) (forall ((A4 tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A4)) (=> (not (= A4 tptp.bot_bot_set_nat)) (exists ((X4 tptp.nat)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X4) A4)) (forall ((Xa tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat Xa) A4)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Xa) X4)) (= X4 Xa))))))))) (forall ((A4 tptp.set_int)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A4)) (=> (not (= A4 tptp.bot_bot_set_int)) (exists ((X4 tptp.int)) (and (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X4) A4)) (forall ((Xa tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Xa) A4)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Xa) X4)) (= X4 Xa))))))))) (forall ((A4 tptp.set_real)) (=> (tptp.finite_finite_real A4) (=> (not (= A4 tptp.bot_bot_set_real)) (exists ((X4 tptp.real)) (and (tptp.member_real X4 A4) (forall ((Xa tptp.real)) (=> (tptp.member_real Xa A4) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X4) Xa)) (= X4 Xa))))))))) (forall ((A4 tptp.set_set_int)) (=> (tptp.finite6197958912794628473et_int A4) (=> (not (= A4 tptp.bot_bot_set_set_int)) (exists ((X4 tptp.set_int)) (and (tptp.member_set_int X4 A4) (forall ((Xa tptp.set_int)) (=> (tptp.member_set_int Xa A4) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int X4) Xa)) (= X4 Xa))))))))) (forall ((A4 tptp.set_rat)) (=> (tptp.finite_finite_rat A4) (=> (not (= A4 tptp.bot_bot_set_rat)) (exists ((X4 tptp.rat)) (and (tptp.member_rat X4 A4) (forall ((Xa tptp.rat)) (=> (tptp.member_rat Xa A4) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X4) Xa)) (= X4 Xa))))))))) (forall ((A4 tptp.set_num)) (=> (tptp.finite_finite_num A4) (=> (not (= A4 tptp.bot_bot_set_num)) (exists ((X4 tptp.num)) (and (tptp.member_num X4 A4) (forall ((Xa tptp.num)) (=> (tptp.member_num Xa A4) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X4) Xa)) (= X4 Xa))))))))) (forall ((A4 tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A4)) (=> (not (= A4 tptp.bot_bot_set_nat)) (exists ((X4 tptp.nat)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X4) A4)) (forall ((Xa tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat Xa) A4)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X4) Xa)) (= X4 Xa))))))))) (forall ((A4 tptp.set_int)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A4)) (=> (not (= A4 tptp.bot_bot_set_int)) (exists ((X4 tptp.int)) (and (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X4) A4)) (forall ((Xa tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Xa) A4)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X4) Xa)) (= X4 Xa))))))))) (forall ((N tptp.nat) (C tptp.complex)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex (tptp.collect_complex (tptp.aa_com1553036987509291606x_bool (tptp.aTP_Lamm_fd N) C)))))) (forall ((Mi tptp.nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (X tptp.nat) (Ma tptp.nat) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat Deg) _let_1))) (let ((_let_3 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high Mi) _let_2))) (let ((_let_4 (tptp.nth_VEBT_VEBT TreeList _let_3))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_3) (tptp.size_s6755466524823107622T_VEBT TreeList))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Mi)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat _let_1) Deg)) (=> (not (= X Ma)) (= (tptp.vEBT_vebt_insert (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Mi) Ma)) Deg TreeList Summary) X) (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat X) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat Mi) Ma))) Deg (tptp.list_u1324408373059187874T_VEBT TreeList _let_3 (tptp.vEBT_vebt_insert _let_4 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low Mi) _let_2))) (tptp.if_VEBT_VEBT (tptp.aa_VEBT_VEBT_bool tptp.vEBT_VEBT_minNull _let_4) (tptp.vEBT_vebt_insert Summary _let_3) Summary)))))))))))) (forall ((X tptp.nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Mi tptp.nat) (Ma tptp.nat) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat Deg) _let_1))) (let ((_let_3 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high X) _let_2))) (let ((_let_4 (tptp.nth_VEBT_VEBT TreeList _let_3))) (let ((_let_5 (tptp.product_Pair_nat_nat Mi))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_3) (tptp.size_s6755466524823107622T_VEBT TreeList))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Mi) X)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat _let_1) Deg)) (=> (not (= X Ma)) (= (tptp.vEBT_vebt_insert (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat _let_5 Ma)) Deg TreeList Summary) X) (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat _let_5 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat X) Ma))) Deg (tptp.list_u1324408373059187874T_VEBT TreeList _let_3 (tptp.vEBT_vebt_insert _let_4 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low X) _let_2))) (tptp.if_VEBT_VEBT (tptp.aa_VEBT_VEBT_bool tptp.vEBT_VEBT_minNull _let_4) (tptp.vEBT_vebt_insert Summary _let_3) Summary))))))))))))) (forall ((P tptp.fun_nat_fun_nat_bool) (M tptp.nat) (N tptp.nat)) (=> (forall ((M3 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool P M3) tptp.zero_zero_nat))) (=> (forall ((M3 tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool P N2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat M3) N2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool P M3) N2))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool P M) N))))) (forall ((N tptp.nat) (K tptp.int) (L tptp.int)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.aa_int_int (tptp.bit_concat_bit (tptp.aa_nat_nat tptp.suc N) K) L) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.modulo_modulo_int K) _let_1)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int _let_1) (tptp.aa_int_int (tptp.bit_concat_bit N (tptp.aa_int_int (tptp.divide_divide_int K) _let_1)) L)))))) (forall ((X tptp.set_int)) (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int X) X))) (forall ((X tptp.rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) X))) (forall ((X tptp.num)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X) X))) (forall ((X tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X) X))) (forall ((X tptp.int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X) X))) (forall ((A tptp.set_int)) (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int A) A))) (forall ((A tptp.rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) A))) (forall ((A tptp.num)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A) A))) (forall ((A tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) A))) (forall ((A tptp.int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) A))) (forall ((Xs tptp.list_VEBT_VEBT) (I tptp.nat) (X tptp.vEBT_VEBT)) (= (tptp.size_s6755466524823107622T_VEBT (tptp.list_u1324408373059187874T_VEBT Xs I X)) (tptp.size_s6755466524823107622T_VEBT Xs))) (forall ((Xs tptp.list_bool) (I tptp.nat) (X tptp.bool)) (= (tptp.size_size_list_bool (tptp.list_update_bool Xs I X)) (tptp.size_size_list_bool Xs))) (forall ((Xs tptp.list_nat) (I tptp.nat) (X tptp.nat)) (= (tptp.size_size_list_nat (tptp.list_update_nat Xs I X)) (tptp.size_size_list_nat Xs))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat (tptp.aa_nat_nat tptp.suc M)) (tptp.aa_nat_nat tptp.suc N)) (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat M) N)))) (forall ((N tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat N) tptp.zero_zero_nat) N)) (forall ((N tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat tptp.zero_zero_nat) N) N)) (forall ((A tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat A) tptp.zero_zero_nat) A)) (forall ((A tptp.nat) (B2 tptp.nat)) (= (= tptp.zero_zero_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat A) B2)) (and (= A tptp.zero_zero_nat) (= B2 tptp.zero_zero_nat)))) (forall ((A tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat tptp.zero_zero_nat) A) A)) (forall ((A tptp.nat) (B2 tptp.nat)) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat A) B2) tptp.zero_zero_nat) (and (= A tptp.zero_zero_nat) (= B2 tptp.zero_zero_nat)))) (forall ((I tptp.nat) (J tptp.nat) (Xs tptp.list_int) (X tptp.int)) (=> (not (= I J)) (= (tptp.aa_nat_int (tptp.nth_int (tptp.list_update_int Xs I X)) J) (tptp.aa_nat_int (tptp.nth_int Xs) J)))) (forall ((I tptp.nat) (J tptp.nat) (Xs tptp.list_nat) (X tptp.nat)) (=> (not (= I J)) (= (tptp.aa_nat_nat (tptp.nth_nat (tptp.list_update_nat Xs I X)) J) (tptp.aa_nat_nat (tptp.nth_nat Xs) J)))) (forall ((I tptp.nat) (J tptp.nat) (Xs tptp.list_VEBT_VEBT) (X tptp.vEBT_VEBT)) (=> (not (= I J)) (= (tptp.nth_VEBT_VEBT (tptp.list_u1324408373059187874T_VEBT Xs I X) J) (tptp.nth_VEBT_VEBT Xs J)))) (forall ((Xs tptp.list_int) (I tptp.nat)) (= (tptp.list_update_int Xs I (tptp.aa_nat_int (tptp.nth_int Xs) I)) Xs)) (forall ((Xs tptp.list_nat) (I tptp.nat)) (= (tptp.list_update_nat Xs I (tptp.aa_nat_nat (tptp.nth_nat Xs) I)) Xs)) (forall ((Xs tptp.list_VEBT_VEBT) (I tptp.nat)) (= (tptp.list_u1324408373059187874T_VEBT Xs I (tptp.nth_VEBT_VEBT Xs I)) Xs)) (forall ((K tptp.int) (L tptp.int)) (= (tptp.aa_int_int (tptp.bit_concat_bit tptp.zero_zero_nat K) L) L)) (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (tptp.numera1916890842035813515d_enat U))) (let ((_let_2 (tptp.numera1916890842035813515d_enat V))) (let ((_let_3 (tptp.aa_Ext7969882492699152700d_enat (tptp.aa_Ext3475206891998675565d_enat tptp.ord_ma741700101516333627d_enat _let_1) _let_2))) (let ((_let_4 (tptp.pp (tptp.aa_Ext2772979874139974381t_bool (tptp.ord_le2932123472753598470d_enat _let_1) _let_2)))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))) (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (tptp.aa_num_real tptp.numeral_numeral_real U))) (let ((_let_2 (tptp.aa_num_real tptp.numeral_numeral_real V))) (let ((_let_3 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.ord_max_real _let_1) _let_2))) (let ((_let_4 (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real _let_1) _let_2)))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))) (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (tptp.aa_num_rat tptp.numeral_numeral_rat U))) (let ((_let_2 (tptp.aa_num_rat tptp.numeral_numeral_rat V))) (let ((_let_3 (tptp.aa_rat_rat (tptp.ord_max_rat _let_1) _let_2))) (let ((_let_4 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat _let_1) _let_2)))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))) (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat U))) (let ((_let_2 (tptp.aa_num_nat tptp.numeral_numeral_nat V))) (let ((_let_3 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat _let_1) _let_2))) (let ((_let_4 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat _let_1) _let_2)))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))) (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int U))) (let ((_let_2 (tptp.aa_num_int tptp.numeral_numeral_int V))) (let ((_let_3 (tptp.aa_int_int (tptp.ord_max_int _let_1) _let_2))) (let ((_let_4 (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int _let_1) _let_2)))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))) (forall ((X tptp.num)) (let ((_let_1 (tptp.numera1916890842035813515d_enat X))) (= (tptp.aa_Ext7969882492699152700d_enat (tptp.aa_Ext3475206891998675565d_enat tptp.ord_ma741700101516333627d_enat _let_1) tptp.zero_z5237406670263579293d_enat) _let_1))) (forall ((X tptp.num)) (let ((_let_1 (tptp.aa_num_real tptp.numeral_numeral_real X))) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.ord_max_real _let_1) tptp.zero_zero_real) _let_1))) (forall ((X tptp.num)) (let ((_let_1 (tptp.aa_num_rat tptp.numeral_numeral_rat X))) (= (tptp.aa_rat_rat (tptp.ord_max_rat _let_1) tptp.zero_zero_rat) _let_1))) (forall ((X tptp.num)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat X))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat _let_1) tptp.zero_zero_nat) _let_1))) (forall ((X tptp.num)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int X))) (= (tptp.aa_int_int (tptp.ord_max_int _let_1) tptp.zero_zero_int) _let_1))) (forall ((X tptp.num)) (let ((_let_1 (tptp.numera1916890842035813515d_enat X))) (= (tptp.aa_Ext7969882492699152700d_enat (tptp.aa_Ext3475206891998675565d_enat tptp.ord_ma741700101516333627d_enat tptp.zero_z5237406670263579293d_enat) _let_1) _let_1))) (forall ((X tptp.num)) (let ((_let_1 (tptp.aa_num_real tptp.numeral_numeral_real X))) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.ord_max_real tptp.zero_zero_real) _let_1) _let_1))) (forall ((X tptp.num)) (let ((_let_1 (tptp.aa_num_rat tptp.numeral_numeral_rat X))) (= (tptp.aa_rat_rat (tptp.ord_max_rat tptp.zero_zero_rat) _let_1) _let_1))) (forall ((X tptp.num)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat X))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat tptp.zero_zero_nat) _let_1) _let_1))) (forall ((X tptp.num)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int X))) (= (tptp.aa_int_int (tptp.ord_max_int tptp.zero_zero_int) _let_1) _let_1))) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.ord_max_real tptp.zero_zero_real) tptp.one_one_real) tptp.one_one_real) (= (tptp.aa_rat_rat (tptp.ord_max_rat tptp.zero_zero_rat) tptp.one_one_rat) tptp.one_one_rat) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat tptp.zero_zero_nat) tptp.one_one_nat) tptp.one_one_nat) (= (tptp.aa_Ext7969882492699152700d_enat (tptp.aa_Ext3475206891998675565d_enat tptp.ord_ma741700101516333627d_enat tptp.zero_z5237406670263579293d_enat) tptp.one_on7984719198319812577d_enat) tptp.one_on7984719198319812577d_enat) (= (tptp.aa_int_int (tptp.ord_max_int tptp.zero_zero_int) tptp.one_one_int) tptp.one_one_int) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.ord_max_real tptp.one_one_real) tptp.zero_zero_real) tptp.one_one_real) (= (tptp.aa_rat_rat (tptp.ord_max_rat tptp.one_one_rat) tptp.zero_zero_rat) tptp.one_one_rat) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat tptp.one_one_nat) tptp.zero_zero_nat) tptp.one_one_nat) (= (tptp.aa_Ext7969882492699152700d_enat (tptp.aa_Ext3475206891998675565d_enat tptp.ord_ma741700101516333627d_enat tptp.one_on7984719198319812577d_enat) tptp.zero_z5237406670263579293d_enat) tptp.one_on7984719198319812577d_enat) (= (tptp.aa_int_int (tptp.ord_max_int tptp.one_one_int) tptp.zero_zero_int) tptp.one_one_int) (forall ((X tptp.num)) (let ((_let_1 (tptp.numera1916890842035813515d_enat X))) (= (tptp.aa_Ext7969882492699152700d_enat (tptp.aa_Ext3475206891998675565d_enat tptp.ord_ma741700101516333627d_enat _let_1) tptp.one_on7984719198319812577d_enat) _let_1))) (forall ((X tptp.num)) (let ((_let_1 (tptp.aa_num_real tptp.numeral_numeral_real X))) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.ord_max_real _let_1) tptp.one_one_real) _let_1))) (forall ((X tptp.num)) (let ((_let_1 (tptp.aa_num_rat tptp.numeral_numeral_rat X))) (= (tptp.aa_rat_rat (tptp.ord_max_rat _let_1) tptp.one_one_rat) _let_1))) (forall ((X tptp.num)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat X))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat _let_1) tptp.one_one_nat) _let_1))) (forall ((X tptp.num)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int X))) (= (tptp.aa_int_int (tptp.ord_max_int _let_1) tptp.one_one_int) _let_1))) (forall ((X tptp.num)) (let ((_let_1 (tptp.numera1916890842035813515d_enat X))) (= (tptp.aa_Ext7969882492699152700d_enat (tptp.aa_Ext3475206891998675565d_enat tptp.ord_ma741700101516333627d_enat tptp.one_on7984719198319812577d_enat) _let_1) _let_1))) (forall ((X tptp.num)) (let ((_let_1 (tptp.aa_num_real tptp.numeral_numeral_real X))) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.ord_max_real tptp.one_one_real) _let_1) _let_1))) (forall ((X tptp.num)) (let ((_let_1 (tptp.aa_num_rat tptp.numeral_numeral_rat X))) (= (tptp.aa_rat_rat (tptp.ord_max_rat tptp.one_one_rat) _let_1) _let_1))) (forall ((X tptp.num)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat X))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat tptp.one_one_nat) _let_1) _let_1))) (forall ((X tptp.num)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int X))) (= (tptp.aa_int_int (tptp.ord_max_int tptp.one_one_int) _let_1) _let_1))) (forall ((Xs tptp.list_VEBT_VEBT) (I tptp.nat) (X tptp.vEBT_VEBT)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.size_s6755466524823107622T_VEBT Xs)) I)) (= (tptp.list_u1324408373059187874T_VEBT Xs I X) Xs))) (forall ((Xs tptp.list_bool) (I tptp.nat) (X tptp.bool)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.size_size_list_bool Xs)) I)) (= (tptp.list_update_bool Xs I X) Xs))) (forall ((Xs tptp.list_nat) (I tptp.nat) (X tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.size_size_list_nat Xs)) I)) (= (tptp.list_update_nat Xs I X) Xs))) (forall ((N tptp.nat) (K tptp.int) (L tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.bit_concat_bit N K) L))) (tptp.pp (tptp.aa_int_bool _let_1 L))))) (forall ((N tptp.nat) (K tptp.int) (L tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.bit_concat_bit N K) L)) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int L) tptp.zero_zero_int)))) (forall ((I tptp.nat) (Xs tptp.list_int) (X tptp.int)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I) (tptp.size_size_list_int Xs))) (= (tptp.aa_nat_int (tptp.nth_int (tptp.list_update_int Xs I X)) I) X))) (forall ((I tptp.nat) (Xs tptp.list_VEBT_VEBT) (X tptp.vEBT_VEBT)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I) (tptp.size_s6755466524823107622T_VEBT Xs))) (= (tptp.nth_VEBT_VEBT (tptp.list_u1324408373059187874T_VEBT Xs I X) I) X))) (forall ((I tptp.nat) (Xs tptp.list_bool) (X tptp.bool)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I) (tptp.size_size_list_bool Xs))) (= (tptp.pp (tptp.aa_nat_bool (tptp.nth_bool (tptp.list_update_bool Xs I X)) I)) (tptp.pp X)))) (forall ((I tptp.nat) (Xs tptp.list_nat) (X tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I) (tptp.size_size_list_nat Xs))) (= (tptp.aa_nat_nat (tptp.nth_nat (tptp.list_update_nat Xs I X)) I) X))) (forall ((I tptp.nat) (Xs tptp.list_int) (J tptp.nat)) (let ((_let_1 (tptp.nth_int Xs))) (let ((_let_2 (tptp.size_size_list_int Xs))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I) _let_2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat J) _let_2)) (= (tptp.set_int2 (tptp.list_update_int (tptp.list_update_int Xs I (tptp.aa_nat_int _let_1 J)) J (tptp.aa_nat_int _let_1 I))) (tptp.set_int2 Xs))))))) (forall ((I tptp.nat) (Xs tptp.list_VEBT_VEBT) (J tptp.nat)) (let ((_let_1 (tptp.size_s6755466524823107622T_VEBT Xs))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I) _let_1)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat J) _let_1)) (= (tptp.set_VEBT_VEBT2 (tptp.list_u1324408373059187874T_VEBT (tptp.list_u1324408373059187874T_VEBT Xs I (tptp.nth_VEBT_VEBT Xs J)) J (tptp.nth_VEBT_VEBT Xs I))) (tptp.set_VEBT_VEBT2 Xs)))))) (forall ((I tptp.nat) (Xs tptp.list_bool) (J tptp.nat)) (let ((_let_1 (tptp.nth_bool Xs))) (let ((_let_2 (tptp.size_size_list_bool Xs))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I) _let_2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat J) _let_2)) (= (tptp.set_bool2 (tptp.list_update_bool (tptp.list_update_bool Xs I (tptp.aa_nat_bool _let_1 J)) J (tptp.aa_nat_bool _let_1 I))) (tptp.set_bool2 Xs))))))) (forall ((I tptp.nat) (Xs tptp.list_nat) (J tptp.nat)) (let ((_let_1 (tptp.nth_nat Xs))) (let ((_let_2 (tptp.size_size_list_nat Xs))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I) _let_2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat J) _let_2)) (= (tptp.set_nat2 (tptp.list_update_nat (tptp.list_update_nat Xs I (tptp.aa_nat_nat _let_1 J)) J (tptp.aa_nat_nat _let_1 I))) (tptp.set_nat2 Xs))))))) (forall ((A tptp.extended_enat) (B2 tptp.extended_enat)) (let ((_let_1 (tptp.aa_Ext7969882492699152700d_enat (tptp.aa_Ext3475206891998675565d_enat tptp.ord_ma741700101516333627d_enat A) B2))) (let ((_let_2 (tptp.pp (tptp.aa_Ext2772979874139974381t_bool (tptp.ord_le2932123472753598470d_enat A) B2)))) (and (=> _let_2 (= _let_1 B2)) (=> (not _let_2) (= _let_1 A)))))) (forall ((A tptp.set_int) (B2 tptp.set_int)) (let ((_let_1 (tptp.ord_max_set_int A B2))) (let ((_let_2 (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int A) B2)))) (and (=> _let_2 (= _let_1 B2)) (=> (not _let_2) (= _let_1 A)))))) (forall ((A tptp.rat) (B2 tptp.rat)) (let ((_let_1 (tptp.aa_rat_rat (tptp.ord_max_rat A) B2))) (let ((_let_2 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B2)))) (and (=> _let_2 (= _let_1 B2)) (=> (not _let_2) (= _let_1 A)))))) (forall ((A tptp.num) (B2 tptp.num)) (let ((_let_1 (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.ord_max_num A) B2))) (let ((_let_2 (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A) B2)))) (and (=> _let_2 (= _let_1 B2)) (=> (not _let_2) (= _let_1 A)))))) (forall ((A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat A) B2))) (let ((_let_2 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B2)))) (and (=> _let_2 (= _let_1 B2)) (=> (not _let_2) (= _let_1 A)))))) (forall ((A tptp.int) (B2 tptp.int)) (let ((_let_1 (tptp.aa_int_int (tptp.ord_max_int A) B2))) (let ((_let_2 (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B2)))) (and (=> _let_2 (= _let_1 B2)) (=> (not _let_2) (= _let_1 A)))))) (forall ((Y tptp.extended_enat) (X tptp.extended_enat)) (=> (tptp.pp (tptp.aa_Ext2772979874139974381t_bool (tptp.ord_le2932123472753598470d_enat Y) X)) (= (tptp.aa_Ext7969882492699152700d_enat (tptp.aa_Ext3475206891998675565d_enat tptp.ord_ma741700101516333627d_enat X) Y) X))) (forall ((Y tptp.set_int) (X tptp.set_int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int Y) X)) (= (tptp.ord_max_set_int X Y) X))) (forall ((Y tptp.rat) (X tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat Y) X)) (= (tptp.aa_rat_rat (tptp.ord_max_rat X) Y) X))) (forall ((Y tptp.num) (X tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num Y) X)) (= (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.ord_max_num X) Y) X))) (forall ((Y tptp.nat) (X tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Y) X)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat X) Y) X))) (forall ((Y tptp.int) (X tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Y) X)) (= (tptp.aa_int_int (tptp.ord_max_int X) Y) X))) (forall ((X tptp.extended_enat) (Y tptp.extended_enat)) (=> (tptp.pp (tptp.aa_Ext2772979874139974381t_bool (tptp.ord_le2932123472753598470d_enat X) Y)) (= (tptp.aa_Ext7969882492699152700d_enat (tptp.aa_Ext3475206891998675565d_enat tptp.ord_ma741700101516333627d_enat X) Y) Y))) (forall ((X tptp.set_int) (Y tptp.set_int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int X) Y)) (= (tptp.ord_max_set_int X Y) Y))) (forall ((X tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) Y)) (= (tptp.aa_rat_rat (tptp.ord_max_rat X) Y) Y))) (forall ((X tptp.num) (Y tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X) Y)) (= (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.ord_max_num X) Y) Y))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X) Y)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat X) Y) Y))) (forall ((X tptp.int) (Y tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X) Y)) (= (tptp.aa_int_int (tptp.ord_max_int X) Y) Y))) (forall ((X tptp.real) (Y tptp.real) (Z tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.ord_max_real X) Y)) Z) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.ord_max_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) Z)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real Y) Z)))) (forall ((X tptp.rat) (Y tptp.rat) (Z tptp.rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.ord_max_rat X) Y)) Z) (tptp.aa_rat_rat (tptp.ord_max_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat X) Z)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat Y) Z)))) (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat X) Y)) Z) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat X) Z)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Y) Z)))) (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.ord_max_int X) Y)) Z) (tptp.aa_int_int (tptp.ord_max_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int X) Z)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int Y) Z)))) (forall ((X tptp.real) (Y tptp.real) (Z tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X))) (= (tptp.aa_real_real _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.ord_max_real Y) Z)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.ord_max_real (tptp.aa_real_real _let_1 Y)) (tptp.aa_real_real _let_1 Z))))) (forall ((X tptp.rat) (Y tptp.rat) (Z tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat X))) (= (tptp.aa_rat_rat _let_1 (tptp.aa_rat_rat (tptp.ord_max_rat Y) Z)) (tptp.aa_rat_rat (tptp.ord_max_rat (tptp.aa_rat_rat _let_1 Y)) (tptp.aa_rat_rat _let_1 Z))))) (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat X))) (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat Y) Z)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat (tptp.aa_nat_nat _let_1 Y)) (tptp.aa_nat_nat _let_1 Z))))) (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.plus_plus_int X))) (= (tptp.aa_int_int _let_1 (tptp.aa_int_int (tptp.ord_max_int Y) Z)) (tptp.aa_int_int (tptp.ord_max_int (tptp.aa_int_int _let_1 Y)) (tptp.aa_int_int _let_1 Z))))) (forall ((X tptp.real) (Y tptp.real) (Z tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.ord_max_real X) Y)) Z) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.ord_max_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real X) Z)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real Y) Z)))) (forall ((X tptp.rat) (Y tptp.rat) (Z tptp.rat)) (= (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_rat_rat (tptp.ord_max_rat X) Y)) Z) (tptp.aa_rat_rat (tptp.ord_max_rat (tptp.aa_rat_rat (tptp.minus_minus_rat X) Z)) (tptp.aa_rat_rat (tptp.minus_minus_rat Y) Z)))) (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_int_int (tptp.ord_max_int X) Y)) Z) (tptp.aa_int_int (tptp.ord_max_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int X) Z)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int Y) Z)))) (forall ((M tptp.nat) (N tptp.nat) (Q2 tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat M) N)) Q2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) Q2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N) Q2)))) (forall ((M tptp.nat) (N tptp.nat) (Q2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M))) (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat N) Q2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat (tptp.aa_nat_nat _let_1 N)) (tptp.aa_nat_nat _let_1 Q2))))) (forall ((M tptp.nat) (N tptp.nat) (Q2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat M))) (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat N) Q2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat (tptp.aa_nat_nat _let_1 N)) (tptp.aa_nat_nat _let_1 Q2))))) (forall ((M tptp.nat) (N tptp.nat) (Q2 tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat M) N)) Q2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat M) Q2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat N) Q2)))) (forall ((X5 tptp.extended_enat) (Xa tptp.extended_enat)) (let ((_let_1 (tptp.aa_Ext7969882492699152700d_enat (tptp.aa_Ext3475206891998675565d_enat tptp.ord_ma741700101516333627d_enat X5) Xa))) (let ((_let_2 (tptp.pp (tptp.aa_Ext2772979874139974381t_bool (tptp.ord_le2932123472753598470d_enat X5) Xa)))) (and (=> _let_2 (= _let_1 Xa)) (=> (not _let_2) (= _let_1 X5)))))) (forall ((X5 tptp.set_int) (Xa tptp.set_int)) (let ((_let_1 (tptp.ord_max_set_int X5 Xa))) (let ((_let_2 (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int X5) Xa)))) (and (=> _let_2 (= _let_1 Xa)) (=> (not _let_2) (= _let_1 X5)))))) (forall ((X5 tptp.rat) (Xa tptp.rat)) (let ((_let_1 (tptp.aa_rat_rat (tptp.ord_max_rat X5) Xa))) (let ((_let_2 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X5) Xa)))) (and (=> _let_2 (= _let_1 Xa)) (=> (not _let_2) (= _let_1 X5)))))) (forall ((X5 tptp.num) (Xa tptp.num)) (let ((_let_1 (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.ord_max_num X5) Xa))) (let ((_let_2 (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X5) Xa)))) (and (=> _let_2 (= _let_1 Xa)) (=> (not _let_2) (= _let_1 X5)))))) (forall ((X5 tptp.nat) (Xa tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat X5) Xa))) (let ((_let_2 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X5) Xa)))) (and (=> _let_2 (= _let_1 Xa)) (=> (not _let_2) (= _let_1 X5)))))) (forall ((X5 tptp.int) (Xa tptp.int)) (let ((_let_1 (tptp.aa_int_int (tptp.ord_max_int X5) Xa))) (let ((_let_2 (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X5) Xa)))) (and (=> _let_2 (= _let_1 Xa)) (=> (not _let_2) (= _let_1 X5)))))) (forall ((N tptp.nat) (K tptp.int) (M tptp.nat) (L tptp.int) (R tptp.int)) (let ((_let_1 (tptp.bit_concat_bit N K))) (= (tptp.aa_int_int _let_1 (tptp.aa_int_int (tptp.bit_concat_bit M L) R)) (tptp.aa_int_int (tptp.bit_concat_bit (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) N) (tptp.aa_int_int _let_1 L)) R)))) (forall ((N tptp.nat) (M tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) M)) M) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat N) M))) (forall ((Xs tptp.list_real) (A4 tptp.set_real) (X tptp.real) (I tptp.nat)) (=> (tptp.ord_less_eq_set_real (tptp.set_real2 Xs) A4) (=> (tptp.member_real X A4) (tptp.ord_less_eq_set_real (tptp.set_real2 (tptp.list_update_real Xs I X)) A4)))) (forall ((Xs tptp.list_complex) (A4 tptp.set_complex) (X tptp.complex) (I tptp.nat)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.ord_le211207098394363844omplex (tptp.set_complex2 Xs)) A4)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex X) A4)) (tptp.pp (tptp.aa_set_complex_bool (tptp.ord_le211207098394363844omplex (tptp.set_complex2 (tptp.list_update_complex Xs I X))) A4))))) (forall ((Xs tptp.list_nat) (A4 tptp.set_nat) (X tptp.nat) (I tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat (tptp.set_nat2 Xs)) A4)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X) A4)) (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat (tptp.set_nat2 (tptp.list_update_nat Xs I X))) A4))))) (forall ((Xs tptp.list_VEBT_VEBT) (A4 tptp.set_VEBT_VEBT) (X tptp.vEBT_VEBT) (I tptp.nat)) (=> (tptp.ord_le4337996190870823476T_VEBT (tptp.set_VEBT_VEBT2 Xs) A4) (=> (tptp.pp (tptp.aa_set8260762808118238015T_bool (tptp.aa_VEB289770264548726718T_bool tptp.member_VEBT_VEBT X) A4)) (tptp.ord_le4337996190870823476T_VEBT (tptp.set_VEBT_VEBT2 (tptp.list_u1324408373059187874T_VEBT Xs I X)) A4)))) (forall ((Xs tptp.list_int) (A4 tptp.set_int) (X tptp.int) (I tptp.nat)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int (tptp.set_int2 Xs)) A4)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X) A4)) (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int (tptp.set_int2 (tptp.list_update_int Xs I X))) A4))))) (forall ((N tptp.nat) (Xs tptp.list_real) (X tptp.real)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N) (tptp.size_size_list_real Xs))) (tptp.member_real X (tptp.set_real2 (tptp.list_update_real Xs N X))))) (forall ((N tptp.nat) (Xs tptp.list_complex) (X tptp.complex)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N) (tptp.size_s3451745648224563538omplex Xs))) (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex X) (tptp.set_complex2 (tptp.list_update_complex Xs N X)))))) (forall ((N tptp.nat) (Xs tptp.list_int) (X tptp.int)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N) (tptp.size_size_list_int Xs))) (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X) (tptp.set_int2 (tptp.list_update_int Xs N X)))))) (forall ((N tptp.nat) (Xs tptp.list_VEBT_VEBT) (X tptp.vEBT_VEBT)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N) (tptp.size_s6755466524823107622T_VEBT Xs))) (tptp.pp (tptp.aa_set8260762808118238015T_bool (tptp.aa_VEB289770264548726718T_bool tptp.member_VEBT_VEBT X) (tptp.set_VEBT_VEBT2 (tptp.list_u1324408373059187874T_VEBT Xs N X)))))) (forall ((N tptp.nat) (Xs tptp.list_bool) (X tptp.bool)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N) (tptp.size_size_list_bool Xs))) (tptp.member_bool X (tptp.set_bool2 (tptp.list_update_bool Xs N X))))) (forall ((N tptp.nat) (Xs tptp.list_nat) (X tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N) (tptp.size_size_list_nat Xs))) (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X) (tptp.set_nat2 (tptp.list_update_nat Xs N X)))))) (forall ((A tptp.rat) (B2 tptp.rat)) (= (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B2))) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B2) A)) (not (= B2 A))))) (forall ((A tptp.num) (B2 tptp.num)) (= (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A) B2))) (and (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num B2) A)) (not (= B2 A))))) (forall ((A tptp.nat) (B2 tptp.nat)) (= (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B2))) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B2) A)) (not (= B2 A))))) (forall ((A tptp.int) (B2 tptp.int)) (= (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B2))) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B2) A)) (not (= B2 A))))) (forall ((X tptp.rat) (Y tptp.rat) (Z tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X))) (let ((_let_2 (tptp.pp (tptp.aa_rat_bool _let_1 Y)))) (let ((_let_3 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat Z))) (let ((_let_4 (tptp.pp (tptp.aa_rat_bool _let_3 X)))) (let ((_let_5 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat Y))) (let ((_let_6 (tptp.pp (tptp.aa_rat_bool _let_5 Z)))) (let ((_let_7 (tptp.pp (tptp.aa_rat_bool _let_5 X)))) (let ((_let_8 (tptp.pp (tptp.aa_rat_bool _let_3 Y)))) (let ((_let_9 (tptp.pp (tptp.aa_rat_bool _let_1 Z)))) (=> (=> _let_2 (not _let_6)) (=> (=> _let_7 (not _let_9)) (=> (=> _let_9 (not _let_8)) (=> (=> _let_8 (not _let_7)) (=> (=> _let_6 (not _let_4)) (not (=> _let_4 (not _let_2)))))))))))))))))) (forall ((X tptp.num) (Y tptp.num) (Z tptp.num)) (let ((_let_1 (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X))) (let ((_let_2 (tptp.pp (tptp.aa_num_bool _let_1 Y)))) (let ((_let_3 (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num Z))) (let ((_let_4 (tptp.pp (tptp.aa_num_bool _let_3 X)))) (let ((_let_5 (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num Y))) (let ((_let_6 (tptp.pp (tptp.aa_num_bool _let_5 Z)))) (let ((_let_7 (tptp.pp (tptp.aa_num_bool _let_5 X)))) (let ((_let_8 (tptp.pp (tptp.aa_num_bool _let_3 Y)))) (let ((_let_9 (tptp.pp (tptp.aa_num_bool _let_1 Z)))) (=> (=> _let_2 (not _let_6)) (=> (=> _let_7 (not _let_9)) (=> (=> _let_9 (not _let_8)) (=> (=> _let_8 (not _let_7)) (=> (=> _let_6 (not _let_4)) (not (=> _let_4 (not _let_2)))))))))))))))))) (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X))) (let ((_let_2 (tptp.pp (tptp.aa_nat_bool _let_1 Y)))) (let ((_let_3 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Z))) (let ((_let_4 (tptp.pp (tptp.aa_nat_bool _let_3 X)))) (let ((_let_5 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Y))) (let ((_let_6 (tptp.pp (tptp.aa_nat_bool _let_5 Z)))) (let ((_let_7 (tptp.pp (tptp.aa_nat_bool _let_5 X)))) (let ((_let_8 (tptp.pp (tptp.aa_nat_bool _let_3 Y)))) (let ((_let_9 (tptp.pp (tptp.aa_nat_bool _let_1 Z)))) (=> (=> _let_2 (not _let_6)) (=> (=> _let_7 (not _let_9)) (=> (=> _let_9 (not _let_8)) (=> (=> _let_8 (not _let_7)) (=> (=> _let_6 (not _let_4)) (not (=> _let_4 (not _let_2)))))))))))))))))) (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X))) (let ((_let_2 (tptp.pp (tptp.aa_int_bool _let_1 Y)))) (let ((_let_3 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Z))) (let ((_let_4 (tptp.pp (tptp.aa_int_bool _let_3 X)))) (let ((_let_5 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Y))) (let ((_let_6 (tptp.pp (tptp.aa_int_bool _let_5 Z)))) (let ((_let_7 (tptp.pp (tptp.aa_int_bool _let_5 X)))) (let ((_let_8 (tptp.pp (tptp.aa_int_bool _let_3 Y)))) (let ((_let_9 (tptp.pp (tptp.aa_int_bool _let_1 Z)))) (=> (=> _let_2 (not _let_6)) (=> (=> _let_7 (not _let_9)) (=> (=> _let_9 (not _let_8)) (=> (=> _let_8 (not _let_7)) (=> (=> _let_6 (not _let_4)) (not (=> _let_4 (not _let_2)))))))))))))))))) (forall ((X tptp.set_int) (Y tptp.set_int)) (= (= X Y) (and (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int X) Y)) (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int Y) X))))) (forall ((X tptp.rat) (Y tptp.rat)) (= (= X Y) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) Y)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat Y) X))))) (forall ((X tptp.num) (Y tptp.num)) (= (= X Y) (and (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X) Y)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num Y) X))))) (forall ((X tptp.nat) (Y tptp.nat)) (= (= X Y) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X) Y)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Y) X))))) (forall ((X tptp.int) (Y tptp.int)) (= (= X Y) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X) Y)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Y) X))))) (forall ((A tptp.set_int) (B2 tptp.set_int) (C tptp.set_int)) (=> (= A B2) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int B2) C)) (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int A) C))))) (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat)) (=> (= A B2) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B2) C)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) C))))) (forall ((A tptp.num) (B2 tptp.num) (C tptp.num)) (=> (= A B2) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num B2) C)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A) C))))) (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (=> (= A B2) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B2) C)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) C))))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (=> (= A B2) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B2) C)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) C))))) (forall ((A tptp.set_int) (B2 tptp.set_int) (C tptp.set_int)) (let ((_let_1 (tptp.ord_less_eq_set_int A))) (=> (tptp.pp (tptp.aa_set_int_bool _let_1 B2)) (=> (= B2 C) (tptp.pp (tptp.aa_set_int_bool _let_1 C)))))) (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 B2)) (=> (= B2 C) (tptp.pp (tptp.aa_rat_bool _let_1 C)))))) (forall ((A tptp.num) (B2 tptp.num) (C tptp.num)) (let ((_let_1 (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A))) (=> (tptp.pp (tptp.aa_num_bool _let_1 B2)) (=> (= B2 C) (tptp.pp (tptp.aa_num_bool _let_1 C)))))) (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 B2)) (=> (= B2 C) (tptp.pp (tptp.aa_nat_bool _let_1 C)))))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A))) (=> (tptp.pp (tptp.aa_int_bool _let_1 B2)) (=> (= B2 C) (tptp.pp (tptp.aa_int_bool _let_1 C)))))) (forall ((X tptp.set_int) (Y tptp.set_int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int X) Y)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int Y) X)) (= X Y)))) (forall ((X tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) Y)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat Y) X)) (= X Y)))) (forall ((X tptp.num) (Y tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X) Y)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num Y) X)) (= X Y)))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X) Y)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Y) X)) (= X Y)))) (forall ((X tptp.int) (Y tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X) Y)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Y) X)) (= X Y)))) (forall ((A tptp.set_int) (B2 tptp.set_int) (C tptp.set_int)) (let ((_let_1 (tptp.ord_less_eq_set_int A))) (=> (tptp.pp (tptp.aa_set_int_bool _let_1 B2)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int B2) C)) (tptp.pp (tptp.aa_set_int_bool _let_1 C)))))) (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 B2)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B2) C)) (tptp.pp (tptp.aa_rat_bool _let_1 C)))))) (forall ((A tptp.num) (B2 tptp.num) (C tptp.num)) (let ((_let_1 (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A))) (=> (tptp.pp (tptp.aa_num_bool _let_1 B2)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num B2) C)) (tptp.pp (tptp.aa_num_bool _let_1 C)))))) (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 B2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B2) C)) (tptp.pp (tptp.aa_nat_bool _let_1 C)))))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A))) (=> (tptp.pp (tptp.aa_int_bool _let_1 B2)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B2) C)) (tptp.pp (tptp.aa_int_bool _let_1 C)))))) (forall ((X tptp.set_int) (Y tptp.set_int) (Z tptp.set_int)) (let ((_let_1 (tptp.ord_less_eq_set_int X))) (=> (tptp.pp (tptp.aa_set_int_bool _let_1 Y)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int Y) Z)) (tptp.pp (tptp.aa_set_int_bool _let_1 Z)))))) (forall ((X tptp.rat) (Y tptp.rat) (Z tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 Y)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat Y) Z)) (tptp.pp (tptp.aa_rat_bool _let_1 Z)))))) (forall ((X tptp.num) (Y tptp.num) (Z tptp.num)) (let ((_let_1 (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X))) (=> (tptp.pp (tptp.aa_num_bool _let_1 Y)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num Y) Z)) (tptp.pp (tptp.aa_num_bool _let_1 Z)))))) (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 Y)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Y) Z)) (tptp.pp (tptp.aa_nat_bool _let_1 Z)))))) (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X))) (=> (tptp.pp (tptp.aa_int_bool _let_1 Y)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Y) Z)) (tptp.pp (tptp.aa_int_bool _let_1 Z)))))) (forall ((P tptp.fun_rat_fun_rat_bool) (A tptp.rat) (B2 tptp.rat)) (=> (forall ((A3 tptp.rat) (B3 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A3) B3)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool P A3) B3)))) (=> (forall ((A3 tptp.rat) (B3 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool P B3) A3)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool P A3) B3)))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool P A) B2))))) (forall ((P tptp.fun_num_fun_num_bool) (A tptp.num) (B2 tptp.num)) (=> (forall ((A3 tptp.num) (B3 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A3) B3)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool P A3) B3)))) (=> (forall ((A3 tptp.num) (B3 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool P B3) A3)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool P A3) B3)))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool P A) B2))))) (forall ((P tptp.fun_nat_fun_nat_bool) (A tptp.nat) (B2 tptp.nat)) (=> (forall ((A3 tptp.nat) (B3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A3) B3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool P A3) B3)))) (=> (forall ((A3 tptp.nat) (B3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool P B3) A3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool P A3) B3)))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool P A) B2))))) (forall ((P tptp.fun_int_fun_int_bool) (A tptp.int) (B2 tptp.int)) (=> (forall ((A3 tptp.int) (B3 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A3) B3)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool P A3) B3)))) (=> (forall ((A3 tptp.int) (B3 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool P B3) A3)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool P A3) B3)))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool P A) B2))))) (forall ((A tptp.set_int) (B2 tptp.set_int)) (= (= A B2) (and (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int B2) A)) (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int A) B2))))) (forall ((A tptp.rat) (B2 tptp.rat)) (= (= A B2) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B2) A)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B2))))) (forall ((A tptp.num) (B2 tptp.num)) (= (= A B2) (and (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num B2) A)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A) B2))))) (forall ((A tptp.nat) (B2 tptp.nat)) (= (= A B2) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B2) A)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B2))))) (forall ((A tptp.int) (B2 tptp.int)) (= (= A B2) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B2) A)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B2))))) (forall ((B2 tptp.set_int) (A tptp.set_int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int B2) A)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int A) B2)) (= A B2)))) (forall ((B2 tptp.rat) (A tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B2) A)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B2)) (= A B2)))) (forall ((B2 tptp.num) (A tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num B2) A)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A) B2)) (= A B2)))) (forall ((B2 tptp.nat) (A tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B2) A)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B2)) (= A B2)))) (forall ((B2 tptp.int) (A tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B2) A)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B2)) (= A B2)))) (forall ((B2 tptp.set_int) (A tptp.set_int) (C tptp.set_int)) (let ((_let_1 (tptp.ord_less_eq_set_int C))) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int B2) A)) (=> (tptp.pp (tptp.aa_set_int_bool _let_1 B2)) (tptp.pp (tptp.aa_set_int_bool _let_1 A)))))) (forall ((B2 tptp.rat) (A tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat C))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B2) A)) (=> (tptp.pp (tptp.aa_rat_bool _let_1 B2)) (tptp.pp (tptp.aa_rat_bool _let_1 A)))))) (forall ((B2 tptp.num) (A tptp.num) (C tptp.num)) (let ((_let_1 (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num C))) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num B2) A)) (=> (tptp.pp (tptp.aa_num_bool _let_1 B2)) (tptp.pp (tptp.aa_num_bool _let_1 A)))))) (forall ((B2 tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat C))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B2) A)) (=> (tptp.pp (tptp.aa_nat_bool _let_1 B2)) (tptp.pp (tptp.aa_nat_bool _let_1 A)))))) (forall ((B2 tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int C))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B2) A)) (=> (tptp.pp (tptp.aa_int_bool _let_1 B2)) (tptp.pp (tptp.aa_int_bool _let_1 A)))))) (forall ((A tptp.set_int) (B2 tptp.set_int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int A) B2)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int B2) A)) (= A B2)))) (forall ((A tptp.rat) (B2 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B2)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B2) A)) (= A B2)))) (forall ((A tptp.num) (B2 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A) B2)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num B2) A)) (= A B2)))) (forall ((A tptp.nat) (B2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B2) A)) (= A B2)))) (forall ((A tptp.int) (B2 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B2)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B2) A)) (= A B2)))) (forall ((A tptp.set_int) (B2 tptp.set_int)) (= (= A B2) (and (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int A) B2)) (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int B2) A))))) (forall ((A tptp.rat) (B2 tptp.rat)) (= (= A B2) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B2)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B2) A))))) (forall ((A tptp.num) (B2 tptp.num)) (= (= A B2) (and (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A) B2)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num B2) A))))) (forall ((A tptp.nat) (B2 tptp.nat)) (= (= A B2) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B2) A))))) (forall ((A tptp.int) (B2 tptp.int)) (= (= A B2) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B2)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B2) A))))) (forall ((A tptp.rat) (F tptp.fun_rat_rat) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat F B2))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B2) C)) (=> (forall ((X4 tptp.rat) (Y4 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X4) Y4)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat F X4)) (tptp.aa_rat_rat F Y4))))) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat F C)))))))) (forall ((A tptp.rat) (F tptp.fun_num_rat) (B2 tptp.num) (C tptp.num)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_num_rat F B2))) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num B2) C)) (=> (forall ((X4 tptp.num) (Y4 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X4) Y4)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_num_rat F X4)) (tptp.aa_num_rat F Y4))))) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_num_rat F C)))))))) (forall ((A tptp.rat) (F tptp.fun_nat_rat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_nat_rat F B2))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B2) C)) (=> (forall ((X4 tptp.nat) (Y4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X4) Y4)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat F X4)) (tptp.aa_nat_rat F Y4))))) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_nat_rat F C)))))))) (forall ((A tptp.rat) (F tptp.fun_int_rat) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_int_rat F B2))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B2) C)) (=> (forall ((X4 tptp.int) (Y4 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X4) Y4)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_int_rat F X4)) (tptp.aa_int_rat F Y4))))) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_int_rat F C)))))))) (forall ((A tptp.num) (F tptp.fun_rat_num) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A))) (=> (tptp.pp (tptp.aa_num_bool _let_1 (tptp.aa_rat_num F B2))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B2) C)) (=> (forall ((X4 tptp.rat) (Y4 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X4) Y4)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_rat_num F X4)) (tptp.aa_rat_num F Y4))))) (tptp.pp (tptp.aa_num_bool _let_1 (tptp.aa_rat_num F C)))))))) (forall ((A tptp.num) (F tptp.fun_num_num) (B2 tptp.num) (C tptp.num)) (let ((_let_1 (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A))) (=> (tptp.pp (tptp.aa_num_bool _let_1 (tptp.aa_num_num F B2))) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num B2) C)) (=> (forall ((X4 tptp.num) (Y4 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X4) Y4)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_num_num F X4)) (tptp.aa_num_num F Y4))))) (tptp.pp (tptp.aa_num_bool _let_1 (tptp.aa_num_num F C)))))))) (forall ((A tptp.num) (F tptp.fun_nat_num) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A))) (=> (tptp.pp (tptp.aa_num_bool _let_1 (tptp.aa_nat_num F B2))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B2) C)) (=> (forall ((X4 tptp.nat) (Y4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X4) Y4)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_nat_num F X4)) (tptp.aa_nat_num F Y4))))) (tptp.pp (tptp.aa_num_bool _let_1 (tptp.aa_nat_num F C)))))))) (forall ((A tptp.num) (F tptp.fun_int_num) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A))) (=> (tptp.pp (tptp.aa_num_bool _let_1 (tptp.aa_int_num F B2))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B2) C)) (=> (forall ((X4 tptp.int) (Y4 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X4) Y4)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_int_num F X4)) (tptp.aa_int_num F Y4))))) (tptp.pp (tptp.aa_num_bool _let_1 (tptp.aa_int_num F C)))))))) (forall ((A tptp.nat) (F tptp.fun_rat_nat) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_rat_nat F B2))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B2) C)) (=> (forall ((X4 tptp.rat) (Y4 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X4) Y4)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_rat_nat F X4)) (tptp.aa_rat_nat F Y4))))) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_rat_nat F C)))))))) (forall ((A tptp.nat) (F tptp.fun_num_nat) (B2 tptp.num) (C tptp.num)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_num_nat F B2))) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num B2) C)) (=> (forall ((X4 tptp.num) (Y4 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X4) Y4)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_num_nat F X4)) (tptp.aa_num_nat F Y4))))) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_num_nat F C)))))))) (forall ((A tptp.rat) (B2 tptp.rat) (F tptp.fun_rat_rat) (C tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B2)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat F B2)) C)) (=> (forall ((X4 tptp.rat) (Y4 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X4) Y4)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat F X4)) (tptp.aa_rat_rat F Y4))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat F A)) C)))))) (forall ((A tptp.rat) (B2 tptp.rat) (F tptp.fun_rat_num) (C tptp.num)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B2)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_rat_num F B2)) C)) (=> (forall ((X4 tptp.rat) (Y4 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X4) Y4)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_rat_num F X4)) (tptp.aa_rat_num F Y4))))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_rat_num F A)) C)))))) (forall ((A tptp.rat) (B2 tptp.rat) (F tptp.fun_rat_nat) (C tptp.nat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_rat_nat F B2)) C)) (=> (forall ((X4 tptp.rat) (Y4 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X4) Y4)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_rat_nat F X4)) (tptp.aa_rat_nat F Y4))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_rat_nat F A)) C)))))) (forall ((A tptp.rat) (B2 tptp.rat) (F tptp.fun_rat_int) (C tptp.int)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B2)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_rat_int F B2)) C)) (=> (forall ((X4 tptp.rat) (Y4 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X4) Y4)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_rat_int F X4)) (tptp.aa_rat_int F Y4))))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_rat_int F A)) C)))))) (forall ((A tptp.num) (B2 tptp.num) (F tptp.fun_num_rat) (C tptp.rat)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A) B2)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_num_rat F B2)) C)) (=> (forall ((X4 tptp.num) (Y4 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X4) Y4)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_num_rat F X4)) (tptp.aa_num_rat F Y4))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_num_rat F A)) C)))))) (forall ((A tptp.num) (B2 tptp.num) (F tptp.fun_num_num) (C tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A) B2)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_num_num F B2)) C)) (=> (forall ((X4 tptp.num) (Y4 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X4) Y4)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_num_num F X4)) (tptp.aa_num_num F Y4))))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_num_num F A)) C)))))) (forall ((A tptp.num) (B2 tptp.num) (F tptp.fun_num_nat) (C tptp.nat)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A) B2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_num_nat F B2)) C)) (=> (forall ((X4 tptp.num) (Y4 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X4) Y4)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_num_nat F X4)) (tptp.aa_num_nat F Y4))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_num_nat F A)) C)))))) (forall ((A tptp.num) (B2 tptp.num) (F tptp.fun_num_int) (C tptp.int)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A) B2)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_num_int F B2)) C)) (=> (forall ((X4 tptp.num) (Y4 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X4) Y4)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_num_int F X4)) (tptp.aa_num_int F Y4))))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_num_int F A)) C)))))) (forall ((A tptp.nat) (B2 tptp.nat) (F tptp.fun_nat_rat) (C tptp.rat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B2)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat F B2)) C)) (=> (forall ((X4 tptp.nat) (Y4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X4) Y4)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat F X4)) (tptp.aa_nat_rat F Y4))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat F A)) C)))))) (forall ((A tptp.nat) (B2 tptp.nat) (F tptp.fun_nat_num) (C tptp.num)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B2)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_nat_num F B2)) C)) (=> (forall ((X4 tptp.nat) (Y4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X4) Y4)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_nat_num F X4)) (tptp.aa_nat_num F Y4))))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_nat_num F A)) C)))))) (forall ((X tptp.set_int) (Y tptp.set_int)) (=> (= X Y) (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int X) Y)))) (forall ((X tptp.rat) (Y tptp.rat)) (=> (= X Y) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) Y)))) (forall ((X tptp.num) (Y tptp.num)) (=> (= X Y) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X) Y)))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (= X Y) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X) Y)))) (forall ((X tptp.int) (Y tptp.int)) (=> (= X Y) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X) Y)))) (forall ((X tptp.rat) (Y tptp.rat)) (or (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) Y)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat Y) X)))) (forall ((X tptp.num) (Y tptp.num)) (or (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X) Y)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num Y) X)))) (forall ((X tptp.nat) (Y tptp.nat)) (or (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X) Y)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Y) X)))) (forall ((X tptp.int) (Y tptp.int)) (or (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X) Y)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Y) X)))) (forall ((A tptp.rat) (F tptp.fun_rat_rat) (B2 tptp.rat) (C tptp.rat)) (=> (= A (tptp.aa_rat_rat F B2)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B2) C)) (=> (forall ((X4 tptp.rat) (Y4 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X4) Y4)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat F X4)) (tptp.aa_rat_rat F Y4))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) (tptp.aa_rat_rat F C))))))) (forall ((A tptp.num) (F tptp.fun_rat_num) (B2 tptp.rat) (C tptp.rat)) (=> (= A (tptp.aa_rat_num F B2)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B2) C)) (=> (forall ((X4 tptp.rat) (Y4 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X4) Y4)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_rat_num F X4)) (tptp.aa_rat_num F Y4))))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A) (tptp.aa_rat_num F C))))))) (forall ((A tptp.nat) (F tptp.fun_rat_nat) (B2 tptp.rat) (C tptp.rat)) (=> (= A (tptp.aa_rat_nat F B2)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B2) C)) (=> (forall ((X4 tptp.rat) (Y4 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X4) Y4)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_rat_nat F X4)) (tptp.aa_rat_nat F Y4))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) (tptp.aa_rat_nat F C))))))) (forall ((A tptp.int) (F tptp.fun_rat_int) (B2 tptp.rat) (C tptp.rat)) (=> (= A (tptp.aa_rat_int F B2)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B2) C)) (=> (forall ((X4 tptp.rat) (Y4 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X4) Y4)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_rat_int F X4)) (tptp.aa_rat_int F Y4))))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) (tptp.aa_rat_int F C))))))) (forall ((A tptp.rat) (F tptp.fun_num_rat) (B2 tptp.num) (C tptp.num)) (=> (= A (tptp.aa_num_rat F B2)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num B2) C)) (=> (forall ((X4 tptp.num) (Y4 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X4) Y4)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_num_rat F X4)) (tptp.aa_num_rat F Y4))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) (tptp.aa_num_rat F C))))))) (forall ((A tptp.num) (F tptp.fun_num_num) (B2 tptp.num) (C tptp.num)) (=> (= A (tptp.aa_num_num F B2)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num B2) C)) (=> (forall ((X4 tptp.num) (Y4 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X4) Y4)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_num_num F X4)) (tptp.aa_num_num F Y4))))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A) (tptp.aa_num_num F C))))))) (forall ((A tptp.nat) (F tptp.fun_num_nat) (B2 tptp.num) (C tptp.num)) (=> (= A (tptp.aa_num_nat F B2)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num B2) C)) (=> (forall ((X4 tptp.num) (Y4 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X4) Y4)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_num_nat F X4)) (tptp.aa_num_nat F Y4))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) (tptp.aa_num_nat F C))))))) (forall ((A tptp.int) (F tptp.fun_num_int) (B2 tptp.num) (C tptp.num)) (=> (= A (tptp.aa_num_int F B2)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num B2) C)) (=> (forall ((X4 tptp.num) (Y4 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X4) Y4)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_num_int F X4)) (tptp.aa_num_int F Y4))))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) (tptp.aa_num_int F C))))))) (forall ((A tptp.rat) (F tptp.fun_nat_rat) (B2 tptp.nat) (C tptp.nat)) (=> (= A (tptp.aa_nat_rat F B2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B2) C)) (=> (forall ((X4 tptp.nat) (Y4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X4) Y4)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat F X4)) (tptp.aa_nat_rat F Y4))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) (tptp.aa_nat_rat F C))))))) (forall ((A tptp.num) (F tptp.fun_nat_num) (B2 tptp.nat) (C tptp.nat)) (=> (= A (tptp.aa_nat_num F B2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B2) C)) (=> (forall ((X4 tptp.nat) (Y4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X4) Y4)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_nat_num F X4)) (tptp.aa_nat_num F Y4))))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A) (tptp.aa_nat_num F C))))))) (forall ((A tptp.rat) (B2 tptp.rat) (F tptp.fun_rat_rat) (C tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B2)) (=> (= (tptp.aa_rat_rat F B2) C) (=> (forall ((X4 tptp.rat) (Y4 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X4) Y4)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat F X4)) (tptp.aa_rat_rat F Y4))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat F A)) C)))))) (forall ((A tptp.rat) (B2 tptp.rat) (F tptp.fun_rat_num) (C tptp.num)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B2)) (=> (= (tptp.aa_rat_num F B2) C) (=> (forall ((X4 tptp.rat) (Y4 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X4) Y4)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_rat_num F X4)) (tptp.aa_rat_num F Y4))))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_rat_num F A)) C)))))) (forall ((A tptp.rat) (B2 tptp.rat) (F tptp.fun_rat_nat) (C tptp.nat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B2)) (=> (= (tptp.aa_rat_nat F B2) C) (=> (forall ((X4 tptp.rat) (Y4 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X4) Y4)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_rat_nat F X4)) (tptp.aa_rat_nat F Y4))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_rat_nat F A)) C)))))) (forall ((A tptp.rat) (B2 tptp.rat) (F tptp.fun_rat_int) (C tptp.int)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B2)) (=> (= (tptp.aa_rat_int F B2) C) (=> (forall ((X4 tptp.rat) (Y4 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X4) Y4)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_rat_int F X4)) (tptp.aa_rat_int F Y4))))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_rat_int F A)) C)))))) (forall ((A tptp.num) (B2 tptp.num) (F tptp.fun_num_rat) (C tptp.rat)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A) B2)) (=> (= (tptp.aa_num_rat F B2) C) (=> (forall ((X4 tptp.num) (Y4 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X4) Y4)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_num_rat F X4)) (tptp.aa_num_rat F Y4))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_num_rat F A)) C)))))) (forall ((A tptp.num) (B2 tptp.num) (F tptp.fun_num_num) (C tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A) B2)) (=> (= (tptp.aa_num_num F B2) C) (=> (forall ((X4 tptp.num) (Y4 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X4) Y4)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_num_num F X4)) (tptp.aa_num_num F Y4))))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_num_num F A)) C)))))) (forall ((A tptp.num) (B2 tptp.num) (F tptp.fun_num_nat) (C tptp.nat)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A) B2)) (=> (= (tptp.aa_num_nat F B2) C) (=> (forall ((X4 tptp.num) (Y4 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X4) Y4)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_num_nat F X4)) (tptp.aa_num_nat F Y4))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_num_nat F A)) C)))))) (forall ((A tptp.num) (B2 tptp.num) (F tptp.fun_num_int) (C tptp.int)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A) B2)) (=> (= (tptp.aa_num_int F B2) C) (=> (forall ((X4 tptp.num) (Y4 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X4) Y4)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_num_int F X4)) (tptp.aa_num_int F Y4))))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_num_int F A)) C)))))) (forall ((A tptp.nat) (B2 tptp.nat) (F tptp.fun_nat_rat) (C tptp.rat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B2)) (=> (= (tptp.aa_nat_rat F B2) C) (=> (forall ((X4 tptp.nat) (Y4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X4) Y4)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat F X4)) (tptp.aa_nat_rat F Y4))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat F A)) C)))))) (forall ((A tptp.nat) (B2 tptp.nat) (F tptp.fun_nat_num) (C tptp.num)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B2)) (=> (= (tptp.aa_nat_num F B2) C) (=> (forall ((X4 tptp.nat) (Y4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X4) Y4)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_nat_num F X4)) (tptp.aa_nat_num F Y4))))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_nat_num F A)) C)))))) (forall ((X tptp.rat) (Y tptp.rat)) (=> (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) Y))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat Y) X)))) (forall ((X tptp.num) (Y tptp.num)) (=> (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X) Y))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num Y) X)))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X) Y))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Y) X)))) (forall ((X tptp.int) (Y tptp.int)) (=> (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X) Y))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Y) X)))) (forall ((Y tptp.set_int) (X tptp.set_int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int Y) X)) (= (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int X) Y)) (= X Y)))) (forall ((Y tptp.rat) (X tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat Y) X)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) Y)) (= X Y)))) (forall ((Y tptp.num) (X tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num Y) X)) (= (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X) Y)) (= X Y)))) (forall ((Y tptp.nat) (X tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Y) X)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X) Y)) (= X Y)))) (forall ((Y tptp.int) (X tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Y) X)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X) Y)) (= X Y)))) (forall ((I tptp.nat) (Xs tptp.list_int) (J tptp.nat) (X tptp.int)) (let ((_let_1 (tptp.aa_nat_int (tptp.nth_int (tptp.list_update_int Xs I X)) J))) (let ((_let_2 (= I J))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I) (tptp.size_size_list_int Xs))) (and (=> _let_2 (= _let_1 X)) (=> (not _let_2) (= _let_1 (tptp.aa_nat_int (tptp.nth_int Xs) J)))))))) (forall ((I tptp.nat) (Xs tptp.list_VEBT_VEBT) (J tptp.nat) (X tptp.vEBT_VEBT)) (let ((_let_1 (tptp.nth_VEBT_VEBT (tptp.list_u1324408373059187874T_VEBT Xs I X) J))) (let ((_let_2 (= I J))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I) (tptp.size_s6755466524823107622T_VEBT Xs))) (and (=> _let_2 (= _let_1 X)) (=> (not _let_2) (= _let_1 (tptp.nth_VEBT_VEBT Xs J)))))))) (forall ((I tptp.nat) (Xs tptp.list_bool) (X tptp.bool) (J tptp.nat)) (let ((_let_1 (= I J))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I) (tptp.size_size_list_bool Xs))) (= (tptp.pp (tptp.aa_nat_bool (tptp.nth_bool (tptp.list_update_bool Xs I X)) J)) (and (=> _let_1 (tptp.pp X)) (=> (not _let_1) (tptp.pp (tptp.aa_nat_bool (tptp.nth_bool Xs) J)))))))) (forall ((I tptp.nat) (Xs tptp.list_nat) (J tptp.nat) (X tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.nth_nat (tptp.list_update_nat Xs I X)) J))) (let ((_let_2 (= I J))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I) (tptp.size_size_list_nat Xs))) (and (=> _let_2 (= _let_1 X)) (=> (not _let_2) (= _let_1 (tptp.aa_nat_nat (tptp.nth_nat Xs) J)))))))) (forall ((I tptp.nat) (Xs tptp.list_int) (X tptp.int)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I) (tptp.size_size_list_int Xs))) (= (= (tptp.list_update_int Xs I X) Xs) (= (tptp.aa_nat_int (tptp.nth_int Xs) I) X)))) (forall ((I tptp.nat) (Xs tptp.list_VEBT_VEBT) (X tptp.vEBT_VEBT)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I) (tptp.size_s6755466524823107622T_VEBT Xs))) (= (= (tptp.list_u1324408373059187874T_VEBT Xs I X) Xs) (= (tptp.nth_VEBT_VEBT Xs I) X)))) (forall ((I tptp.nat) (Xs tptp.list_bool) (X tptp.bool)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I) (tptp.size_size_list_bool Xs))) (= (= (tptp.list_update_bool Xs I X) Xs) (= (tptp.pp (tptp.aa_nat_bool (tptp.nth_bool Xs) I)) (tptp.pp X))))) (forall ((I tptp.nat) (Xs tptp.list_nat) (X tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I) (tptp.size_size_list_nat Xs))) (= (= (tptp.list_update_nat Xs I X) Xs) (= (tptp.aa_nat_nat (tptp.nth_nat Xs) I) X)))) (forall ((X tptp.real)) (exists ((Y4 tptp.real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y4) X)))) (forall ((X tptp.rat)) (exists ((Y4 tptp.rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Y4) X)))) (forall ((X tptp.int)) (exists ((Y4 tptp.int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Y4) X)))) (forall ((X tptp.real)) (exists ((X_12 tptp.real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) X_12)))) (forall ((X tptp.rat)) (exists ((X_12 tptp.rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) X_12)))) (forall ((X tptp.nat)) (exists ((X_12 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) X_12)))) (forall ((X tptp.int)) (exists ((X_12 tptp.int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) X_12)))) (forall ((X tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Y)) (exists ((Z4 tptp.real)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Z4)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Z4) Y)))))) (forall ((X tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) Y)) (exists ((Z4 tptp.rat)) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) Z4)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Z4) Y)))))) (forall ((X tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Y)) (not (= X Y)))) (forall ((X tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) Y)) (not (= X Y)))) (forall ((X tptp.num) (Y tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X) Y)) (not (= X Y)))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Y)) (not (= X Y)))) (forall ((X tptp.int) (Y tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) Y)) (not (= X Y)))) (forall ((A tptp.real) (B2 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B2)) (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B2) A))))) (forall ((A tptp.rat) (B2 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B2)) (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B2) A))))) (forall ((A tptp.num) (B2 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num A) B2)) (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num B2) A))))) (forall ((A tptp.nat) (B2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) B2)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat B2) A))))) (forall ((A tptp.int) (B2 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B2)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B2) A))))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (=> (= A B2) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B2) C)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) C))))) (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat)) (=> (= A B2) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B2) C)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) C))))) (forall ((A tptp.num) (B2 tptp.num) (C tptp.num)) (=> (= A B2) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num B2) C)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num A) C))))) (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (=> (= A B2) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat B2) C)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) C))))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (=> (= A B2) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B2) C)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) C))))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A))) (=> (tptp.pp (tptp.aa_real_bool _let_1 B2)) (=> (= B2 C) (tptp.pp (tptp.aa_real_bool _let_1 C)))))) (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 B2)) (=> (= B2 C) (tptp.pp (tptp.aa_rat_bool _let_1 C)))))) (forall ((A tptp.num) (B2 tptp.num) (C tptp.num)) (let ((_let_1 (tptp.aa_num_fun_num_bool tptp.ord_less_num A))) (=> (tptp.pp (tptp.aa_num_bool _let_1 B2)) (=> (= B2 C) (tptp.pp (tptp.aa_num_bool _let_1 C)))))) (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 B2)) (=> (= B2 C) (tptp.pp (tptp.aa_nat_bool _let_1 C)))))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_int A))) (=> (tptp.pp (tptp.aa_int_bool _let_1 B2)) (=> (= B2 C) (tptp.pp (tptp.aa_int_bool _let_1 C)))))) (forall ((P tptp.fun_nat_bool) (A tptp.nat)) (=> (forall ((X4 tptp.nat)) (=> (forall ((Y5 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Y5) X4)) (tptp.pp (tptp.aa_nat_bool P Y5)))) (tptp.pp (tptp.aa_nat_bool P X4)))) (tptp.pp (tptp.aa_nat_bool P A)))) (forall ((Y tptp.real) (X tptp.real)) (=> (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y) X))) (= (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Y))) (= X Y)))) (forall ((Y tptp.rat) (X tptp.rat)) (=> (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Y) X))) (= (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) Y))) (= X Y)))) (forall ((Y tptp.num) (X tptp.num)) (=> (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num Y) X))) (= (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X) Y))) (= X Y)))) (forall ((Y tptp.nat) (X tptp.nat)) (=> (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Y) X))) (= (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Y))) (= X Y)))) (forall ((Y tptp.int) (X tptp.int)) (=> (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Y) X))) (= (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) Y))) (= X Y)))) (forall ((X tptp.real) (Y tptp.real)) (=> (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Y))) (=> (not (= X Y)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y) X))))) (forall ((X tptp.rat) (Y tptp.rat)) (=> (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) Y))) (=> (not (= X Y)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Y) X))))) (forall ((X tptp.num) (Y tptp.num)) (=> (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X) Y))) (=> (not (= X Y)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num Y) X))))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Y))) (=> (not (= X Y)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Y) X))))) (forall ((X tptp.int) (Y tptp.int)) (=> (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) Y))) (=> (not (= X Y)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Y) X))))) (forall ((B2 tptp.real) (A tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B2) A)) (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B2))))) (forall ((B2 tptp.rat) (A tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B2) A)) (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B2))))) (forall ((B2 tptp.num) (A tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num B2) A)) (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num A) B2))))) (forall ((B2 tptp.nat) (A tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat B2) A)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) B2))))) (forall ((B2 tptp.int) (A tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B2) A)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B2))))) (forall ((A tptp.real)) (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) A)))) (forall ((A tptp.rat)) (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) A)))) (forall ((A tptp.num)) (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num A) A)))) (forall ((A tptp.nat)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) A)))) (forall ((A tptp.int)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) A)))) (forall ((P tptp.fun_nat_bool)) (= (exists ((X_1 tptp.nat)) (tptp.pp (tptp.aa_nat_bool P X_1))) (exists ((N5 tptp.nat)) (and (tptp.pp (tptp.aa_nat_bool P N5)) (forall ((M6 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M6) N5)) (not (tptp.pp (tptp.aa_nat_bool P M6))))))))) (forall ((P tptp.fun_re1255401033344146673l_bool) (A tptp.real) (B2 tptp.real)) (=> (forall ((A3 tptp.real) (B3 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A3) B3)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool P A3) B3)))) (=> (forall ((A3 tptp.real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool P A3) A3))) (=> (forall ((A3 tptp.real) (B3 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool P B3) A3)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool P A3) B3)))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool P A) B2)))))) (forall ((P tptp.fun_rat_fun_rat_bool) (A tptp.rat) (B2 tptp.rat)) (=> (forall ((A3 tptp.rat) (B3 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A3) B3)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool P A3) B3)))) (=> (forall ((A3 tptp.rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool P A3) A3))) (=> (forall ((A3 tptp.rat) (B3 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool P B3) A3)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool P A3) B3)))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool P A) B2)))))) (forall ((P tptp.fun_num_fun_num_bool) (A tptp.num) (B2 tptp.num)) (=> (forall ((A3 tptp.num) (B3 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num A3) B3)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool P A3) B3)))) (=> (forall ((A3 tptp.num)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool P A3) A3))) (=> (forall ((A3 tptp.num) (B3 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool P B3) A3)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool P A3) B3)))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool P A) B2)))))) (forall ((P tptp.fun_nat_fun_nat_bool) (A tptp.nat) (B2 tptp.nat)) (=> (forall ((A3 tptp.nat) (B3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A3) B3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool P A3) B3)))) (=> (forall ((A3 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool P A3) A3))) (=> (forall ((A3 tptp.nat) (B3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool P B3) A3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool P A3) B3)))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool P A) B2)))))) (forall ((P tptp.fun_int_fun_int_bool) (A tptp.int) (B2 tptp.int)) (=> (forall ((A3 tptp.int) (B3 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A3) B3)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool P A3) B3)))) (=> (forall ((A3 tptp.int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool P A3) A3))) (=> (forall ((A3 tptp.int) (B3 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool P B3) A3)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool P A3) B3)))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool P A) B2)))))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A))) (=> (tptp.pp (tptp.aa_real_bool _let_1 B2)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B2) C)) (tptp.pp (tptp.aa_real_bool _let_1 C)))))) (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 B2)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B2) C)) (tptp.pp (tptp.aa_rat_bool _let_1 C)))))) (forall ((A tptp.num) (B2 tptp.num) (C tptp.num)) (let ((_let_1 (tptp.aa_num_fun_num_bool tptp.ord_less_num A))) (=> (tptp.pp (tptp.aa_num_bool _let_1 B2)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num B2) C)) (tptp.pp (tptp.aa_num_bool _let_1 C)))))) (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 B2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat B2) C)) (tptp.pp (tptp.aa_nat_bool _let_1 C)))))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_int A))) (=> (tptp.pp (tptp.aa_int_bool _let_1 B2)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B2) C)) (tptp.pp (tptp.aa_int_bool _let_1 C)))))) (forall ((X tptp.real) (Y tptp.real)) (= (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Y))) (or (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y) X)) (= X Y)))) (forall ((X tptp.rat) (Y tptp.rat)) (= (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) Y))) (or (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Y) X)) (= X Y)))) (forall ((X tptp.num) (Y tptp.num)) (= (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X) Y))) (or (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num Y) X)) (= X Y)))) (forall ((X tptp.nat) (Y tptp.nat)) (= (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Y))) (or (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Y) X)) (= X Y)))) (forall ((X tptp.int) (Y tptp.int)) (= (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) Y))) (or (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Y) X)) (= X Y)))) (forall ((B2 tptp.real) (A tptp.real) (C tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real C))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B2) A)) (=> (tptp.pp (tptp.aa_real_bool _let_1 B2)) (tptp.pp (tptp.aa_real_bool _let_1 A)))))) (forall ((B2 tptp.rat) (A tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat C))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B2) A)) (=> (tptp.pp (tptp.aa_rat_bool _let_1 B2)) (tptp.pp (tptp.aa_rat_bool _let_1 A)))))) (forall ((B2 tptp.num) (A tptp.num) (C tptp.num)) (let ((_let_1 (tptp.aa_num_fun_num_bool tptp.ord_less_num C))) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num B2) A)) (=> (tptp.pp (tptp.aa_num_bool _let_1 B2)) (tptp.pp (tptp.aa_num_bool _let_1 A)))))) (forall ((B2 tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat C))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat B2) A)) (=> (tptp.pp (tptp.aa_nat_bool _let_1 B2)) (tptp.pp (tptp.aa_nat_bool _let_1 A)))))) (forall ((B2 tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_int C))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B2) A)) (=> (tptp.pp (tptp.aa_int_bool _let_1 B2)) (tptp.pp (tptp.aa_int_bool _let_1 A)))))) (forall ((A tptp.real) (B2 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B2)) (not (= A B2)))) (forall ((A tptp.rat) (B2 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B2)) (not (= A B2)))) (forall ((A tptp.num) (B2 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num A) B2)) (not (= A B2)))) (forall ((A tptp.nat) (B2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) B2)) (not (= A B2)))) (forall ((A tptp.int) (B2 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B2)) (not (= A B2)))) (forall ((B2 tptp.real) (A tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B2) A)) (not (= A B2)))) (forall ((B2 tptp.rat) (A tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B2) A)) (not (= A B2)))) (forall ((B2 tptp.num) (A tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num B2) A)) (not (= A B2)))) (forall ((B2 tptp.nat) (A tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat B2) A)) (not (= A B2)))) (forall ((B2 tptp.int) (A tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B2) A)) (not (= A B2)))) (forall ((X tptp.real) (Y tptp.real)) (=> (not (= X Y)) (=> (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Y))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y) X))))) (forall ((X tptp.rat) (Y tptp.rat)) (=> (not (= X Y)) (=> (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) Y))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Y) X))))) (forall ((X tptp.num) (Y tptp.num)) (=> (not (= X Y)) (=> (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X) Y))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num Y) X))))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (not (= X Y)) (=> (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Y))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Y) X))))) (forall ((X tptp.int) (Y tptp.int)) (=> (not (= X Y)) (=> (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) Y))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Y) X))))) (forall ((X tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Y)) (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y) X))))) (forall ((X tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) Y)) (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Y) X))))) (forall ((X tptp.num) (Y tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X) Y)) (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num Y) X))))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Y)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Y) X))))) (forall ((X tptp.int) (Y tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) Y)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Y) X))))) (forall ((X tptp.real) (Y tptp.real)) (= (not (= X Y)) (or (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Y)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y) X))))) (forall ((X tptp.rat) (Y tptp.rat)) (= (not (= X Y)) (or (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) Y)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Y) X))))) (forall ((X tptp.num) (Y tptp.num)) (= (not (= X Y)) (or (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X) Y)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num Y) X))))) (forall ((X tptp.nat) (Y tptp.nat)) (= (not (= X Y)) (or (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Y)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Y) X))))) (forall ((X tptp.int) (Y tptp.int)) (= (not (= X Y)) (or (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) Y)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Y) X))))) (forall ((A tptp.real) (B2 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B2)) (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B2) A))))) (forall ((A tptp.rat) (B2 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B2)) (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B2) A))))) (forall ((A tptp.num) (B2 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num A) B2)) (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num B2) A))))) (forall ((A tptp.nat) (B2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) B2)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat B2) A))))) (forall ((A tptp.int) (B2 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B2)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B2) A))))) (forall ((X tptp.real) (Y tptp.real) (Z tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X))) (=> (tptp.pp (tptp.aa_real_bool _let_1 Y)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y) Z)) (tptp.pp (tptp.aa_real_bool _let_1 Z)))))) (forall ((X tptp.rat) (Y tptp.rat) (Z tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 Y)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Y) Z)) (tptp.pp (tptp.aa_rat_bool _let_1 Z)))))) (forall ((X tptp.num) (Y tptp.num) (Z tptp.num)) (let ((_let_1 (tptp.aa_num_fun_num_bool tptp.ord_less_num X))) (=> (tptp.pp (tptp.aa_num_bool _let_1 Y)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num Y) Z)) (tptp.pp (tptp.aa_num_bool _let_1 Z)))))) (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 Y)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Y) Z)) (tptp.pp (tptp.aa_nat_bool _let_1 Z)))))) (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_int X))) (=> (tptp.pp (tptp.aa_int_bool _let_1 Y)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Y) Z)) (tptp.pp (tptp.aa_int_bool _let_1 Z)))))) (forall ((A tptp.real) (F tptp.fun_real_real) (B2 tptp.real) (C tptp.real)) (=> (= A (tptp.aa_real_real F B2)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B2) C)) (=> (forall ((X4 tptp.real) (Y4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X4) Y4)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real F X4)) (tptp.aa_real_real F Y4))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) (tptp.aa_real_real F C))))))) (forall ((A tptp.rat) (F tptp.fun_real_rat) (B2 tptp.real) (C tptp.real)) (=> (= A (tptp.aa_real_rat F B2)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B2) C)) (=> (forall ((X4 tptp.real) (Y4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X4) Y4)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_real_rat F X4)) (tptp.aa_real_rat F Y4))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) (tptp.aa_real_rat F C))))))) (forall ((A tptp.num) (F tptp.fun_real_num) (B2 tptp.real) (C tptp.real)) (=> (= A (tptp.aa_real_num F B2)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B2) C)) (=> (forall ((X4 tptp.real) (Y4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X4) Y4)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num (tptp.aa_real_num F X4)) (tptp.aa_real_num F Y4))))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num A) (tptp.aa_real_num F C))))))) (forall ((A tptp.nat) (F tptp.fun_real_nat) (B2 tptp.real) (C tptp.real)) (=> (= A (tptp.aa_real_nat F B2)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B2) C)) (=> (forall ((X4 tptp.real) (Y4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X4) Y4)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_real_nat F X4)) (tptp.aa_real_nat F Y4))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) (tptp.aa_real_nat F C))))))) (forall ((A tptp.int) (F tptp.fun_real_int) (B2 tptp.real) (C tptp.real)) (=> (= A (tptp.aa_real_int F B2)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B2) C)) (=> (forall ((X4 tptp.real) (Y4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X4) Y4)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_real_int F X4)) (tptp.aa_real_int F Y4))))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) (tptp.aa_real_int F C))))))) (forall ((A tptp.real) (F tptp.fun_rat_real) (B2 tptp.rat) (C tptp.rat)) (=> (= A (tptp.aa_rat_real F B2)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B2) C)) (=> (forall ((X4 tptp.rat) (Y4 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X4) Y4)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_rat_real F X4)) (tptp.aa_rat_real F Y4))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) (tptp.aa_rat_real F C))))))) (forall ((A tptp.rat) (F tptp.fun_rat_rat) (B2 tptp.rat) (C tptp.rat)) (=> (= A (tptp.aa_rat_rat F B2)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B2) C)) (=> (forall ((X4 tptp.rat) (Y4 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X4) Y4)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat F X4)) (tptp.aa_rat_rat F Y4))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) (tptp.aa_rat_rat F C))))))) (forall ((A tptp.num) (F tptp.fun_rat_num) (B2 tptp.rat) (C tptp.rat)) (=> (= A (tptp.aa_rat_num F B2)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B2) C)) (=> (forall ((X4 tptp.rat) (Y4 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X4) Y4)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num (tptp.aa_rat_num F X4)) (tptp.aa_rat_num F Y4))))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num A) (tptp.aa_rat_num F C))))))) (forall ((A tptp.nat) (F tptp.fun_rat_nat) (B2 tptp.rat) (C tptp.rat)) (=> (= A (tptp.aa_rat_nat F B2)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B2) C)) (=> (forall ((X4 tptp.rat) (Y4 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X4) Y4)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_rat_nat F X4)) (tptp.aa_rat_nat F Y4))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) (tptp.aa_rat_nat F C))))))) (forall ((A tptp.int) (F tptp.fun_rat_int) (B2 tptp.rat) (C tptp.rat)) (=> (= A (tptp.aa_rat_int F B2)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B2) C)) (=> (forall ((X4 tptp.rat) (Y4 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X4) Y4)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_rat_int F X4)) (tptp.aa_rat_int F Y4))))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) (tptp.aa_rat_int F C))))))) (forall ((A tptp.real) (B2 tptp.real) (F tptp.fun_real_real) (C tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B2)) (=> (= (tptp.aa_real_real F B2) C) (=> (forall ((X4 tptp.real) (Y4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X4) Y4)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real F X4)) (tptp.aa_real_real F Y4))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real F A)) C)))))) (forall ((A tptp.real) (B2 tptp.real) (F tptp.fun_real_rat) (C tptp.rat)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B2)) (=> (= (tptp.aa_real_rat F B2) C) (=> (forall ((X4 tptp.real) (Y4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X4) Y4)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_real_rat F X4)) (tptp.aa_real_rat F Y4))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_real_rat F A)) C)))))) (forall ((A tptp.real) (B2 tptp.real) (F tptp.fun_real_num) (C tptp.num)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B2)) (=> (= (tptp.aa_real_num F B2) C) (=> (forall ((X4 tptp.real) (Y4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X4) Y4)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num (tptp.aa_real_num F X4)) (tptp.aa_real_num F Y4))))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num (tptp.aa_real_num F A)) C)))))) (forall ((A tptp.real) (B2 tptp.real) (F tptp.fun_real_nat) (C tptp.nat)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B2)) (=> (= (tptp.aa_real_nat F B2) C) (=> (forall ((X4 tptp.real) (Y4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X4) Y4)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_real_nat F X4)) (tptp.aa_real_nat F Y4))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_real_nat F A)) C)))))) (forall ((A tptp.real) (B2 tptp.real) (F tptp.fun_real_int) (C tptp.int)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B2)) (=> (= (tptp.aa_real_int F B2) C) (=> (forall ((X4 tptp.real) (Y4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X4) Y4)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_real_int F X4)) (tptp.aa_real_int F Y4))))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_real_int F A)) C)))))) (forall ((A tptp.rat) (B2 tptp.rat) (F tptp.fun_rat_real) (C tptp.real)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B2)) (=> (= (tptp.aa_rat_real F B2) C) (=> (forall ((X4 tptp.rat) (Y4 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X4) Y4)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_rat_real F X4)) (tptp.aa_rat_real F Y4))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_rat_real F A)) C)))))) (forall ((A tptp.rat) (B2 tptp.rat) (F tptp.fun_rat_rat) (C tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B2)) (=> (= (tptp.aa_rat_rat F B2) C) (=> (forall ((X4 tptp.rat) (Y4 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X4) Y4)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat F X4)) (tptp.aa_rat_rat F Y4))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat F A)) C)))))) (forall ((A tptp.rat) (B2 tptp.rat) (F tptp.fun_rat_num) (C tptp.num)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B2)) (=> (= (tptp.aa_rat_num F B2) C) (=> (forall ((X4 tptp.rat) (Y4 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X4) Y4)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num (tptp.aa_rat_num F X4)) (tptp.aa_rat_num F Y4))))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num (tptp.aa_rat_num F A)) C)))))) (forall ((A tptp.rat) (B2 tptp.rat) (F tptp.fun_rat_nat) (C tptp.nat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B2)) (=> (= (tptp.aa_rat_nat F B2) C) (=> (forall ((X4 tptp.rat) (Y4 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X4) Y4)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_rat_nat F X4)) (tptp.aa_rat_nat F Y4))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_rat_nat F A)) C)))))) (forall ((A tptp.rat) (B2 tptp.rat) (F tptp.fun_rat_int) (C tptp.int)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B2)) (=> (= (tptp.aa_rat_int F B2) C) (=> (forall ((X4 tptp.rat) (Y4 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X4) Y4)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_rat_int F X4)) (tptp.aa_rat_int F Y4))))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_rat_int F A)) C)))))) (forall ((X tptp.real)) (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) X)))) (forall ((X tptp.rat)) (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) X)))) (forall ((X tptp.num)) (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X) X)))) (forall ((X tptp.nat)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) X)))) (forall ((X tptp.int)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) X)))) (forall ((A tptp.real) (F tptp.fun_real_real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A))) (=> (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real F B2))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B2) C)) (=> (forall ((X4 tptp.real) (Y4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X4) Y4)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real F X4)) (tptp.aa_real_real F Y4))))) (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real F C)))))))) (forall ((A tptp.real) (F tptp.fun_rat_real) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A))) (=> (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_rat_real F B2))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B2) C)) (=> (forall ((X4 tptp.rat) (Y4 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X4) Y4)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_rat_real F X4)) (tptp.aa_rat_real F Y4))))) (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_rat_real F C)))))))) (forall ((A tptp.real) (F tptp.fun_num_real) (B2 tptp.num) (C tptp.num)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A))) (=> (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_num_real F B2))) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num B2) C)) (=> (forall ((X4 tptp.num) (Y4 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X4) Y4)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_num_real F X4)) (tptp.aa_num_real F Y4))))) (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_num_real F C)))))))) (forall ((A tptp.real) (F tptp.fun_nat_real) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A))) (=> (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_nat_real F B2))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat B2) C)) (=> (forall ((X4 tptp.nat) (Y4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X4) Y4)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_nat_real F X4)) (tptp.aa_nat_real F Y4))))) (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_nat_real F C)))))))) (forall ((A tptp.real) (F tptp.fun_int_real) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A))) (=> (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_int_real F B2))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B2) C)) (=> (forall ((X4 tptp.int) (Y4 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X4) Y4)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_int_real F X4)) (tptp.aa_int_real F Y4))))) (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_int_real F C)))))))) (forall ((A tptp.rat) (F tptp.fun_real_rat) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_real_rat F B2))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B2) C)) (=> (forall ((X4 tptp.real) (Y4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X4) Y4)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_real_rat F X4)) (tptp.aa_real_rat F Y4))))) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_real_rat F C)))))))) (forall ((A tptp.rat) (F tptp.fun_rat_rat) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat F B2))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B2) C)) (=> (forall ((X4 tptp.rat) (Y4 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X4) Y4)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat F X4)) (tptp.aa_rat_rat F Y4))))) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat F C)))))))) (forall ((A tptp.rat) (F tptp.fun_num_rat) (B2 tptp.num) (C tptp.num)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_num_rat F B2))) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num B2) C)) (=> (forall ((X4 tptp.num) (Y4 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X4) Y4)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_num_rat F X4)) (tptp.aa_num_rat F Y4))))) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_num_rat F C)))))))) (forall ((A tptp.rat) (F tptp.fun_nat_rat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_nat_rat F B2))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat B2) C)) (=> (forall ((X4 tptp.nat) (Y4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X4) Y4)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_nat_rat F X4)) (tptp.aa_nat_rat F Y4))))) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_nat_rat F C)))))))) (forall ((A tptp.rat) (F tptp.fun_int_rat) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_int_rat F B2))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B2) C)) (=> (forall ((X4 tptp.int) (Y4 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X4) Y4)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_int_rat F X4)) (tptp.aa_int_rat F Y4))))) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_int_rat F C)))))))) (forall ((A tptp.real) (B2 tptp.real) (F tptp.fun_real_real) (C tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B2)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real F B2)) C)) (=> (forall ((X4 tptp.real) (Y4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X4) Y4)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real F X4)) (tptp.aa_real_real F Y4))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real F A)) C)))))) (forall ((A tptp.real) (B2 tptp.real) (F tptp.fun_real_rat) (C tptp.rat)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B2)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_real_rat F B2)) C)) (=> (forall ((X4 tptp.real) (Y4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X4) Y4)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_real_rat F X4)) (tptp.aa_real_rat F Y4))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_real_rat F A)) C)))))) (forall ((A tptp.real) (B2 tptp.real) (F tptp.fun_real_num) (C tptp.num)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B2)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num (tptp.aa_real_num F B2)) C)) (=> (forall ((X4 tptp.real) (Y4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X4) Y4)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num (tptp.aa_real_num F X4)) (tptp.aa_real_num F Y4))))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num (tptp.aa_real_num F A)) C)))))) (forall ((A tptp.real) (B2 tptp.real) (F tptp.fun_real_nat) (C tptp.nat)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_real_nat F B2)) C)) (=> (forall ((X4 tptp.real) (Y4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X4) Y4)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_real_nat F X4)) (tptp.aa_real_nat F Y4))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_real_nat F A)) C)))))) (forall ((A tptp.real) (B2 tptp.real) (F tptp.fun_real_int) (C tptp.int)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B2)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_real_int F B2)) C)) (=> (forall ((X4 tptp.real) (Y4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X4) Y4)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_real_int F X4)) (tptp.aa_real_int F Y4))))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_real_int F A)) C)))))) (forall ((A tptp.rat) (B2 tptp.rat) (F tptp.fun_rat_real) (C tptp.real)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B2)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_rat_real F B2)) C)) (=> (forall ((X4 tptp.rat) (Y4 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X4) Y4)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_rat_real F X4)) (tptp.aa_rat_real F Y4))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_rat_real F A)) C)))))) (forall ((A tptp.rat) (B2 tptp.rat) (F tptp.fun_rat_rat) (C tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B2)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat F B2)) C)) (=> (forall ((X4 tptp.rat) (Y4 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X4) Y4)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat F X4)) (tptp.aa_rat_rat F Y4))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat F A)) C)))))) (forall ((A tptp.rat) (B2 tptp.rat) (F tptp.fun_rat_num) (C tptp.num)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B2)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num (tptp.aa_rat_num F B2)) C)) (=> (forall ((X4 tptp.rat) (Y4 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X4) Y4)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num (tptp.aa_rat_num F X4)) (tptp.aa_rat_num F Y4))))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num (tptp.aa_rat_num F A)) C)))))) (forall ((A tptp.rat) (B2 tptp.rat) (F tptp.fun_rat_nat) (C tptp.nat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_rat_nat F B2)) C)) (=> (forall ((X4 tptp.rat) (Y4 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X4) Y4)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_rat_nat F X4)) (tptp.aa_rat_nat F Y4))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_rat_nat F A)) C)))))) (forall ((A tptp.rat) (B2 tptp.rat) (F tptp.fun_rat_int) (C tptp.int)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B2)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_rat_int F B2)) C)) (=> (forall ((X4 tptp.rat) (Y4 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X4) Y4)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_rat_int F X4)) (tptp.aa_rat_int F Y4))))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_rat_int F A)) C)))))) (forall ((X tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Y)) (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y) X))))) (forall ((X tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) Y)) (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Y) X))))) (forall ((X tptp.num) (Y tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X) Y)) (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num Y) X))))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Y)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Y) X))))) (forall ((X tptp.int) (Y tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) Y)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Y) X))))) (forall ((X tptp.real) (Y tptp.real) (P tptp.bool)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Y)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y) X)) (tptp.pp P)))) (forall ((X tptp.rat) (Y tptp.rat) (P tptp.bool)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) Y)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Y) X)) (tptp.pp P)))) (forall ((X tptp.num) (Y tptp.num) (P tptp.bool)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X) Y)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num Y) X)) (tptp.pp P)))) (forall ((X tptp.nat) (Y tptp.nat) (P tptp.bool)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Y)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Y) X)) (tptp.pp P)))) (forall ((X tptp.int) (Y tptp.int) (P tptp.bool)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) Y)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Y) X)) (tptp.pp P)))) (forall ((X tptp.real) (Y tptp.real)) (or (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Y)) (= X Y) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y) X)))) (forall ((X tptp.rat) (Y tptp.rat)) (or (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) Y)) (= X Y) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Y) X)))) (forall ((X tptp.num) (Y tptp.num)) (or (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X) Y)) (= X Y) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num Y) X)))) (forall ((X tptp.nat) (Y tptp.nat)) (or (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Y)) (= X Y) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Y) X)))) (forall ((X tptp.int) (Y tptp.int)) (or (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) Y)) (= X Y) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Y) X)))) (forall ((X tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Y)) (not (= X Y)))) (forall ((X tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) Y)) (not (= X Y)))) (forall ((X tptp.num) (Y tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X) Y)) (not (= X Y)))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Y)) (not (= X Y)))) (forall ((X tptp.int) (Y tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) Y)) (not (= X Y)))) (forall ((X tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Y)) (not (= Y X)))) (forall ((X tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) Y)) (not (= Y X)))) (forall ((X tptp.num) (Y tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X) Y)) (not (= Y X)))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Y)) (not (= Y X)))) (forall ((X tptp.int) (Y tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) Y)) (not (= Y X)))) (forall ((X tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Y)) (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y) X))))) (forall ((X tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) Y)) (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Y) X))))) (forall ((X tptp.num) (Y tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X) Y)) (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num Y) X))))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Y)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Y) X))))) (forall ((X tptp.int) (Y tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) Y)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Y) X))))) (forall ((X tptp.product_prod_int_int)) (not (forall ((D2 tptp.int) (I3 tptp.int)) (not (= X (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int D2) I3)))))) (forall ((X tptp.produc6768802789813714928nt_int)) (not (forall ((F2 tptp.fun_in6429348457993719614e_term) (D2 tptp.int) (I3 tptp.int)) (not (= X (tptp.produc4852315488734385442nt_int F2 (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int D2) I3))))))) (forall ((X tptp.produc4441460161354545860nt_int)) (not (forall ((F2 tptp.fun_Pr9164807099015279978e_term) (D2 tptp.int) (I3 tptp.int)) (not (= X (tptp.produc1560874099174258678nt_int F2 (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int D2) I3))))))) (forall ((Y tptp.real) (X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y) X)) (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Y))))) (forall ((Y tptp.set_int) (X tptp.set_int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int Y) X)) (not (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_set_int X) Y))))) (forall ((Y tptp.rat) (X tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat Y) X)) (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) Y))))) (forall ((Y tptp.num) (X tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num Y) X)) (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X) Y))))) (forall ((Y tptp.nat) (X tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Y) X)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Y))))) (forall ((Y tptp.int) (X tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Y) X)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) Y))))) (forall ((X tptp.real) (Y tptp.real)) (=> (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Y))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y) X)))) (forall ((X tptp.rat) (Y tptp.rat)) (=> (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) Y))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat Y) X)))) (forall ((X tptp.num) (Y tptp.num)) (=> (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X) Y))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num Y) X)))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Y))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Y) X)))) (forall ((X tptp.int) (Y tptp.int)) (=> (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) Y))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Y) X)))) (forall ((A tptp.real) (B2 tptp.real)) (= (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B2))) (or (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) B2))) (= A B2)))) (forall ((A tptp.set_int) (B2 tptp.set_int)) (= (not (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_set_int A) B2))) (or (not (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int A) B2))) (= A B2)))) (forall ((A tptp.rat) (B2 tptp.rat)) (= (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B2))) (or (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B2))) (= A B2)))) (forall ((A tptp.num) (B2 tptp.num)) (= (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num A) B2))) (or (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A) B2))) (= A B2)))) (forall ((A tptp.nat) (B2 tptp.nat)) (= (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) B2))) (or (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B2))) (= A B2)))) (forall ((A tptp.int) (B2 tptp.int)) (= (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B2))) (or (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B2))) (= A B2)))) (forall ((X tptp.real) (Y tptp.real)) (=> (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Y))) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) Y)) (= X Y)))) (forall ((X tptp.set_int) (Y tptp.set_int)) (=> (not (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_set_int X) Y))) (= (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int X) Y)) (= X Y)))) (forall ((X tptp.rat) (Y tptp.rat)) (=> (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) Y))) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) Y)) (= X Y)))) (forall ((X tptp.num) (Y tptp.num)) (=> (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X) Y))) (= (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X) Y)) (= X Y)))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Y))) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X) Y)) (= X Y)))) (forall ((X tptp.int) (Y tptp.int)) (=> (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) Y))) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X) Y)) (= X Y)))) (forall ((X tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) Y)) (= (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Y))) (= X Y)))) (forall ((X tptp.set_int) (Y tptp.set_int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int X) Y)) (= (not (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_set_int X) Y))) (= X Y)))) (forall ((X tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) Y)) (= (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) Y))) (= X Y)))) (forall ((X tptp.num) (Y tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X) Y)) (= (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X) Y))) (= X Y)))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X) Y)) (= (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Y))) (= X Y)))) (forall ((X tptp.int) (Y tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X) Y)) (= (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) Y))) (= X Y)))) (forall ((Z tptp.real) (Y tptp.real)) (=> (forall ((X4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Z) X4)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y) X4)))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y) Z)))) (forall ((Z tptp.rat) (Y tptp.rat)) (=> (forall ((X4 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Z) X4)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat Y) X4)))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat Y) Z)))) (forall ((Y tptp.real) (Z tptp.real)) (=> (forall ((X4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X4) Y)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X4) Z)))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y) Z)))) (forall ((Y tptp.rat) (Z tptp.rat)) (=> (forall ((X4 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X4) Y)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X4) Z)))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat Y) Z)))) (forall ((X tptp.real) (Y tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Y)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) Y)) (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y) X)))))) (forall ((X tptp.set_int) (Y tptp.set_int)) (= (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_set_int X) Y)) (and (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int X) Y)) (not (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int Y) X)))))) (forall ((X tptp.rat) (Y tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) Y)) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) Y)) (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat Y) X)))))) (forall ((X tptp.num) (Y tptp.num)) (= (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X) Y)) (and (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X) Y)) (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num Y) X)))))) (forall ((X tptp.nat) (Y tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Y)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X) Y)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Y) X)))))) (forall ((X tptp.int) (Y tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) Y)) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X) Y)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Y) X)))))) (forall ((Y tptp.real) (X tptp.real)) (=> (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y) X))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Y)))) (forall ((Y tptp.rat) (X tptp.rat)) (=> (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat Y) X))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) Y)))) (forall ((Y tptp.num) (X tptp.num)) (=> (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num Y) X))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X) Y)))) (forall ((Y tptp.nat) (X tptp.nat)) (=> (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Y) X))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Y)))) (forall ((Y tptp.int) (X tptp.int)) (=> (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Y) X))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) Y)))) (forall ((A tptp.real) (B2 tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) B2)) (or (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B2)) (= A B2)))) (forall ((A tptp.set_int) (B2 tptp.set_int)) (= (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int A) B2)) (or (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_set_int A) B2)) (= A B2)))) (forall ((A tptp.rat) (B2 tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B2)) (or (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B2)) (= A B2)))) (forall ((A tptp.num) (B2 tptp.num)) (= (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A) B2)) (or (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num A) B2)) (= A B2)))) (forall ((A tptp.nat) (B2 tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B2)) (or (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) B2)) (= A B2)))) (forall ((A tptp.int) (B2 tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B2)) (or (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B2)) (= A B2)))) (forall ((A tptp.real) (B2 tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B2)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) B2)) (not (= A B2))))) (forall ((A tptp.set_int) (B2 tptp.set_int)) (= (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_set_int A) B2)) (and (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int A) B2)) (not (= A B2))))) (forall ((A tptp.rat) (B2 tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B2)) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B2)) (not (= A B2))))) (forall ((A tptp.num) (B2 tptp.num)) (= (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num A) B2)) (and (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A) B2)) (not (= A B2))))) (forall ((A tptp.nat) (B2 tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) B2)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B2)) (not (= A B2))))) (forall ((A tptp.int) (B2 tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B2)) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B2)) (not (= A B2))))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) B2)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B2) C)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) C))))) (forall ((A tptp.set_int) (B2 tptp.set_int) (C tptp.set_int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int A) B2)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_set_int B2) C)) (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_set_int A) C))))) (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B2)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B2) C)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) C))))) (forall ((A tptp.num) (B2 tptp.num) (C tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A) B2)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num B2) C)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num A) C))))) (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat B2) C)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) C))))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B2)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B2) C)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) C))))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A))) (=> (tptp.pp (tptp.aa_real_bool _let_1 B2)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real B2) C)) (tptp.pp (tptp.aa_real_bool _let_1 C)))))) (forall ((A tptp.set_int) (B2 tptp.set_int) (C tptp.set_int)) (let ((_let_1 (tptp.ord_less_set_int A))) (=> (tptp.pp (tptp.aa_set_int_bool _let_1 B2)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int B2) C)) (tptp.pp (tptp.aa_set_int_bool _let_1 C)))))) (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 B2)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B2) C)) (tptp.pp (tptp.aa_rat_bool _let_1 C)))))) (forall ((A tptp.num) (B2 tptp.num) (C tptp.num)) (let ((_let_1 (tptp.aa_num_fun_num_bool tptp.ord_less_num A))) (=> (tptp.pp (tptp.aa_num_bool _let_1 B2)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num B2) C)) (tptp.pp (tptp.aa_num_bool _let_1 C)))))) (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 B2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B2) C)) (tptp.pp (tptp.aa_nat_bool _let_1 C)))))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_int A))) (=> (tptp.pp (tptp.aa_int_bool _let_1 B2)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B2) C)) (tptp.pp (tptp.aa_int_bool _let_1 C)))))) (forall ((A tptp.real) (B2 tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B2)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) B2)) (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real B2) A)))))) (forall ((A tptp.set_int) (B2 tptp.set_int)) (= (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_set_int A) B2)) (and (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int A) B2)) (not (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int B2) A)))))) (forall ((A tptp.rat) (B2 tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B2)) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B2)) (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B2) A)))))) (forall ((A tptp.num) (B2 tptp.num)) (= (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num A) B2)) (and (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A) B2)) (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num B2) A)))))) (forall ((A tptp.nat) (B2 tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) B2)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B2)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B2) A)))))) (forall ((A tptp.int) (B2 tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B2)) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B2)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B2) A)))))) (forall ((Z tptp.real) (X tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Z) X)) (=> (forall ((W2 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Z) W2)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real W2) X)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y) W2))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y) Z))))) (forall ((Z tptp.rat) (X tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Z) X)) (=> (forall ((W2 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Z) W2)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat W2) X)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat Y) W2))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat Y) Z))))) (forall ((X tptp.real) (Y tptp.real) (Z tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Y)) (=> (forall ((W2 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) W2)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real W2) Y)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real W2) Z))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y) Z))))) (forall ((X tptp.rat) (Y tptp.rat) (Z tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) Y)) (=> (forall ((W2 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) W2)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat W2) Y)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat W2) Z))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat Y) Z))))) (forall ((B2 tptp.real) (A tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real B2) A)) (or (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B2) A)) (= A B2)))) (forall ((B2 tptp.set_int) (A tptp.set_int)) (= (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int B2) A)) (or (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_set_int B2) A)) (= A B2)))) (forall ((B2 tptp.rat) (A tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B2) A)) (or (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B2) A)) (= A B2)))) (forall ((B2 tptp.num) (A tptp.num)) (= (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num B2) A)) (or (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num B2) A)) (= A B2)))) (forall ((B2 tptp.nat) (A tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B2) A)) (or (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat B2) A)) (= A B2)))) (forall ((B2 tptp.int) (A tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B2) A)) (or (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B2) A)) (= A B2)))) (forall ((B2 tptp.real) (A tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B2) A)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real B2) A)) (not (= A B2))))) (forall ((B2 tptp.set_int) (A tptp.set_int)) (= (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_set_int B2) A)) (and (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int B2) A)) (not (= A B2))))) (forall ((B2 tptp.rat) (A tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B2) A)) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B2) A)) (not (= A B2))))) (forall ((B2 tptp.num) (A tptp.num)) (= (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num B2) A)) (and (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num B2) A)) (not (= A B2))))) (forall ((B2 tptp.nat) (A tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat B2) A)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B2) A)) (not (= A B2))))) (forall ((B2 tptp.int) (A tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B2) A)) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B2) A)) (not (= A B2))))) (forall ((B2 tptp.real) (A tptp.real) (C tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real C))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real B2) A)) (=> (tptp.pp (tptp.aa_real_bool _let_1 B2)) (tptp.pp (tptp.aa_real_bool _let_1 A)))))) (forall ((B2 tptp.set_int) (A tptp.set_int) (C tptp.set_int)) (let ((_let_1 (tptp.ord_less_set_int C))) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int B2) A)) (=> (tptp.pp (tptp.aa_set_int_bool _let_1 B2)) (tptp.pp (tptp.aa_set_int_bool _let_1 A)))))) (forall ((B2 tptp.rat) (A tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat C))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B2) A)) (=> (tptp.pp (tptp.aa_rat_bool _let_1 B2)) (tptp.pp (tptp.aa_rat_bool _let_1 A)))))) (forall ((B2 tptp.num) (A tptp.num) (C tptp.num)) (let ((_let_1 (tptp.aa_num_fun_num_bool tptp.ord_less_num C))) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num B2) A)) (=> (tptp.pp (tptp.aa_num_bool _let_1 B2)) (tptp.pp (tptp.aa_num_bool _let_1 A)))))) (forall ((B2 tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat C))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B2) A)) (=> (tptp.pp (tptp.aa_nat_bool _let_1 B2)) (tptp.pp (tptp.aa_nat_bool _let_1 A)))))) (forall ((B2 tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_int C))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B2) A)) (=> (tptp.pp (tptp.aa_int_bool _let_1 B2)) (tptp.pp (tptp.aa_int_bool _let_1 A)))))) (forall ((B2 tptp.real) (A tptp.real) (C tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B2) A)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real C) B2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real C) A))))) (forall ((B2 tptp.set_int) (A tptp.set_int) (C tptp.set_int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_set_int B2) A)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int C) B2)) (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_set_int C) A))))) (forall ((B2 tptp.rat) (A tptp.rat) (C tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B2) A)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat C) B2)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat C) A))))) (forall ((B2 tptp.num) (A tptp.num) (C tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num B2) A)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num C) B2)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num C) A))))) (forall ((B2 tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat B2) A)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat C) B2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat C) A))))) (forall ((B2 tptp.int) (A tptp.int) (C tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B2) A)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int C) B2)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int C) A))))) (forall ((B2 tptp.real) (A tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B2) A)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real B2) A)) (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) B2)))))) (forall ((B2 tptp.set_int) (A tptp.set_int)) (= (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_set_int B2) A)) (and (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int B2) A)) (not (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int A) B2)))))) (forall ((B2 tptp.rat) (A tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B2) A)) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B2) A)) (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B2)))))) (forall ((B2 tptp.num) (A tptp.num)) (= (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num B2) A)) (and (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num B2) A)) (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A) B2)))))) (forall ((B2 tptp.nat) (A tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat B2) A)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B2) A)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B2)))))) (forall ((B2 tptp.int) (A tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B2) A)) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B2) A)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B2)))))) (forall ((A tptp.real) (B2 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) B2)))) (forall ((A tptp.set_int) (B2 tptp.set_int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_set_int A) B2)) (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int A) B2)))) (forall ((A tptp.rat) (B2 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B2)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B2)))) (forall ((A tptp.num) (B2 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num A) B2)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A) B2)))) (forall ((A tptp.nat) (B2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) B2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B2)))) (forall ((A tptp.int) (B2 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B2)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B2)))) (forall ((B2 tptp.real) (A tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B2) A)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real B2) A)))) (forall ((B2 tptp.set_int) (A tptp.set_int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_set_int B2) A)) (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int B2) A)))) (forall ((B2 tptp.rat) (A tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B2) A)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B2) A)))) (forall ((B2 tptp.num) (A tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num B2) A)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num B2) A)))) (forall ((B2 tptp.nat) (A tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat B2) A)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B2) A)))) (forall ((B2 tptp.int) (A tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B2) A)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B2) A)))) (forall ((X tptp.real) (Y tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) Y)) (or (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Y)) (= X Y)))) (forall ((X tptp.set_int) (Y tptp.set_int)) (= (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int X) Y)) (or (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_set_int X) Y)) (= X Y)))) (forall ((X tptp.rat) (Y tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) Y)) (or (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) Y)) (= X Y)))) (forall ((X tptp.num) (Y tptp.num)) (= (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X) Y)) (or (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X) Y)) (= X Y)))) (forall ((X tptp.nat) (Y tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X) Y)) (or (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Y)) (= X Y)))) (forall ((X tptp.int) (Y tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X) Y)) (or (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) Y)) (= X Y)))) (forall ((X tptp.real) (Y tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Y)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) Y)) (not (= X Y))))) (forall ((X tptp.set_int) (Y tptp.set_int)) (= (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_set_int X) Y)) (and (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int X) Y)) (not (= X Y))))) (forall ((X tptp.rat) (Y tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) Y)) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) Y)) (not (= X Y))))) (forall ((X tptp.num) (Y tptp.num)) (= (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X) Y)) (and (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X) Y)) (not (= X Y))))) (forall ((X tptp.nat) (Y tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Y)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X) Y)) (not (= X Y))))) (forall ((X tptp.int) (Y tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) Y)) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X) Y)) (not (= X Y))))) (forall ((X tptp.real) (Y tptp.real)) (= (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) Y))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y) X)))) (forall ((X tptp.rat) (Y tptp.rat)) (= (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) Y))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Y) X)))) (forall ((X tptp.num) (Y tptp.num)) (= (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X) Y))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num Y) X)))) (forall ((X tptp.nat) (Y tptp.nat)) (= (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X) Y))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Y) X)))) (forall ((X tptp.int) (Y tptp.int)) (= (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X) Y))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Y) X)))) (forall ((X tptp.real) (Y tptp.real)) (= (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Y))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y) X)))) (forall ((X tptp.rat) (Y tptp.rat)) (= (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) Y))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat Y) X)))) (forall ((X tptp.num) (Y tptp.num)) (= (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X) Y))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num Y) X)))) (forall ((X tptp.nat) (Y tptp.nat)) (= (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Y))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Y) X)))) (forall ((X tptp.int) (Y tptp.int)) (= (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) Y))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Y) X)))) (forall ((X tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Y)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) Y)))) (forall ((X tptp.set_int) (Y tptp.set_int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_set_int X) Y)) (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int X) Y)))) (forall ((X tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) Y)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) Y)))) (forall ((X tptp.num) (Y tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X) Y)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X) Y)))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Y)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X) Y)))) (forall ((X tptp.int) (Y tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) Y)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X) Y)))) (forall ((A tptp.real) (B2 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) B2)) (=> (not (= A B2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B2))))) (forall ((A tptp.set_int) (B2 tptp.set_int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int A) B2)) (=> (not (= A B2)) (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_set_int A) B2))))) (forall ((A tptp.rat) (B2 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B2)) (=> (not (= A B2)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B2))))) (forall ((A tptp.num) (B2 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A) B2)) (=> (not (= A B2)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num A) B2))))) (forall ((A tptp.nat) (B2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B2)) (=> (not (= A B2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) B2))))) (forall ((A tptp.int) (B2 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B2)) (=> (not (= A B2)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B2))))) (forall ((A tptp.real) (B2 tptp.real)) (=> (not (= A B2)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) B2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B2))))) (forall ((A tptp.set_int) (B2 tptp.set_int)) (=> (not (= A B2)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int A) B2)) (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_set_int A) B2))))) (forall ((A tptp.rat) (B2 tptp.rat)) (=> (not (= A B2)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B2)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B2))))) (forall ((A tptp.num) (B2 tptp.num)) (=> (not (= A B2)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A) B2)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num A) B2))))) (forall ((A tptp.nat) (B2 tptp.nat)) (=> (not (= A B2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) B2))))) (forall ((A tptp.int) (B2 tptp.int)) (=> (not (= A B2)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B2)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B2))))) (forall ((X tptp.real) (Y tptp.real) (Z tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) Y)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y) Z)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Z))))) (forall ((X tptp.set_int) (Y tptp.set_int) (Z tptp.set_int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int X) Y)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_set_int Y) Z)) (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_set_int X) Z))))) (forall ((X tptp.rat) (Y tptp.rat) (Z tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) Y)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Y) Z)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) Z))))) (forall ((X tptp.num) (Y tptp.num) (Z tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X) Y)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num Y) Z)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X) Z))))) (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X) Y)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Y) Z)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Z))))) (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X) Y)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Y) Z)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) Z))))) (forall ((X tptp.real) (Y tptp.real) (Z tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X))) (=> (tptp.pp (tptp.aa_real_bool _let_1 Y)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y) Z)) (tptp.pp (tptp.aa_real_bool _let_1 Z)))))) (forall ((X tptp.set_int) (Y tptp.set_int) (Z tptp.set_int)) (let ((_let_1 (tptp.ord_less_set_int X))) (=> (tptp.pp (tptp.aa_set_int_bool _let_1 Y)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int Y) Z)) (tptp.pp (tptp.aa_set_int_bool _let_1 Z)))))) (forall ((X tptp.rat) (Y tptp.rat) (Z tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 Y)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat Y) Z)) (tptp.pp (tptp.aa_rat_bool _let_1 Z)))))) (forall ((X tptp.num) (Y tptp.num) (Z tptp.num)) (let ((_let_1 (tptp.aa_num_fun_num_bool tptp.ord_less_num X))) (=> (tptp.pp (tptp.aa_num_bool _let_1 Y)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num Y) Z)) (tptp.pp (tptp.aa_num_bool _let_1 Z)))))) (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 Y)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Y) Z)) (tptp.pp (tptp.aa_nat_bool _let_1 Z)))))) (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_int X))) (=> (tptp.pp (tptp.aa_int_bool _let_1 Y)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Y) Z)) (tptp.pp (tptp.aa_int_bool _let_1 Z)))))) (forall ((A tptp.real) (F tptp.fun_real_real) (B2 tptp.real) (C tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) (tptp.aa_real_real F B2))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B2) C)) (=> (forall ((X4 tptp.real) (Y4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X4) Y4)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real F X4)) (tptp.aa_real_real F Y4))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) (tptp.aa_real_real F C))))))) (forall ((A tptp.real) (F tptp.fun_rat_real) (B2 tptp.rat) (C tptp.rat)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) (tptp.aa_rat_real F B2))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B2) C)) (=> (forall ((X4 tptp.rat) (Y4 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X4) Y4)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_rat_real F X4)) (tptp.aa_rat_real F Y4))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) (tptp.aa_rat_real F C))))))) (forall ((A tptp.real) (F tptp.fun_num_real) (B2 tptp.num) (C tptp.num)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) (tptp.aa_num_real F B2))) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num B2) C)) (=> (forall ((X4 tptp.num) (Y4 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X4) Y4)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_num_real F X4)) (tptp.aa_num_real F Y4))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) (tptp.aa_num_real F C))))))) (forall ((A tptp.real) (F tptp.fun_nat_real) (B2 tptp.nat) (C tptp.nat)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) (tptp.aa_nat_real F B2))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat B2) C)) (=> (forall ((X4 tptp.nat) (Y4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X4) Y4)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_nat_real F X4)) (tptp.aa_nat_real F Y4))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) (tptp.aa_nat_real F C))))))) (forall ((A tptp.real) (F tptp.fun_int_real) (B2 tptp.int) (C tptp.int)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) (tptp.aa_int_real F B2))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B2) C)) (=> (forall ((X4 tptp.int) (Y4 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X4) Y4)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_int_real F X4)) (tptp.aa_int_real F Y4))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) (tptp.aa_int_real F C))))))) (forall ((A tptp.rat) (F tptp.fun_real_rat) (B2 tptp.real) (C tptp.real)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) (tptp.aa_real_rat F B2))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B2) C)) (=> (forall ((X4 tptp.real) (Y4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X4) Y4)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_real_rat F X4)) (tptp.aa_real_rat F Y4))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) (tptp.aa_real_rat F C))))))) (forall ((A tptp.rat) (F tptp.fun_rat_rat) (B2 tptp.rat) (C tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) (tptp.aa_rat_rat F B2))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B2) C)) (=> (forall ((X4 tptp.rat) (Y4 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X4) Y4)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat F X4)) (tptp.aa_rat_rat F Y4))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) (tptp.aa_rat_rat F C))))))) (forall ((A tptp.rat) (F tptp.fun_num_rat) (B2 tptp.num) (C tptp.num)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) (tptp.aa_num_rat F B2))) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num B2) C)) (=> (forall ((X4 tptp.num) (Y4 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X4) Y4)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_num_rat F X4)) (tptp.aa_num_rat F Y4))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) (tptp.aa_num_rat F C))))))) (forall ((A tptp.rat) (F tptp.fun_nat_rat) (B2 tptp.nat) (C tptp.nat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) (tptp.aa_nat_rat F B2))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat B2) C)) (=> (forall ((X4 tptp.nat) (Y4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X4) Y4)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_nat_rat F X4)) (tptp.aa_nat_rat F Y4))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) (tptp.aa_nat_rat F C))))))) (forall ((A tptp.rat) (F tptp.fun_int_rat) (B2 tptp.int) (C tptp.int)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) (tptp.aa_int_rat F B2))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B2) C)) (=> (forall ((X4 tptp.int) (Y4 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X4) Y4)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_int_rat F X4)) (tptp.aa_int_rat F Y4))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) (tptp.aa_int_rat F C))))))) (forall ((A tptp.rat) (B2 tptp.rat) (F tptp.fun_rat_real) (C tptp.real)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B2)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_rat_real F B2)) C)) (=> (forall ((X4 tptp.rat) (Y4 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X4) Y4)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_rat_real F X4)) (tptp.aa_rat_real F Y4))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_rat_real F A)) C)))))) (forall ((A tptp.rat) (B2 tptp.rat) (F tptp.fun_rat_rat) (C tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B2)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat F B2)) C)) (=> (forall ((X4 tptp.rat) (Y4 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X4) Y4)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat F X4)) (tptp.aa_rat_rat F Y4))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat F A)) C)))))) (forall ((A tptp.rat) (B2 tptp.rat) (F tptp.fun_rat_num) (C tptp.num)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B2)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num (tptp.aa_rat_num F B2)) C)) (=> (forall ((X4 tptp.rat) (Y4 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X4) Y4)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_rat_num F X4)) (tptp.aa_rat_num F Y4))))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num (tptp.aa_rat_num F A)) C)))))) (forall ((A tptp.rat) (B2 tptp.rat) (F tptp.fun_rat_nat) (C tptp.nat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_rat_nat F B2)) C)) (=> (forall ((X4 tptp.rat) (Y4 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X4) Y4)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_rat_nat F X4)) (tptp.aa_rat_nat F Y4))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_rat_nat F A)) C)))))) (forall ((A tptp.rat) (B2 tptp.rat) (F tptp.fun_rat_int) (C tptp.int)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B2)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_rat_int F B2)) C)) (=> (forall ((X4 tptp.rat) (Y4 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X4) Y4)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_rat_int F X4)) (tptp.aa_rat_int F Y4))))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_rat_int F A)) C)))))) (forall ((A tptp.num) (B2 tptp.num) (F tptp.fun_num_real) (C tptp.real)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A) B2)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_num_real F B2)) C)) (=> (forall ((X4 tptp.num) (Y4 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X4) Y4)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_num_real F X4)) (tptp.aa_num_real F Y4))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_num_real F A)) C)))))) (forall ((A tptp.num) (B2 tptp.num) (F tptp.fun_num_rat) (C tptp.rat)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A) B2)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_num_rat F B2)) C)) (=> (forall ((X4 tptp.num) (Y4 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X4) Y4)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_num_rat F X4)) (tptp.aa_num_rat F Y4))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_num_rat F A)) C)))))) (forall ((A tptp.num) (B2 tptp.num) (F tptp.fun_num_num) (C tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A) B2)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num (tptp.aa_num_num F B2)) C)) (=> (forall ((X4 tptp.num) (Y4 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X4) Y4)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_num_num F X4)) (tptp.aa_num_num F Y4))))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num (tptp.aa_num_num F A)) C)))))) (forall ((A tptp.num) (B2 tptp.num) (F tptp.fun_num_nat) (C tptp.nat)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A) B2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_num_nat F B2)) C)) (=> (forall ((X4 tptp.num) (Y4 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X4) Y4)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_num_nat F X4)) (tptp.aa_num_nat F Y4))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_num_nat F A)) C)))))) (forall ((A tptp.num) (B2 tptp.num) (F tptp.fun_num_int) (C tptp.int)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A) B2)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_num_int F B2)) C)) (=> (forall ((X4 tptp.num) (Y4 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X4) Y4)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_num_int F X4)) (tptp.aa_num_int F Y4))))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_num_int F A)) C)))))) (forall ((A tptp.real) (F tptp.fun_rat_real) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A))) (=> (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_rat_real F B2))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B2) C)) (=> (forall ((X4 tptp.rat) (Y4 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X4) Y4)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_rat_real F X4)) (tptp.aa_rat_real F Y4))))) (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_rat_real F C)))))))) (forall ((A tptp.rat) (F tptp.fun_rat_rat) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat F B2))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B2) C)) (=> (forall ((X4 tptp.rat) (Y4 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X4) Y4)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat F X4)) (tptp.aa_rat_rat F Y4))))) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat F C)))))))) (forall ((A tptp.num) (F tptp.fun_rat_num) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_num_fun_num_bool tptp.ord_less_num A))) (=> (tptp.pp (tptp.aa_num_bool _let_1 (tptp.aa_rat_num F B2))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B2) C)) (=> (forall ((X4 tptp.rat) (Y4 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X4) Y4)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_rat_num F X4)) (tptp.aa_rat_num F Y4))))) (tptp.pp (tptp.aa_num_bool _let_1 (tptp.aa_rat_num F C)))))))) (forall ((A tptp.nat) (F tptp.fun_rat_nat) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_rat_nat F B2))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B2) C)) (=> (forall ((X4 tptp.rat) (Y4 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X4) Y4)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_rat_nat F X4)) (tptp.aa_rat_nat F Y4))))) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_rat_nat F C)))))))) (forall ((A tptp.int) (F tptp.fun_rat_int) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_int A))) (=> (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_rat_int F B2))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B2) C)) (=> (forall ((X4 tptp.rat) (Y4 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X4) Y4)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_rat_int F X4)) (tptp.aa_rat_int F Y4))))) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_rat_int F C)))))))) (forall ((A tptp.real) (F tptp.fun_num_real) (B2 tptp.num) (C tptp.num)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A))) (=> (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_num_real F B2))) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num B2) C)) (=> (forall ((X4 tptp.num) (Y4 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X4) Y4)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_num_real F X4)) (tptp.aa_num_real F Y4))))) (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_num_real F C)))))))) (forall ((A tptp.rat) (F tptp.fun_num_rat) (B2 tptp.num) (C tptp.num)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_num_rat F B2))) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num B2) C)) (=> (forall ((X4 tptp.num) (Y4 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X4) Y4)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_num_rat F X4)) (tptp.aa_num_rat F Y4))))) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_num_rat F C)))))))) (forall ((A tptp.num) (F tptp.fun_num_num) (B2 tptp.num) (C tptp.num)) (let ((_let_1 (tptp.aa_num_fun_num_bool tptp.ord_less_num A))) (=> (tptp.pp (tptp.aa_num_bool _let_1 (tptp.aa_num_num F B2))) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num B2) C)) (=> (forall ((X4 tptp.num) (Y4 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X4) Y4)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_num_num F X4)) (tptp.aa_num_num F Y4))))) (tptp.pp (tptp.aa_num_bool _let_1 (tptp.aa_num_num F C)))))))) (forall ((A tptp.nat) (F tptp.fun_num_nat) (B2 tptp.num) (C tptp.num)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_num_nat F B2))) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num B2) C)) (=> (forall ((X4 tptp.num) (Y4 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X4) Y4)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_num_nat F X4)) (tptp.aa_num_nat F Y4))))) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_num_nat F C)))))))) (forall ((A tptp.int) (F tptp.fun_num_int) (B2 tptp.num) (C tptp.num)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_int A))) (=> (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_num_int F B2))) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num B2) C)) (=> (forall ((X4 tptp.num) (Y4 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X4) Y4)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_num_int F X4)) (tptp.aa_num_int F Y4))))) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_num_int F C)))))))) (forall ((A tptp.real) (B2 tptp.real) (F tptp.fun_real_real) (C tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B2)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real F B2)) C)) (=> (forall ((X4 tptp.real) (Y4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X4) Y4)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real F X4)) (tptp.aa_real_real F Y4))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real F A)) C)))))) (forall ((A tptp.rat) (B2 tptp.rat) (F tptp.fun_rat_real) (C tptp.real)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B2)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_rat_real F B2)) C)) (=> (forall ((X4 tptp.rat) (Y4 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X4) Y4)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_rat_real F X4)) (tptp.aa_rat_real F Y4))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_rat_real F A)) C)))))) (forall ((A tptp.num) (B2 tptp.num) (F tptp.fun_num_real) (C tptp.real)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num A) B2)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_num_real F B2)) C)) (=> (forall ((X4 tptp.num) (Y4 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X4) Y4)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_num_real F X4)) (tptp.aa_num_real F Y4))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_num_real F A)) C)))))) (forall ((A tptp.nat) (B2 tptp.nat) (F tptp.fun_nat_real) (C tptp.real)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) B2)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_nat_real F B2)) C)) (=> (forall ((X4 tptp.nat) (Y4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X4) Y4)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_nat_real F X4)) (tptp.aa_nat_real F Y4))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_nat_real F A)) C)))))) (forall ((A tptp.int) (B2 tptp.int) (F tptp.fun_int_real) (C tptp.real)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B2)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_int_real F B2)) C)) (=> (forall ((X4 tptp.int) (Y4 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X4) Y4)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_int_real F X4)) (tptp.aa_int_real F Y4))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_int_real F A)) C)))))) (forall ((A tptp.real) (B2 tptp.real) (F tptp.fun_real_rat) (C tptp.rat)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B2)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_real_rat F B2)) C)) (=> (forall ((X4 tptp.real) (Y4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X4) Y4)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_real_rat F X4)) (tptp.aa_real_rat F Y4))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_real_rat F A)) C)))))) (forall ((A tptp.rat) (B2 tptp.rat) (F tptp.fun_rat_rat) (C tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B2)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat F B2)) C)) (=> (forall ((X4 tptp.rat) (Y4 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X4) Y4)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat F X4)) (tptp.aa_rat_rat F Y4))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat F A)) C)))))) (forall ((A tptp.num) (B2 tptp.num) (F tptp.fun_num_rat) (C tptp.rat)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num A) B2)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_num_rat F B2)) C)) (=> (forall ((X4 tptp.num) (Y4 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X4) Y4)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_num_rat F X4)) (tptp.aa_num_rat F Y4))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_num_rat F A)) C)))))) (forall ((A tptp.nat) (B2 tptp.nat) (F tptp.fun_nat_rat) (C tptp.rat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) B2)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat F B2)) C)) (=> (forall ((X4 tptp.nat) (Y4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X4) Y4)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_nat_rat F X4)) (tptp.aa_nat_rat F Y4))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_nat_rat F A)) C)))))) (forall ((A tptp.int) (B2 tptp.int) (F tptp.fun_int_rat) (C tptp.rat)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B2)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_int_rat F B2)) C)) (=> (forall ((X4 tptp.int) (Y4 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X4) Y4)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_int_rat F X4)) (tptp.aa_int_rat F Y4))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_int_rat F A)) C)))))) (forall ((X tptp.real) (Y tptp.real)) (or (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) Y)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y) X)))) (forall ((X tptp.rat) (Y tptp.rat)) (or (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) Y)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Y) X)))) (forall ((X tptp.num) (Y tptp.num)) (or (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X) Y)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num Y) X)))) (forall ((X tptp.nat) (Y tptp.nat)) (or (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X) Y)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Y) X)))) (forall ((X tptp.int) (Y tptp.int)) (or (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X) Y)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Y) X)))) (forall ((X tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) Y)) (or (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Y)) (= X Y)))) (forall ((X tptp.set_int) (Y tptp.set_int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int X) Y)) (or (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_set_int X) Y)) (= X Y)))) (forall ((X tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) Y)) (or (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) Y)) (= X Y)))) (forall ((X tptp.num) (Y tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X) Y)) (or (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X) Y)) (= X Y)))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X) Y)) (or (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Y)) (= X Y)))) (forall ((X tptp.int) (Y tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X) Y)) (or (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) Y)) (= X Y)))) (forall ((A tptp.set_nat)) (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat tptp.bot_bot_set_nat) A))) (forall ((A tptp.extended_enat)) (tptp.pp (tptp.aa_Ext2772979874139974381t_bool (tptp.ord_le2932123472753598470d_enat tptp.bot_bo4199563552545308370d_enat) A))) (forall ((A tptp.set_real)) (tptp.ord_less_eq_set_real tptp.bot_bot_set_real A)) (forall ((A tptp.set_int)) (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int tptp.bot_bot_set_int) A))) (forall ((A tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.bot_bot_nat) A))) (forall ((A tptp.set_nat)) (= (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat A) tptp.bot_bot_set_nat)) (= A tptp.bot_bot_set_nat))) (forall ((A tptp.extended_enat)) (= (tptp.pp (tptp.aa_Ext2772979874139974381t_bool (tptp.ord_le2932123472753598470d_enat A) tptp.bot_bo4199563552545308370d_enat)) (= A tptp.bot_bo4199563552545308370d_enat))) (forall ((A tptp.set_real)) (= (tptp.ord_less_eq_set_real A tptp.bot_bot_set_real) (= A tptp.bot_bot_set_real))) (forall ((A tptp.set_int)) (= (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int A) tptp.bot_bot_set_int)) (= A tptp.bot_bot_set_int))) (forall ((A tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) tptp.bot_bot_nat)) (= A tptp.bot_bot_nat))) (forall ((A tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat A) tptp.bot_bot_set_nat)) (= A tptp.bot_bot_set_nat))) (forall ((A tptp.extended_enat)) (=> (tptp.pp (tptp.aa_Ext2772979874139974381t_bool (tptp.ord_le2932123472753598470d_enat A) tptp.bot_bo4199563552545308370d_enat)) (= A tptp.bot_bo4199563552545308370d_enat))) (forall ((A tptp.set_real)) (=> (tptp.ord_less_eq_set_real A tptp.bot_bot_set_real) (= A tptp.bot_bot_set_real))) (forall ((A tptp.set_int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int A) tptp.bot_bot_set_int)) (= A tptp.bot_bot_set_int))) (forall ((A tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) tptp.bot_bot_nat)) (= A tptp.bot_bot_nat))) (forall ((A tptp.set_nat)) (not (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_set_nat A) tptp.bot_bot_set_nat)))) (forall ((A tptp.extended_enat)) (not (tptp.pp (tptp.aa_Ext2772979874139974381t_bool (tptp.ord_le72135733267957522d_enat A) tptp.bot_bo4199563552545308370d_enat)))) (forall ((A tptp.set_int)) (not (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_set_int A) tptp.bot_bot_set_int)))) (forall ((A tptp.set_real)) (not (tptp.ord_less_set_real A tptp.bot_bot_set_real))) (forall ((A tptp.nat)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) tptp.bot_bot_nat)))) (forall ((A tptp.set_nat)) (= (not (= A tptp.bot_bot_set_nat)) (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_set_nat tptp.bot_bot_set_nat) A)))) (forall ((A tptp.extended_enat)) (= (not (= A tptp.bot_bo4199563552545308370d_enat)) (tptp.pp (tptp.aa_Ext2772979874139974381t_bool (tptp.ord_le72135733267957522d_enat tptp.bot_bo4199563552545308370d_enat) A)))) (forall ((A tptp.set_int)) (= (not (= A tptp.bot_bot_set_int)) (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_set_int tptp.bot_bot_set_int) A)))) (forall ((A tptp.set_real)) (= (not (= A tptp.bot_bot_set_real)) (tptp.ord_less_set_real tptp.bot_bot_set_real A))) (forall ((A tptp.nat)) (= (not (= A tptp.bot_bot_nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.bot_bot_nat) A)))) (forall ((P tptp.fun_nat_fun_nat_bool) (A tptp.nat) (B2 tptp.nat)) (=> (forall ((A3 tptp.nat) (B3 tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool P A3) B3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool P B3) A3)))) (=> (forall ((A3 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool P A3) tptp.zero_zero_nat))) (=> (forall ((A3 tptp.nat) (B3 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool P A3))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 B3)) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A3) B3)))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool P A) B2)))))) (forall ((Mi tptp.nat) (Ma tptp.nat) (Va tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat tptp.suc Va)))) (let ((_let_2 (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Mi) Ma)) _let_1 TreeList Summary))) (let ((_let_3 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat _let_1) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_4 (tptp.if_nat (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Mi)))) (let ((_let_5 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat _let_4 Mi) X))) (let ((_let_6 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high _let_5) _let_3))) (let ((_let_7 (tptp.nth_VEBT_VEBT TreeList _let_6))) (let ((_let_8 (tptp.aa_nat_fun_nat_bool tptp.fequal_nat X))) (= (tptp.vEBT_vebt_insert _let_2 X) (tptp.if_VEBT_VEBT (tptp.aa_bool_bool (tptp.fconj (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_6) (tptp.size_s6755466524823107622T_VEBT TreeList))) (tptp.aa_bool_bool tptp.fNot (tptp.aa_bool_bool (tptp.fdisj (tptp.aa_nat_bool _let_8 Mi)) (tptp.aa_nat_bool _let_8 Ma)))) (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat _let_4 X) Mi)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat _let_5) Ma))) _let_1 (tptp.list_u1324408373059187874T_VEBT TreeList _let_6 (tptp.vEBT_vebt_insert _let_7 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low _let_5) _let_3))) (tptp.if_VEBT_VEBT (tptp.aa_VEBT_VEBT_bool tptp.vEBT_VEBT_minNull _let_7) (tptp.vEBT_vebt_insert Summary _let_6) Summary)) _let_2))))))))))) (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y tptp.vEBT_VEBT)) (=> (= (tptp.vEBT_vebt_insert X Xa2) Y) (=> (forall ((A3 tptp.bool) (B3 tptp.bool)) (let ((_let_1 (tptp.vEBT_Leaf A3 B3))) (let ((_let_2 (= Xa2 tptp.one_one_nat))) (let ((_let_3 (= Xa2 tptp.zero_zero_nat))) (=> (= X _let_1) (not (and (=> _let_3 (= Y (tptp.vEBT_Leaf tptp.fTrue B3))) (=> (not _let_3) (and (=> _let_2 (= Y (tptp.vEBT_Leaf A3 tptp.fTrue))) (=> (not _let_2) (= Y _let_1))))))))))) (=> (forall ((Info2 tptp.option4927543243414619207at_nat) (Ts2 tptp.list_VEBT_VEBT) (S3 tptp.vEBT_VEBT)) (let ((_let_1 (tptp.vEBT_Node Info2 tptp.zero_zero_nat Ts2 S3))) (=> (= X _let_1) (not (= Y _let_1))))) (=> (forall ((Info2 tptp.option4927543243414619207at_nat) (Ts2 tptp.list_VEBT_VEBT) (S3 tptp.vEBT_VEBT)) (let ((_let_1 (tptp.vEBT_Node Info2 (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat) Ts2 S3))) (=> (= X _let_1) (not (= Y _let_1))))) (=> (forall ((V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat tptp.suc V2)))) (=> (= X (tptp.vEBT_Node tptp.none_P5556105721700978146at_nat _let_1 TreeList2 Summary2)) (not (= Y (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Xa2) Xa2)) _let_1 TreeList2 Summary2)))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat tptp.suc Va2)))) (let ((_let_2 (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Mi2) Ma2)) _let_1 TreeList2 Summary2))) (let ((_let_3 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat _let_1) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_4 (tptp.if_nat (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Xa2) Mi2)))) (let ((_let_5 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat _let_4 Mi2) Xa2))) (let ((_let_6 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high _let_5) _let_3))) (let ((_let_7 (tptp.nth_VEBT_VEBT TreeList2 _let_6))) (let ((_let_8 (tptp.aa_nat_fun_nat_bool tptp.fequal_nat Xa2))) (=> (= X _let_2) (not (= Y (tptp.if_VEBT_VEBT (tptp.aa_bool_bool (tptp.fconj (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_6) (tptp.size_s6755466524823107622T_VEBT TreeList2))) (tptp.aa_bool_bool tptp.fNot (tptp.aa_bool_bool (tptp.fdisj (tptp.aa_nat_bool _let_8 Mi2)) (tptp.aa_nat_bool _let_8 Ma2)))) (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat _let_4 Xa2) Mi2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat _let_5) Ma2))) _let_1 (tptp.list_u1324408373059187874T_VEBT TreeList2 _let_6 (tptp.vEBT_vebt_insert _let_7 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low _let_5) _let_3))) (tptp.if_VEBT_VEBT (tptp.aa_VEBT_VEBT_bool tptp.vEBT_VEBT_minNull _let_7) (tptp.vEBT_vebt_insert Summary2 _let_6) Summary2)) _let_2)))))))))))))))))))) (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y tptp.vEBT_VEBT)) (=> (= (tptp.vEBT_vebt_insert X Xa2) Y) (=> (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_insert_rel (tptp.produc738532404422230701BT_nat X Xa2)) (=> (forall ((A3 tptp.bool) (B3 tptp.bool)) (let ((_let_1 (tptp.vEBT_Leaf A3 B3))) (let ((_let_2 (= Xa2 tptp.one_one_nat))) (let ((_let_3 (= Xa2 tptp.zero_zero_nat))) (=> (= X _let_1) (=> (and (=> _let_3 (= Y (tptp.vEBT_Leaf tptp.fTrue B3))) (=> (not _let_3) (and (=> _let_2 (= Y (tptp.vEBT_Leaf A3 tptp.fTrue))) (=> (not _let_2) (= Y _let_1))))) (not (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_insert_rel (tptp.produc738532404422230701BT_nat _let_1 Xa2))))))))) (=> (forall ((Info2 tptp.option4927543243414619207at_nat) (Ts2 tptp.list_VEBT_VEBT) (S3 tptp.vEBT_VEBT)) (let ((_let_1 (tptp.vEBT_Node Info2 tptp.zero_zero_nat Ts2 S3))) (=> (= X _let_1) (=> (= Y _let_1) (not (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_insert_rel (tptp.produc738532404422230701BT_nat _let_1 Xa2))))))) (=> (forall ((Info2 tptp.option4927543243414619207at_nat) (Ts2 tptp.list_VEBT_VEBT) (S3 tptp.vEBT_VEBT)) (let ((_let_1 (tptp.vEBT_Node Info2 (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat) Ts2 S3))) (=> (= X _let_1) (=> (= Y _let_1) (not (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_insert_rel (tptp.produc738532404422230701BT_nat _let_1 Xa2))))))) (=> (forall ((V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat tptp.suc V2)))) (let ((_let_2 (tptp.vEBT_Node tptp.none_P5556105721700978146at_nat _let_1 TreeList2 Summary2))) (=> (= X _let_2) (=> (= Y (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Xa2) Xa2)) _let_1 TreeList2 Summary2)) (not (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_insert_rel (tptp.produc738532404422230701BT_nat _let_2 Xa2)))))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat tptp.suc Va2)))) (let ((_let_2 (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Mi2) Ma2)) _let_1 TreeList2 Summary2))) (let ((_let_3 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat _let_1) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_4 (tptp.if_nat (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Xa2) Mi2)))) (let ((_let_5 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat _let_4 Mi2) Xa2))) (let ((_let_6 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high _let_5) _let_3))) (let ((_let_7 (tptp.nth_VEBT_VEBT TreeList2 _let_6))) (let ((_let_8 (tptp.aa_nat_fun_nat_bool tptp.fequal_nat Xa2))) (=> (= X _let_2) (=> (= Y (tptp.if_VEBT_VEBT (tptp.aa_bool_bool (tptp.fconj (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_6) (tptp.size_s6755466524823107622T_VEBT TreeList2))) (tptp.aa_bool_bool tptp.fNot (tptp.aa_bool_bool (tptp.fdisj (tptp.aa_nat_bool _let_8 Mi2)) (tptp.aa_nat_bool _let_8 Ma2)))) (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat _let_4 Xa2) Mi2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat _let_5) Ma2))) _let_1 (tptp.list_u1324408373059187874T_VEBT TreeList2 _let_6 (tptp.vEBT_vebt_insert _let_7 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low _let_5) _let_3))) (tptp.if_VEBT_VEBT (tptp.aa_VEBT_VEBT_bool tptp.vEBT_VEBT_minNull _let_7) (tptp.vEBT_vebt_insert Summary2 _let_6) Summary2)) _let_2)) (not (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_insert_rel (tptp.produc738532404422230701BT_nat _let_2 Xa2)))))))))))))))))))))) (forall ((X tptp.extended_enat) (Y tptp.extended_enat) (Z tptp.extended_enat)) (= (tptp.pp (tptp.aa_Ext2772979874139974381t_bool (tptp.ord_le72135733267957522d_enat (tptp.aa_Ext7969882492699152700d_enat (tptp.aa_Ext3475206891998675565d_enat tptp.ord_ma741700101516333627d_enat X) Y)) Z)) (and (tptp.pp (tptp.aa_Ext2772979874139974381t_bool (tptp.ord_le72135733267957522d_enat X) Z)) (tptp.pp (tptp.aa_Ext2772979874139974381t_bool (tptp.ord_le72135733267957522d_enat Y) Z))))) (forall ((X tptp.real) (Y tptp.real) (Z tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.ord_max_real X) Y)) Z)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Z)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y) Z))))) (forall ((X tptp.rat) (Y tptp.rat) (Z tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.ord_max_rat X) Y)) Z)) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) Z)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Y) Z))))) (forall ((X tptp.num) (Y tptp.num) (Z tptp.num)) (= (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.ord_max_num X) Y)) Z)) (and (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X) Z)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num Y) Z))))) (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat X) Y)) Z)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Z)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Y) Z))))) (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.ord_max_int X) Y)) Z)) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) Z)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Y) Z))))) (forall ((A tptp.extended_enat) (B2 tptp.extended_enat)) (=> (tptp.pp (tptp.aa_Ext2772979874139974381t_bool (tptp.ord_le72135733267957522d_enat A) B2)) (= (tptp.aa_Ext7969882492699152700d_enat (tptp.aa_Ext3475206891998675565d_enat tptp.ord_ma741700101516333627d_enat A) B2) B2))) (forall ((A tptp.real) (B2 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B2)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.ord_max_real A) B2) B2))) (forall ((A tptp.rat) (B2 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B2)) (= (tptp.aa_rat_rat (tptp.ord_max_rat A) B2) B2))) (forall ((A tptp.num) (B2 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num A) B2)) (= (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.ord_max_num A) B2) B2))) (forall ((A tptp.nat) (B2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) B2)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat A) B2) B2))) (forall ((A tptp.int) (B2 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B2)) (= (tptp.aa_int_int (tptp.ord_max_int A) B2) B2))) (forall ((B2 tptp.extended_enat) (A tptp.extended_enat)) (=> (tptp.pp (tptp.aa_Ext2772979874139974381t_bool (tptp.ord_le72135733267957522d_enat B2) A)) (= (tptp.aa_Ext7969882492699152700d_enat (tptp.aa_Ext3475206891998675565d_enat tptp.ord_ma741700101516333627d_enat A) B2) A))) (forall ((B2 tptp.real) (A tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B2) A)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.ord_max_real A) B2) A))) (forall ((B2 tptp.rat) (A tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B2) A)) (= (tptp.aa_rat_rat (tptp.ord_max_rat A) B2) A))) (forall ((B2 tptp.num) (A tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num B2) A)) (= (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.ord_max_num A) B2) A))) (forall ((B2 tptp.nat) (A tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat B2) A)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat A) B2) A))) (forall ((B2 tptp.int) (A tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B2) A)) (= (tptp.aa_int_int (tptp.ord_max_int A) B2) A))) (forall ((B2 tptp.extended_enat) (A tptp.extended_enat)) (=> (tptp.pp (tptp.aa_Ext2772979874139974381t_bool (tptp.ord_le2932123472753598470d_enat B2) A)) (= (tptp.aa_Ext7969882492699152700d_enat (tptp.aa_Ext3475206891998675565d_enat tptp.ord_ma741700101516333627d_enat A) B2) A))) (forall ((B2 tptp.rat) (A tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B2) A)) (= (tptp.aa_rat_rat (tptp.ord_max_rat A) B2) A))) (forall ((B2 tptp.num) (A tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num B2) A)) (= (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.ord_max_num A) B2) A))) (forall ((B2 tptp.nat) (A tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B2) A)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat A) B2) A))) (forall ((B2 tptp.int) (A tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B2) A)) (= (tptp.aa_int_int (tptp.ord_max_int A) B2) A))) (forall ((A tptp.extended_enat) (B2 tptp.extended_enat)) (=> (tptp.pp (tptp.aa_Ext2772979874139974381t_bool (tptp.ord_le2932123472753598470d_enat A) B2)) (= (tptp.aa_Ext7969882492699152700d_enat (tptp.aa_Ext3475206891998675565d_enat tptp.ord_ma741700101516333627d_enat A) B2) B2))) (forall ((A tptp.rat) (B2 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B2)) (= (tptp.aa_rat_rat (tptp.ord_max_rat A) B2) B2))) (forall ((A tptp.num) (B2 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A) B2)) (= (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.ord_max_num A) B2) B2))) (forall ((A tptp.nat) (B2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B2)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat A) B2) B2))) (forall ((A tptp.int) (B2 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B2)) (= (tptp.aa_int_int (tptp.ord_max_int A) B2) B2))) (forall ((B2 tptp.extended_enat) (C tptp.extended_enat) (A tptp.extended_enat)) (= (tptp.pp (tptp.aa_Ext2772979874139974381t_bool (tptp.ord_le2932123472753598470d_enat (tptp.aa_Ext7969882492699152700d_enat (tptp.aa_Ext3475206891998675565d_enat tptp.ord_ma741700101516333627d_enat B2) C)) A)) (and (tptp.pp (tptp.aa_Ext2772979874139974381t_bool (tptp.ord_le2932123472753598470d_enat B2) A)) (tptp.pp (tptp.aa_Ext2772979874139974381t_bool (tptp.ord_le2932123472753598470d_enat C) A))))) (forall ((B2 tptp.rat) (C tptp.rat) (A tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.ord_max_rat B2) C)) A)) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B2) A)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat C) A))))) (forall ((B2 tptp.num) (C tptp.num) (A tptp.num)) (= (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.ord_max_num B2) C)) A)) (and (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num B2) A)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num C) A))))) (forall ((B2 tptp.nat) (C tptp.nat) (A tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat B2) C)) A)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B2) A)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat C) A))))) (forall ((B2 tptp.int) (C tptp.int) (A tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.ord_max_int B2) C)) A)) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B2) A)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int C) A))))) (= (tptp.aa_complex_complex tptp.neg_nu7009210354673126013omplex tptp.one_one_complex) _let_50) (= (tptp.aa_real_real tptp.neg_numeral_dbl_real tptp.one_one_real) _let_28) (= (tptp.aa_rat_rat tptp.neg_numeral_dbl_rat tptp.one_one_rat) _let_69) (= (tptp.aa_int_int tptp.neg_numeral_dbl_int tptp.one_one_int) _let_44) (forall ((Q2 tptp.extended_enat)) (= (tptp.aa_Ext7969882492699152700d_enat (tptp.aa_Ext3475206891998675565d_enat tptp.ord_ma741700101516333627d_enat tptp.zero_z5237406670263579293d_enat) Q2) Q2)) (forall ((Q2 tptp.extended_enat)) (= (tptp.aa_Ext7969882492699152700d_enat (tptp.aa_Ext3475206891998675565d_enat tptp.ord_ma741700101516333627d_enat Q2) tptp.zero_z5237406670263579293d_enat) Q2)) (= (tptp.aa_complex_complex tptp.neg_nu7009210354673126013omplex tptp.zero_zero_complex) tptp.zero_zero_complex) (= (tptp.aa_real_real tptp.neg_numeral_dbl_real tptp.zero_zero_real) tptp.zero_zero_real) (= (tptp.aa_rat_rat tptp.neg_numeral_dbl_rat tptp.zero_zero_rat) tptp.zero_zero_rat) (= (tptp.aa_int_int tptp.neg_numeral_dbl_int tptp.zero_zero_int) tptp.zero_zero_int) (forall ((K tptp.num)) (= (tptp.aa_complex_complex tptp.neg_nu7009210354673126013omplex (tptp.numera6690914467698888265omplex K)) (tptp.numera6690914467698888265omplex (tptp.aa_num_num tptp.bit0 K)))) (forall ((K tptp.num)) (= (tptp.aa_real_real tptp.neg_numeral_dbl_real (tptp.aa_num_real tptp.numeral_numeral_real K)) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 K)))) (forall ((K tptp.num)) (= (tptp.aa_rat_rat tptp.neg_numeral_dbl_rat (tptp.aa_num_rat tptp.numeral_numeral_rat K)) (tptp.aa_num_rat tptp.numeral_numeral_rat (tptp.aa_num_num tptp.bit0 K)))) (forall ((K tptp.num)) (= (tptp.aa_int_int tptp.neg_numeral_dbl_int (tptp.aa_num_int tptp.numeral_numeral_int K)) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 K)))) (= tptp.bot_bot_nat tptp.zero_zero_nat) (= tptp.bot_bo4199563552545308370d_enat tptp.zero_z5237406670263579293d_enat) (forall ((X tptp.real)) (= (tptp.aa_real_real tptp.neg_numeral_dbl_real X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) X))) (forall ((X tptp.rat)) (= (tptp.aa_rat_rat tptp.neg_numeral_dbl_rat X) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat X) X))) (forall ((X tptp.int)) (= (tptp.aa_int_int tptp.neg_numeral_dbl_int X) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int X) X))) (forall ((C tptp.extended_enat) (B2 tptp.extended_enat) (A tptp.extended_enat)) (let ((_let_1 (tptp.ord_le2932123472753598470d_enat C))) (=> (tptp.pp (tptp.aa_Ext2772979874139974381t_bool _let_1 B2)) (tptp.pp (tptp.aa_Ext2772979874139974381t_bool _let_1 (tptp.aa_Ext7969882492699152700d_enat (tptp.aa_Ext3475206891998675565d_enat tptp.ord_ma741700101516333627d_enat A) B2)))))) (forall ((C tptp.rat) (B2 tptp.rat) (A tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat C))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 B2)) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat (tptp.ord_max_rat A) B2)))))) (forall ((C tptp.num) (B2 tptp.num) (A tptp.num)) (let ((_let_1 (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num C))) (=> (tptp.pp (tptp.aa_num_bool _let_1 B2)) (tptp.pp (tptp.aa_num_bool _let_1 (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.ord_max_num A) B2)))))) (forall ((C tptp.nat) (B2 tptp.nat) (A tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat C))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 B2)) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat A) B2)))))) (forall ((C tptp.int) (B2 tptp.int) (A tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int C))) (=> (tptp.pp (tptp.aa_int_bool _let_1 B2)) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.ord_max_int A) B2)))))) (forall ((C tptp.extended_enat) (A tptp.extended_enat) (B2 tptp.extended_enat)) (let ((_let_1 (tptp.ord_le2932123472753598470d_enat C))) (=> (tptp.pp (tptp.aa_Ext2772979874139974381t_bool _let_1 A)) (tptp.pp (tptp.aa_Ext2772979874139974381t_bool _let_1 (tptp.aa_Ext7969882492699152700d_enat (tptp.aa_Ext3475206891998675565d_enat tptp.ord_ma741700101516333627d_enat A) B2)))))) (forall ((C tptp.rat) (A tptp.rat) (B2 tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat C))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 A)) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat (tptp.ord_max_rat A) B2)))))) (forall ((C tptp.num) (A tptp.num) (B2 tptp.num)) (let ((_let_1 (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num C))) (=> (tptp.pp (tptp.aa_num_bool _let_1 A)) (tptp.pp (tptp.aa_num_bool _let_1 (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.ord_max_num A) B2)))))) (forall ((C tptp.nat) (A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat C))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 A)) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat A) B2)))))) (forall ((C tptp.int) (A tptp.int) (B2 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int C))) (=> (tptp.pp (tptp.aa_int_bool _let_1 A)) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.ord_max_int A) B2)))))) (forall ((A tptp.extended_enat) (B2 tptp.extended_enat)) (= (tptp.pp (tptp.aa_Ext2772979874139974381t_bool (tptp.ord_le2932123472753598470d_enat A) B2)) (= (tptp.aa_Ext7969882492699152700d_enat (tptp.aa_Ext3475206891998675565d_enat tptp.ord_ma741700101516333627d_enat A) B2) B2))) (forall ((A tptp.rat) (B2 tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B2)) (= (tptp.aa_rat_rat (tptp.ord_max_rat A) B2) B2))) (forall ((A tptp.num) (B2 tptp.num)) (= (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A) B2)) (= (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.ord_max_num A) B2) B2))) (forall ((A tptp.nat) (B2 tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B2)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat A) B2) B2))) (forall ((A tptp.int) (B2 tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B2)) (= (tptp.aa_int_int (tptp.ord_max_int A) B2) B2))) (forall ((B2 tptp.extended_enat) (A tptp.extended_enat)) (= (tptp.pp (tptp.aa_Ext2772979874139974381t_bool (tptp.ord_le2932123472753598470d_enat B2) A)) (= (tptp.aa_Ext7969882492699152700d_enat (tptp.aa_Ext3475206891998675565d_enat tptp.ord_ma741700101516333627d_enat A) B2) A))) (forall ((B2 tptp.rat) (A tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B2) A)) (= (tptp.aa_rat_rat (tptp.ord_max_rat A) B2) A))) (forall ((B2 tptp.num) (A tptp.num)) (= (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num B2) A)) (= (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.ord_max_num A) B2) A))) (forall ((B2 tptp.nat) (A tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B2) A)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat A) B2) A))) (forall ((B2 tptp.int) (A tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B2) A)) (= (tptp.aa_int_int (tptp.ord_max_int A) B2) A))) (forall ((Z tptp.extended_enat) (X tptp.extended_enat) (Y tptp.extended_enat)) (let ((_let_1 (tptp.ord_le2932123472753598470d_enat Z))) (= (tptp.pp (tptp.aa_Ext2772979874139974381t_bool _let_1 (tptp.aa_Ext7969882492699152700d_enat (tptp.aa_Ext3475206891998675565d_enat tptp.ord_ma741700101516333627d_enat X) Y))) (or (tptp.pp (tptp.aa_Ext2772979874139974381t_bool _let_1 X)) (tptp.pp (tptp.aa_Ext2772979874139974381t_bool _let_1 Y)))))) (forall ((Z tptp.rat) (X tptp.rat) (Y tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat Z))) (= (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat (tptp.ord_max_rat X) Y))) (or (tptp.pp (tptp.aa_rat_bool _let_1 X)) (tptp.pp (tptp.aa_rat_bool _let_1 Y)))))) (forall ((Z tptp.num) (X tptp.num) (Y tptp.num)) (let ((_let_1 (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num Z))) (= (tptp.pp (tptp.aa_num_bool _let_1 (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.ord_max_num X) Y))) (or (tptp.pp (tptp.aa_num_bool _let_1 X)) (tptp.pp (tptp.aa_num_bool _let_1 Y)))))) (forall ((Z tptp.nat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Z))) (= (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat X) Y))) (or (tptp.pp (tptp.aa_nat_bool _let_1 X)) (tptp.pp (tptp.aa_nat_bool _let_1 Y)))))) (forall ((Z tptp.int) (X tptp.int) (Y tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Z))) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.ord_max_int X) Y))) (or (tptp.pp (tptp.aa_int_bool _let_1 X)) (tptp.pp (tptp.aa_int_bool _let_1 Y)))))) (forall ((B2 tptp.extended_enat) (A tptp.extended_enat)) (tptp.pp (tptp.aa_Ext2772979874139974381t_bool (tptp.ord_le2932123472753598470d_enat B2) (tptp.aa_Ext7969882492699152700d_enat (tptp.aa_Ext3475206891998675565d_enat tptp.ord_ma741700101516333627d_enat A) B2)))) (forall ((B2 tptp.rat) (A tptp.rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B2) (tptp.aa_rat_rat (tptp.ord_max_rat A) B2)))) (forall ((B2 tptp.num) (A tptp.num)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num B2) (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.ord_max_num A) B2)))) (forall ((B2 tptp.nat) (A tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat A) B2)))) (forall ((B2 tptp.int) (A tptp.int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B2) (tptp.aa_int_int (tptp.ord_max_int A) B2)))) (forall ((A tptp.extended_enat) (B2 tptp.extended_enat)) (tptp.pp (tptp.aa_Ext2772979874139974381t_bool (tptp.ord_le2932123472753598470d_enat A) (tptp.aa_Ext7969882492699152700d_enat (tptp.aa_Ext3475206891998675565d_enat tptp.ord_ma741700101516333627d_enat A) B2)))) (forall ((A tptp.rat) (B2 tptp.rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) (tptp.aa_rat_rat (tptp.ord_max_rat A) B2)))) (forall ((A tptp.num) (B2 tptp.num)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A) (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.ord_max_num A) B2)))) (forall ((A tptp.nat) (B2 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat A) B2)))) (forall ((A tptp.int) (B2 tptp.int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) (tptp.aa_int_int (tptp.ord_max_int A) B2)))) (forall ((B2 tptp.extended_enat) (A tptp.extended_enat)) (= (tptp.pp (tptp.aa_Ext2772979874139974381t_bool (tptp.ord_le2932123472753598470d_enat B2) A)) (= A (tptp.aa_Ext7969882492699152700d_enat (tptp.aa_Ext3475206891998675565d_enat tptp.ord_ma741700101516333627d_enat A) B2)))) (forall ((B2 tptp.rat) (A tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B2) A)) (= A (tptp.aa_rat_rat (tptp.ord_max_rat A) B2)))) (forall ((B2 tptp.num) (A tptp.num)) (= (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num B2) A)) (= A (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.ord_max_num A) B2)))) (forall ((B2 tptp.nat) (A tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B2) A)) (= A (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat A) B2)))) (forall ((B2 tptp.int) (A tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B2) A)) (= A (tptp.aa_int_int (tptp.ord_max_int A) B2)))) (forall ((B2 tptp.extended_enat) (A tptp.extended_enat) (C tptp.extended_enat)) (=> (tptp.pp (tptp.aa_Ext2772979874139974381t_bool (tptp.ord_le2932123472753598470d_enat B2) A)) (=> (tptp.pp (tptp.aa_Ext2772979874139974381t_bool (tptp.ord_le2932123472753598470d_enat C) A)) (tptp.pp (tptp.aa_Ext2772979874139974381t_bool (tptp.ord_le2932123472753598470d_enat (tptp.aa_Ext7969882492699152700d_enat (tptp.aa_Ext3475206891998675565d_enat tptp.ord_ma741700101516333627d_enat B2) C)) A))))) (forall ((B2 tptp.rat) (A tptp.rat) (C tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B2) A)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat C) A)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.ord_max_rat B2) C)) A))))) (forall ((B2 tptp.num) (A tptp.num) (C tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num B2) A)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num C) A)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.ord_max_num B2) C)) A))))) (forall ((B2 tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B2) A)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat C) A)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat B2) C)) A))))) (forall ((B2 tptp.int) (A tptp.int) (C tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B2) A)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int C) A)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.ord_max_int B2) C)) A))))) (forall ((B2 tptp.extended_enat) (C tptp.extended_enat) (A tptp.extended_enat)) (=> (tptp.pp (tptp.aa_Ext2772979874139974381t_bool (tptp.ord_le2932123472753598470d_enat (tptp.aa_Ext7969882492699152700d_enat (tptp.aa_Ext3475206891998675565d_enat tptp.ord_ma741700101516333627d_enat B2) C)) A)) (not (=> (tptp.pp (tptp.aa_Ext2772979874139974381t_bool (tptp.ord_le2932123472753598470d_enat B2) A)) (not (tptp.pp (tptp.aa_Ext2772979874139974381t_bool (tptp.ord_le2932123472753598470d_enat C) A))))))) (forall ((B2 tptp.rat) (C tptp.rat) (A tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.ord_max_rat B2) C)) A)) (not (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B2) A)) (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat C) A))))))) (forall ((B2 tptp.num) (C tptp.num) (A tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.ord_max_num B2) C)) A)) (not (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num B2) A)) (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num C) A))))))) (forall ((B2 tptp.nat) (C tptp.nat) (A tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat B2) C)) A)) (not (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B2) A)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat C) A))))))) (forall ((B2 tptp.int) (C tptp.int) (A tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.ord_max_int B2) C)) A)) (not (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B2) A)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int C) A))))))) (forall ((A tptp.extended_enat) (B2 tptp.extended_enat)) (=> (= A (tptp.aa_Ext7969882492699152700d_enat (tptp.aa_Ext3475206891998675565d_enat tptp.ord_ma741700101516333627d_enat A) B2)) (tptp.pp (tptp.aa_Ext2772979874139974381t_bool (tptp.ord_le2932123472753598470d_enat B2) A)))) (forall ((A tptp.rat) (B2 tptp.rat)) (=> (= A (tptp.aa_rat_rat (tptp.ord_max_rat A) B2)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B2) A)))) (forall ((A tptp.num) (B2 tptp.num)) (=> (= A (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.ord_max_num A) B2)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num B2) A)))) (forall ((A tptp.nat) (B2 tptp.nat)) (=> (= A (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat A) B2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B2) A)))) (forall ((A tptp.int) (B2 tptp.int)) (=> (= A (tptp.aa_int_int (tptp.ord_max_int A) B2)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B2) A)))) (forall ((B2 tptp.extended_enat) (A tptp.extended_enat)) (=> (tptp.pp (tptp.aa_Ext2772979874139974381t_bool (tptp.ord_le2932123472753598470d_enat B2) A)) (= A (tptp.aa_Ext7969882492699152700d_enat (tptp.aa_Ext3475206891998675565d_enat tptp.ord_ma741700101516333627d_enat A) B2)))) (forall ((B2 tptp.rat) (A tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B2) A)) (= A (tptp.aa_rat_rat (tptp.ord_max_rat A) B2)))) (forall ((B2 tptp.num) (A tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num B2) A)) (= A (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.ord_max_num A) B2)))) (forall ((B2 tptp.nat) (A tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B2) A)) (= A (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat A) B2)))) (forall ((B2 tptp.int) (A tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B2) A)) (= A (tptp.aa_int_int (tptp.ord_max_int A) B2)))) (forall ((C tptp.extended_enat) (A tptp.extended_enat) (D tptp.extended_enat) (B2 tptp.extended_enat)) (=> (tptp.pp (tptp.aa_Ext2772979874139974381t_bool (tptp.ord_le2932123472753598470d_enat C) A)) (=> (tptp.pp (tptp.aa_Ext2772979874139974381t_bool (tptp.ord_le2932123472753598470d_enat D) B2)) (tptp.pp (tptp.aa_Ext2772979874139974381t_bool (tptp.ord_le2932123472753598470d_enat (tptp.aa_Ext7969882492699152700d_enat (tptp.aa_Ext3475206891998675565d_enat tptp.ord_ma741700101516333627d_enat C) D)) (tptp.aa_Ext7969882492699152700d_enat (tptp.aa_Ext3475206891998675565d_enat tptp.ord_ma741700101516333627d_enat A) B2)))))) (forall ((C tptp.rat) (A tptp.rat) (D tptp.rat) (B2 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat C) A)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat D) B2)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.ord_max_rat C) D)) (tptp.aa_rat_rat (tptp.ord_max_rat A) B2)))))) (forall ((C tptp.num) (A tptp.num) (D tptp.num) (B2 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num C) A)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num D) B2)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.ord_max_num C) D)) (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.ord_max_num A) B2)))))) (forall ((C tptp.nat) (A tptp.nat) (D tptp.nat) (B2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat C) A)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat D) B2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat C) D)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat A) B2)))))) (forall ((C tptp.int) (A tptp.int) (D tptp.int) (B2 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int C) A)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int D) B2)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.ord_max_int C) D)) (tptp.aa_int_int (tptp.ord_max_int A) B2)))))) (forall ((Z tptp.extended_enat) (X tptp.extended_enat) (Y tptp.extended_enat)) (let ((_let_1 (tptp.ord_le72135733267957522d_enat Z))) (= (tptp.pp (tptp.aa_Ext2772979874139974381t_bool _let_1 (tptp.aa_Ext7969882492699152700d_enat (tptp.aa_Ext3475206891998675565d_enat tptp.ord_ma741700101516333627d_enat X) Y))) (or (tptp.pp (tptp.aa_Ext2772979874139974381t_bool _let_1 X)) (tptp.pp (tptp.aa_Ext2772979874139974381t_bool _let_1 Y)))))) (forall ((Z tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Z))) (= (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.ord_max_real X) Y))) (or (tptp.pp (tptp.aa_real_bool _let_1 X)) (tptp.pp (tptp.aa_real_bool _let_1 Y)))))) (forall ((Z tptp.rat) (X tptp.rat) (Y tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Z))) (= (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat (tptp.ord_max_rat X) Y))) (or (tptp.pp (tptp.aa_rat_bool _let_1 X)) (tptp.pp (tptp.aa_rat_bool _let_1 Y)))))) (forall ((Z tptp.num) (X tptp.num) (Y tptp.num)) (let ((_let_1 (tptp.aa_num_fun_num_bool tptp.ord_less_num Z))) (= (tptp.pp (tptp.aa_num_bool _let_1 (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.ord_max_num X) Y))) (or (tptp.pp (tptp.aa_num_bool _let_1 X)) (tptp.pp (tptp.aa_num_bool _let_1 Y)))))) (forall ((Z tptp.nat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Z))) (= (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat X) Y))) (or (tptp.pp (tptp.aa_nat_bool _let_1 X)) (tptp.pp (tptp.aa_nat_bool _let_1 Y)))))) (forall ((Z tptp.int) (X tptp.int) (Y tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_int Z))) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.ord_max_int X) Y))) (or (tptp.pp (tptp.aa_int_bool _let_1 X)) (tptp.pp (tptp.aa_int_bool _let_1 Y)))))) (forall ((B2 tptp.extended_enat) (C tptp.extended_enat) (A tptp.extended_enat)) (=> (tptp.pp (tptp.aa_Ext2772979874139974381t_bool (tptp.ord_le72135733267957522d_enat (tptp.aa_Ext7969882492699152700d_enat (tptp.aa_Ext3475206891998675565d_enat tptp.ord_ma741700101516333627d_enat B2) C)) A)) (not (=> (tptp.pp (tptp.aa_Ext2772979874139974381t_bool (tptp.ord_le72135733267957522d_enat B2) A)) (not (tptp.pp (tptp.aa_Ext2772979874139974381t_bool (tptp.ord_le72135733267957522d_enat C) A))))))) (forall ((B2 tptp.real) (C tptp.real) (A tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.ord_max_real B2) C)) A)) (not (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B2) A)) (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real C) A))))))) (forall ((B2 tptp.rat) (C tptp.rat) (A tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.ord_max_rat B2) C)) A)) (not (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B2) A)) (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat C) A))))))) (forall ((B2 tptp.num) (C tptp.num) (A tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.ord_max_num B2) C)) A)) (not (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num B2) A)) (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num C) A))))))) (forall ((B2 tptp.nat) (C tptp.nat) (A tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat B2) C)) A)) (not (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat B2) A)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat C) A))))))) (forall ((B2 tptp.int) (C tptp.int) (A tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.ord_max_int B2) C)) A)) (not (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B2) A)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int C) A))))))) (forall ((B2 tptp.extended_enat) (A tptp.extended_enat)) (= (tptp.pp (tptp.aa_Ext2772979874139974381t_bool (tptp.ord_le72135733267957522d_enat B2) A)) (and (= A (tptp.aa_Ext7969882492699152700d_enat (tptp.aa_Ext3475206891998675565d_enat tptp.ord_ma741700101516333627d_enat A) B2)) (not (= A B2))))) (forall ((B2 tptp.real) (A tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B2) A)) (and (= A (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.ord_max_real A) B2)) (not (= A B2))))) (forall ((B2 tptp.rat) (A tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B2) A)) (and (= A (tptp.aa_rat_rat (tptp.ord_max_rat A) B2)) (not (= A B2))))) (forall ((B2 tptp.num) (A tptp.num)) (= (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num B2) A)) (and (= A (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.ord_max_num A) B2)) (not (= A B2))))) (forall ((B2 tptp.nat) (A tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat B2) A)) (and (= A (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat A) B2)) (not (= A B2))))) (forall ((B2 tptp.int) (A tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B2) A)) (and (= A (tptp.aa_int_int (tptp.ord_max_int A) B2)) (not (= A B2))))) (forall ((C tptp.extended_enat) (A tptp.extended_enat) (B2 tptp.extended_enat)) (let ((_let_1 (tptp.ord_le72135733267957522d_enat C))) (=> (tptp.pp (tptp.aa_Ext2772979874139974381t_bool _let_1 A)) (tptp.pp (tptp.aa_Ext2772979874139974381t_bool _let_1 (tptp.aa_Ext7969882492699152700d_enat (tptp.aa_Ext3475206891998675565d_enat tptp.ord_ma741700101516333627d_enat A) B2)))))) (forall ((C tptp.real) (A tptp.real) (B2 tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real C))) (=> (tptp.pp (tptp.aa_real_bool _let_1 A)) (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.ord_max_real A) B2)))))) (forall ((C tptp.rat) (A tptp.rat) (B2 tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat C))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 A)) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat (tptp.ord_max_rat A) B2)))))) (forall ((C tptp.num) (A tptp.num) (B2 tptp.num)) (let ((_let_1 (tptp.aa_num_fun_num_bool tptp.ord_less_num C))) (=> (tptp.pp (tptp.aa_num_bool _let_1 A)) (tptp.pp (tptp.aa_num_bool _let_1 (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.ord_max_num A) B2)))))) (forall ((C tptp.nat) (A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat C))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 A)) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat A) B2)))))) (forall ((C tptp.int) (A tptp.int) (B2 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_int C))) (=> (tptp.pp (tptp.aa_int_bool _let_1 A)) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.ord_max_int A) B2)))))) (forall ((C tptp.extended_enat) (B2 tptp.extended_enat) (A tptp.extended_enat)) (let ((_let_1 (tptp.ord_le72135733267957522d_enat C))) (=> (tptp.pp (tptp.aa_Ext2772979874139974381t_bool _let_1 B2)) (tptp.pp (tptp.aa_Ext2772979874139974381t_bool _let_1 (tptp.aa_Ext7969882492699152700d_enat (tptp.aa_Ext3475206891998675565d_enat tptp.ord_ma741700101516333627d_enat A) B2)))))) (forall ((C tptp.real) (B2 tptp.real) (A tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real C))) (=> (tptp.pp (tptp.aa_real_bool _let_1 B2)) (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.ord_max_real A) B2)))))) (forall ((C tptp.rat) (B2 tptp.rat) (A tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat C))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 B2)) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat (tptp.ord_max_rat A) B2)))))) (forall ((C tptp.num) (B2 tptp.num) (A tptp.num)) (let ((_let_1 (tptp.aa_num_fun_num_bool tptp.ord_less_num C))) (=> (tptp.pp (tptp.aa_num_bool _let_1 B2)) (tptp.pp (tptp.aa_num_bool _let_1 (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.ord_max_num A) B2)))))) (forall ((C tptp.nat) (B2 tptp.nat) (A tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat C))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 B2)) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat A) B2)))))) (forall ((C tptp.int) (B2 tptp.int) (A tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_int C))) (=> (tptp.pp (tptp.aa_int_bool _let_1 B2)) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.ord_max_int A) B2)))))) (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat _let_1) N))) (let ((_let_3 (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat tptp.one_one_nat))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat _let_1) A)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat _let_3 A)) _let_2) (tptp.aa_nat_nat _let_3 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A) _let_2))))))))) (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_nat_int (tptp.power_power_int _let_1) N))) (let ((_let_3 (tptp.aa_int_fun_int_int tptp.plus_plus_int tptp.one_one_int))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int _let_1) A)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (= (tptp.aa_int_int (tptp.modulo_modulo_int (tptp.aa_int_int _let_3 A)) _let_2) (tptp.aa_int_int _let_3 (tptp.aa_int_int (tptp.modulo_modulo_int A) _let_2))))))))) (forall ((A tptp.code_integer) (N tptp.nat)) (let ((_let_1 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger _let_1) N))) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer _let_1) A)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (= (tptp.modulo364778990260209775nteger (tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer A) _let_2) (tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer (tptp.modulo364778990260209775nteger A _let_2)))))))) (forall ((X tptp.fun_nat_nat) (X2 tptp.nat)) (= (tptp.size_option_nat X (tptp.some_nat X2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat X X2)) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)))) (forall ((X tptp.fun_Pr2602117396471556196at_nat) (X2 tptp.product_prod_nat_nat)) (= (tptp.size_o8335143837870341156at_nat X (tptp.some_P7363390416028606310at_nat X2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_Pro4243173770044397973at_nat X X2)) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)))) (forall ((X tptp.fun_num_nat) (X2 tptp.num)) (= (tptp.size_option_num X (tptp.some_num X2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_num_nat X X2)) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)))) (forall ((A tptp.code_integer) (N tptp.nat)) (let ((_let_1 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger _let_1) N))) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer _let_1) A)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (= (tptp.divide6298287555418463151nteger (tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer A) _let_2) (tptp.divide6298287555418463151nteger A _let_2))))))) (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat _let_1) N))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat _let_1) A)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat tptp.one_one_nat) A)) _let_2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) _let_2))))))) (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_nat_int (tptp.power_power_int _let_1) N))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int _let_1) A)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (= (tptp.aa_int_int (tptp.divide_divide_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int tptp.one_one_int) A)) _let_2) (tptp.aa_int_int (tptp.divide_divide_int A) _let_2))))))) (forall ((N tptp.nat) (A tptp.code_integer)) (let ((_let_1 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.bit_ri6519982836138164636nteger (tptp.aa_nat_nat tptp.suc N) A) (tptp.plus_p5714425477246183910nteger (tptp.modulo364778990260209775nteger A _let_1) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger _let_1) (tptp.bit_ri6519982836138164636nteger N (tptp.divide6298287555418463151nteger A _let_1))))))) (forall ((N tptp.nat) (A tptp.int)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.aa_int_int (tptp.bit_ri631733984087533419it_int (tptp.aa_nat_nat tptp.suc N)) A) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.modulo_modulo_int A) _let_1)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int _let_1) (tptp.aa_int_int (tptp.bit_ri631733984087533419it_int N) (tptp.aa_int_int (tptp.divide_divide_int A) _let_1))))))) (forall ((X7 tptp.set_real)) (=> (not (= X7 tptp.bot_bot_set_real)) (=> (forall ((X4 tptp.real)) (=> (tptp.member_real X4 X7) (exists ((Xa tptp.real)) (and (tptp.member_real Xa X7) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X4) Xa)))))) (not (tptp.finite_finite_real X7))))) (forall ((X7 tptp.set_rat)) (=> (not (= X7 tptp.bot_bot_set_rat)) (=> (forall ((X4 tptp.rat)) (=> (tptp.member_rat X4 X7) (exists ((Xa tptp.rat)) (and (tptp.member_rat Xa X7) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X4) Xa)))))) (not (tptp.finite_finite_rat X7))))) (forall ((X7 tptp.set_num)) (=> (not (= X7 tptp.bot_bot_set_num)) (=> (forall ((X4 tptp.num)) (=> (tptp.member_num X4 X7) (exists ((Xa tptp.num)) (and (tptp.member_num Xa X7) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X4) Xa)))))) (not (tptp.finite_finite_num X7))))) (forall ((X7 tptp.set_nat)) (=> (not (= X7 tptp.bot_bot_set_nat)) (=> (forall ((X4 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X4) X7)) (exists ((Xa tptp.nat)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat Xa) X7)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X4) Xa)))))) (not (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat X7)))))) (forall ((X7 tptp.set_int)) (=> (not (= X7 tptp.bot_bot_set_int)) (=> (forall ((X4 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X4) X7)) (exists ((Xa tptp.int)) (and (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Xa) X7)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X4) Xa)))))) (not (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int X7)))))) (forall ((M tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat M) tptp.one_one_nat)) (= M tptp.one_one_nat))) (forall ((A tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer tptp.zero_z3403309356797280102nteger) A)) (= A tptp.zero_z3403309356797280102nteger))) (forall ((A tptp.complex)) (= (tptp.pp (tptp.aa_complex_bool (tptp.aa_com1553036987509291606x_bool tptp.dvd_dvd_complex tptp.zero_zero_complex) A)) (= A tptp.zero_zero_complex))) (forall ((A tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.dvd_dvd_real tptp.zero_zero_real) A)) (= A tptp.zero_zero_real))) (forall ((A tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.dvd_dvd_rat tptp.zero_zero_rat) A)) (= A tptp.zero_zero_rat))) (forall ((A tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat tptp.zero_zero_nat) A)) (= A tptp.zero_zero_nat))) (forall ((A tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int tptp.zero_zero_int) A)) (= A tptp.zero_zero_int))) (forall ((A tptp.code_integer)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer A) tptp.zero_z3403309356797280102nteger))) (forall ((A tptp.complex)) (tptp.pp (tptp.aa_complex_bool (tptp.aa_com1553036987509291606x_bool tptp.dvd_dvd_complex A) tptp.zero_zero_complex))) (forall ((A tptp.real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.dvd_dvd_real A) tptp.zero_zero_real))) (forall ((A tptp.rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.dvd_dvd_rat A) tptp.zero_zero_rat))) (forall ((A tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat A) tptp.zero_zero_nat))) (forall ((A tptp.int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int A) tptp.zero_zero_int))) (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer A))) (= (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.plus_p5714425477246183910nteger A B2))) (tptp.pp (tptp.aa_Code_integer_bool _let_1 B2))))) (forall ((A tptp.real) (B2 tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.dvd_dvd_real A))) (= (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) B2))) (tptp.pp (tptp.aa_real_bool _let_1 B2))))) (forall ((A tptp.rat) (B2 tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.dvd_dvd_rat A))) (= (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) B2))) (tptp.pp (tptp.aa_rat_bool _let_1 B2))))) (forall ((A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat A))) (= (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) B2))) (tptp.pp (tptp.aa_nat_bool _let_1 B2))))) (forall ((A tptp.int) (B2 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int A))) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) B2))) (tptp.pp (tptp.aa_int_bool _let_1 B2))))) (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer A))) (= (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.plus_p5714425477246183910nteger B2 A))) (tptp.pp (tptp.aa_Code_integer_bool _let_1 B2))))) (forall ((A tptp.real) (B2 tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.dvd_dvd_real A))) (= (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real B2) A))) (tptp.pp (tptp.aa_real_bool _let_1 B2))))) (forall ((A tptp.rat) (B2 tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.dvd_dvd_rat A))) (= (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat B2) A))) (tptp.pp (tptp.aa_rat_bool _let_1 B2))))) (forall ((A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat A))) (= (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat B2) A))) (tptp.pp (tptp.aa_nat_bool _let_1 B2))))) (forall ((A tptp.int) (B2 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int A))) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int B2) A))) (tptp.pp (tptp.aa_int_bool _let_1 B2))))) (forall ((M tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat))) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat M) _let_1)) (= M _let_1)))) (forall ((K tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)) K))) (forall ((A tptp.code_integer) (B2 tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer A))) (=> (tptp.pp (tptp.aa_Code_integer_bool _let_1 B2)) (=> (tptp.pp (tptp.aa_Code_integer_bool _let_1 C)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.divide6298287555418463151nteger B2 A)) (tptp.divide6298287555418463151nteger C A))) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer B2) C))))))) (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat A))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 B2)) (=> (tptp.pp (tptp.aa_nat_bool _let_1 C)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat B2) A)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat C) A))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat B2) C))))))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int A))) (=> (tptp.pp (tptp.aa_int_bool _let_1 B2)) (=> (tptp.pp (tptp.aa_int_bool _let_1 C)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_int_int (tptp.divide_divide_int B2) A)) (tptp.aa_int_int (tptp.divide_divide_int C) A))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int B2) C))))))) (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat K))) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_nat_nat _let_1 M)) (tptp.aa_nat_nat _let_1 N))) (or (= K tptp.zero_zero_nat) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat M) N)))))) (forall ((N tptp.nat)) (= (tptp.aa_int_int (tptp.bit_ri631733984087533419it_int N) tptp.zero_zero_int) tptp.zero_zero_int)) (forall ((A tptp.code_integer) (B2 tptp.code_integer) (C tptp.code_integer)) (=> (not (= A tptp.zero_z3403309356797280102nteger)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B2) A)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger C) A))) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer B2) C))))) (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B2) A)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat C) A))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat B2) C))))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (=> (not (= A tptp.zero_zero_int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B2) A)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int C) A))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int B2) C))))) (forall ((A tptp.code_integer) (B2 tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A))) (=> (not (= A tptp.zero_z3403309356797280102nteger)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.aa_Cod1783974652533396728nteger _let_1 B2)) (tptp.aa_Cod1783974652533396728nteger _let_1 C))) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer B2) C)))))) (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A))) (=> (not (= A tptp.zero_zero_nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_nat_nat _let_1 B2)) (tptp.aa_nat_nat _let_1 C))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat B2) C)))))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.times_times_int A))) (=> (not (= A tptp.zero_zero_int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_int_int _let_1 B2)) (tptp.aa_int_int _let_1 C))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int B2) C)))))) (forall ((A tptp.code_integer) (C tptp.code_integer) (B2 tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) C)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B2) C))) (or (= C tptp.zero_z3403309356797280102nteger) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer A) B2))))) (forall ((A tptp.complex) (C tptp.complex) (B2 tptp.complex)) (= (tptp.pp (tptp.aa_complex_bool (tptp.aa_com1553036987509291606x_bool tptp.dvd_dvd_complex (tptp.aa_complex_complex (tptp.times_times_complex A) C)) (tptp.aa_complex_complex (tptp.times_times_complex B2) C))) (or (= C tptp.zero_zero_complex) (tptp.pp (tptp.aa_complex_bool (tptp.aa_com1553036987509291606x_bool tptp.dvd_dvd_complex A) B2))))) (forall ((A tptp.real) (C tptp.real) (B2 tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.dvd_dvd_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) C)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real B2) C))) (or (= C tptp.zero_zero_real) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.dvd_dvd_real A) B2))))) (forall ((A tptp.rat) (C tptp.rat) (B2 tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.dvd_dvd_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) C)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat B2) C))) (or (= C tptp.zero_zero_rat) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.dvd_dvd_rat A) B2))))) (forall ((A tptp.int) (C tptp.int) (B2 tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B2) C))) (or (= C tptp.zero_zero_int) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int A) B2))))) (forall ((C tptp.code_integer) (A tptp.code_integer) (B2 tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger C))) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.aa_Cod1783974652533396728nteger _let_1 A)) (tptp.aa_Cod1783974652533396728nteger _let_1 B2))) (or (= C tptp.zero_z3403309356797280102nteger) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer A) B2)))))) (forall ((C tptp.complex) (A tptp.complex) (B2 tptp.complex)) (let ((_let_1 (tptp.times_times_complex C))) (= (tptp.pp (tptp.aa_complex_bool (tptp.aa_com1553036987509291606x_bool tptp.dvd_dvd_complex (tptp.aa_complex_complex _let_1 A)) (tptp.aa_complex_complex _let_1 B2))) (or (= C tptp.zero_zero_complex) (tptp.pp (tptp.aa_complex_bool (tptp.aa_com1553036987509291606x_bool tptp.dvd_dvd_complex A) B2)))))) (forall ((C tptp.real) (A tptp.real) (B2 tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.times_times_real C))) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.dvd_dvd_real (tptp.aa_real_real _let_1 A)) (tptp.aa_real_real _let_1 B2))) (or (= C tptp.zero_zero_real) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.dvd_dvd_real A) B2)))))) (forall ((C tptp.rat) (A tptp.rat) (B2 tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_rat tptp.times_times_rat C))) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.dvd_dvd_rat (tptp.aa_rat_rat _let_1 A)) (tptp.aa_rat_rat _let_1 B2))) (or (= C tptp.zero_zero_rat) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.dvd_dvd_rat A) B2)))))) (forall ((C tptp.int) (A tptp.int) (B2 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.times_times_int C))) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_int_int _let_1 A)) (tptp.aa_int_int _let_1 B2))) (or (= C tptp.zero_zero_int) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int A) B2)))))) (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer B2) tptp.one_one_Code_integer)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) B2)) tptp.one_one_Code_integer))))) (forall ((A tptp.nat) (B2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat A) tptp.one_one_nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat B2) tptp.one_one_nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) B2)) tptp.one_one_nat))))) (forall ((A tptp.int) (B2 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int A) tptp.one_one_int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int B2) tptp.one_one_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) B2)) tptp.one_one_int))))) (forall ((A tptp.code_integer) (B2 tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer A))) (= (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.plus_p5714425477246183910nteger B2 (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger C) A)))) (tptp.pp (tptp.aa_Code_integer_bool _let_1 B2))))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.dvd_dvd_real A))) (= (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real B2) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real C) A)))) (tptp.pp (tptp.aa_real_bool _let_1 B2))))) (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.dvd_dvd_rat A))) (= (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat B2) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat C) A)))) (tptp.pp (tptp.aa_rat_bool _let_1 B2))))) (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat A))) (= (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat B2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat C) A)))) (tptp.pp (tptp.aa_nat_bool _let_1 B2))))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int A))) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int B2) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int C) A)))) (tptp.pp (tptp.aa_int_bool _let_1 B2))))) (forall ((A tptp.code_integer) (C tptp.code_integer) (B2 tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer A))) (= (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger C) A) B2))) (tptp.pp (tptp.aa_Code_integer_bool _let_1 B2))))) (forall ((A tptp.real) (C tptp.real) (B2 tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.dvd_dvd_real A))) (= (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real C) A)) B2))) (tptp.pp (tptp.aa_real_bool _let_1 B2))))) (forall ((A tptp.rat) (C tptp.rat) (B2 tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.dvd_dvd_rat A))) (= (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat C) A)) B2))) (tptp.pp (tptp.aa_rat_bool _let_1 B2))))) (forall ((A tptp.nat) (C tptp.nat) (B2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat A))) (= (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat C) A)) B2))) (tptp.pp (tptp.aa_nat_bool _let_1 B2))))) (forall ((A tptp.int) (C tptp.int) (B2 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int A))) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int C) A)) B2))) (tptp.pp (tptp.aa_int_bool _let_1 B2))))) (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer A) B2)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) (tptp.divide6298287555418463151nteger B2 A)) B2))) (forall ((A tptp.nat) (B2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat A) B2)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat B2) A)) B2))) (forall ((A tptp.int) (B2 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int A) B2)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) (tptp.aa_int_int (tptp.divide_divide_int B2) A)) B2))) (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer A) B2)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.divide6298287555418463151nteger B2 A)) A) B2))) (forall ((A tptp.nat) (B2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat A) B2)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat B2) A)) A) B2))) (forall ((A tptp.int) (B2 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int A) B2)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.divide_divide_int B2) A)) A) B2))) (forall ((A tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer)) (= (tptp.divide6298287555418463151nteger tptp.one_one_Code_integer (tptp.divide6298287555418463151nteger tptp.one_one_Code_integer A)) A))) (forall ((A tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat tptp.one_one_nat))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat A) tptp.one_one_nat)) (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat _let_1 A)) A)))) (forall ((A tptp.int)) (let ((_let_1 (tptp.divide_divide_int tptp.one_one_int))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int A) tptp.one_one_int)) (= (tptp.aa_int_int _let_1 (tptp.aa_int_int _let_1 A)) A)))) (forall ((A tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.divide6298287555418463151nteger tptp.one_one_Code_integer A)) tptp.one_one_Code_integer)))) (forall ((A tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat A) tptp.one_one_nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat tptp.one_one_nat) A)) tptp.one_one_nat)))) (forall ((A tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int A) tptp.one_one_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_int_int (tptp.divide_divide_int tptp.one_one_int) A)) tptp.one_one_int)))) (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer B2) tptp.one_one_Code_integer)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.divide6298287555418463151nteger A B2)) tptp.one_one_Code_integer))))) (forall ((A tptp.nat) (B2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat A) tptp.one_one_nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat B2) tptp.one_one_nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) B2)) tptp.one_one_nat))))) (forall ((A tptp.int) (B2 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int A) tptp.one_one_int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int B2) tptp.one_one_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_int_int (tptp.divide_divide_int A) B2)) tptp.one_one_int))))) (forall ((C tptp.code_integer) (A tptp.code_integer) (B2 tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer C))) (=> (tptp.pp (tptp.aa_Code_integer_bool _let_1 A)) (=> (tptp.pp (tptp.aa_Code_integer_bool _let_1 B2)) (= (tptp.divide6298287555418463151nteger (tptp.plus_p5714425477246183910nteger A B2) C) (tptp.plus_p5714425477246183910nteger (tptp.divide6298287555418463151nteger A C) (tptp.divide6298287555418463151nteger B2 C))))))) (forall ((C tptp.nat) (A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat C))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 A)) (=> (tptp.pp (tptp.aa_nat_bool _let_1 B2)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) B2)) C) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) C)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat B2) C))))))) (forall ((C tptp.int) (A tptp.int) (B2 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int C))) (=> (tptp.pp (tptp.aa_int_bool _let_1 A)) (=> (tptp.pp (tptp.aa_int_bool _let_1 B2)) (= (tptp.aa_int_int (tptp.divide_divide_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) B2)) C) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.divide_divide_int A) C)) (tptp.aa_int_int (tptp.divide_divide_int B2) C))))))) (forall ((C tptp.code_integer) (A tptp.code_integer) (B2 tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer C))) (=> (tptp.pp (tptp.aa_Code_integer_bool _let_1 A)) (=> (tptp.pp (tptp.aa_Code_integer_bool _let_1 B2)) (= (tptp.divide6298287555418463151nteger (tptp.minus_8373710615458151222nteger A B2) C) (tptp.minus_8373710615458151222nteger (tptp.divide6298287555418463151nteger A C) (tptp.divide6298287555418463151nteger B2 C))))))) (forall ((C tptp.int) (A tptp.int) (B2 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int C))) (=> (tptp.pp (tptp.aa_int_bool _let_1 A)) (=> (tptp.pp (tptp.aa_int_bool _let_1 B2)) (= (tptp.aa_int_int (tptp.divide_divide_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) B2)) C) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_int_int (tptp.divide_divide_int A) C)) (tptp.aa_int_int (tptp.divide_divide_int B2) C))))))) (forall ((A tptp.nat) (B2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat A) B2)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat B2) A) tptp.zero_zero_nat))) (forall ((A tptp.int) (B2 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int A) B2)) (= (tptp.aa_int_int (tptp.modulo_modulo_int B2) A) tptp.zero_zero_int))) (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer A) B2)) (= (tptp.modulo364778990260209775nteger B2 A) tptp.zero_z3403309356797280102nteger))) (forall ((N tptp.nat)) (= (tptp.aa_int_int (tptp.bit_ri631733984087533419it_int (tptp.aa_nat_nat tptp.suc N)) tptp.one_one_int) tptp.one_one_int)) (forall ((K tptp.num)) (= (tptp.aa_int_int (tptp.bit_ri631733984087533419it_int (tptp.aa_num_nat tptp.numeral_numeral_nat K)) tptp.one_one_int) tptp.one_one_int)) (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B2) (tptp.divide6298287555418463151nteger tptp.one_one_Code_integer A)) (tptp.divide6298287555418463151nteger B2 A)))) (forall ((A tptp.nat) (B2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat A) tptp.one_one_nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat tptp.one_one_nat) A)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat B2) A)))) (forall ((A tptp.int) (B2 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int A) tptp.one_one_int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B2) (tptp.aa_int_int (tptp.divide_divide_int tptp.one_one_int) A)) (tptp.aa_int_int (tptp.divide_divide_int B2) A)))) (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.divide6298287555418463151nteger B2 A)) A) B2))) (forall ((A tptp.nat) (B2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat A) tptp.one_one_nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat B2) A)) A) B2))) (forall ((A tptp.int) (B2 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int A) tptp.one_one_int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.divide_divide_int B2) A)) A) B2))) (forall ((N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat tptp.suc N)))) (tptp.pp (tptp.aa_nat_bool _let_1 N))))) (forall ((N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat tptp.suc N))) (not (tptp.pp (tptp.aa_nat_bool _let_1 N)))))) (forall ((N tptp.nat) (A tptp.nat) (B2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A) N)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat B2) N))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat A) B2))))) (forall ((N tptp.nat) (A tptp.int) (B2 tptp.int)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_nat_int (tptp.power_power_int A) N)) (tptp.aa_nat_int (tptp.power_power_int B2) N))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int A) B2))))) (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) B2))) (or (tptp.pp (tptp.aa_Code_integer_bool _let_1 A)) (tptp.pp (tptp.aa_Code_integer_bool _let_1 B2)))))) (forall ((A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) B2))) (or (tptp.pp (tptp.aa_nat_bool _let_1 A)) (tptp.pp (tptp.aa_nat_bool _let_1 B2)))))) (forall ((A tptp.int) (B2 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) B2))) (or (tptp.pp (tptp.aa_int_bool _let_1 A)) (tptp.pp (tptp.aa_int_bool _let_1 B2)))))) (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.plus_p5714425477246183910nteger A B2))) (= (tptp.pp (tptp.aa_Code_integer_bool _let_1 A)) (tptp.pp (tptp.aa_Code_integer_bool _let_1 B2)))))) (forall ((A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) B2))) (= (tptp.pp (tptp.aa_nat_bool _let_1 A)) (tptp.pp (tptp.aa_nat_bool _let_1 B2)))))) (forall ((A tptp.int) (B2 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) B2))) (= (tptp.pp (tptp.aa_int_bool _let_1 A)) (tptp.pp (tptp.aa_int_bool _let_1 B2)))))) (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (not (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.plus_p5714425477246183910nteger A B2)))) (not (= (not (tptp.pp (tptp.aa_Code_integer_bool _let_1 A))) (not (tptp.pp (tptp.aa_Code_integer_bool _let_1 B2)))))))) (forall ((A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (not (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) B2)))) (not (= (not (tptp.pp (tptp.aa_nat_bool _let_1 A))) (not (tptp.pp (tptp.aa_nat_bool _let_1 B2)))))))) (forall ((A tptp.int) (B2 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (not (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) B2)))) (not (= (not (tptp.pp (tptp.aa_int_bool _let_1 A))) (not (tptp.pp (tptp.aa_int_bool _let_1 B2)))))))) (forall ((A tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat _let_1))) (= (tptp.pp (tptp.aa_nat_bool _let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A) _let_1))) (tptp.pp (tptp.aa_nat_bool _let_2 A)))))) (forall ((A tptp.int)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int _let_1))) (= (tptp.pp (tptp.aa_int_bool _let_2 (tptp.aa_int_int (tptp.modulo_modulo_int A) _let_1))) (tptp.pp (tptp.aa_int_bool _let_2 A)))))) (forall ((A tptp.code_integer)) (let ((_let_1 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer _let_1))) (= (tptp.pp (tptp.aa_Code_integer_bool _let_2 (tptp.modulo364778990260209775nteger A _let_1))) (tptp.pp (tptp.aa_Code_integer_bool _let_2 A)))))) (forall ((N tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat _let_1) N)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat tptp.suc N)) _let_1) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat N) _let_1))))) (forall ((N tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat _let_1) N))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat tptp.suc N)) _let_1) (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat N) _let_1)))))) (forall ((N tptp.nat) (K tptp.num)) (= (tptp.aa_int_int (tptp.bit_ri631733984087533419it_int (tptp.aa_nat_nat tptp.suc N)) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 K))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.bit_ri631733984087533419it_int N) (tptp.aa_num_int tptp.numeral_numeral_int K))) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))))) (forall ((A tptp.real) (W tptp.num)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (let ((_let_2 (tptp.aa_num_nat tptp.numeral_numeral_nat W))) (let ((_let_3 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) _let_2)))) (= (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real A) _let_2))) (or _let_3 (and (not _let_3) (tptp.pp (tptp.aa_real_bool _let_1 A))))))))) (forall ((A tptp.rat) (W tptp.num)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat))) (let ((_let_2 (tptp.aa_num_nat tptp.numeral_numeral_nat W))) (let ((_let_3 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) _let_2)))) (= (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_nat_rat (tptp.power_power_rat A) _let_2))) (or _let_3 (and (not _let_3) (tptp.pp (tptp.aa_rat_bool _let_1 A))))))))) (forall ((A tptp.int) (W tptp.num)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_2 (tptp.aa_num_nat tptp.numeral_numeral_nat W))) (let ((_let_3 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) _let_2)))) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_nat_int (tptp.power_power_int A) _let_2))) (or _let_3 (and (not _let_3) (tptp.pp (tptp.aa_int_bool _let_1 A))))))))) (forall ((A tptp.real) (W tptp.num)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat W))) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real A) _let_1)) tptp.zero_zero_real)) (and (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) _let_1))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) tptp.zero_zero_real)))))) (forall ((A tptp.rat) (W tptp.num)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat W))) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_nat_rat (tptp.power_power_rat A) _let_1)) tptp.zero_zero_rat)) (and (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) _let_1))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) tptp.zero_zero_rat)))))) (forall ((A tptp.int) (W tptp.num)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat W))) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_nat_int (tptp.power_power_int A) _let_1)) tptp.zero_zero_int)) (and (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) _let_1))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) tptp.zero_zero_int)))))) (forall ((A tptp.real) (N tptp.nat)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real A) N)) tptp.zero_zero_real)) (and (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) tptp.zero_zero_real))))) (forall ((A tptp.rat) (N tptp.nat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_nat_rat (tptp.power_power_rat A) N)) tptp.zero_zero_rat)) (and (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) tptp.zero_zero_rat))))) (forall ((A tptp.int) (N tptp.nat)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_nat_int (tptp.power_power_int A) N)) tptp.zero_zero_int)) (and (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) tptp.zero_zero_int))))) (forall ((A tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.plus_p5714425477246183910nteger A tptp.one_one_Code_integer))) (not (tptp.pp (tptp.aa_Code_integer_bool _let_1 A)))))) (forall ((A tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) tptp.one_one_nat))) (not (tptp.pp (tptp.aa_nat_bool _let_1 A)))))) (forall ((A tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) tptp.one_one_int))) (not (tptp.pp (tptp.aa_int_bool _let_1 A)))))) (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.minus_8373710615458151222nteger A B2))) (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.plus_p5714425477246183910nteger A B2)))))) (forall ((A tptp.int) (B2 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) B2))) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) B2)))))) (forall ((N tptp.nat)) (=> (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N))) (= (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat))) N))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) N))) (or (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N)) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) N))))))) (forall ((A tptp.real) (W tptp.num)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real))) (let ((_let_2 (tptp.aa_num_nat tptp.numeral_numeral_nat W))) (let ((_let_3 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) _let_2)))) (= (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real A) _let_2))) (or (= _let_2 tptp.zero_zero_nat) (and _let_3 (not (= A tptp.zero_zero_real))) (and (not _let_3) (tptp.pp (tptp.aa_real_bool _let_1 A))))))))) (forall ((A tptp.rat) (W tptp.num)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat))) (let ((_let_2 (tptp.aa_num_nat tptp.numeral_numeral_nat W))) (let ((_let_3 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) _let_2)))) (= (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_nat_rat (tptp.power_power_rat A) _let_2))) (or (= _let_2 tptp.zero_zero_nat) (and _let_3 (not (= A tptp.zero_zero_rat))) (and (not _let_3) (tptp.pp (tptp.aa_rat_bool _let_1 A))))))))) (forall ((A tptp.int) (W tptp.num)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int))) (let ((_let_2 (tptp.aa_num_nat tptp.numeral_numeral_nat W))) (let ((_let_3 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) _let_2)))) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_nat_int (tptp.power_power_int A) _let_2))) (or (= _let_2 tptp.zero_zero_nat) (and _let_3 (not (= A tptp.zero_zero_int))) (and (not _let_3) (tptp.pp (tptp.aa_int_bool _let_1 A))))))))) (forall ((A tptp.code_integer)) (let ((_let_1 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer _let_1) A)) (= (tptp.divide6298287555418463151nteger (tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer A) _let_1) (tptp.divide6298287555418463151nteger A _let_1))))) (forall ((A tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat _let_1) A)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat tptp.one_one_nat) A)) _let_1) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) _let_1))))) (forall ((A tptp.int)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int _let_1) A)) (= (tptp.aa_int_int (tptp.divide_divide_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int tptp.one_one_int) A)) _let_1) (tptp.aa_int_int (tptp.divide_divide_int A) _let_1))))) (forall ((A tptp.code_integer)) (let ((_let_1 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer _let_1) A)) (= (tptp.divide6298287555418463151nteger (tptp.plus_p5714425477246183910nteger A tptp.one_one_Code_integer) _let_1) (tptp.divide6298287555418463151nteger A _let_1))))) (forall ((A tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat _let_1) A)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) tptp.one_one_nat)) _let_1) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) _let_1))))) (forall ((A tptp.int)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int _let_1) A)) (= (tptp.aa_int_int (tptp.divide_divide_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) tptp.one_one_int)) _let_1) (tptp.aa_int_int (tptp.divide_divide_int A) _let_1))))) (forall ((A tptp.code_integer)) (let ((_let_1 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (not (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer _let_1) A))) (= (tptp.divide6298287555418463151nteger (tptp.plus_p5714425477246183910nteger A tptp.one_one_Code_integer) _let_1) (tptp.plus_p5714425477246183910nteger (tptp.divide6298287555418463151nteger A _let_1) tptp.one_one_Code_integer))))) (forall ((A tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat _let_1) A))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) tptp.one_one_nat)) _let_1) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) _let_1)) tptp.one_one_nat))))) (forall ((A tptp.int)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int _let_1) A))) (= (tptp.aa_int_int (tptp.divide_divide_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) tptp.one_one_int)) _let_1) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.divide_divide_int A) _let_1)) tptp.one_one_int))))) (forall ((A tptp.code_integer) (N tptp.nat)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger A) N))) (and (tptp.pp (tptp.aa_Code_integer_bool _let_1 A)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)))))) (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A) N))) (and (tptp.pp (tptp.aa_nat_bool _let_1 A)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)))))) (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_nat_int (tptp.power_power_int A) N))) (and (tptp.pp (tptp.aa_int_bool _let_1 A)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)))))) (forall ((N tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat _let_1) N))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat _let_1) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat N) _let_1)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) tptp.one_one_nat))))) (forall ((A tptp.code_integer)) (let ((_let_1 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (not (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer _let_1) A))) (= (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger _let_1) (tptp.divide6298287555418463151nteger A _let_1)) tptp.one_one_Code_integer) A)))) (forall ((A tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat _let_1) A))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat _let_1) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) _let_1))) tptp.one_one_nat) A)))) (forall ((A tptp.int)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int _let_1) A))) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int _let_1) (tptp.aa_int_int (tptp.divide_divide_int A) _let_1))) tptp.one_one_int) A)))) (forall ((A tptp.real) (W tptp.num)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat W))) (let ((_let_2 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) _let_1)))) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real A) _let_1)) tptp.zero_zero_real)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) _let_1)) (or (and (not _let_2) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) tptp.zero_zero_real))) (and _let_2 (= A tptp.zero_zero_real)))))))) (forall ((A tptp.rat) (W tptp.num)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat W))) (let ((_let_2 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) _let_1)))) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat (tptp.power_power_rat A) _let_1)) tptp.zero_zero_rat)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) _let_1)) (or (and (not _let_2) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) tptp.zero_zero_rat))) (and _let_2 (= A tptp.zero_zero_rat)))))))) (forall ((A tptp.int) (W tptp.num)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat W))) (let ((_let_2 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) _let_1)))) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int (tptp.power_power_int A) _let_1)) tptp.zero_zero_int)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) _let_1)) (or (and (not _let_2) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) tptp.zero_zero_int))) (and _let_2 (= A tptp.zero_zero_int)))))))) (forall ((N tptp.nat)) (let ((_let_1 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer _let_1) (tptp.minus_8373710615458151222nteger (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger _let_1) N) tptp.one_one_Code_integer))) (= N tptp.zero_zero_nat)))) (forall ((N tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat _let_1) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat _let_1) N)) tptp.one_one_nat))) (= N tptp.zero_zero_nat)))) (forall ((N tptp.nat)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int _let_1) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_nat_int (tptp.power_power_int _let_1) N)) tptp.one_one_int))) (= N tptp.zero_zero_nat)))) (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat A))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 B2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat B2) C)) (tptp.pp (tptp.aa_nat_bool _let_1 C)))))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int A))) (=> (tptp.pp (tptp.aa_int_bool _let_1 B2)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int B2) C)) (tptp.pp (tptp.aa_int_bool _let_1 C)))))) (forall ((A tptp.code_integer) (B2 tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer A))) (=> (tptp.pp (tptp.aa_Code_integer_bool _let_1 B2)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer B2) C)) (tptp.pp (tptp.aa_Code_integer_bool _let_1 C)))))) (forall ((A tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat A) A))) (forall ((A tptp.int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int A) A))) (forall ((A tptp.code_integer)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer A) A))) (forall ((A tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer tptp.zero_z3403309356797280102nteger) A)) (= A tptp.zero_z3403309356797280102nteger))) (forall ((A tptp.complex)) (=> (tptp.pp (tptp.aa_complex_bool (tptp.aa_com1553036987509291606x_bool tptp.dvd_dvd_complex tptp.zero_zero_complex) A)) (= A tptp.zero_zero_complex))) (forall ((A tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.dvd_dvd_real tptp.zero_zero_real) A)) (= A tptp.zero_zero_real))) (forall ((A tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.dvd_dvd_rat tptp.zero_zero_rat) A)) (= A tptp.zero_zero_rat))) (forall ((A tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat tptp.zero_zero_nat) A)) (= A tptp.zero_zero_nat))) (forall ((A tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int tptp.zero_zero_int) A)) (= A tptp.zero_zero_int))) (forall ((P2 tptp.nat) (A tptp.nat) (B2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat P2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) B2))) (not (forall ((X4 tptp.nat) (Y4 tptp.nat)) (=> (= P2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat X4) Y4)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat X4) A)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat Y4) B2))))))))) (forall ((P2 tptp.int) (A tptp.int) (B2 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int P2) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) B2))) (not (forall ((X4 tptp.int) (Y4 tptp.int)) (=> (= P2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int X4) Y4)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int X4) A)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int Y4) B2))))))))) (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B2) C))) (exists ((B7 tptp.nat) (C5 tptp.nat)) (and (= A (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B7) C5)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat B7) B2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat C5) C)))))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int A) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B2) C))) (exists ((B7 tptp.int) (C5 tptp.int)) (and (= A (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B7) C5)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int B7) B2)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int C5) C)))))) (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer A) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B2) A)))) (forall ((A tptp.real) (B2 tptp.real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.dvd_dvd_real A) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real B2) A)))) (forall ((A tptp.rat) (B2 tptp.rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.dvd_dvd_rat A) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat B2) A)))) (forall ((A tptp.nat) (B2 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B2) A)))) (forall ((A tptp.int) (B2 tptp.int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int A) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B2) A)))) (forall ((A tptp.code_integer) (B2 tptp.code_integer) (C tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) B2)) C)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer B2) C)))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.dvd_dvd_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) B2)) C)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.dvd_dvd_real B2) C)))) (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.dvd_dvd_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) B2)) C)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.dvd_dvd_rat B2) C)))) (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) B2)) C)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat B2) C)))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) B2)) C)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int B2) C)))) (forall ((A tptp.code_integer) (B2 tptp.code_integer) (C tptp.code_integer) (D tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer A) B2)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer C) D)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) C)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B2) D)))))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real) (D tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.dvd_dvd_real A) B2)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.dvd_dvd_real C) D)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.dvd_dvd_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) C)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real B2) D)))))) (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat) (D tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.dvd_dvd_rat A) B2)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.dvd_dvd_rat C) D)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.dvd_dvd_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) C)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat B2) D)))))) (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat) (D tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat A) B2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat C) D)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) C)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B2) D)))))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int) (D tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int A) B2)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int C) D)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B2) D)))))) (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer A) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) B2)))) (forall ((A tptp.real) (B2 tptp.real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.dvd_dvd_real A) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) B2)))) (forall ((A tptp.rat) (B2 tptp.rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.dvd_dvd_rat A) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) B2)))) (forall ((A tptp.nat) (B2 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) B2)))) (forall ((A tptp.int) (B2 tptp.int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int A) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) B2)))) (forall ((A tptp.code_integer) (B2 tptp.code_integer) (C tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) B2)) C)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer A) C)))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.dvd_dvd_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) B2)) C)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.dvd_dvd_real A) C)))) (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.dvd_dvd_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) B2)) C)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.dvd_dvd_rat A) C)))) (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) B2)) C)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat A) C)))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) B2)) C)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int A) C)))) (forall ((A tptp.code_integer) (B2 tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer A))) (=> (tptp.pp (tptp.aa_Code_integer_bool _let_1 B2)) (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B2) C)))))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.dvd_dvd_real A))) (=> (tptp.pp (tptp.aa_real_bool _let_1 B2)) (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real B2) C)))))) (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.dvd_dvd_rat A))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 B2)) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat B2) C)))))) (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat A))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 B2)) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B2) C)))))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int A))) (=> (tptp.pp (tptp.aa_int_bool _let_1 B2)) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B2) C)))))) (forall ((A tptp.code_integer) (C tptp.code_integer) (B2 tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer A))) (=> (tptp.pp (tptp.aa_Code_integer_bool _let_1 C)) (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B2) C)))))) (forall ((A tptp.real) (C tptp.real) (B2 tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.dvd_dvd_real A))) (=> (tptp.pp (tptp.aa_real_bool _let_1 C)) (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real B2) C)))))) (forall ((A tptp.rat) (C tptp.rat) (B2 tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.dvd_dvd_rat A))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 C)) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat B2) C)))))) (forall ((A tptp.nat) (C tptp.nat) (B2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat A))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 C)) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B2) C)))))) (forall ((A tptp.int) (C tptp.int) (B2 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int A))) (=> (tptp.pp (tptp.aa_int_bool _let_1 C)) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B2) C)))))) (forall ((B2 tptp.code_integer) (A tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer B2) A)) (exists ((K2 tptp.code_integer)) (= A (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B2) K2))))) (forall ((B2 tptp.real) (A tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.dvd_dvd_real B2) A)) (exists ((K2 tptp.real)) (= A (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real B2) K2))))) (forall ((B2 tptp.rat) (A tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.dvd_dvd_rat B2) A)) (exists ((K2 tptp.rat)) (= A (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat B2) K2))))) (forall ((B2 tptp.nat) (A tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat B2) A)) (exists ((K2 tptp.nat)) (= A (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B2) K2))))) (forall ((B2 tptp.int) (A tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int B2) A)) (exists ((K2 tptp.int)) (= A (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B2) K2))))) (forall ((A tptp.code_integer) (B2 tptp.code_integer) (K tptp.code_integer)) (=> (= A (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B2) K)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer B2) A)))) (forall ((A tptp.real) (B2 tptp.real) (K tptp.real)) (=> (= A (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real B2) K)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.dvd_dvd_real B2) A)))) (forall ((A tptp.rat) (B2 tptp.rat) (K tptp.rat)) (=> (= A (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat B2) K)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.dvd_dvd_rat B2) A)))) (forall ((A tptp.nat) (B2 tptp.nat) (K tptp.nat)) (=> (= A (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B2) K)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat B2) A)))) (forall ((A tptp.int) (B2 tptp.int) (K tptp.int)) (=> (= A (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B2) K)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int B2) A)))) (forall ((B2 tptp.code_integer) (A tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer B2) A)) (not (forall ((K3 tptp.code_integer)) (not (= A (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B2) K3))))))) (forall ((B2 tptp.real) (A tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.dvd_dvd_real B2) A)) (not (forall ((K3 tptp.real)) (not (= A (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real B2) K3))))))) (forall ((B2 tptp.rat) (A tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.dvd_dvd_rat B2) A)) (not (forall ((K3 tptp.rat)) (not (= A (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat B2) K3))))))) (forall ((B2 tptp.nat) (A tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat B2) A)) (not (forall ((K3 tptp.nat)) (not (= A (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B2) K3))))))) (forall ((B2 tptp.int) (A tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int B2) A)) (not (forall ((K3 tptp.int)) (not (= A (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B2) K3))))))) (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer A))) (=> (tptp.pp (tptp.aa_Code_integer_bool _let_1 B2)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer B2) tptp.one_one_Code_integer)) (tptp.pp (tptp.aa_Code_integer_bool _let_1 tptp.one_one_Code_integer)))))) (forall ((A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat A))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 B2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat B2) tptp.one_one_nat)) (tptp.pp (tptp.aa_nat_bool _let_1 tptp.one_one_nat)))))) (forall ((A tptp.int) (B2 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int A))) (=> (tptp.pp (tptp.aa_int_bool _let_1 B2)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int B2) tptp.one_one_int)) (tptp.pp (tptp.aa_int_bool _let_1 tptp.one_one_int)))))) (forall ((B2 tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer B2))) (=> (tptp.pp (tptp.aa_Code_integer_bool _let_1 tptp.one_one_Code_integer)) (tptp.pp (tptp.aa_Code_integer_bool _let_1 A))))) (forall ((B2 tptp.nat) (A tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat B2))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 tptp.one_one_nat)) (tptp.pp (tptp.aa_nat_bool _let_1 A))))) (forall ((B2 tptp.int) (A tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int B2))) (=> (tptp.pp (tptp.aa_int_bool _let_1 tptp.one_one_int)) (tptp.pp (tptp.aa_int_bool _let_1 A))))) (forall ((A tptp.code_integer)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer tptp.one_one_Code_integer) A))) (forall ((A tptp.complex)) (tptp.pp (tptp.aa_complex_bool (tptp.aa_com1553036987509291606x_bool tptp.dvd_dvd_complex tptp.one_one_complex) A))) (forall ((A tptp.real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.dvd_dvd_real tptp.one_one_real) A))) (forall ((A tptp.rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.dvd_dvd_rat tptp.one_one_rat) A))) (forall ((A tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat tptp.one_one_nat) A))) (forall ((A tptp.int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int tptp.one_one_int) A))) (forall ((A tptp.code_integer) (B2 tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer A))) (=> (tptp.pp (tptp.aa_Code_integer_bool _let_1 B2)) (=> (tptp.pp (tptp.aa_Code_integer_bool _let_1 C)) (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.plus_p5714425477246183910nteger B2 C))))))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.dvd_dvd_real A))) (=> (tptp.pp (tptp.aa_real_bool _let_1 B2)) (=> (tptp.pp (tptp.aa_real_bool _let_1 C)) (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real B2) C))))))) (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.dvd_dvd_rat A))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 B2)) (=> (tptp.pp (tptp.aa_rat_bool _let_1 C)) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat B2) C))))))) (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat A))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 B2)) (=> (tptp.pp (tptp.aa_nat_bool _let_1 C)) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat B2) C))))))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int A))) (=> (tptp.pp (tptp.aa_int_bool _let_1 B2)) (=> (tptp.pp (tptp.aa_int_bool _let_1 C)) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int B2) C))))))) (forall ((A tptp.code_integer) (C tptp.code_integer) (B2 tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer A))) (=> (tptp.pp (tptp.aa_Code_integer_bool _let_1 C)) (= (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.plus_p5714425477246183910nteger B2 C))) (tptp.pp (tptp.aa_Code_integer_bool _let_1 B2)))))) (forall ((A tptp.real) (C tptp.real) (B2 tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.dvd_dvd_real A))) (=> (tptp.pp (tptp.aa_real_bool _let_1 C)) (= (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real B2) C))) (tptp.pp (tptp.aa_real_bool _let_1 B2)))))) (forall ((A tptp.rat) (C tptp.rat) (B2 tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.dvd_dvd_rat A))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 C)) (= (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat B2) C))) (tptp.pp (tptp.aa_rat_bool _let_1 B2)))))) (forall ((A tptp.nat) (C tptp.nat) (B2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat A))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 C)) (= (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat B2) C))) (tptp.pp (tptp.aa_nat_bool _let_1 B2)))))) (forall ((A tptp.int) (C tptp.int) (B2 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int A))) (=> (tptp.pp (tptp.aa_int_bool _let_1 C)) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int B2) C))) (tptp.pp (tptp.aa_int_bool _let_1 B2)))))) (forall ((A tptp.code_integer) (B2 tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer A))) (=> (tptp.pp (tptp.aa_Code_integer_bool _let_1 B2)) (= (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.plus_p5714425477246183910nteger B2 C))) (tptp.pp (tptp.aa_Code_integer_bool _let_1 C)))))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.dvd_dvd_real A))) (=> (tptp.pp (tptp.aa_real_bool _let_1 B2)) (= (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real B2) C))) (tptp.pp (tptp.aa_real_bool _let_1 C)))))) (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.dvd_dvd_rat A))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 B2)) (= (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat B2) C))) (tptp.pp (tptp.aa_rat_bool _let_1 C)))))) (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat A))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 B2)) (= (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat B2) C))) (tptp.pp (tptp.aa_nat_bool _let_1 C)))))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int A))) (=> (tptp.pp (tptp.aa_int_bool _let_1 B2)) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int B2) C))) (tptp.pp (tptp.aa_int_bool _let_1 C)))))) (forall ((X tptp.code_integer) (Y tptp.code_integer) (Z tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer X))) (=> (tptp.pp (tptp.aa_Code_integer_bool _let_1 Y)) (=> (tptp.pp (tptp.aa_Code_integer_bool _let_1 Z)) (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.minus_8373710615458151222nteger Y Z))))))) (forall ((X tptp.complex) (Y tptp.complex) (Z tptp.complex)) (let ((_let_1 (tptp.aa_com1553036987509291606x_bool tptp.dvd_dvd_complex X))) (=> (tptp.pp (tptp.aa_complex_bool _let_1 Y)) (=> (tptp.pp (tptp.aa_complex_bool _let_1 Z)) (tptp.pp (tptp.aa_complex_bool _let_1 (tptp.aa_complex_complex (tptp.minus_minus_complex Y) Z))))))) (forall ((X tptp.real) (Y tptp.real) (Z tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.dvd_dvd_real X))) (=> (tptp.pp (tptp.aa_real_bool _let_1 Y)) (=> (tptp.pp (tptp.aa_real_bool _let_1 Z)) (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real Y) Z))))))) (forall ((X tptp.rat) (Y tptp.rat) (Z tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.dvd_dvd_rat X))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 Y)) (=> (tptp.pp (tptp.aa_rat_bool _let_1 Z)) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat (tptp.minus_minus_rat Y) Z))))))) (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int X))) (=> (tptp.pp (tptp.aa_int_bool _let_1 Y)) (=> (tptp.pp (tptp.aa_int_bool _let_1 Z)) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int Y) Z))))))) (forall ((A tptp.code_integer) (C tptp.code_integer) (B2 tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer A))) (= (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.minus_8373710615458151222nteger C B2))) (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.minus_8373710615458151222nteger B2 C)))))) (forall ((A tptp.int) (C tptp.int) (B2 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int A))) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int C) B2))) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int B2) C)))))) (forall ((D tptp.code_integer) (B2 tptp.code_integer) (A tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer D) B2)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer B2) A)) (= (tptp.divide6298287555418463151nteger (tptp.divide6298287555418463151nteger A D) (tptp.divide6298287555418463151nteger B2 D)) (tptp.divide6298287555418463151nteger A B2))))) (forall ((D tptp.nat) (B2 tptp.nat) (A tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat D) B2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat B2) A)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat _let_1 D)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat B2) D)) (tptp.aa_nat_nat _let_1 B2)))))) (forall ((D tptp.int) (B2 tptp.int) (A tptp.int)) (let ((_let_1 (tptp.divide_divide_int A))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int D) B2)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int B2) A)) (= (tptp.aa_int_int (tptp.divide_divide_int (tptp.aa_int_int _let_1 D)) (tptp.aa_int_int (tptp.divide_divide_int B2) D)) (tptp.aa_int_int _let_1 B2)))))) (forall ((A tptp.code_integer) (C tptp.code_integer) (B2 tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer C))) (=> (= (tptp.divide6298287555418463151nteger A C) (tptp.divide6298287555418463151nteger B2 C)) (=> (tptp.pp (tptp.aa_Code_integer_bool _let_1 A)) (=> (tptp.pp (tptp.aa_Code_integer_bool _let_1 B2)) (= A B2)))))) (forall ((A tptp.complex) (C tptp.complex) (B2 tptp.complex)) (let ((_let_1 (tptp.aa_com1553036987509291606x_bool tptp.dvd_dvd_complex C))) (=> (= (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex A) C) (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex B2) C)) (=> (tptp.pp (tptp.aa_complex_bool _let_1 A)) (=> (tptp.pp (tptp.aa_complex_bool _let_1 B2)) (= A B2)))))) (forall ((A tptp.real) (C tptp.real) (B2 tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.dvd_dvd_real C))) (=> (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real A) C) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real B2) C)) (=> (tptp.pp (tptp.aa_real_bool _let_1 A)) (=> (tptp.pp (tptp.aa_real_bool _let_1 B2)) (= A B2)))))) (forall ((A tptp.rat) (C tptp.rat) (B2 tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.dvd_dvd_rat C))) (=> (= (tptp.aa_rat_rat (tptp.divide_divide_rat A) C) (tptp.aa_rat_rat (tptp.divide_divide_rat B2) C)) (=> (tptp.pp (tptp.aa_rat_bool _let_1 A)) (=> (tptp.pp (tptp.aa_rat_bool _let_1 B2)) (= A B2)))))) (forall ((A tptp.nat) (C tptp.nat) (B2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat C))) (=> (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) C) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat B2) C)) (=> (tptp.pp (tptp.aa_nat_bool _let_1 A)) (=> (tptp.pp (tptp.aa_nat_bool _let_1 B2)) (= A B2)))))) (forall ((A tptp.int) (C tptp.int) (B2 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int C))) (=> (= (tptp.aa_int_int (tptp.divide_divide_int A) C) (tptp.aa_int_int (tptp.divide_divide_int B2) C)) (=> (tptp.pp (tptp.aa_int_bool _let_1 A)) (=> (tptp.pp (tptp.aa_int_bool _let_1 B2)) (= A B2)))))) (forall ((C tptp.code_integer) (A tptp.code_integer) (B2 tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer C))) (=> (tptp.pp (tptp.aa_Code_integer_bool _let_1 A)) (=> (tptp.pp (tptp.aa_Code_integer_bool _let_1 B2)) (= (= (tptp.divide6298287555418463151nteger A C) (tptp.divide6298287555418463151nteger B2 C)) (= A B2)))))) (forall ((C tptp.complex) (A tptp.complex) (B2 tptp.complex)) (let ((_let_1 (tptp.aa_com1553036987509291606x_bool tptp.dvd_dvd_complex C))) (=> (tptp.pp (tptp.aa_complex_bool _let_1 A)) (=> (tptp.pp (tptp.aa_complex_bool _let_1 B2)) (= (= (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex A) C) (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex B2) C)) (= A B2)))))) (forall ((C tptp.real) (A tptp.real) (B2 tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.dvd_dvd_real C))) (=> (tptp.pp (tptp.aa_real_bool _let_1 A)) (=> (tptp.pp (tptp.aa_real_bool _let_1 B2)) (= (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real A) C) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real B2) C)) (= A B2)))))) (forall ((C tptp.rat) (A tptp.rat) (B2 tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.dvd_dvd_rat C))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 A)) (=> (tptp.pp (tptp.aa_rat_bool _let_1 B2)) (= (= (tptp.aa_rat_rat (tptp.divide_divide_rat A) C) (tptp.aa_rat_rat (tptp.divide_divide_rat B2) C)) (= A B2)))))) (forall ((C tptp.nat) (A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat C))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 A)) (=> (tptp.pp (tptp.aa_nat_bool _let_1 B2)) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) C) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat B2) C)) (= A B2)))))) (forall ((C tptp.int) (A tptp.int) (B2 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int C))) (=> (tptp.pp (tptp.aa_int_bool _let_1 A)) (=> (tptp.pp (tptp.aa_int_bool _let_1 B2)) (= (= (tptp.aa_int_int (tptp.divide_divide_int A) C) (tptp.aa_int_int (tptp.divide_divide_int B2) C)) (= A B2)))))) (forall ((X tptp.code_integer) (Y tptp.code_integer) (N tptp.nat)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer X) Y)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger X) N)) (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger Y) N))))) (forall ((X tptp.nat) (Y tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat X) Y)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat X) N)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat Y) N))))) (forall ((X tptp.real) (Y tptp.real) (N tptp.nat)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.dvd_dvd_real X) Y)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.dvd_dvd_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) N)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Y) N))))) (forall ((X tptp.int) (Y tptp.int) (N tptp.nat)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int X) Y)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_nat_int (tptp.power_power_int X) N)) (tptp.aa_nat_int (tptp.power_power_int Y) N))))) (forall ((X tptp.complex) (Y tptp.complex) (N tptp.nat)) (=> (tptp.pp (tptp.aa_complex_bool (tptp.aa_com1553036987509291606x_bool tptp.dvd_dvd_complex X) Y)) (tptp.pp (tptp.aa_complex_bool (tptp.aa_com1553036987509291606x_bool tptp.dvd_dvd_complex (tptp.aa_nat_complex (tptp.power_power_complex X) N)) (tptp.aa_nat_complex (tptp.power_power_complex Y) N))))) (forall ((C tptp.nat) (B2 tptp.nat) (A tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat C) B2)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat _let_1 B2)) C) (tptp.aa_nat_nat _let_1 C))))) (forall ((C tptp.int) (B2 tptp.int) (A tptp.int)) (let ((_let_1 (tptp.modulo_modulo_int A))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int C) B2)) (= (tptp.aa_int_int (tptp.modulo_modulo_int (tptp.aa_int_int _let_1 B2)) C) (tptp.aa_int_int _let_1 C))))) (forall ((C tptp.code_integer) (B2 tptp.code_integer) (A tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer C) B2)) (= (tptp.modulo364778990260209775nteger (tptp.modulo364778990260209775nteger A B2) C) (tptp.modulo364778990260209775nteger A C)))) (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat K))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 M)) (=> (tptp.pp (tptp.aa_nat_bool _let_1 N)) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat M) N))))))) (forall ((K tptp.int) (M tptp.int) (N tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int K))) (=> (tptp.pp (tptp.aa_int_bool _let_1 M)) (=> (tptp.pp (tptp.aa_int_bool _let_1 N)) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.modulo_modulo_int M) N))))))) (forall ((K tptp.code_integer) (M tptp.code_integer) (N tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer K))) (=> (tptp.pp (tptp.aa_Code_integer_bool _let_1 M)) (=> (tptp.pp (tptp.aa_Code_integer_bool _let_1 N)) (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.modulo364778990260209775nteger M N))))))) (forall ((C tptp.nat) (A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat C))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A) B2))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 B2)) (tptp.pp (tptp.aa_nat_bool _let_1 A)))))) (forall ((C tptp.int) (A tptp.int) (B2 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int C))) (=> (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.modulo_modulo_int A) B2))) (=> (tptp.pp (tptp.aa_int_bool _let_1 B2)) (tptp.pp (tptp.aa_int_bool _let_1 A)))))) (forall ((C tptp.code_integer) (A tptp.code_integer) (B2 tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer C))) (=> (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.modulo364778990260209775nteger A B2))) (=> (tptp.pp (tptp.aa_Code_integer_bool _let_1 B2)) (tptp.pp (tptp.aa_Code_integer_bool _let_1 A)))))) (forall ((C tptp.nat) (B2 tptp.nat) (A tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat C))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 B2)) (= (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A) B2))) (tptp.pp (tptp.aa_nat_bool _let_1 A)))))) (forall ((C tptp.int) (B2 tptp.int) (A tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int C))) (=> (tptp.pp (tptp.aa_int_bool _let_1 B2)) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.modulo_modulo_int A) B2))) (tptp.pp (tptp.aa_int_bool _let_1 A)))))) (forall ((C tptp.code_integer) (B2 tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer C))) (=> (tptp.pp (tptp.aa_Code_integer_bool _let_1 B2)) (= (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.modulo364778990260209775nteger A B2))) (tptp.pp (tptp.aa_Code_integer_bool _let_1 A)))))) (forall ((N tptp.nat) (K tptp.int) (L tptp.int)) (let ((_let_1 (tptp.bit_ri631733984087533419it_int N))) (= (tptp.aa_int_int _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int _let_1 K)) (tptp.aa_int_int _let_1 L))) (tptp.aa_int_int _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int K) L))))) (forall ((N tptp.nat) (K tptp.int) (L tptp.int)) (let ((_let_1 (tptp.bit_ri631733984087533419it_int N))) (= (tptp.aa_int_int _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int _let_1 K)) (tptp.aa_int_int _let_1 L))) (tptp.aa_int_int _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int K) L))))) (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat K))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 M)) (=> (tptp.pp (tptp.aa_nat_bool _let_1 N)) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) N))))))) (forall ((N tptp.nat) (K tptp.int) (L tptp.int)) (let ((_let_1 (tptp.bit_ri631733984087533419it_int N))) (= (tptp.aa_int_int _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_int_int _let_1 K)) (tptp.aa_int_int _let_1 L))) (tptp.aa_int_int _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int K) L))))) (forall ((A tptp.complex) (B2 tptp.complex)) (= (tptp.pp (tptp.aa_set_complex_bool (tptp.ord_le211207098394363844omplex (tptp.collect_complex (tptp.aa_com1553036987509291606x_bool tptp.aTP_Lamm_fe A))) (tptp.collect_complex (tptp.aa_com1553036987509291606x_bool tptp.aTP_Lamm_fe B2)))) (tptp.pp (tptp.aa_complex_bool (tptp.aa_com1553036987509291606x_bool tptp.dvd_dvd_complex A) B2)))) (forall ((A tptp.real) (B2 tptp.real)) (= (tptp.ord_less_eq_set_real (tptp.collect_real (tptp.aa_rea7809428808904475482l_bool tptp.aTP_Lamm_ff A)) (tptp.collect_real (tptp.aa_rea7809428808904475482l_bool tptp.aTP_Lamm_ff B2))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.dvd_dvd_real A) B2)))) (forall ((A tptp.nat) (B2 tptp.nat)) (= (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat (tptp.collect_nat (tptp.aa_nat_fun_nat_bool tptp.aTP_Lamm_fg A))) (tptp.collect_nat (tptp.aa_nat_fun_nat_bool tptp.aTP_Lamm_fg B2)))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat A) B2)))) (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (= (tptp.ord_le7084787975880047091nteger (tptp.collect_Code_integer (tptp.aa_Cod7250484176784686200r_bool tptp.aTP_Lamm_fh A)) (tptp.collect_Code_integer (tptp.aa_Cod7250484176784686200r_bool tptp.aTP_Lamm_fh B2))) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer A) B2)))) (forall ((A tptp.int) (B2 tptp.int)) (= (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int (tptp.collect_int (tptp.aa_int_fun_int_bool tptp.aTP_Lamm_fi A))) (tptp.collect_int (tptp.aa_int_fun_int_bool tptp.aTP_Lamm_fi B2)))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int A) B2)))) (forall ((A tptp.complex) (B2 tptp.complex)) (= (tptp.pp (tptp.aa_set_complex_bool (tptp.ord_less_set_complex (tptp.collect_complex (tptp.aa_com1553036987509291606x_bool tptp.aTP_Lamm_fe A))) (tptp.collect_complex (tptp.aa_com1553036987509291606x_bool tptp.aTP_Lamm_fe B2)))) (and (tptp.pp (tptp.aa_complex_bool (tptp.aa_com1553036987509291606x_bool tptp.dvd_dvd_complex A) B2)) (not (tptp.pp (tptp.aa_complex_bool (tptp.aa_com1553036987509291606x_bool tptp.dvd_dvd_complex B2) A)))))) (forall ((A tptp.real) (B2 tptp.real)) (= (tptp.ord_less_set_real (tptp.collect_real (tptp.aa_rea7809428808904475482l_bool tptp.aTP_Lamm_ff A)) (tptp.collect_real (tptp.aa_rea7809428808904475482l_bool tptp.aTP_Lamm_ff B2))) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.dvd_dvd_real A) B2)) (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.dvd_dvd_real B2) A)))))) (forall ((A tptp.nat) (B2 tptp.nat)) (= (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_set_nat (tptp.collect_nat (tptp.aa_nat_fun_nat_bool tptp.aTP_Lamm_fg A))) (tptp.collect_nat (tptp.aa_nat_fun_nat_bool tptp.aTP_Lamm_fg B2)))) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat A) B2)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat B2) A)))))) (forall ((A tptp.int) (B2 tptp.int)) (= (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_set_int (tptp.collect_int (tptp.aa_int_fun_int_bool tptp.aTP_Lamm_fi A))) (tptp.collect_int (tptp.aa_int_fun_int_bool tptp.aTP_Lamm_fi B2)))) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int A) B2)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int B2) A)))))) (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (= (tptp.ord_le1307284697595431911nteger (tptp.collect_Code_integer (tptp.aa_Cod7250484176784686200r_bool tptp.aTP_Lamm_fh A)) (tptp.collect_Code_integer (tptp.aa_Cod7250484176784686200r_bool tptp.aTP_Lamm_fh B2))) (and (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer A) B2)) (not (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer B2) A)))))) (forall ((M tptp.nat) (A tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.bit_ri6519982836138164636nteger M A))) (tptp.pp (tptp.aa_Code_integer_bool _let_1 A))))) (forall ((M tptp.nat) (A tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.bit_ri631733984087533419it_int M) A))) (tptp.pp (tptp.aa_int_bool _let_1 A))))) (not (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer tptp.zero_z3403309356797280102nteger) tptp.one_one_Code_integer))) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat tptp.zero_zero_nat) tptp.one_one_nat))) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int tptp.zero_zero_int) tptp.one_one_int))) (forall ((D tptp.code_integer) (S tptp.code_integer)) (exists ((Z4 tptp.code_integer)) (forall ((X5 tptp.code_integer)) (let ((_let_1 (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer D) (tptp.plus_p5714425477246183910nteger X5 S))))) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger Z4) X5)) (= _let_1 _let_1)))))) (forall ((D tptp.real) (S tptp.real)) (exists ((Z4 tptp.real)) (forall ((X5 tptp.real)) (let ((_let_1 (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.dvd_dvd_real D) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X5) S))))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Z4) X5)) (= _let_1 _let_1)))))) (forall ((D tptp.rat) (S tptp.rat)) (exists ((Z4 tptp.rat)) (forall ((X5 tptp.rat)) (let ((_let_1 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.dvd_dvd_rat D) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat X5) S))))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Z4) X5)) (= _let_1 _let_1)))))) (forall ((D tptp.nat) (S tptp.nat)) (exists ((Z4 tptp.nat)) (forall ((X5 tptp.nat)) (let ((_let_1 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat D) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat X5) S))))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Z4) X5)) (= _let_1 _let_1)))))) (forall ((D tptp.int) (S tptp.int)) (exists ((Z4 tptp.int)) (forall ((X5 tptp.int)) (let ((_let_1 (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int D) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int X5) S))))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Z4) X5)) (= _let_1 _let_1)))))) (forall ((D tptp.code_integer) (S tptp.code_integer)) (exists ((Z4 tptp.code_integer)) (forall ((X5 tptp.code_integer)) (let ((_let_1 (not (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer D) (tptp.plus_p5714425477246183910nteger X5 S)))))) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger Z4) X5)) (= _let_1 _let_1)))))) (forall ((D tptp.real) (S tptp.real)) (exists ((Z4 tptp.real)) (forall ((X5 tptp.real)) (let ((_let_1 (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.dvd_dvd_real D) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X5) S)))))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Z4) X5)) (= _let_1 _let_1)))))) (forall ((D tptp.rat) (S tptp.rat)) (exists ((Z4 tptp.rat)) (forall ((X5 tptp.rat)) (let ((_let_1 (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.dvd_dvd_rat D) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat X5) S)))))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Z4) X5)) (= _let_1 _let_1)))))) (forall ((D tptp.nat) (S tptp.nat)) (exists ((Z4 tptp.nat)) (forall ((X5 tptp.nat)) (let ((_let_1 (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat D) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat X5) S)))))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Z4) X5)) (= _let_1 _let_1)))))) (forall ((D tptp.int) (S tptp.int)) (exists ((Z4 tptp.int)) (forall ((X5 tptp.int)) (let ((_let_1 (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int D) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int X5) S)))))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Z4) X5)) (= _let_1 _let_1)))))) (forall ((D tptp.code_integer) (S tptp.code_integer)) (exists ((Z4 tptp.code_integer)) (forall ((X5 tptp.code_integer)) (let ((_let_1 (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer D) (tptp.plus_p5714425477246183910nteger X5 S))))) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger X5) Z4)) (= _let_1 _let_1)))))) (forall ((D tptp.real) (S tptp.real)) (exists ((Z4 tptp.real)) (forall ((X5 tptp.real)) (let ((_let_1 (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.dvd_dvd_real D) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X5) S))))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X5) Z4)) (= _let_1 _let_1)))))) (forall ((D tptp.rat) (S tptp.rat)) (exists ((Z4 tptp.rat)) (forall ((X5 tptp.rat)) (let ((_let_1 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.dvd_dvd_rat D) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat X5) S))))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X5) Z4)) (= _let_1 _let_1)))))) (forall ((D tptp.nat) (S tptp.nat)) (exists ((Z4 tptp.nat)) (forall ((X5 tptp.nat)) (let ((_let_1 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat D) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat X5) S))))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X5) Z4)) (= _let_1 _let_1)))))) (forall ((D tptp.int) (S tptp.int)) (exists ((Z4 tptp.int)) (forall ((X5 tptp.int)) (let ((_let_1 (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int D) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int X5) S))))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X5) Z4)) (= _let_1 _let_1)))))) (forall ((D tptp.code_integer) (S tptp.code_integer)) (exists ((Z4 tptp.code_integer)) (forall ((X5 tptp.code_integer)) (let ((_let_1 (not (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer D) (tptp.plus_p5714425477246183910nteger X5 S)))))) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger X5) Z4)) (= _let_1 _let_1)))))) (forall ((D tptp.real) (S tptp.real)) (exists ((Z4 tptp.real)) (forall ((X5 tptp.real)) (let ((_let_1 (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.dvd_dvd_real D) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X5) S)))))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X5) Z4)) (= _let_1 _let_1)))))) (forall ((D tptp.rat) (S tptp.rat)) (exists ((Z4 tptp.rat)) (forall ((X5 tptp.rat)) (let ((_let_1 (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.dvd_dvd_rat D) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat X5) S)))))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X5) Z4)) (= _let_1 _let_1)))))) (forall ((D tptp.nat) (S tptp.nat)) (exists ((Z4 tptp.nat)) (forall ((X5 tptp.nat)) (let ((_let_1 (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat D) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat X5) S)))))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X5) Z4)) (= _let_1 _let_1)))))) (forall ((D tptp.int) (S tptp.int)) (exists ((Z4 tptp.int)) (forall ((X5 tptp.int)) (let ((_let_1 (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int D) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int X5) S)))))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X5) Z4)) (= _let_1 _let_1)))))) (forall ((B2 tptp.code_integer) (A tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer B2) A)) (= (= (tptp.divide6298287555418463151nteger A B2) tptp.zero_z3403309356797280102nteger) (= A tptp.zero_z3403309356797280102nteger)))) (forall ((B2 tptp.complex) (A tptp.complex)) (=> (tptp.pp (tptp.aa_complex_bool (tptp.aa_com1553036987509291606x_bool tptp.dvd_dvd_complex B2) A)) (= (= (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex A) B2) tptp.zero_zero_complex) (= A tptp.zero_zero_complex)))) (forall ((B2 tptp.real) (A tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.dvd_dvd_real B2) A)) (= (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real A) B2) tptp.zero_zero_real) (= A tptp.zero_zero_real)))) (forall ((B2 tptp.rat) (A tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.dvd_dvd_rat B2) A)) (= (= (tptp.aa_rat_rat (tptp.divide_divide_rat A) B2) tptp.zero_zero_rat) (= A tptp.zero_zero_rat)))) (forall ((B2 tptp.nat) (A tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat B2) A)) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) B2) tptp.zero_zero_nat) (= A tptp.zero_zero_nat)))) (forall ((B2 tptp.int) (A tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int B2) A)) (= (= (tptp.aa_int_int (tptp.divide_divide_int A) B2) tptp.zero_zero_int) (= A tptp.zero_zero_int)))) (forall ((A tptp.code_integer) (B2 tptp.code_integer) (C tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer)) (= (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B2) A) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger C) A)) (= B2 C)))) (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat A) tptp.one_one_nat)) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B2) A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat C) A)) (= B2 C)))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int A) tptp.one_one_int)) (= (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B2) A) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int C) A)) (= B2 C)))) (forall ((A tptp.code_integer) (B2 tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A))) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer)) (= (= (tptp.aa_Cod1783974652533396728nteger _let_1 B2) (tptp.aa_Cod1783974652533396728nteger _let_1 C)) (= B2 C))))) (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat A) tptp.one_one_nat)) (= (= (tptp.aa_nat_nat _let_1 B2) (tptp.aa_nat_nat _let_1 C)) (= B2 C))))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.times_times_int A))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int A) tptp.one_one_int)) (= (= (tptp.aa_int_int _let_1 B2) (tptp.aa_int_int _let_1 C)) (= B2 C))))) (forall ((A tptp.code_integer) (B2 tptp.code_integer) (C tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) B2)) C)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer B2) C))))) (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat A) tptp.one_one_nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) B2)) C)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat B2) C))))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int A) tptp.one_one_int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) B2)) C)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int B2) C))))) (forall ((B2 tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer A))) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer B2) tptp.one_one_Code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B2) C))) (tptp.pp (tptp.aa_Code_integer_bool _let_1 C)))))) (forall ((B2 tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat B2) tptp.one_one_nat)) (= (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B2) C))) (tptp.pp (tptp.aa_nat_bool _let_1 C)))))) (forall ((B2 tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int A))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int B2) tptp.one_one_int)) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B2) C))) (tptp.pp (tptp.aa_int_bool _let_1 C)))))) (forall ((B2 tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer B2) tptp.one_one_Code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) B2)) C)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer A) C))))) (forall ((B2 tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat B2) tptp.one_one_nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) B2)) C)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat A) C))))) (forall ((B2 tptp.int) (A tptp.int) (C tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int B2) tptp.one_one_int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) B2)) C)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int A) C))))) (forall ((B2 tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer A))) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer B2) tptp.one_one_Code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger C) B2))) (tptp.pp (tptp.aa_Code_integer_bool _let_1 C)))))) (forall ((B2 tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat B2) tptp.one_one_nat)) (= (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat C) B2))) (tptp.pp (tptp.aa_nat_bool _let_1 C)))))) (forall ((B2 tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int A))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int B2) tptp.one_one_int)) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int C) B2))) (tptp.pp (tptp.aa_int_bool _let_1 C)))))) (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) B2)) tptp.one_one_Code_integer)) (and (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer B2) tptp.one_one_Code_integer))))) (forall ((A tptp.nat) (B2 tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) B2)) tptp.one_one_nat)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat A) tptp.one_one_nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat B2) tptp.one_one_nat))))) (forall ((A tptp.int) (B2 tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) B2)) tptp.one_one_int)) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int A) tptp.one_one_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int B2) tptp.one_one_int))))) (forall ((B2 tptp.code_integer) (A tptp.code_integer) (D tptp.code_integer) (C tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer B2) A)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer D) C)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.divide6298287555418463151nteger A B2)) (tptp.divide6298287555418463151nteger C D)) (tptp.divide6298287555418463151nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) C) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B2) D)))))) (forall ((B2 tptp.nat) (A tptp.nat) (D tptp.nat) (C tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat B2) A)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat D) C)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) B2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat C) D)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) C)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B2) D)))))) (forall ((B2 tptp.int) (A tptp.int) (D tptp.int) (C tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int B2) A)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int D) C)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.divide_divide_int A) B2)) (tptp.aa_int_int (tptp.divide_divide_int C) D)) (tptp.aa_int_int (tptp.divide_divide_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B2) D)))))) (forall ((A tptp.code_integer) (C tptp.code_integer) (B2 tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) C)) B2)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer A) (tptp.divide6298287555418463151nteger B2 C))))) (forall ((A tptp.nat) (C tptp.nat) (B2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) C)) B2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat B2) C))))) (forall ((A tptp.int) (C tptp.int) (B2 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) C)) B2)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int A) (tptp.aa_int_int (tptp.divide_divide_int B2) C))))) (forall ((B2 tptp.code_integer) (C tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B2) C))) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer _let_1) A)) (= (tptp.divide6298287555418463151nteger A _let_1) (tptp.divide6298287555418463151nteger (tptp.divide6298287555418463151nteger A B2) C))))) (forall ((B2 tptp.nat) (C tptp.nat) (A tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A))) (let ((_let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B2) C))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat _let_2) A)) (= (tptp.aa_nat_nat _let_1 _let_2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat _let_1 B2)) C)))))) (forall ((B2 tptp.int) (C tptp.int) (A tptp.int)) (let ((_let_1 (tptp.divide_divide_int A))) (let ((_let_2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B2) C))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int _let_2) A)) (= (tptp.aa_int_int _let_1 _let_2) (tptp.aa_int_int (tptp.divide_divide_int (tptp.aa_int_int _let_1 B2)) C)))))) (forall ((C tptp.code_integer) (B2 tptp.code_integer) (A tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer C) B2)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer B2) A)) (= (tptp.divide6298287555418463151nteger A (tptp.divide6298287555418463151nteger B2 C)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.divide6298287555418463151nteger A B2)) C))))) (forall ((C tptp.nat) (B2 tptp.nat) (A tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat C) B2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat B2) A)) (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat B2) C)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat _let_1 B2)) C)))))) (forall ((C tptp.int) (B2 tptp.int) (A tptp.int)) (let ((_let_1 (tptp.divide_divide_int A))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int C) B2)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int B2) A)) (= (tptp.aa_int_int _let_1 (tptp.aa_int_int (tptp.divide_divide_int B2) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int _let_1 B2)) C)))))) (forall ((C tptp.code_integer) (B2 tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A))) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer C) B2)) (= (tptp.aa_Cod1783974652533396728nteger _let_1 (tptp.divide6298287555418463151nteger B2 C)) (tptp.divide6298287555418463151nteger (tptp.aa_Cod1783974652533396728nteger _let_1 B2) C))))) (forall ((C tptp.nat) (B2 tptp.nat) (A tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat C) B2)) (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat B2) C)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat _let_1 B2)) C))))) (forall ((C tptp.int) (B2 tptp.int) (A tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.times_times_int A))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int C) B2)) (= (tptp.aa_int_int _let_1 (tptp.aa_int_int (tptp.divide_divide_int B2) C)) (tptp.aa_int_int (tptp.divide_divide_int (tptp.aa_int_int _let_1 B2)) C))))) (forall ((C tptp.code_integer) (B2 tptp.code_integer) (A tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer C) B2)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.divide6298287555418463151nteger B2 C)) A) (tptp.divide6298287555418463151nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B2) A) C)))) (forall ((C tptp.nat) (B2 tptp.nat) (A tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat C) B2)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat B2) C)) A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B2) A)) C)))) (forall ((C tptp.int) (B2 tptp.int) (A tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int C) B2)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.divide_divide_int B2) C)) A) (tptp.aa_int_int (tptp.divide_divide_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B2) A)) C)))) (forall ((B2 tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer A))) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer B2) tptp.one_one_Code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.divide6298287555418463151nteger C B2))) (tptp.pp (tptp.aa_Code_integer_bool _let_1 C)))))) (forall ((B2 tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat B2) tptp.one_one_nat)) (= (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat C) B2))) (tptp.pp (tptp.aa_nat_bool _let_1 C)))))) (forall ((B2 tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int A))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int B2) tptp.one_one_int)) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.divide_divide_int C) B2))) (tptp.pp (tptp.aa_int_bool _let_1 C)))))) (forall ((B2 tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer B2) tptp.one_one_Code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.divide6298287555418463151nteger A B2)) C)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer A) C))))) (forall ((B2 tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat B2) tptp.one_one_nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) B2)) C)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat A) C))))) (forall ((B2 tptp.int) (A tptp.int) (C tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int B2) tptp.one_one_int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_int_int (tptp.divide_divide_int A) B2)) C)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int A) C))))) (forall ((A tptp.code_integer) (B2 tptp.code_integer) (C tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer)) (= (= (tptp.divide6298287555418463151nteger B2 A) (tptp.divide6298287555418463151nteger C A)) (= B2 C)))) (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat A) tptp.one_one_nat)) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat B2) A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat C) A)) (= B2 C)))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int A) tptp.one_one_int)) (= (= (tptp.aa_int_int (tptp.divide_divide_int B2) A) (tptp.aa_int_int (tptp.divide_divide_int C) A)) (= B2 C)))) (forall ((C tptp.code_integer) (A tptp.code_integer) (B2 tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer C) A)) (= (tptp.divide6298287555418463151nteger (tptp.plus_p5714425477246183910nteger A B2) C) (tptp.plus_p5714425477246183910nteger (tptp.divide6298287555418463151nteger A C) (tptp.divide6298287555418463151nteger B2 C))))) (forall ((C tptp.nat) (A tptp.nat) (B2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat C) A)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) B2)) C) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) C)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat B2) C))))) (forall ((C tptp.int) (A tptp.int) (B2 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int C) A)) (= (tptp.aa_int_int (tptp.divide_divide_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) B2)) C) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.divide_divide_int A) C)) (tptp.aa_int_int (tptp.divide_divide_int B2) C))))) (forall ((C tptp.code_integer) (B2 tptp.code_integer) (A tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer C) B2)) (= (tptp.divide6298287555418463151nteger (tptp.plus_p5714425477246183910nteger A B2) C) (tptp.plus_p5714425477246183910nteger (tptp.divide6298287555418463151nteger A C) (tptp.divide6298287555418463151nteger B2 C))))) (forall ((C tptp.nat) (B2 tptp.nat) (A tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat C) B2)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) B2)) C) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) C)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat B2) C))))) (forall ((C tptp.int) (B2 tptp.int) (A tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int C) B2)) (= (tptp.aa_int_int (tptp.divide_divide_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) B2)) C) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.divide_divide_int A) C)) (tptp.aa_int_int (tptp.divide_divide_int B2) C))))) (forall ((B2 tptp.code_integer) (A tptp.code_integer) (N tptp.nat)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer B2) A)) (= (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger (tptp.divide6298287555418463151nteger A B2)) N) (tptp.divide6298287555418463151nteger (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger A) N) (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger B2) N))))) (forall ((B2 tptp.nat) (A tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat B2) A)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) B2)) N) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A) N)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat B2) N))))) (forall ((B2 tptp.int) (A tptp.int) (N tptp.nat)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int B2) A)) (= (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_int_int (tptp.divide_divide_int A) B2)) N) (tptp.aa_int_int (tptp.divide_divide_int (tptp.aa_nat_int (tptp.power_power_int A) N)) (tptp.aa_nat_int (tptp.power_power_int B2) N))))) (forall ((A tptp.nat) (B2 tptp.nat)) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A) B2) tptp.zero_zero_nat) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat B2) A)))) (forall ((A tptp.int) (B2 tptp.int)) (= (= (tptp.aa_int_int (tptp.modulo_modulo_int A) B2) tptp.zero_zero_int) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int B2) A)))) (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (= (= (tptp.modulo364778990260209775nteger A B2) tptp.zero_z3403309356797280102nteger) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer B2) A)))) (forall ((A tptp.nat) (B2 tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat A) B2)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat B2) A) tptp.zero_zero_nat))) (forall ((A tptp.int) (B2 tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int A) B2)) (= (tptp.aa_int_int (tptp.modulo_modulo_int B2) A) tptp.zero_zero_int))) (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer A) B2)) (= (tptp.modulo364778990260209775nteger B2 A) tptp.zero_z3403309356797280102nteger))) (forall ((A tptp.nat) (B2 tptp.nat)) (=> (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A) B2) tptp.zero_zero_nat) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat B2) A)))) (forall ((A tptp.int) (B2 tptp.int)) (=> (= (tptp.aa_int_int (tptp.modulo_modulo_int A) B2) tptp.zero_zero_int) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int B2) A)))) (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (=> (= (tptp.modulo364778990260209775nteger A B2) tptp.zero_z3403309356797280102nteger) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer B2) A)))) (forall ((X tptp.code_integer) (Y tptp.code_integer) (N tptp.nat) (M tptp.nat)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer X) Y)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N) M)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger X) N)) (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger Y) M)))))) (forall ((X tptp.nat) (Y tptp.nat) (N tptp.nat) (M tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat X) Y)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N) M)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat X) N)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat Y) M)))))) (forall ((X tptp.real) (Y tptp.real) (N tptp.nat) (M tptp.nat)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.dvd_dvd_real X) Y)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N) M)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.dvd_dvd_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) N)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Y) M)))))) (forall ((X tptp.int) (Y tptp.int) (N tptp.nat) (M tptp.nat)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int X) Y)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N) M)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_nat_int (tptp.power_power_int X) N)) (tptp.aa_nat_int (tptp.power_power_int Y) M)))))) (forall ((X tptp.complex) (Y tptp.complex) (N tptp.nat) (M tptp.nat)) (=> (tptp.pp (tptp.aa_complex_bool (tptp.aa_com1553036987509291606x_bool tptp.dvd_dvd_complex X) Y)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N) M)) (tptp.pp (tptp.aa_complex_bool (tptp.aa_com1553036987509291606x_bool tptp.dvd_dvd_complex (tptp.aa_nat_complex (tptp.power_power_complex X) N)) (tptp.aa_nat_complex (tptp.power_power_complex Y) M)))))) (forall ((A tptp.code_integer) (N tptp.nat) (B2 tptp.code_integer) (M tptp.nat)) (let ((_let_1 (tptp.power_8256067586552552935nteger A))) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.aa_nat_Code_integer _let_1 N)) B2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.aa_nat_Code_integer _let_1 M)) B2)))))) (forall ((A tptp.nat) (N tptp.nat) (B2 tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_nat_nat _let_1 N)) B2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_nat_nat _let_1 M)) B2)))))) (forall ((A tptp.real) (N tptp.nat) (B2 tptp.real) (M tptp.nat)) (let ((_let_1 (tptp.aa_real_fun_nat_real tptp.power_power_real A))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.dvd_dvd_real (tptp.aa_nat_real _let_1 N)) B2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.dvd_dvd_real (tptp.aa_nat_real _let_1 M)) B2)))))) (forall ((A tptp.int) (N tptp.nat) (B2 tptp.int) (M tptp.nat)) (let ((_let_1 (tptp.power_power_int A))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_nat_int _let_1 N)) B2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_nat_int _let_1 M)) B2)))))) (forall ((A tptp.complex) (N tptp.nat) (B2 tptp.complex) (M tptp.nat)) (let ((_let_1 (tptp.power_power_complex A))) (=> (tptp.pp (tptp.aa_complex_bool (tptp.aa_com1553036987509291606x_bool tptp.dvd_dvd_complex (tptp.aa_nat_complex _let_1 N)) B2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)) (tptp.pp (tptp.aa_complex_bool (tptp.aa_com1553036987509291606x_bool tptp.dvd_dvd_complex (tptp.aa_nat_complex _let_1 M)) B2)))))) (forall ((M tptp.nat) (N tptp.nat) (A tptp.code_integer)) (let ((_let_1 (tptp.power_8256067586552552935nteger A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.aa_nat_Code_integer _let_1 M)) (tptp.aa_nat_Code_integer _let_1 N)))))) (forall ((M tptp.nat) (N tptp.nat) (A tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_nat_nat _let_1 M)) (tptp.aa_nat_nat _let_1 N)))))) (forall ((M tptp.nat) (N tptp.nat) (A tptp.real)) (let ((_let_1 (tptp.aa_real_fun_nat_real tptp.power_power_real A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.dvd_dvd_real (tptp.aa_nat_real _let_1 M)) (tptp.aa_nat_real _let_1 N)))))) (forall ((M tptp.nat) (N tptp.nat) (A tptp.int)) (let ((_let_1 (tptp.power_power_int A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_nat_int _let_1 M)) (tptp.aa_nat_int _let_1 N)))))) (forall ((M tptp.nat) (N tptp.nat) (A tptp.complex)) (let ((_let_1 (tptp.power_power_complex A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)) (tptp.pp (tptp.aa_complex_bool (tptp.aa_com1553036987509291606x_bool tptp.dvd_dvd_complex (tptp.aa_nat_complex _let_1 M)) (tptp.aa_nat_complex _let_1 N)))))) (forall ((A tptp.int) (C tptp.int) (B2 tptp.int)) (= (= (tptp.aa_int_int (tptp.modulo_modulo_int A) C) (tptp.aa_int_int (tptp.modulo_modulo_int B2) C)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int C) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) B2))))) (forall ((A tptp.code_integer) (C tptp.code_integer) (B2 tptp.code_integer)) (= (= (tptp.modulo364778990260209775nteger A C) (tptp.modulo364778990260209775nteger B2 C)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer C) (tptp.minus_8373710615458151222nteger A B2))))) (forall ((B2 tptp.nat) (A tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat B2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A) B2))))) (forall ((B2 tptp.int) (A tptp.int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int B2) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) (tptp.aa_int_int (tptp.modulo_modulo_int A) B2))))) (forall ((B2 tptp.code_integer) (A tptp.code_integer)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer B2) (tptp.minus_8373710615458151222nteger A (tptp.modulo364778990260209775nteger A B2))))) (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 N)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat M) N)) (tptp.pp (tptp.aa_nat_bool _let_1 M)))))) (forall ((M tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) M)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat N) M)))))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat M))) (= (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) M))) (or (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N) M)) (tptp.pp (tptp.aa_nat_bool _let_1 N)))))) (forall ((M tptp.int) (N tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.pp (tptp.aa_int_bool _let_1 M)) (=> (tptp.pp (tptp.aa_int_bool _let_1 N)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int M) N)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int N) M)) (= M N))))))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat M))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)) (= (tptp.pp (tptp.aa_nat_bool _let_1 N)) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) M))))))) (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat K))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) N))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 M)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N) M)) (tptp.pp (tptp.aa_nat_bool _let_1 N))))))) (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat K))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) N))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 N)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N) M)) (tptp.pp (tptp.aa_nat_bool _let_1 M))))))) (forall ((M tptp.int) (N tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) M)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int M) N)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int N) M)))))) (forall ((K tptp.int) (M tptp.int) (T tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.times_times_int K))) (=> (not (= K tptp.zero_zero_int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int M) T)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_int_int _let_1 M)) (tptp.aa_int_int _let_1 T))))))) (forall ((K tptp.int) (M tptp.int) (N tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.times_times_int K))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_int_int _let_1 M)) (tptp.aa_int_int _let_1 N))) (=> (not (= K tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int M) N)))))) (forall ((A tptp.nat) (B2 tptp.nat)) (exists ((D2 tptp.nat) (X4 tptp.nat) (Y4 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A))) (let ((_let_2 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B2))) (let ((_let_3 (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat D2))) (and (tptp.pp (tptp.aa_nat_bool _let_3 A)) (tptp.pp (tptp.aa_nat_bool _let_3 B2)) (or (= (tptp.aa_nat_nat _let_1 X4) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat _let_2 Y4)) D2)) (= (tptp.aa_nat_nat _let_2 X4) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat _let_1 Y4)) D2))))))))) (forall ((D tptp.nat) (A tptp.nat) (B2 tptp.nat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A))) (let ((_let_2 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B2))) (let ((_let_3 (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat D))) (=> (tptp.pp (tptp.aa_nat_bool _let_3 A)) (=> (tptp.pp (tptp.aa_nat_bool _let_3 B2)) (=> (or (= (tptp.aa_nat_nat _let_1 X) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat _let_2 Y)) D)) (= (tptp.aa_nat_nat _let_2 X) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat _let_1 Y)) D))) (exists ((X4 tptp.nat) (Y4 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A))) (let ((_let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) B2))) (let ((_let_3 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat _let_2))) (let ((_let_4 (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat D))) (and (tptp.pp (tptp.aa_nat_bool _let_4 A)) (tptp.pp (tptp.aa_nat_bool _let_4 _let_2)) (or (= (tptp.aa_nat_nat _let_1 X4) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat _let_3 Y4)) D)) (= (tptp.aa_nat_nat _let_3 X4) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat _let_1 Y4)) D)))))))))))))))) (forall ((A tptp.nat) (B2 tptp.nat)) (exists ((D2 tptp.nat) (X4 tptp.nat) (Y4 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A))) (let ((_let_2 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B2))) (let ((_let_3 (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat D2))) (and (tptp.pp (tptp.aa_nat_bool _let_3 A)) (tptp.pp (tptp.aa_nat_bool _let_3 B2)) (or (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat _let_1 X4)) (tptp.aa_nat_nat _let_2 Y4)) D2) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat _let_2 X4)) (tptp.aa_nat_nat _let_1 Y4)) D2)))))))) (forall ((A tptp.int) (D tptp.int) (X tptp.int) (T tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.plus_plus_int X))) (let ((_let_2 (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int A))) (=> (tptp.pp (tptp.aa_int_bool _let_2 D)) (= (tptp.pp (tptp.aa_int_bool _let_2 (tptp.aa_int_int _let_1 T))) (tptp.pp (tptp.aa_int_bool _let_2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int C) D))) T)))))))) (forall ((K tptp.int) (N tptp.int) (M tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int K))) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int N) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int K) M)))) (tptp.pp (tptp.aa_int_bool _let_1 N))))) (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat _let_1))) (=> (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat X) _let_1) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat Y) _let_1)) (=> (= (tptp.pp (tptp.aa_nat_bool _let_2 X)) (tptp.pp (tptp.aa_nat_bool _let_2 Y))) (= X Y)))))) (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer)) (not (=> (not (= A tptp.zero_z3403309356797280102nteger)) (forall ((C2 tptp.code_integer)) (not (= B2 (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) C2)))))))) (forall ((A tptp.nat) (B2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat A) tptp.one_one_nat)) (not (=> (not (= A tptp.zero_zero_nat)) (forall ((C2 tptp.nat)) (not (= B2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) C2)))))))) (forall ((A tptp.int) (B2 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int A) tptp.one_one_int)) (not (=> (not (= A tptp.zero_zero_int)) (forall ((C2 tptp.int)) (not (= B2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) C2)))))))) (forall ((P tptp.fun_Co8822979462182099027r_bool) (L tptp.code_integer)) (= (exists ((X3 tptp.code_integer)) (tptp.pp (tptp.aa_Code_integer_bool P (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger L) X3)))) (exists ((X3 tptp.code_integer)) (and (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer L) (tptp.plus_p5714425477246183910nteger X3 tptp.zero_z3403309356797280102nteger))) (tptp.pp (tptp.aa_Code_integer_bool P X3)))))) (forall ((P tptp.fun_complex_bool) (L tptp.complex)) (= (exists ((X3 tptp.complex)) (tptp.pp (tptp.aa_complex_bool P (tptp.aa_complex_complex (tptp.times_times_complex L) X3)))) (exists ((X3 tptp.complex)) (and (tptp.pp (tptp.aa_complex_bool (tptp.aa_com1553036987509291606x_bool tptp.dvd_dvd_complex L) (tptp.aa_complex_complex (tptp.plus_plus_complex X3) tptp.zero_zero_complex))) (tptp.pp (tptp.aa_complex_bool P X3)))))) (forall ((P tptp.fun_real_bool) (L tptp.real)) (= (exists ((X3 tptp.real)) (tptp.pp (tptp.aa_real_bool P (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real L) X3)))) (exists ((X3 tptp.real)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.dvd_dvd_real L) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X3) tptp.zero_zero_real))) (tptp.pp (tptp.aa_real_bool P X3)))))) (forall ((P tptp.fun_rat_bool) (L tptp.rat)) (= (exists ((X3 tptp.rat)) (tptp.pp (tptp.aa_rat_bool P (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat L) X3)))) (exists ((X3 tptp.rat)) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.dvd_dvd_rat L) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat X3) tptp.zero_zero_rat))) (tptp.pp (tptp.aa_rat_bool P X3)))))) (forall ((P tptp.fun_nat_bool) (L tptp.nat)) (= (exists ((X3 tptp.nat)) (tptp.pp (tptp.aa_nat_bool P (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat L) X3)))) (exists ((X3 tptp.nat)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat L) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat X3) tptp.zero_zero_nat))) (tptp.pp (tptp.aa_nat_bool P X3)))))) (forall ((P tptp.fun_int_bool) (L tptp.int)) (= (exists ((X3 tptp.int)) (tptp.pp (tptp.aa_int_bool P (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int L) X3)))) (exists ((X3 tptp.int)) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int L) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int X3) tptp.zero_zero_int))) (tptp.pp (tptp.aa_int_bool P X3)))))) (forall ((A tptp.code_integer) (B2 tptp.code_integer) (C tptp.code_integer)) (=> (not (= A tptp.zero_z3403309356797280102nteger)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer A) B2)) (= (= (tptp.divide6298287555418463151nteger B2 A) C) (= B2 (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger C) A)))))) (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat A) B2)) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat B2) A) C) (= B2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat C) A)))))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (=> (not (= A tptp.zero_zero_int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int A) B2)) (= (= (tptp.aa_int_int (tptp.divide_divide_int B2) A) C) (= B2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int C) A)))))) (forall ((B2 tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (=> (not (= B2 tptp.zero_z3403309356797280102nteger)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer B2) A)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.divide6298287555418463151nteger A B2)) C)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer A) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger C) B2))))))) (forall ((B2 tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (not (= B2 tptp.zero_zero_nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat B2) A)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) B2)) C)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat C) B2))))))) (forall ((B2 tptp.int) (A tptp.int) (C tptp.int)) (=> (not (= B2 tptp.zero_zero_int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int B2) A)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_int_int (tptp.divide_divide_int A) B2)) C)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int A) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int C) B2))))))) (forall ((C tptp.code_integer) (B2 tptp.code_integer) (A tptp.code_integer)) (=> (not (= C tptp.zero_z3403309356797280102nteger)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer C) B2)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer A) (tptp.divide6298287555418463151nteger B2 C))) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) C)) B2)))))) (forall ((C tptp.nat) (B2 tptp.nat) (A tptp.nat)) (=> (not (= C tptp.zero_zero_nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat C) B2)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat B2) C))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) C)) B2)))))) (forall ((C tptp.int) (B2 tptp.int) (A tptp.int)) (=> (not (= C tptp.zero_zero_int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int C) B2)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int A) (tptp.aa_int_int (tptp.divide_divide_int B2) C))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) C)) B2)))))) (forall ((A tptp.code_integer) (C tptp.code_integer) (B2 tptp.code_integer) (D tptp.code_integer)) (=> (not (= A tptp.zero_z3403309356797280102nteger)) (=> (not (= C tptp.zero_z3403309356797280102nteger)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer A) B2)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer C) D)) (= (= (tptp.divide6298287555418463151nteger B2 A) (tptp.divide6298287555418463151nteger D C)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B2) C) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) D)))))))) (forall ((A tptp.nat) (C tptp.nat) (B2 tptp.nat) (D tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (=> (not (= C tptp.zero_zero_nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat A) B2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat C) D)) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat B2) A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat D) C)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B2) C) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) D)))))))) (forall ((A tptp.int) (C tptp.int) (B2 tptp.int) (D tptp.int)) (=> (not (= A tptp.zero_zero_int)) (=> (not (= C tptp.zero_zero_int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int A) B2)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int C) D)) (= (= (tptp.aa_int_int (tptp.divide_divide_int B2) A) (tptp.aa_int_int (tptp.divide_divide_int D) C)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B2) C) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) D)))))))) (forall ((B2 tptp.code_integer) (A tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer B2) tptp.one_one_Code_integer)) (= (= (tptp.divide6298287555418463151nteger A B2) tptp.zero_z3403309356797280102nteger) (= A tptp.zero_z3403309356797280102nteger)))) (forall ((B2 tptp.nat) (A tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat B2) tptp.one_one_nat)) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) B2) tptp.zero_zero_nat) (= A tptp.zero_zero_nat)))) (forall ((B2 tptp.int) (A tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int B2) tptp.one_one_int)) (= (= (tptp.aa_int_int (tptp.divide_divide_int A) B2) tptp.zero_zero_int) (= A tptp.zero_zero_int)))) (forall ((N tptp.num)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 N))))) (forall ((N tptp.num)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 N))))) (forall ((N tptp.num)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 N))))) (forall ((D tptp.code_integer) (D4 tptp.code_integer) (T tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer D) D4)) (forall ((X5 tptp.code_integer) (K4 tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer D))) (= (not (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.plus_p5714425477246183910nteger X5 T)))) (not (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.plus_p5714425477246183910nteger (tptp.minus_8373710615458151222nteger X5 (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger K4) D4)) T))))))))) (forall ((D tptp.complex) (D4 tptp.complex) (T tptp.complex)) (=> (tptp.pp (tptp.aa_complex_bool (tptp.aa_com1553036987509291606x_bool tptp.dvd_dvd_complex D) D4)) (forall ((X5 tptp.complex) (K4 tptp.complex)) (let ((_let_1 (tptp.aa_com1553036987509291606x_bool tptp.dvd_dvd_complex D))) (= (not (tptp.pp (tptp.aa_complex_bool _let_1 (tptp.aa_complex_complex (tptp.plus_plus_complex X5) T)))) (not (tptp.pp (tptp.aa_complex_bool _let_1 (tptp.aa_complex_complex (tptp.plus_plus_complex (tptp.aa_complex_complex (tptp.minus_minus_complex X5) (tptp.aa_complex_complex (tptp.times_times_complex K4) D4))) T))))))))) (forall ((D tptp.real) (D4 tptp.real) (T tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.dvd_dvd_real D) D4)) (forall ((X5 tptp.real) (K4 tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.dvd_dvd_real D))) (= (not (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X5) T)))) (not (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real X5) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real K4) D4))) T))))))))) (forall ((D tptp.rat) (D4 tptp.rat) (T tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.dvd_dvd_rat D) D4)) (forall ((X5 tptp.rat) (K4 tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.dvd_dvd_rat D))) (= (not (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat X5) T)))) (not (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.minus_minus_rat X5) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat K4) D4))) T))))))))) (forall ((D tptp.int) (D4 tptp.int) (T tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int D) D4)) (forall ((X5 tptp.int) (K4 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int D))) (= (not (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int X5) T)))) (not (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int X5) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int K4) D4))) T))))))))) (forall ((D tptp.code_integer) (D4 tptp.code_integer) (T tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer D) D4)) (forall ((X5 tptp.code_integer) (K4 tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer D))) (= (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.plus_p5714425477246183910nteger X5 T))) (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.plus_p5714425477246183910nteger (tptp.minus_8373710615458151222nteger X5 (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger K4) D4)) T)))))))) (forall ((D tptp.complex) (D4 tptp.complex) (T tptp.complex)) (=> (tptp.pp (tptp.aa_complex_bool (tptp.aa_com1553036987509291606x_bool tptp.dvd_dvd_complex D) D4)) (forall ((X5 tptp.complex) (K4 tptp.complex)) (let ((_let_1 (tptp.aa_com1553036987509291606x_bool tptp.dvd_dvd_complex D))) (= (tptp.pp (tptp.aa_complex_bool _let_1 (tptp.aa_complex_complex (tptp.plus_plus_complex X5) T))) (tptp.pp (tptp.aa_complex_bool _let_1 (tptp.aa_complex_complex (tptp.plus_plus_complex (tptp.aa_complex_complex (tptp.minus_minus_complex X5) (tptp.aa_complex_complex (tptp.times_times_complex K4) D4))) T)))))))) (forall ((D tptp.real) (D4 tptp.real) (T tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.dvd_dvd_real D) D4)) (forall ((X5 tptp.real) (K4 tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.dvd_dvd_real D))) (= (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X5) T))) (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real X5) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real K4) D4))) T)))))))) (forall ((D tptp.rat) (D4 tptp.rat) (T tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.dvd_dvd_rat D) D4)) (forall ((X5 tptp.rat) (K4 tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.dvd_dvd_rat D))) (= (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat X5) T))) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.minus_minus_rat X5) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat K4) D4))) T)))))))) (forall ((D tptp.int) (D4 tptp.int) (T tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int D) D4)) (forall ((X5 tptp.int) (K4 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int D))) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int X5) T))) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int X5) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int K4) D4))) T)))))))) (forall ((B2 tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer B2) tptp.one_one_Code_integer)) (= (= (tptp.divide6298287555418463151nteger A B2) C) (= A (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger C) B2))))) (forall ((B2 tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat B2) tptp.one_one_nat)) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) B2) C) (= A (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat C) B2))))) (forall ((B2 tptp.int) (A tptp.int) (C tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int B2) tptp.one_one_int)) (= (= (tptp.aa_int_int (tptp.divide_divide_int A) B2) C) (= A (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int C) B2))))) (forall ((B2 tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer B2) tptp.one_one_Code_integer)) (= (= A (tptp.divide6298287555418463151nteger C B2)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) B2) C)))) (forall ((B2 tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat B2) tptp.one_one_nat)) (= (= A (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat C) B2)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) B2) C)))) (forall ((B2 tptp.int) (A tptp.int) (C tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int B2) tptp.one_one_int)) (= (= A (tptp.aa_int_int (tptp.divide_divide_int C) B2)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) B2) C)))) (forall ((C tptp.code_integer) (B2 tptp.code_integer) (A tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer C) tptp.one_one_Code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer B2) A)) (= (tptp.divide6298287555418463151nteger A (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B2) C)) (tptp.divide6298287555418463151nteger (tptp.divide6298287555418463151nteger A B2) C))))) (forall ((C tptp.nat) (B2 tptp.nat) (A tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat C) tptp.one_one_nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat B2) A)) (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B2) C)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat _let_1 B2)) C)))))) (forall ((C tptp.int) (B2 tptp.int) (A tptp.int)) (let ((_let_1 (tptp.divide_divide_int A))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int C) tptp.one_one_int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int B2) A)) (= (tptp.aa_int_int _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B2) C)) (tptp.aa_int_int (tptp.divide_divide_int (tptp.aa_int_int _let_1 B2)) C)))))) (forall ((B2 tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer B2) tptp.one_one_Code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.divide6298287555418463151nteger A B2)) C) (tptp.divide6298287555418463151nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) C) B2)))) (forall ((B2 tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat B2) tptp.one_one_nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) B2)) C) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) C)) B2)))) (forall ((B2 tptp.int) (A tptp.int) (C tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int B2) tptp.one_one_int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.divide_divide_int A) B2)) C) (tptp.aa_int_int (tptp.divide_divide_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) C)) B2)))) (forall ((C tptp.code_integer) (A tptp.code_integer) (B2 tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A))) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer C) tptp.one_one_Code_integer)) (= (tptp.aa_Cod1783974652533396728nteger _let_1 (tptp.divide6298287555418463151nteger B2 C)) (tptp.divide6298287555418463151nteger (tptp.aa_Cod1783974652533396728nteger _let_1 B2) C))))) (forall ((C tptp.nat) (A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat C) tptp.one_one_nat)) (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat B2) C)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat _let_1 B2)) C))))) (forall ((C tptp.int) (A tptp.int) (B2 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.times_times_int A))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int C) tptp.one_one_int)) (= (tptp.aa_int_int _let_1 (tptp.aa_int_int (tptp.divide_divide_int B2) C)) (tptp.aa_int_int (tptp.divide_divide_int (tptp.aa_int_int _let_1 B2)) C))))) (forall ((B2 tptp.code_integer) (C tptp.code_integer) (A tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer B2) tptp.one_one_Code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer C) tptp.one_one_Code_integer)) (= (tptp.divide6298287555418463151nteger A (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B2) C)) (tptp.divide6298287555418463151nteger (tptp.divide6298287555418463151nteger A B2) C))))) (forall ((B2 tptp.nat) (C tptp.nat) (A tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat B2) tptp.one_one_nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat C) tptp.one_one_nat)) (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B2) C)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat _let_1 B2)) C)))))) (forall ((B2 tptp.int) (C tptp.int) (A tptp.int)) (let ((_let_1 (tptp.divide_divide_int A))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int B2) tptp.one_one_int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int C) tptp.one_one_int)) (= (tptp.aa_int_int _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B2) C)) (tptp.aa_int_int (tptp.divide_divide_int (tptp.aa_int_int _let_1 B2)) C)))))) (forall ((B2 tptp.nat) (A tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat B2) tptp.one_one_nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A) B2) tptp.zero_zero_nat))) (forall ((B2 tptp.int) (A tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int B2) tptp.one_one_int)) (= (tptp.aa_int_int (tptp.modulo_modulo_int A) B2) tptp.zero_zero_int))) (forall ((B2 tptp.code_integer) (A tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer B2) tptp.one_one_Code_integer)) (= (tptp.modulo364778990260209775nteger A B2) tptp.zero_z3403309356797280102nteger))) (forall ((A tptp.code_integer) (N tptp.nat)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger A) N)) tptp.one_one_Code_integer)) (or (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer)) (= N tptp.zero_zero_nat)))) (forall ((A tptp.nat) (N tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A) N)) tptp.one_one_nat)) (or (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat A) tptp.one_one_nat)) (= N tptp.zero_zero_nat)))) (forall ((A tptp.int) (N tptp.nat)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_nat_int (tptp.power_power_int A) N)) tptp.one_one_int)) (or (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int A) tptp.one_one_int)) (= N tptp.zero_zero_nat)))) (forall ((K tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat K) N)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) N))))) (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat K))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) K)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_nat_nat _let_1 M)) (tptp.aa_nat_nat _let_1 N))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat M) N)))))) (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat K))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_nat_nat _let_1 M)) (tptp.aa_nat_nat _let_1 N))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) K)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat M) N)))))) (forall ((A tptp.nat) (B2 tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (exists ((D2 tptp.nat) (X4 tptp.nat) (Y4 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat D2))) (and (tptp.pp (tptp.aa_nat_bool _let_1 A)) (tptp.pp (tptp.aa_nat_bool _let_1 B2)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) X4) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B2) Y4)) D2))))))) (forall ((Z tptp.int) (N tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int Z) N)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) N)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Z) N))))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat M) N))) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat N) M))))) (forall ((N tptp.nat) (M tptp.nat) (Q2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N) M)) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat M) Q2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat N) Q2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat Q2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) N)))))) (forall ((X tptp.product_prod_nat_nat)) (not (forall ((K3 tptp.nat) (M3 tptp.nat)) (not (= X (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat K3) M3)))))) (forall ((M tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) M)) (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat (tptp.collect_nat (tptp.aa_nat_fun_nat_bool tptp.aTP_Lamm_fg M)))))) (tptp.pp (tptp.aa_Code_integer_bool _let_141 tptp.zero_z3403309356797280102nteger)) (tptp.pp (tptp.aa_nat_bool _let_140 tptp.zero_zero_nat)) (tptp.pp (tptp.aa_int_bool _let_139 tptp.zero_zero_int)) (forall ((A tptp.code_integer) (C tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer)) (not (=> (not (= A tptp.zero_z3403309356797280102nteger)) (forall ((B3 tptp.code_integer)) (=> (not (= B3 tptp.zero_z3403309356797280102nteger)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer B3) tptp.one_one_Code_integer)) (=> (= (tptp.divide6298287555418463151nteger tptp.one_one_Code_integer A) B3) (=> (= (tptp.divide6298287555418463151nteger tptp.one_one_Code_integer B3) A) (=> (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) B3) tptp.one_one_Code_integer) (not (= (tptp.divide6298287555418463151nteger C A) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger C) B3))))))))))))) (forall ((A tptp.nat) (C tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat A) tptp.one_one_nat)) (not (=> (not (= A tptp.zero_zero_nat)) (forall ((B3 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat tptp.one_one_nat))) (=> (not (= B3 tptp.zero_zero_nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat B3) tptp.one_one_nat)) (=> (= (tptp.aa_nat_nat _let_1 A) B3) (=> (= (tptp.aa_nat_nat _let_1 B3) A) (=> (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) B3) tptp.one_one_nat) (not (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat C) A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat C) B3)))))))))))))) (forall ((A tptp.int) (C tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int A) tptp.one_one_int)) (not (=> (not (= A tptp.zero_zero_int)) (forall ((B3 tptp.int)) (let ((_let_1 (tptp.divide_divide_int tptp.one_one_int))) (=> (not (= B3 tptp.zero_zero_int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int B3) tptp.one_one_int)) (=> (= (tptp.aa_int_int _let_1 A) B3) (=> (= (tptp.aa_int_int _let_1 B3) A) (=> (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) B3) tptp.one_one_int) (not (= (tptp.aa_int_int (tptp.divide_divide_int C) A) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int C) B3)))))))))))))) (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (=> (not (= A tptp.zero_z3403309356797280102nteger)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer B2) tptp.one_one_Code_integer)) (= (tptp.divide6298287555418463151nteger A (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) B2)) (tptp.divide6298287555418463151nteger tptp.one_one_Code_integer B2))))) (forall ((A tptp.nat) (B2 tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat B2) tptp.one_one_nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) B2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat tptp.one_one_nat) B2))))) (forall ((A tptp.int) (B2 tptp.int)) (=> (not (= A tptp.zero_zero_int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int B2) tptp.one_one_int)) (= (tptp.aa_int_int (tptp.divide_divide_int A) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) B2)) (tptp.aa_int_int (tptp.divide_divide_int tptp.one_one_int) B2))))) (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (=> (not (= A tptp.zero_z3403309356797280102nteger)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer B2) tptp.one_one_Code_integer)) (= (tptp.divide6298287555418463151nteger A (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B2) A)) (tptp.divide6298287555418463151nteger tptp.one_one_Code_integer B2))))) (forall ((A tptp.nat) (B2 tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat B2) tptp.one_one_nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B2) A)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat tptp.one_one_nat) B2))))) (forall ((A tptp.int) (B2 tptp.int)) (=> (not (= A tptp.zero_zero_int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int B2) tptp.one_one_int)) (= (tptp.aa_int_int (tptp.divide_divide_int A) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B2) A)) (tptp.aa_int_int (tptp.divide_divide_int tptp.one_one_int) B2))))) (forall ((A tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))) A)) (not (forall ((B3 tptp.code_integer)) (not (= A (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))) B3))))))) (forall ((A tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) A)) (not (forall ((B3 tptp.nat)) (not (= A (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) B3))))))) (forall ((A tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) A)) (not (forall ((B3 tptp.int)) (not (= A (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) B3))))))) (not (tptp.pp (tptp.aa_Code_integer_bool _let_141 tptp.one_one_Code_integer))) (not (tptp.pp (tptp.aa_nat_bool _let_140 tptp.one_one_nat))) (not (tptp.pp (tptp.aa_int_bool _let_139 tptp.one_one_int))) (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))))) (=> (not (tptp.pp (tptp.aa_Code_integer_bool _let_1 A))) (=> (not (tptp.pp (tptp.aa_Code_integer_bool _let_1 B2))) (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.plus_p5714425477246183910nteger A B2))))))) (forall ((A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (=> (not (tptp.pp (tptp.aa_nat_bool _let_1 A))) (=> (not (tptp.pp (tptp.aa_nat_bool _let_1 B2))) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) B2))))))) (forall ((A tptp.int) (B2 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))))) (=> (not (tptp.pp (tptp.aa_int_bool _let_1 A))) (=> (not (tptp.pp (tptp.aa_int_bool _let_1 B2))) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) B2))))))) (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (let ((_let_1 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer _let_1))) (= (= A B2) (and (= (tptp.pp (tptp.aa_Code_integer_bool _let_2 A)) (tptp.pp (tptp.aa_Code_integer_bool _let_2 B2))) (= (tptp.divide6298287555418463151nteger A _let_1) (tptp.divide6298287555418463151nteger B2 _let_1))))))) (forall ((A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat _let_1))) (= (= A B2) (and (= (tptp.pp (tptp.aa_nat_bool _let_2 A)) (tptp.pp (tptp.aa_nat_bool _let_2 B2))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) _let_1) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat B2) _let_1))))))) (forall ((A tptp.int) (B2 tptp.int)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int _let_1))) (= (= A B2) (and (= (tptp.pp (tptp.aa_int_bool _let_2 A)) (tptp.pp (tptp.aa_int_bool _let_2 B2))) (= (tptp.aa_int_int (tptp.divide_divide_int A) _let_1) (tptp.aa_int_int (tptp.divide_divide_int B2) _let_1))))))) (forall ((X tptp.code_integer) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.power_8256067586552552935nteger X))) (=> (not (= X tptp.zero_z3403309356797280102nteger)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.aa_nat_Code_integer _let_1 M)) (tptp.aa_nat_Code_integer _let_1 N))) (or (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer X) tptp.one_one_Code_integer)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N))))))) (forall ((X tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat X))) (=> (not (= X tptp.zero_zero_nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_nat_nat _let_1 M)) (tptp.aa_nat_nat _let_1 N))) (or (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat X) tptp.one_one_nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N))))))) (forall ((X tptp.int) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.power_power_int X))) (=> (not (= X tptp.zero_zero_int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_nat_int _let_1 M)) (tptp.aa_nat_int _let_1 N))) (or (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int X) tptp.one_one_int)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N))))))) (forall ((N tptp.nat) (X tptp.code_integer)) (=> (or (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (= X tptp.one_one_Code_integer)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer X) (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger X) N))))) (forall ((N tptp.nat) (X tptp.rat)) (=> (or (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (= X tptp.one_one_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.dvd_dvd_rat X) (tptp.aa_nat_rat (tptp.power_power_rat X) N))))) (forall ((N tptp.nat) (X tptp.nat)) (=> (or (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (= X tptp.one_one_nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat X) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat X) N))))) (forall ((N tptp.nat) (X tptp.real)) (=> (or (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (= X tptp.one_one_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.dvd_dvd_real X) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) N))))) (forall ((N tptp.nat) (X tptp.int)) (=> (or (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (= X tptp.one_one_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int X) (tptp.aa_nat_int (tptp.power_power_int X) N))))) (forall ((N tptp.nat) (X tptp.complex)) (=> (or (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (= X tptp.one_one_complex)) (tptp.pp (tptp.aa_complex_bool (tptp.aa_com1553036987509291606x_bool tptp.dvd_dvd_complex X) (tptp.aa_nat_complex (tptp.power_power_complex X) N))))) (forall ((N tptp.nat)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (let ((_let_2 (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1)))) (= (tptp.pp (tptp.aa_nat_bool _let_2 N)) (tptp.pp (tptp.aa_nat_bool _let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat N) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 _let_1))))))))) (forall ((M tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) M)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat N) M)) M)) (= N tptp.one_one_nat)))) (forall ((M tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) M)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat M) N)) M)) (= N tptp.one_one_nat)))) (forall ((Q2 tptp.nat) (N tptp.nat) (R tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat R) M))) (let ((_let_2 (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat M))) (let ((_let_3 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Q2))) (=> (tptp.pp (tptp.aa_nat_bool _let_3 N)) (=> (tptp.pp (tptp.aa_nat_bool _let_3 _let_1)) (= (tptp.pp (tptp.aa_nat_bool _let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) Q2))) (tptp.pp (tptp.aa_nat_bool _let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat _let_1) Q2))))))))))) (forall ((I tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat I))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_nat_nat _let_1 M)) (tptp.aa_nat_nat _let_1 N))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.one_one_nat) I)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)))))) (forall ((R tptp.nat) (N tptp.nat) (M tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat R) N)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat R) M)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat N) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) R))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat M) N) R))))) (forall ((K tptp.int) (L tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.modulo_modulo_int K) L))) (or (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int L) K)) (and (= L tptp.zero_zero_int) (tptp.pp (tptp.aa_int_bool _let_1 K))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) L)))))) (forall ((A tptp.code_integer)) (let ((_let_1 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer _let_1) A)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger _let_1) (tptp.divide6298287555418463151nteger A _let_1)) A)))) (forall ((A tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat _let_1) A)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat _let_1) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) _let_1)) A)))) (forall ((A tptp.int)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int _let_1) A)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int _let_1) (tptp.aa_int_int (tptp.divide_divide_int A) _let_1)) A)))) (forall ((A tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat _let_1) A)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A) _let_1) tptp.zero_zero_nat)))) (forall ((A tptp.int)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int _let_1) A)) (= (tptp.aa_int_int (tptp.modulo_modulo_int A) _let_1) tptp.zero_zero_int)))) (forall ((A tptp.code_integer)) (let ((_let_1 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer _let_1) A)) (= (tptp.modulo364778990260209775nteger A _let_1) tptp.zero_z3403309356797280102nteger)))) (forall ((A tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat _let_1) A))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A) _let_1) tptp.one_one_nat)))) (forall ((A tptp.int)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int _let_1) A))) (= (tptp.aa_int_int (tptp.modulo_modulo_int A) _let_1) tptp.one_one_int)))) (forall ((A tptp.code_integer)) (let ((_let_1 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (not (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer _let_1) A))) (= (tptp.modulo364778990260209775nteger A _let_1) tptp.one_one_Code_integer)))) (forall ((N tptp.nat) (A tptp.real) (B2 tptp.real)) (=> (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) B2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real A) N)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real B2) N)))))) (forall ((N tptp.nat) (A tptp.rat) (B2 tptp.rat)) (=> (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B2)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat (tptp.power_power_rat A) N)) (tptp.aa_nat_rat (tptp.power_power_rat B2) N)))))) (forall ((N tptp.nat) (A tptp.int) (B2 tptp.int)) (=> (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B2)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int (tptp.power_power_int A) N)) (tptp.aa_nat_int (tptp.power_power_int B2) N)))))) (forall ((N tptp.nat)) (=> (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)))) (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat K))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) K)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_nat_nat _let_1 M)) (tptp.aa_nat_nat _let_1 N))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)))))) (forall ((N tptp.nat) (K tptp.int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.bit_ri631733984087533419it_int N) K)) (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) N)))) (forall ((M tptp.nat) (A tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.bit_se8260200283734997820nteger M A))) (or (tptp.pp (tptp.aa_Code_integer_bool _let_1 A)) (= M tptp.zero_zero_nat))))) (forall ((M tptp.nat) (A tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.bit_se4203085406695923979it_int M) A))) (or (tptp.pp (tptp.aa_int_bool _let_1 A)) (= M tptp.zero_zero_nat))))) (forall ((M tptp.nat) (A tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se4205575877204974255it_nat M) A))) (or (tptp.pp (tptp.aa_nat_bool _let_1 A)) (= M tptp.zero_zero_nat))))) (forall ((M tptp.nat) (A tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.bit_se2793503036327961859nteger M A))) (and (tptp.pp (tptp.aa_Code_integer_bool _let_1 A)) (not (= M tptp.zero_zero_nat)))))) (forall ((M tptp.nat) (A tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.bit_se7879613467334960850it_int M) A))) (and (tptp.pp (tptp.aa_int_bool _let_1 A)) (not (= M tptp.zero_zero_nat)))))) (forall ((M tptp.nat) (A tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se7882103937844011126it_nat M) A))) (and (tptp.pp (tptp.aa_nat_bool _let_1 A)) (not (= M tptp.zero_zero_nat)))))) (forall ((M tptp.nat) (A tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.bit_se1345352211410354436nteger M A))) (not (= (tptp.pp (tptp.aa_Code_integer_bool _let_1 A)) (= M tptp.zero_zero_nat)))))) (forall ((M tptp.nat) (A tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.bit_se2159334234014336723it_int M) A))) (not (= (tptp.pp (tptp.aa_int_bool _let_1 A)) (= M tptp.zero_zero_nat)))))) (forall ((M tptp.nat) (A tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se2161824704523386999it_nat M) A))) (not (= (tptp.pp (tptp.aa_nat_bool _let_1 A)) (= M tptp.zero_zero_nat)))))) (forall ((K tptp.int) (L tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int K) L))) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int K) L)))))) (forall ((A tptp.code_integer)) (=> (not (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))) A))) (not (forall ((B3 tptp.code_integer)) (not (= A (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))) B3) tptp.one_one_Code_integer))))))) (forall ((A tptp.nat)) (=> (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) A))) (not (forall ((B3 tptp.nat)) (not (= A (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) B3)) tptp.one_one_nat))))))) (forall ((A tptp.int)) (=> (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) A))) (not (forall ((B3 tptp.int)) (not (= A (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) B3)) tptp.one_one_int))))))) (forall ((A tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A) _let_1))) (let ((_let_3 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat _let_1) A)))) (=> (=> _let_3 (not (= _let_2 tptp.zero_zero_nat))) (not (=> (not _let_3) (not (= _let_2 tptp.one_one_nat))))))))) (forall ((A tptp.int)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_int_int (tptp.modulo_modulo_int A) _let_1))) (let ((_let_3 (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int _let_1) A)))) (=> (=> _let_3 (not (= _let_2 tptp.zero_zero_int))) (not (=> (not _let_3) (not (= _let_2 tptp.one_one_int))))))))) (forall ((A tptp.code_integer)) (let ((_let_1 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.modulo364778990260209775nteger A _let_1))) (let ((_let_3 (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer _let_1) A)))) (=> (=> _let_3 (not (= _let_2 tptp.zero_z3403309356797280102nteger))) (not (=> (not _let_3) (not (= _let_2 tptp.one_one_Code_integer))))))))) (forall ((A tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A) _let_1))) (let ((_let_3 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat _let_1) A)))) (and (=> _let_3 (= _let_2 tptp.zero_zero_nat)) (=> (not _let_3) (= _let_2 tptp.one_one_nat))))))) (forall ((A tptp.int)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_int_int (tptp.modulo_modulo_int A) _let_1))) (let ((_let_3 (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int _let_1) A)))) (and (=> _let_3 (= _let_2 tptp.zero_zero_int)) (=> (not _let_3) (= _let_2 tptp.one_one_int))))))) (forall ((A tptp.code_integer)) (let ((_let_1 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.modulo364778990260209775nteger A _let_1))) (let ((_let_3 (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer _let_1) A)))) (and (=> _let_3 (= _let_2 tptp.zero_z3403309356797280102nteger)) (=> (not _let_3) (= _let_2 tptp.one_one_Code_integer))))))) (forall ((N tptp.nat) (A tptp.real)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real A) N))))) (forall ((N tptp.nat) (A tptp.rat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_nat_rat (tptp.power_power_rat A) N))))) (forall ((N tptp.nat) (A tptp.int)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.aa_nat_int (tptp.power_power_int A) N))))) (forall ((N tptp.nat) (A tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N))) (= (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real A) N))) (tptp.pp (tptp.aa_real_bool _let_1 A)))))) (forall ((N tptp.nat) (A tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N))) (= (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_nat_rat (tptp.power_power_rat A) N))) (tptp.pp (tptp.aa_rat_bool _let_1 A)))))) (forall ((N tptp.nat) (A tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N))) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_nat_int (tptp.power_power_int A) N))) (tptp.pp (tptp.aa_int_bool _let_1 A)))))) (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (let ((_let_2 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N)))) (= (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real A) N))) (or _let_2 (and (not _let_2) (tptp.pp (tptp.aa_real_bool _let_1 A)))))))) (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat))) (let ((_let_2 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N)))) (= (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_nat_rat (tptp.power_power_rat A) N))) (or _let_2 (and (not _let_2) (tptp.pp (tptp.aa_rat_bool _let_1 A)))))))) (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_2 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N)))) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_nat_int (tptp.power_power_int A) N))) (or _let_2 (and (not _let_2) (tptp.pp (tptp.aa_int_bool _let_1 A)))))))) (forall ((K tptp.int) (N tptp.nat)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int K) (tptp.aa_int_int (tptp.bit_ri631733984087533419it_int N) K))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int K) (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) N))))) (forall ((N tptp.nat) (K tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.bit_ri631733984087533419it_int N) K)) K)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) N)) K)))) (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real))) (let ((_let_2 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N)))) (= (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real A) N))) (or (= N tptp.zero_zero_nat) (and _let_2 (not (= A tptp.zero_zero_real))) (and (not _let_2) (tptp.pp (tptp.aa_real_bool _let_1 A)))))))) (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat))) (let ((_let_2 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N)))) (= (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_nat_rat (tptp.power_power_rat A) N))) (or (= N tptp.zero_zero_nat) (and _let_2 (not (= A tptp.zero_zero_rat))) (and (not _let_2) (tptp.pp (tptp.aa_rat_bool _let_1 A)))))))) (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int))) (let ((_let_2 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N)))) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_nat_int (tptp.power_power_int A) N))) (or (= N tptp.zero_zero_nat) (and _let_2 (not (= A tptp.zero_zero_int))) (and (not _let_2) (tptp.pp (tptp.aa_int_bool _let_1 A)))))))) (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int _let_1 N)) K)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.bit_ri631733984087533419it_int N) K)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int K) (tptp.aa_nat_int _let_1 (tptp.aa_nat_nat tptp.suc N)))))))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.power_8256067586552552935nteger _let_1))) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer _let_1) (tptp.divide6298287555418463151nteger (tptp.minus_8373710615458151222nteger (tptp.aa_nat_Code_integer _let_2 M) tptp.one_one_Code_integer) (tptp.aa_nat_Code_integer _let_2 N)))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)))))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat _let_1))) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat _let_1) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat _let_2 M)) tptp.one_one_nat)) (tptp.aa_nat_nat _let_2 N)))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)))))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.power_power_int _let_1))) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int _let_1) (tptp.aa_int_int (tptp.divide_divide_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_nat_int _let_2 M)) tptp.one_one_int)) (tptp.aa_nat_int _let_2 N)))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)))))) (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N)))) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real A) N)) tptp.zero_zero_real)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (or (and (not _let_1) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) tptp.zero_zero_real))) (and _let_1 (= A tptp.zero_zero_real))))))) (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N)))) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat (tptp.power_power_rat A) N)) tptp.zero_zero_rat)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (or (and (not _let_1) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) tptp.zero_zero_rat))) (and _let_1 (= A tptp.zero_zero_rat))))))) (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N)))) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int (tptp.power_power_int A) N)) tptp.zero_zero_int)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (or (and (not _let_1) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) tptp.zero_zero_int))) (and _let_1 (= A tptp.zero_zero_int))))))) (forall ((X tptp.fun_nat_nat)) (= (tptp.size_option_nat X tptp.none_nat) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat))) (forall ((X tptp.fun_Pr2602117396471556196at_nat)) (= (tptp.size_o8335143837870341156at_nat X tptp.none_P5556105721700978146at_nat) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat))) (forall ((X tptp.fun_num_nat)) (= (tptp.size_option_num X tptp.none_num) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat))) (forall ((N tptp.nat)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (let ((_let_2 (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1))) (let ((_let_3 (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat))) (=> (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat N) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 _let_1))) _let_3) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat _let_2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) _let_3)) _let_2)))))))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.power_8256067586552552935nteger _let_1))) (let ((_let_3 (tptp.aa_nat_Code_integer _let_2 N))) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer _let_1) (tptp.divide6298287555418463151nteger (tptp.minus_8373710615458151222nteger (tptp.aa_nat_Code_integer _let_2 M) tptp.one_one_Code_integer) _let_3))) (or (= _let_3 tptp.zero_z3403309356797280102nteger) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)))))))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat _let_1))) (let ((_let_3 (tptp.aa_nat_nat _let_2 N))) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat _let_1) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat _let_2 M)) tptp.one_one_nat)) _let_3))) (or (= _let_3 tptp.zero_zero_nat) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)))))))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.power_power_int _let_1))) (let ((_let_3 (tptp.aa_nat_int _let_2 N))) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int _let_1) (tptp.aa_int_int (tptp.divide_divide_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_nat_int _let_2 M)) tptp.one_one_int)) _let_3))) (or (= _let_3 tptp.zero_zero_int) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)))))))) (forall ((A tptp.code_integer) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.power_8256067586552552935nteger _let_1))) (let ((_let_3 (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer _let_1))) (let ((_let_4 (tptp.aa_nat_Code_integer _let_2 N))) (= (tptp.pp (tptp.aa_Code_integer_bool _let_3 (tptp.divide6298287555418463151nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) (tptp.aa_nat_Code_integer _let_2 M)) _let_4))) (or (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N) M)) (= _let_4 tptp.zero_z3403309356797280102nteger) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)) (tptp.pp (tptp.aa_Code_integer_bool _let_3 (tptp.divide6298287555418463151nteger A (tptp.aa_nat_Code_integer _let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) M))))))))))))) (forall ((A tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat _let_1))) (let ((_let_3 (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat _let_1))) (let ((_let_4 (tptp.aa_nat_nat _let_2 N))) (= (tptp.pp (tptp.aa_nat_bool _let_3 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) (tptp.aa_nat_nat _let_2 M))) _let_4))) (or (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N) M)) (= _let_4 tptp.zero_zero_nat) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)) (tptp.pp (tptp.aa_nat_bool _let_3 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) (tptp.aa_nat_nat _let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) M))))))))))))) (forall ((A tptp.int) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.power_power_int _let_1))) (let ((_let_3 (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int _let_1))) (let ((_let_4 (tptp.aa_nat_int _let_2 N))) (= (tptp.pp (tptp.aa_int_bool _let_3 (tptp.aa_int_int (tptp.divide_divide_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) (tptp.aa_nat_int _let_2 M))) _let_4))) (or (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N) M)) (= _let_4 tptp.zero_zero_int) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)) (tptp.pp (tptp.aa_int_bool _let_3 (tptp.aa_int_int (tptp.divide_divide_int A) (tptp.aa_nat_int _let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) M))))))))))))) (forall ((S2 tptp.set_real)) (=> (tptp.finite_finite_real S2) (=> (not (= S2 tptp.bot_bot_set_real)) (exists ((X4 tptp.real)) (and (tptp.member_real X4 S2) (not (exists ((Xa tptp.real)) (and (tptp.member_real Xa S2) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Xa) X4)))))))))) (forall ((S2 tptp.set_rat)) (=> (tptp.finite_finite_rat S2) (=> (not (= S2 tptp.bot_bot_set_rat)) (exists ((X4 tptp.rat)) (and (tptp.member_rat X4 S2) (not (exists ((Xa tptp.rat)) (and (tptp.member_rat Xa S2) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Xa) X4)))))))))) (forall ((S2 tptp.set_num)) (=> (tptp.finite_finite_num S2) (=> (not (= S2 tptp.bot_bot_set_num)) (exists ((X4 tptp.num)) (and (tptp.member_num X4 S2) (not (exists ((Xa tptp.num)) (and (tptp.member_num Xa S2) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num Xa) X4)))))))))) (forall ((S2 tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat S2)) (=> (not (= S2 tptp.bot_bot_set_nat)) (exists ((X4 tptp.nat)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X4) S2)) (not (exists ((Xa tptp.nat)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat Xa) S2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Xa) X4)))))))))) (forall ((S2 tptp.set_int)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int S2)) (=> (not (= S2 tptp.bot_bot_set_int)) (exists ((X4 tptp.int)) (and (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X4) S2)) (not (exists ((Xa tptp.int)) (and (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Xa) S2)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Xa) X4)))))))))) (forall ((N tptp.nat)) (= (tptp.aa_nat_nat tptp.nat_triangle N) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat N) (tptp.aa_nat_nat tptp.suc N))) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (forall ((X tptp.nat) (Y tptp.vEBT_VEBT)) (let ((_let_1 (not (= Y (tptp.vEBT_Leaf tptp.fFalse tptp.fFalse))))) (=> (= (tptp.vEBT_vebt_buildup X) Y) (=> (=> (= X tptp.zero_zero_nat) _let_1) (=> (=> (= X (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)) _let_1) (not (forall ((Va2 tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat tptp.suc Va2)))) (let ((_let_3 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat _let_2) _let_1))) (let ((_let_4 (tptp.aa_nat_nat tptp.suc _let_3))) (let ((_let_5 (tptp.vEBT_vebt_buildup _let_3))) (let ((_let_6 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat _let_1))) (let ((_let_7 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat _let_1) _let_2)))) (=> (= X _let_2) (not (and (=> _let_7 (= Y (tptp.vEBT_Node tptp.none_P5556105721700978146at_nat _let_2 (tptp.replicate_VEBT_VEBT (tptp.aa_nat_nat _let_6 _let_3) _let_5) _let_5))) (=> (not _let_7) (= Y (tptp.vEBT_Node tptp.none_P5556105721700978146at_nat _let_2 (tptp.replicate_VEBT_VEBT (tptp.aa_nat_nat _let_6 _let_4) _let_5) (tptp.vEBT_vebt_buildup _let_4))))))))))))))))))))) (forall ((N tptp.nat) (A tptp.code_integer)) (let ((_let_1 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.modulo364778990260209775nteger A _let_1))) (let ((_let_3 (tptp.bit_ri6519982836138164636nteger N A))) (let ((_let_4 (= N tptp.zero_zero_nat))) (and (=> _let_4 (= _let_3 (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger _let_2))) (=> (not _let_4) (= _let_3 (tptp.plus_p5714425477246183910nteger _let_2 (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger _let_1) (tptp.bit_ri6519982836138164636nteger (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) tptp.one_one_nat) (tptp.divide6298287555418463151nteger A _let_1)))))))))))) (forall ((N tptp.nat) (A tptp.int)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_int_int (tptp.modulo_modulo_int A) _let_1))) (let ((_let_3 (tptp.aa_int_int (tptp.bit_ri631733984087533419it_int N) A))) (let ((_let_4 (= N tptp.zero_zero_nat))) (and (=> _let_4 (= _let_3 (tptp.aa_int_int tptp.uminus_uminus_int _let_2))) (=> (not _let_4) (= _let_3 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int _let_2) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int _let_1) (tptp.aa_int_int (tptp.bit_ri631733984087533419it_int (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) tptp.one_one_nat)) (tptp.aa_int_int (tptp.divide_divide_int A) _let_1)))))))))))) (forall ((A tptp.code_integer)) (let ((_let_1 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.bit_se1345352211410354436nteger tptp.zero_zero_nat A) (tptp.plus_p5714425477246183910nteger (tptp.zero_n356916108424825756nteger (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer _let_1) A)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger _let_1) (tptp.divide6298287555418463151nteger A _let_1)))))) (forall ((A tptp.int)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.aa_int_int (tptp.bit_se2159334234014336723it_int tptp.zero_zero_nat) A) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_bool_int tptp.zero_n2684676970156552555ol_int (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int _let_1) A))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int _let_1) (tptp.aa_int_int (tptp.divide_divide_int A) _let_1)))))) (forall ((A tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se2161824704523386999it_nat tptp.zero_zero_nat) A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.zero_n2687167440665602831ol_nat (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat _let_1) A))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat _let_1) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) _let_1)))))) (forall ((N tptp.nat) (X tptp.nat)) (= (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat (tptp.aa_nat_nat tptp.suc N)) (tptp.nat_set_decode X))) (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat N) (tptp.nat_set_decode (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat X) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))))))) (forall ((X tptp.set_nat) (Y tptp.set_nat)) (= (= (tptp.minus_minus_set_nat X Y) tptp.bot_bot_set_nat) (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat X) Y)))) (forall ((X tptp.set_real) (Y tptp.set_real)) (= (= (tptp.minus_minus_set_real X Y) tptp.bot_bot_set_real) (tptp.ord_less_eq_set_real X Y))) (forall ((X tptp.set_int) (Y tptp.set_int)) (= (= (tptp.minus_minus_set_int X Y) tptp.bot_bot_set_int) (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int X) Y)))) (forall ((R tptp.complex) (A tptp.complex) (B2 tptp.complex) (C tptp.complex) (D tptp.complex)) (let ((_let_1 (tptp.times_times_complex R))) (=> (not (= R tptp.zero_zero_complex)) (=> (and (= A B2) (not (= C D))) (not (= (tptp.aa_complex_complex (tptp.plus_plus_complex A) (tptp.aa_complex_complex _let_1 C)) (tptp.aa_complex_complex (tptp.plus_plus_complex B2) (tptp.aa_complex_complex _let_1 D)))))))) (forall ((R tptp.real) (A tptp.real) (B2 tptp.real) (C tptp.real) (D tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.times_times_real R))) (=> (not (= R tptp.zero_zero_real)) (=> (and (= A B2) (not (= C D))) (not (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) (tptp.aa_real_real _let_1 C)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real B2) (tptp.aa_real_real _let_1 D)))))))) (forall ((R tptp.rat) (A tptp.rat) (B2 tptp.rat) (C tptp.rat) (D tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_rat tptp.times_times_rat R))) (=> (not (= R tptp.zero_zero_rat)) (=> (and (= A B2) (not (= C D))) (not (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) (tptp.aa_rat_rat _let_1 C)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat B2) (tptp.aa_rat_rat _let_1 D)))))))) (forall ((R tptp.nat) (A tptp.nat) (B2 tptp.nat) (C tptp.nat) (D tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat R))) (=> (not (= R tptp.zero_zero_nat)) (=> (and (= A B2) (not (= C D))) (not (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) (tptp.aa_nat_nat _let_1 C)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat B2) (tptp.aa_nat_nat _let_1 D)))))))) (forall ((R tptp.int) (A tptp.int) (B2 tptp.int) (C tptp.int) (D tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.times_times_int R))) (=> (not (= R tptp.zero_zero_int)) (=> (and (= A B2) (not (= C D))) (not (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) (tptp.aa_int_int _let_1 C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int B2) (tptp.aa_int_int _let_1 D)))))))) (forall ((I tptp.nat) (N tptp.nat) (P tptp.fun_int_bool) (X tptp.int)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I) N)) (=> (tptp.pp (tptp.aa_int_bool P X)) (tptp.pp (tptp.aa_int_bool P (tptp.aa_nat_int (tptp.nth_int (tptp.replicate_int N X)) I)))))) (forall ((I tptp.nat) (N tptp.nat) (P tptp.fun_nat_bool) (X tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I) N)) (=> (tptp.pp (tptp.aa_nat_bool P X)) (tptp.pp (tptp.aa_nat_bool P (tptp.aa_nat_nat (tptp.nth_nat (tptp.replicate_nat N X)) I)))))) (forall ((I tptp.nat) (N tptp.nat) (P tptp.fun_VEBT_VEBT_bool) (X tptp.vEBT_VEBT)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I) N)) (=> (tptp.pp (tptp.aa_VEBT_VEBT_bool P X)) (tptp.pp (tptp.aa_VEBT_VEBT_bool P (tptp.nth_VEBT_VEBT (tptp.replicate_VEBT_VEBT N X) I)))))) (forall ((A tptp.real)) (= (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_real_real tptp.uminus_uminus_real A)) A)) (forall ((A tptp.int)) (= (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_int_int tptp.uminus_uminus_int A)) A)) (forall ((A tptp.complex)) (= (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex A)) A)) (forall ((A tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A)) A)) (forall ((A tptp.rat)) (= (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat A)) A)) (forall ((A tptp.real) (B2 tptp.real)) (= (= (tptp.aa_real_real tptp.uminus_uminus_real A) (tptp.aa_real_real tptp.uminus_uminus_real B2)) (= A B2))) (forall ((A tptp.int) (B2 tptp.int)) (= (= (tptp.aa_int_int tptp.uminus_uminus_int A) (tptp.aa_int_int tptp.uminus_uminus_int B2)) (= A B2))) (forall ((A tptp.complex) (B2 tptp.complex)) (= (= (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex A) (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex B2)) (= A B2))) (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (= (= (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger B2)) (= A B2))) (forall ((A tptp.rat) (B2 tptp.rat)) (= (= (tptp.aa_rat_rat tptp.uminus_uminus_rat A) (tptp.aa_rat_rat tptp.uminus_uminus_rat B2)) (= A B2))) (forall ((B2 tptp.real)) (= (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_real_real tptp.uminus_uminus_real B2)) B2)) (forall ((B2 tptp.int)) (= (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_int_int tptp.uminus_uminus_int B2)) B2)) (forall ((B2 tptp.complex)) (= (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex B2)) B2)) (forall ((B2 tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger B2)) B2)) (forall ((B2 tptp.rat)) (= (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat B2)) B2)) (forall ((A4 tptp.set_int) (B4 tptp.set_int)) (= (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int (tptp.uminus1532241313380277803et_int A4)) (tptp.uminus1532241313380277803et_int B4))) (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int B4) A4)))) (forall ((A4 tptp.set_int) (B4 tptp.set_int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int A4) B4)) (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int (tptp.uminus1532241313380277803et_int B4)) (tptp.uminus1532241313380277803et_int A4))))) (forall ((X tptp.set_int) (Y tptp.set_int)) (= (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int (tptp.uminus1532241313380277803et_int X)) (tptp.uminus1532241313380277803et_int Y))) (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int Y) X)))) (forall ((B2 tptp.real) (A tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real B2)) (tptp.aa_real_real tptp.uminus_uminus_real A))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) B2)))) (forall ((B2 tptp.code_integer) (A tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger B2)) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A))) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger A) B2)))) (forall ((B2 tptp.rat) (A tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat B2)) (tptp.aa_rat_rat tptp.uminus_uminus_rat A))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B2)))) (forall ((B2 tptp.int) (A tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.uminus_uminus_int B2)) (tptp.aa_int_int tptp.uminus_uminus_int A))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B2)))) (= (tptp.aa_real_real tptp.uminus_uminus_real tptp.zero_zero_real) tptp.zero_zero_real) (= (tptp.aa_int_int tptp.uminus_uminus_int tptp.zero_zero_int) tptp.zero_zero_int) (= (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex tptp.zero_zero_complex) tptp.zero_zero_complex) (= (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger) (= (tptp.aa_rat_rat tptp.uminus_uminus_rat tptp.zero_zero_rat) tptp.zero_zero_rat) (forall ((A tptp.real)) (= (= tptp.zero_zero_real (tptp.aa_real_real tptp.uminus_uminus_real A)) (= tptp.zero_zero_real A))) (forall ((A tptp.int)) (= (= tptp.zero_zero_int (tptp.aa_int_int tptp.uminus_uminus_int A)) (= tptp.zero_zero_int A))) (forall ((A tptp.complex)) (= (= tptp.zero_zero_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex A)) (= tptp.zero_zero_complex A))) (forall ((A tptp.code_integer)) (= (= tptp.zero_z3403309356797280102nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A)) (= tptp.zero_z3403309356797280102nteger A))) (forall ((A tptp.rat)) (= (= tptp.zero_zero_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat A)) (= tptp.zero_zero_rat A))) (forall ((A tptp.real)) (= (= (tptp.aa_real_real tptp.uminus_uminus_real A) tptp.zero_zero_real) (= A tptp.zero_zero_real))) (forall ((A tptp.int)) (= (= (tptp.aa_int_int tptp.uminus_uminus_int A) tptp.zero_zero_int) (= A tptp.zero_zero_int))) (forall ((A tptp.complex)) (= (= (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex A) tptp.zero_zero_complex) (= A tptp.zero_zero_complex))) (forall ((A tptp.code_integer)) (= (= (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A) tptp.zero_z3403309356797280102nteger) (= A tptp.zero_z3403309356797280102nteger))) (forall ((A tptp.rat)) (= (= (tptp.aa_rat_rat tptp.uminus_uminus_rat A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))) (forall ((A tptp.real)) (= (= A (tptp.aa_real_real tptp.uminus_uminus_real A)) (= A tptp.zero_zero_real))) (forall ((A tptp.int)) (= (= A (tptp.aa_int_int tptp.uminus_uminus_int A)) (= A tptp.zero_zero_int))) (forall ((A tptp.code_integer)) (= (= A (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A)) (= A tptp.zero_z3403309356797280102nteger))) (forall ((A tptp.rat)) (= (= A (tptp.aa_rat_rat tptp.uminus_uminus_rat A)) (= A tptp.zero_zero_rat))) (forall ((A tptp.real)) (= (= (tptp.aa_real_real tptp.uminus_uminus_real A) A) (= A tptp.zero_zero_real))) (forall ((A tptp.int)) (= (= (tptp.aa_int_int tptp.uminus_uminus_int A) A) (= A tptp.zero_zero_int))) (forall ((A tptp.code_integer)) (= (= (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A) A) (= A tptp.zero_z3403309356797280102nteger))) (forall ((A tptp.rat)) (= (= (tptp.aa_rat_rat tptp.uminus_uminus_rat A) A) (= A tptp.zero_zero_rat))) (forall ((B2 tptp.real) (A tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.uminus_uminus_real B2)) (tptp.aa_real_real tptp.uminus_uminus_real A))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B2)))) (forall ((B2 tptp.int) (A tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int tptp.uminus_uminus_int B2)) (tptp.aa_int_int tptp.uminus_uminus_int A))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B2)))) (forall ((B2 tptp.code_integer) (A tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger B2)) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A))) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger A) B2)))) (forall ((B2 tptp.rat) (A tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat B2)) (tptp.aa_rat_rat tptp.uminus_uminus_rat A))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B2)))) (forall ((M tptp.num) (N tptp.num)) (= (= (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real M)) (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real N))) (= M N))) (forall ((M tptp.num) (N tptp.num)) (= (= (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int M)) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int N))) (= M N))) (forall ((M tptp.num) (N tptp.num)) (= (= (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.numera6690914467698888265omplex M)) (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.numera6690914467698888265omplex N))) (= M N))) (forall ((M tptp.num) (N tptp.num)) (= (= (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger M)) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger N))) (= M N))) (forall ((M tptp.num) (N tptp.num)) (= (= (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat M)) (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat N))) (= M N))) (forall ((A tptp.real) (B2 tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real tptp.uminus_uminus_real A)) B2) (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) B2)))) (forall ((A tptp.int) (B2 tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int tptp.uminus_uminus_int A)) B2) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) B2)))) (forall ((A tptp.complex) (B2 tptp.complex)) (= (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex A)) B2) (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.aa_complex_complex (tptp.times_times_complex A) B2)))) (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A)) B2) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) B2)))) (forall ((A tptp.rat) (B2 tptp.rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat A)) B2) (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) B2)))) (forall ((A tptp.real) (B2 tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real tptp.uminus_uminus_real A)) (tptp.aa_real_real tptp.uminus_uminus_real B2)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) B2))) (forall ((A tptp.int) (B2 tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int tptp.uminus_uminus_int A)) (tptp.aa_int_int tptp.uminus_uminus_int B2)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) B2))) (forall ((A tptp.complex) (B2 tptp.complex)) (= (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex A)) (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex B2)) (tptp.aa_complex_complex (tptp.times_times_complex A) B2))) (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A)) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger B2)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) B2))) (forall ((A tptp.rat) (B2 tptp.rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat A)) (tptp.aa_rat_rat tptp.uminus_uminus_rat B2)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) B2))) (forall ((A tptp.real) (B2 tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A))) (= (tptp.aa_real_real _let_1 (tptp.aa_real_real tptp.uminus_uminus_real B2)) (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_real_real _let_1 B2))))) (forall ((A tptp.int) (B2 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.times_times_int A))) (= (tptp.aa_int_int _let_1 (tptp.aa_int_int tptp.uminus_uminus_int B2)) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_int_int _let_1 B2))))) (forall ((A tptp.complex) (B2 tptp.complex)) (let ((_let_1 (tptp.times_times_complex A))) (= (tptp.aa_complex_complex _let_1 (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex B2)) (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.aa_complex_complex _let_1 B2))))) (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A))) (= (tptp.aa_Cod1783974652533396728nteger _let_1 (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger B2)) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_Cod1783974652533396728nteger _let_1 B2))))) (forall ((A tptp.rat) (B2 tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A))) (= (tptp.aa_rat_rat _let_1 (tptp.aa_rat_rat tptp.uminus_uminus_rat B2)) (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_rat_rat _let_1 B2))))) (forall ((A tptp.real) (B2 tptp.real)) (= (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) B2)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real tptp.uminus_uminus_real A)) (tptp.aa_real_real tptp.uminus_uminus_real B2)))) (forall ((A tptp.int) (B2 tptp.int)) (= (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) B2)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int tptp.uminus_uminus_int A)) (tptp.aa_int_int tptp.uminus_uminus_int B2)))) (forall ((A tptp.complex) (B2 tptp.complex)) (= (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.aa_complex_complex (tptp.plus_plus_complex A) B2)) (tptp.aa_complex_complex (tptp.plus_plus_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex A)) (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex B2)))) (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.plus_p5714425477246183910nteger A B2)) (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger B2)))) (forall ((A tptp.rat) (B2 tptp.rat)) (= (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) B2)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat A)) (tptp.aa_rat_rat tptp.uminus_uminus_rat B2)))) (forall ((A tptp.real) (B2 tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real tptp.uminus_uminus_real A)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) B2)) B2)) (forall ((A tptp.int) (B2 tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int tptp.uminus_uminus_int A)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) B2)) B2)) (forall ((A tptp.complex) (B2 tptp.complex)) (= (tptp.aa_complex_complex (tptp.plus_plus_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex A)) (tptp.aa_complex_complex (tptp.plus_plus_complex A) B2)) B2)) (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (= (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A) (tptp.plus_p5714425477246183910nteger A B2)) B2)) (forall ((A tptp.rat) (B2 tptp.rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat A)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) B2)) B2)) (forall ((A tptp.real) (B2 tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real tptp.uminus_uminus_real A)) B2)) B2)) (forall ((A tptp.int) (B2 tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int tptp.uminus_uminus_int A)) B2)) B2)) (forall ((A tptp.complex) (B2 tptp.complex)) (= (tptp.aa_complex_complex (tptp.plus_plus_complex A) (tptp.aa_complex_complex (tptp.plus_plus_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex A)) B2)) B2)) (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (= (tptp.plus_p5714425477246183910nteger A (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A) B2)) B2)) (forall ((A tptp.rat) (B2 tptp.rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat A)) B2)) B2)) (forall ((A tptp.real) (B2 tptp.real)) (= (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A) B2)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real B2) A))) (forall ((A tptp.int) (B2 tptp.int)) (= (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) B2)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int B2) A))) (forall ((A tptp.complex) (B2 tptp.complex)) (= (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.aa_complex_complex (tptp.minus_minus_complex A) B2)) (tptp.aa_complex_complex (tptp.minus_minus_complex B2) A))) (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.minus_8373710615458151222nteger A B2)) (tptp.minus_8373710615458151222nteger B2 A))) (forall ((A tptp.rat) (B2 tptp.rat)) (= (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_rat_rat (tptp.minus_minus_rat A) B2)) (tptp.aa_rat_rat (tptp.minus_minus_rat B2) A))) (forall ((A tptp.int) (B2 tptp.int)) (= (tptp.aa_int_int (tptp.divide_divide_int (tptp.aa_int_int tptp.uminus_uminus_int A)) (tptp.aa_int_int tptp.uminus_uminus_int B2)) (tptp.aa_int_int (tptp.divide_divide_int A) B2))) (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (= (tptp.divide6298287555418463151nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger B2)) (tptp.divide6298287555418463151nteger A B2))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.dvd_dvd_real X))) (= (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real tptp.uminus_uminus_real Y))) (tptp.pp (tptp.aa_real_bool _let_1 Y))))) (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int X))) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int tptp.uminus_uminus_int Y))) (tptp.pp (tptp.aa_int_bool _let_1 Y))))) (forall ((X tptp.complex) (Y tptp.complex)) (let ((_let_1 (tptp.aa_com1553036987509291606x_bool tptp.dvd_dvd_complex X))) (= (tptp.pp (tptp.aa_complex_bool _let_1 (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex Y))) (tptp.pp (tptp.aa_complex_bool _let_1 Y))))) (forall ((X tptp.code_integer) (Y tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer X))) (= (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger Y))) (tptp.pp (tptp.aa_Code_integer_bool _let_1 Y))))) (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.dvd_dvd_rat X))) (= (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat tptp.uminus_uminus_rat Y))) (tptp.pp (tptp.aa_rat_bool _let_1 Y))))) (forall ((X tptp.real) (Y tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.dvd_dvd_real (tptp.aa_real_real tptp.uminus_uminus_real X)) Y)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.dvd_dvd_real X) Y)))) (forall ((X tptp.int) (Y tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_int_int tptp.uminus_uminus_int X)) Y)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int X) Y)))) (forall ((X tptp.complex) (Y tptp.complex)) (= (tptp.pp (tptp.aa_complex_bool (tptp.aa_com1553036987509291606x_bool tptp.dvd_dvd_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex X)) Y)) (tptp.pp (tptp.aa_complex_bool (tptp.aa_com1553036987509291606x_bool tptp.dvd_dvd_complex X) Y)))) (forall ((X tptp.code_integer) (Y tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger X)) Y)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer X) Y)))) (forall ((X tptp.rat) (Y tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.dvd_dvd_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat X)) Y)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.dvd_dvd_rat X) Y)))) (forall ((A tptp.int) (B2 tptp.int)) (= (tptp.aa_int_int (tptp.modulo_modulo_int (tptp.aa_int_int tptp.uminus_uminus_int A)) (tptp.aa_int_int tptp.uminus_uminus_int B2)) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_int_int (tptp.modulo_modulo_int A) B2)))) (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (= (tptp.modulo364778990260209775nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger B2)) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.modulo364778990260209775nteger A B2)))) (forall ((P tptp.bool) (Q tptp.bool)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.zero_n2052037380579107095ol_rat P)) (tptp.zero_n2052037380579107095ol_rat Q))) (=> (tptp.pp P) (tptp.pp Q)))) (forall ((P tptp.bool) (Q tptp.bool)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.zero_n2687167440665602831ol_nat P)) (tptp.zero_n2687167440665602831ol_nat Q))) (=> (tptp.pp P) (tptp.pp Q)))) (forall ((P tptp.bool) (Q tptp.bool)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_bool_int tptp.zero_n2684676970156552555ol_int P)) (tptp.aa_bool_int tptp.zero_n2684676970156552555ol_int Q))) (=> (tptp.pp P) (tptp.pp Q)))) (forall ((P tptp.bool) (Q tptp.bool)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.zero_n356916108424825756nteger P)) (tptp.zero_n356916108424825756nteger Q))) (=> (tptp.pp P) (tptp.pp Q)))) (= (tptp.zero_n1201886186963655149omplex tptp.fFalse) tptp.zero_zero_complex) (= (tptp.zero_n3304061248610475627l_real tptp.fFalse) tptp.zero_zero_real) (= (tptp.zero_n2052037380579107095ol_rat tptp.fFalse) tptp.zero_zero_rat) (= (tptp.zero_n2687167440665602831ol_nat tptp.fFalse) tptp.zero_zero_nat) (= (tptp.aa_bool_int tptp.zero_n2684676970156552555ol_int tptp.fFalse) tptp.zero_zero_int) (= (tptp.zero_n356916108424825756nteger tptp.fFalse) tptp.zero_z3403309356797280102nteger) (forall ((P tptp.bool)) (= (= (tptp.zero_n1201886186963655149omplex P) tptp.zero_zero_complex) (not (tptp.pp P)))) (forall ((P tptp.bool)) (= (= (tptp.zero_n3304061248610475627l_real P) tptp.zero_zero_real) (not (tptp.pp P)))) (forall ((P tptp.bool)) (= (= (tptp.zero_n2052037380579107095ol_rat P) tptp.zero_zero_rat) (not (tptp.pp P)))) (forall ((P tptp.bool)) (= (= (tptp.zero_n2687167440665602831ol_nat P) tptp.zero_zero_nat) (not (tptp.pp P)))) (forall ((P tptp.bool)) (= (= (tptp.aa_bool_int tptp.zero_n2684676970156552555ol_int P) tptp.zero_zero_int) (not (tptp.pp P)))) (forall ((P tptp.bool)) (= (= (tptp.zero_n356916108424825756nteger P) tptp.zero_z3403309356797280102nteger) (not (tptp.pp P)))) (forall ((X tptp.real) (A tptp.real)) (= (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) (tptp.aa_real_real tptp.uminus_uminus_real A)) tptp.zero_zero_real) (= X A))) (forall ((P tptp.bool) (Q tptp.bool)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.zero_n3304061248610475627l_real P)) (tptp.zero_n3304061248610475627l_real Q))) (and (not (tptp.pp P)) (tptp.pp Q)))) (forall ((P tptp.bool) (Q tptp.bool)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.zero_n2052037380579107095ol_rat P)) (tptp.zero_n2052037380579107095ol_rat Q))) (and (not (tptp.pp P)) (tptp.pp Q)))) (forall ((P tptp.bool) (Q tptp.bool)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.zero_n2687167440665602831ol_nat P)) (tptp.zero_n2687167440665602831ol_nat Q))) (and (not (tptp.pp P)) (tptp.pp Q)))) (forall ((P tptp.bool) (Q tptp.bool)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_bool_int tptp.zero_n2684676970156552555ol_int P)) (tptp.aa_bool_int tptp.zero_n2684676970156552555ol_int Q))) (and (not (tptp.pp P)) (tptp.pp Q)))) (forall ((P tptp.bool) (Q tptp.bool)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.zero_n356916108424825756nteger P)) (tptp.zero_n356916108424825756nteger Q))) (and (not (tptp.pp P)) (tptp.pp Q)))) (= (tptp.zero_n1201886186963655149omplex tptp.fTrue) tptp.one_one_complex) (= (tptp.zero_n3304061248610475627l_real tptp.fTrue) tptp.one_one_real) (= (tptp.zero_n2052037380579107095ol_rat tptp.fTrue) tptp.one_one_rat) (= (tptp.zero_n2687167440665602831ol_nat tptp.fTrue) tptp.one_one_nat) (= (tptp.aa_bool_int tptp.zero_n2684676970156552555ol_int tptp.fTrue) tptp.one_one_int) (= (tptp.zero_n356916108424825756nteger tptp.fTrue) tptp.one_one_Code_integer) (forall ((P tptp.bool)) (= (= (tptp.zero_n1201886186963655149omplex P) tptp.one_one_complex) (tptp.pp P))) (forall ((P tptp.bool)) (= (= (tptp.zero_n3304061248610475627l_real P) tptp.one_one_real) (tptp.pp P))) (forall ((P tptp.bool)) (= (= (tptp.zero_n2052037380579107095ol_rat P) tptp.one_one_rat) (tptp.pp P))) (forall ((P tptp.bool)) (= (= (tptp.zero_n2687167440665602831ol_nat P) tptp.one_one_nat) (tptp.pp P))) (forall ((P tptp.bool)) (= (= (tptp.aa_bool_int tptp.zero_n2684676970156552555ol_int P) tptp.one_one_int) (tptp.pp P))) (forall ((P tptp.bool)) (= (= (tptp.zero_n356916108424825756nteger P) tptp.one_one_Code_integer) (tptp.pp P))) (forall ((N tptp.nat) (X tptp.vEBT_VEBT)) (= (tptp.size_s6755466524823107622T_VEBT (tptp.replicate_VEBT_VEBT N X)) N)) (forall ((N tptp.nat) (X tptp.bool)) (= (tptp.size_size_list_bool (tptp.replicate_bool N X)) N)) (forall ((N tptp.nat) (X tptp.nat)) (= (tptp.size_size_list_nat (tptp.replicate_nat N X)) N)) (forall ((P tptp.bool) (Q tptp.bool)) (= (tptp.zero_n2687167440665602831ol_nat (tptp.aa_bool_bool (tptp.fdisj P) Q)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat (tptp.zero_n2687167440665602831ol_nat P)) (tptp.zero_n2687167440665602831ol_nat Q)))) (forall ((P tptp.bool) (Q tptp.bool)) (= (tptp.aa_bool_int tptp.zero_n2684676970156552555ol_int (tptp.aa_bool_bool (tptp.fdisj P) Q)) (tptp.aa_int_int (tptp.ord_max_int (tptp.aa_bool_int tptp.zero_n2684676970156552555ol_int P)) (tptp.aa_bool_int tptp.zero_n2684676970156552555ol_int Q)))) (forall ((P tptp.bool) (Q tptp.bool)) (= (tptp.zero_n356916108424825756nteger (tptp.aa_bool_bool (tptp.fdisj P) Q)) (tptp.ord_max_Code_integer (tptp.zero_n356916108424825756nteger P) (tptp.zero_n356916108424825756nteger Q)))) (forall ((A tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real A)) A)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) A)))) (forall ((A tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A)) A)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A)))) (forall ((A tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat A)) A)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) A)))) (forall ((A tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.uminus_uminus_int A)) A)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) A)))) (forall ((A tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A))) (= (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real tptp.uminus_uminus_real A))) (tptp.pp (tptp.aa_real_bool _let_1 tptp.zero_zero_real))))) (forall ((A tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger A))) (= (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A))) (tptp.pp (tptp.aa_Code_integer_bool _let_1 tptp.zero_z3403309356797280102nteger))))) (forall ((A tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A))) (= (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat tptp.uminus_uminus_rat A))) (tptp.pp (tptp.aa_rat_bool _let_1 tptp.zero_zero_rat))))) (forall ((A tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A))) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int tptp.uminus_uminus_int A))) (tptp.pp (tptp.aa_int_bool _let_1 tptp.zero_zero_int))))) (forall ((A tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real A)) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) A)))) (forall ((A tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A)) tptp.zero_z3403309356797280102nteger)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A)))) (forall ((A tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat A)) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) A)))) (forall ((A tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.uminus_uminus_int A)) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) A)))) (forall ((A tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_real_real tptp.uminus_uminus_real A))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) tptp.zero_zero_real)))) (forall ((A tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A))) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger A) tptp.zero_z3403309356797280102nteger)))) (forall ((A tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_rat_rat tptp.uminus_uminus_rat A))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) tptp.zero_zero_rat)))) (forall ((A tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.aa_int_int tptp.uminus_uminus_int A))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) tptp.zero_zero_int)))) (forall ((A tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.uminus_uminus_real A)) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) A)))) (forall ((A tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int tptp.uminus_uminus_int A)) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) A)))) (forall ((A tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A)) tptp.zero_z3403309356797280102nteger)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A)))) (forall ((A tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat A)) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) A)))) (forall ((A tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) (tptp.aa_real_real tptp.uminus_uminus_real A))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) tptp.zero_zero_real)))) (forall ((A tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) (tptp.aa_int_int tptp.uminus_uminus_int A))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) tptp.zero_zero_int)))) (forall ((A tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A))) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger A) tptp.zero_z3403309356797280102nteger)))) (forall ((A tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) (tptp.aa_rat_rat tptp.uminus_uminus_rat A))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) tptp.zero_zero_rat)))) (forall ((A tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.uminus_uminus_real A)) A)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) A)))) (forall ((A tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int tptp.uminus_uminus_int A)) A)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) A)))) (forall ((A tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A)) A)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A)))) (forall ((A tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat A)) A)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) A)))) (forall ((A tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A))) (= (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real tptp.uminus_uminus_real A))) (tptp.pp (tptp.aa_real_bool _let_1 tptp.zero_zero_real))))) (forall ((A tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_int A))) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int tptp.uminus_uminus_int A))) (tptp.pp (tptp.aa_int_bool _let_1 tptp.zero_zero_int))))) (forall ((A tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger A))) (= (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A))) (tptp.pp (tptp.aa_Code_integer_bool _let_1 tptp.zero_z3403309356797280102nteger))))) (forall ((A tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A))) (= (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat tptp.uminus_uminus_rat A))) (tptp.pp (tptp.aa_rat_bool _let_1 tptp.zero_zero_rat))))) (forall ((A tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real tptp.uminus_uminus_real A)) A) tptp.zero_zero_real)) (forall ((A tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int tptp.uminus_uminus_int A)) A) tptp.zero_zero_int)) (forall ((A tptp.complex)) (= (tptp.aa_complex_complex (tptp.plus_plus_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex A)) A) tptp.zero_zero_complex)) (forall ((A tptp.code_integer)) (= (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A) A) tptp.zero_z3403309356797280102nteger)) (forall ((A tptp.rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat A)) A) tptp.zero_zero_rat)) (forall ((A tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) (tptp.aa_real_real tptp.uminus_uminus_real A)) tptp.zero_zero_real)) (forall ((A tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) (tptp.aa_int_int tptp.uminus_uminus_int A)) tptp.zero_zero_int)) (forall ((A tptp.complex)) (= (tptp.aa_complex_complex (tptp.plus_plus_complex A) (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex A)) tptp.zero_zero_complex)) (forall ((A tptp.code_integer)) (= (tptp.plus_p5714425477246183910nteger A (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A)) tptp.zero_z3403309356797280102nteger)) (forall ((A tptp.rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) (tptp.aa_rat_rat tptp.uminus_uminus_rat A)) tptp.zero_zero_rat)) (forall ((B2 tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real tptp.zero_zero_real) B2) (tptp.aa_real_real tptp.uminus_uminus_real B2))) (forall ((B2 tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int tptp.zero_zero_int) B2) (tptp.aa_int_int tptp.uminus_uminus_int B2))) (forall ((B2 tptp.complex)) (= (tptp.aa_complex_complex (tptp.minus_minus_complex tptp.zero_zero_complex) B2) (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex B2))) (forall ((B2 tptp.code_integer)) (= (tptp.minus_8373710615458151222nteger tptp.zero_z3403309356797280102nteger B2) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger B2))) (forall ((B2 tptp.rat)) (= (tptp.aa_rat_rat (tptp.minus_minus_rat tptp.zero_zero_rat) B2) (tptp.aa_rat_rat tptp.uminus_uminus_rat B2))) (forall ((A tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real tptp.zero_zero_real) A) (tptp.aa_real_real tptp.uminus_uminus_real A))) (forall ((A tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int tptp.zero_zero_int) A) (tptp.aa_int_int tptp.uminus_uminus_int A))) (forall ((A tptp.complex)) (= (tptp.aa_complex_complex (tptp.minus_minus_complex tptp.zero_zero_complex) A) (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex A))) (forall ((A tptp.code_integer)) (= (tptp.minus_8373710615458151222nteger tptp.zero_z3403309356797280102nteger A) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A))) (forall ((A tptp.rat)) (= (tptp.aa_rat_rat (tptp.minus_minus_rat tptp.zero_zero_rat) A) (tptp.aa_rat_rat tptp.uminus_uminus_rat A))) (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (tptp.aa_num_real tptp.numeral_numeral_real N))) (let ((_let_2 (tptp.aa_num_real tptp.numeral_numeral_real M))) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real tptp.uminus_uminus_real _let_2)) (tptp.aa_real_real tptp.uminus_uminus_real _let_1)) (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real _let_2) _let_1)))))) (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int N))) (let ((_let_2 (tptp.aa_num_int tptp.numeral_numeral_int M))) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int tptp.uminus_uminus_int _let_2)) (tptp.aa_int_int tptp.uminus_uminus_int _let_1)) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int _let_2) _let_1)))))) (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (tptp.numera6690914467698888265omplex N))) (let ((_let_2 (tptp.numera6690914467698888265omplex M))) (= (tptp.aa_complex_complex (tptp.plus_plus_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex _let_2)) (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex _let_1)) (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.aa_complex_complex (tptp.plus_plus_complex _let_2) _let_1)))))) (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger N))) (let ((_let_2 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger M))) (= (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger _let_2) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger _let_1)) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.plus_p5714425477246183910nteger _let_2 _let_1)))))) (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (tptp.aa_num_rat tptp.numeral_numeral_rat N))) (let ((_let_2 (tptp.aa_num_rat tptp.numeral_numeral_rat M))) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat _let_2)) (tptp.aa_rat_rat tptp.uminus_uminus_rat _let_1)) (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat _let_2) _let_1)))))) (forall ((Z tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)) Z) (tptp.aa_real_real tptp.uminus_uminus_real Z))) (forall ((Z tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int)) Z) (tptp.aa_int_int tptp.uminus_uminus_int Z))) (forall ((Z tptp.complex)) (= (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex tptp.one_one_complex)) Z) (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex Z))) (forall ((Z tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) Z) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger Z))) (forall ((Z tptp.rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat tptp.one_one_rat)) Z) (tptp.aa_rat_rat tptp.uminus_uminus_rat Z))) (forall ((Z tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real Z) (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)) (tptp.aa_real_real tptp.uminus_uminus_real Z))) (forall ((Z tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int Z) (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int)) (tptp.aa_int_int tptp.uminus_uminus_int Z))) (forall ((Z tptp.complex)) (= (tptp.aa_complex_complex (tptp.times_times_complex Z) (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex Z))) (forall ((Z tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger Z) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger Z))) (forall ((Z tptp.rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat Z) (tptp.aa_rat_rat tptp.uminus_uminus_rat tptp.one_one_rat)) (tptp.aa_rat_rat tptp.uminus_uminus_rat Z))) (forall ((A tptp.real) (B2 tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real tptp.uminus_uminus_real A)) B2) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real B2) A))) (forall ((A tptp.int) (B2 tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int tptp.uminus_uminus_int A)) B2) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int B2) A))) (forall ((A tptp.complex) (B2 tptp.complex)) (= (tptp.aa_complex_complex (tptp.plus_plus_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex A)) B2) (tptp.aa_complex_complex (tptp.minus_minus_complex B2) A))) (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (= (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A) B2) (tptp.minus_8373710615458151222nteger B2 A))) (forall ((A tptp.rat) (B2 tptp.rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat A)) B2) (tptp.aa_rat_rat (tptp.minus_minus_rat B2) A))) (forall ((A tptp.real) (B2 tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A) (tptp.aa_real_real tptp.uminus_uminus_real B2)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) B2))) (forall ((A tptp.int) (B2 tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) (tptp.aa_int_int tptp.uminus_uminus_int B2)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) B2))) (forall ((A tptp.complex) (B2 tptp.complex)) (= (tptp.aa_complex_complex (tptp.minus_minus_complex A) (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex B2)) (tptp.aa_complex_complex (tptp.plus_plus_complex A) B2))) (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (= (tptp.minus_8373710615458151222nteger A (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger B2)) (tptp.plus_p5714425477246183910nteger A B2))) (forall ((A tptp.rat) (B2 tptp.rat)) (= (tptp.aa_rat_rat (tptp.minus_minus_rat A) (tptp.aa_rat_rat tptp.uminus_uminus_rat B2)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) B2))) (forall ((X tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real X) (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)) (tptp.aa_real_real tptp.uminus_uminus_real X))) (forall ((X tptp.complex)) (= (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex X) (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex X))) (forall ((X tptp.rat)) (= (tptp.aa_rat_rat (tptp.divide_divide_rat X) (tptp.aa_rat_rat tptp.uminus_uminus_rat tptp.one_one_rat)) (tptp.aa_rat_rat tptp.uminus_uminus_rat X))) (forall ((A tptp.int)) (= (tptp.aa_int_int (tptp.divide_divide_int A) (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int)) (tptp.aa_int_int tptp.uminus_uminus_int A))) (forall ((A tptp.code_integer)) (= (tptp.divide6298287555418463151nteger A (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A))) (forall ((B2 tptp.int) (A tptp.int)) (= (tptp.aa_int_int (tptp.modulo_modulo_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int B2) A)) B2) (tptp.aa_int_int (tptp.modulo_modulo_int (tptp.aa_int_int tptp.uminus_uminus_int A)) B2))) (forall ((B2 tptp.code_integer) (A tptp.code_integer)) (= (tptp.modulo364778990260209775nteger (tptp.minus_8373710615458151222nteger B2 A) B2) (tptp.modulo364778990260209775nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A) B2))) (forall ((P tptp.bool)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) (tptp.zero_n3304061248610475627l_real P))) (tptp.pp P))) (forall ((P tptp.bool)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) (tptp.zero_n2052037380579107095ol_rat P))) (tptp.pp P))) (forall ((P tptp.bool)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.zero_n2687167440665602831ol_nat P))) (tptp.pp P))) (forall ((P tptp.bool)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) (tptp.aa_bool_int tptp.zero_n2684676970156552555ol_int P))) (tptp.pp P))) (forall ((P tptp.bool)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (tptp.zero_n356916108424825756nteger P))) (tptp.pp P))) (forall ((P tptp.bool)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.zero_n3304061248610475627l_real P)) tptp.one_one_real)) (not (tptp.pp P)))) (forall ((P tptp.bool)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.zero_n2052037380579107095ol_rat P)) tptp.one_one_rat)) (not (tptp.pp P)))) (forall ((P tptp.bool)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.zero_n2687167440665602831ol_nat P)) tptp.one_one_nat)) (not (tptp.pp P)))) (forall ((P tptp.bool)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_bool_int tptp.zero_n2684676970156552555ol_int P)) tptp.one_one_int)) (not (tptp.pp P)))) (forall ((P tptp.bool)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.zero_n356916108424825756nteger P)) tptp.one_one_Code_integer)) (not (tptp.pp P)))) (forall ((P tptp.bool)) (= (tptp.zero_n1201886186963655149omplex (tptp.aa_bool_bool tptp.fNot P)) (tptp.aa_complex_complex (tptp.minus_minus_complex tptp.one_one_complex) (tptp.zero_n1201886186963655149omplex P)))) (forall ((P tptp.bool)) (= (tptp.zero_n3304061248610475627l_real (tptp.aa_bool_bool tptp.fNot P)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real tptp.one_one_real) (tptp.zero_n3304061248610475627l_real P)))) (forall ((P tptp.bool)) (= (tptp.zero_n2052037380579107095ol_rat (tptp.aa_bool_bool tptp.fNot P)) (tptp.aa_rat_rat (tptp.minus_minus_rat tptp.one_one_rat) (tptp.zero_n2052037380579107095ol_rat P)))) (forall ((P tptp.bool)) (= (tptp.aa_bool_int tptp.zero_n2684676970156552555ol_int (tptp.aa_bool_bool tptp.fNot P)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int tptp.one_one_int) (tptp.aa_bool_int tptp.zero_n2684676970156552555ol_int P)))) (forall ((P tptp.bool)) (= (tptp.zero_n356916108424825756nteger (tptp.aa_bool_bool tptp.fNot P)) (tptp.minus_8373710615458151222nteger tptp.one_one_Code_integer (tptp.zero_n356916108424825756nteger P)))) (forall ((N tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat _let_1) N) (tptp.zero_n2687167440665602831ol_nat (tptp.aa_bool_bool tptp.fNot (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.fequal_nat N) _let_1)))))) (forall ((N tptp.nat)) (let ((_let_1 (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (= (tptp.bit_ri6519982836138164636nteger N _let_1) _let_1))) (forall ((N tptp.nat)) (let ((_let_1 (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int))) (= (tptp.aa_int_int (tptp.bit_ri631733984087533419it_int N) _let_1) _let_1))) (forall ((N tptp.nat) (A tptp.int) (P tptp.fun_int_bool)) (= (forall ((X3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X3) (tptp.set_int2 (tptp.replicate_int N A)))) (tptp.pp (tptp.aa_int_bool P X3)))) (or (tptp.pp (tptp.aa_int_bool P A)) (= N tptp.zero_zero_nat)))) (forall ((N tptp.nat) (A tptp.nat) (P tptp.fun_nat_bool)) (= (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) (tptp.set_nat2 (tptp.replicate_nat N A)))) (tptp.pp (tptp.aa_nat_bool P X3)))) (or (tptp.pp (tptp.aa_nat_bool P A)) (= N tptp.zero_zero_nat)))) (forall ((N tptp.nat) (A tptp.vEBT_VEBT) (P tptp.fun_VEBT_VEBT_bool)) (= (forall ((X3 tptp.vEBT_VEBT)) (=> (tptp.pp (tptp.aa_set8260762808118238015T_bool (tptp.aa_VEB289770264548726718T_bool tptp.member_VEBT_VEBT X3) (tptp.set_VEBT_VEBT2 (tptp.replicate_VEBT_VEBT N A)))) (tptp.pp (tptp.aa_VEBT_VEBT_bool P X3)))) (or (tptp.pp (tptp.aa_VEBT_VEBT_bool P A)) (= N tptp.zero_zero_nat)))) (forall ((N tptp.nat) (A tptp.int) (P tptp.fun_int_bool)) (= (exists ((X3 tptp.int)) (and (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X3) (tptp.set_int2 (tptp.replicate_int N A)))) (tptp.pp (tptp.aa_int_bool P X3)))) (and (tptp.pp (tptp.aa_int_bool P A)) (not (= N tptp.zero_zero_nat))))) (forall ((N tptp.nat) (A tptp.nat) (P tptp.fun_nat_bool)) (= (exists ((X3 tptp.nat)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) (tptp.set_nat2 (tptp.replicate_nat N A)))) (tptp.pp (tptp.aa_nat_bool P X3)))) (and (tptp.pp (tptp.aa_nat_bool P A)) (not (= N tptp.zero_zero_nat))))) (forall ((N tptp.nat) (A tptp.vEBT_VEBT) (P tptp.fun_VEBT_VEBT_bool)) (= (exists ((X3 tptp.vEBT_VEBT)) (and (tptp.pp (tptp.aa_set8260762808118238015T_bool (tptp.aa_VEB289770264548726718T_bool tptp.member_VEBT_VEBT X3) (tptp.set_VEBT_VEBT2 (tptp.replicate_VEBT_VEBT N A)))) (tptp.pp (tptp.aa_VEBT_VEBT_bool P X3)))) (and (tptp.pp (tptp.aa_VEBT_VEBT_bool P A)) (not (= N tptp.zero_zero_nat))))) (forall ((X tptp.real) (N tptp.nat) (Y tptp.real)) (= (tptp.member_real X (tptp.set_real2 (tptp.replicate_real N Y))) (and (= X Y) (not (= N tptp.zero_zero_nat))))) (forall ((X tptp.complex) (N tptp.nat) (Y tptp.complex)) (= (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex X) (tptp.set_complex2 (tptp.replicate_complex N Y)))) (and (= X Y) (not (= N tptp.zero_zero_nat))))) (forall ((X tptp.int) (N tptp.nat) (Y tptp.int)) (= (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X) (tptp.set_int2 (tptp.replicate_int N Y)))) (and (= X Y) (not (= N tptp.zero_zero_nat))))) (forall ((X tptp.nat) (N tptp.nat) (Y tptp.nat)) (= (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X) (tptp.set_nat2 (tptp.replicate_nat N Y)))) (and (= X Y) (not (= N tptp.zero_zero_nat))))) (forall ((X tptp.vEBT_VEBT) (N tptp.nat) (Y tptp.vEBT_VEBT)) (= (tptp.pp (tptp.aa_set8260762808118238015T_bool (tptp.aa_VEB289770264548726718T_bool tptp.member_VEBT_VEBT X) (tptp.set_VEBT_VEBT2 (tptp.replicate_VEBT_VEBT N Y)))) (and (= X Y) (not (= N tptp.zero_zero_nat))))) (forall ((I tptp.nat) (N tptp.nat) (X tptp.int)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I) N)) (= (tptp.aa_nat_int (tptp.nth_int (tptp.replicate_int N X)) I) X))) (forall ((I tptp.nat) (N tptp.nat) (X tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I) N)) (= (tptp.aa_nat_nat (tptp.nth_nat (tptp.replicate_nat N X)) I) X))) (forall ((I tptp.nat) (N tptp.nat) (X tptp.vEBT_VEBT)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I) N)) (= (tptp.nth_VEBT_VEBT (tptp.replicate_VEBT_VEBT N X) I) X))) (forall ((K tptp.num)) (let ((_let_1 (tptp.aa_num_real tptp.numeral_numeral_real K))) (= (tptp.aa_real_real tptp.neg_numeral_dbl_real (tptp.aa_real_real tptp.uminus_uminus_real _let_1)) (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_real_real tptp.neg_numeral_dbl_real _let_1))))) (forall ((K tptp.num)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int K))) (= (tptp.aa_int_int tptp.neg_numeral_dbl_int (tptp.aa_int_int tptp.uminus_uminus_int _let_1)) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_int_int tptp.neg_numeral_dbl_int _let_1))))) (forall ((K tptp.num)) (let ((_let_1 (tptp.numera6690914467698888265omplex K))) (= (tptp.aa_complex_complex tptp.neg_nu7009210354673126013omplex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex _let_1)) (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.aa_complex_complex tptp.neg_nu7009210354673126013omplex _let_1))))) (forall ((K tptp.num)) (let ((_let_1 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger K))) (= (tptp.neg_nu8804712462038260780nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger _let_1)) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.neg_nu8804712462038260780nteger _let_1))))) (forall ((K tptp.num)) (let ((_let_1 (tptp.aa_num_rat tptp.numeral_numeral_rat K))) (= (tptp.aa_rat_rat tptp.neg_numeral_dbl_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat _let_1)) (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_rat_rat tptp.neg_numeral_dbl_rat _let_1))))) (forall ((N tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N))) (= (tptp.aa_nat_nat tptp.nat_triangle _let_1) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat tptp.nat_triangle N)) _let_1)))) (= (tptp.aa_real_real _let_135 tptp.one_one_real) tptp.zero_zero_real) (= (tptp.aa_int_int _let_134 tptp.one_one_int) tptp.zero_zero_int) (= (tptp.aa_complex_complex _let_133 tptp.one_one_complex) tptp.zero_zero_complex) (= (tptp.plus_p5714425477246183910nteger _let_83 tptp.one_one_Code_integer) tptp.zero_z3403309356797280102nteger) (= (tptp.aa_rat_rat _let_132 tptp.one_one_rat) tptp.zero_zero_rat) (= (tptp.aa_real_real _let_138 _let_57) tptp.zero_zero_real) (= (tptp.aa_int_int _let_137 _let_37) tptp.zero_zero_int) (= (tptp.aa_complex_complex _let_49 _let_54) tptp.zero_zero_complex) (= (tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer _let_83) tptp.zero_z3403309356797280102nteger) (= (tptp.aa_rat_rat _let_136 _let_38) tptp.zero_zero_rat) (= (tptp.aa_real_real _let_127 _let_57) tptp.zero_zero_real) (= (tptp.aa_int_int _let_126 _let_37) tptp.zero_zero_int) (= (tptp.aa_complex_complex _let_125 _let_54) tptp.zero_zero_complex) (= (tptp.minus_8373710615458151222nteger _let_83 _let_83) tptp.zero_z3403309356797280102nteger) (= (tptp.aa_rat_rat _let_124 _let_38) tptp.zero_zero_rat) (forall ((N tptp.num)) (= (= (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real) (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real N))) (= N tptp.one))) (forall ((N tptp.num)) (= (= (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int N))) (= N tptp.one))) (forall ((N tptp.num)) (= (= (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex tptp.one_one_complex) (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.numera6690914467698888265omplex N))) (= N tptp.one))) (forall ((N tptp.num)) (= (= (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger N))) (= N tptp.one))) (forall ((N tptp.num)) (= (= (tptp.aa_rat_rat tptp.uminus_uminus_rat tptp.one_one_rat) (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat N))) (= N tptp.one))) (forall ((N tptp.num)) (= (= (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real N)) (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)) (= N tptp.one))) (forall ((N tptp.num)) (= (= (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int N)) (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int)) (= N tptp.one))) (forall ((N tptp.num)) (= (= (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.numera6690914467698888265omplex N)) (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (= N tptp.one))) (forall ((N tptp.num)) (= (= (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger N)) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (= N tptp.one))) (forall ((N tptp.num)) (= (= (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat N)) (tptp.aa_rat_rat tptp.uminus_uminus_rat tptp.one_one_rat)) (= N tptp.one))) (forall ((N tptp.nat)) (let ((_let_1 (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)) N))) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real _let_1) _let_1) tptp.one_one_real))) (forall ((N tptp.nat)) (let ((_let_1 (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int)) N))) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int _let_1) _let_1) tptp.one_one_int))) (forall ((N tptp.nat)) (let ((_let_1 (tptp.aa_nat_complex (tptp.power_power_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex tptp.one_one_complex)) N))) (= (tptp.aa_complex_complex (tptp.times_times_complex _let_1) _let_1) tptp.one_one_complex))) (forall ((N tptp.nat)) (let ((_let_1 (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) N))) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger _let_1) _let_1) tptp.one_one_Code_integer))) (forall ((N tptp.nat)) (let ((_let_1 (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat tptp.one_one_rat)) N))) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat _let_1) _let_1) tptp.one_one_rat))) (forall ((N tptp.nat) (A tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)) N)))) (= (tptp.aa_real_real _let_1 (tptp.aa_real_real _let_1 A)) A))) (forall ((N tptp.nat) (A tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int)) N)))) (= (tptp.aa_int_int _let_1 (tptp.aa_int_int _let_1 A)) A))) (forall ((N tptp.nat) (A tptp.complex)) (let ((_let_1 (tptp.times_times_complex (tptp.aa_nat_complex (tptp.power_power_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex tptp.one_one_complex)) N)))) (= (tptp.aa_complex_complex _let_1 (tptp.aa_complex_complex _let_1 A)) A))) (forall ((N tptp.nat) (A tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) N)))) (= (tptp.aa_Cod1783974652533396728nteger _let_1 (tptp.aa_Cod1783974652533396728nteger _let_1 A)) A))) (forall ((N tptp.nat) (A tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat tptp.one_one_rat)) N)))) (= (tptp.aa_rat_rat _let_1 (tptp.aa_rat_rat _let_1 A)) A))) (forall ((A tptp.int)) (= (tptp.aa_int_int (tptp.modulo_modulo_int A) (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int)) tptp.zero_zero_int)) (forall ((A tptp.code_integer)) (= (tptp.modulo364778990260209775nteger A (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.zero_z3403309356797280102nteger)) (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (tptp.aa_num_real tptp.numeral_numeral_real U))) (let ((_let_2 (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real V)))) (let ((_let_3 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.ord_max_real _let_1) _let_2))) (let ((_let_4 (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real _let_1) _let_2)))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))) (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger U))) (let ((_let_2 (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger V)))) (let ((_let_3 (tptp.ord_max_Code_integer _let_1 _let_2))) (let ((_let_4 (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger _let_1) _let_2)))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))) (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (tptp.aa_num_rat tptp.numeral_numeral_rat U))) (let ((_let_2 (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat V)))) (let ((_let_3 (tptp.aa_rat_rat (tptp.ord_max_rat _let_1) _let_2))) (let ((_let_4 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat _let_1) _let_2)))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))) (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int U))) (let ((_let_2 (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int V)))) (let ((_let_3 (tptp.aa_int_int (tptp.ord_max_int _let_1) _let_2))) (let ((_let_4 (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int _let_1) _let_2)))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))) (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real U)))) (let ((_let_2 (tptp.aa_num_real tptp.numeral_numeral_real V))) (let ((_let_3 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.ord_max_real _let_1) _let_2))) (let ((_let_4 (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real _let_1) _let_2)))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))) (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger U)))) (let ((_let_2 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger V))) (let ((_let_3 (tptp.ord_max_Code_integer _let_1 _let_2))) (let ((_let_4 (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger _let_1) _let_2)))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))) (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat U)))) (let ((_let_2 (tptp.aa_num_rat tptp.numeral_numeral_rat V))) (let ((_let_3 (tptp.aa_rat_rat (tptp.ord_max_rat _let_1) _let_2))) (let ((_let_4 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat _let_1) _let_2)))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))) (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int U)))) (let ((_let_2 (tptp.aa_num_int tptp.numeral_numeral_int V))) (let ((_let_3 (tptp.aa_int_int (tptp.ord_max_int _let_1) _let_2))) (let ((_let_4 (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int _let_1) _let_2)))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))) (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real U)))) (let ((_let_2 (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real V)))) (let ((_let_3 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.ord_max_real _let_1) _let_2))) (let ((_let_4 (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real _let_1) _let_2)))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))) (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger U)))) (let ((_let_2 (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger V)))) (let ((_let_3 (tptp.ord_max_Code_integer _let_1 _let_2))) (let ((_let_4 (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger _let_1) _let_2)))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))) (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat U)))) (let ((_let_2 (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat V)))) (let ((_let_3 (tptp.aa_rat_rat (tptp.ord_max_rat _let_1) _let_2))) (let ((_let_4 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat _let_1) _let_2)))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))) (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int U)))) (let ((_let_2 (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int V)))) (let ((_let_3 (tptp.aa_int_int (tptp.ord_max_int _let_1) _let_2))) (let ((_let_4 (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int _let_1) _let_2)))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))) (forall ((V tptp.num) (W tptp.num) (Y tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real V))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real W))) Y)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num V) W)))) Y))) (forall ((V tptp.num) (W tptp.num) (Y tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int V))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int W))) Y)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num V) W)))) Y))) (forall ((V tptp.num) (W tptp.num) (Y tptp.complex)) (= (tptp.aa_complex_complex (tptp.plus_plus_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.numera6690914467698888265omplex V))) (tptp.aa_complex_complex (tptp.plus_plus_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.numera6690914467698888265omplex W))) Y)) (tptp.aa_complex_complex (tptp.plus_plus_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.numera6690914467698888265omplex (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num V) W)))) Y))) (forall ((V tptp.num) (W tptp.num) (Y tptp.code_integer)) (= (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger V)) (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger W)) Y)) (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num V) W))) Y))) (forall ((V tptp.num) (W tptp.num) (Y tptp.rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat V))) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat W))) Y)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num V) W)))) Y))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real M))) (tptp.aa_num_real tptp.numeral_numeral_real N)) (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num M) N))))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int M))) (tptp.aa_num_int tptp.numeral_numeral_int N)) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num M) N))))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.aa_complex_complex (tptp.minus_minus_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.numera6690914467698888265omplex M))) (tptp.numera6690914467698888265omplex N)) (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.numera6690914467698888265omplex (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num M) N))))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.minus_8373710615458151222nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger M)) (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger N)) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num M) N))))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat M))) (tptp.aa_num_rat tptp.numeral_numeral_rat N)) (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num M) N))))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_num_real tptp.numeral_numeral_real M)) (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real N))) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num M) N)))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_num_int tptp.numeral_numeral_int M)) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int N))) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num M) N)))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.aa_complex_complex (tptp.minus_minus_complex (tptp.numera6690914467698888265omplex M)) (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.numera6690914467698888265omplex N))) (tptp.numera6690914467698888265omplex (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num M) N)))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.minus_8373710615458151222nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger M) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger N))) (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num M) N)))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat M)) (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat N))) (tptp.aa_num_rat tptp.numeral_numeral_rat (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num M) N)))) (forall ((V tptp.num) (W tptp.num) (Y tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real V))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real W))) Y)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.times_times_num V) W))) Y))) (forall ((V tptp.num) (W tptp.num) (Y tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int V))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int W))) Y)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.times_times_num V) W))) Y))) (forall ((V tptp.num) (W tptp.num) (Y tptp.complex)) (= (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.numera6690914467698888265omplex V))) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.numera6690914467698888265omplex W))) Y)) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.numera6690914467698888265omplex (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.times_times_num V) W))) Y))) (forall ((V tptp.num) (W tptp.num) (Y tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger V))) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger W))) Y)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.times_times_num V) W))) Y))) (forall ((V tptp.num) (W tptp.num) (Y tptp.rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat V))) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat W))) Y)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_num_rat tptp.numeral_numeral_rat (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.times_times_num V) W))) Y))) (forall ((V tptp.num) (W tptp.num) (Y tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_num_real tptp.numeral_numeral_real V)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real W))) Y)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.times_times_num V) W)))) Y))) (forall ((V tptp.num) (W tptp.num) (Y tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_num_int tptp.numeral_numeral_int V)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int W))) Y)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.times_times_num V) W)))) Y))) (forall ((V tptp.num) (W tptp.num) (Y tptp.complex)) (= (tptp.aa_complex_complex (tptp.times_times_complex (tptp.numera6690914467698888265omplex V)) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.numera6690914467698888265omplex W))) Y)) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.numera6690914467698888265omplex (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.times_times_num V) W)))) Y))) (forall ((V tptp.num) (W tptp.num) (Y tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger V)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger W))) Y)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.times_times_num V) W)))) Y))) (forall ((V tptp.num) (W tptp.num) (Y tptp.rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_num_rat tptp.numeral_numeral_rat V)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat W))) Y)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.times_times_num V) W)))) Y))) (forall ((V tptp.num) (W tptp.num) (Y tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real V))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_num_real tptp.numeral_numeral_real W)) Y)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.times_times_num V) W)))) Y))) (forall ((V tptp.num) (W tptp.num) (Y tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int V))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_num_int tptp.numeral_numeral_int W)) Y)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.times_times_num V) W)))) Y))) (forall ((V tptp.num) (W tptp.num) (Y tptp.complex)) (= (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.numera6690914467698888265omplex V))) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.numera6690914467698888265omplex W)) Y)) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.numera6690914467698888265omplex (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.times_times_num V) W)))) Y))) (forall ((V tptp.num) (W tptp.num) (Y tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger V))) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger W)) Y)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.times_times_num V) W)))) Y))) (forall ((V tptp.num) (W tptp.num) (Y tptp.rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat V))) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_num_rat tptp.numeral_numeral_rat W)) Y)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.times_times_num V) W)))) Y))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_num_real tptp.numeral_numeral_real M)) (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real N))) (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.times_times_num M) N))))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_num_int tptp.numeral_numeral_int M)) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int N))) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.times_times_num M) N))))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.aa_complex_complex (tptp.times_times_complex (tptp.numera6690914467698888265omplex M)) (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.numera6690914467698888265omplex N))) (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.numera6690914467698888265omplex (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.times_times_num M) N))))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger M)) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger N))) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.times_times_num M) N))))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_num_rat tptp.numeral_numeral_rat M)) (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat N))) (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.times_times_num M) N))))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real M))) (tptp.aa_num_real tptp.numeral_numeral_real N)) (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.times_times_num M) N))))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int M))) (tptp.aa_num_int tptp.numeral_numeral_int N)) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.times_times_num M) N))))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.numera6690914467698888265omplex M))) (tptp.numera6690914467698888265omplex N)) (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.numera6690914467698888265omplex (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.times_times_num M) N))))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger M))) (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger N)) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.times_times_num M) N))))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat M))) (tptp.aa_num_rat tptp.numeral_numeral_rat N)) (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.times_times_num M) N))))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real M))) (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real N))) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.times_times_num M) N)))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int M))) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int N))) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.times_times_num M) N)))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.numera6690914467698888265omplex M))) (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.numera6690914467698888265omplex N))) (tptp.numera6690914467698888265omplex (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.times_times_num M) N)))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger M))) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger N))) (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.times_times_num M) N)))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat M))) (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat N))) (tptp.aa_num_rat tptp.numeral_numeral_rat (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.times_times_num M) N)))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real M))) (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real N)))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num N) M)))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger M))) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger N)))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num N) M)))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat M))) (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat N)))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num N) M)))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int M))) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int N)))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num N) M)))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real M))) (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real N)))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num N) M)))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int M))) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int N)))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num N) M)))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger M))) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger N)))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num N) M)))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat M))) (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat N)))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num N) M)))) (forall ((M tptp.num)) (= (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)) (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real M))))) (not (= M tptp.one)))) (forall ((M tptp.num)) (= (not (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger M))))) (not (= M tptp.one)))) (forall ((M tptp.num)) (= (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat tptp.one_one_rat)) (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat M))))) (not (= M tptp.one)))) (forall ((M tptp.num)) (= (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int)) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int M))))) (not (= M tptp.one)))) (forall ((B2 tptp.real) (W tptp.num) (A tptp.real)) (let ((_let_1 (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real W)))) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real B2) _let_1)) A)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) _let_1)) B2))))) (forall ((B2 tptp.rat) (W tptp.num) (A tptp.rat)) (let ((_let_1 (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat W)))) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.divide_divide_rat B2) _let_1)) A)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) _let_1)) B2))))) (forall ((A tptp.real) (B2 tptp.real) (W tptp.num)) (let ((_let_1 (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real W)))) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real B2) _let_1))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real B2) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) _let_1)))))) (forall ((A tptp.rat) (B2 tptp.rat) (W tptp.num)) (let ((_let_1 (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat W)))) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) (tptp.aa_rat_rat (tptp.divide_divide_rat B2) _let_1))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B2) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) _let_1)))))) (forall ((B2 tptp.real) (W tptp.num) (A tptp.real)) (let ((_let_1 (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real W)))) (let ((_let_2 (= _let_1 tptp.zero_zero_real))) (= (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real B2) _let_1) A) (and (=> (not _let_2) (= B2 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) _let_1))) (=> _let_2 (= A tptp.zero_zero_real))))))) (forall ((B2 tptp.complex) (W tptp.num) (A tptp.complex)) (let ((_let_1 (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.numera6690914467698888265omplex W)))) (let ((_let_2 (= _let_1 tptp.zero_zero_complex))) (= (= (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex B2) _let_1) A) (and (=> (not _let_2) (= B2 (tptp.aa_complex_complex (tptp.times_times_complex A) _let_1))) (=> _let_2 (= A tptp.zero_zero_complex))))))) (forall ((B2 tptp.rat) (W tptp.num) (A tptp.rat)) (let ((_let_1 (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat W)))) (let ((_let_2 (= _let_1 tptp.zero_zero_rat))) (= (= (tptp.aa_rat_rat (tptp.divide_divide_rat B2) _let_1) A) (and (=> (not _let_2) (= B2 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) _let_1))) (=> _let_2 (= A tptp.zero_zero_rat))))))) (forall ((A tptp.real) (B2 tptp.real) (W tptp.num)) (let ((_let_1 (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real W)))) (let ((_let_2 (= _let_1 tptp.zero_zero_real))) (= (= A (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real B2) _let_1)) (and (=> (not _let_2) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) _let_1) B2)) (=> _let_2 (= A tptp.zero_zero_real))))))) (forall ((A tptp.complex) (B2 tptp.complex) (W tptp.num)) (let ((_let_1 (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.numera6690914467698888265omplex W)))) (let ((_let_2 (= _let_1 tptp.zero_zero_complex))) (= (= A (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex B2) _let_1)) (and (=> (not _let_2) (= (tptp.aa_complex_complex (tptp.times_times_complex A) _let_1) B2)) (=> _let_2 (= A tptp.zero_zero_complex))))))) (forall ((A tptp.rat) (B2 tptp.rat) (W tptp.num)) (let ((_let_1 (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat W)))) (let ((_let_2 (= _let_1 tptp.zero_zero_rat))) (= (= A (tptp.aa_rat_rat (tptp.divide_divide_rat B2) _let_1)) (and (=> (not _let_2) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) _let_1) B2)) (=> _let_2 (= A tptp.zero_zero_rat))))))) (forall ((M tptp.num)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real M))) (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real))) (not (= M tptp.one)))) (forall ((M tptp.num)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int M))) (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int))) (not (= M tptp.one)))) (forall ((M tptp.num)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger M))) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (not (= M tptp.one)))) (forall ((M tptp.num)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat M))) (tptp.aa_rat_rat tptp.uminus_uminus_rat tptp.one_one_rat))) (not (= M tptp.one)))) (forall ((B2 tptp.real) (W tptp.num) (A tptp.real)) (let ((_let_1 (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real W)))) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real B2) _let_1)) A)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) _let_1)) B2))))) (forall ((B2 tptp.rat) (W tptp.num) (A tptp.rat)) (let ((_let_1 (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat W)))) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.divide_divide_rat B2) _let_1)) A)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) _let_1)) B2))))) (forall ((A tptp.real) (B2 tptp.real) (W tptp.num)) (let ((_let_1 (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real W)))) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real B2) _let_1))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B2) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) _let_1)))))) (forall ((A tptp.rat) (B2 tptp.rat) (W tptp.num)) (let ((_let_1 (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat W)))) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) (tptp.aa_rat_rat (tptp.divide_divide_rat B2) _let_1))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B2) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) _let_1)))))) (forall ((A tptp.real)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real tptp.uminus_uminus_real A)) _let_1) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real A) _let_1)))) (forall ((A tptp.int)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_int_int tptp.uminus_uminus_int A)) _let_1) (tptp.aa_nat_int (tptp.power_power_int A) _let_1)))) (forall ((A tptp.complex)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.aa_nat_complex (tptp.power_power_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex A)) _let_1) (tptp.aa_nat_complex (tptp.power_power_complex A) _let_1)))) (forall ((A tptp.code_integer)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A)) _let_1) (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger A) _let_1)))) (forall ((A tptp.rat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat A)) _let_1) (tptp.aa_nat_rat (tptp.power_power_rat A) _let_1)))) (forall ((P2 tptp.bool)) (= (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.zero_n2687167440665602831ol_nat P2)))) (tptp.pp P2))) (forall ((P2 tptp.bool)) (= (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_bool_int tptp.zero_n2684676970156552555ol_int P2)))) (tptp.pp P2))) (forall ((P2 tptp.bool)) (= (not (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.zero_n356916108424825756nteger P2)))) (tptp.pp P2))) (= (tptp.aa_real_real _let_135 _let_57) _let_121) (= (tptp.aa_int_int _let_134 _let_37) _let_120) (= (tptp.aa_complex_complex _let_133 _let_54) _let_119) (= (tptp.plus_p5714425477246183910nteger _let_83 _let_83) _let_118) (= (tptp.aa_rat_rat _let_132 _let_38) _let_117) (= (tptp.aa_real_real _let_131 _let_57) _let_28) (= (tptp.aa_int_int _let_130 _let_37) _let_44) (= (tptp.aa_complex_complex _let_129 _let_54) _let_50) (= (tptp.minus_8373710615458151222nteger tptp.one_one_Code_integer _let_83) _let_35) (= (tptp.aa_rat_rat _let_128 _let_38) _let_69) (= (tptp.aa_real_real _let_127 tptp.one_one_real) _let_121) (= (tptp.aa_int_int _let_126 tptp.one_one_int) _let_120) (= (tptp.aa_complex_complex _let_125 tptp.one_one_complex) _let_119) (= (tptp.minus_8373710615458151222nteger _let_83 tptp.one_one_Code_integer) _let_118) (= (tptp.aa_rat_rat _let_124 tptp.one_one_rat) _let_117) (= (tptp.aa_int_int (tptp.divide_divide_int _let_37) _let_44) _let_37) (= (tptp.divide6298287555418463151nteger _let_83 _let_35) _let_83) _let_123 _let_122 _let_123 _let_122 (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N))) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real tptp.uminus_uminus_real A)) _let_1) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real A) _let_1)))) (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N))) (= (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_int_int tptp.uminus_uminus_int A)) _let_1) (tptp.aa_nat_int (tptp.power_power_int A) _let_1)))) (forall ((A tptp.complex) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N))) (= (tptp.aa_nat_complex (tptp.power_power_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex A)) _let_1) (tptp.aa_nat_complex (tptp.power_power_complex A) _let_1)))) (forall ((A tptp.code_integer) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N))) (= (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A)) _let_1) (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger A) _let_1)))) (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N))) (= (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat A)) _let_1) (tptp.aa_nat_rat (tptp.power_power_rat A) _let_1)))) (forall ((B2 tptp.bool)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.zero_n2687167440665602831ol_nat B2)) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) tptp.zero_zero_nat)) (forall ((B2 tptp.bool)) (= (tptp.aa_int_int (tptp.divide_divide_int (tptp.aa_bool_int tptp.zero_n2684676970156552555ol_int B2)) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) tptp.zero_zero_int)) (forall ((B2 tptp.bool)) (= (tptp.divide6298287555418463151nteger (tptp.zero_n356916108424825756nteger B2) (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))) tptp.zero_z3403309356797280102nteger)) (forall ((N tptp.nat) (A tptp.real)) (=> (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N))) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real tptp.uminus_uminus_real A)) N) (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real A) N))))) (forall ((N tptp.nat) (A tptp.int)) (=> (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N))) (= (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_int_int tptp.uminus_uminus_int A)) N) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_nat_int (tptp.power_power_int A) N))))) (forall ((N tptp.nat) (A tptp.complex)) (=> (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N))) (= (tptp.aa_nat_complex (tptp.power_power_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex A)) N) (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.aa_nat_complex (tptp.power_power_complex A) N))))) (forall ((N tptp.nat) (A tptp.code_integer)) (=> (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N))) (= (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A)) N) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger A) N))))) (forall ((N tptp.nat) (A tptp.rat)) (=> (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N))) (= (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat A)) N) (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_nat_rat (tptp.power_power_rat A) N))))) (forall ((N tptp.nat) (A tptp.real)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real tptp.uminus_uminus_real A)) N) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real A) N)))) (forall ((N tptp.nat) (A tptp.int)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N)) (= (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_int_int tptp.uminus_uminus_int A)) N) (tptp.aa_nat_int (tptp.power_power_int A) N)))) (forall ((N tptp.nat) (A tptp.complex)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N)) (= (tptp.aa_nat_complex (tptp.power_power_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex A)) N) (tptp.aa_nat_complex (tptp.power_power_complex A) N)))) (forall ((N tptp.nat) (A tptp.code_integer)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N)) (= (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A)) N) (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger A) N)))) (forall ((N tptp.nat) (A tptp.rat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N)) (= (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat A)) N) (tptp.aa_nat_rat (tptp.power_power_rat A) N)))) (forall ((N tptp.num)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real tptp.one_one_real) (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real N))) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num tptp.one) N)))) (forall ((N tptp.num)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int tptp.one_one_int) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int N))) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num tptp.one) N)))) (forall ((N tptp.num)) (= (tptp.aa_complex_complex (tptp.minus_minus_complex tptp.one_one_complex) (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.numera6690914467698888265omplex N))) (tptp.numera6690914467698888265omplex (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num tptp.one) N)))) (forall ((N tptp.num)) (= (tptp.minus_8373710615458151222nteger tptp.one_one_Code_integer (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger N))) (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num tptp.one) N)))) (forall ((N tptp.num)) (= (tptp.aa_rat_rat (tptp.minus_minus_rat tptp.one_one_rat) (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat N))) (tptp.aa_num_rat tptp.numeral_numeral_rat (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num tptp.one) N)))) (forall ((M tptp.num)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real M))) tptp.one_one_real) (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num M) tptp.one))))) (forall ((M tptp.num)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int M))) tptp.one_one_int) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num M) tptp.one))))) (forall ((M tptp.num)) (= (tptp.aa_complex_complex (tptp.minus_minus_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.numera6690914467698888265omplex M))) tptp.one_one_complex) (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.numera6690914467698888265omplex (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num M) tptp.one))))) (forall ((M tptp.num)) (= (tptp.minus_8373710615458151222nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger M)) tptp.one_one_Code_integer) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num M) tptp.one))))) (forall ((M tptp.num)) (= (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat M))) tptp.one_one_rat) (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num M) tptp.one))))) (forall ((N tptp.nat) (K tptp.num)) (= (tptp.aa_int_int (tptp.bit_ri631733984087533419it_int (tptp.aa_nat_nat tptp.suc N)) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 K)))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.bit_ri631733984087533419it_int N) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int K)))) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))))) (forall ((X tptp.nat)) (= (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat tptp.zero_zero_nat) (tptp.nat_set_decode X))) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) X))))) (= (tptp.aa_real_real tptp.neg_numeral_dbl_real _let_57) _let_121) (= (tptp.aa_int_int tptp.neg_numeral_dbl_int _let_37) _let_120) (= (tptp.aa_complex_complex tptp.neg_nu7009210354673126013omplex _let_54) _let_119) (= (tptp.neg_nu8804712462038260780nteger _let_83) _let_118) (= (tptp.aa_rat_rat tptp.neg_numeral_dbl_rat _let_38) _let_117) (forall ((N tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N)) tptp.one_one_real)) (forall ((N tptp.nat)) (= (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N)) tptp.one_one_int)) (forall ((N tptp.nat)) (= (tptp.aa_nat_complex (tptp.power_power_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N)) tptp.one_one_complex)) (forall ((N tptp.nat)) (= (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N)) tptp.one_one_Code_integer)) (forall ((N tptp.nat)) (= (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat tptp.one_one_rat)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N)) tptp.one_one_rat)) (forall ((N tptp.nat)) (let ((_let_1 (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real))) (=> (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N))) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real _let_1) N) _let_1)))) (forall ((N tptp.nat)) (let ((_let_1 (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int))) (=> (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N))) (= (tptp.aa_nat_int (tptp.power_power_int _let_1) N) _let_1)))) (forall ((N tptp.nat)) (let ((_let_1 (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex tptp.one_one_complex))) (=> (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N))) (= (tptp.aa_nat_complex (tptp.power_power_complex _let_1) N) _let_1)))) (forall ((N tptp.nat)) (let ((_let_1 (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (=> (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N))) (= (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger _let_1) N) _let_1)))) (forall ((N tptp.nat)) (let ((_let_1 (tptp.aa_rat_rat tptp.uminus_uminus_rat tptp.one_one_rat))) (=> (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N))) (= (tptp.aa_nat_rat (tptp.power_power_rat _let_1) N) _let_1)))) (forall ((N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)) N) tptp.one_one_real))) (forall ((N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N)) (= (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int)) N) tptp.one_one_int))) (forall ((N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N)) (= (tptp.aa_nat_complex (tptp.power_power_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex tptp.one_one_complex)) N) tptp.one_one_complex))) (forall ((N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N)) (= (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) N) tptp.one_one_Code_integer))) (forall ((N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N)) (= (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat tptp.one_one_rat)) N) tptp.one_one_rat))) (forall ((A tptp.code_integer)) (= (tptp.bit_ri6519982836138164636nteger tptp.zero_zero_nat A) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.modulo364778990260209775nteger A (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one)))))) (forall ((A tptp.int)) (= (tptp.aa_int_int (tptp.bit_ri631733984087533419it_int tptp.zero_zero_nat) A) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_int_int (tptp.modulo_modulo_int A) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one)))))) (forall ((N tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat tptp.one_one_nat) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N)) (tptp.zero_n2687167440665602831ol_nat (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.fequal_nat N) tptp.zero_zero_nat)))) (forall ((N tptp.nat)) (= (tptp.aa_int_int (tptp.divide_divide_int tptp.one_one_int) (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) N)) (tptp.aa_bool_int tptp.zero_n2684676970156552555ol_int (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.fequal_nat N) tptp.zero_zero_nat)))) (forall ((N tptp.nat)) (= (tptp.divide6298287555418463151nteger tptp.one_one_Code_integer (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))) N)) (tptp.zero_n356916108424825756nteger (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.fequal_nat N) tptp.zero_zero_nat)))) (forall ((N tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat tptp.one_one_nat) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N)) (tptp.zero_n2687167440665602831ol_nat (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.fequal_nat N) tptp.zero_zero_nat)))) (forall ((N tptp.nat)) (= (tptp.aa_int_int (tptp.divide_divide_int tptp.one_one_int) (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) N)) (tptp.aa_bool_int tptp.zero_n2684676970156552555ol_int (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.fequal_nat N) tptp.zero_zero_nat)))) (forall ((N tptp.nat)) (= (tptp.divide6298287555418463151nteger tptp.one_one_Code_integer (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))) N)) (tptp.zero_n356916108424825756nteger (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.fequal_nat N) tptp.zero_zero_nat)))) (forall ((N tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat tptp.one_one_nat) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N)) (tptp.zero_n2687167440665602831ol_nat (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)))) (forall ((N tptp.nat)) (= (tptp.aa_int_int (tptp.modulo_modulo_int tptp.one_one_int) (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) N)) (tptp.aa_bool_int tptp.zero_n2684676970156552555ol_int (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)))) (forall ((N tptp.nat)) (= (tptp.modulo364778990260209775nteger tptp.one_one_Code_integer (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))) N)) (tptp.zero_n356916108424825756nteger (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)))) (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (tptp.bit_ri631733984087533419it_int N))) (= (tptp.aa_int_int _let_1 (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_int_int _let_1 K))) (tptp.aa_int_int _let_1 (tptp.aa_int_int tptp.uminus_uminus_int K))))) (forall ((M tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat M) N)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat N) M)) (= M N)))) (forall ((A tptp.real) (B2 tptp.real)) (= (= A (tptp.aa_real_real tptp.uminus_uminus_real B2)) (= B2 (tptp.aa_real_real tptp.uminus_uminus_real A)))) (forall ((A tptp.int) (B2 tptp.int)) (= (= A (tptp.aa_int_int tptp.uminus_uminus_int B2)) (= B2 (tptp.aa_int_int tptp.uminus_uminus_int A)))) (forall ((A tptp.complex) (B2 tptp.complex)) (= (= A (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex B2)) (= B2 (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex A)))) (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (= (= A (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger B2)) (= B2 (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A)))) (forall ((A tptp.rat) (B2 tptp.rat)) (= (= A (tptp.aa_rat_rat tptp.uminus_uminus_rat B2)) (= B2 (tptp.aa_rat_rat tptp.uminus_uminus_rat A)))) (forall ((A tptp.real) (B2 tptp.real)) (= (= (tptp.aa_real_real tptp.uminus_uminus_real A) B2) (= (tptp.aa_real_real tptp.uminus_uminus_real B2) A))) (forall ((A tptp.int) (B2 tptp.int)) (= (= (tptp.aa_int_int tptp.uminus_uminus_int A) B2) (= (tptp.aa_int_int tptp.uminus_uminus_int B2) A))) (forall ((A tptp.complex) (B2 tptp.complex)) (= (= (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex A) B2) (= (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex B2) A))) (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (= (= (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A) B2) (= (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger B2) A))) (forall ((A tptp.rat) (B2 tptp.rat)) (= (= (tptp.aa_rat_rat tptp.uminus_uminus_rat A) B2) (= (tptp.aa_rat_rat tptp.uminus_uminus_rat B2) A))) (forall ((P2 tptp.bool) (Q2 tptp.bool)) (= (= (tptp.zero_n2687167440665602831ol_nat P2) (tptp.zero_n2687167440665602831ol_nat Q2)) (= (tptp.pp P2) (tptp.pp Q2)))) (forall ((P2 tptp.bool) (Q2 tptp.bool)) (= (= (tptp.aa_bool_int tptp.zero_n2684676970156552555ol_int P2) (tptp.aa_bool_int tptp.zero_n2684676970156552555ol_int Q2)) (= (tptp.pp P2) (tptp.pp Q2)))) (forall ((P2 tptp.bool) (Q2 tptp.bool)) (= (= (tptp.zero_n356916108424825756nteger P2) (tptp.zero_n356916108424825756nteger Q2)) (= (tptp.pp P2) (tptp.pp Q2)))) (forall ((A tptp.real) (B2 tptp.real)) (=> (= A B2) (= (tptp.aa_real_real tptp.uminus_uminus_real A) (tptp.aa_real_real tptp.uminus_uminus_real B2)))) (forall ((A tptp.int) (B2 tptp.int)) (=> (= A B2) (= (tptp.aa_int_int tptp.uminus_uminus_int A) (tptp.aa_int_int tptp.uminus_uminus_int B2)))) (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (=> (= A B2) (= (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger B2)))) (forall ((A tptp.rat) (B2 tptp.rat)) (=> (= A B2) (= (tptp.aa_rat_rat tptp.uminus_uminus_rat A) (tptp.aa_rat_rat tptp.uminus_uminus_rat B2)))) (forall ((X tptp.set_int) (Y tptp.set_int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int X) Y)) (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int (tptp.uminus1532241313380277803et_int Y)) (tptp.uminus1532241313380277803et_int X))))) (forall ((Y tptp.set_int) (X tptp.set_int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int Y) (tptp.uminus1532241313380277803et_int X))) (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int X) (tptp.uminus1532241313380277803et_int Y))))) (forall ((Y tptp.set_int) (X tptp.set_int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int (tptp.uminus1532241313380277803et_int Y)) X)) (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int (tptp.uminus1532241313380277803et_int X)) Y)))) (forall ((P tptp.bool) (Q tptp.bool)) (= (tptp.zero_n3304061248610475627l_real (tptp.aa_bool_bool (tptp.fconj P) Q)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.zero_n3304061248610475627l_real P)) (tptp.zero_n3304061248610475627l_real Q)))) (forall ((P tptp.bool) (Q tptp.bool)) (= (tptp.zero_n2052037380579107095ol_rat (tptp.aa_bool_bool (tptp.fconj P) Q)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.zero_n2052037380579107095ol_rat P)) (tptp.zero_n2052037380579107095ol_rat Q)))) (forall ((P tptp.bool) (Q tptp.bool)) (= (tptp.zero_n2687167440665602831ol_nat (tptp.aa_bool_bool (tptp.fconj P) Q)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.zero_n2687167440665602831ol_nat P)) (tptp.zero_n2687167440665602831ol_nat Q)))) (forall ((P tptp.bool) (Q tptp.bool)) (= (tptp.aa_bool_int tptp.zero_n2684676970156552555ol_int (tptp.aa_bool_bool (tptp.fconj P) Q)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_bool_int tptp.zero_n2684676970156552555ol_int P)) (tptp.aa_bool_int tptp.zero_n2684676970156552555ol_int Q)))) (forall ((P tptp.bool) (Q tptp.bool)) (= (tptp.zero_n356916108424825756nteger (tptp.aa_bool_bool (tptp.fconj P) Q)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.zero_n356916108424825756nteger P)) (tptp.zero_n356916108424825756nteger Q)))) (forall ((A tptp.real) (B2 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) B2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real B2)) (tptp.aa_real_real tptp.uminus_uminus_real A))))) (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger A) B2)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger B2)) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A))))) (forall ((A tptp.rat) (B2 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B2)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat B2)) (tptp.aa_rat_rat tptp.uminus_uminus_rat A))))) (forall ((A tptp.int) (B2 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B2)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.uminus_uminus_int B2)) (tptp.aa_int_int tptp.uminus_uminus_int A))))) (forall ((A tptp.real) (B2 tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real A)) B2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real B2)) A)))) (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A)) B2)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger B2)) A)))) (forall ((A tptp.rat) (B2 tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat A)) B2)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat B2)) A)))) (forall ((A tptp.int) (B2 tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.uminus_uminus_int A)) B2)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.uminus_uminus_int B2)) A)))) (forall ((A tptp.real) (B2 tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) (tptp.aa_real_real tptp.uminus_uminus_real B2))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real B2) (tptp.aa_real_real tptp.uminus_uminus_real A))))) (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger A) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger B2))) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger B2) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A))))) (forall ((A tptp.rat) (B2 tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) (tptp.aa_rat_rat tptp.uminus_uminus_rat B2))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B2) (tptp.aa_rat_rat tptp.uminus_uminus_rat A))))) (forall ((A tptp.int) (B2 tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) (tptp.aa_int_int tptp.uminus_uminus_int B2))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B2) (tptp.aa_int_int tptp.uminus_uminus_int A))))) (forall ((A tptp.real) (B2 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.uminus_uminus_real B2)) (tptp.aa_real_real tptp.uminus_uminus_real A))))) (forall ((A tptp.int) (B2 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B2)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int tptp.uminus_uminus_int B2)) (tptp.aa_int_int tptp.uminus_uminus_int A))))) (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger A) B2)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger B2)) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A))))) (forall ((A tptp.rat) (B2 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B2)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat B2)) (tptp.aa_rat_rat tptp.uminus_uminus_rat A))))) (forall ((A tptp.real) (B2 tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.uminus_uminus_real A)) B2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.uminus_uminus_real B2)) A)))) (forall ((A tptp.int) (B2 tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int tptp.uminus_uminus_int A)) B2)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int tptp.uminus_uminus_int B2)) A)))) (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A)) B2)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger B2)) A)))) (forall ((A tptp.rat) (B2 tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat A)) B2)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat B2)) A)))) (forall ((A tptp.real) (B2 tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) (tptp.aa_real_real tptp.uminus_uminus_real B2))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B2) (tptp.aa_real_real tptp.uminus_uminus_real A))))) (forall ((A tptp.int) (B2 tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) (tptp.aa_int_int tptp.uminus_uminus_int B2))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B2) (tptp.aa_int_int tptp.uminus_uminus_int A))))) (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger A) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger B2))) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger B2) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A))))) (forall ((A tptp.rat) (B2 tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) (tptp.aa_rat_rat tptp.uminus_uminus_rat B2))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B2) (tptp.aa_rat_rat tptp.uminus_uminus_rat A))))) (forall ((M tptp.num) (N tptp.num)) (not (= (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real M)) (tptp.aa_num_real tptp.numeral_numeral_real N)))) (forall ((M tptp.num) (N tptp.num)) (not (= (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int M)) (tptp.aa_num_int tptp.numeral_numeral_int N)))) (forall ((M tptp.num) (N tptp.num)) (not (= (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.numera6690914467698888265omplex M)) (tptp.numera6690914467698888265omplex N)))) (forall ((M tptp.num) (N tptp.num)) (not (= (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger M)) (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger N)))) (forall ((M tptp.num) (N tptp.num)) (not (= (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat M)) (tptp.aa_num_rat tptp.numeral_numeral_rat N)))) (forall ((M tptp.num) (N tptp.num)) (not (= (tptp.aa_num_real tptp.numeral_numeral_real M) (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real N))))) (forall ((M tptp.num) (N tptp.num)) (not (= (tptp.aa_num_int tptp.numeral_numeral_int M) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int N))))) (forall ((M tptp.num) (N tptp.num)) (not (= (tptp.numera6690914467698888265omplex M) (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.numera6690914467698888265omplex N))))) (forall ((M tptp.num) (N tptp.num)) (not (= (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger M) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger N))))) (forall ((M tptp.num) (N tptp.num)) (not (= (tptp.aa_num_rat tptp.numeral_numeral_rat M) (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat N))))) (forall ((A tptp.real) (B2 tptp.real)) (= (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) A) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real B2) B2)) (or (= A B2) (= A (tptp.aa_real_real tptp.uminus_uminus_real B2))))) (forall ((A tptp.int) (B2 tptp.int)) (= (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) A) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B2) B2)) (or (= A B2) (= A (tptp.aa_int_int tptp.uminus_uminus_int B2))))) (forall ((A tptp.complex) (B2 tptp.complex)) (= (= (tptp.aa_complex_complex (tptp.times_times_complex A) A) (tptp.aa_complex_complex (tptp.times_times_complex B2) B2)) (or (= A B2) (= A (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex B2))))) (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (= (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) A) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B2) B2)) (or (= A B2) (= A (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger B2))))) (forall ((A tptp.rat) (B2 tptp.rat)) (= (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) A) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat B2) B2)) (or (= A B2) (= A (tptp.aa_rat_rat tptp.uminus_uminus_rat B2))))) (forall ((A tptp.real) (B2 tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real tptp.uminus_uminus_real A)) B2) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) (tptp.aa_real_real tptp.uminus_uminus_real B2)))) (forall ((A tptp.int) (B2 tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int tptp.uminus_uminus_int A)) B2) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) (tptp.aa_int_int tptp.uminus_uminus_int B2)))) (forall ((A tptp.complex) (B2 tptp.complex)) (= (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex A)) B2) (tptp.aa_complex_complex (tptp.times_times_complex A) (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex B2)))) (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A)) B2) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger B2)))) (forall ((A tptp.rat) (B2 tptp.rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat A)) B2) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) (tptp.aa_rat_rat tptp.uminus_uminus_rat B2)))) (not (= tptp.one_one_real _let_57)) (not (= tptp.one_one_int _let_37)) (not (= tptp.one_one_complex _let_54)) (not (= tptp.one_one_Code_integer _let_83)) (not (= tptp.one_one_rat _let_38)) (forall ((A tptp.real) (B2 tptp.real)) (= (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) B2)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real tptp.uminus_uminus_real B2)) (tptp.aa_real_real tptp.uminus_uminus_real A)))) (forall ((A tptp.int) (B2 tptp.int)) (= (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) B2)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int tptp.uminus_uminus_int B2)) (tptp.aa_int_int tptp.uminus_uminus_int A)))) (forall ((A tptp.complex) (B2 tptp.complex)) (= (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.aa_complex_complex (tptp.plus_plus_complex A) B2)) (tptp.aa_complex_complex (tptp.plus_plus_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex B2)) (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex A)))) (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.plus_p5714425477246183910nteger A B2)) (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger B2) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A)))) (forall ((A tptp.rat) (B2 tptp.rat)) (= (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) B2)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat B2)) (tptp.aa_rat_rat tptp.uminus_uminus_rat A)))) (forall ((A tptp.real) (B2 tptp.real)) (= (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) B2)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real tptp.uminus_uminus_real B2)) (tptp.aa_real_real tptp.uminus_uminus_real A)))) (forall ((A tptp.int) (B2 tptp.int)) (= (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) B2)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int tptp.uminus_uminus_int B2)) (tptp.aa_int_int tptp.uminus_uminus_int A)))) (forall ((A tptp.complex) (B2 tptp.complex)) (= (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.aa_complex_complex (tptp.plus_plus_complex A) B2)) (tptp.aa_complex_complex (tptp.plus_plus_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex B2)) (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex A)))) (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.plus_p5714425477246183910nteger A B2)) (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger B2) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A)))) (forall ((A tptp.rat) (B2 tptp.rat)) (= (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) B2)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat B2)) (tptp.aa_rat_rat tptp.uminus_uminus_rat A)))) (forall ((A4 tptp.real) (K tptp.real) (A tptp.real)) (=> (= A4 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real K) A)) (= (tptp.aa_real_real tptp.uminus_uminus_real A4) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real tptp.uminus_uminus_real K)) (tptp.aa_real_real tptp.uminus_uminus_real A))))) (forall ((A4 tptp.int) (K tptp.int) (A tptp.int)) (=> (= A4 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int K) A)) (= (tptp.aa_int_int tptp.uminus_uminus_int A4) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int tptp.uminus_uminus_int K)) (tptp.aa_int_int tptp.uminus_uminus_int A))))) (forall ((A4 tptp.complex) (K tptp.complex) (A tptp.complex)) (=> (= A4 (tptp.aa_complex_complex (tptp.plus_plus_complex K) A)) (= (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex A4) (tptp.aa_complex_complex (tptp.plus_plus_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex K)) (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex A))))) (forall ((A4 tptp.code_integer) (K tptp.code_integer) (A tptp.code_integer)) (=> (= A4 (tptp.plus_p5714425477246183910nteger K A)) (= (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A4) (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger K) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A))))) (forall ((A4 tptp.rat) (K tptp.rat) (A tptp.rat)) (=> (= A4 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat K) A)) (= (tptp.aa_rat_rat tptp.uminus_uminus_rat A4) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat K)) (tptp.aa_rat_rat tptp.uminus_uminus_rat A))))) (forall ((A tptp.real) (B2 tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real tptp.uminus_uminus_real A)) (tptp.aa_real_real tptp.uminus_uminus_real B2)) (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A) B2)))) (forall ((A tptp.int) (B2 tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_int_int tptp.uminus_uminus_int A)) (tptp.aa_int_int tptp.uminus_uminus_int B2)) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) B2)))) (forall ((A tptp.complex) (B2 tptp.complex)) (= (tptp.aa_complex_complex (tptp.minus_minus_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex A)) (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex B2)) (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.aa_complex_complex (tptp.minus_minus_complex A) B2)))) (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (= (tptp.minus_8373710615458151222nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger B2)) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.minus_8373710615458151222nteger A B2)))) (forall ((A tptp.rat) (B2 tptp.rat)) (= (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat A)) (tptp.aa_rat_rat tptp.uminus_uminus_rat B2)) (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_rat_rat (tptp.minus_minus_rat A) B2)))) (forall ((B2 tptp.real) (A tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real tptp.uminus_uminus_real B2)) A) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real tptp.uminus_uminus_real A)) B2))) (forall ((B2 tptp.int) (A tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_int_int tptp.uminus_uminus_int B2)) A) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_int_int tptp.uminus_uminus_int A)) B2))) (forall ((B2 tptp.complex) (A tptp.complex)) (= (tptp.aa_complex_complex (tptp.minus_minus_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex B2)) A) (tptp.aa_complex_complex (tptp.minus_minus_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex A)) B2))) (forall ((B2 tptp.code_integer) (A tptp.code_integer)) (= (tptp.minus_8373710615458151222nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger B2) A) (tptp.minus_8373710615458151222nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A) B2))) (forall ((B2 tptp.rat) (A tptp.rat)) (= (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat B2)) A) (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat A)) B2))) (forall ((A tptp.real) (B2 tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real A))) (= (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_real_real _let_1 B2)) (tptp.aa_real_real _let_1 (tptp.aa_real_real tptp.uminus_uminus_real B2))))) (forall ((A tptp.complex) (B2 tptp.complex)) (let ((_let_1 (tptp.divide1717551699836669952omplex A))) (= (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.aa_complex_complex _let_1 B2)) (tptp.aa_complex_complex _let_1 (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex B2))))) (forall ((A tptp.rat) (B2 tptp.rat)) (let ((_let_1 (tptp.divide_divide_rat A))) (= (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_rat_rat _let_1 B2)) (tptp.aa_rat_rat _let_1 (tptp.aa_rat_rat tptp.uminus_uminus_rat B2))))) (forall ((A tptp.real) (B2 tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real tptp.uminus_uminus_real A)) (tptp.aa_real_real tptp.uminus_uminus_real B2)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real A) B2))) (forall ((A tptp.complex) (B2 tptp.complex)) (= (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex A)) (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex B2)) (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex A) B2))) (forall ((A tptp.rat) (B2 tptp.rat)) (= (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat A)) (tptp.aa_rat_rat tptp.uminus_uminus_rat B2)) (tptp.aa_rat_rat (tptp.divide_divide_rat A) B2))) (forall ((A tptp.real) (B2 tptp.real)) (= (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real A) B2)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real tptp.uminus_uminus_real A)) B2))) (forall ((A tptp.complex) (B2 tptp.complex)) (= (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex A) B2)) (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex A)) B2))) (forall ((A tptp.rat) (B2 tptp.rat)) (= (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_rat_rat (tptp.divide_divide_rat A) B2)) (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat A)) B2))) (forall ((A tptp.int) (B2 tptp.int)) (= (tptp.aa_int_int (tptp.divide_divide_int A) (tptp.aa_int_int tptp.uminus_uminus_int B2)) (tptp.aa_int_int (tptp.divide_divide_int (tptp.aa_int_int tptp.uminus_uminus_int A)) B2))) (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (= (tptp.divide6298287555418463151nteger A (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger B2)) (tptp.divide6298287555418463151nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A) B2))) (forall ((A tptp.int) (B2 tptp.int)) (= (tptp.aa_int_int (tptp.modulo_modulo_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_int_int (tptp.modulo_modulo_int A) B2))) B2) (tptp.aa_int_int (tptp.modulo_modulo_int (tptp.aa_int_int tptp.uminus_uminus_int A)) B2))) (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (= (tptp.modulo364778990260209775nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.modulo364778990260209775nteger A B2)) B2) (tptp.modulo364778990260209775nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A) B2))) (forall ((A tptp.int) (B2 tptp.int) (A2 tptp.int)) (=> (= (tptp.aa_int_int (tptp.modulo_modulo_int A) B2) (tptp.aa_int_int (tptp.modulo_modulo_int A2) B2)) (= (tptp.aa_int_int (tptp.modulo_modulo_int (tptp.aa_int_int tptp.uminus_uminus_int A)) B2) (tptp.aa_int_int (tptp.modulo_modulo_int (tptp.aa_int_int tptp.uminus_uminus_int A2)) B2)))) (forall ((A tptp.code_integer) (B2 tptp.code_integer) (A2 tptp.code_integer)) (=> (= (tptp.modulo364778990260209775nteger A B2) (tptp.modulo364778990260209775nteger A2 B2)) (= (tptp.modulo364778990260209775nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A) B2) (tptp.modulo364778990260209775nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A2) B2)))) (forall ((A tptp.int) (B2 tptp.int)) (= (tptp.aa_int_int (tptp.modulo_modulo_int A) (tptp.aa_int_int tptp.uminus_uminus_int B2)) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_int_int (tptp.modulo_modulo_int (tptp.aa_int_int tptp.uminus_uminus_int A)) B2)))) (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (= (tptp.modulo364778990260209775nteger A (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger B2)) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.modulo364778990260209775nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A) B2)))) (forall ((P tptp.bool)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.zero_n3304061248610475627l_real P)))) (forall ((P tptp.bool)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.zero_n2052037380579107095ol_rat P)))) (forall ((P tptp.bool)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) (tptp.zero_n2687167440665602831ol_nat P)))) (forall ((P tptp.bool)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.aa_bool_int tptp.zero_n2684676970156552555ol_int P)))) (forall ((P tptp.bool)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (tptp.zero_n356916108424825756nteger P)))) (forall ((P tptp.bool)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.zero_n3304061248610475627l_real P)) tptp.one_one_real))) (forall ((P tptp.bool)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.zero_n2052037380579107095ol_rat P)) tptp.one_one_rat))) (forall ((P tptp.bool)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.zero_n2687167440665602831ol_nat P)) tptp.one_one_nat))) (forall ((P tptp.bool)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_bool_int tptp.zero_n2684676970156552555ol_int P)) tptp.one_one_int))) (forall ((P tptp.bool)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.zero_n356916108424825756nteger P)) tptp.one_one_Code_integer))) (forall ((P2 tptp.bool)) (let ((_let_1 (tptp.zero_n1201886186963655149omplex P2))) (let ((_let_2 (tptp.pp P2))) (and (=> _let_2 (= _let_1 tptp.one_one_complex)) (=> (not _let_2) (= _let_1 tptp.zero_zero_complex)))))) (forall ((P2 tptp.bool)) (let ((_let_1 (tptp.zero_n3304061248610475627l_real P2))) (let ((_let_2 (tptp.pp P2))) (and (=> _let_2 (= _let_1 tptp.one_one_real)) (=> (not _let_2) (= _let_1 tptp.zero_zero_real)))))) (forall ((P2 tptp.bool)) (let ((_let_1 (tptp.zero_n2052037380579107095ol_rat P2))) (let ((_let_2 (tptp.pp P2))) (and (=> _let_2 (= _let_1 tptp.one_one_rat)) (=> (not _let_2) (= _let_1 tptp.zero_zero_rat)))))) (forall ((P2 tptp.bool)) (let ((_let_1 (tptp.zero_n2687167440665602831ol_nat P2))) (let ((_let_2 (tptp.pp P2))) (and (=> _let_2 (= _let_1 tptp.one_one_nat)) (=> (not _let_2) (= _let_1 tptp.zero_zero_nat)))))) (forall ((P2 tptp.bool)) (let ((_let_1 (tptp.aa_bool_int tptp.zero_n2684676970156552555ol_int P2))) (let ((_let_2 (tptp.pp P2))) (and (=> _let_2 (= _let_1 tptp.one_one_int)) (=> (not _let_2) (= _let_1 tptp.zero_zero_int)))))) (forall ((P2 tptp.bool)) (let ((_let_1 (tptp.zero_n356916108424825756nteger P2))) (let ((_let_2 (tptp.pp P2))) (and (=> _let_2 (= _let_1 tptp.one_one_Code_integer)) (=> (not _let_2) (= _let_1 tptp.zero_z3403309356797280102nteger)))))) (forall ((P tptp.fun_complex_bool) (P2 tptp.bool)) (let ((_let_1 (tptp.pp P2))) (= (tptp.pp (tptp.aa_complex_bool P (tptp.zero_n1201886186963655149omplex P2))) (and (=> _let_1 (tptp.pp (tptp.aa_complex_bool P tptp.one_one_complex))) (=> (not _let_1) (tptp.pp (tptp.aa_complex_bool P tptp.zero_zero_complex))))))) (forall ((P tptp.fun_real_bool) (P2 tptp.bool)) (let ((_let_1 (tptp.pp P2))) (= (tptp.pp (tptp.aa_real_bool P (tptp.zero_n3304061248610475627l_real P2))) (and (=> _let_1 (tptp.pp (tptp.aa_real_bool P tptp.one_one_real))) (=> (not _let_1) (tptp.pp (tptp.aa_real_bool P tptp.zero_zero_real))))))) (forall ((P tptp.fun_rat_bool) (P2 tptp.bool)) (let ((_let_1 (tptp.pp P2))) (= (tptp.pp (tptp.aa_rat_bool P (tptp.zero_n2052037380579107095ol_rat P2))) (and (=> _let_1 (tptp.pp (tptp.aa_rat_bool P tptp.one_one_rat))) (=> (not _let_1) (tptp.pp (tptp.aa_rat_bool P tptp.zero_zero_rat))))))) (forall ((P tptp.fun_nat_bool) (P2 tptp.bool)) (let ((_let_1 (tptp.pp P2))) (= (tptp.pp (tptp.aa_nat_bool P (tptp.zero_n2687167440665602831ol_nat P2))) (and (=> _let_1 (tptp.pp (tptp.aa_nat_bool P tptp.one_one_nat))) (=> (not _let_1) (tptp.pp (tptp.aa_nat_bool P tptp.zero_zero_nat))))))) (forall ((P tptp.fun_int_bool) (P2 tptp.bool)) (let ((_let_1 (tptp.pp P2))) (= (tptp.pp (tptp.aa_int_bool P (tptp.aa_bool_int tptp.zero_n2684676970156552555ol_int P2))) (and (=> _let_1 (tptp.pp (tptp.aa_int_bool P tptp.one_one_int))) (=> (not _let_1) (tptp.pp (tptp.aa_int_bool P tptp.zero_zero_int))))))) (forall ((P tptp.fun_Co8822979462182099027r_bool) (P2 tptp.bool)) (let ((_let_1 (tptp.pp P2))) (= (tptp.pp (tptp.aa_Code_integer_bool P (tptp.zero_n356916108424825756nteger P2))) (and (=> _let_1 (tptp.pp (tptp.aa_Code_integer_bool P tptp.one_one_Code_integer))) (=> (not _let_1) (tptp.pp (tptp.aa_Code_integer_bool P tptp.zero_z3403309356797280102nteger))))))) (forall ((P tptp.fun_complex_bool) (P2 tptp.bool)) (let ((_let_1 (tptp.pp P2))) (= (tptp.pp (tptp.aa_complex_bool P (tptp.zero_n1201886186963655149omplex P2))) (not (or (and _let_1 (not (tptp.pp (tptp.aa_complex_bool P tptp.one_one_complex)))) (and (not _let_1) (not (tptp.pp (tptp.aa_complex_bool P tptp.zero_zero_complex))))))))) (forall ((P tptp.fun_real_bool) (P2 tptp.bool)) (let ((_let_1 (tptp.pp P2))) (= (tptp.pp (tptp.aa_real_bool P (tptp.zero_n3304061248610475627l_real P2))) (not (or (and _let_1 (not (tptp.pp (tptp.aa_real_bool P tptp.one_one_real)))) (and (not _let_1) (not (tptp.pp (tptp.aa_real_bool P tptp.zero_zero_real))))))))) (forall ((P tptp.fun_rat_bool) (P2 tptp.bool)) (let ((_let_1 (tptp.pp P2))) (= (tptp.pp (tptp.aa_rat_bool P (tptp.zero_n2052037380579107095ol_rat P2))) (not (or (and _let_1 (not (tptp.pp (tptp.aa_rat_bool P tptp.one_one_rat)))) (and (not _let_1) (not (tptp.pp (tptp.aa_rat_bool P tptp.zero_zero_rat))))))))) (forall ((P tptp.fun_nat_bool) (P2 tptp.bool)) (let ((_let_1 (tptp.pp P2))) (= (tptp.pp (tptp.aa_nat_bool P (tptp.zero_n2687167440665602831ol_nat P2))) (not (or (and _let_1 (not (tptp.pp (tptp.aa_nat_bool P tptp.one_one_nat)))) (and (not _let_1) (not (tptp.pp (tptp.aa_nat_bool P tptp.zero_zero_nat))))))))) (forall ((P tptp.fun_int_bool) (P2 tptp.bool)) (let ((_let_1 (tptp.pp P2))) (= (tptp.pp (tptp.aa_int_bool P (tptp.aa_bool_int tptp.zero_n2684676970156552555ol_int P2))) (not (or (and _let_1 (not (tptp.pp (tptp.aa_int_bool P tptp.one_one_int)))) (and (not _let_1) (not (tptp.pp (tptp.aa_int_bool P tptp.zero_zero_int))))))))) (forall ((P tptp.fun_Co8822979462182099027r_bool) (P2 tptp.bool)) (let ((_let_1 (tptp.pp P2))) (= (tptp.pp (tptp.aa_Code_integer_bool P (tptp.zero_n356916108424825756nteger P2))) (not (or (and _let_1 (not (tptp.pp (tptp.aa_Code_integer_bool P tptp.one_one_Code_integer)))) (and (not _let_1) (not (tptp.pp (tptp.aa_Code_integer_bool P tptp.zero_z3403309356797280102nteger))))))))) (forall ((M tptp.num) (N tptp.num)) (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_num_real tptp.numeral_numeral_real M)) (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real N)))))) (forall ((M tptp.num) (N tptp.num)) (not (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger M)) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger N)))))) (forall ((M tptp.num) (N tptp.num)) (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_num_rat tptp.numeral_numeral_rat M)) (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat N)))))) (forall ((M tptp.num) (N tptp.num)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_num_int tptp.numeral_numeral_int M)) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int N)))))) (forall ((M tptp.num) (N tptp.num)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real M))) (tptp.aa_num_real tptp.numeral_numeral_real N)))) (forall ((M tptp.num) (N tptp.num)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger M))) (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger N)))) (forall ((M tptp.num) (N tptp.num)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat M))) (tptp.aa_num_rat tptp.numeral_numeral_rat N)))) (forall ((M tptp.num) (N tptp.num)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int M))) (tptp.aa_num_int tptp.numeral_numeral_int N)))) (forall ((N tptp.num)) (not (= tptp.zero_zero_real (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real N))))) (forall ((N tptp.num)) (not (= tptp.zero_zero_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int N))))) (forall ((N tptp.num)) (not (= tptp.zero_zero_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.numera6690914467698888265omplex N))))) (forall ((N tptp.num)) (not (= tptp.zero_z3403309356797280102nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger N))))) (forall ((N tptp.num)) (not (= tptp.zero_zero_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat N))))) (forall ((M tptp.num) (N tptp.num)) (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_num_real tptp.numeral_numeral_real M)) (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real N)))))) (forall ((M tptp.num) (N tptp.num)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_num_int tptp.numeral_numeral_int M)) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int N)))))) (forall ((M tptp.num) (N tptp.num)) (not (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger M)) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger N)))))) (forall ((M tptp.num) (N tptp.num)) (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_num_rat tptp.numeral_numeral_rat M)) (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat N)))))) (forall ((M tptp.num) (N tptp.num)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real M))) (tptp.aa_num_real tptp.numeral_numeral_real N)))) (forall ((M tptp.num) (N tptp.num)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int M))) (tptp.aa_num_int tptp.numeral_numeral_int N)))) (forall ((M tptp.num) (N tptp.num)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger M))) (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger N)))) (forall ((M tptp.num) (N tptp.num)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat M))) (tptp.aa_num_rat tptp.numeral_numeral_rat N)))) (tptp.pp (tptp.aa_real_bool _let_108 tptp.one_one_real)) (tptp.pp (tptp.aa_Code_integer_bool _let_107 tptp.one_one_Code_integer)) (tptp.pp (tptp.aa_rat_bool _let_106 tptp.one_one_rat)) (tptp.pp (tptp.aa_int_bool _let_105 tptp.one_one_int)) (not (tptp.pp (tptp.aa_real_bool _let_116 _let_57))) (not (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) _let_83))) (not (tptp.pp (tptp.aa_rat_bool _let_115 _let_38))) (not (tptp.pp (tptp.aa_int_bool _let_114 _let_37))) (not (= tptp.zero_zero_real _let_57)) (not (= tptp.zero_zero_int _let_37)) (not (= tptp.zero_zero_complex _let_54)) (not (= tptp.zero_z3403309356797280102nteger _let_83)) (not (= tptp.zero_zero_rat _let_38)) (forall ((A tptp.real) (B2 tptp.real)) (= (= (tptp.aa_real_real tptp.uminus_uminus_real A) B2) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) B2) tptp.zero_zero_real))) (forall ((A tptp.int) (B2 tptp.int)) (= (= (tptp.aa_int_int tptp.uminus_uminus_int A) B2) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) B2) tptp.zero_zero_int))) (forall ((A tptp.complex) (B2 tptp.complex)) (= (= (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex A) B2) (= (tptp.aa_complex_complex (tptp.plus_plus_complex A) B2) tptp.zero_zero_complex))) (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (= (= (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A) B2) (= (tptp.plus_p5714425477246183910nteger A B2) tptp.zero_z3403309356797280102nteger))) (forall ((A tptp.rat) (B2 tptp.rat)) (= (= (tptp.aa_rat_rat tptp.uminus_uminus_rat A) B2) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) B2) tptp.zero_zero_rat))) (forall ((A tptp.real) (B2 tptp.real)) (= (= A (tptp.aa_real_real tptp.uminus_uminus_real B2)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) B2) tptp.zero_zero_real))) (forall ((A tptp.int) (B2 tptp.int)) (= (= A (tptp.aa_int_int tptp.uminus_uminus_int B2)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) B2) tptp.zero_zero_int))) (forall ((A tptp.complex) (B2 tptp.complex)) (= (= A (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex B2)) (= (tptp.aa_complex_complex (tptp.plus_plus_complex A) B2) tptp.zero_zero_complex))) (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (= (= A (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger B2)) (= (tptp.plus_p5714425477246183910nteger A B2) tptp.zero_z3403309356797280102nteger))) (forall ((A tptp.rat) (B2 tptp.rat)) (= (= A (tptp.aa_rat_rat tptp.uminus_uminus_rat B2)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) B2) tptp.zero_zero_rat))) (forall ((A tptp.real) (B2 tptp.real)) (=> (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) B2) tptp.zero_zero_real) (= (tptp.aa_real_real tptp.uminus_uminus_real A) B2))) (forall ((A tptp.int) (B2 tptp.int)) (=> (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) B2) tptp.zero_zero_int) (= (tptp.aa_int_int tptp.uminus_uminus_int A) B2))) (forall ((A tptp.complex) (B2 tptp.complex)) (=> (= (tptp.aa_complex_complex (tptp.plus_plus_complex A) B2) tptp.zero_zero_complex) (= (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex A) B2))) (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (=> (= (tptp.plus_p5714425477246183910nteger A B2) tptp.zero_z3403309356797280102nteger) (= (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A) B2))) (forall ((A tptp.rat) (B2 tptp.rat)) (=> (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) B2) tptp.zero_zero_rat) (= (tptp.aa_rat_rat tptp.uminus_uminus_rat A) B2))) (forall ((A tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real tptp.uminus_uminus_real A)) A) tptp.zero_zero_real)) (forall ((A tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int tptp.uminus_uminus_int A)) A) tptp.zero_zero_int)) (forall ((A tptp.complex)) (= (tptp.aa_complex_complex (tptp.plus_plus_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex A)) A) tptp.zero_zero_complex)) (forall ((A tptp.code_integer)) (= (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A) A) tptp.zero_z3403309356797280102nteger)) (forall ((A tptp.rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat A)) A) tptp.zero_zero_rat)) (forall ((A tptp.real) (B2 tptp.real)) (= (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) B2) tptp.zero_zero_real) (= B2 (tptp.aa_real_real tptp.uminus_uminus_real A)))) (forall ((A tptp.int) (B2 tptp.int)) (= (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) B2) tptp.zero_zero_int) (= B2 (tptp.aa_int_int tptp.uminus_uminus_int A)))) (forall ((A tptp.complex) (B2 tptp.complex)) (= (= (tptp.aa_complex_complex (tptp.plus_plus_complex A) B2) tptp.zero_zero_complex) (= B2 (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex A)))) (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (= (= (tptp.plus_p5714425477246183910nteger A B2) tptp.zero_z3403309356797280102nteger) (= B2 (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A)))) (forall ((A tptp.rat) (B2 tptp.rat)) (= (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) B2) tptp.zero_zero_rat) (= B2 (tptp.aa_rat_rat tptp.uminus_uminus_rat A)))) (tptp.pp (tptp.aa_real_bool _let_102 tptp.one_one_real)) (tptp.pp (tptp.aa_int_bool _let_101 tptp.one_one_int)) (tptp.pp (tptp.aa_Code_integer_bool _let_100 tptp.one_one_Code_integer)) (tptp.pp (tptp.aa_rat_bool _let_99 tptp.one_one_rat)) (not (tptp.pp (tptp.aa_real_bool _let_113 _let_57))) (not (tptp.pp (tptp.aa_int_bool _let_112 _let_37))) (not (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) _let_83))) (not (tptp.pp (tptp.aa_rat_bool _let_111 _let_38))) (forall ((W tptp.num) (X tptp.real)) (let ((_let_1 (tptp.aa_num_real tptp.numeral_numeral_real W))) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real _let_1) (tptp.aa_real_real tptp.uminus_uminus_real X)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real X) (tptp.aa_real_real tptp.uminus_uminus_real _let_1))))) (forall ((W tptp.num) (X tptp.int)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int W))) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int _let_1) (tptp.aa_int_int tptp.uminus_uminus_int X)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int X) (tptp.aa_int_int tptp.uminus_uminus_int _let_1))))) (forall ((W tptp.num) (X tptp.complex)) (let ((_let_1 (tptp.numera6690914467698888265omplex W))) (= (tptp.aa_complex_complex (tptp.times_times_complex _let_1) (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex X)) (tptp.aa_complex_complex (tptp.times_times_complex X) (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex _let_1))))) (forall ((W tptp.num) (X tptp.code_integer)) (let ((_let_1 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger W))) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger _let_1) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger X)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger X) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger _let_1))))) (forall ((W tptp.num) (X tptp.rat)) (let ((_let_1 (tptp.aa_num_rat tptp.numeral_numeral_rat W))) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat _let_1) (tptp.aa_rat_rat tptp.uminus_uminus_rat X)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat X) (tptp.aa_rat_rat tptp.uminus_uminus_rat _let_1))))) (forall ((B2 tptp.real) (A tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real A))) (=> (not (= B2 tptp.zero_zero_real)) (= (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_real_real _let_1 B2)) (tptp.aa_real_real _let_1 (tptp.aa_real_real tptp.uminus_uminus_real B2)))))) (forall ((B2 tptp.complex) (A tptp.complex)) (let ((_let_1 (tptp.divide1717551699836669952omplex A))) (=> (not (= B2 tptp.zero_zero_complex)) (= (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.aa_complex_complex _let_1 B2)) (tptp.aa_complex_complex _let_1 (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex B2)))))) (forall ((B2 tptp.rat) (A tptp.rat)) (let ((_let_1 (tptp.divide_divide_rat A))) (=> (not (= B2 tptp.zero_zero_rat)) (= (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_rat_rat _let_1 B2)) (tptp.aa_rat_rat _let_1 (tptp.aa_rat_rat tptp.uminus_uminus_rat B2)))))) (forall ((B2 tptp.real) (A tptp.real)) (=> (not (= B2 tptp.zero_zero_real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real tptp.uminus_uminus_real A)) (tptp.aa_real_real tptp.uminus_uminus_real B2)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real A) B2)))) (forall ((B2 tptp.complex) (A tptp.complex)) (=> (not (= B2 tptp.zero_zero_complex)) (= (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex A)) (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex B2)) (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex A) B2)))) (forall ((B2 tptp.rat) (A tptp.rat)) (=> (not (= B2 tptp.zero_zero_rat)) (= (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat A)) (tptp.aa_rat_rat tptp.uminus_uminus_rat B2)) (tptp.aa_rat_rat (tptp.divide_divide_rat A) B2)))) (forall ((N tptp.num)) (not (= tptp.one_one_real (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real N))))) (forall ((N tptp.num)) (not (= tptp.one_one_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int N))))) (forall ((N tptp.num)) (not (= tptp.one_one_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.numera6690914467698888265omplex N))))) (forall ((N tptp.num)) (not (= tptp.one_one_Code_integer (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger N))))) (forall ((N tptp.num)) (not (= tptp.one_one_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat N))))) (forall ((N tptp.num)) (not (= (tptp.aa_num_real tptp.numeral_numeral_real N) (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)))) (forall ((N tptp.num)) (not (= (tptp.aa_num_int tptp.numeral_numeral_int N) (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int)))) (forall ((N tptp.num)) (not (= (tptp.numera6690914467698888265omplex N) (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex tptp.one_one_complex)))) (forall ((N tptp.num)) (not (= (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger N) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))) (forall ((N tptp.num)) (not (= (tptp.aa_num_rat tptp.numeral_numeral_rat N) (tptp.aa_rat_rat tptp.uminus_uminus_rat tptp.one_one_rat)))) (forall ((X tptp.real)) (= (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real X) X) tptp.one_one_real) (or (= X tptp.one_one_real) (= X (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real))))) (forall ((X tptp.int)) (= (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int X) X) tptp.one_one_int) (or (= X tptp.one_one_int) (= X (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int))))) (forall ((X tptp.complex)) (= (= (tptp.aa_complex_complex (tptp.times_times_complex X) X) tptp.one_one_complex) (or (= X tptp.one_one_complex) (= X (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex tptp.one_one_complex))))) (forall ((X tptp.code_integer)) (= (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger X) X) tptp.one_one_Code_integer) (or (= X tptp.one_one_Code_integer) (= X (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))) (forall ((X tptp.rat)) (= (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat X) X) tptp.one_one_rat) (or (= X tptp.one_one_rat) (= X (tptp.aa_rat_rat tptp.uminus_uminus_rat tptp.one_one_rat))))) (forall ((A tptp.real) (B2 tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A) B2) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) (tptp.aa_real_real tptp.uminus_uminus_real B2)))) (forall ((A tptp.int) (B2 tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) B2) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) (tptp.aa_int_int tptp.uminus_uminus_int B2)))) (forall ((A tptp.complex) (B2 tptp.complex)) (= (tptp.aa_complex_complex (tptp.minus_minus_complex A) B2) (tptp.aa_complex_complex (tptp.plus_plus_complex A) (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex B2)))) (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (= (tptp.minus_8373710615458151222nteger A B2) (tptp.plus_p5714425477246183910nteger A (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger B2)))) (forall ((A tptp.rat) (B2 tptp.rat)) (= (tptp.aa_rat_rat (tptp.minus_minus_rat A) B2) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) (tptp.aa_rat_rat tptp.uminus_uminus_rat B2)))) (forall ((A tptp.real) (B2 tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A) B2) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) (tptp.aa_real_real tptp.uminus_uminus_real B2)))) (forall ((A tptp.int) (B2 tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) B2) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) (tptp.aa_int_int tptp.uminus_uminus_int B2)))) (forall ((A tptp.complex) (B2 tptp.complex)) (= (tptp.aa_complex_complex (tptp.minus_minus_complex A) B2) (tptp.aa_complex_complex (tptp.plus_plus_complex A) (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex B2)))) (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (= (tptp.minus_8373710615458151222nteger A B2) (tptp.plus_p5714425477246183910nteger A (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger B2)))) (forall ((A tptp.rat) (B2 tptp.rat)) (= (tptp.aa_rat_rat (tptp.minus_minus_rat A) B2) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) (tptp.aa_rat_rat tptp.uminus_uminus_rat B2)))) (forall ((B4 tptp.real) (K tptp.real) (B2 tptp.real) (A tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A))) (=> (= B4 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real K) B2)) (= (tptp.aa_real_real _let_1 B4) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real tptp.uminus_uminus_real K)) (tptp.aa_real_real _let_1 B2)))))) (forall ((B4 tptp.int) (K tptp.int) (B2 tptp.int) (A tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.minus_minus_int A))) (=> (= B4 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int K) B2)) (= (tptp.aa_int_int _let_1 B4) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int tptp.uminus_uminus_int K)) (tptp.aa_int_int _let_1 B2)))))) (forall ((B4 tptp.complex) (K tptp.complex) (B2 tptp.complex) (A tptp.complex)) (let ((_let_1 (tptp.minus_minus_complex A))) (=> (= B4 (tptp.aa_complex_complex (tptp.plus_plus_complex K) B2)) (= (tptp.aa_complex_complex _let_1 B4) (tptp.aa_complex_complex (tptp.plus_plus_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex K)) (tptp.aa_complex_complex _let_1 B2)))))) (forall ((B4 tptp.code_integer) (K tptp.code_integer) (B2 tptp.code_integer) (A tptp.code_integer)) (=> (= B4 (tptp.plus_p5714425477246183910nteger K B2)) (= (tptp.minus_8373710615458151222nteger A B4) (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger K) (tptp.minus_8373710615458151222nteger A B2))))) (forall ((B4 tptp.rat) (K tptp.rat) (B2 tptp.rat) (A tptp.rat)) (let ((_let_1 (tptp.minus_minus_rat A))) (=> (= B4 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat K) B2)) (= (tptp.aa_rat_rat _let_1 B4) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat K)) (tptp.aa_rat_rat _let_1 B2)))))) (forall ((Xs tptp.list_int) (X tptp.int)) (=> (forall ((X4 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X4) (tptp.set_int2 Xs))) (= X4 X))) (= (tptp.replicate_int (tptp.size_size_list_int Xs) X) Xs))) (forall ((Xs tptp.list_VEBT_VEBT) (X tptp.vEBT_VEBT)) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (tptp.pp (tptp.aa_set8260762808118238015T_bool (tptp.aa_VEB289770264548726718T_bool tptp.member_VEBT_VEBT X4) (tptp.set_VEBT_VEBT2 Xs))) (= X4 X))) (= (tptp.replicate_VEBT_VEBT (tptp.size_s6755466524823107622T_VEBT Xs) X) Xs))) (forall ((Xs tptp.list_bool) (X tptp.bool)) (=> (forall ((X4 tptp.bool)) (=> (tptp.member_bool X4 (tptp.set_bool2 Xs)) (= (tptp.pp X4) (tptp.pp X)))) (= (tptp.replicate_bool (tptp.size_size_list_bool Xs) X) Xs))) (forall ((Xs tptp.list_nat) (X tptp.nat)) (=> (forall ((X4 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X4) (tptp.set_nat2 Xs))) (= X4 X))) (= (tptp.replicate_nat (tptp.size_size_list_nat Xs) X) Xs))) (forall ((Xs tptp.list_real) (N tptp.nat) (X tptp.real)) (=> (= (tptp.size_size_list_real Xs) N) (=> (forall ((Y4 tptp.real)) (=> (tptp.member_real Y4 (tptp.set_real2 Xs)) (= Y4 X))) (= Xs (tptp.replicate_real N X))))) (forall ((Xs tptp.list_complex) (N tptp.nat) (X tptp.complex)) (=> (= (tptp.size_s3451745648224563538omplex Xs) N) (=> (forall ((Y4 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex Y4) (tptp.set_complex2 Xs))) (= Y4 X))) (= Xs (tptp.replicate_complex N X))))) (forall ((Xs tptp.list_int) (N tptp.nat) (X tptp.int)) (=> (= (tptp.size_size_list_int Xs) N) (=> (forall ((Y4 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Y4) (tptp.set_int2 Xs))) (= Y4 X))) (= Xs (tptp.replicate_int N X))))) (forall ((Xs tptp.list_VEBT_VEBT) (N tptp.nat) (X tptp.vEBT_VEBT)) (=> (= (tptp.size_s6755466524823107622T_VEBT Xs) N) (=> (forall ((Y4 tptp.vEBT_VEBT)) (=> (tptp.pp (tptp.aa_set8260762808118238015T_bool (tptp.aa_VEB289770264548726718T_bool tptp.member_VEBT_VEBT Y4) (tptp.set_VEBT_VEBT2 Xs))) (= Y4 X))) (= Xs (tptp.replicate_VEBT_VEBT N X))))) (forall ((Xs tptp.list_bool) (N tptp.nat) (X tptp.bool)) (=> (= (tptp.size_size_list_bool Xs) N) (=> (forall ((Y4 tptp.bool)) (=> (tptp.member_bool Y4 (tptp.set_bool2 Xs)) (= (tptp.pp Y4) (tptp.pp X)))) (= Xs (tptp.replicate_bool N X))))) (forall ((Xs tptp.list_nat) (N tptp.nat) (X tptp.nat)) (=> (= (tptp.size_size_list_nat Xs) N) (=> (forall ((Y4 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat Y4) (tptp.set_nat2 Xs))) (= Y4 X))) (= Xs (tptp.replicate_nat N X))))) (forall ((B2 tptp.real) (A tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.dvd_dvd_real B2) A)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real tptp.uminus_uminus_real A)) B2) (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real A) B2))))) (forall ((B2 tptp.int) (A tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int B2) A)) (= (tptp.aa_int_int (tptp.divide_divide_int (tptp.aa_int_int tptp.uminus_uminus_int A)) B2) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_int_int (tptp.divide_divide_int A) B2))))) (forall ((B2 tptp.complex) (A tptp.complex)) (=> (tptp.pp (tptp.aa_complex_bool (tptp.aa_com1553036987509291606x_bool tptp.dvd_dvd_complex B2) A)) (= (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex A)) B2) (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex A) B2))))) (forall ((B2 tptp.code_integer) (A tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer B2) A)) (= (tptp.divide6298287555418463151nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A) B2) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.divide6298287555418463151nteger A B2))))) (forall ((B2 tptp.rat) (A tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.dvd_dvd_rat B2) A)) (= (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat A)) B2) (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_rat_rat (tptp.divide_divide_rat A) B2))))) (forall ((B2 tptp.real) (A tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real A))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.dvd_dvd_real B2) A)) (= (tptp.aa_real_real _let_1 (tptp.aa_real_real tptp.uminus_uminus_real B2)) (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_real_real _let_1 B2)))))) (forall ((B2 tptp.int) (A tptp.int)) (let ((_let_1 (tptp.divide_divide_int A))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int B2) A)) (= (tptp.aa_int_int _let_1 (tptp.aa_int_int tptp.uminus_uminus_int B2)) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_int_int _let_1 B2)))))) (forall ((B2 tptp.complex) (A tptp.complex)) (let ((_let_1 (tptp.divide1717551699836669952omplex A))) (=> (tptp.pp (tptp.aa_complex_bool (tptp.aa_com1553036987509291606x_bool tptp.dvd_dvd_complex B2) A)) (= (tptp.aa_complex_complex _let_1 (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex B2)) (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.aa_complex_complex _let_1 B2)))))) (forall ((B2 tptp.code_integer) (A tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer B2) A)) (= (tptp.divide6298287555418463151nteger A (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger B2)) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.divide6298287555418463151nteger A B2))))) (forall ((B2 tptp.rat) (A tptp.rat)) (let ((_let_1 (tptp.divide_divide_rat A))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.dvd_dvd_rat B2) A)) (= (tptp.aa_rat_rat _let_1 (tptp.aa_rat_rat tptp.uminus_uminus_rat B2)) (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_rat_rat _let_1 B2)))))) (forall ((A4 tptp.set_nat)) (= (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat A4) (tptp.uminus5710092332889474511et_nat A4))) (= A4 tptp.bot_bot_set_nat))) (forall ((A4 tptp.set_real)) (= (tptp.ord_less_eq_set_real A4 (tptp.uminus612125837232591019t_real A4)) (= A4 tptp.bot_bot_set_real))) (forall ((A4 tptp.set_int)) (= (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int A4) (tptp.uminus1532241313380277803et_int A4))) (= A4 tptp.bot_bot_set_int))) (forall ((U tptp.real) (X tptp.real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real U) U))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real X) X)))) (forall ((M tptp.int) (N tptp.int)) (=> (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int M) N) tptp.one_one_int) (or (= M tptp.one_one_int) (= M (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int))))) (forall ((M tptp.int) (N tptp.int)) (let ((_let_1 (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int))) (= (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int M) N) tptp.one_one_int) (or (and (= M tptp.one_one_int) (= N tptp.one_one_int)) (and (= M _let_1) (= N _let_1)))))) (forall ((X tptp.real) (Y tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real X) Y) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) (tptp.aa_real_real tptp.uminus_uminus_real Y)))) (forall ((N tptp.num)) (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real N)))))) (forall ((N tptp.num)) (not (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger N)))))) (forall ((N tptp.num)) (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat N)))))) (forall ((N tptp.num)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int N)))))) (forall ((N tptp.num)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real N))) tptp.zero_zero_real))) (forall ((N tptp.num)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger N))) tptp.zero_z3403309356797280102nteger))) (forall ((N tptp.num)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat N))) tptp.zero_zero_rat))) (forall ((N tptp.num)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int N))) tptp.zero_zero_int))) (forall ((N tptp.num)) (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real N)))))) (forall ((N tptp.num)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int N)))))) (forall ((N tptp.num)) (not (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger N)))))) (forall ((N tptp.num)) (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat N)))))) (forall ((N tptp.num)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real N))) tptp.zero_zero_real))) (forall ((N tptp.num)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int N))) tptp.zero_zero_int))) (forall ((N tptp.num)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger N))) tptp.zero_z3403309356797280102nteger))) (forall ((N tptp.num)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat N))) tptp.zero_zero_rat))) (not (tptp.pp (tptp.aa_real_bool _let_75 _let_57))) (not (tptp.pp (tptp.aa_Code_integer_bool _let_40 _let_83))) (not (tptp.pp (tptp.aa_rat_bool _let_110 _let_38))) (not (tptp.pp (tptp.aa_int_bool _let_109 _let_37))) (tptp.pp (tptp.aa_real_bool _let_108 tptp.zero_zero_real)) (tptp.pp (tptp.aa_Code_integer_bool _let_107 tptp.zero_z3403309356797280102nteger)) (tptp.pp (tptp.aa_rat_bool _let_106 tptp.zero_zero_rat)) (tptp.pp (tptp.aa_int_bool _let_105 tptp.zero_zero_int)) (not (tptp.pp (tptp.aa_real_bool _let_76 _let_57))) (not (tptp.pp (tptp.aa_int_bool _let_104 _let_37))) (not (tptp.pp (tptp.aa_Code_integer_bool _let_39 _let_83))) (not (tptp.pp (tptp.aa_rat_bool _let_103 _let_38))) (tptp.pp (tptp.aa_real_bool _let_102 tptp.zero_zero_real)) (tptp.pp (tptp.aa_int_bool _let_101 tptp.zero_zero_int)) (tptp.pp (tptp.aa_Code_integer_bool _let_100 tptp.zero_z3403309356797280102nteger)) (tptp.pp (tptp.aa_rat_bool _let_99 tptp.zero_zero_rat)) (forall ((M tptp.num)) (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.one_one_real) (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real M)))))) (forall ((M tptp.num)) (not (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger M)))))) (forall ((M tptp.num)) (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.one_one_rat) (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat M)))))) (forall ((M tptp.num)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.one_one_int) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int M)))))) (forall ((M tptp.num)) (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_num_real tptp.numeral_numeral_real M)) (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real))))) (forall ((M tptp.num)) (not (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger M)) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))) (forall ((M tptp.num)) (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_num_rat tptp.numeral_numeral_rat M)) (tptp.aa_rat_rat tptp.uminus_uminus_rat tptp.one_one_rat))))) (forall ((M tptp.num)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_num_int tptp.numeral_numeral_int M)) (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int))))) (forall ((M tptp.num)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real M))) (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)))) (forall ((M tptp.num)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger M))) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))) (forall ((M tptp.num)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat M))) (tptp.aa_rat_rat tptp.uminus_uminus_rat tptp.one_one_rat)))) (forall ((M tptp.num)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int M))) (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int)))) (forall ((M tptp.num)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)) (tptp.aa_num_real tptp.numeral_numeral_real M)))) (forall ((M tptp.num)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger M)))) (forall ((M tptp.num)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat tptp.one_one_rat)) (tptp.aa_num_rat tptp.numeral_numeral_rat M)))) (forall ((M tptp.num)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int)) (tptp.aa_num_int tptp.numeral_numeral_int M)))) (forall ((M tptp.num)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real M))) tptp.one_one_real))) (forall ((M tptp.num)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger M))) tptp.one_one_Code_integer))) (forall ((M tptp.num)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat M))) tptp.one_one_rat))) (forall ((M tptp.num)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int M))) tptp.one_one_int))) (forall ((M tptp.num)) (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)) (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real M)))))) (forall ((M tptp.num)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int)) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int M)))))) (forall ((M tptp.num)) (not (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger M)))))) (forall ((M tptp.num)) (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat tptp.one_one_rat)) (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat M)))))) (forall ((M tptp.num)) (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real) (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real M)))))) (forall ((M tptp.num)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.one_one_int) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int M)))))) (forall ((M tptp.num)) (not (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger M)))))) (forall ((M tptp.num)) (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.one_one_rat) (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat M)))))) (forall ((M tptp.num)) (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_num_real tptp.numeral_numeral_real M)) (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real))))) (forall ((M tptp.num)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_num_int tptp.numeral_numeral_int M)) (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int))))) (forall ((M tptp.num)) (not (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger M)) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))) (forall ((M tptp.num)) (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_num_rat tptp.numeral_numeral_rat M)) (tptp.aa_rat_rat tptp.uminus_uminus_rat tptp.one_one_rat))))) (forall ((M tptp.num)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)) (tptp.aa_num_real tptp.numeral_numeral_real M)))) (forall ((M tptp.num)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int)) (tptp.aa_num_int tptp.numeral_numeral_int M)))) (forall ((M tptp.num)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger M)))) (forall ((M tptp.num)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat tptp.one_one_rat)) (tptp.aa_num_rat tptp.numeral_numeral_rat M)))) (forall ((M tptp.num)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real M))) tptp.one_one_real))) (forall ((M tptp.num)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int M))) tptp.one_one_int))) (forall ((M tptp.num)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger M))) tptp.one_one_Code_integer))) (forall ((M tptp.num)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat M))) tptp.one_one_rat))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (= C tptp.zero_zero_real))) (= (= A (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real B2) C))) (and (=> (not _let_1) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) C) (tptp.aa_real_real tptp.uminus_uminus_real B2))) (=> _let_1 (= A tptp.zero_zero_real)))))) (forall ((A tptp.complex) (B2 tptp.complex) (C tptp.complex)) (let ((_let_1 (= C tptp.zero_zero_complex))) (= (= A (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex B2) C))) (and (=> (not _let_1) (= (tptp.aa_complex_complex (tptp.times_times_complex A) C) (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex B2))) (=> _let_1 (= A tptp.zero_zero_complex)))))) (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (= C tptp.zero_zero_rat))) (= (= A (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_rat_rat (tptp.divide_divide_rat B2) C))) (and (=> (not _let_1) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) C) (tptp.aa_rat_rat tptp.uminus_uminus_rat B2))) (=> _let_1 (= A tptp.zero_zero_rat)))))) (forall ((B2 tptp.real) (C tptp.real) (A tptp.real)) (let ((_let_1 (= C tptp.zero_zero_real))) (= (= (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real B2) C)) A) (and (=> (not _let_1) (= (tptp.aa_real_real tptp.uminus_uminus_real B2) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) C))) (=> _let_1 (= A tptp.zero_zero_real)))))) (forall ((B2 tptp.complex) (C tptp.complex) (A tptp.complex)) (let ((_let_1 (= C tptp.zero_zero_complex))) (= (= (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex B2) C)) A) (and (=> (not _let_1) (= (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex B2) (tptp.aa_complex_complex (tptp.times_times_complex A) C))) (=> _let_1 (= A tptp.zero_zero_complex)))))) (forall ((B2 tptp.rat) (C tptp.rat) (A tptp.rat)) (let ((_let_1 (= C tptp.zero_zero_rat))) (= (= (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_rat_rat (tptp.divide_divide_rat B2) C)) A) (and (=> (not _let_1) (= (tptp.aa_rat_rat tptp.uminus_uminus_rat B2) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) C))) (=> _let_1 (= A tptp.zero_zero_rat)))))) (forall ((B2 tptp.real) (A tptp.real) (C tptp.real)) (=> (not (= B2 tptp.zero_zero_real)) (= (= (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real A) B2)) C) (= (tptp.aa_real_real tptp.uminus_uminus_real A) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real C) B2))))) (forall ((B2 tptp.complex) (A tptp.complex) (C tptp.complex)) (=> (not (= B2 tptp.zero_zero_complex)) (= (= (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex A) B2)) C) (= (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex A) (tptp.aa_complex_complex (tptp.times_times_complex C) B2))))) (forall ((B2 tptp.rat) (A tptp.rat) (C tptp.rat)) (=> (not (= B2 tptp.zero_zero_rat)) (= (= (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_rat_rat (tptp.divide_divide_rat A) B2)) C) (= (tptp.aa_rat_rat tptp.uminus_uminus_rat A) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat C) B2))))) (forall ((B2 tptp.real) (C tptp.real) (A tptp.real)) (=> (not (= B2 tptp.zero_zero_real)) (= (= C (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real A) B2))) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real C) B2) (tptp.aa_real_real tptp.uminus_uminus_real A))))) (forall ((B2 tptp.complex) (C tptp.complex) (A tptp.complex)) (=> (not (= B2 tptp.zero_zero_complex)) (= (= C (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex A) B2))) (= (tptp.aa_complex_complex (tptp.times_times_complex C) B2) (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex A))))) (forall ((B2 tptp.rat) (C tptp.rat) (A tptp.rat)) (=> (not (= B2 tptp.zero_zero_rat)) (= (= C (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_rat_rat (tptp.divide_divide_rat A) B2))) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat C) B2) (tptp.aa_rat_rat tptp.uminus_uminus_rat A))))) (forall ((B2 tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real B2) (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real tptp.one))) (tptp.aa_real_real tptp.uminus_uminus_real B2))) (forall ((B2 tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B2) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int tptp.one))) (tptp.aa_int_int tptp.uminus_uminus_int B2))) (forall ((B2 tptp.complex)) (= (tptp.aa_complex_complex (tptp.times_times_complex B2) (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.numera6690914467698888265omplex tptp.one))) (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex B2))) (forall ((B2 tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B2) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger tptp.one))) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger B2))) (forall ((B2 tptp.rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat B2) (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat tptp.one))) (tptp.aa_rat_rat tptp.uminus_uminus_rat B2))) (forall ((B2 tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real tptp.one))) B2) (tptp.aa_real_real tptp.uminus_uminus_real B2))) (forall ((B2 tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int tptp.one))) B2) (tptp.aa_int_int tptp.uminus_uminus_int B2))) (forall ((B2 tptp.complex)) (= (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.numera6690914467698888265omplex tptp.one))) B2) (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex B2))) (forall ((B2 tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger tptp.one))) B2) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger B2))) (forall ((B2 tptp.rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat tptp.one))) B2) (tptp.aa_rat_rat tptp.uminus_uminus_rat B2))) (forall ((A tptp.real) (B2 tptp.real)) (= (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real A) B2) (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)) (and (not (= B2 tptp.zero_zero_real)) (= A (tptp.aa_real_real tptp.uminus_uminus_real B2))))) (forall ((A tptp.complex) (B2 tptp.complex)) (= (= (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex A) B2) (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (and (not (= B2 tptp.zero_zero_complex)) (= A (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex B2))))) (forall ((A tptp.rat) (B2 tptp.rat)) (= (= (tptp.aa_rat_rat (tptp.divide_divide_rat A) B2) (tptp.aa_rat_rat tptp.uminus_uminus_rat tptp.one_one_rat)) (and (not (= B2 tptp.zero_zero_rat)) (= A (tptp.aa_rat_rat tptp.uminus_uminus_rat B2))))) (= (tptp.aa_real_real tptp.uminus_uminus_real _let_98) _let_57) (= (tptp.aa_int_int tptp.uminus_uminus_int _let_97) _let_37) (= (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex _let_96) _let_54) (= (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger tptp.one)) _let_83) (= (tptp.aa_rat_rat tptp.uminus_uminus_rat _let_95) _let_38) (forall ((A tptp.real) (N tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real tptp.uminus_uminus_real A)) N) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)) N)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real A) N)))) (forall ((A tptp.int) (N tptp.nat)) (= (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_int_int tptp.uminus_uminus_int A)) N) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int)) N)) (tptp.aa_nat_int (tptp.power_power_int A) N)))) (forall ((A tptp.complex) (N tptp.nat)) (= (tptp.aa_nat_complex (tptp.power_power_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex A)) N) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_nat_complex (tptp.power_power_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex tptp.one_one_complex)) N)) (tptp.aa_nat_complex (tptp.power_power_complex A) N)))) (forall ((A tptp.code_integer) (N tptp.nat)) (= (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A)) N) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) N)) (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger A) N)))) (forall ((A tptp.rat) (N tptp.nat)) (= (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat A)) N) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat tptp.one_one_rat)) N)) (tptp.aa_nat_rat (tptp.power_power_rat A) N)))) (forall ((X tptp.real) (K tptp.num)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 K)))) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real tptp.uminus_uminus_real X)) _let_1) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) _let_1)))) (forall ((X tptp.int) (K tptp.num)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 K)))) (= (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_int_int tptp.uminus_uminus_int X)) _let_1) (tptp.aa_nat_int (tptp.power_power_int X) _let_1)))) (forall ((X tptp.complex) (K tptp.num)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 K)))) (= (tptp.aa_nat_complex (tptp.power_power_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex X)) _let_1) (tptp.aa_nat_complex (tptp.power_power_complex X) _let_1)))) (forall ((X tptp.code_integer) (K tptp.num)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 K)))) (= (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger X)) _let_1) (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger X) _let_1)))) (forall ((X tptp.rat) (K tptp.num)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 K)))) (= (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat X)) _let_1) (tptp.aa_nat_rat (tptp.power_power_rat X) _let_1)))) (forall ((X tptp.real) (Y tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) Y)) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y) (tptp.aa_real_real tptp.uminus_uminus_real X))))) (forall ((X tptp.real) (Y tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) Y))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.uminus_uminus_real X)) Y)))) (forall ((X tptp.real) (Y tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) Y)) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y) (tptp.aa_real_real tptp.uminus_uminus_real X))))) (forall ((X tptp.real) (Y tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) Y))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real X)) Y)))) (forall ((C tptp.real) (B2 tptp.real) (A tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) C)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real B2) C))) A)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.uminus_uminus_real B2)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) C)))))) (forall ((C tptp.rat) (B2 tptp.rat) (A tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) C)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_rat_rat (tptp.divide_divide_rat B2) C))) A)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat B2)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) C)))))) (forall ((C tptp.real) (A tptp.real) (B2 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) C)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real B2) C)))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) C)) (tptp.aa_real_real tptp.uminus_uminus_real B2)))))) (forall ((C tptp.rat) (A tptp.rat) (B2 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) C)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_rat_rat (tptp.divide_divide_rat B2) C)))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) C)) (tptp.aa_rat_rat tptp.uminus_uminus_rat B2)))))) (forall ((C tptp.real) (B2 tptp.real) (A tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real C) tptp.zero_zero_real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real B2) C))) A)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) C)) (tptp.aa_real_real tptp.uminus_uminus_real B2)))))) (forall ((C tptp.rat) (B2 tptp.rat) (A tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat C) tptp.zero_zero_rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_rat_rat (tptp.divide_divide_rat B2) C))) A)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) C)) (tptp.aa_rat_rat tptp.uminus_uminus_rat B2)))))) (forall ((C tptp.real) (A tptp.real) (B2 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real C) tptp.zero_zero_real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real B2) C)))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.uminus_uminus_real B2)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) C)))))) (forall ((C tptp.rat) (A tptp.rat) (B2 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat C) tptp.zero_zero_rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_rat_rat (tptp.divide_divide_rat B2) C)))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat B2)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) C)))))) (forall ((B2 tptp.real) (C tptp.real) (A tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real))) (let ((_let_2 (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real C) tptp.zero_zero_real)))) (let ((_let_3 (tptp.aa_real_real tptp.uminus_uminus_real B2))) (let ((_let_4 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) C))) (let ((_let_5 (tptp.pp (tptp.aa_real_bool _let_1 C)))) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real B2) C))) A)) (and (=> _let_5 (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real _let_3) _let_4))) (=> (not _let_5) (and (=> _let_2 (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real _let_4) _let_3))) (=> (not _let_2) (tptp.pp (tptp.aa_real_bool _let_1 A))))))))))))) (forall ((B2 tptp.rat) (C tptp.rat) (A tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat))) (let ((_let_2 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat C) tptp.zero_zero_rat)))) (let ((_let_3 (tptp.aa_rat_rat tptp.uminus_uminus_rat B2))) (let ((_let_4 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) C))) (let ((_let_5 (tptp.pp (tptp.aa_rat_bool _let_1 C)))) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_rat_rat (tptp.divide_divide_rat B2) C))) A)) (and (=> _let_5 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat _let_3) _let_4))) (=> (not _let_5) (and (=> _let_2 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat _let_4) _let_3))) (=> (not _let_2) (tptp.pp (tptp.aa_rat_bool _let_1 A))))))))))))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A))) (let ((_let_2 (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real C) tptp.zero_zero_real)))) (let ((_let_3 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) C))) (let ((_let_4 (tptp.aa_real_real tptp.uminus_uminus_real B2))) (let ((_let_5 (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) C)))) (= (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real B2) C)))) (and (=> _let_5 (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real _let_3) _let_4))) (=> (not _let_5) (and (=> _let_2 (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real _let_4) _let_3))) (=> (not _let_2) (tptp.pp (tptp.aa_real_bool _let_1 tptp.zero_zero_real))))))))))))) (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A))) (let ((_let_2 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat C) tptp.zero_zero_rat)))) (let ((_let_3 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) C))) (let ((_let_4 (tptp.aa_rat_rat tptp.uminus_uminus_rat B2))) (let ((_let_5 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) C)))) (= (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_rat_rat (tptp.divide_divide_rat B2) C)))) (and (=> _let_5 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat _let_3) _let_4))) (=> (not _let_5) (and (=> _let_2 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat _let_4) _let_3))) (=> (not _let_2) (tptp.pp (tptp.aa_rat_bool _let_1 tptp.zero_zero_rat))))))))))))) (forall ((B2 tptp.real) (C tptp.real) (W tptp.num)) (let ((_let_1 (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real W)))) (let ((_let_2 (= C tptp.zero_zero_real))) (= (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real B2) C) _let_1) (and (=> (not _let_2) (= B2 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real _let_1) C))) (=> _let_2 (= _let_1 tptp.zero_zero_real))))))) (forall ((B2 tptp.complex) (C tptp.complex) (W tptp.num)) (let ((_let_1 (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.numera6690914467698888265omplex W)))) (let ((_let_2 (= C tptp.zero_zero_complex))) (= (= (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex B2) C) _let_1) (and (=> (not _let_2) (= B2 (tptp.aa_complex_complex (tptp.times_times_complex _let_1) C))) (=> _let_2 (= _let_1 tptp.zero_zero_complex))))))) (forall ((B2 tptp.rat) (C tptp.rat) (W tptp.num)) (let ((_let_1 (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat W)))) (let ((_let_2 (= C tptp.zero_zero_rat))) (= (= (tptp.aa_rat_rat (tptp.divide_divide_rat B2) C) _let_1) (and (=> (not _let_2) (= B2 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat _let_1) C))) (=> _let_2 (= _let_1 tptp.zero_zero_rat))))))) (forall ((W tptp.num) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real W)))) (let ((_let_2 (= C tptp.zero_zero_real))) (= (= _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real B2) C)) (and (=> (not _let_2) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real _let_1) C) B2)) (=> _let_2 (= _let_1 tptp.zero_zero_real))))))) (forall ((W tptp.num) (B2 tptp.complex) (C tptp.complex)) (let ((_let_1 (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.numera6690914467698888265omplex W)))) (let ((_let_2 (= C tptp.zero_zero_complex))) (= (= _let_1 (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex B2) C)) (and (=> (not _let_2) (= (tptp.aa_complex_complex (tptp.times_times_complex _let_1) C) B2)) (=> _let_2 (= _let_1 tptp.zero_zero_complex))))))) (forall ((W tptp.num) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat W)))) (let ((_let_2 (= C tptp.zero_zero_rat))) (= (= _let_1 (tptp.aa_rat_rat (tptp.divide_divide_rat B2) C)) (and (=> (not _let_2) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat _let_1) C) B2)) (=> _let_2 (= _let_1 tptp.zero_zero_rat))))))) (forall ((M tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat (tptp.nat_set_decode M)) (tptp.nat_set_decode N))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)))) (forall ((Z tptp.real) (A tptp.real) (B2 tptp.real)) (let ((_let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real A) Z))) B2))) (let ((_let_2 (= Z tptp.zero_zero_real))) (and (=> _let_2 (= _let_1 B2)) (=> (not _let_2) (= _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real tptp.uminus_uminus_real A)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real B2) Z))) Z))))))) (forall ((Z tptp.complex) (A tptp.complex) (B2 tptp.complex)) (let ((_let_1 (tptp.aa_complex_complex (tptp.plus_plus_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex A) Z))) B2))) (let ((_let_2 (= Z tptp.zero_zero_complex))) (and (=> _let_2 (= _let_1 B2)) (=> (not _let_2) (= _let_1 (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex (tptp.aa_complex_complex (tptp.plus_plus_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex A)) (tptp.aa_complex_complex (tptp.times_times_complex B2) Z))) Z))))))) (forall ((Z tptp.rat) (A tptp.rat) (B2 tptp.rat)) (let ((_let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_rat_rat (tptp.divide_divide_rat A) Z))) B2))) (let ((_let_2 (= Z tptp.zero_zero_rat))) (and (=> _let_2 (= _let_1 B2)) (=> (not _let_2) (= _let_1 (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat A)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat B2) Z))) Z))))))) (forall ((Z tptp.real) (X tptp.real) (Y tptp.real)) (=> (not (= Z tptp.zero_zero_real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real X) Z))) Y) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real tptp.uminus_uminus_real X)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real Y) Z))) Z)))) (forall ((Z tptp.complex) (X tptp.complex) (Y tptp.complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (tptp.aa_complex_complex (tptp.plus_plus_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex X) Z))) Y) (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex (tptp.aa_complex_complex (tptp.plus_plus_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex X)) (tptp.aa_complex_complex (tptp.times_times_complex Y) Z))) Z)))) (forall ((Z tptp.rat) (X tptp.rat) (Y tptp.rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_rat_rat (tptp.divide_divide_rat X) Z))) Y) (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat X)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat Y) Z))) Z)))) (forall ((Z tptp.real) (A tptp.real) (B2 tptp.real)) (let ((_let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real A) Z))) B2))) (let ((_let_2 (= Z tptp.zero_zero_real))) (and (=> _let_2 (= _let_1 (tptp.aa_real_real tptp.uminus_uminus_real B2))) (=> (not _let_2) (= _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real tptp.uminus_uminus_real A)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real B2) Z))) Z))))))) (forall ((Z tptp.complex) (A tptp.complex) (B2 tptp.complex)) (let ((_let_1 (tptp.aa_complex_complex (tptp.minus_minus_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex A) Z))) B2))) (let ((_let_2 (= Z tptp.zero_zero_complex))) (and (=> _let_2 (= _let_1 (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex B2))) (=> (not _let_2) (= _let_1 (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex (tptp.aa_complex_complex (tptp.minus_minus_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex A)) (tptp.aa_complex_complex (tptp.times_times_complex B2) Z))) Z))))))) (forall ((Z tptp.rat) (A tptp.rat) (B2 tptp.rat)) (let ((_let_1 (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_rat_rat (tptp.divide_divide_rat A) Z))) B2))) (let ((_let_2 (= Z tptp.zero_zero_rat))) (and (=> _let_2 (= _let_1 (tptp.aa_rat_rat tptp.uminus_uminus_rat B2))) (=> (not _let_2) (= _let_1 (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat A)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat B2) Z))) Z))))))) (forall ((Z tptp.real) (A tptp.real) (B2 tptp.real)) (let ((_let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real A) Z)) B2))) (let ((_let_2 (= Z tptp.zero_zero_real))) (and (=> _let_2 (= _let_1 (tptp.aa_real_real tptp.uminus_uminus_real B2))) (=> (not _let_2) (= _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real B2) Z))) Z))))))) (forall ((Z tptp.complex) (A tptp.complex) (B2 tptp.complex)) (let ((_let_1 (tptp.aa_complex_complex (tptp.minus_minus_complex (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex A) Z)) B2))) (let ((_let_2 (= Z tptp.zero_zero_complex))) (and (=> _let_2 (= _let_1 (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex B2))) (=> (not _let_2) (= _let_1 (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex (tptp.aa_complex_complex (tptp.minus_minus_complex A) (tptp.aa_complex_complex (tptp.times_times_complex B2) Z))) Z))))))) (forall ((Z tptp.rat) (A tptp.rat) (B2 tptp.rat)) (let ((_let_1 (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_rat_rat (tptp.divide_divide_rat A) Z)) B2))) (let ((_let_2 (= Z tptp.zero_zero_rat))) (and (=> _let_2 (= _let_1 (tptp.aa_rat_rat tptp.uminus_uminus_rat B2))) (=> (not _let_2) (= _let_1 (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_rat_rat (tptp.minus_minus_rat A) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat B2) Z))) Z))))))) (forall ((Z tptp.real) (X tptp.real) (Y tptp.real)) (=> (not (= Z tptp.zero_zero_real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real X) Z))) Y) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real tptp.uminus_uminus_real X)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real Y) Z))) Z)))) (forall ((Z tptp.complex) (X tptp.complex) (Y tptp.complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (tptp.aa_complex_complex (tptp.minus_minus_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex X) Z))) Y) (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex (tptp.aa_complex_complex (tptp.minus_minus_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex X)) (tptp.aa_complex_complex (tptp.times_times_complex Y) Z))) Z)))) (forall ((Z tptp.rat) (X tptp.rat) (Y tptp.rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_rat_rat (tptp.divide_divide_rat X) Z))) Y) (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat X)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat Y) Z))) Z)))) (forall ((A tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int tptp.uminus_uminus_int A))) (tptp.pp (tptp.aa_int_bool _let_1 A))))) (forall ((A tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A))) (tptp.pp (tptp.aa_Code_integer_bool _let_1 A))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) _let_1) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Y) _let_1)) (or (= X Y) (= X (tptp.aa_real_real tptp.uminus_uminus_real Y)))))) (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (= (tptp.aa_nat_int (tptp.power_power_int X) _let_1) (tptp.aa_nat_int (tptp.power_power_int Y) _let_1)) (or (= X Y) (= X (tptp.aa_int_int tptp.uminus_uminus_int Y)))))) (forall ((X tptp.complex) (Y tptp.complex)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (= (tptp.aa_nat_complex (tptp.power_power_complex X) _let_1) (tptp.aa_nat_complex (tptp.power_power_complex Y) _let_1)) (or (= X Y) (= X (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex Y)))))) (forall ((X tptp.code_integer) (Y tptp.code_integer)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (= (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger X) _let_1) (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger Y) _let_1)) (or (= X Y) (= X (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger Y)))))) (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (= (tptp.aa_nat_rat (tptp.power_power_rat X) _let_1) (tptp.aa_nat_rat (tptp.power_power_rat Y) _let_1)) (or (= X Y) (= X (tptp.aa_rat_rat tptp.uminus_uminus_rat Y)))))) (forall ((N tptp.nat) (A tptp.real)) (let ((_let_1 (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real A) N))) (let ((_let_2 (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real tptp.uminus_uminus_real A)) N))) (let ((_let_3 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N)))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (tptp.aa_real_real tptp.uminus_uminus_real _let_1)))))))) (forall ((N tptp.nat) (A tptp.int)) (let ((_let_1 (tptp.aa_nat_int (tptp.power_power_int A) N))) (let ((_let_2 (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_int_int tptp.uminus_uminus_int A)) N))) (let ((_let_3 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N)))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (tptp.aa_int_int tptp.uminus_uminus_int _let_1)))))))) (forall ((N tptp.nat) (A tptp.complex)) (let ((_let_1 (tptp.aa_nat_complex (tptp.power_power_complex A) N))) (let ((_let_2 (tptp.aa_nat_complex (tptp.power_power_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex A)) N))) (let ((_let_3 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N)))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex _let_1)))))))) (forall ((N tptp.nat) (A tptp.code_integer)) (let ((_let_1 (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger A) N))) (let ((_let_2 (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A)) N))) (let ((_let_3 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N)))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger _let_1)))))))) (forall ((N tptp.nat) (A tptp.rat)) (let ((_let_1 (tptp.aa_nat_rat (tptp.power_power_rat A) N))) (let ((_let_2 (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat A)) N))) (let ((_let_3 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N)))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (tptp.aa_rat_rat tptp.uminus_uminus_rat _let_1)))))))) (forall ((A4 tptp.int) (B4 tptp.int) (N tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A4) B4)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) (tptp.aa_int_int tptp.uminus_uminus_int N))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.divide_divide_int B4) N)) (tptp.aa_int_int (tptp.divide_divide_int A4) N)))))) (forall ((B2 tptp.int)) (let ((_let_1 (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) B2)) (= (tptp.aa_int_int (tptp.divide_divide_int _let_1) B2) _let_1)))) (forall ((A tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.zero_n2687167440665602831ol_nat (tptp.aa_bool_bool tptp.fNot (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat _let_1) A))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A) _let_1)))) (forall ((A tptp.int)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.aa_bool_int tptp.zero_n2684676970156552555ol_int (tptp.aa_bool_bool tptp.fNot (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int _let_1) A))) (tptp.aa_int_int (tptp.modulo_modulo_int A) _let_1)))) (forall ((A tptp.code_integer)) (let ((_let_1 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.zero_n356916108424825756nteger (tptp.aa_bool_bool tptp.fNot (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer _let_1) A))) (tptp.modulo364778990260209775nteger A _let_1)))) (forall ((C tptp.real) (B2 tptp.real) (A tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) C)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real B2) C))) A)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real B2)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) C)))))) (forall ((C tptp.rat) (B2 tptp.rat) (A tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) C)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_rat_rat (tptp.divide_divide_rat B2) C))) A)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat B2)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) C)))))) (forall ((C tptp.real) (A tptp.real) (B2 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) C)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real B2) C)))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) C)) (tptp.aa_real_real tptp.uminus_uminus_real B2)))))) (forall ((C tptp.rat) (A tptp.rat) (B2 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) C)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_rat_rat (tptp.divide_divide_rat B2) C)))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) C)) (tptp.aa_rat_rat tptp.uminus_uminus_rat B2)))))) (forall ((C tptp.real) (B2 tptp.real) (A tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real C) tptp.zero_zero_real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real B2) C))) A)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) C)) (tptp.aa_real_real tptp.uminus_uminus_real B2)))))) (forall ((C tptp.rat) (B2 tptp.rat) (A tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat C) tptp.zero_zero_rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_rat_rat (tptp.divide_divide_rat B2) C))) A)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) C)) (tptp.aa_rat_rat tptp.uminus_uminus_rat B2)))))) (forall ((C tptp.real) (A tptp.real) (B2 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real C) tptp.zero_zero_real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real B2) C)))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real B2)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) C)))))) (forall ((C tptp.rat) (A tptp.rat) (B2 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat C) tptp.zero_zero_rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_rat_rat (tptp.divide_divide_rat B2) C)))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat B2)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) C)))))) (forall ((B2 tptp.real) (C tptp.real) (A tptp.real)) (let ((_let_1 (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real C) tptp.zero_zero_real)))) (let ((_let_2 (tptp.aa_real_real tptp.uminus_uminus_real B2))) (let ((_let_3 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) C))) (let ((_let_4 (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) C)))) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real B2) C))) A)) (and (=> _let_4 (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real _let_2) _let_3))) (=> (not _let_4) (and (=> _let_1 (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real _let_3) _let_2))) (=> (not _let_1) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) A)))))))))))) (forall ((B2 tptp.rat) (C tptp.rat) (A tptp.rat)) (let ((_let_1 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat C) tptp.zero_zero_rat)))) (let ((_let_2 (tptp.aa_rat_rat tptp.uminus_uminus_rat B2))) (let ((_let_3 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) C))) (let ((_let_4 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) C)))) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_rat_rat (tptp.divide_divide_rat B2) C))) A)) (and (=> _let_4 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat _let_2) _let_3))) (=> (not _let_4) (and (=> _let_1 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat _let_3) _let_2))) (=> (not _let_1) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) A)))))))))))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A))) (let ((_let_2 (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real C) tptp.zero_zero_real)))) (let ((_let_3 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) C))) (let ((_let_4 (tptp.aa_real_real tptp.uminus_uminus_real B2))) (let ((_let_5 (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) C)))) (= (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real B2) C)))) (and (=> _let_5 (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real _let_3) _let_4))) (=> (not _let_5) (and (=> _let_2 (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real _let_4) _let_3))) (=> (not _let_2) (tptp.pp (tptp.aa_real_bool _let_1 tptp.zero_zero_real))))))))))))) (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A))) (let ((_let_2 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat C) tptp.zero_zero_rat)))) (let ((_let_3 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) C))) (let ((_let_4 (tptp.aa_rat_rat tptp.uminus_uminus_rat B2))) (let ((_let_5 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) C)))) (= (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_rat_rat (tptp.divide_divide_rat B2) C)))) (and (=> _let_5 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat _let_3) _let_4))) (=> (not _let_5) (and (=> _let_2 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat _let_4) _let_3))) (=> (not _let_2) (tptp.pp (tptp.aa_rat_bool _let_1 tptp.zero_zero_rat))))))))))))) (forall ((W tptp.num) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real W)))) (let ((_let_2 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real _let_1))) (let ((_let_3 (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real C) tptp.zero_zero_real)))) (let ((_let_4 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real _let_1) C))) (let ((_let_5 (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) C)))) (= (tptp.pp (tptp.aa_real_bool _let_2 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real B2) C))) (and (=> _let_5 (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real _let_4) B2))) (=> (not _let_5) (and (=> _let_3 (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B2) _let_4))) (=> (not _let_3) (tptp.pp (tptp.aa_real_bool _let_2 tptp.zero_zero_real))))))))))))) (forall ((W tptp.num) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat W)))) (let ((_let_2 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat _let_1))) (let ((_let_3 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat C) tptp.zero_zero_rat)))) (let ((_let_4 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat _let_1) C))) (let ((_let_5 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) C)))) (= (tptp.pp (tptp.aa_rat_bool _let_2 (tptp.aa_rat_rat (tptp.divide_divide_rat B2) C))) (and (=> _let_5 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat _let_4) B2))) (=> (not _let_5) (and (=> _let_3 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B2) _let_4))) (=> (not _let_3) (tptp.pp (tptp.aa_rat_bool _let_2 tptp.zero_zero_rat))))))))))))) (forall ((B2 tptp.real) (C tptp.real) (W tptp.num)) (let ((_let_1 (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real W)))) (let ((_let_2 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real))) (let ((_let_3 (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real C) tptp.zero_zero_real)))) (let ((_let_4 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real _let_1) C))) (let ((_let_5 (tptp.pp (tptp.aa_real_bool _let_2 C)))) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real B2) C)) _let_1)) (and (=> _let_5 (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B2) _let_4))) (=> (not _let_5) (and (=> _let_3 (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real _let_4) B2))) (=> (not _let_3) (tptp.pp (tptp.aa_real_bool _let_2 _let_1))))))))))))) (forall ((B2 tptp.rat) (C tptp.rat) (W tptp.num)) (let ((_let_1 (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat W)))) (let ((_let_2 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat))) (let ((_let_3 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat C) tptp.zero_zero_rat)))) (let ((_let_4 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat _let_1) C))) (let ((_let_5 (tptp.pp (tptp.aa_rat_bool _let_2 C)))) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.divide_divide_rat B2) C)) _let_1)) (and (=> _let_5 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B2) _let_4))) (=> (not _let_5) (and (=> _let_3 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat _let_4) B2))) (=> (not _let_3) (tptp.pp (tptp.aa_rat_bool _let_2 _let_1))))))))))))) (forall ((A tptp.real)) (= (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real A) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) tptp.one_one_real) (or (= A tptp.one_one_real) (= A (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real))))) (forall ((A tptp.int)) (= (= (tptp.aa_nat_int (tptp.power_power_int A) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) tptp.one_one_int) (or (= A tptp.one_one_int) (= A (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int))))) (forall ((A tptp.complex)) (= (= (tptp.aa_nat_complex (tptp.power_power_complex A) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) tptp.one_one_complex) (or (= A tptp.one_one_complex) (= A (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex tptp.one_one_complex))))) (forall ((A tptp.code_integer)) (= (= (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger A) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) tptp.one_one_Code_integer) (or (= A tptp.one_one_Code_integer) (= A (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))) (forall ((A tptp.rat)) (= (= (tptp.aa_nat_rat (tptp.power_power_rat A) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) tptp.one_one_rat) (or (= A tptp.one_one_rat) (= A (tptp.aa_rat_rat tptp.uminus_uminus_rat tptp.one_one_rat))))) (forall ((N tptp.nat)) (let ((_let_1 (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real))) (let ((_let_2 (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real _let_1) N))) (let ((_let_3 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N)))) (and (=> _let_3 (= _let_2 tptp.one_one_real)) (=> (not _let_3) (= _let_2 _let_1))))))) (forall ((N tptp.nat)) (let ((_let_1 (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int))) (let ((_let_2 (tptp.aa_nat_int (tptp.power_power_int _let_1) N))) (let ((_let_3 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N)))) (and (=> _let_3 (= _let_2 tptp.one_one_int)) (=> (not _let_3) (= _let_2 _let_1))))))) (forall ((N tptp.nat)) (let ((_let_1 (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex tptp.one_one_complex))) (let ((_let_2 (tptp.aa_nat_complex (tptp.power_power_complex _let_1) N))) (let ((_let_3 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N)))) (and (=> _let_3 (= _let_2 tptp.one_one_complex)) (=> (not _let_3) (= _let_2 _let_1))))))) (forall ((N tptp.nat)) (let ((_let_1 (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (let ((_let_2 (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger _let_1) N))) (let ((_let_3 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N)))) (and (=> _let_3 (= _let_2 tptp.one_one_Code_integer)) (=> (not _let_3) (= _let_2 _let_1))))))) (forall ((N tptp.nat)) (let ((_let_1 (tptp.aa_rat_rat tptp.uminus_uminus_rat tptp.one_one_rat))) (let ((_let_2 (tptp.aa_nat_rat (tptp.power_power_rat _let_1) N))) (let ((_let_3 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N)))) (and (=> _let_3 (= _let_2 tptp.one_one_rat)) (=> (not _let_3) (= _let_2 _let_1))))))) (forall ((K tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) N)) (= (tptp.aa_nat_real _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N) K)) (tptp.aa_nat_real _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) K)))))) (forall ((K tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.power_power_int (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int)))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) N)) (= (tptp.aa_nat_int _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N) K)) (tptp.aa_nat_int _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) K)))))) (forall ((K tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.power_power_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex tptp.one_one_complex)))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) N)) (= (tptp.aa_nat_complex _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N) K)) (tptp.aa_nat_complex _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) K)))))) (forall ((K tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.power_8256067586552552935nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) N)) (= (tptp.aa_nat_Code_integer _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N) K)) (tptp.aa_nat_Code_integer _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) K)))))) (forall ((K tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.power_power_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat tptp.one_one_rat)))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) N)) (= (tptp.aa_nat_rat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N) K)) (tptp.aa_nat_rat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) K)))))) (forall ((U tptp.real) (X tptp.real)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real U) _let_1))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) _let_1))))) (forall ((N tptp.nat) (K tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.bit_ri631733984087533419it_int N) K)) K)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) N))) K)))) (forall ((N tptp.nat) (K tptp.int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) N))) (tptp.aa_int_int (tptp.bit_ri631733984087533419it_int N) K)))) (forall ((K tptp.int) (N tptp.nat)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_int K))) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.bit_ri631733984087533419it_int N) K))) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) N))))))) (forall ((L tptp.int) (K tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) L)) (= (tptp.aa_int_int (tptp.modulo_modulo_int (tptp.aa_int_int tptp.uminus_uminus_int K)) L) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int L) tptp.one_one_int)) (tptp.aa_int_int (tptp.modulo_modulo_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int K) tptp.one_one_int)) L))))) (forall ((B2 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) B2)) (= (tptp.aa_int_int (tptp.modulo_modulo_int (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int)) B2) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int B2) tptp.one_one_int)))) (forall ((A tptp.int) (B2 tptp.int) (Q2 tptp.int) (R tptp.int)) (let ((_let_1 (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.fequal_int R) tptp.zero_zero_int))) (let ((_let_2 (tptp.aa_int_int tptp.uminus_uminus_int Q2))) (=> (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.eucl_rel_int A B2) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int Q2) R))) (=> (not (= B2 tptp.zero_zero_int)) (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.eucl_rel_int (tptp.aa_int_int tptp.uminus_uminus_int A) B2) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int (tptp.aa_int_int (tptp.if_int _let_1 _let_2) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int _let_2) tptp.one_one_int))) (tptp.aa_int_int (tptp.if_int _let_1 tptp.zero_zero_int) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int B2) R)))))))))) (forall ((P tptp.fun_nat_bool) (A tptp.nat)) (=> (forall ((A3 tptp.nat)) (=> (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A3) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) A3) (tptp.pp (tptp.aa_nat_bool P A3)))) (=> (forall ((A3 tptp.nat) (B3 tptp.bool)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.zero_n2687167440665602831ol_nat B3)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat _let_1) A3)))) (=> (tptp.pp (tptp.aa_nat_bool P A3)) (=> (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat _let_2) _let_1) A3) (tptp.pp (tptp.aa_nat_bool P _let_2))))))) (tptp.pp (tptp.aa_nat_bool P A))))) (forall ((P tptp.fun_int_bool) (A tptp.int)) (=> (forall ((A3 tptp.int)) (=> (= (tptp.aa_int_int (tptp.divide_divide_int A3) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) A3) (tptp.pp (tptp.aa_int_bool P A3)))) (=> (forall ((A3 tptp.int) (B3 tptp.bool)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_bool_int tptp.zero_n2684676970156552555ol_int B3)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int _let_1) A3)))) (=> (tptp.pp (tptp.aa_int_bool P A3)) (=> (= (tptp.aa_int_int (tptp.divide_divide_int _let_2) _let_1) A3) (tptp.pp (tptp.aa_int_bool P _let_2))))))) (tptp.pp (tptp.aa_int_bool P A))))) (forall ((P tptp.fun_Co8822979462182099027r_bool) (A tptp.code_integer)) (=> (forall ((A3 tptp.code_integer)) (=> (= (tptp.divide6298287555418463151nteger A3 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))) A3) (tptp.pp (tptp.aa_Code_integer_bool P A3)))) (=> (forall ((A3 tptp.code_integer) (B3 tptp.bool)) (let ((_let_1 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.plus_p5714425477246183910nteger (tptp.zero_n356916108424825756nteger B3) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger _let_1) A3)))) (=> (tptp.pp (tptp.aa_Code_integer_bool P A3)) (=> (= (tptp.divide6298287555418463151nteger _let_2 _let_1) A3) (tptp.pp (tptp.aa_Code_integer_bool P _let_2))))))) (tptp.pp (tptp.aa_Code_integer_bool P A))))) (forall ((W tptp.num) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real W)))) (let ((_let_2 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real _let_1))) (let ((_let_3 (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real C) tptp.zero_zero_real)))) (let ((_let_4 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real _let_1) C))) (let ((_let_5 (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) C)))) (= (tptp.pp (tptp.aa_real_bool _let_2 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real B2) C))) (and (=> _let_5 (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real _let_4) B2))) (=> (not _let_5) (and (=> _let_3 (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real B2) _let_4))) (=> (not _let_3) (tptp.pp (tptp.aa_real_bool _let_2 tptp.zero_zero_real))))))))))))) (forall ((W tptp.num) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat W)))) (let ((_let_2 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat _let_1))) (let ((_let_3 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat C) tptp.zero_zero_rat)))) (let ((_let_4 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat _let_1) C))) (let ((_let_5 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) C)))) (= (tptp.pp (tptp.aa_rat_bool _let_2 (tptp.aa_rat_rat (tptp.divide_divide_rat B2) C))) (and (=> _let_5 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat _let_4) B2))) (=> (not _let_5) (and (=> _let_3 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B2) _let_4))) (=> (not _let_3) (tptp.pp (tptp.aa_rat_bool _let_2 tptp.zero_zero_rat))))))))))))) (forall ((B2 tptp.real) (C tptp.real) (W tptp.num)) (let ((_let_1 (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real W)))) (let ((_let_2 (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real C) tptp.zero_zero_real)))) (let ((_let_3 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real _let_1) C))) (let ((_let_4 (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) C)))) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real B2) C)) _let_1)) (and (=> _let_4 (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real B2) _let_3))) (=> (not _let_4) (and (=> _let_2 (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real _let_3) B2))) (=> (not _let_2) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) _let_1)))))))))))) (forall ((B2 tptp.rat) (C tptp.rat) (W tptp.num)) (let ((_let_1 (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat W)))) (let ((_let_2 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat C) tptp.zero_zero_rat)))) (let ((_let_3 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat _let_1) C))) (let ((_let_4 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) C)))) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.divide_divide_rat B2) C)) _let_1)) (and (=> _let_4 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B2) _let_3))) (=> (not _let_4) (and (=> _let_2 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat _let_3) B2))) (=> (not _let_2) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1)))))))))))) (forall ((X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) tptp.one_one_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) tptp.one_one_real))))) (forall ((X tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) X)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger X) tptp.one_one_Code_integer)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger X) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) tptp.one_one_Code_integer))))) (forall ((X tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat tptp.one_one_rat)) X)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) tptp.one_one_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat (tptp.power_power_rat X) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) tptp.one_one_rat))))) (forall ((X tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int)) X)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X) tptp.one_one_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int (tptp.power_power_int X) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) tptp.one_one_int))))) (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real tptp.uminus_uminus_real A)) N))) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real _let_1) _let_1) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N))))) (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_int_int tptp.uminus_uminus_int A)) N))) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int _let_1) _let_1) (tptp.aa_nat_int (tptp.power_power_int A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N))))) (forall ((A tptp.complex) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_complex (tptp.power_power_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex A)) N))) (= (tptp.aa_complex_complex (tptp.times_times_complex _let_1) _let_1) (tptp.aa_nat_complex (tptp.power_power_complex A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N))))) (forall ((A tptp.code_integer) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A)) N))) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger _let_1) _let_1) (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N))))) (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat A)) N))) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat _let_1) _let_1) (tptp.aa_nat_rat (tptp.power_power_rat A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N))))) (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) N))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.uminus_uminus_int _let_1)) K)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int K) _let_1)) (= (tptp.aa_int_int (tptp.bit_ri631733984087533419it_int N) K) K))))) (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) N))) (= (= (tptp.aa_int_int (tptp.bit_ri631733984087533419it_int N) K) K) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.uminus_uminus_int _let_1)) K)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int K) _let_1)))))) (forall ((N tptp.nat)) (let ((_let_1 (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int))) (= (tptp.aa_int_int (tptp.divide_divide_int _let_1) (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) N)) _let_1))) (forall ((K tptp.int) (L tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) K)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int K) L)) tptp.zero_zero_int)) (= (tptp.aa_int_int (tptp.divide_divide_int K) L) (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int))))) (forall ((B2 tptp.complex) (A tptp.complex)) (= (= B2 (tptp.aa_complex_complex (tptp.plus_plus_complex B2) A)) (= A tptp.zero_zero_complex))) (forall ((B2 tptp.real) (A tptp.real)) (= (= B2 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real B2) A)) (= A tptp.zero_zero_real))) (forall ((B2 tptp.rat) (A tptp.rat)) (= (= B2 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat B2) A)) (= A tptp.zero_zero_rat))) (forall ((B2 tptp.nat) (A tptp.nat)) (= (= B2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat B2) A)) (= A tptp.zero_zero_nat))) (forall ((B2 tptp.int) (A tptp.int)) (= (= B2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int B2) A)) (= A tptp.zero_zero_int))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_2 (tptp.aa_nat_nat _let_1 M))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat _let_2) (tptp.aa_nat_nat _let_1 N)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.zero_n2687167440665602831ol_nat (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N))) _let_2))))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_2 (tptp.aa_nat_int _let_1 M))) (= (tptp.aa_int_int (tptp.modulo_modulo_int _let_2) (tptp.aa_nat_int _let_1 N)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_bool_int tptp.zero_n2684676970156552555ol_int (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N))) _let_2))))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.power_8256067586552552935nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_2 (tptp.aa_nat_Code_integer _let_1 M))) (= (tptp.modulo364778990260209775nteger _let_2 (tptp.aa_nat_Code_integer _let_1 N)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.zero_n356916108424825756nteger (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N))) _let_2))))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real) (D tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.times_times_real B2))) (let ((_let_2 (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A))) (= (and (not (= A B2)) (not (= C D))) (not (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real _let_2 C)) (tptp.aa_real_real _let_1 D)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real _let_2 D)) (tptp.aa_real_real _let_1 C)))))))) (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat) (D tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_rat tptp.times_times_rat B2))) (let ((_let_2 (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A))) (= (and (not (= A B2)) (not (= C D))) (not (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat _let_2 C)) (tptp.aa_rat_rat _let_1 D)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat _let_2 D)) (tptp.aa_rat_rat _let_1 C)))))))) (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat) (D tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B2))) (let ((_let_2 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A))) (= (and (not (= A B2)) (not (= C D))) (not (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat _let_2 C)) (tptp.aa_nat_nat _let_1 D)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat _let_2 D)) (tptp.aa_nat_nat _let_1 C)))))))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int) (D tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.times_times_int B2))) (let ((_let_2 (tptp.aa_int_fun_int_int tptp.times_times_int A))) (= (and (not (= A B2)) (not (= C D))) (not (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int _let_2 C)) (tptp.aa_int_int _let_1 D)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int _let_2 D)) (tptp.aa_int_int _let_1 C)))))))) (forall ((W tptp.real) (Y tptp.real) (X tptp.real) (Z tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.times_times_real X))) (let ((_let_2 (tptp.aa_rea7340605660300375871l_real tptp.times_times_real W))) (= (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real _let_2 Y)) (tptp.aa_real_real _let_1 Z)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real _let_2 Z)) (tptp.aa_real_real _let_1 Y))) (or (= W X) (= Y Z)))))) (forall ((W tptp.rat) (Y tptp.rat) (X tptp.rat) (Z tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_rat tptp.times_times_rat X))) (let ((_let_2 (tptp.aa_rat_fun_rat_rat tptp.times_times_rat W))) (= (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat _let_2 Y)) (tptp.aa_rat_rat _let_1 Z)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat _let_2 Z)) (tptp.aa_rat_rat _let_1 Y))) (or (= W X) (= Y Z)))))) (forall ((W tptp.nat) (Y tptp.nat) (X tptp.nat) (Z tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat X))) (let ((_let_2 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat W))) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat _let_2 Y)) (tptp.aa_nat_nat _let_1 Z)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat _let_2 Z)) (tptp.aa_nat_nat _let_1 Y))) (or (= W X) (= Y Z)))))) (forall ((W tptp.int) (Y tptp.int) (X tptp.int) (Z tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.times_times_int X))) (let ((_let_2 (tptp.aa_int_fun_int_int tptp.times_times_int W))) (= (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int _let_2 Y)) (tptp.aa_int_int _let_1 Z)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int _let_2 Z)) (tptp.aa_int_int _let_1 Y))) (or (= W X) (= Y Z)))))) (forall ((N tptp.nat)) (let ((_let_1 (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real))) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real _let_1) (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N))) _let_1))) (forall ((N tptp.nat)) (let ((_let_1 (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int))) (= (tptp.aa_nat_int (tptp.power_power_int _let_1) (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N))) _let_1))) (forall ((N tptp.nat)) (let ((_let_1 (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex tptp.one_one_complex))) (= (tptp.aa_nat_complex (tptp.power_power_complex _let_1) (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N))) _let_1))) (forall ((N tptp.nat)) (let ((_let_1 (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (= (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger _let_1) (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N))) _let_1))) (forall ((N tptp.nat)) (let ((_let_1 (tptp.aa_rat_rat tptp.uminus_uminus_rat tptp.one_one_rat))) (= (tptp.aa_nat_rat (tptp.power_power_rat _let_1) (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N))) _let_1))) (forall ((P tptp.fun_int_bool) (K tptp.int)) (=> (tptp.pp (tptp.aa_int_bool P tptp.zero_zero_int)) (=> (tptp.pp (tptp.aa_int_bool P (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int))) (=> (forall ((K3 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool P K3)) (=> (not (= K3 tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool P (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int K3) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one)))))))) (=> (forall ((K3 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool P K3)) (=> (not (= K3 (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int))) (tptp.pp (tptp.aa_int_bool P (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int tptp.one_one_int) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int K3) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))))))))) (tptp.pp (tptp.aa_int_bool P K))))))) (forall ((K tptp.int) (N tptp.nat)) (let ((_let_1 (tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int K) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_nat_int _let_1 N)))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int K) (tptp.aa_nat_int _let_1 (tptp.aa_nat_nat tptp.suc N)))) (tptp.aa_int_int (tptp.bit_ri631733984087533419it_int N) K)))))) (forall ((X tptp.nat)) (= (tptp.nat_set_decode X) (tptp.collect_nat (tptp.aa_nat_fun_nat_bool tptp.aTP_Lamm_fj X)))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_2 (tptp.aa_nat_nat _let_1 M))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat _let_2) (tptp.aa_nat_nat _let_1 N)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.zero_n2687167440665602831ol_nat (tptp.aa_bool_bool (tptp.fconj (tptp.aa_bool_bool tptp.fNot (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.fequal_nat _let_2) tptp.zero_zero_nat))) (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N) M)))) (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) N))))))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_2 (tptp.aa_nat_int _let_1 M))) (= (tptp.aa_int_int (tptp.divide_divide_int _let_2) (tptp.aa_nat_int _let_1 N)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_bool_int tptp.zero_n2684676970156552555ol_int (tptp.aa_bool_bool (tptp.fconj (tptp.aa_bool_bool tptp.fNot (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.fequal_int _let_2) tptp.zero_zero_int))) (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N) M)))) (tptp.aa_nat_int _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) N))))))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.power_8256067586552552935nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_2 (tptp.aa_nat_Code_integer _let_1 M))) (= (tptp.divide6298287555418463151nteger _let_2 (tptp.aa_nat_Code_integer _let_1 N)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.zero_n356916108424825756nteger (tptp.aa_bool_bool (tptp.fconj (tptp.aa_bool_bool tptp.fNot (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.fequal_Code_integer _let_2) tptp.zero_z3403309356797280102nteger))) (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N) M)))) (tptp.aa_nat_Code_integer _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) N))))))) (forall ((Va tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat tptp.suc Va)))) (let ((_let_3 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat _let_2) _let_1))) (let ((_let_4 (tptp.aa_nat_nat tptp.suc _let_3))) (let ((_let_5 (tptp.vEBT_vebt_buildup _let_3))) (let ((_let_6 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat _let_1))) (let ((_let_7 (tptp.vEBT_vebt_buildup _let_2))) (let ((_let_8 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat _let_1) _let_2)))) (and (=> _let_8 (= _let_7 (tptp.vEBT_Node tptp.none_P5556105721700978146at_nat _let_2 (tptp.replicate_VEBT_VEBT (tptp.aa_nat_nat _let_6 _let_3) _let_5) _let_5))) (=> (not _let_8) (= _let_7 (tptp.vEBT_Node tptp.none_P5556105721700978146at_nat _let_2 (tptp.replicate_VEBT_VEBT (tptp.aa_nat_nat _let_6 _let_4) _let_5) (tptp.vEBT_vebt_buildup _let_4)))))))))))))) (forall ((Q2 tptp.int) (R tptp.int)) (= (tptp.adjust_div (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int Q2) R)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int Q2) (tptp.aa_bool_int tptp.zero_n2684676970156552555ol_int (tptp.aa_bool_bool tptp.fNot (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.fequal_int R) tptp.zero_zero_int)))))) (forall ((N tptp.nat) (K tptp.num)) (= (tptp.aa_int_int (tptp.bit_ri631733984087533419it_int (tptp.aa_nat_nat tptp.suc N)) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit1 K)))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.bit_ri631733984087533419it_int N) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int K))) tptp.one_one_int))) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one)))) tptp.one_one_int))) (forall ((X tptp.nat) (Y tptp.vEBT_VEBT)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat))) (let ((_let_2 (tptp.accp_nat tptp.vEBT_v4011308405150292612up_rel))) (let ((_let_3 (= Y (tptp.vEBT_Leaf tptp.fFalse tptp.fFalse)))) (=> (= (tptp.vEBT_vebt_buildup X) Y) (=> (tptp.pp (tptp.aa_nat_bool _let_2 X)) (=> (=> (= X tptp.zero_zero_nat) (=> _let_3 (not (tptp.pp (tptp.aa_nat_bool _let_2 tptp.zero_zero_nat))))) (=> (=> (= X _let_1) (=> _let_3 (not (tptp.pp (tptp.aa_nat_bool _let_2 _let_1))))) (not (forall ((Va2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat tptp.suc Va2)))) (let ((_let_2 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_3 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat _let_1) _let_2))) (let ((_let_4 (tptp.aa_nat_nat tptp.suc _let_3))) (let ((_let_5 (tptp.vEBT_vebt_buildup _let_3))) (let ((_let_6 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat _let_2))) (let ((_let_7 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat _let_2) _let_1)))) (=> (= X _let_1) (=> (and (=> _let_7 (= Y (tptp.vEBT_Node tptp.none_P5556105721700978146at_nat _let_1 (tptp.replicate_VEBT_VEBT (tptp.aa_nat_nat _let_6 _let_3) _let_5) _let_5))) (=> (not _let_7) (= Y (tptp.vEBT_Node tptp.none_P5556105721700978146at_nat _let_1 (tptp.replicate_VEBT_VEBT (tptp.aa_nat_nat _let_6 _let_4) _let_5) (tptp.vEBT_vebt_buildup _let_4))))) (not (tptp.pp (tptp.aa_nat_bool (tptp.accp_nat tptp.vEBT_v4011308405150292612up_rel) _let_1)))))))))))))))))))))) (forall ((X tptp.real)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (let ((_let_2 (tptp.aa_num_real tptp.numeral_numeral_real _let_1))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.one_one_real) _let_2))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real tptp.uminus_uminus_real X)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real _let_2) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1))))) (tptp.aa_real_real tptp.ln_ln_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real tptp.one_one_real) X))))))))) (forall ((X tptp.real)) (= (tptp.aa_real_real tptp.artanh_real X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real tptp.ln_ln_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real tptp.one_one_real) X)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real tptp.one_one_real) X)))) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))))) (forall ((M tptp.int) (N tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int M) N)) (= (tptp.groups4538972089207619220nt_int tptp.aTP_Lamm_am (tptp.aa_int_set_int (tptp.aa_int8639817059373041269et_int tptp.set_or1266510415728281911st_int M) N)) (tptp.aa_int_int (tptp.divide_divide_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int N) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int N) tptp.one_one_int))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int M) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int M) tptp.one_one_int)))) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one)))))) (forall ((L tptp.num) (Qr tptp.product_prod_nat_nat)) (= (tptp.unique5026877609467782581ep_nat L Qr) (tptp.aa_Pro262675715343573244at_nat (tptp.produc2626176000494625587at_nat (tptp.aTP_Lamm_fk L)) Qr))) (forall ((L tptp.num) (Qr tptp.product_prod_int_int)) (= (tptp.aa_Pro6970504127699319548nt_int (tptp.unique5024387138958732305ep_int L) Qr) (tptp.aa_Pro6970504127699319548nt_int (tptp.produc4245557441103728435nt_int (tptp.aTP_Lamm_fl L)) Qr))) (forall ((L tptp.num) (Qr tptp.produc8923325533196201883nteger)) (= (tptp.unique4921790084139445826nteger L Qr) (tptp.produc6916734918728496179nteger (tptp.aTP_Lamm_fm L) Qr))) (forall ((M tptp.num) (N tptp.num)) (= (= (tptp.aa_num_num tptp.bit1 M) (tptp.aa_num_num tptp.bit1 N)) (= M N))) (forall ((X32 tptp.num) (Y32 tptp.num)) (= (= (tptp.aa_num_num tptp.bit1 X32) (tptp.aa_num_num tptp.bit1 Y32)) (= X32 Y32))) (forall ((M tptp.num) (N tptp.num)) (not (= (tptp.aa_num_num tptp.bit0 M) (tptp.aa_num_num tptp.bit1 N)))) (forall ((M tptp.num) (N tptp.num)) (not (= (tptp.aa_num_num tptp.bit1 M) (tptp.aa_num_num tptp.bit0 N)))) (forall ((N tptp.num)) (not (= tptp.one (tptp.aa_num_num tptp.bit1 N)))) (forall ((M tptp.num)) (not (= (tptp.aa_num_num tptp.bit1 M) tptp.one))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_num_num tptp.bit1 M)) (tptp.aa_num_num tptp.bit1 N))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num M) N)))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num (tptp.aa_num_num tptp.bit1 M)) (tptp.aa_num_num tptp.bit1 N))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num M) N)))) (forall ((F tptp.fun_nat_fun_nat_nat) (A tptp.nat) (B2 tptp.nat)) (= (tptp.aa_Pro4243173770044397973at_nat (tptp.produc6842872674320459806at_nat F) (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat A) B2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat F A) B2))) (forall ((F tptp.fun_na1668100129766719005at_nat) (A tptp.nat) (B2 tptp.nat)) (= (tptp.aa_Pro8023792847356852296at_nat (tptp.produc4528391901023682385at_nat F) (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat A) B2)) (tptp.aa_nat7997280740862404369at_nat (tptp.aa_nat5682243440470347102at_nat F A) B2))) (forall ((F tptp.fun_na4786964484885125043t_bool) (A tptp.nat) (B2 tptp.nat)) (= (tptp.aa_Pro595088089689268830t_bool (tptp.produc5023667602222594023t_bool F) (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat A) B2)) (tptp.aa_nat4401263874371387303t_bool (tptp.aa_nat4909001760120733684t_bool F A) B2))) (forall ((F tptp.fun_in1696471567231710611nt_int) (A tptp.int) (B2 tptp.int)) (= (tptp.aa_Pro6970504127699319548nt_int (tptp.produc4245557441103728435nt_int F) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int A) B2)) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int F A) B2))) (forall ((F tptp.fun_int_fun_int_bool) (A tptp.int) (B2 tptp.int)) (= (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.produc8560705615207772305t_bool F) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int A) B2))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool F A) B2)))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool _let_1 X)) (=> (tptp.pp (tptp.aa_real_bool _let_1 Y)) (= (= (tptp.aa_real_real tptp.ln_ln_real X) (tptp.aa_real_real tptp.ln_ln_real Y)) (= X Y)))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool _let_1 X)) (=> (tptp.pp (tptp.aa_real_bool _let_1 Y)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.ln_ln_real X)) (tptp.aa_real_real tptp.ln_ln_real Y))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Y))))))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num (tptp.aa_num_num tptp.bit1 M)) (tptp.aa_num_num tptp.bit0 N)) (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num M) N)))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num (tptp.aa_num_num tptp.bit0 M)) (tptp.aa_num_num tptp.bit1 N)) (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num M) N)))) (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (tptp.aa_num_fun_num_num tptp.times_times_num (tptp.aa_num_num tptp.bit1 M)))) (= (tptp.aa_num_num _let_1 (tptp.aa_num_num tptp.bit0 N)) (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num _let_1 N))))) (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit1 N))) (= (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.times_times_num (tptp.aa_num_num tptp.bit0 M)) _let_1) (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.times_times_num M) _let_1))))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_num_num tptp.bit0 M)) (tptp.aa_num_num tptp.bit1 N))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num M) N)))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num (tptp.aa_num_num tptp.bit1 M)) (tptp.aa_num_num tptp.bit0 N))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num M) N)))) (forall ((M tptp.num)) (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_num_num tptp.bit1 M)) tptp.one)))) (forall ((N tptp.num)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num tptp.one) (tptp.aa_num_num tptp.bit1 N)))) (forall ((V tptp.num) (W tptp.num)) (= (tptp.aa_int_int (tptp.divide_divide_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit1 V))) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 W))) (tptp.aa_int_int (tptp.divide_divide_int (tptp.aa_num_int tptp.numeral_numeral_int V)) (tptp.aa_num_int tptp.numeral_numeral_int W)))) (forall ((N tptp.num)) (= (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num tptp.one) (tptp.aa_num_num tptp.bit0 N)) (tptp.aa_num_num tptp.bit1 N))) (forall ((N tptp.num)) (= (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num tptp.one) (tptp.aa_num_num tptp.bit1 N)) (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num N) tptp.one)))) (forall ((M tptp.num)) (= (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num (tptp.aa_num_num tptp.bit0 M)) tptp.one) (tptp.aa_num_num tptp.bit1 M))) (forall ((M tptp.num)) (= (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num (tptp.aa_num_num tptp.bit1 M)) tptp.one) (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num M) tptp.one)))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num (tptp.aa_num_num tptp.bit1 M)) (tptp.aa_num_num tptp.bit1 N)) (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num M) N)) tptp.one)))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool _let_1 X)) (=> (tptp.pp (tptp.aa_real_bool _let_1 Y)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.ln_ln_real X)) (tptp.aa_real_real tptp.ln_ln_real Y))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) Y))))))) (forall ((X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) X)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.ln_ln_real X)) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) tptp.one_one_real))))) (forall ((X tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool _let_1 X)) (= (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real tptp.ln_ln_real X))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real) X)))))) (forall ((X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) X)) (= (= (tptp.aa_real_real tptp.ln_ln_real X) tptp.zero_zero_real) (= X tptp.one_one_real)))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.times_times_num (tptp.aa_num_num tptp.bit1 M)) (tptp.aa_num_num tptp.bit1 N)) (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num M) N)) (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.times_times_num M) N)))))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_num_num tptp.bit1 M)) (tptp.aa_num_num tptp.bit0 N))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num M) N)))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num (tptp.aa_num_num tptp.bit0 M)) (tptp.aa_num_num tptp.bit1 N))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num M) N)))) (forall ((X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) X)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_real_real tptp.ln_ln_real X))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.one_one_real) X))))) (forall ((X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) X)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.ln_ln_real X)) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) tptp.one_one_real))))) (forall ((M tptp.nat) (V tptp.num)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat V))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat tptp.suc M)))) _let_1) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 tptp.one))) M)) _let_1)))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat M))) (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat tptp.suc N)))) (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 tptp.one))) N))))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat M))) (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat tptp.suc N)))) (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 tptp.one))) N))))) (forall ((M tptp.nat) (V tptp.num)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat V))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat tptp.suc M)))) _let_1) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 tptp.one))) M)) _let_1)))) (forall ((V tptp.num) (W tptp.num)) (= (tptp.aa_int_int (tptp.modulo_modulo_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit1 V))) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 W))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_int_int (tptp.modulo_modulo_int (tptp.aa_num_int tptp.numeral_numeral_int V)) (tptp.aa_num_int tptp.numeral_numeral_int W)))) tptp.one_one_int))) (forall ((N tptp.nat) (K tptp.num)) (= (tptp.aa_int_int (tptp.bit_ri631733984087533419it_int (tptp.aa_nat_nat tptp.suc N)) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit1 K))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.bit_ri631733984087533419it_int N) (tptp.aa_num_int tptp.numeral_numeral_int K))) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one)))) tptp.one_one_int))) (forall ((X2 tptp.num) (X32 tptp.num)) (not (= (tptp.aa_num_num tptp.bit0 X2) (tptp.aa_num_num tptp.bit1 X32)))) (forall ((X32 tptp.num)) (not (= tptp.one (tptp.aa_num_num tptp.bit1 X32)))) (forall ((F tptp.fun_nat_fun_nat_nat) (X1 tptp.nat) (X2 tptp.nat)) (= (tptp.aa_Pro4243173770044397973at_nat (tptp.produc6842872674320459806at_nat F) (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat X1) X2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat F X1) X2))) (forall ((F tptp.fun_na1668100129766719005at_nat) (X1 tptp.nat) (X2 tptp.nat)) (= (tptp.aa_Pro8023792847356852296at_nat (tptp.produc4528391901023682385at_nat F) (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat X1) X2)) (tptp.aa_nat7997280740862404369at_nat (tptp.aa_nat5682243440470347102at_nat F X1) X2))) (forall ((F tptp.fun_na4786964484885125043t_bool) (X1 tptp.nat) (X2 tptp.nat)) (= (tptp.aa_Pro595088089689268830t_bool (tptp.produc5023667602222594023t_bool F) (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat X1) X2)) (tptp.aa_nat4401263874371387303t_bool (tptp.aa_nat4909001760120733684t_bool F X1) X2))) (forall ((F tptp.fun_in1696471567231710611nt_int) (X1 tptp.int) (X2 tptp.int)) (= (tptp.aa_Pro6970504127699319548nt_int (tptp.produc4245557441103728435nt_int F) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int X1) X2)) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int F X1) X2))) (forall ((F tptp.fun_int_fun_int_bool) (X1 tptp.int) (X2 tptp.int)) (= (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.produc8560705615207772305t_bool F) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int X1) X2))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool F X1) X2)))) (forall ((K5 tptp.set_nat) (F tptp.fun_nat_rat) (G tptp.fun_nat_rat)) (=> (forall ((I3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat I3) K5)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat F I3)) (tptp.aa_nat_rat G I3))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.groups2906978787729119204at_rat F K5)) (tptp.groups2906978787729119204at_rat G K5))))) (forall ((K5 tptp.set_real) (F tptp.fun_real_rat) (G tptp.fun_real_rat)) (=> (forall ((I3 tptp.real)) (=> (tptp.member_real I3 K5) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_real_rat F I3)) (tptp.aa_real_rat G I3))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.groups1300246762558778688al_rat F K5)) (tptp.groups1300246762558778688al_rat G K5))))) (forall ((K5 tptp.set_int) (F tptp.fun_int_rat) (G tptp.fun_int_rat)) (=> (forall ((I3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int I3) K5)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_int_rat F I3)) (tptp.aa_int_rat G I3))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.groups3906332499630173760nt_rat F K5)) (tptp.groups3906332499630173760nt_rat G K5))))) (forall ((K5 tptp.set_complex) (F tptp.fun_complex_rat) (G tptp.fun_complex_rat)) (=> (forall ((I3 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex I3) K5)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_complex_rat F I3)) (tptp.aa_complex_rat G I3))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.groups5058264527183730370ex_rat F K5)) (tptp.groups5058264527183730370ex_rat G K5))))) (forall ((K5 tptp.set_real) (F tptp.fun_real_nat) (G tptp.fun_real_nat)) (=> (forall ((I3 tptp.real)) (=> (tptp.member_real I3 K5) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_real_nat F I3)) (tptp.aa_real_nat G I3))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.groups1935376822645274424al_nat F K5)) (tptp.groups1935376822645274424al_nat G K5))))) (forall ((K5 tptp.set_int) (F tptp.fun_int_nat) (G tptp.fun_int_nat)) (=> (forall ((I3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int I3) K5)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_int_nat F I3)) (tptp.aa_int_nat G I3))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.groups4541462559716669496nt_nat F K5)) (tptp.groups4541462559716669496nt_nat G K5))))) (forall ((K5 tptp.set_complex) (F tptp.fun_complex_nat) (G tptp.fun_complex_nat)) (=> (forall ((I3 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex I3) K5)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_complex_nat F I3)) (tptp.aa_complex_nat G I3))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.groups5693394587270226106ex_nat F K5)) (tptp.groups5693394587270226106ex_nat G K5))))) (forall ((K5 tptp.set_nat) (F tptp.fun_nat_int) (G tptp.fun_nat_int)) (=> (forall ((I3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat I3) K5)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int F I3)) (tptp.aa_nat_int G I3))))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.groups3539618377306564664at_int F K5)) (tptp.groups3539618377306564664at_int G K5))))) (forall ((K5 tptp.set_real) (F tptp.fun_real_int) (G tptp.fun_real_int)) (=> (forall ((I3 tptp.real)) (=> (tptp.member_real I3 K5) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_real_int F I3)) (tptp.aa_real_int G I3))))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.groups1932886352136224148al_int F K5)) (tptp.groups1932886352136224148al_int G K5))))) (forall ((K5 tptp.set_complex) (F tptp.fun_complex_int) (G tptp.fun_complex_int)) (=> (forall ((I3 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex I3) K5)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_complex_int F I3)) (tptp.aa_complex_int G I3))))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.groups5690904116761175830ex_int F K5)) (tptp.groups5690904116761175830ex_int G K5))))) (forall ((F tptp.fun_int_int) (A4 tptp.set_int) (G tptp.fun_int_int) (B4 tptp.set_int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.groups4538972089207619220nt_int F A4)) (tptp.groups4538972089207619220nt_int G B4)) (tptp.groups4538972089207619220nt_int (tptp.aa_set7310040872927613301nt_int (tptp.aa_fun8076508010538293575nt_int (tptp.aTP_Lamm_fo F) G) B4) A4))) (forall ((F tptp.fun_complex_complex) (A4 tptp.set_complex) (G tptp.fun_complex_complex) (B4 tptp.set_complex)) (= (tptp.aa_complex_complex (tptp.times_times_complex (tptp.groups7754918857620584856omplex F A4)) (tptp.groups7754918857620584856omplex G B4)) (tptp.groups7754918857620584856omplex (tptp.aa_set7743095458595710203omplex (tptp.aa_fun1583801116089702097omplex (tptp.aTP_Lamm_fq F) G) B4) A4))) (forall ((F tptp.fun_nat_nat) (A4 tptp.set_nat) (G tptp.fun_nat_nat) (B4 tptp.set_nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat F) A4)) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat G) B4)) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_set6537093552120046177at_nat (tptp.aa_fun4561837934398617467at_nat (tptp.aTP_Lamm_fs F) G) B4)) A4))) (forall ((F tptp.fun_nat_real) (A4 tptp.set_nat) (G tptp.fun_nat_real) (B4 tptp.set_nat)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.groups6591440286371151544t_real F A4)) (tptp.groups6591440286371151544t_real G B4)) (tptp.groups6591440286371151544t_real (tptp.aa_set1166323925324055613t_real (tptp.aa_fun1400677770452585267t_real (tptp.aTP_Lamm_fu F) G) B4) A4))) (forall ((F tptp.fun_int_int) (A4 tptp.set_int) (R tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.groups4538972089207619220nt_int F A4)) R) (tptp.groups4538972089207619220nt_int (tptp.aa_int_fun_int_int (tptp.aTP_Lamm_fv F) R) A4))) (forall ((F tptp.fun_complex_complex) (A4 tptp.set_complex) (R tptp.complex)) (= (tptp.aa_complex_complex (tptp.times_times_complex (tptp.groups7754918857620584856omplex F A4)) R) (tptp.groups7754918857620584856omplex (tptp.aa_com3342990543769683525omplex (tptp.aTP_Lamm_fw F) R) A4))) (forall ((F tptp.fun_nat_nat) (A4 tptp.set_nat) (R tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat F) A4)) R) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_nat_fun_nat_nat (tptp.aTP_Lamm_fx F) R)) A4))) (forall ((F tptp.fun_nat_real) (A4 tptp.set_nat) (R tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.groups6591440286371151544t_real F A4)) R) (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_fy F) R) A4))) (forall ((R tptp.int) (F tptp.fun_int_int) (A4 tptp.set_int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int R) (tptp.groups4538972089207619220nt_int F A4)) (tptp.groups4538972089207619220nt_int (tptp.aa_fun6280345759651049192nt_int (tptp.aTP_Lamm_fz R) F) A4))) (forall ((R tptp.complex) (F tptp.fun_complex_complex) (A4 tptp.set_complex)) (= (tptp.aa_complex_complex (tptp.times_times_complex R) (tptp.groups7754918857620584856omplex F A4)) (tptp.groups7754918857620584856omplex (tptp.aa_fun3187328805393345264omplex (tptp.aTP_Lamm_ga R) F) A4))) (forall ((R tptp.nat) (F tptp.fun_nat_nat) (A4 tptp.set_nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat R) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat F) A4)) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_fun5791449513213591928at_nat (tptp.aTP_Lamm_gb R) F)) A4))) (forall ((R tptp.real) (F tptp.fun_nat_real) (A4 tptp.set_nat)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real R) (tptp.groups6591440286371151544t_real F A4)) (tptp.groups6591440286371151544t_real (tptp.aa_fun1839206346889086768t_real (tptp.aTP_Lamm_gc R) F) A4))) (forall ((G tptp.fun_int_int) (H tptp.fun_int_int) (A4 tptp.set_int)) (= (tptp.groups4538972089207619220nt_int (tptp.aa_fun6280345759651049192nt_int (tptp.aTP_Lamm_gd G) H) A4) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.groups4538972089207619220nt_int G A4)) (tptp.groups4538972089207619220nt_int H A4)))) (forall ((G tptp.fun_complex_complex) (H tptp.fun_complex_complex) (A4 tptp.set_complex)) (= (tptp.groups7754918857620584856omplex (tptp.aa_fun3187328805393345264omplex (tptp.aTP_Lamm_ge G) H) A4) (tptp.aa_complex_complex (tptp.plus_plus_complex (tptp.groups7754918857620584856omplex G A4)) (tptp.groups7754918857620584856omplex H A4)))) (forall ((G tptp.fun_nat_nat) (H tptp.fun_nat_nat) (A4 tptp.set_nat)) (= (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_fun5791449513213591928at_nat (tptp.aTP_Lamm_gf G) H)) A4) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat G) A4)) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat H) A4)))) (forall ((G tptp.fun_nat_real) (H tptp.fun_nat_real) (A4 tptp.set_nat)) (= (tptp.groups6591440286371151544t_real (tptp.aa_fun1839206346889086768t_real (tptp.aTP_Lamm_gg G) H) A4) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.groups6591440286371151544t_real G A4)) (tptp.groups6591440286371151544t_real H A4)))) (forall ((F tptp.fun_int_int) (G tptp.fun_int_int) (A4 tptp.set_int)) (= (tptp.groups4538972089207619220nt_int (tptp.aa_fun6280345759651049192nt_int (tptp.aTP_Lamm_gh F) G) A4) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.groups4538972089207619220nt_int F A4)) (tptp.groups4538972089207619220nt_int G A4)))) (forall ((F tptp.fun_complex_complex) (G tptp.fun_complex_complex) (A4 tptp.set_complex)) (= (tptp.groups7754918857620584856omplex (tptp.aa_fun3187328805393345264omplex (tptp.aTP_Lamm_gi F) G) A4) (tptp.aa_complex_complex (tptp.minus_minus_complex (tptp.groups7754918857620584856omplex F A4)) (tptp.groups7754918857620584856omplex G A4)))) (forall ((F tptp.fun_nat_real) (G tptp.fun_nat_real) (A4 tptp.set_nat)) (= (tptp.groups6591440286371151544t_real (tptp.aa_fun1839206346889086768t_real (tptp.aTP_Lamm_gj F) G) A4) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.groups6591440286371151544t_real F A4)) (tptp.groups6591440286371151544t_real G A4)))) (forall ((F tptp.fun_complex_complex) (A4 tptp.set_complex) (R tptp.complex)) (= (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex (tptp.groups7754918857620584856omplex F A4)) R) (tptp.groups7754918857620584856omplex (tptp.aa_com3342990543769683525omplex (tptp.aTP_Lamm_gk F) R) A4))) (forall ((F tptp.fun_nat_real) (A4 tptp.set_nat) (R tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.groups6591440286371151544t_real F A4)) R) (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_gl F) R) A4))) (forall ((F tptp.fun_int_int) (A tptp.int) (A4 tptp.set_int)) (= (tptp.aa_int_int (tptp.modulo_modulo_int (tptp.groups4538972089207619220nt_int (tptp.aa_int_fun_int_int (tptp.aTP_Lamm_gm F) A) A4)) A) (tptp.aa_int_int (tptp.modulo_modulo_int (tptp.groups4538972089207619220nt_int F A4)) A))) (forall ((F tptp.fun_nat_nat) (A tptp.nat) (A4 tptp.set_nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_nat_fun_nat_nat (tptp.aTP_Lamm_gn F) A)) A4)) A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat F) A4)) A))) (forall ((F tptp.fun_nat_fun_nat_nat) (G tptp.fun_Pr2602117396471556196at_nat)) (=> (forall ((X4 tptp.nat) (Y4 tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat F X4) Y4) (tptp.aa_Pro4243173770044397973at_nat G (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat X4) Y4)))) (= (tptp.produc6842872674320459806at_nat F) G))) (forall ((F tptp.fun_na1668100129766719005at_nat) (G tptp.fun_Pr2477239776880934807at_nat)) (=> (forall ((X4 tptp.nat) (Y4 tptp.nat)) (= (tptp.aa_nat7997280740862404369at_nat (tptp.aa_nat5682243440470347102at_nat F X4) Y4) (tptp.aa_Pro8023792847356852296at_nat G (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat X4) Y4)))) (= (tptp.produc4528391901023682385at_nat F) G))) (forall ((F tptp.fun_na4786964484885125043t_bool) (G tptp.fun_Pr248683899324676269t_bool)) (=> (forall ((X4 tptp.nat) (Y4 tptp.nat)) (= (tptp.aa_nat4401263874371387303t_bool (tptp.aa_nat4909001760120733684t_bool F X4) Y4) (tptp.aa_Pro595088089689268830t_bool G (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat X4) Y4)))) (= (tptp.produc5023667602222594023t_bool F) G))) (forall ((F tptp.fun_in1696471567231710611nt_int) (G tptp.fun_Pr2478283820680522243nt_int)) (=> (forall ((X4 tptp.int) (Y4 tptp.int)) (= (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int F X4) Y4) (tptp.aa_Pro6970504127699319548nt_int G (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int X4) Y4)))) (= (tptp.produc4245557441103728435nt_int F) G))) (forall ((F tptp.fun_int_fun_int_bool) (G tptp.fun_Pr803113274115125473t_bool)) (=> (forall ((X4 tptp.int) (Y4 tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool F X4) Y4)) (tptp.pp (tptp.aa_Pro4501881432599481050t_bool G (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int X4) Y4))))) (= (tptp.produc8560705615207772305t_bool F) G))) (forall ((F tptp.fun_Pr2602117396471556196at_nat)) (= (tptp.produc6842872674320459806at_nat (tptp.aTP_Lamm_go F)) F)) (forall ((F tptp.fun_Pr2477239776880934807at_nat)) (= (tptp.produc4528391901023682385at_nat (tptp.aTP_Lamm_gp F)) F)) (forall ((F tptp.fun_Pr248683899324676269t_bool)) (= (tptp.produc5023667602222594023t_bool (tptp.aTP_Lamm_gq F)) F)) (forall ((F tptp.fun_Pr2478283820680522243nt_int)) (= (tptp.produc4245557441103728435nt_int (tptp.aTP_Lamm_gr F)) F)) (forall ((F tptp.fun_Pr803113274115125473t_bool)) (= (tptp.produc8560705615207772305t_bool (tptp.aTP_Lamm_gs F)) F)) (forall ((Q tptp.fun_nat_bool) (P tptp.fun_nat_fun_nat_nat) (Z tptp.product_prod_nat_nat)) (=> (tptp.pp (tptp.aa_nat_bool Q (tptp.aa_Pro4243173770044397973at_nat (tptp.produc6842872674320459806at_nat P) Z))) (not (forall ((X4 tptp.nat) (Y4 tptp.nat)) (=> (= Z (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat X4) Y4)) (not (tptp.pp (tptp.aa_nat_bool Q (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat P X4) Y4))))))))) (forall ((Q tptp.fun_fu7919257609373989805t_bool) (P tptp.fun_na1668100129766719005at_nat) (Z tptp.product_prod_nat_nat)) (=> (tptp.pp (tptp.aa_fun4519828053337421206t_bool Q (tptp.aa_Pro8023792847356852296at_nat (tptp.produc4528391901023682385at_nat P) Z))) (not (forall ((X4 tptp.nat) (Y4 tptp.nat)) (=> (= Z (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat X4) Y4)) (not (tptp.pp (tptp.aa_fun4519828053337421206t_bool Q (tptp.aa_nat7997280740862404369at_nat (tptp.aa_nat5682243440470347102at_nat P X4) Y4))))))))) (forall ((Q tptp.fun_fu5641360819561228055l_bool) (P tptp.fun_na4786964484885125043t_bool) (Z tptp.product_prod_nat_nat)) (=> (tptp.pp (tptp.aa_fun8663595511526100224l_bool Q (tptp.aa_Pro595088089689268830t_bool (tptp.produc5023667602222594023t_bool P) Z))) (not (forall ((X4 tptp.nat) (Y4 tptp.nat)) (=> (= Z (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat X4) Y4)) (not (tptp.pp (tptp.aa_fun8663595511526100224l_bool Q (tptp.aa_nat4401263874371387303t_bool (tptp.aa_nat4909001760120733684t_bool P X4) Y4))))))))) (forall ((Q tptp.fun_Pr803113274115125473t_bool) (P tptp.fun_in1696471567231710611nt_int) (Z tptp.product_prod_int_int)) (=> (tptp.pp (tptp.aa_Pro4501881432599481050t_bool Q (tptp.aa_Pro6970504127699319548nt_int (tptp.produc4245557441103728435nt_int P) Z))) (not (forall ((X4 tptp.int) (Y4 tptp.int)) (=> (= Z (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int X4) Y4)) (not (tptp.pp (tptp.aa_Pro4501881432599481050t_bool Q (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int P X4) Y4))))))))) (forall ((Q tptp.fun_bool_bool) (P tptp.fun_int_fun_int_bool) (Z tptp.product_prod_int_int)) (=> (tptp.pp (tptp.aa_bool_bool Q (tptp.aa_Pro4501881432599481050t_bool (tptp.produc8560705615207772305t_bool P) Z))) (not (forall ((X4 tptp.int) (Y4 tptp.int)) (=> (= Z (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int X4) Y4)) (not (tptp.pp (tptp.aa_bool_bool Q (tptp.aa_int_bool (tptp.aa_int_fun_int_bool P X4) Y4))))))))) (forall ((A4 tptp.set_real) (F tptp.fun_real_real)) (=> (forall ((X4 tptp.real)) (=> (tptp.member_real X4 A4) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_real_real F X4))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.groups8097168146408367636l_real F A4))))) (forall ((A4 tptp.set_int) (F tptp.fun_int_real)) (=> (forall ((X4 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X4) A4)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_int_real F X4))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.groups8778361861064173332t_real F A4))))) (forall ((A4 tptp.set_complex) (F tptp.fun_complex_real)) (=> (forall ((X4 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex X4) A4)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_complex_real F X4))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.groups5808333547571424918x_real F A4))))) (forall ((A4 tptp.set_nat) (F tptp.fun_nat_rat)) (=> (forall ((X4 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X4) A4)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_nat_rat F X4))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.groups2906978787729119204at_rat F A4))))) (forall ((A4 tptp.set_real) (F tptp.fun_real_rat)) (=> (forall ((X4 tptp.real)) (=> (tptp.member_real X4 A4) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_real_rat F X4))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.groups1300246762558778688al_rat F A4))))) (forall ((A4 tptp.set_int) (F tptp.fun_int_rat)) (=> (forall ((X4 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X4) A4)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_int_rat F X4))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.groups3906332499630173760nt_rat F A4))))) (forall ((A4 tptp.set_complex) (F tptp.fun_complex_rat)) (=> (forall ((X4 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex X4) A4)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_complex_rat F X4))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.groups5058264527183730370ex_rat F A4))))) (forall ((A4 tptp.set_real) (F tptp.fun_real_nat)) (=> (forall ((X4 tptp.real)) (=> (tptp.member_real X4 A4) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) (tptp.aa_real_nat F X4))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) (tptp.groups1935376822645274424al_nat F A4))))) (forall ((A4 tptp.set_int) (F tptp.fun_int_nat)) (=> (forall ((X4 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X4) A4)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) (tptp.aa_int_nat F X4))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) (tptp.groups4541462559716669496nt_nat F A4))))) (forall ((A4 tptp.set_complex) (F tptp.fun_complex_nat)) (=> (forall ((X4 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex X4) A4)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) (tptp.aa_complex_nat F X4))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) (tptp.groups5693394587270226106ex_nat F A4))))) (forall ((A4 tptp.set_real) (F tptp.fun_real_real)) (=> (forall ((X4 tptp.real)) (=> (tptp.member_real X4 A4) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real F X4)) tptp.zero_zero_real)))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.groups8097168146408367636l_real F A4)) tptp.zero_zero_real)))) (forall ((A4 tptp.set_int) (F tptp.fun_int_real)) (=> (forall ((X4 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X4) A4)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_int_real F X4)) tptp.zero_zero_real)))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.groups8778361861064173332t_real F A4)) tptp.zero_zero_real)))) (forall ((A4 tptp.set_complex) (F tptp.fun_complex_real)) (=> (forall ((X4 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex X4) A4)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_complex_real F X4)) tptp.zero_zero_real)))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.groups5808333547571424918x_real F A4)) tptp.zero_zero_real)))) (forall ((A4 tptp.set_nat) (F tptp.fun_nat_rat)) (=> (forall ((X4 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X4) A4)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat F X4)) tptp.zero_zero_rat)))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.groups2906978787729119204at_rat F A4)) tptp.zero_zero_rat)))) (forall ((A4 tptp.set_real) (F tptp.fun_real_rat)) (=> (forall ((X4 tptp.real)) (=> (tptp.member_real X4 A4) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_real_rat F X4)) tptp.zero_zero_rat)))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.groups1300246762558778688al_rat F A4)) tptp.zero_zero_rat)))) (forall ((A4 tptp.set_int) (F tptp.fun_int_rat)) (=> (forall ((X4 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X4) A4)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_int_rat F X4)) tptp.zero_zero_rat)))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.groups3906332499630173760nt_rat F A4)) tptp.zero_zero_rat)))) (forall ((A4 tptp.set_complex) (F tptp.fun_complex_rat)) (=> (forall ((X4 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex X4) A4)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_complex_rat F X4)) tptp.zero_zero_rat)))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.groups5058264527183730370ex_rat F A4)) tptp.zero_zero_rat)))) (forall ((A4 tptp.set_real) (F tptp.fun_real_nat)) (=> (forall ((X4 tptp.real)) (=> (tptp.member_real X4 A4) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_real_nat F X4)) tptp.zero_zero_nat)))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.groups1935376822645274424al_nat F A4)) tptp.zero_zero_nat)))) (forall ((A4 tptp.set_int) (F tptp.fun_int_nat)) (=> (forall ((X4 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X4) A4)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_int_nat F X4)) tptp.zero_zero_nat)))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.groups4541462559716669496nt_nat F A4)) tptp.zero_zero_nat)))) (forall ((A4 tptp.set_complex) (F tptp.fun_complex_nat)) (=> (forall ((X4 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex X4) A4)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_complex_nat F X4)) tptp.zero_zero_nat)))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.groups5693394587270226106ex_nat F A4)) tptp.zero_zero_nat)))) (forall ((F tptp.fun_real_rat) (I5 tptp.set_real) (G tptp.fun_real_rat) (I tptp.real)) (=> (= (tptp.groups1300246762558778688al_rat F I5) (tptp.groups1300246762558778688al_rat G I5)) (=> (forall ((I3 tptp.real)) (=> (tptp.member_real I3 I5) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_real_rat F I3)) (tptp.aa_real_rat G I3))))) (=> (tptp.member_real I I5) (=> (tptp.finite_finite_real I5) (= (tptp.aa_real_rat F I) (tptp.aa_real_rat G I))))))) (forall ((F tptp.fun_nat_rat) (I5 tptp.set_nat) (G tptp.fun_nat_rat) (I tptp.nat)) (=> (= (tptp.groups2906978787729119204at_rat F I5) (tptp.groups2906978787729119204at_rat G I5)) (=> (forall ((I3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat I3) I5)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat F I3)) (tptp.aa_nat_rat G I3))))) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat I) I5)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat I5)) (= (tptp.aa_nat_rat F I) (tptp.aa_nat_rat G I))))))) (forall ((F tptp.fun_int_rat) (I5 tptp.set_int) (G tptp.fun_int_rat) (I tptp.int)) (=> (= (tptp.groups3906332499630173760nt_rat F I5) (tptp.groups3906332499630173760nt_rat G I5)) (=> (forall ((I3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int I3) I5)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_int_rat F I3)) (tptp.aa_int_rat G I3))))) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int I) I5)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int I5)) (= (tptp.aa_int_rat F I) (tptp.aa_int_rat G I))))))) (forall ((F tptp.fun_complex_rat) (I5 tptp.set_complex) (G tptp.fun_complex_rat) (I tptp.complex)) (=> (= (tptp.groups5058264527183730370ex_rat F I5) (tptp.groups5058264527183730370ex_rat G I5)) (=> (forall ((I3 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex I3) I5)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_complex_rat F I3)) (tptp.aa_complex_rat G I3))))) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex I) I5)) (=> (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex I5)) (= (tptp.aa_complex_rat F I) (tptp.aa_complex_rat G I))))))) (forall ((F tptp.fun_real_nat) (I5 tptp.set_real) (G tptp.fun_real_nat) (I tptp.real)) (=> (= (tptp.groups1935376822645274424al_nat F I5) (tptp.groups1935376822645274424al_nat G I5)) (=> (forall ((I3 tptp.real)) (=> (tptp.member_real I3 I5) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_real_nat F I3)) (tptp.aa_real_nat G I3))))) (=> (tptp.member_real I I5) (=> (tptp.finite_finite_real I5) (= (tptp.aa_real_nat F I) (tptp.aa_real_nat G I))))))) (forall ((F tptp.fun_int_nat) (I5 tptp.set_int) (G tptp.fun_int_nat) (I tptp.int)) (=> (= (tptp.groups4541462559716669496nt_nat F I5) (tptp.groups4541462559716669496nt_nat G I5)) (=> (forall ((I3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int I3) I5)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_int_nat F I3)) (tptp.aa_int_nat G I3))))) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int I) I5)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int I5)) (= (tptp.aa_int_nat F I) (tptp.aa_int_nat G I))))))) (forall ((F tptp.fun_complex_nat) (I5 tptp.set_complex) (G tptp.fun_complex_nat) (I tptp.complex)) (=> (= (tptp.groups5693394587270226106ex_nat F I5) (tptp.groups5693394587270226106ex_nat G I5)) (=> (forall ((I3 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex I3) I5)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_complex_nat F I3)) (tptp.aa_complex_nat G I3))))) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex I) I5)) (=> (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex I5)) (= (tptp.aa_complex_nat F I) (tptp.aa_complex_nat G I))))))) (forall ((F tptp.fun_real_int) (I5 tptp.set_real) (G tptp.fun_real_int) (I tptp.real)) (=> (= (tptp.groups1932886352136224148al_int F I5) (tptp.groups1932886352136224148al_int G I5)) (=> (forall ((I3 tptp.real)) (=> (tptp.member_real I3 I5) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_real_int F I3)) (tptp.aa_real_int G I3))))) (=> (tptp.member_real I I5) (=> (tptp.finite_finite_real I5) (= (tptp.aa_real_int F I) (tptp.aa_real_int G I))))))) (forall ((F tptp.fun_nat_int) (I5 tptp.set_nat) (G tptp.fun_nat_int) (I tptp.nat)) (=> (= (tptp.groups3539618377306564664at_int F I5) (tptp.groups3539618377306564664at_int G I5)) (=> (forall ((I3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat I3) I5)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int F I3)) (tptp.aa_nat_int G I3))))) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat I) I5)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat I5)) (= (tptp.aa_nat_int F I) (tptp.aa_nat_int G I))))))) (forall ((F tptp.fun_complex_int) (I5 tptp.set_complex) (G tptp.fun_complex_int) (I tptp.complex)) (=> (= (tptp.groups5690904116761175830ex_int F I5) (tptp.groups5690904116761175830ex_int G I5)) (=> (forall ((I3 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex I3) I5)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_complex_int F I3)) (tptp.aa_complex_int G I3))))) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex I) I5)) (=> (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex I5)) (= (tptp.aa_complex_int F I) (tptp.aa_complex_int G I))))))) (forall ((X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) X)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.ln_ln_real X)) X)))) (forall ((X tptp.product_prod_num_num)) (=> (not (= X (tptp.product_Pair_num_num tptp.one tptp.one))) (=> (forall ((N2 tptp.num)) (not (= X (tptp.product_Pair_num_num tptp.one (tptp.aa_num_num tptp.bit0 N2))))) (=> (forall ((N2 tptp.num)) (not (= X (tptp.product_Pair_num_num tptp.one (tptp.aa_num_num tptp.bit1 N2))))) (=> (forall ((M3 tptp.num)) (not (= X (tptp.product_Pair_num_num (tptp.aa_num_num tptp.bit0 M3) tptp.one)))) (=> (forall ((M3 tptp.num) (N2 tptp.num)) (not (= X (tptp.product_Pair_num_num (tptp.aa_num_num tptp.bit0 M3) (tptp.aa_num_num tptp.bit0 N2))))) (=> (forall ((M3 tptp.num) (N2 tptp.num)) (not (= X (tptp.product_Pair_num_num (tptp.aa_num_num tptp.bit0 M3) (tptp.aa_num_num tptp.bit1 N2))))) (=> (forall ((M3 tptp.num)) (not (= X (tptp.product_Pair_num_num (tptp.aa_num_num tptp.bit1 M3) tptp.one)))) (=> (forall ((M3 tptp.num) (N2 tptp.num)) (not (= X (tptp.product_Pair_num_num (tptp.aa_num_num tptp.bit1 M3) (tptp.aa_num_num tptp.bit0 N2))))) (not (forall ((M3 tptp.num) (N2 tptp.num)) (not (= X (tptp.product_Pair_num_num (tptp.aa_num_num tptp.bit1 M3) (tptp.aa_num_num tptp.bit1 N2))))))))))))))) (forall ((Y tptp.num)) (=> (not (= Y tptp.one)) (=> (forall ((X22 tptp.num)) (not (= Y (tptp.aa_num_num tptp.bit0 X22)))) (not (forall ((X33 tptp.num)) (not (= Y (tptp.aa_num_num tptp.bit1 X33)))))))) (forall ((S tptp.set_int) (T tptp.set_int) (G tptp.fun_int_real) (I tptp.fun_int_int) (F tptp.fun_int_real)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int S)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int T)) (=> (forall ((X4 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X4) T)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_int_real G X4))))) (=> (forall ((X4 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X4) S)) (exists ((Xa tptp.int)) (and (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Xa) T)) (= (tptp.aa_int_int I Xa) X4) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_int_real F X4)) (tptp.aa_int_real G Xa))))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.groups8778361861064173332t_real F S)) (tptp.groups8778361861064173332t_real G T)))))))) (forall ((S tptp.set_int) (T tptp.set_complex) (G tptp.fun_complex_real) (I tptp.fun_complex_int) (F tptp.fun_int_real)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int S)) (=> (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex T)) (=> (forall ((X4 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex X4) T)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_complex_real G X4))))) (=> (forall ((X4 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X4) S)) (exists ((Xa tptp.complex)) (and (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex Xa) T)) (= (tptp.aa_complex_int I Xa) X4) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_int_real F X4)) (tptp.aa_complex_real G Xa))))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.groups8778361861064173332t_real F S)) (tptp.groups5808333547571424918x_real G T)))))))) (forall ((S tptp.set_complex) (T tptp.set_int) (G tptp.fun_int_real) (I tptp.fun_int_complex) (F tptp.fun_complex_real)) (=> (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex S)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int T)) (=> (forall ((X4 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X4) T)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_int_real G X4))))) (=> (forall ((X4 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex X4) S)) (exists ((Xa tptp.int)) (and (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Xa) T)) (= (tptp.aa_int_complex I Xa) X4) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_complex_real F X4)) (tptp.aa_int_real G Xa))))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.groups5808333547571424918x_real F S)) (tptp.groups8778361861064173332t_real G T)))))))) (forall ((S tptp.set_complex) (T tptp.set_complex) (G tptp.fun_complex_real) (I tptp.fun_complex_complex) (F tptp.fun_complex_real)) (=> (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex S)) (=> (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex T)) (=> (forall ((X4 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex X4) T)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_complex_real G X4))))) (=> (forall ((X4 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex X4) S)) (exists ((Xa tptp.complex)) (and (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex Xa) T)) (= (tptp.aa_complex_complex I Xa) X4) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_complex_real F X4)) (tptp.aa_complex_real G Xa))))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.groups5808333547571424918x_real F S)) (tptp.groups5808333547571424918x_real G T)))))))) (forall ((S tptp.set_nat) (T tptp.set_nat) (G tptp.fun_nat_rat) (I tptp.fun_nat_nat) (F tptp.fun_nat_rat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat S)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat T)) (=> (forall ((X4 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X4) T)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_nat_rat G X4))))) (=> (forall ((X4 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X4) S)) (exists ((Xa tptp.nat)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat Xa) T)) (= (tptp.aa_nat_nat I Xa) X4) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat F X4)) (tptp.aa_nat_rat G Xa))))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.groups2906978787729119204at_rat F S)) (tptp.groups2906978787729119204at_rat G T)))))))) (forall ((S tptp.set_nat) (T tptp.set_int) (G tptp.fun_int_rat) (I tptp.fun_int_nat) (F tptp.fun_nat_rat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat S)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int T)) (=> (forall ((X4 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X4) T)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_int_rat G X4))))) (=> (forall ((X4 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X4) S)) (exists ((Xa tptp.int)) (and (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Xa) T)) (= (tptp.aa_int_nat I Xa) X4) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat F X4)) (tptp.aa_int_rat G Xa))))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.groups2906978787729119204at_rat F S)) (tptp.groups3906332499630173760nt_rat G T)))))))) (forall ((S tptp.set_nat) (T tptp.set_complex) (G tptp.fun_complex_rat) (I tptp.fun_complex_nat) (F tptp.fun_nat_rat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat S)) (=> (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex T)) (=> (forall ((X4 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex X4) T)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_complex_rat G X4))))) (=> (forall ((X4 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X4) S)) (exists ((Xa tptp.complex)) (and (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex Xa) T)) (= (tptp.aa_complex_nat I Xa) X4) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat F X4)) (tptp.aa_complex_rat G Xa))))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.groups2906978787729119204at_rat F S)) (tptp.groups5058264527183730370ex_rat G T)))))))) (forall ((S tptp.set_int) (T tptp.set_nat) (G tptp.fun_nat_rat) (I tptp.fun_nat_int) (F tptp.fun_int_rat)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int S)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat T)) (=> (forall ((X4 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X4) T)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_nat_rat G X4))))) (=> (forall ((X4 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X4) S)) (exists ((Xa tptp.nat)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat Xa) T)) (= (tptp.aa_nat_int I Xa) X4) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_int_rat F X4)) (tptp.aa_nat_rat G Xa))))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.groups3906332499630173760nt_rat F S)) (tptp.groups2906978787729119204at_rat G T)))))))) (forall ((S tptp.set_int) (T tptp.set_int) (G tptp.fun_int_rat) (I tptp.fun_int_int) (F tptp.fun_int_rat)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int S)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int T)) (=> (forall ((X4 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X4) T)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_int_rat G X4))))) (=> (forall ((X4 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X4) S)) (exists ((Xa tptp.int)) (and (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Xa) T)) (= (tptp.aa_int_int I Xa) X4) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_int_rat F X4)) (tptp.aa_int_rat G Xa))))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.groups3906332499630173760nt_rat F S)) (tptp.groups3906332499630173760nt_rat G T)))))))) (forall ((S tptp.set_int) (T tptp.set_complex) (G tptp.fun_complex_rat) (I tptp.fun_complex_int) (F tptp.fun_int_rat)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int S)) (=> (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex T)) (=> (forall ((X4 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex X4) T)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_complex_rat G X4))))) (=> (forall ((X4 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X4) S)) (exists ((Xa tptp.complex)) (and (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex Xa) T)) (= (tptp.aa_complex_int I Xa) X4) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_int_rat F X4)) (tptp.aa_complex_rat G Xa))))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.groups3906332499630173760nt_rat F S)) (tptp.groups5058264527183730370ex_rat G T)))))))) (forall ((A4 tptp.set_real) (F tptp.fun_real_real)) (=> (tptp.finite_finite_real A4) (=> (forall ((X4 tptp.real)) (=> (tptp.member_real X4 A4) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_real_real F X4))))) (= (= (tptp.groups8097168146408367636l_real F A4) tptp.zero_zero_real) (forall ((X3 tptp.real)) (=> (tptp.member_real X3 A4) (= (tptp.aa_real_real F X3) tptp.zero_zero_real))))))) (forall ((A4 tptp.set_int) (F tptp.fun_int_real)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A4)) (=> (forall ((X4 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X4) A4)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_int_real F X4))))) (= (= (tptp.groups8778361861064173332t_real F A4) tptp.zero_zero_real) (forall ((X3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X3) A4)) (= (tptp.aa_int_real F X3) tptp.zero_zero_real))))))) (forall ((A4 tptp.set_complex) (F tptp.fun_complex_real)) (=> (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex A4)) (=> (forall ((X4 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex X4) A4)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_complex_real F X4))))) (= (= (tptp.groups5808333547571424918x_real F A4) tptp.zero_zero_real) (forall ((X3 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex X3) A4)) (= (tptp.aa_complex_real F X3) tptp.zero_zero_real))))))) (forall ((A4 tptp.set_real) (F tptp.fun_real_rat)) (=> (tptp.finite_finite_real A4) (=> (forall ((X4 tptp.real)) (=> (tptp.member_real X4 A4) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_real_rat F X4))))) (= (= (tptp.groups1300246762558778688al_rat F A4) tptp.zero_zero_rat) (forall ((X3 tptp.real)) (=> (tptp.member_real X3 A4) (= (tptp.aa_real_rat F X3) tptp.zero_zero_rat))))))) (forall ((A4 tptp.set_nat) (F tptp.fun_nat_rat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A4)) (=> (forall ((X4 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X4) A4)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_nat_rat F X4))))) (= (= (tptp.groups2906978787729119204at_rat F A4) tptp.zero_zero_rat) (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) A4)) (= (tptp.aa_nat_rat F X3) tptp.zero_zero_rat))))))) (forall ((A4 tptp.set_int) (F tptp.fun_int_rat)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A4)) (=> (forall ((X4 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X4) A4)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_int_rat F X4))))) (= (= (tptp.groups3906332499630173760nt_rat F A4) tptp.zero_zero_rat) (forall ((X3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X3) A4)) (= (tptp.aa_int_rat F X3) tptp.zero_zero_rat))))))) (forall ((A4 tptp.set_complex) (F tptp.fun_complex_rat)) (=> (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex A4)) (=> (forall ((X4 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex X4) A4)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_complex_rat F X4))))) (= (= (tptp.groups5058264527183730370ex_rat F A4) tptp.zero_zero_rat) (forall ((X3 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex X3) A4)) (= (tptp.aa_complex_rat F X3) tptp.zero_zero_rat))))))) (forall ((A4 tptp.set_real) (F tptp.fun_real_nat)) (=> (tptp.finite_finite_real A4) (=> (forall ((X4 tptp.real)) (=> (tptp.member_real X4 A4) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) (tptp.aa_real_nat F X4))))) (= (= (tptp.groups1935376822645274424al_nat F A4) tptp.zero_zero_nat) (forall ((X3 tptp.real)) (=> (tptp.member_real X3 A4) (= (tptp.aa_real_nat F X3) tptp.zero_zero_nat))))))) (forall ((A4 tptp.set_int) (F tptp.fun_int_nat)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A4)) (=> (forall ((X4 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X4) A4)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) (tptp.aa_int_nat F X4))))) (= (= (tptp.groups4541462559716669496nt_nat F A4) tptp.zero_zero_nat) (forall ((X3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X3) A4)) (= (tptp.aa_int_nat F X3) tptp.zero_zero_nat))))))) (forall ((A4 tptp.set_complex) (F tptp.fun_complex_nat)) (=> (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex A4)) (=> (forall ((X4 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex X4) A4)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) (tptp.aa_complex_nat F X4))))) (= (= (tptp.groups5693394587270226106ex_nat F A4) tptp.zero_zero_nat) (forall ((X3 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex X3) A4)) (= (tptp.aa_complex_nat F X3) tptp.zero_zero_nat))))))) (forall ((A4 tptp.set_int) (F tptp.fun_int_real) (G tptp.fun_int_real)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A4)) (=> (forall ((X4 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X4) A4)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_int_real F X4)) (tptp.aa_int_real G X4))))) (=> (exists ((X5 tptp.int)) (and (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X5) A4)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_int_real F X5)) (tptp.aa_int_real G X5))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.groups8778361861064173332t_real F A4)) (tptp.groups8778361861064173332t_real G A4))))))) (forall ((A4 tptp.set_complex) (F tptp.fun_complex_real) (G tptp.fun_complex_real)) (=> (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex A4)) (=> (forall ((X4 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex X4) A4)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_complex_real F X4)) (tptp.aa_complex_real G X4))))) (=> (exists ((X5 tptp.complex)) (and (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex X5) A4)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_complex_real F X5)) (tptp.aa_complex_real G X5))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.groups5808333547571424918x_real F A4)) (tptp.groups5808333547571424918x_real G A4))))))) (forall ((A4 tptp.set_nat) (F tptp.fun_nat_rat) (G tptp.fun_nat_rat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A4)) (=> (forall ((X4 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X4) A4)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat F X4)) (tptp.aa_nat_rat G X4))))) (=> (exists ((X5 tptp.nat)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X5) A4)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_nat_rat F X5)) (tptp.aa_nat_rat G X5))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.groups2906978787729119204at_rat F A4)) (tptp.groups2906978787729119204at_rat G A4))))))) (forall ((A4 tptp.set_int) (F tptp.fun_int_rat) (G tptp.fun_int_rat)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A4)) (=> (forall ((X4 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X4) A4)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_int_rat F X4)) (tptp.aa_int_rat G X4))))) (=> (exists ((X5 tptp.int)) (and (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X5) A4)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_int_rat F X5)) (tptp.aa_int_rat G X5))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.groups3906332499630173760nt_rat F A4)) (tptp.groups3906332499630173760nt_rat G A4))))))) (forall ((A4 tptp.set_complex) (F tptp.fun_complex_rat) (G tptp.fun_complex_rat)) (=> (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex A4)) (=> (forall ((X4 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex X4) A4)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_complex_rat F X4)) (tptp.aa_complex_rat G X4))))) (=> (exists ((X5 tptp.complex)) (and (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex X5) A4)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_complex_rat F X5)) (tptp.aa_complex_rat G X5))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.groups5058264527183730370ex_rat F A4)) (tptp.groups5058264527183730370ex_rat G A4))))))) (forall ((A4 tptp.set_int) (F tptp.fun_int_nat) (G tptp.fun_int_nat)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A4)) (=> (forall ((X4 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X4) A4)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_int_nat F X4)) (tptp.aa_int_nat G X4))))) (=> (exists ((X5 tptp.int)) (and (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X5) A4)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_int_nat F X5)) (tptp.aa_int_nat G X5))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.groups4541462559716669496nt_nat F A4)) (tptp.groups4541462559716669496nt_nat G A4))))))) (forall ((A4 tptp.set_complex) (F tptp.fun_complex_nat) (G tptp.fun_complex_nat)) (=> (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex A4)) (=> (forall ((X4 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex X4) A4)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_complex_nat F X4)) (tptp.aa_complex_nat G X4))))) (=> (exists ((X5 tptp.complex)) (and (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex X5) A4)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_complex_nat F X5)) (tptp.aa_complex_nat G X5))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.groups5693394587270226106ex_nat F A4)) (tptp.groups5693394587270226106ex_nat G A4))))))) (forall ((A4 tptp.set_nat) (F tptp.fun_nat_int) (G tptp.fun_nat_int)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A4)) (=> (forall ((X4 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X4) A4)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int F X4)) (tptp.aa_nat_int G X4))))) (=> (exists ((X5 tptp.nat)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X5) A4)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_nat_int F X5)) (tptp.aa_nat_int G X5))))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.groups3539618377306564664at_int F A4)) (tptp.groups3539618377306564664at_int G A4))))))) (forall ((A4 tptp.set_complex) (F tptp.fun_complex_int) (G tptp.fun_complex_int)) (=> (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex A4)) (=> (forall ((X4 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex X4) A4)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_complex_int F X4)) (tptp.aa_complex_int G X4))))) (=> (exists ((X5 tptp.complex)) (and (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex X5) A4)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_complex_int F X5)) (tptp.aa_complex_int G X5))))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.groups5690904116761175830ex_int F A4)) (tptp.groups5690904116761175830ex_int G A4))))))) (forall ((A4 tptp.set_int) (F tptp.fun_int_int) (G tptp.fun_int_int)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A4)) (=> (forall ((X4 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X4) A4)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int F X4)) (tptp.aa_int_int G X4))))) (=> (exists ((X5 tptp.int)) (and (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X5) A4)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int F X5)) (tptp.aa_int_int G X5))))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.groups4538972089207619220nt_int F A4)) (tptp.groups4538972089207619220nt_int G A4))))))) (forall ((R2 tptp.fun_co1378794544173401837x_bool) (S2 tptp.set_nat) (H tptp.fun_nat_complex) (G tptp.fun_nat_complex)) (=> (tptp.pp (tptp.aa_complex_bool (tptp.aa_com1553036987509291606x_bool R2 tptp.zero_zero_complex) tptp.zero_zero_complex)) (=> (forall ((X15 tptp.complex) (Y15 tptp.complex) (X22 tptp.complex) (Y22 tptp.complex)) (=> (and (tptp.pp (tptp.aa_complex_bool (tptp.aa_com1553036987509291606x_bool R2 X15) X22)) (tptp.pp (tptp.aa_complex_bool (tptp.aa_com1553036987509291606x_bool R2 Y15) Y22))) (tptp.pp (tptp.aa_complex_bool (tptp.aa_com1553036987509291606x_bool R2 (tptp.aa_complex_complex (tptp.plus_plus_complex X15) Y15)) (tptp.aa_complex_complex (tptp.plus_plus_complex X22) Y22))))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat S2)) (=> (forall ((X4 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X4) S2)) (tptp.pp (tptp.aa_complex_bool (tptp.aa_com1553036987509291606x_bool R2 (tptp.aa_nat_complex H X4)) (tptp.aa_nat_complex G X4))))) (tptp.pp (tptp.aa_complex_bool (tptp.aa_com1553036987509291606x_bool R2 (tptp.groups2073611262835488442omplex H S2)) (tptp.groups2073611262835488442omplex G S2)))))))) (forall ((R2 tptp.fun_co1378794544173401837x_bool) (S2 tptp.set_int) (H tptp.fun_int_complex) (G tptp.fun_int_complex)) (=> (tptp.pp (tptp.aa_complex_bool (tptp.aa_com1553036987509291606x_bool R2 tptp.zero_zero_complex) tptp.zero_zero_complex)) (=> (forall ((X15 tptp.complex) (Y15 tptp.complex) (X22 tptp.complex) (Y22 tptp.complex)) (=> (and (tptp.pp (tptp.aa_complex_bool (tptp.aa_com1553036987509291606x_bool R2 X15) X22)) (tptp.pp (tptp.aa_complex_bool (tptp.aa_com1553036987509291606x_bool R2 Y15) Y22))) (tptp.pp (tptp.aa_complex_bool (tptp.aa_com1553036987509291606x_bool R2 (tptp.aa_complex_complex (tptp.plus_plus_complex X15) Y15)) (tptp.aa_complex_complex (tptp.plus_plus_complex X22) Y22))))) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int S2)) (=> (forall ((X4 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X4) S2)) (tptp.pp (tptp.aa_complex_bool (tptp.aa_com1553036987509291606x_bool R2 (tptp.aa_int_complex H X4)) (tptp.aa_int_complex G X4))))) (tptp.pp (tptp.aa_complex_bool (tptp.aa_com1553036987509291606x_bool R2 (tptp.groups3049146728041665814omplex H S2)) (tptp.groups3049146728041665814omplex G S2)))))))) (forall ((R2 tptp.fun_re1255401033344146673l_bool) (S2 tptp.set_int) (H tptp.fun_int_real) (G tptp.fun_int_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool R2 tptp.zero_zero_real) tptp.zero_zero_real)) (=> (forall ((X15 tptp.real) (Y15 tptp.real) (X22 tptp.real) (Y22 tptp.real)) (=> (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool R2 X15) X22)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool R2 Y15) Y22))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool R2 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X15) Y15)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X22) Y22))))) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int S2)) (=> (forall ((X4 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X4) S2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool R2 (tptp.aa_int_real H X4)) (tptp.aa_int_real G X4))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool R2 (tptp.groups8778361861064173332t_real H S2)) (tptp.groups8778361861064173332t_real G S2)))))))) (forall ((R2 tptp.fun_re1255401033344146673l_bool) (S2 tptp.set_complex) (H tptp.fun_complex_real) (G tptp.fun_complex_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool R2 tptp.zero_zero_real) tptp.zero_zero_real)) (=> (forall ((X15 tptp.real) (Y15 tptp.real) (X22 tptp.real) (Y22 tptp.real)) (=> (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool R2 X15) X22)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool R2 Y15) Y22))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool R2 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X15) Y15)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X22) Y22))))) (=> (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex S2)) (=> (forall ((X4 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex X4) S2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool R2 (tptp.aa_complex_real H X4)) (tptp.aa_complex_real G X4))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool R2 (tptp.groups5808333547571424918x_real H S2)) (tptp.groups5808333547571424918x_real G S2)))))))) (forall ((R2 tptp.fun_rat_fun_rat_bool) (S2 tptp.set_nat) (H tptp.fun_nat_rat) (G tptp.fun_nat_rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool R2 tptp.zero_zero_rat) tptp.zero_zero_rat)) (=> (forall ((X15 tptp.rat) (Y15 tptp.rat) (X22 tptp.rat) (Y22 tptp.rat)) (=> (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool R2 X15) X22)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool R2 Y15) Y22))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool R2 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat X15) Y15)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat X22) Y22))))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat S2)) (=> (forall ((X4 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X4) S2)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool R2 (tptp.aa_nat_rat H X4)) (tptp.aa_nat_rat G X4))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool R2 (tptp.groups2906978787729119204at_rat H S2)) (tptp.groups2906978787729119204at_rat G S2)))))))) (forall ((R2 tptp.fun_rat_fun_rat_bool) (S2 tptp.set_int) (H tptp.fun_int_rat) (G tptp.fun_int_rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool R2 tptp.zero_zero_rat) tptp.zero_zero_rat)) (=> (forall ((X15 tptp.rat) (Y15 tptp.rat) (X22 tptp.rat) (Y22 tptp.rat)) (=> (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool R2 X15) X22)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool R2 Y15) Y22))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool R2 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat X15) Y15)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat X22) Y22))))) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int S2)) (=> (forall ((X4 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X4) S2)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool R2 (tptp.aa_int_rat H X4)) (tptp.aa_int_rat G X4))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool R2 (tptp.groups3906332499630173760nt_rat H S2)) (tptp.groups3906332499630173760nt_rat G S2)))))))) (forall ((R2 tptp.fun_rat_fun_rat_bool) (S2 tptp.set_complex) (H tptp.fun_complex_rat) (G tptp.fun_complex_rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool R2 tptp.zero_zero_rat) tptp.zero_zero_rat)) (=> (forall ((X15 tptp.rat) (Y15 tptp.rat) (X22 tptp.rat) (Y22 tptp.rat)) (=> (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool R2 X15) X22)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool R2 Y15) Y22))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool R2 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat X15) Y15)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat X22) Y22))))) (=> (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex S2)) (=> (forall ((X4 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex X4) S2)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool R2 (tptp.aa_complex_rat H X4)) (tptp.aa_complex_rat G X4))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool R2 (tptp.groups5058264527183730370ex_rat H S2)) (tptp.groups5058264527183730370ex_rat G S2)))))))) (forall ((R2 tptp.fun_nat_fun_nat_bool) (S2 tptp.set_int) (H tptp.fun_int_nat) (G tptp.fun_int_nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool R2 tptp.zero_zero_nat) tptp.zero_zero_nat)) (=> (forall ((X15 tptp.nat) (Y15 tptp.nat) (X22 tptp.nat) (Y22 tptp.nat)) (=> (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool R2 X15) X22)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool R2 Y15) Y22))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool R2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat X15) Y15)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat X22) Y22))))) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int S2)) (=> (forall ((X4 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X4) S2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool R2 (tptp.aa_int_nat H X4)) (tptp.aa_int_nat G X4))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool R2 (tptp.groups4541462559716669496nt_nat H S2)) (tptp.groups4541462559716669496nt_nat G S2)))))))) (forall ((R2 tptp.fun_nat_fun_nat_bool) (S2 tptp.set_complex) (H tptp.fun_complex_nat) (G tptp.fun_complex_nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool R2 tptp.zero_zero_nat) tptp.zero_zero_nat)) (=> (forall ((X15 tptp.nat) (Y15 tptp.nat) (X22 tptp.nat) (Y22 tptp.nat)) (=> (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool R2 X15) X22)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool R2 Y15) Y22))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool R2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat X15) Y15)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat X22) Y22))))) (=> (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex S2)) (=> (forall ((X4 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex X4) S2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool R2 (tptp.aa_complex_nat H X4)) (tptp.aa_complex_nat G X4))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool R2 (tptp.groups5693394587270226106ex_nat H S2)) (tptp.groups5693394587270226106ex_nat G S2)))))))) (forall ((R2 tptp.fun_int_fun_int_bool) (S2 tptp.set_nat) (H tptp.fun_nat_int) (G tptp.fun_nat_int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool R2 tptp.zero_zero_int) tptp.zero_zero_int)) (=> (forall ((X15 tptp.int) (Y15 tptp.int) (X22 tptp.int) (Y22 tptp.int)) (=> (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool R2 X15) X22)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool R2 Y15) Y22))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool R2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int X15) Y15)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int X22) Y22))))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat S2)) (=> (forall ((X4 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X4) S2)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool R2 (tptp.aa_nat_int H X4)) (tptp.aa_nat_int G X4))))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool R2 (tptp.groups3539618377306564664at_int H S2)) (tptp.groups3539618377306564664at_int G S2)))))))) (forall ((A4 tptp.set_complex) (F tptp.fun_complex_real) (G tptp.fun_complex_real)) (=> (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex A4)) (=> (not (= A4 tptp.bot_bot_set_complex)) (=> (forall ((X4 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex X4) A4)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_complex_real F X4)) (tptp.aa_complex_real G X4))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.groups5808333547571424918x_real F A4)) (tptp.groups5808333547571424918x_real G A4))))))) (forall ((A4 tptp.set_int) (F tptp.fun_int_real) (G tptp.fun_int_real)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A4)) (=> (not (= A4 tptp.bot_bot_set_int)) (=> (forall ((X4 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X4) A4)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_int_real F X4)) (tptp.aa_int_real G X4))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.groups8778361861064173332t_real F A4)) (tptp.groups8778361861064173332t_real G A4))))))) (forall ((A4 tptp.set_real) (F tptp.fun_real_real) (G tptp.fun_real_real)) (=> (tptp.finite_finite_real A4) (=> (not (= A4 tptp.bot_bot_set_real)) (=> (forall ((X4 tptp.real)) (=> (tptp.member_real X4 A4) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real F X4)) (tptp.aa_real_real G X4))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.groups8097168146408367636l_real F A4)) (tptp.groups8097168146408367636l_real G A4))))))) (forall ((A4 tptp.set_complex) (F tptp.fun_complex_rat) (G tptp.fun_complex_rat)) (=> (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex A4)) (=> (not (= A4 tptp.bot_bot_set_complex)) (=> (forall ((X4 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex X4) A4)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_complex_rat F X4)) (tptp.aa_complex_rat G X4))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.groups5058264527183730370ex_rat F A4)) (tptp.groups5058264527183730370ex_rat G A4))))))) (forall ((A4 tptp.set_nat) (F tptp.fun_nat_rat) (G tptp.fun_nat_rat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A4)) (=> (not (= A4 tptp.bot_bot_set_nat)) (=> (forall ((X4 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X4) A4)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_nat_rat F X4)) (tptp.aa_nat_rat G X4))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.groups2906978787729119204at_rat F A4)) (tptp.groups2906978787729119204at_rat G A4))))))) (forall ((A4 tptp.set_int) (F tptp.fun_int_rat) (G tptp.fun_int_rat)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A4)) (=> (not (= A4 tptp.bot_bot_set_int)) (=> (forall ((X4 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X4) A4)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_int_rat F X4)) (tptp.aa_int_rat G X4))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.groups3906332499630173760nt_rat F A4)) (tptp.groups3906332499630173760nt_rat G A4))))))) (forall ((A4 tptp.set_real) (F tptp.fun_real_rat) (G tptp.fun_real_rat)) (=> (tptp.finite_finite_real A4) (=> (not (= A4 tptp.bot_bot_set_real)) (=> (forall ((X4 tptp.real)) (=> (tptp.member_real X4 A4) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_real_rat F X4)) (tptp.aa_real_rat G X4))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.groups1300246762558778688al_rat F A4)) (tptp.groups1300246762558778688al_rat G A4))))))) (forall ((A4 tptp.set_complex) (F tptp.fun_complex_nat) (G tptp.fun_complex_nat)) (=> (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex A4)) (=> (not (= A4 tptp.bot_bot_set_complex)) (=> (forall ((X4 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex X4) A4)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_complex_nat F X4)) (tptp.aa_complex_nat G X4))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.groups5693394587270226106ex_nat F A4)) (tptp.groups5693394587270226106ex_nat G A4))))))) (forall ((A4 tptp.set_int) (F tptp.fun_int_nat) (G tptp.fun_int_nat)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A4)) (=> (not (= A4 tptp.bot_bot_set_int)) (=> (forall ((X4 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X4) A4)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_int_nat F X4)) (tptp.aa_int_nat G X4))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.groups4541462559716669496nt_nat F A4)) (tptp.groups4541462559716669496nt_nat G A4))))))) (forall ((A4 tptp.set_real) (F tptp.fun_real_nat) (G tptp.fun_real_nat)) (=> (tptp.finite_finite_real A4) (=> (not (= A4 tptp.bot_bot_set_real)) (=> (forall ((X4 tptp.real)) (=> (tptp.member_real X4 A4) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_real_nat F X4)) (tptp.aa_real_nat G X4))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.groups1935376822645274424al_nat F A4)) (tptp.groups1935376822645274424al_nat G A4))))))) (forall ((X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) X)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.ln_ln_real X)) X)))) (forall ((X tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real tptp.ln_ln_real X))) (=> (tptp.pp (tptp.aa_real_bool _let_1 X)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real) X)))))) (forall ((X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) tptp.one_one_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.ln_ln_real X)) tptp.zero_zero_real))))) (forall ((X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real) X)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) (tptp.aa_real_real tptp.ln_ln_real X))))) (forall ((X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.one_one_real) X)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_real_real tptp.ln_ln_real X))))) (forall ((N tptp.num)) (let ((_let_1 (tptp.numera6690914467698888265omplex N))) (= (tptp.numera6690914467698888265omplex (tptp.aa_num_num tptp.bit1 N)) (tptp.aa_complex_complex (tptp.plus_plus_complex (tptp.aa_complex_complex (tptp.plus_plus_complex _let_1) _let_1)) tptp.one_one_complex)))) (forall ((N tptp.num)) (let ((_let_1 (tptp.aa_num_real tptp.numeral_numeral_real N))) (= (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit1 N)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real _let_1) _let_1)) tptp.one_one_real)))) (forall ((N tptp.num)) (let ((_let_1 (tptp.aa_num_rat tptp.numeral_numeral_rat N))) (= (tptp.aa_num_rat tptp.numeral_numeral_rat (tptp.aa_num_num tptp.bit1 N)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat _let_1) _let_1)) tptp.one_one_rat)))) (forall ((N tptp.num)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat N))) (= (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 N)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat _let_1) _let_1)) tptp.one_one_nat)))) (forall ((N tptp.num)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int N))) (= (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit1 N)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int _let_1) _let_1)) tptp.one_one_int)))) (forall ((N tptp.num)) (= (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 N)) (tptp.aa_nat_nat tptp.suc (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 N))))) (forall ((M tptp.num) (Q2 tptp.num) (N tptp.num)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 Q2)))) (not (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 M))) _let_1) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 N))) _let_1))))) (forall ((M tptp.num) (Q2 tptp.num) (N tptp.num)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 Q2)))) (not (= (tptp.aa_int_int (tptp.modulo_modulo_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 M))) _let_1) (tptp.aa_int_int (tptp.modulo_modulo_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit1 N))) _let_1))))) (forall ((M tptp.num) (Q2 tptp.num) (N tptp.num)) (let ((_let_1 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 Q2)))) (not (= (tptp.modulo364778990260209775nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 M)) _let_1) (tptp.modulo364778990260209775nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit1 N)) _let_1))))) (forall ((M tptp.num) (Q2 tptp.num) (N tptp.num)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 Q2)))) (not (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 M))) _let_1) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 N))) _let_1))))) (forall ((M tptp.num) (Q2 tptp.num) (N tptp.num)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 Q2)))) (not (= (tptp.aa_int_int (tptp.modulo_modulo_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit1 M))) _let_1) (tptp.aa_int_int (tptp.modulo_modulo_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 N))) _let_1))))) (forall ((M tptp.num) (Q2 tptp.num) (N tptp.num)) (let ((_let_1 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 Q2)))) (not (= (tptp.modulo364778990260209775nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit1 M)) _let_1) (tptp.modulo364778990260209775nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 N)) _let_1))))) (forall ((M tptp.num) (Q2 tptp.num) (N tptp.num)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat Q2))) (let ((_let_2 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 Q2)))) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 M))) _let_2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 N))) _let_2)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_num_nat tptp.numeral_numeral_nat M)) _let_1) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_num_nat tptp.numeral_numeral_nat N)) _let_1)))))) (forall ((M tptp.num) (Q2 tptp.num) (N tptp.num)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int Q2))) (let ((_let_2 (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 Q2)))) (= (= (tptp.aa_int_int (tptp.modulo_modulo_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit1 M))) _let_2) (tptp.aa_int_int (tptp.modulo_modulo_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit1 N))) _let_2)) (= (tptp.aa_int_int (tptp.modulo_modulo_int (tptp.aa_num_int tptp.numeral_numeral_int M)) _let_1) (tptp.aa_int_int (tptp.modulo_modulo_int (tptp.aa_num_int tptp.numeral_numeral_int N)) _let_1)))))) (forall ((M tptp.num) (Q2 tptp.num) (N tptp.num)) (let ((_let_1 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger Q2))) (let ((_let_2 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 Q2)))) (= (= (tptp.modulo364778990260209775nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit1 M)) _let_2) (tptp.modulo364778990260209775nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit1 N)) _let_2)) (= (tptp.modulo364778990260209775nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger M) _let_1) (tptp.modulo364778990260209775nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger N) _let_1)))))) (forall ((X tptp.real) (K tptp.num)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 K)))) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real tptp.uminus_uminus_real X)) _let_1) (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) _let_1))))) (forall ((X tptp.int) (K tptp.num)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 K)))) (= (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_int_int tptp.uminus_uminus_int X)) _let_1) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_nat_int (tptp.power_power_int X) _let_1))))) (forall ((X tptp.complex) (K tptp.num)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 K)))) (= (tptp.aa_nat_complex (tptp.power_power_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex X)) _let_1) (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.aa_nat_complex (tptp.power_power_complex X) _let_1))))) (forall ((X tptp.code_integer) (K tptp.num)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 K)))) (= (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger X)) _let_1) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger X) _let_1))))) (forall ((X tptp.rat) (K tptp.num)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 K)))) (= (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat X)) _let_1) (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_nat_rat (tptp.power_power_rat X) _let_1))))) (forall ((S tptp.set_real) (F tptp.fun_real_real) (B4 tptp.real) (I tptp.real)) (=> (tptp.finite_finite_real S) (=> (forall ((I3 tptp.real)) (=> (tptp.member_real I3 S) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_real_real F I3))))) (=> (= (tptp.groups8097168146408367636l_real F S) B4) (=> (tptp.member_real I S) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real F I)) B4))))))) (forall ((S tptp.set_int) (F tptp.fun_int_real) (B4 tptp.real) (I tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int S)) (=> (forall ((I3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int I3) S)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_int_real F I3))))) (=> (= (tptp.groups8778361861064173332t_real F S) B4) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int I) S)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_int_real F I)) B4))))))) (forall ((S tptp.set_complex) (F tptp.fun_complex_real) (B4 tptp.real) (I tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex S)) (=> (forall ((I3 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex I3) S)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_complex_real F I3))))) (=> (= (tptp.groups5808333547571424918x_real F S) B4) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex I) S)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_complex_real F I)) B4))))))) (forall ((S tptp.set_real) (F tptp.fun_real_rat) (B4 tptp.rat) (I tptp.real)) (=> (tptp.finite_finite_real S) (=> (forall ((I3 tptp.real)) (=> (tptp.member_real I3 S) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_real_rat F I3))))) (=> (= (tptp.groups1300246762558778688al_rat F S) B4) (=> (tptp.member_real I S) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_real_rat F I)) B4))))))) (forall ((S tptp.set_nat) (F tptp.fun_nat_rat) (B4 tptp.rat) (I tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat S)) (=> (forall ((I3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat I3) S)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_nat_rat F I3))))) (=> (= (tptp.groups2906978787729119204at_rat F S) B4) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat I) S)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat F I)) B4))))))) (forall ((S tptp.set_int) (F tptp.fun_int_rat) (B4 tptp.rat) (I tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int S)) (=> (forall ((I3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int I3) S)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_int_rat F I3))))) (=> (= (tptp.groups3906332499630173760nt_rat F S) B4) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int I) S)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_int_rat F I)) B4))))))) (forall ((S tptp.set_complex) (F tptp.fun_complex_rat) (B4 tptp.rat) (I tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex S)) (=> (forall ((I3 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex I3) S)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_complex_rat F I3))))) (=> (= (tptp.groups5058264527183730370ex_rat F S) B4) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex I) S)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_complex_rat F I)) B4))))))) (forall ((S tptp.set_real) (F tptp.fun_real_nat) (B4 tptp.nat) (I tptp.real)) (=> (tptp.finite_finite_real S) (=> (forall ((I3 tptp.real)) (=> (tptp.member_real I3 S) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) (tptp.aa_real_nat F I3))))) (=> (= (tptp.groups1935376822645274424al_nat F S) B4) (=> (tptp.member_real I S) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_real_nat F I)) B4))))))) (forall ((S tptp.set_int) (F tptp.fun_int_nat) (B4 tptp.nat) (I tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int S)) (=> (forall ((I3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int I3) S)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) (tptp.aa_int_nat F I3))))) (=> (= (tptp.groups4541462559716669496nt_nat F S) B4) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int I) S)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_int_nat F I)) B4))))))) (forall ((S tptp.set_complex) (F tptp.fun_complex_nat) (B4 tptp.nat) (I tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex S)) (=> (forall ((I3 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex I3) S)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) (tptp.aa_complex_nat F I3))))) (=> (= (tptp.groups5693394587270226106ex_nat F S) B4) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex I) S)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_complex_nat F I)) B4))))))) (forall ((S tptp.set_real) (F tptp.fun_real_real) (I tptp.real)) (=> (tptp.finite_finite_real S) (=> (forall ((I3 tptp.real)) (=> (tptp.member_real I3 S) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_real_real F I3))))) (=> (= (tptp.groups8097168146408367636l_real F S) tptp.zero_zero_real) (=> (tptp.member_real I S) (= (tptp.aa_real_real F I) tptp.zero_zero_real)))))) (forall ((S tptp.set_int) (F tptp.fun_int_real) (I tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int S)) (=> (forall ((I3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int I3) S)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_int_real F I3))))) (=> (= (tptp.groups8778361861064173332t_real F S) tptp.zero_zero_real) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int I) S)) (= (tptp.aa_int_real F I) tptp.zero_zero_real)))))) (forall ((S tptp.set_complex) (F tptp.fun_complex_real) (I tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex S)) (=> (forall ((I3 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex I3) S)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_complex_real F I3))))) (=> (= (tptp.groups5808333547571424918x_real F S) tptp.zero_zero_real) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex I) S)) (= (tptp.aa_complex_real F I) tptp.zero_zero_real)))))) (forall ((S tptp.set_real) (F tptp.fun_real_rat) (I tptp.real)) (=> (tptp.finite_finite_real S) (=> (forall ((I3 tptp.real)) (=> (tptp.member_real I3 S) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_real_rat F I3))))) (=> (= (tptp.groups1300246762558778688al_rat F S) tptp.zero_zero_rat) (=> (tptp.member_real I S) (= (tptp.aa_real_rat F I) tptp.zero_zero_rat)))))) (forall ((S tptp.set_nat) (F tptp.fun_nat_rat) (I tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat S)) (=> (forall ((I3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat I3) S)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_nat_rat F I3))))) (=> (= (tptp.groups2906978787729119204at_rat F S) tptp.zero_zero_rat) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat I) S)) (= (tptp.aa_nat_rat F I) tptp.zero_zero_rat)))))) (forall ((S tptp.set_int) (F tptp.fun_int_rat) (I tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int S)) (=> (forall ((I3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int I3) S)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_int_rat F I3))))) (=> (= (tptp.groups3906332499630173760nt_rat F S) tptp.zero_zero_rat) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int I) S)) (= (tptp.aa_int_rat F I) tptp.zero_zero_rat)))))) (forall ((S tptp.set_complex) (F tptp.fun_complex_rat) (I tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex S)) (=> (forall ((I3 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex I3) S)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_complex_rat F I3))))) (=> (= (tptp.groups5058264527183730370ex_rat F S) tptp.zero_zero_rat) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex I) S)) (= (tptp.aa_complex_rat F I) tptp.zero_zero_rat)))))) (forall ((S tptp.set_real) (F tptp.fun_real_nat) (I tptp.real)) (=> (tptp.finite_finite_real S) (=> (forall ((I3 tptp.real)) (=> (tptp.member_real I3 S) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) (tptp.aa_real_nat F I3))))) (=> (= (tptp.groups1935376822645274424al_nat F S) tptp.zero_zero_nat) (=> (tptp.member_real I S) (= (tptp.aa_real_nat F I) tptp.zero_zero_nat)))))) (forall ((S tptp.set_int) (F tptp.fun_int_nat) (I tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int S)) (=> (forall ((I3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int I3) S)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) (tptp.aa_int_nat F I3))))) (=> (= (tptp.groups4541462559716669496nt_nat F S) tptp.zero_zero_nat) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int I) S)) (= (tptp.aa_int_nat F I) tptp.zero_zero_nat)))))) (forall ((S tptp.set_complex) (F tptp.fun_complex_nat) (I tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex S)) (=> (forall ((I3 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex I3) S)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) (tptp.aa_complex_nat F I3))))) (=> (= (tptp.groups5693394587270226106ex_nat F S) tptp.zero_zero_nat) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex I) S)) (= (tptp.aa_complex_nat F I) tptp.zero_zero_nat)))))) (forall ((N tptp.num)) (let ((_let_1 (tptp.numera6690914467698888265omplex N))) (= (tptp.numera6690914467698888265omplex (tptp.aa_num_num tptp.bit1 N)) (tptp.aa_complex_complex (tptp.plus_plus_complex (tptp.aa_complex_complex (tptp.plus_plus_complex _let_1) _let_1)) tptp.one_one_complex)))) (forall ((N tptp.num)) (let ((_let_1 (tptp.aa_num_real tptp.numeral_numeral_real N))) (= (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit1 N)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real _let_1) _let_1)) tptp.one_one_real)))) (forall ((N tptp.num)) (let ((_let_1 (tptp.aa_num_rat tptp.numeral_numeral_rat N))) (= (tptp.aa_num_rat tptp.numeral_numeral_rat (tptp.aa_num_num tptp.bit1 N)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat _let_1) _let_1)) tptp.one_one_rat)))) (forall ((N tptp.num)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat N))) (= (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 N)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat _let_1) _let_1)) tptp.one_one_nat)))) (forall ((N tptp.num)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int N))) (= (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit1 N)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int _let_1) _let_1)) tptp.one_one_int)))) (forall ((Z tptp.complex) (W tptp.num)) (let ((_let_1 (tptp.power_power_complex Z))) (let ((_let_2 (tptp.aa_nat_complex _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat W)))) (= (tptp.aa_nat_complex _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 W))) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_complex_complex (tptp.times_times_complex Z) _let_2)) _let_2))))) (forall ((Z tptp.real) (W tptp.num)) (let ((_let_1 (tptp.aa_real_fun_nat_real tptp.power_power_real Z))) (let ((_let_2 (tptp.aa_nat_real _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat W)))) (= (tptp.aa_nat_real _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 W))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real Z) _let_2)) _let_2))))) (forall ((Z tptp.rat) (W tptp.num)) (let ((_let_1 (tptp.power_power_rat Z))) (let ((_let_2 (tptp.aa_nat_rat _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat W)))) (= (tptp.aa_nat_rat _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 W))) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat Z) _let_2)) _let_2))))) (forall ((Z tptp.nat) (W tptp.num)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat Z))) (let ((_let_2 (tptp.aa_nat_nat _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat W)))) (= (tptp.aa_nat_nat _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 W))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat Z) _let_2)) _let_2))))) (forall ((Z tptp.int) (W tptp.num)) (let ((_let_1 (tptp.power_power_int Z))) (let ((_let_2 (tptp.aa_nat_int _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat W)))) (= (tptp.aa_nat_int _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 W))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int Z) _let_2)) _let_2))))) (forall ((I5 tptp.set_real) (I tptp.real) (F tptp.fun_real_real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real))) (=> (tptp.finite_finite_real I5) (=> (tptp.member_real I I5) (=> (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real F I))) (=> (forall ((I3 tptp.real)) (=> (tptp.member_real I3 I5) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_real_real F I3))))) (tptp.pp (tptp.aa_real_bool _let_1 (tptp.groups8097168146408367636l_real F I5))))))))) (forall ((I5 tptp.set_int) (I tptp.int) (F tptp.fun_int_real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int I5)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int I) I5)) (=> (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_int_real F I))) (=> (forall ((I3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int I3) I5)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_int_real F I3))))) (tptp.pp (tptp.aa_real_bool _let_1 (tptp.groups8778361861064173332t_real F I5))))))))) (forall ((I5 tptp.set_complex) (I tptp.complex) (F tptp.fun_complex_real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex I5)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex I) I5)) (=> (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_complex_real F I))) (=> (forall ((I3 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex I3) I5)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_complex_real F I3))))) (tptp.pp (tptp.aa_real_bool _let_1 (tptp.groups5808333547571424918x_real F I5))))))))) (forall ((I5 tptp.set_real) (I tptp.real) (F tptp.fun_real_rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat))) (=> (tptp.finite_finite_real I5) (=> (tptp.member_real I I5) (=> (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_real_rat F I))) (=> (forall ((I3 tptp.real)) (=> (tptp.member_real I3 I5) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_real_rat F I3))))) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.groups1300246762558778688al_rat F I5))))))))) (forall ((I5 tptp.set_nat) (I tptp.nat) (F tptp.fun_nat_rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat I5)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat I) I5)) (=> (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_nat_rat F I))) (=> (forall ((I3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat I3) I5)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_nat_rat F I3))))) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.groups2906978787729119204at_rat F I5))))))))) (forall ((I5 tptp.set_int) (I tptp.int) (F tptp.fun_int_rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat))) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int I5)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int I) I5)) (=> (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_int_rat F I))) (=> (forall ((I3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int I3) I5)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_int_rat F I3))))) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.groups3906332499630173760nt_rat F I5))))))))) (forall ((I5 tptp.set_complex) (I tptp.complex) (F tptp.fun_complex_rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat))) (=> (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex I5)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex I) I5)) (=> (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_complex_rat F I))) (=> (forall ((I3 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex I3) I5)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_complex_rat F I3))))) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.groups5058264527183730370ex_rat F I5))))))))) (forall ((I5 tptp.set_real) (I tptp.real) (F tptp.fun_real_nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat))) (=> (tptp.finite_finite_real I5) (=> (tptp.member_real I I5) (=> (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_real_nat F I))) (=> (forall ((I3 tptp.real)) (=> (tptp.member_real I3 I5) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) (tptp.aa_real_nat F I3))))) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.groups1935376822645274424al_nat F I5))))))))) (forall ((I5 tptp.set_int) (I tptp.int) (F tptp.fun_int_nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat))) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int I5)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int I) I5)) (=> (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_int_nat F I))) (=> (forall ((I3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int I3) I5)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) (tptp.aa_int_nat F I3))))) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.groups4541462559716669496nt_nat F I5))))))))) (forall ((I5 tptp.set_complex) (I tptp.complex) (F tptp.fun_complex_nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat))) (=> (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex I5)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex I) I5)) (=> (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_complex_nat F I))) (=> (forall ((I3 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex I3) I5)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) (tptp.aa_complex_nat F I3))))) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.groups5693394587270226106ex_nat F I5))))))))) (forall ((I5 tptp.set_complex) (F tptp.fun_complex_real)) (=> (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex I5)) (=> (not (= I5 tptp.bot_bot_set_complex)) (=> (forall ((I3 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex I3) I5)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) (tptp.aa_complex_real F I3))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) (tptp.groups5808333547571424918x_real F I5))))))) (forall ((I5 tptp.set_int) (F tptp.fun_int_real)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int I5)) (=> (not (= I5 tptp.bot_bot_set_int)) (=> (forall ((I3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int I3) I5)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) (tptp.aa_int_real F I3))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) (tptp.groups8778361861064173332t_real F I5))))))) (forall ((I5 tptp.set_real) (F tptp.fun_real_real)) (=> (tptp.finite_finite_real I5) (=> (not (= I5 tptp.bot_bot_set_real)) (=> (forall ((I3 tptp.real)) (=> (tptp.member_real I3 I5) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) (tptp.aa_real_real F I3))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) (tptp.groups8097168146408367636l_real F I5))))))) (forall ((I5 tptp.set_complex) (F tptp.fun_complex_rat)) (=> (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex I5)) (=> (not (= I5 tptp.bot_bot_set_complex)) (=> (forall ((I3 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex I3) I5)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) (tptp.aa_complex_rat F I3))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) (tptp.groups5058264527183730370ex_rat F I5))))))) (forall ((I5 tptp.set_nat) (F tptp.fun_nat_rat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat I5)) (=> (not (= I5 tptp.bot_bot_set_nat)) (=> (forall ((I3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat I3) I5)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) (tptp.aa_nat_rat F I3))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) (tptp.groups2906978787729119204at_rat F I5))))))) (forall ((I5 tptp.set_int) (F tptp.fun_int_rat)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int I5)) (=> (not (= I5 tptp.bot_bot_set_int)) (=> (forall ((I3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int I3) I5)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) (tptp.aa_int_rat F I3))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) (tptp.groups3906332499630173760nt_rat F I5))))))) (forall ((I5 tptp.set_real) (F tptp.fun_real_rat)) (=> (tptp.finite_finite_real I5) (=> (not (= I5 tptp.bot_bot_set_real)) (=> (forall ((I3 tptp.real)) (=> (tptp.member_real I3 I5) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) (tptp.aa_real_rat F I3))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) (tptp.groups1300246762558778688al_rat F I5))))))) (forall ((I5 tptp.set_complex) (F tptp.fun_complex_nat)) (=> (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex I5)) (=> (not (= I5 tptp.bot_bot_set_complex)) (=> (forall ((I3 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex I3) I5)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.aa_complex_nat F I3))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.groups5693394587270226106ex_nat F I5))))))) (forall ((I5 tptp.set_int) (F tptp.fun_int_nat)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int I5)) (=> (not (= I5 tptp.bot_bot_set_int)) (=> (forall ((I3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int I3) I5)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.aa_int_nat F I3))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.groups4541462559716669496nt_nat F I5))))))) (forall ((I5 tptp.set_real) (F tptp.fun_real_nat)) (=> (tptp.finite_finite_real I5) (=> (not (= I5 tptp.bot_bot_set_real)) (=> (forall ((I3 tptp.real)) (=> (tptp.member_real I3 I5) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.aa_real_nat F I3))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.groups1935376822645274424al_nat F I5))))))) (forall ((X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_real_real tptp.ln_ln_real X))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) X)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.one_one_real) X))))) (forall ((C4 tptp.set_real) (A4 tptp.set_real) (B4 tptp.set_real) (G tptp.fun_real_complex) (H tptp.fun_real_complex)) (=> (tptp.finite_finite_real C4) (=> (tptp.ord_less_eq_set_real A4 C4) (=> (tptp.ord_less_eq_set_real B4 C4) (=> (forall ((A3 tptp.real)) (=> (tptp.member_real A3 (tptp.minus_minus_set_real C4 A4)) (= (tptp.aa_real_complex G A3) tptp.zero_zero_complex))) (=> (forall ((B3 tptp.real)) (=> (tptp.member_real B3 (tptp.minus_minus_set_real C4 B4)) (= (tptp.aa_real_complex H B3) tptp.zero_zero_complex))) (= (= (tptp.groups5754745047067104278omplex G A4) (tptp.groups5754745047067104278omplex H B4)) (= (tptp.groups5754745047067104278omplex G C4) (tptp.groups5754745047067104278omplex H C4))))))))) (forall ((C4 tptp.set_nat) (A4 tptp.set_nat) (B4 tptp.set_nat) (G tptp.fun_nat_complex) (H tptp.fun_nat_complex)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat C4)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat A4) C4)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat B4) C4)) (=> (forall ((A3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat A3) (tptp.minus_minus_set_nat C4 A4))) (= (tptp.aa_nat_complex G A3) tptp.zero_zero_complex))) (=> (forall ((B3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat B3) (tptp.minus_minus_set_nat C4 B4))) (= (tptp.aa_nat_complex H B3) tptp.zero_zero_complex))) (= (= (tptp.groups2073611262835488442omplex G A4) (tptp.groups2073611262835488442omplex H B4)) (= (tptp.groups2073611262835488442omplex G C4) (tptp.groups2073611262835488442omplex H C4))))))))) (forall ((C4 tptp.set_real) (A4 tptp.set_real) (B4 tptp.set_real) (G tptp.fun_real_real) (H tptp.fun_real_real)) (=> (tptp.finite_finite_real C4) (=> (tptp.ord_less_eq_set_real A4 C4) (=> (tptp.ord_less_eq_set_real B4 C4) (=> (forall ((A3 tptp.real)) (=> (tptp.member_real A3 (tptp.minus_minus_set_real C4 A4)) (= (tptp.aa_real_real G A3) tptp.zero_zero_real))) (=> (forall ((B3 tptp.real)) (=> (tptp.member_real B3 (tptp.minus_minus_set_real C4 B4)) (= (tptp.aa_real_real H B3) tptp.zero_zero_real))) (= (= (tptp.groups8097168146408367636l_real G A4) (tptp.groups8097168146408367636l_real H B4)) (= (tptp.groups8097168146408367636l_real G C4) (tptp.groups8097168146408367636l_real H C4))))))))) (forall ((C4 tptp.set_complex) (A4 tptp.set_complex) (B4 tptp.set_complex) (G tptp.fun_complex_real) (H tptp.fun_complex_real)) (=> (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex C4)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.ord_le211207098394363844omplex A4) C4)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.ord_le211207098394363844omplex B4) C4)) (=> (forall ((A3 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex A3) (tptp.minus_811609699411566653omplex C4 A4))) (= (tptp.aa_complex_real G A3) tptp.zero_zero_real))) (=> (forall ((B3 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex B3) (tptp.minus_811609699411566653omplex C4 B4))) (= (tptp.aa_complex_real H B3) tptp.zero_zero_real))) (= (= (tptp.groups5808333547571424918x_real G A4) (tptp.groups5808333547571424918x_real H B4)) (= (tptp.groups5808333547571424918x_real G C4) (tptp.groups5808333547571424918x_real H C4))))))))) (forall ((C4 tptp.set_real) (A4 tptp.set_real) (B4 tptp.set_real) (G tptp.fun_real_rat) (H tptp.fun_real_rat)) (=> (tptp.finite_finite_real C4) (=> (tptp.ord_less_eq_set_real A4 C4) (=> (tptp.ord_less_eq_set_real B4 C4) (=> (forall ((A3 tptp.real)) (=> (tptp.member_real A3 (tptp.minus_minus_set_real C4 A4)) (= (tptp.aa_real_rat G A3) tptp.zero_zero_rat))) (=> (forall ((B3 tptp.real)) (=> (tptp.member_real B3 (tptp.minus_minus_set_real C4 B4)) (= (tptp.aa_real_rat H B3) tptp.zero_zero_rat))) (= (= (tptp.groups1300246762558778688al_rat G A4) (tptp.groups1300246762558778688al_rat H B4)) (= (tptp.groups1300246762558778688al_rat G C4) (tptp.groups1300246762558778688al_rat H C4))))))))) (forall ((C4 tptp.set_nat) (A4 tptp.set_nat) (B4 tptp.set_nat) (G tptp.fun_nat_rat) (H tptp.fun_nat_rat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat C4)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat A4) C4)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat B4) C4)) (=> (forall ((A3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat A3) (tptp.minus_minus_set_nat C4 A4))) (= (tptp.aa_nat_rat G A3) tptp.zero_zero_rat))) (=> (forall ((B3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat B3) (tptp.minus_minus_set_nat C4 B4))) (= (tptp.aa_nat_rat H B3) tptp.zero_zero_rat))) (= (= (tptp.groups2906978787729119204at_rat G A4) (tptp.groups2906978787729119204at_rat H B4)) (= (tptp.groups2906978787729119204at_rat G C4) (tptp.groups2906978787729119204at_rat H C4))))))))) (forall ((C4 tptp.set_complex) (A4 tptp.set_complex) (B4 tptp.set_complex) (G tptp.fun_complex_rat) (H tptp.fun_complex_rat)) (=> (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex C4)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.ord_le211207098394363844omplex A4) C4)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.ord_le211207098394363844omplex B4) C4)) (=> (forall ((A3 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex A3) (tptp.minus_811609699411566653omplex C4 A4))) (= (tptp.aa_complex_rat G A3) tptp.zero_zero_rat))) (=> (forall ((B3 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex B3) (tptp.minus_811609699411566653omplex C4 B4))) (= (tptp.aa_complex_rat H B3) tptp.zero_zero_rat))) (= (= (tptp.groups5058264527183730370ex_rat G A4) (tptp.groups5058264527183730370ex_rat H B4)) (= (tptp.groups5058264527183730370ex_rat G C4) (tptp.groups5058264527183730370ex_rat H C4))))))))) (forall ((C4 tptp.set_real) (A4 tptp.set_real) (B4 tptp.set_real) (G tptp.fun_real_nat) (H tptp.fun_real_nat)) (=> (tptp.finite_finite_real C4) (=> (tptp.ord_less_eq_set_real A4 C4) (=> (tptp.ord_less_eq_set_real B4 C4) (=> (forall ((A3 tptp.real)) (=> (tptp.member_real A3 (tptp.minus_minus_set_real C4 A4)) (= (tptp.aa_real_nat G A3) tptp.zero_zero_nat))) (=> (forall ((B3 tptp.real)) (=> (tptp.member_real B3 (tptp.minus_minus_set_real C4 B4)) (= (tptp.aa_real_nat H B3) tptp.zero_zero_nat))) (= (= (tptp.groups1935376822645274424al_nat G A4) (tptp.groups1935376822645274424al_nat H B4)) (= (tptp.groups1935376822645274424al_nat G C4) (tptp.groups1935376822645274424al_nat H C4))))))))) (forall ((C4 tptp.set_complex) (A4 tptp.set_complex) (B4 tptp.set_complex) (G tptp.fun_complex_nat) (H tptp.fun_complex_nat)) (=> (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex C4)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.ord_le211207098394363844omplex A4) C4)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.ord_le211207098394363844omplex B4) C4)) (=> (forall ((A3 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex A3) (tptp.minus_811609699411566653omplex C4 A4))) (= (tptp.aa_complex_nat G A3) tptp.zero_zero_nat))) (=> (forall ((B3 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex B3) (tptp.minus_811609699411566653omplex C4 B4))) (= (tptp.aa_complex_nat H B3) tptp.zero_zero_nat))) (= (= (tptp.groups5693394587270226106ex_nat G A4) (tptp.groups5693394587270226106ex_nat H B4)) (= (tptp.groups5693394587270226106ex_nat G C4) (tptp.groups5693394587270226106ex_nat H C4))))))))) (forall ((C4 tptp.set_real) (A4 tptp.set_real) (B4 tptp.set_real) (G tptp.fun_real_int) (H tptp.fun_real_int)) (=> (tptp.finite_finite_real C4) (=> (tptp.ord_less_eq_set_real A4 C4) (=> (tptp.ord_less_eq_set_real B4 C4) (=> (forall ((A3 tptp.real)) (=> (tptp.member_real A3 (tptp.minus_minus_set_real C4 A4)) (= (tptp.aa_real_int G A3) tptp.zero_zero_int))) (=> (forall ((B3 tptp.real)) (=> (tptp.member_real B3 (tptp.minus_minus_set_real C4 B4)) (= (tptp.aa_real_int H B3) tptp.zero_zero_int))) (= (= (tptp.groups1932886352136224148al_int G A4) (tptp.groups1932886352136224148al_int H B4)) (= (tptp.groups1932886352136224148al_int G C4) (tptp.groups1932886352136224148al_int H C4))))))))) (forall ((C4 tptp.set_real) (A4 tptp.set_real) (B4 tptp.set_real) (G tptp.fun_real_complex) (H tptp.fun_real_complex)) (=> (tptp.finite_finite_real C4) (=> (tptp.ord_less_eq_set_real A4 C4) (=> (tptp.ord_less_eq_set_real B4 C4) (=> (forall ((A3 tptp.real)) (=> (tptp.member_real A3 (tptp.minus_minus_set_real C4 A4)) (= (tptp.aa_real_complex G A3) tptp.zero_zero_complex))) (=> (forall ((B3 tptp.real)) (=> (tptp.member_real B3 (tptp.minus_minus_set_real C4 B4)) (= (tptp.aa_real_complex H B3) tptp.zero_zero_complex))) (=> (= (tptp.groups5754745047067104278omplex G C4) (tptp.groups5754745047067104278omplex H C4)) (= (tptp.groups5754745047067104278omplex G A4) (tptp.groups5754745047067104278omplex H B4))))))))) (forall ((C4 tptp.set_nat) (A4 tptp.set_nat) (B4 tptp.set_nat) (G tptp.fun_nat_complex) (H tptp.fun_nat_complex)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat C4)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat A4) C4)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat B4) C4)) (=> (forall ((A3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat A3) (tptp.minus_minus_set_nat C4 A4))) (= (tptp.aa_nat_complex G A3) tptp.zero_zero_complex))) (=> (forall ((B3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat B3) (tptp.minus_minus_set_nat C4 B4))) (= (tptp.aa_nat_complex H B3) tptp.zero_zero_complex))) (=> (= (tptp.groups2073611262835488442omplex G C4) (tptp.groups2073611262835488442omplex H C4)) (= (tptp.groups2073611262835488442omplex G A4) (tptp.groups2073611262835488442omplex H B4))))))))) (forall ((C4 tptp.set_real) (A4 tptp.set_real) (B4 tptp.set_real) (G tptp.fun_real_real) (H tptp.fun_real_real)) (=> (tptp.finite_finite_real C4) (=> (tptp.ord_less_eq_set_real A4 C4) (=> (tptp.ord_less_eq_set_real B4 C4) (=> (forall ((A3 tptp.real)) (=> (tptp.member_real A3 (tptp.minus_minus_set_real C4 A4)) (= (tptp.aa_real_real G A3) tptp.zero_zero_real))) (=> (forall ((B3 tptp.real)) (=> (tptp.member_real B3 (tptp.minus_minus_set_real C4 B4)) (= (tptp.aa_real_real H B3) tptp.zero_zero_real))) (=> (= (tptp.groups8097168146408367636l_real G C4) (tptp.groups8097168146408367636l_real H C4)) (= (tptp.groups8097168146408367636l_real G A4) (tptp.groups8097168146408367636l_real H B4))))))))) (forall ((C4 tptp.set_complex) (A4 tptp.set_complex) (B4 tptp.set_complex) (G tptp.fun_complex_real) (H tptp.fun_complex_real)) (=> (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex C4)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.ord_le211207098394363844omplex A4) C4)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.ord_le211207098394363844omplex B4) C4)) (=> (forall ((A3 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex A3) (tptp.minus_811609699411566653omplex C4 A4))) (= (tptp.aa_complex_real G A3) tptp.zero_zero_real))) (=> (forall ((B3 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex B3) (tptp.minus_811609699411566653omplex C4 B4))) (= (tptp.aa_complex_real H B3) tptp.zero_zero_real))) (=> (= (tptp.groups5808333547571424918x_real G C4) (tptp.groups5808333547571424918x_real H C4)) (= (tptp.groups5808333547571424918x_real G A4) (tptp.groups5808333547571424918x_real H B4))))))))) (forall ((C4 tptp.set_real) (A4 tptp.set_real) (B4 tptp.set_real) (G tptp.fun_real_rat) (H tptp.fun_real_rat)) (=> (tptp.finite_finite_real C4) (=> (tptp.ord_less_eq_set_real A4 C4) (=> (tptp.ord_less_eq_set_real B4 C4) (=> (forall ((A3 tptp.real)) (=> (tptp.member_real A3 (tptp.minus_minus_set_real C4 A4)) (= (tptp.aa_real_rat G A3) tptp.zero_zero_rat))) (=> (forall ((B3 tptp.real)) (=> (tptp.member_real B3 (tptp.minus_minus_set_real C4 B4)) (= (tptp.aa_real_rat H B3) tptp.zero_zero_rat))) (=> (= (tptp.groups1300246762558778688al_rat G C4) (tptp.groups1300246762558778688al_rat H C4)) (= (tptp.groups1300246762558778688al_rat G A4) (tptp.groups1300246762558778688al_rat H B4))))))))) (forall ((C4 tptp.set_nat) (A4 tptp.set_nat) (B4 tptp.set_nat) (G tptp.fun_nat_rat) (H tptp.fun_nat_rat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat C4)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat A4) C4)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat B4) C4)) (=> (forall ((A3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat A3) (tptp.minus_minus_set_nat C4 A4))) (= (tptp.aa_nat_rat G A3) tptp.zero_zero_rat))) (=> (forall ((B3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat B3) (tptp.minus_minus_set_nat C4 B4))) (= (tptp.aa_nat_rat H B3) tptp.zero_zero_rat))) (=> (= (tptp.groups2906978787729119204at_rat G C4) (tptp.groups2906978787729119204at_rat H C4)) (= (tptp.groups2906978787729119204at_rat G A4) (tptp.groups2906978787729119204at_rat H B4))))))))) (forall ((C4 tptp.set_complex) (A4 tptp.set_complex) (B4 tptp.set_complex) (G tptp.fun_complex_rat) (H tptp.fun_complex_rat)) (=> (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex C4)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.ord_le211207098394363844omplex A4) C4)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.ord_le211207098394363844omplex B4) C4)) (=> (forall ((A3 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex A3) (tptp.minus_811609699411566653omplex C4 A4))) (= (tptp.aa_complex_rat G A3) tptp.zero_zero_rat))) (=> (forall ((B3 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex B3) (tptp.minus_811609699411566653omplex C4 B4))) (= (tptp.aa_complex_rat H B3) tptp.zero_zero_rat))) (=> (= (tptp.groups5058264527183730370ex_rat G C4) (tptp.groups5058264527183730370ex_rat H C4)) (= (tptp.groups5058264527183730370ex_rat G A4) (tptp.groups5058264527183730370ex_rat H B4))))))))) (forall ((C4 tptp.set_real) (A4 tptp.set_real) (B4 tptp.set_real) (G tptp.fun_real_nat) (H tptp.fun_real_nat)) (=> (tptp.finite_finite_real C4) (=> (tptp.ord_less_eq_set_real A4 C4) (=> (tptp.ord_less_eq_set_real B4 C4) (=> (forall ((A3 tptp.real)) (=> (tptp.member_real A3 (tptp.minus_minus_set_real C4 A4)) (= (tptp.aa_real_nat G A3) tptp.zero_zero_nat))) (=> (forall ((B3 tptp.real)) (=> (tptp.member_real B3 (tptp.minus_minus_set_real C4 B4)) (= (tptp.aa_real_nat H B3) tptp.zero_zero_nat))) (=> (= (tptp.groups1935376822645274424al_nat G C4) (tptp.groups1935376822645274424al_nat H C4)) (= (tptp.groups1935376822645274424al_nat G A4) (tptp.groups1935376822645274424al_nat H B4))))))))) (forall ((C4 tptp.set_complex) (A4 tptp.set_complex) (B4 tptp.set_complex) (G tptp.fun_complex_nat) (H tptp.fun_complex_nat)) (=> (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex C4)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.ord_le211207098394363844omplex A4) C4)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.ord_le211207098394363844omplex B4) C4)) (=> (forall ((A3 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex A3) (tptp.minus_811609699411566653omplex C4 A4))) (= (tptp.aa_complex_nat G A3) tptp.zero_zero_nat))) (=> (forall ((B3 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex B3) (tptp.minus_811609699411566653omplex C4 B4))) (= (tptp.aa_complex_nat H B3) tptp.zero_zero_nat))) (=> (= (tptp.groups5693394587270226106ex_nat G C4) (tptp.groups5693394587270226106ex_nat H C4)) (= (tptp.groups5693394587270226106ex_nat G A4) (tptp.groups5693394587270226106ex_nat H B4))))))))) (forall ((C4 tptp.set_real) (A4 tptp.set_real) (B4 tptp.set_real) (G tptp.fun_real_int) (H tptp.fun_real_int)) (=> (tptp.finite_finite_real C4) (=> (tptp.ord_less_eq_set_real A4 C4) (=> (tptp.ord_less_eq_set_real B4 C4) (=> (forall ((A3 tptp.real)) (=> (tptp.member_real A3 (tptp.minus_minus_set_real C4 A4)) (= (tptp.aa_real_int G A3) tptp.zero_zero_int))) (=> (forall ((B3 tptp.real)) (=> (tptp.member_real B3 (tptp.minus_minus_set_real C4 B4)) (= (tptp.aa_real_int H B3) tptp.zero_zero_int))) (=> (= (tptp.groups1932886352136224148al_int G C4) (tptp.groups1932886352136224148al_int H C4)) (= (tptp.groups1932886352136224148al_int G A4) (tptp.groups1932886352136224148al_int H B4))))))))) (forall ((T3 tptp.set_nat) (S2 tptp.set_nat) (G tptp.fun_nat_complex)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat T3)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat S2) T3)) (=> (forall ((X4 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X4) (tptp.minus_minus_set_nat T3 S2))) (= (tptp.aa_nat_complex G X4) tptp.zero_zero_complex))) (= (tptp.groups2073611262835488442omplex G S2) (tptp.groups2073611262835488442omplex G T3)))))) (forall ((T3 tptp.set_complex) (S2 tptp.set_complex) (G tptp.fun_complex_real)) (=> (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex T3)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.ord_le211207098394363844omplex S2) T3)) (=> (forall ((X4 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex X4) (tptp.minus_811609699411566653omplex T3 S2))) (= (tptp.aa_complex_real G X4) tptp.zero_zero_real))) (= (tptp.groups5808333547571424918x_real G S2) (tptp.groups5808333547571424918x_real G T3)))))) (forall ((T3 tptp.set_nat) (S2 tptp.set_nat) (G tptp.fun_nat_rat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat T3)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat S2) T3)) (=> (forall ((X4 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X4) (tptp.minus_minus_set_nat T3 S2))) (= (tptp.aa_nat_rat G X4) tptp.zero_zero_rat))) (= (tptp.groups2906978787729119204at_rat G S2) (tptp.groups2906978787729119204at_rat G T3)))))) (forall ((T3 tptp.set_complex) (S2 tptp.set_complex) (G tptp.fun_complex_rat)) (=> (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex T3)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.ord_le211207098394363844omplex S2) T3)) (=> (forall ((X4 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex X4) (tptp.minus_811609699411566653omplex T3 S2))) (= (tptp.aa_complex_rat G X4) tptp.zero_zero_rat))) (= (tptp.groups5058264527183730370ex_rat G S2) (tptp.groups5058264527183730370ex_rat G T3)))))) (forall ((T3 tptp.set_complex) (S2 tptp.set_complex) (G tptp.fun_complex_nat)) (=> (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex T3)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.ord_le211207098394363844omplex S2) T3)) (=> (forall ((X4 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex X4) (tptp.minus_811609699411566653omplex T3 S2))) (= (tptp.aa_complex_nat G X4) tptp.zero_zero_nat))) (= (tptp.groups5693394587270226106ex_nat G S2) (tptp.groups5693394587270226106ex_nat G T3)))))) (forall ((T3 tptp.set_nat) (S2 tptp.set_nat) (G tptp.fun_nat_int)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat T3)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat S2) T3)) (=> (forall ((X4 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X4) (tptp.minus_minus_set_nat T3 S2))) (= (tptp.aa_nat_int G X4) tptp.zero_zero_int))) (= (tptp.groups3539618377306564664at_int G S2) (tptp.groups3539618377306564664at_int G T3)))))) (forall ((T3 tptp.set_complex) (S2 tptp.set_complex) (G tptp.fun_complex_int)) (=> (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex T3)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.ord_le211207098394363844omplex S2) T3)) (=> (forall ((X4 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex X4) (tptp.minus_811609699411566653omplex T3 S2))) (= (tptp.aa_complex_int G X4) tptp.zero_zero_int))) (= (tptp.groups5690904116761175830ex_int G S2) (tptp.groups5690904116761175830ex_int G T3)))))) (forall ((T3 tptp.set_int) (S2 tptp.set_int) (G tptp.fun_int_complex)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int T3)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int S2) T3)) (=> (forall ((X4 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X4) (tptp.minus_minus_set_int T3 S2))) (= (tptp.aa_int_complex G X4) tptp.zero_zero_complex))) (= (tptp.groups3049146728041665814omplex G S2) (tptp.groups3049146728041665814omplex G T3)))))) (forall ((T3 tptp.set_int) (S2 tptp.set_int) (G tptp.fun_int_real)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int T3)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int S2) T3)) (=> (forall ((X4 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X4) (tptp.minus_minus_set_int T3 S2))) (= (tptp.aa_int_real G X4) tptp.zero_zero_real))) (= (tptp.groups8778361861064173332t_real G S2) (tptp.groups8778361861064173332t_real G T3)))))) (forall ((T3 tptp.set_int) (S2 tptp.set_int) (G tptp.fun_int_rat)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int T3)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int S2) T3)) (=> (forall ((X4 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X4) (tptp.minus_minus_set_int T3 S2))) (= (tptp.aa_int_rat G X4) tptp.zero_zero_rat))) (= (tptp.groups3906332499630173760nt_rat G S2) (tptp.groups3906332499630173760nt_rat G T3)))))) (forall ((T3 tptp.set_nat) (S2 tptp.set_nat) (G tptp.fun_nat_complex)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat T3)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat S2) T3)) (=> (forall ((X4 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X4) (tptp.minus_minus_set_nat T3 S2))) (= (tptp.aa_nat_complex G X4) tptp.zero_zero_complex))) (= (tptp.groups2073611262835488442omplex G T3) (tptp.groups2073611262835488442omplex G S2)))))) (forall ((T3 tptp.set_complex) (S2 tptp.set_complex) (G tptp.fun_complex_real)) (=> (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex T3)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.ord_le211207098394363844omplex S2) T3)) (=> (forall ((X4 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex X4) (tptp.minus_811609699411566653omplex T3 S2))) (= (tptp.aa_complex_real G X4) tptp.zero_zero_real))) (= (tptp.groups5808333547571424918x_real G T3) (tptp.groups5808333547571424918x_real G S2)))))) (forall ((T3 tptp.set_nat) (S2 tptp.set_nat) (G tptp.fun_nat_rat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat T3)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat S2) T3)) (=> (forall ((X4 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X4) (tptp.minus_minus_set_nat T3 S2))) (= (tptp.aa_nat_rat G X4) tptp.zero_zero_rat))) (= (tptp.groups2906978787729119204at_rat G T3) (tptp.groups2906978787729119204at_rat G S2)))))) (forall ((T3 tptp.set_complex) (S2 tptp.set_complex) (G tptp.fun_complex_rat)) (=> (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex T3)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.ord_le211207098394363844omplex S2) T3)) (=> (forall ((X4 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex X4) (tptp.minus_811609699411566653omplex T3 S2))) (= (tptp.aa_complex_rat G X4) tptp.zero_zero_rat))) (= (tptp.groups5058264527183730370ex_rat G T3) (tptp.groups5058264527183730370ex_rat G S2)))))) (forall ((T3 tptp.set_complex) (S2 tptp.set_complex) (G tptp.fun_complex_nat)) (=> (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex T3)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.ord_le211207098394363844omplex S2) T3)) (=> (forall ((X4 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex X4) (tptp.minus_811609699411566653omplex T3 S2))) (= (tptp.aa_complex_nat G X4) tptp.zero_zero_nat))) (= (tptp.groups5693394587270226106ex_nat G T3) (tptp.groups5693394587270226106ex_nat G S2)))))) (forall ((T3 tptp.set_nat) (S2 tptp.set_nat) (G tptp.fun_nat_int)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat T3)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat S2) T3)) (=> (forall ((X4 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X4) (tptp.minus_minus_set_nat T3 S2))) (= (tptp.aa_nat_int G X4) tptp.zero_zero_int))) (= (tptp.groups3539618377306564664at_int G T3) (tptp.groups3539618377306564664at_int G S2)))))) (forall ((T3 tptp.set_complex) (S2 tptp.set_complex) (G tptp.fun_complex_int)) (=> (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex T3)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.ord_le211207098394363844omplex S2) T3)) (=> (forall ((X4 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex X4) (tptp.minus_811609699411566653omplex T3 S2))) (= (tptp.aa_complex_int G X4) tptp.zero_zero_int))) (= (tptp.groups5690904116761175830ex_int G T3) (tptp.groups5690904116761175830ex_int G S2)))))) (forall ((T3 tptp.set_int) (S2 tptp.set_int) (G tptp.fun_int_complex)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int T3)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int S2) T3)) (=> (forall ((X4 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X4) (tptp.minus_minus_set_int T3 S2))) (= (tptp.aa_int_complex G X4) tptp.zero_zero_complex))) (= (tptp.groups3049146728041665814omplex G T3) (tptp.groups3049146728041665814omplex G S2)))))) (forall ((T3 tptp.set_int) (S2 tptp.set_int) (G tptp.fun_int_real)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int T3)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int S2) T3)) (=> (forall ((X4 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X4) (tptp.minus_minus_set_int T3 S2))) (= (tptp.aa_int_real G X4) tptp.zero_zero_real))) (= (tptp.groups8778361861064173332t_real G T3) (tptp.groups8778361861064173332t_real G S2)))))) (forall ((T3 tptp.set_int) (S2 tptp.set_int) (G tptp.fun_int_rat)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int T3)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int S2) T3)) (=> (forall ((X4 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X4) (tptp.minus_minus_set_int T3 S2))) (= (tptp.aa_int_rat G X4) tptp.zero_zero_rat))) (= (tptp.groups3906332499630173760nt_rat G T3) (tptp.groups3906332499630173760nt_rat G S2)))))) (forall ((T3 tptp.set_real) (S2 tptp.set_real) (H tptp.fun_real_complex) (G tptp.fun_real_complex)) (=> (tptp.finite_finite_real T3) (=> (tptp.ord_less_eq_set_real S2 T3) (=> (forall ((X4 tptp.real)) (=> (tptp.member_real X4 (tptp.minus_minus_set_real T3 S2)) (= (tptp.aa_real_complex H X4) tptp.zero_zero_complex))) (=> (forall ((X4 tptp.real)) (=> (tptp.member_real X4 S2) (= (tptp.aa_real_complex G X4) (tptp.aa_real_complex H X4)))) (= (tptp.groups5754745047067104278omplex G S2) (tptp.groups5754745047067104278omplex H T3))))))) (forall ((T3 tptp.set_nat) (S2 tptp.set_nat) (H tptp.fun_nat_complex) (G tptp.fun_nat_complex)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat T3)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat S2) T3)) (=> (forall ((X4 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X4) (tptp.minus_minus_set_nat T3 S2))) (= (tptp.aa_nat_complex H X4) tptp.zero_zero_complex))) (=> (forall ((X4 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X4) S2)) (= (tptp.aa_nat_complex G X4) (tptp.aa_nat_complex H X4)))) (= (tptp.groups2073611262835488442omplex G S2) (tptp.groups2073611262835488442omplex H T3))))))) (forall ((T3 tptp.set_real) (S2 tptp.set_real) (H tptp.fun_real_real) (G tptp.fun_real_real)) (=> (tptp.finite_finite_real T3) (=> (tptp.ord_less_eq_set_real S2 T3) (=> (forall ((X4 tptp.real)) (=> (tptp.member_real X4 (tptp.minus_minus_set_real T3 S2)) (= (tptp.aa_real_real H X4) tptp.zero_zero_real))) (=> (forall ((X4 tptp.real)) (=> (tptp.member_real X4 S2) (= (tptp.aa_real_real G X4) (tptp.aa_real_real H X4)))) (= (tptp.groups8097168146408367636l_real G S2) (tptp.groups8097168146408367636l_real H T3))))))) (forall ((T3 tptp.set_complex) (S2 tptp.set_complex) (H tptp.fun_complex_real) (G tptp.fun_complex_real)) (=> (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex T3)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.ord_le211207098394363844omplex S2) T3)) (=> (forall ((X4 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex X4) (tptp.minus_811609699411566653omplex T3 S2))) (= (tptp.aa_complex_real H X4) tptp.zero_zero_real))) (=> (forall ((X4 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex X4) S2)) (= (tptp.aa_complex_real G X4) (tptp.aa_complex_real H X4)))) (= (tptp.groups5808333547571424918x_real G S2) (tptp.groups5808333547571424918x_real H T3))))))) (forall ((T3 tptp.set_real) (S2 tptp.set_real) (H tptp.fun_real_rat) (G tptp.fun_real_rat)) (=> (tptp.finite_finite_real T3) (=> (tptp.ord_less_eq_set_real S2 T3) (=> (forall ((X4 tptp.real)) (=> (tptp.member_real X4 (tptp.minus_minus_set_real T3 S2)) (= (tptp.aa_real_rat H X4) tptp.zero_zero_rat))) (=> (forall ((X4 tptp.real)) (=> (tptp.member_real X4 S2) (= (tptp.aa_real_rat G X4) (tptp.aa_real_rat H X4)))) (= (tptp.groups1300246762558778688al_rat G S2) (tptp.groups1300246762558778688al_rat H T3))))))) (forall ((T3 tptp.set_nat) (S2 tptp.set_nat) (H tptp.fun_nat_rat) (G tptp.fun_nat_rat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat T3)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat S2) T3)) (=> (forall ((X4 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X4) (tptp.minus_minus_set_nat T3 S2))) (= (tptp.aa_nat_rat H X4) tptp.zero_zero_rat))) (=> (forall ((X4 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X4) S2)) (= (tptp.aa_nat_rat G X4) (tptp.aa_nat_rat H X4)))) (= (tptp.groups2906978787729119204at_rat G S2) (tptp.groups2906978787729119204at_rat H T3))))))) (forall ((T3 tptp.set_complex) (S2 tptp.set_complex) (H tptp.fun_complex_rat) (G tptp.fun_complex_rat)) (=> (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex T3)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.ord_le211207098394363844omplex S2) T3)) (=> (forall ((X4 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex X4) (tptp.minus_811609699411566653omplex T3 S2))) (= (tptp.aa_complex_rat H X4) tptp.zero_zero_rat))) (=> (forall ((X4 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex X4) S2)) (= (tptp.aa_complex_rat G X4) (tptp.aa_complex_rat H X4)))) (= (tptp.groups5058264527183730370ex_rat G S2) (tptp.groups5058264527183730370ex_rat H T3))))))) (forall ((T3 tptp.set_real) (S2 tptp.set_real) (H tptp.fun_real_nat) (G tptp.fun_real_nat)) (=> (tptp.finite_finite_real T3) (=> (tptp.ord_less_eq_set_real S2 T3) (=> (forall ((X4 tptp.real)) (=> (tptp.member_real X4 (tptp.minus_minus_set_real T3 S2)) (= (tptp.aa_real_nat H X4) tptp.zero_zero_nat))) (=> (forall ((X4 tptp.real)) (=> (tptp.member_real X4 S2) (= (tptp.aa_real_nat G X4) (tptp.aa_real_nat H X4)))) (= (tptp.groups1935376822645274424al_nat G S2) (tptp.groups1935376822645274424al_nat H T3))))))) (forall ((T3 tptp.set_complex) (S2 tptp.set_complex) (H tptp.fun_complex_nat) (G tptp.fun_complex_nat)) (=> (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex T3)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.ord_le211207098394363844omplex S2) T3)) (=> (forall ((X4 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex X4) (tptp.minus_811609699411566653omplex T3 S2))) (= (tptp.aa_complex_nat H X4) tptp.zero_zero_nat))) (=> (forall ((X4 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex X4) S2)) (= (tptp.aa_complex_nat G X4) (tptp.aa_complex_nat H X4)))) (= (tptp.groups5693394587270226106ex_nat G S2) (tptp.groups5693394587270226106ex_nat H T3))))))) (forall ((T3 tptp.set_real) (S2 tptp.set_real) (H tptp.fun_real_int) (G tptp.fun_real_int)) (=> (tptp.finite_finite_real T3) (=> (tptp.ord_less_eq_set_real S2 T3) (=> (forall ((X4 tptp.real)) (=> (tptp.member_real X4 (tptp.minus_minus_set_real T3 S2)) (= (tptp.aa_real_int H X4) tptp.zero_zero_int))) (=> (forall ((X4 tptp.real)) (=> (tptp.member_real X4 S2) (= (tptp.aa_real_int G X4) (tptp.aa_real_int H X4)))) (= (tptp.groups1932886352136224148al_int G S2) (tptp.groups1932886352136224148al_int H T3))))))) (forall ((T3 tptp.set_real) (S2 tptp.set_real) (G tptp.fun_real_complex) (H tptp.fun_real_complex)) (=> (tptp.finite_finite_real T3) (=> (tptp.ord_less_eq_set_real S2 T3) (=> (forall ((X4 tptp.real)) (=> (tptp.member_real X4 (tptp.minus_minus_set_real T3 S2)) (= (tptp.aa_real_complex G X4) tptp.zero_zero_complex))) (=> (forall ((X4 tptp.real)) (=> (tptp.member_real X4 S2) (= (tptp.aa_real_complex G X4) (tptp.aa_real_complex H X4)))) (= (tptp.groups5754745047067104278omplex G T3) (tptp.groups5754745047067104278omplex H S2))))))) (forall ((T3 tptp.set_nat) (S2 tptp.set_nat) (G tptp.fun_nat_complex) (H tptp.fun_nat_complex)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat T3)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat S2) T3)) (=> (forall ((X4 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X4) (tptp.minus_minus_set_nat T3 S2))) (= (tptp.aa_nat_complex G X4) tptp.zero_zero_complex))) (=> (forall ((X4 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X4) S2)) (= (tptp.aa_nat_complex G X4) (tptp.aa_nat_complex H X4)))) (= (tptp.groups2073611262835488442omplex G T3) (tptp.groups2073611262835488442omplex H S2))))))) (forall ((T3 tptp.set_real) (S2 tptp.set_real) (G tptp.fun_real_real) (H tptp.fun_real_real)) (=> (tptp.finite_finite_real T3) (=> (tptp.ord_less_eq_set_real S2 T3) (=> (forall ((X4 tptp.real)) (=> (tptp.member_real X4 (tptp.minus_minus_set_real T3 S2)) (= (tptp.aa_real_real G X4) tptp.zero_zero_real))) (=> (forall ((X4 tptp.real)) (=> (tptp.member_real X4 S2) (= (tptp.aa_real_real G X4) (tptp.aa_real_real H X4)))) (= (tptp.groups8097168146408367636l_real G T3) (tptp.groups8097168146408367636l_real H S2))))))) (forall ((T3 tptp.set_complex) (S2 tptp.set_complex) (G tptp.fun_complex_real) (H tptp.fun_complex_real)) (=> (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex T3)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.ord_le211207098394363844omplex S2) T3)) (=> (forall ((X4 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex X4) (tptp.minus_811609699411566653omplex T3 S2))) (= (tptp.aa_complex_real G X4) tptp.zero_zero_real))) (=> (forall ((X4 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex X4) S2)) (= (tptp.aa_complex_real G X4) (tptp.aa_complex_real H X4)))) (= (tptp.groups5808333547571424918x_real G T3) (tptp.groups5808333547571424918x_real H S2))))))) (forall ((T3 tptp.set_real) (S2 tptp.set_real) (G tptp.fun_real_rat) (H tptp.fun_real_rat)) (=> (tptp.finite_finite_real T3) (=> (tptp.ord_less_eq_set_real S2 T3) (=> (forall ((X4 tptp.real)) (=> (tptp.member_real X4 (tptp.minus_minus_set_real T3 S2)) (= (tptp.aa_real_rat G X4) tptp.zero_zero_rat))) (=> (forall ((X4 tptp.real)) (=> (tptp.member_real X4 S2) (= (tptp.aa_real_rat G X4) (tptp.aa_real_rat H X4)))) (= (tptp.groups1300246762558778688al_rat G T3) (tptp.groups1300246762558778688al_rat H S2))))))) (forall ((T3 tptp.set_nat) (S2 tptp.set_nat) (G tptp.fun_nat_rat) (H tptp.fun_nat_rat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat T3)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat S2) T3)) (=> (forall ((X4 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X4) (tptp.minus_minus_set_nat T3 S2))) (= (tptp.aa_nat_rat G X4) tptp.zero_zero_rat))) (=> (forall ((X4 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X4) S2)) (= (tptp.aa_nat_rat G X4) (tptp.aa_nat_rat H X4)))) (= (tptp.groups2906978787729119204at_rat G T3) (tptp.groups2906978787729119204at_rat H S2))))))) (forall ((T3 tptp.set_complex) (S2 tptp.set_complex) (G tptp.fun_complex_rat) (H tptp.fun_complex_rat)) (=> (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex T3)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.ord_le211207098394363844omplex S2) T3)) (=> (forall ((X4 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex X4) (tptp.minus_811609699411566653omplex T3 S2))) (= (tptp.aa_complex_rat G X4) tptp.zero_zero_rat))) (=> (forall ((X4 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex X4) S2)) (= (tptp.aa_complex_rat G X4) (tptp.aa_complex_rat H X4)))) (= (tptp.groups5058264527183730370ex_rat G T3) (tptp.groups5058264527183730370ex_rat H S2))))))) (forall ((T3 tptp.set_real) (S2 tptp.set_real) (G tptp.fun_real_nat) (H tptp.fun_real_nat)) (=> (tptp.finite_finite_real T3) (=> (tptp.ord_less_eq_set_real S2 T3) (=> (forall ((X4 tptp.real)) (=> (tptp.member_real X4 (tptp.minus_minus_set_real T3 S2)) (= (tptp.aa_real_nat G X4) tptp.zero_zero_nat))) (=> (forall ((X4 tptp.real)) (=> (tptp.member_real X4 S2) (= (tptp.aa_real_nat G X4) (tptp.aa_real_nat H X4)))) (= (tptp.groups1935376822645274424al_nat G T3) (tptp.groups1935376822645274424al_nat H S2))))))) (forall ((T3 tptp.set_complex) (S2 tptp.set_complex) (G tptp.fun_complex_nat) (H tptp.fun_complex_nat)) (=> (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex T3)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.ord_le211207098394363844omplex S2) T3)) (=> (forall ((X4 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex X4) (tptp.minus_811609699411566653omplex T3 S2))) (= (tptp.aa_complex_nat G X4) tptp.zero_zero_nat))) (=> (forall ((X4 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex X4) S2)) (= (tptp.aa_complex_nat G X4) (tptp.aa_complex_nat H X4)))) (= (tptp.groups5693394587270226106ex_nat G T3) (tptp.groups5693394587270226106ex_nat H S2))))))) (forall ((T3 tptp.set_real) (S2 tptp.set_real) (G tptp.fun_real_int) (H tptp.fun_real_int)) (=> (tptp.finite_finite_real T3) (=> (tptp.ord_less_eq_set_real S2 T3) (=> (forall ((X4 tptp.real)) (=> (tptp.member_real X4 (tptp.minus_minus_set_real T3 S2)) (= (tptp.aa_real_int G X4) tptp.zero_zero_int))) (=> (forall ((X4 tptp.real)) (=> (tptp.member_real X4 S2) (= (tptp.aa_real_int G X4) (tptp.aa_real_int H X4)))) (= (tptp.groups1932886352136224148al_int G T3) (tptp.groups1932886352136224148al_int H S2))))))) (forall ((B4 tptp.set_complex) (A4 tptp.set_complex) (G tptp.fun_complex_real)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.ord_le211207098394363844omplex B4) A4)) (=> (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex A4)) (= (tptp.groups5808333547571424918x_real G A4) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.groups5808333547571424918x_real G (tptp.minus_811609699411566653omplex A4 B4))) (tptp.groups5808333547571424918x_real G B4)))))) (forall ((B4 tptp.set_nat) (A4 tptp.set_nat) (G tptp.fun_nat_rat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat B4) A4)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A4)) (= (tptp.groups2906978787729119204at_rat G A4) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.groups2906978787729119204at_rat G (tptp.minus_minus_set_nat A4 B4))) (tptp.groups2906978787729119204at_rat G B4)))))) (forall ((B4 tptp.set_complex) (A4 tptp.set_complex) (G tptp.fun_complex_rat)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.ord_le211207098394363844omplex B4) A4)) (=> (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex A4)) (= (tptp.groups5058264527183730370ex_rat G A4) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.groups5058264527183730370ex_rat G (tptp.minus_811609699411566653omplex A4 B4))) (tptp.groups5058264527183730370ex_rat G B4)))))) (forall ((B4 tptp.set_complex) (A4 tptp.set_complex) (G tptp.fun_complex_nat)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.ord_le211207098394363844omplex B4) A4)) (=> (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex A4)) (= (tptp.groups5693394587270226106ex_nat G A4) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.groups5693394587270226106ex_nat G (tptp.minus_811609699411566653omplex A4 B4))) (tptp.groups5693394587270226106ex_nat G B4)))))) (forall ((B4 tptp.set_nat) (A4 tptp.set_nat) (G tptp.fun_nat_int)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat B4) A4)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A4)) (= (tptp.groups3539618377306564664at_int G A4) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.groups3539618377306564664at_int G (tptp.minus_minus_set_nat A4 B4))) (tptp.groups3539618377306564664at_int G B4)))))) (forall ((B4 tptp.set_complex) (A4 tptp.set_complex) (G tptp.fun_complex_int)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.ord_le211207098394363844omplex B4) A4)) (=> (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex A4)) (= (tptp.groups5690904116761175830ex_int G A4) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.groups5690904116761175830ex_int G (tptp.minus_811609699411566653omplex A4 B4))) (tptp.groups5690904116761175830ex_int G B4)))))) (forall ((B4 tptp.set_int) (A4 tptp.set_int) (G tptp.fun_int_real)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int B4) A4)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A4)) (= (tptp.groups8778361861064173332t_real G A4) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.groups8778361861064173332t_real G (tptp.minus_minus_set_int A4 B4))) (tptp.groups8778361861064173332t_real G B4)))))) (forall ((B4 tptp.set_int) (A4 tptp.set_int) (G tptp.fun_int_rat)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int B4) A4)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A4)) (= (tptp.groups3906332499630173760nt_rat G A4) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.groups3906332499630173760nt_rat G (tptp.minus_minus_set_int A4 B4))) (tptp.groups3906332499630173760nt_rat G B4)))))) (forall ((B4 tptp.set_int) (A4 tptp.set_int) (G tptp.fun_int_nat)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int B4) A4)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A4)) (= (tptp.groups4541462559716669496nt_nat G A4) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.groups4541462559716669496nt_nat G (tptp.minus_minus_set_int A4 B4))) (tptp.groups4541462559716669496nt_nat G B4)))))) (forall ((B4 tptp.set_int) (A4 tptp.set_int) (G tptp.fun_int_int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int B4) A4)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A4)) (= (tptp.groups4538972089207619220nt_int G A4) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.groups4538972089207619220nt_int G (tptp.minus_minus_set_int A4 B4))) (tptp.groups4538972089207619220nt_int G B4)))))) (forall ((A4 tptp.set_nat) (B4 tptp.set_nat) (F tptp.fun_nat_complex)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A4)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat B4) A4)) (= (tptp.groups2073611262835488442omplex F (tptp.minus_minus_set_nat A4 B4)) (tptp.aa_complex_complex (tptp.minus_minus_complex (tptp.groups2073611262835488442omplex F A4)) (tptp.groups2073611262835488442omplex F B4)))))) (forall ((A4 tptp.set_complex) (B4 tptp.set_complex) (F tptp.fun_complex_real)) (=> (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex A4)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.ord_le211207098394363844omplex B4) A4)) (= (tptp.groups5808333547571424918x_real F (tptp.minus_811609699411566653omplex A4 B4)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.groups5808333547571424918x_real F A4)) (tptp.groups5808333547571424918x_real F B4)))))) (forall ((A4 tptp.set_nat) (B4 tptp.set_nat) (F tptp.fun_nat_rat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A4)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat B4) A4)) (= (tptp.groups2906978787729119204at_rat F (tptp.minus_minus_set_nat A4 B4)) (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.groups2906978787729119204at_rat F A4)) (tptp.groups2906978787729119204at_rat F B4)))))) (forall ((A4 tptp.set_complex) (B4 tptp.set_complex) (F tptp.fun_complex_rat)) (=> (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex A4)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.ord_le211207098394363844omplex B4) A4)) (= (tptp.groups5058264527183730370ex_rat F (tptp.minus_811609699411566653omplex A4 B4)) (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.groups5058264527183730370ex_rat F A4)) (tptp.groups5058264527183730370ex_rat F B4)))))) (forall ((A4 tptp.set_nat) (B4 tptp.set_nat) (F tptp.fun_nat_int)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A4)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat B4) A4)) (= (tptp.groups3539618377306564664at_int F (tptp.minus_minus_set_nat A4 B4)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.groups3539618377306564664at_int F A4)) (tptp.groups3539618377306564664at_int F B4)))))) (forall ((A4 tptp.set_complex) (B4 tptp.set_complex) (F tptp.fun_complex_int)) (=> (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex A4)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.ord_le211207098394363844omplex B4) A4)) (= (tptp.groups5690904116761175830ex_int F (tptp.minus_811609699411566653omplex A4 B4)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.groups5690904116761175830ex_int F A4)) (tptp.groups5690904116761175830ex_int F B4)))))) (forall ((A4 tptp.set_int) (B4 tptp.set_int) (F tptp.fun_int_complex)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A4)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int B4) A4)) (= (tptp.groups3049146728041665814omplex F (tptp.minus_minus_set_int A4 B4)) (tptp.aa_complex_complex (tptp.minus_minus_complex (tptp.groups3049146728041665814omplex F A4)) (tptp.groups3049146728041665814omplex F B4)))))) (forall ((A4 tptp.set_int) (B4 tptp.set_int) (F tptp.fun_int_real)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A4)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int B4) A4)) (= (tptp.groups8778361861064173332t_real F (tptp.minus_minus_set_int A4 B4)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.groups8778361861064173332t_real F A4)) (tptp.groups8778361861064173332t_real F B4)))))) (forall ((A4 tptp.set_int) (B4 tptp.set_int) (F tptp.fun_int_rat)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A4)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int B4) A4)) (= (tptp.groups3906332499630173760nt_rat F (tptp.minus_minus_set_int A4 B4)) (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.groups3906332499630173760nt_rat F A4)) (tptp.groups3906332499630173760nt_rat F B4)))))) (forall ((A4 tptp.set_int) (B4 tptp.set_int) (F tptp.fun_int_int)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A4)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int B4) A4)) (= (tptp.groups4538972089207619220nt_int F (tptp.minus_minus_set_int A4 B4)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.groups4538972089207619220nt_int F A4)) (tptp.groups4538972089207619220nt_int F B4)))))) (forall ((X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) X)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.ln_ln_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real tptp.one_one_real) X))) X)))) (forall ((X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)) X)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.ln_ln_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real tptp.one_one_real) X))) X)))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool _let_1 X)) (=> (tptp.pp (tptp.aa_real_bool _let_1 Y)) (= (tptp.aa_real_real tptp.ln_ln_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real X) Y)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real tptp.ln_ln_real X)) (tptp.aa_real_real tptp.ln_ln_real Y))))))) (forall ((X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) X)) (=> (= (tptp.aa_real_real tptp.ln_ln_real X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real X) tptp.one_one_real)) (= X tptp.one_one_real)))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool _let_1 X)) (=> (tptp.pp (tptp.aa_real_bool _let_1 Y)) (= (tptp.aa_real_real tptp.ln_ln_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real X) Y)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real tptp.ln_ln_real X)) (tptp.aa_real_real tptp.ln_ln_real Y))))))) (forall ((N tptp.num)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 N))) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_num_nat tptp.numeral_numeral_nat N))) (forall ((N tptp.num)) (= (tptp.aa_int_int (tptp.divide_divide_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit1 N))) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_num_int tptp.numeral_numeral_int N))) (forall ((N tptp.num)) (not (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit1 N)))))) (forall ((N tptp.num)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 N)))))) (forall ((N tptp.num)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit1 N)))))) (forall ((N tptp.num) (Q2 tptp.num)) (not (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 N))) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 Q2))) tptp.zero_zero_nat))) (forall ((N tptp.num) (Q2 tptp.num)) (not (= (tptp.aa_int_int (tptp.modulo_modulo_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit1 N))) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 Q2))) tptp.zero_zero_int))) (forall ((N tptp.num) (Q2 tptp.num)) (not (= (tptp.modulo364778990260209775nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit1 N)) (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 Q2))) tptp.zero_z3403309356797280102nteger))) (forall ((A tptp.complex)) (= (tptp.aa_nat_complex (tptp.power_power_complex A) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 tptp.one))) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_complex_complex (tptp.times_times_complex A) A)) A))) (forall ((A tptp.real)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real A) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 tptp.one))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) A)) A))) (forall ((A tptp.rat)) (= (tptp.aa_nat_rat (tptp.power_power_rat A) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 tptp.one))) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) A)) A))) (forall ((A tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 tptp.one))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) A)) A))) (forall ((A tptp.int)) (= (tptp.aa_nat_int (tptp.power_power_int A) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 tptp.one))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) A)) A))) (= (tptp.aa_num_nat tptp.numeral_numeral_nat _let_58) (tptp.aa_nat_nat tptp.suc _let_43)) (forall ((N tptp.nat)) (= (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat tptp.suc N))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 tptp.one))) N))) (forall ((B4 tptp.set_real) (A4 tptp.set_real) (F tptp.fun_real_real)) (=> (tptp.finite_finite_real B4) (=> (tptp.ord_less_eq_set_real A4 B4) (=> (forall ((B3 tptp.real)) (=> (tptp.member_real B3 (tptp.minus_minus_set_real B4 A4)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_real_real F B3))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.groups8097168146408367636l_real F A4)) (tptp.groups8097168146408367636l_real F B4))))))) (forall ((B4 tptp.set_complex) (A4 tptp.set_complex) (F tptp.fun_complex_real)) (=> (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex B4)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.ord_le211207098394363844omplex A4) B4)) (=> (forall ((B3 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex B3) (tptp.minus_811609699411566653omplex B4 A4))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_complex_real F B3))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.groups5808333547571424918x_real F A4)) (tptp.groups5808333547571424918x_real F B4))))))) (forall ((B4 tptp.set_real) (A4 tptp.set_real) (F tptp.fun_real_rat)) (=> (tptp.finite_finite_real B4) (=> (tptp.ord_less_eq_set_real A4 B4) (=> (forall ((B3 tptp.real)) (=> (tptp.member_real B3 (tptp.minus_minus_set_real B4 A4)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_real_rat F B3))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.groups1300246762558778688al_rat F A4)) (tptp.groups1300246762558778688al_rat F B4))))))) (forall ((B4 tptp.set_nat) (A4 tptp.set_nat) (F tptp.fun_nat_rat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat B4)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat A4) B4)) (=> (forall ((B3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat B3) (tptp.minus_minus_set_nat B4 A4))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_nat_rat F B3))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.groups2906978787729119204at_rat F A4)) (tptp.groups2906978787729119204at_rat F B4))))))) (forall ((B4 tptp.set_complex) (A4 tptp.set_complex) (F tptp.fun_complex_rat)) (=> (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex B4)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.ord_le211207098394363844omplex A4) B4)) (=> (forall ((B3 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex B3) (tptp.minus_811609699411566653omplex B4 A4))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_complex_rat F B3))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.groups5058264527183730370ex_rat F A4)) (tptp.groups5058264527183730370ex_rat F B4))))))) (forall ((B4 tptp.set_real) (A4 tptp.set_real) (F tptp.fun_real_nat)) (=> (tptp.finite_finite_real B4) (=> (tptp.ord_less_eq_set_real A4 B4) (=> (forall ((B3 tptp.real)) (=> (tptp.member_real B3 (tptp.minus_minus_set_real B4 A4)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) (tptp.aa_real_nat F B3))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.groups1935376822645274424al_nat F A4)) (tptp.groups1935376822645274424al_nat F B4))))))) (forall ((B4 tptp.set_complex) (A4 tptp.set_complex) (F tptp.fun_complex_nat)) (=> (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex B4)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.ord_le211207098394363844omplex A4) B4)) (=> (forall ((B3 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex B3) (tptp.minus_811609699411566653omplex B4 A4))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) (tptp.aa_complex_nat F B3))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.groups5693394587270226106ex_nat F A4)) (tptp.groups5693394587270226106ex_nat F B4))))))) (forall ((B4 tptp.set_real) (A4 tptp.set_real) (F tptp.fun_real_int)) (=> (tptp.finite_finite_real B4) (=> (tptp.ord_less_eq_set_real A4 B4) (=> (forall ((B3 tptp.real)) (=> (tptp.member_real B3 (tptp.minus_minus_set_real B4 A4)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.aa_real_int F B3))))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.groups1932886352136224148al_int F A4)) (tptp.groups1932886352136224148al_int F B4))))))) (forall ((B4 tptp.set_nat) (A4 tptp.set_nat) (F tptp.fun_nat_int)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat B4)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat A4) B4)) (=> (forall ((B3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat B3) (tptp.minus_minus_set_nat B4 A4))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.aa_nat_int F B3))))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.groups3539618377306564664at_int F A4)) (tptp.groups3539618377306564664at_int F B4))))))) (forall ((B4 tptp.set_complex) (A4 tptp.set_complex) (F tptp.fun_complex_int)) (=> (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex B4)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.ord_le211207098394363844omplex A4) B4)) (=> (forall ((B3 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex B3) (tptp.minus_811609699411566653omplex B4 A4))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.aa_complex_int F B3))))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.groups5690904116761175830ex_int F A4)) (tptp.groups5690904116761175830ex_int F B4))))))) (forall ((X32 tptp.num)) (= (tptp.aa_num_nat tptp.size_size_num (tptp.aa_num_num tptp.bit1 X32)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_num_nat tptp.size_size_num X32)) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)))) (forall ((X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) X)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.ln_ln_real X)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real X) tptp.one_one_real))))) (forall ((X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) tptp.one_one_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.ln_ln_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real tptp.one_one_real) X))) (tptp.aa_real_real tptp.uminus_uminus_real X)))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool _let_1 X)) (=> (tptp.pp (tptp.aa_real_bool _let_1 Y)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real tptp.ln_ln_real X)) (tptp.aa_real_real tptp.ln_ln_real Y))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real X) Y)) Y))))))) (forall ((Q2 tptp.num) (N tptp.num)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 Q2)))) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_num_nat tptp.numeral_numeral_nat tptp.one)) _let_1) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 N))) _let_1)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_num_nat tptp.numeral_numeral_nat N)) (tptp.aa_num_nat tptp.numeral_numeral_nat Q2)) tptp.zero_zero_nat)))) (forall ((Q2 tptp.num) (N tptp.num)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 Q2)))) (= (= (tptp.aa_int_int (tptp.modulo_modulo_int (tptp.aa_num_int tptp.numeral_numeral_int tptp.one)) _let_1) (tptp.aa_int_int (tptp.modulo_modulo_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit1 N))) _let_1)) (= (tptp.aa_int_int (tptp.modulo_modulo_int (tptp.aa_num_int tptp.numeral_numeral_int N)) (tptp.aa_num_int tptp.numeral_numeral_int Q2)) tptp.zero_zero_int)))) (forall ((Q2 tptp.num) (N tptp.num)) (let ((_let_1 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 Q2)))) (= (= (tptp.modulo364778990260209775nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger tptp.one) _let_1) (tptp.modulo364778990260209775nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit1 N)) _let_1)) (= (tptp.modulo364778990260209775nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger N) (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger Q2)) tptp.zero_z3403309356797280102nteger)))) (forall ((M tptp.num) (Q2 tptp.num)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 Q2)))) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 M))) _let_1) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_num_nat tptp.numeral_numeral_nat tptp.one)) _let_1)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_num_nat tptp.numeral_numeral_nat M)) (tptp.aa_num_nat tptp.numeral_numeral_nat Q2)) tptp.zero_zero_nat)))) (forall ((M tptp.num) (Q2 tptp.num)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 Q2)))) (= (= (tptp.aa_int_int (tptp.modulo_modulo_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit1 M))) _let_1) (tptp.aa_int_int (tptp.modulo_modulo_int (tptp.aa_num_int tptp.numeral_numeral_int tptp.one)) _let_1)) (= (tptp.aa_int_int (tptp.modulo_modulo_int (tptp.aa_num_int tptp.numeral_numeral_int M)) (tptp.aa_num_int tptp.numeral_numeral_int Q2)) tptp.zero_zero_int)))) (forall ((M tptp.num) (Q2 tptp.num)) (let ((_let_1 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 Q2)))) (= (= (tptp.modulo364778990260209775nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit1 M)) _let_1) (tptp.modulo364778990260209775nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger tptp.one) _let_1)) (= (tptp.modulo364778990260209775nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger M) (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger Q2)) tptp.zero_z3403309356797280102nteger)))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat tptp.suc M)))) N) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 tptp.one))) M)) N))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat tptp.suc M)))) N) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 tptp.one))) M)) N))) (forall ((B4 tptp.set_real) (A4 tptp.set_real) (B2 tptp.real) (F tptp.fun_real_real)) (=> (tptp.finite_finite_real B4) (=> (tptp.ord_less_eq_set_real A4 B4) (=> (tptp.member_real B2 (tptp.minus_minus_set_real B4 A4)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) (tptp.aa_real_real F B2))) (=> (forall ((X4 tptp.real)) (=> (tptp.member_real X4 B4) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_real_real F X4))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.groups8097168146408367636l_real F A4)) (tptp.groups8097168146408367636l_real F B4))))))))) (forall ((B4 tptp.set_complex) (A4 tptp.set_complex) (B2 tptp.complex) (F tptp.fun_complex_real)) (=> (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex B4)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.ord_le211207098394363844omplex A4) B4)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex B2) (tptp.minus_811609699411566653omplex B4 A4))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) (tptp.aa_complex_real F B2))) (=> (forall ((X4 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex X4) B4)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_complex_real F X4))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.groups5808333547571424918x_real F A4)) (tptp.groups5808333547571424918x_real F B4))))))))) (forall ((B4 tptp.set_real) (A4 tptp.set_real) (B2 tptp.real) (F tptp.fun_real_rat)) (=> (tptp.finite_finite_real B4) (=> (tptp.ord_less_eq_set_real A4 B4) (=> (tptp.member_real B2 (tptp.minus_minus_set_real B4 A4)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) (tptp.aa_real_rat F B2))) (=> (forall ((X4 tptp.real)) (=> (tptp.member_real X4 B4) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_real_rat F X4))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.groups1300246762558778688al_rat F A4)) (tptp.groups1300246762558778688al_rat F B4))))))))) (forall ((B4 tptp.set_nat) (A4 tptp.set_nat) (B2 tptp.nat) (F tptp.fun_nat_rat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat B4)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat A4) B4)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat B2) (tptp.minus_minus_set_nat B4 A4))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) (tptp.aa_nat_rat F B2))) (=> (forall ((X4 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X4) B4)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_nat_rat F X4))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.groups2906978787729119204at_rat F A4)) (tptp.groups2906978787729119204at_rat F B4))))))))) (forall ((B4 tptp.set_complex) (A4 tptp.set_complex) (B2 tptp.complex) (F tptp.fun_complex_rat)) (=> (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex B4)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.ord_le211207098394363844omplex A4) B4)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex B2) (tptp.minus_811609699411566653omplex B4 A4))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) (tptp.aa_complex_rat F B2))) (=> (forall ((X4 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex X4) B4)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_complex_rat F X4))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.groups5058264527183730370ex_rat F A4)) (tptp.groups5058264527183730370ex_rat F B4))))))))) (forall ((B4 tptp.set_real) (A4 tptp.set_real) (B2 tptp.real) (F tptp.fun_real_nat)) (=> (tptp.finite_finite_real B4) (=> (tptp.ord_less_eq_set_real A4 B4) (=> (tptp.member_real B2 (tptp.minus_minus_set_real B4 A4)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.aa_real_nat F B2))) (=> (forall ((X4 tptp.real)) (=> (tptp.member_real X4 B4) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) (tptp.aa_real_nat F X4))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.groups1935376822645274424al_nat F A4)) (tptp.groups1935376822645274424al_nat F B4))))))))) (forall ((B4 tptp.set_complex) (A4 tptp.set_complex) (B2 tptp.complex) (F tptp.fun_complex_nat)) (=> (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex B4)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.ord_le211207098394363844omplex A4) B4)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex B2) (tptp.minus_811609699411566653omplex B4 A4))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.aa_complex_nat F B2))) (=> (forall ((X4 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex X4) B4)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) (tptp.aa_complex_nat F X4))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.groups5693394587270226106ex_nat F A4)) (tptp.groups5693394587270226106ex_nat F B4))))))))) (forall ((B4 tptp.set_real) (A4 tptp.set_real) (B2 tptp.real) (F tptp.fun_real_int)) (=> (tptp.finite_finite_real B4) (=> (tptp.ord_less_eq_set_real A4 B4) (=> (tptp.member_real B2 (tptp.minus_minus_set_real B4 A4)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) (tptp.aa_real_int F B2))) (=> (forall ((X4 tptp.real)) (=> (tptp.member_real X4 B4) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.aa_real_int F X4))))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.groups1932886352136224148al_int F A4)) (tptp.groups1932886352136224148al_int F B4))))))))) (forall ((B4 tptp.set_nat) (A4 tptp.set_nat) (B2 tptp.nat) (F tptp.fun_nat_int)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat B4)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat A4) B4)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat B2) (tptp.minus_minus_set_nat B4 A4))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) (tptp.aa_nat_int F B2))) (=> (forall ((X4 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X4) B4)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.aa_nat_int F X4))))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.groups3539618377306564664at_int F A4)) (tptp.groups3539618377306564664at_int F B4))))))))) (forall ((B4 tptp.set_complex) (A4 tptp.set_complex) (B2 tptp.complex) (F tptp.fun_complex_int)) (=> (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex B4)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.ord_le211207098394363844omplex A4) B4)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex B2) (tptp.minus_811609699411566653omplex B4 A4))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) (tptp.aa_complex_int F B2))) (=> (forall ((X4 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex X4) B4)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.aa_complex_int F X4))))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.groups5690904116761175830ex_int F A4)) (tptp.groups5690904116761175830ex_int F B4))))))))) (forall ((L tptp.num) (Qr tptp.product_prod_nat_nat)) (= (tptp.unique5026877609467782581ep_nat L Qr) (tptp.aa_Pro262675715343573244at_nat (tptp.produc2626176000494625587at_nat (tptp.aTP_Lamm_fk L)) Qr))) (forall ((X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) tptp.one_one_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real X) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (tptp.aa_real_real tptp.ln_ln_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real tptp.one_one_real) X))))))) (forall ((L tptp.num) (Qr tptp.product_prod_int_int)) (= (tptp.aa_Pro6970504127699319548nt_int (tptp.unique5024387138958732305ep_int L) Qr) (tptp.aa_Pro6970504127699319548nt_int (tptp.produc4245557441103728435nt_int (tptp.aTP_Lamm_fl L)) Qr))) (forall ((N tptp.nat)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (let ((_let_2 (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1))) (=> (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat N) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 _let_1))) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 tptp.one))) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat _let_2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat))) _let_2)))))))) (forall ((M tptp.nat)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (let ((_let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat M) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 _let_1))))) (or (= _let_2 tptp.zero_zero_nat) (= _let_2 tptp.one_one_nat) (= _let_2 (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1)) (= _let_2 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 tptp.one))))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.ln_ln_real _let_28)) tptp.one_one_real)) (forall ((M tptp.num) (N tptp.num)) (= (tptp.unique5052692396658037445od_int (tptp.aa_num_num tptp.bit1 M) (tptp.aa_num_num tptp.bit0 N)) (tptp.aa_Pro6970504127699319548nt_int (tptp.produc4245557441103728435nt_int tptp.aTP_Lamm_gt) (tptp.unique5052692396658037445od_int M N)))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.unique5055182867167087721od_nat (tptp.aa_num_num tptp.bit1 M) (tptp.aa_num_num tptp.bit0 N)) (tptp.aa_Pro262675715343573244at_nat (tptp.produc2626176000494625587at_nat tptp.aTP_Lamm_gu) (tptp.unique5055182867167087721od_nat M N)))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.unique3479559517661332726nteger (tptp.aa_num_num tptp.bit1 M) (tptp.aa_num_num tptp.bit0 N)) (tptp.produc6916734918728496179nteger tptp.aTP_Lamm_gv (tptp.unique3479559517661332726nteger M N)))) (forall ((L tptp.num) (K tptp.num)) (= (tptp.aa_int_int (tptp.bit_ri631733984087533419it_int (tptp.aa_num_nat tptp.numeral_numeral_nat L)) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit1 K)))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.bit_ri631733984087533419it_int (tptp.aa_num_nat tptp.pred_numeral L)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int K))) tptp.one_one_int))) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one)))) tptp.one_one_int))) (= (tptp.aa_real_real tptp.neg_nu6075765906172075777c_real _let_57) (tptp.aa_real_real tptp.uminus_uminus_real _let_59)) (= (tptp.aa_int_int tptp.neg_nu3811975205180677377ec_int _let_37) (tptp.aa_int_int tptp.uminus_uminus_int _let_84)) (= (tptp.aa_complex_complex tptp.neg_nu6511756317524482435omplex _let_54) (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex _let_86)) (= (tptp.neg_nu7757733837767384882nteger _let_83) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger _let_58))) (= (tptp.aa_rat_rat tptp.neg_nu3179335615603231917ec_rat _let_38) (tptp.aa_rat_rat tptp.uminus_uminus_rat _let_85)) (forall ((X tptp.real)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (let ((_let_2 (tptp.aa_num_real tptp.numeral_numeral_real _let_1))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.one_one_real) _let_2))) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real tptp.ln_ln_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real tptp.one_one_real) X))) X))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real _let_2) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1)))))))))) (forall ((A tptp.real)) (let ((_let_1 (tptp.aa_real_real tptp.abs_abs_real A))) (= (tptp.aa_real_real tptp.abs_abs_real _let_1) _let_1))) (forall ((A tptp.int)) (let ((_let_1 (tptp.aa_int_int tptp.abs_abs_int A))) (= (tptp.aa_int_int tptp.abs_abs_int _let_1) _let_1))) (forall ((A tptp.code_integer)) (let ((_let_1 (tptp.abs_abs_Code_integer A))) (= (tptp.abs_abs_Code_integer _let_1) _let_1))) (forall ((A tptp.rat)) (let ((_let_1 (tptp.aa_rat_rat tptp.abs_abs_rat A))) (= (tptp.aa_rat_rat tptp.abs_abs_rat _let_1) _let_1))) (forall ((A tptp.real)) (let ((_let_1 (tptp.aa_real_real tptp.abs_abs_real A))) (= (tptp.aa_real_real tptp.abs_abs_real _let_1) _let_1))) (forall ((A tptp.int)) (let ((_let_1 (tptp.aa_int_int tptp.abs_abs_int A))) (= (tptp.aa_int_int tptp.abs_abs_int _let_1) _let_1))) (forall ((A tptp.code_integer)) (let ((_let_1 (tptp.abs_abs_Code_integer A))) (= (tptp.abs_abs_Code_integer _let_1) _let_1))) (forall ((A tptp.rat)) (let ((_let_1 (tptp.aa_rat_rat tptp.abs_abs_rat A))) (= (tptp.aa_rat_rat tptp.abs_abs_rat _let_1) _let_1))) (forall ((F tptp.fun_fu6012121808138353003r_bool) (A tptp.fun_Co6545587727236015215e_term) (B2 tptp.produc8923325533196201883nteger)) (=> (tptp.pp (tptp.aa_Pro5843519176478241656r_bool (tptp.aa_fun5646951941296221740r_bool F A) B2)) (tptp.pp (tptp.aa_Pro7150874649148492216r_bool (tptp.produc401098500374025047r_bool F) (tptp.produc4282985567423050387nteger A B2))))) (forall ((F tptp.fun_fu1674507805476766837r_bool) (A tptp.fun_Pr272337284026993017e_term) (B2 tptp.produc8923325533196201883nteger)) (=> (tptp.pp (tptp.aa_Pro5843519176478241656r_bool (tptp.aa_fun5449300841655810358r_bool F A) B2)) (tptp.pp (tptp.aa_Pro3640759179027349698r_bool (tptp.produc1236900166980094561r_bool F) (tptp.produc7384524951051686153nteger A B2))))) (forall ((F tptp.fun_fu4196931294019812808t_bool) (A tptp.fun_Pr9164807099015279978e_term) (B2 tptp.product_prod_int_int)) (=> (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.aa_fun5300525129335604105t_bool F A) B2)) (tptp.pp (tptp.aa_Pro5031108791230793749t_bool (tptp.produc625993674133193396t_bool F) (tptp.produc1560874099174258678nt_int A B2))))) (forall ((F tptp.fun_fu5117548769634986908t_bool) (A tptp.fun_in6429348457993719614e_term) (B2 tptp.product_prod_int_int)) (=> (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.aa_fun4446166836006121821t_bool F A) B2)) (tptp.pp (tptp.aa_Pro7591400126937138665t_bool (tptp.produc6627716702706253960t_bool F) (tptp.produc4852315488734385442nt_int A B2))))) (forall ((F tptp.fun_int_fun_int_bool) (A tptp.int) (B2 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool F A) B2)) (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.produc8560705615207772305t_bool F) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int A) B2))))) (forall ((P2 tptp.produc5207004643709237345nteger) (C tptp.fun_fu6012121808138353003r_bool)) (=> (forall ((A3 tptp.fun_Co6545587727236015215e_term) (B3 tptp.produc8923325533196201883nteger)) (=> (= P2 (tptp.produc4282985567423050387nteger A3 B3)) (tptp.pp (tptp.aa_Pro5843519176478241656r_bool (tptp.aa_fun5646951941296221740r_bool C A3) B3)))) (tptp.pp (tptp.aa_Pro7150874649148492216r_bool (tptp.produc401098500374025047r_bool C) P2)))) (forall ((P2 tptp.produc1616345218596728535nteger) (C tptp.fun_fu1674507805476766837r_bool)) (=> (forall ((A3 tptp.fun_Pr272337284026993017e_term) (B3 tptp.produc8923325533196201883nteger)) (=> (= P2 (tptp.produc7384524951051686153nteger A3 B3)) (tptp.pp (tptp.aa_Pro5843519176478241656r_bool (tptp.aa_fun5449300841655810358r_bool C A3) B3)))) (tptp.pp (tptp.aa_Pro3640759179027349698r_bool (tptp.produc1236900166980094561r_bool C) P2)))) (forall ((P2 tptp.produc4441460161354545860nt_int) (C tptp.fun_fu4196931294019812808t_bool)) (=> (forall ((A3 tptp.fun_Pr9164807099015279978e_term) (B3 tptp.product_prod_int_int)) (=> (= P2 (tptp.produc1560874099174258678nt_int A3 B3)) (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.aa_fun5300525129335604105t_bool C A3) B3)))) (tptp.pp (tptp.aa_Pro5031108791230793749t_bool (tptp.produc625993674133193396t_bool C) P2)))) (forall ((P2 tptp.produc6768802789813714928nt_int) (C tptp.fun_fu5117548769634986908t_bool)) (=> (forall ((A3 tptp.fun_in6429348457993719614e_term) (B3 tptp.product_prod_int_int)) (=> (= P2 (tptp.produc4852315488734385442nt_int A3 B3)) (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.aa_fun4446166836006121821t_bool C A3) B3)))) (tptp.pp (tptp.aa_Pro7591400126937138665t_bool (tptp.produc6627716702706253960t_bool C) P2)))) (forall ((P2 tptp.product_prod_int_int) (C tptp.fun_int_fun_int_bool)) (=> (forall ((A3 tptp.int) (B3 tptp.int)) (=> (= P2 (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int A3) B3)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool C A3) B3)))) (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.produc8560705615207772305t_bool C) P2)))) (forall ((Z tptp.nat) (C tptp.fun_in2630332840903238488et_nat) (A tptp.int) (B2 tptp.int)) (let ((_let_1 (tptp.member_nat Z))) (=> (tptp.pp (tptp.aa_set_nat_bool _let_1 (tptp.aa_int_set_nat (tptp.aa_int1906528167449992217et_nat C A) B2))) (tptp.pp (tptp.aa_set_nat_bool _let_1 (tptp.produc4251311855443802252et_nat C (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int A) B2))))))) (forall ((Z tptp.real) (C tptp.fun_in6553099857819052212t_real) (A tptp.int) (B2 tptp.int)) (=> (tptp.member_real Z (tptp.aa_int_set_real (tptp.aa_int4847878404602763637t_real C A) B2)) (tptp.member_real Z (tptp.produc6452406959799940328t_real C (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int A) B2))))) (forall ((Z tptp.int) (C tptp.fun_in7040156458970095540et_int) (A tptp.int) (B2 tptp.int)) (let ((_let_1 (tptp.member_int Z))) (=> (tptp.pp (tptp.aa_set_int_bool _let_1 (tptp.aa_int_set_int (tptp.aa_int8639817059373041269et_int C A) B2))) (tptp.pp (tptp.aa_set_int_bool _let_1 (tptp.produc73460835934605544et_int C (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int A) B2))))))) (forall ((Z tptp.complex) (C tptp.fun_in230608924162954550omplex) (A tptp.int) (B2 tptp.int)) (let ((_let_1 (tptp.member_complex Z))) (=> (tptp.pp (tptp.aa_set_complex_bool _let_1 (tptp.aa_int_set_complex (tptp.aa_int6119279391169676535omplex C A) B2))) (tptp.pp (tptp.aa_set_complex_bool _let_1 (tptp.produc8580519160106071146omplex C (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int A) B2))))))) (forall ((Z tptp.nat) (C tptp.fun_fu3482081750474265950et_nat) (A tptp.fun_Co6545587727236015215e_term) (B2 tptp.produc8923325533196201883nteger)) (let ((_let_1 (tptp.member_nat Z))) (=> (tptp.pp (tptp.aa_set_nat_bool _let_1 (tptp.aa_Pro381016180347496421et_nat (tptp.aa_fun3173333638319427527et_nat C A) B2))) (tptp.pp (tptp.aa_set_nat_bool _let_1 (tptp.produc3005202867389586502et_nat C (tptp.produc4282985567423050387nteger A B2))))))) (forall ((Z tptp.real) (C tptp.fun_fu8939667915452561338t_real) (A tptp.fun_Co6545587727236015215e_term) (B2 tptp.produc8923325533196201883nteger)) (=> (tptp.member_real Z (tptp.aa_Pro6515153133580421057t_real (tptp.aa_fun4299200212449711651t_real C A) B2)) (tptp.member_real Z (tptp.produc6662958528406444962t_real C (tptp.produc4282985567423050387nteger A B2))))) (forall ((Z tptp.int) (C tptp.fun_fu7891905368541123002et_int) (A tptp.fun_Co6545587727236015215e_term) (B2 tptp.produc8923325533196201883nteger)) (let ((_let_1 (tptp.member_int Z))) (=> (tptp.pp (tptp.aa_set_int_bool _let_1 (tptp.aa_Pro5426537197693075521et_int (tptp.aa_fun683250493387700771et_int C A) B2))) (tptp.pp (tptp.aa_set_int_bool _let_1 (tptp.produc8050723884735165602et_int C (tptp.produc4282985567423050387nteger A B2))))))) (forall ((Z tptp.complex) (C tptp.fun_fu3393861840643144508omplex) (A tptp.fun_Co6545587727236015215e_term) (B2 tptp.produc8923325533196201883nteger)) (let ((_let_1 (tptp.member_complex Z))) (=> (tptp.pp (tptp.aa_set_complex_bool _let_1 (tptp.aa_Pro5605272939097928131omplex (tptp.aa_fun8289708515469319333omplex C A) B2))) (tptp.pp (tptp.aa_set_complex_bool _let_1 (tptp.produc4085712862462845988omplex C (tptp.produc4282985567423050387nteger A B2))))))) (forall ((Z tptp.nat) (C tptp.fun_fu4770337263308229357et_nat) (A tptp.fun_in6429348457993719614e_term) (B2 tptp.product_prod_int_int)) (let ((_let_1 (tptp.member_nat Z))) (=> (tptp.pp (tptp.aa_set_nat_bool _let_1 (tptp.aa_Pro3599192995643711491et_nat (tptp.aa_fun1858489612225131606et_nat C A) B2))) (tptp.pp (tptp.aa_set_nat_bool _let_1 (tptp.produc2360586433946867413et_nat C (tptp.produc4852315488734385442nt_int A B2))))))) (forall ((Z tptp.real) (C tptp.fun_fu1570079290182735305t_real) (A tptp.fun_in6429348457993719614e_term) (B2 tptp.product_prod_int_int)) (=> (tptp.member_real Z (tptp.aa_Pro7989103684195733727t_real (tptp.aa_fun2257173110403687218t_real C A) B2)) (tptp.member_real Z (tptp.produc4003755410105663153t_real C (tptp.produc4852315488734385442nt_int A B2))))) (forall ((P2 tptp.product_prod_int_int) (Z tptp.nat) (C tptp.fun_in2630332840903238488et_nat)) (=> (forall ((A3 tptp.int) (B3 tptp.int)) (=> (= P2 (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int A3) B3)) (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat Z) (tptp.aa_int_set_nat (tptp.aa_int1906528167449992217et_nat C A3) B3))))) (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat Z) (tptp.produc4251311855443802252et_nat C P2))))) (forall ((P2 tptp.product_prod_int_int) (Z tptp.real) (C tptp.fun_in6553099857819052212t_real)) (=> (forall ((A3 tptp.int) (B3 tptp.int)) (=> (= P2 (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int A3) B3)) (tptp.member_real Z (tptp.aa_int_set_real (tptp.aa_int4847878404602763637t_real C A3) B3)))) (tptp.member_real Z (tptp.produc6452406959799940328t_real C P2)))) (forall ((P2 tptp.product_prod_int_int) (Z tptp.int) (C tptp.fun_in7040156458970095540et_int)) (=> (forall ((A3 tptp.int) (B3 tptp.int)) (=> (= P2 (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int A3) B3)) (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Z) (tptp.aa_int_set_int (tptp.aa_int8639817059373041269et_int C A3) B3))))) (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Z) (tptp.produc73460835934605544et_int C P2))))) (forall ((P2 tptp.product_prod_int_int) (Z tptp.complex) (C tptp.fun_in230608924162954550omplex)) (=> (forall ((A3 tptp.int) (B3 tptp.int)) (=> (= P2 (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int A3) B3)) (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex Z) (tptp.aa_int_set_complex (tptp.aa_int6119279391169676535omplex C A3) B3))))) (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex Z) (tptp.produc8580519160106071146omplex C P2))))) (forall ((P2 tptp.produc5207004643709237345nteger) (Z tptp.nat) (C tptp.fun_fu3482081750474265950et_nat)) (=> (forall ((A3 tptp.fun_Co6545587727236015215e_term) (B3 tptp.produc8923325533196201883nteger)) (=> (= P2 (tptp.produc4282985567423050387nteger A3 B3)) (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat Z) (tptp.aa_Pro381016180347496421et_nat (tptp.aa_fun3173333638319427527et_nat C A3) B3))))) (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat Z) (tptp.produc3005202867389586502et_nat C P2))))) (forall ((P2 tptp.produc5207004643709237345nteger) (Z tptp.real) (C tptp.fun_fu8939667915452561338t_real)) (=> (forall ((A3 tptp.fun_Co6545587727236015215e_term) (B3 tptp.produc8923325533196201883nteger)) (=> (= P2 (tptp.produc4282985567423050387nteger A3 B3)) (tptp.member_real Z (tptp.aa_Pro6515153133580421057t_real (tptp.aa_fun4299200212449711651t_real C A3) B3)))) (tptp.member_real Z (tptp.produc6662958528406444962t_real C P2)))) (forall ((P2 tptp.produc5207004643709237345nteger) (Z tptp.int) (C tptp.fun_fu7891905368541123002et_int)) (=> (forall ((A3 tptp.fun_Co6545587727236015215e_term) (B3 tptp.produc8923325533196201883nteger)) (=> (= P2 (tptp.produc4282985567423050387nteger A3 B3)) (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Z) (tptp.aa_Pro5426537197693075521et_int (tptp.aa_fun683250493387700771et_int C A3) B3))))) (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Z) (tptp.produc8050723884735165602et_int C P2))))) (forall ((P2 tptp.produc5207004643709237345nteger) (Z tptp.complex) (C tptp.fun_fu3393861840643144508omplex)) (=> (forall ((A3 tptp.fun_Co6545587727236015215e_term) (B3 tptp.produc8923325533196201883nteger)) (=> (= P2 (tptp.produc4282985567423050387nteger A3 B3)) (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex Z) (tptp.aa_Pro5605272939097928131omplex (tptp.aa_fun8289708515469319333omplex C A3) B3))))) (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex Z) (tptp.produc4085712862462845988omplex C P2))))) (forall ((P2 tptp.produc6768802789813714928nt_int) (Z tptp.nat) (C tptp.fun_fu4770337263308229357et_nat)) (=> (forall ((A3 tptp.fun_in6429348457993719614e_term) (B3 tptp.product_prod_int_int)) (=> (= P2 (tptp.produc4852315488734385442nt_int A3 B3)) (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat Z) (tptp.aa_Pro3599192995643711491et_nat (tptp.aa_fun1858489612225131606et_nat C A3) B3))))) (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat Z) (tptp.produc2360586433946867413et_nat C P2))))) (forall ((P2 tptp.produc6768802789813714928nt_int) (Z tptp.real) (C tptp.fun_fu1570079290182735305t_real)) (=> (forall ((A3 tptp.fun_in6429348457993719614e_term) (B3 tptp.product_prod_int_int)) (=> (= P2 (tptp.produc4852315488734385442nt_int A3 B3)) (tptp.member_real Z (tptp.aa_Pro7989103684195733727t_real (tptp.aa_fun2257173110403687218t_real C A3) B3)))) (tptp.member_real Z (tptp.produc4003755410105663153t_real C P2)))) (forall ((P2 tptp.product_prod_nat_nat) (C tptp.fun_na4786964484885125043t_bool) (X tptp.product_prod_nat_nat)) (=> (forall ((A3 tptp.nat) (B3 tptp.nat)) (=> (= (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat A3) B3) P2) (tptp.pp (tptp.aa_Pro2232559814647311250t_bool (tptp.aa_nat4401263874371387303t_bool (tptp.aa_nat4909001760120733684t_bool C A3) B3) X)))) (tptp.pp (tptp.aa_Pro2232559814647311250t_bool (tptp.aa_Pro595088089689268830t_bool (tptp.produc5023667602222594023t_bool C) P2) X)))) (forall ((A tptp.code_integer)) (= (= tptp.zero_z3403309356797280102nteger (tptp.abs_abs_Code_integer A)) (= A tptp.zero_z3403309356797280102nteger))) (forall ((A tptp.real)) (= (= tptp.zero_zero_real (tptp.aa_real_real tptp.abs_abs_real A)) (= A tptp.zero_zero_real))) (forall ((A tptp.rat)) (= (= tptp.zero_zero_rat (tptp.aa_rat_rat tptp.abs_abs_rat A)) (= A tptp.zero_zero_rat))) (forall ((A tptp.int)) (= (= tptp.zero_zero_int (tptp.aa_int_int tptp.abs_abs_int A)) (= A tptp.zero_zero_int))) (forall ((A tptp.code_integer)) (= (= (tptp.abs_abs_Code_integer A) tptp.zero_z3403309356797280102nteger) (= A tptp.zero_z3403309356797280102nteger))) (forall ((A tptp.real)) (= (= (tptp.aa_real_real tptp.abs_abs_real A) tptp.zero_zero_real) (= A tptp.zero_zero_real))) (forall ((A tptp.rat)) (= (= (tptp.aa_rat_rat tptp.abs_abs_rat A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))) (forall ((A tptp.int)) (= (= (tptp.aa_int_int tptp.abs_abs_int A) tptp.zero_zero_int) (= A tptp.zero_zero_int))) _let_94 _let_93 _let_92 _let_91 _let_94 (= (tptp.aa_complex_complex tptp.abs_abs_complex tptp.zero_zero_complex) tptp.zero_zero_complex) _let_93 _let_92 _let_91 (forall ((N tptp.num)) (let ((_let_1 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger N))) (= (tptp.abs_abs_Code_integer _let_1) _let_1))) (forall ((N tptp.num)) (let ((_let_1 (tptp.aa_num_real tptp.numeral_numeral_real N))) (= (tptp.aa_real_real tptp.abs_abs_real _let_1) _let_1))) (forall ((N tptp.num)) (let ((_let_1 (tptp.aa_num_rat tptp.numeral_numeral_rat N))) (= (tptp.aa_rat_rat tptp.abs_abs_rat _let_1) _let_1))) (forall ((N tptp.num)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int N))) (= (tptp.aa_int_int tptp.abs_abs_int _let_1) _let_1))) (forall ((A tptp.code_integer)) (let ((_let_1 (tptp.abs_abs_Code_integer A))) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger _let_1) _let_1) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) A)))) (forall ((A tptp.real)) (let ((_let_1 (tptp.aa_real_real tptp.abs_abs_real A))) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real _let_1) _let_1) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) A)))) (forall ((A tptp.rat)) (let ((_let_1 (tptp.aa_rat_rat tptp.abs_abs_rat A))) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat _let_1) _let_1) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) A)))) (forall ((A tptp.int)) (let ((_let_1 (tptp.aa_int_int tptp.abs_abs_int A))) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int _let_1) _let_1) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) A)))) _let_90 (= (tptp.aa_complex_complex tptp.abs_abs_complex tptp.one_one_complex) tptp.one_one_complex) _let_89 _let_88 _let_87 (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (let ((_let_1 (tptp.plus_p5714425477246183910nteger (tptp.abs_abs_Code_integer A) (tptp.abs_abs_Code_integer B2)))) (= (tptp.abs_abs_Code_integer _let_1) _let_1))) (forall ((A tptp.real) (B2 tptp.real)) (let ((_let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real tptp.abs_abs_real A)) (tptp.aa_real_real tptp.abs_abs_real B2)))) (= (tptp.aa_real_real tptp.abs_abs_real _let_1) _let_1))) (forall ((A tptp.rat) (B2 tptp.rat)) (let ((_let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat tptp.abs_abs_rat A)) (tptp.aa_rat_rat tptp.abs_abs_rat B2)))) (= (tptp.aa_rat_rat tptp.abs_abs_rat _let_1) _let_1))) (forall ((A tptp.int) (B2 tptp.int)) (let ((_let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int tptp.abs_abs_int A)) (tptp.aa_int_int tptp.abs_abs_int B2)))) (= (tptp.aa_int_int tptp.abs_abs_int _let_1) _let_1))) (forall ((A tptp.complex) (B2 tptp.complex)) (= (tptp.aa_complex_complex tptp.abs_abs_complex (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex A) B2)) (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex (tptp.aa_complex_complex tptp.abs_abs_complex A)) (tptp.aa_complex_complex tptp.abs_abs_complex B2)))) (forall ((A tptp.real) (B2 tptp.real)) (= (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real A) B2)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real tptp.abs_abs_real A)) (tptp.aa_real_real tptp.abs_abs_real B2)))) (forall ((A tptp.rat) (B2 tptp.rat)) (= (tptp.aa_rat_rat tptp.abs_abs_rat (tptp.aa_rat_rat (tptp.divide_divide_rat A) B2)) (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_rat_rat tptp.abs_abs_rat A)) (tptp.aa_rat_rat tptp.abs_abs_rat B2)))) (forall ((A tptp.real)) (= (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_real_real tptp.uminus_uminus_real A)) (tptp.aa_real_real tptp.abs_abs_real A))) (forall ((A tptp.int)) (= (tptp.aa_int_int tptp.abs_abs_int (tptp.aa_int_int tptp.uminus_uminus_int A)) (tptp.aa_int_int tptp.abs_abs_int A))) (forall ((A tptp.code_integer)) (= (tptp.abs_abs_Code_integer (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A)) (tptp.abs_abs_Code_integer A))) (forall ((A tptp.rat)) (= (tptp.aa_rat_rat tptp.abs_abs_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat A)) (tptp.aa_rat_rat tptp.abs_abs_rat A))) (forall ((A tptp.real)) (= (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_real_real tptp.uminus_uminus_real A)) (tptp.aa_real_real tptp.abs_abs_real A))) (forall ((A tptp.int)) (= (tptp.aa_int_int tptp.abs_abs_int (tptp.aa_int_int tptp.uminus_uminus_int A)) (tptp.aa_int_int tptp.abs_abs_int A))) (forall ((A tptp.complex)) (= (tptp.aa_complex_complex tptp.abs_abs_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex A)) (tptp.aa_complex_complex tptp.abs_abs_complex A))) (forall ((A tptp.code_integer)) (= (tptp.abs_abs_Code_integer (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A)) (tptp.abs_abs_Code_integer A))) (forall ((A tptp.rat)) (= (tptp.aa_rat_rat tptp.abs_abs_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat A)) (tptp.aa_rat_rat tptp.abs_abs_rat A))) (forall ((M tptp.real) (K tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.dvd_dvd_real (tptp.aa_real_real tptp.abs_abs_real M)) K)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.dvd_dvd_real M) K)))) (forall ((M tptp.int) (K tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_int_int tptp.abs_abs_int M)) K)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int M) K)))) (forall ((M tptp.code_integer) (K tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.abs_abs_Code_integer M)) K)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer M) K)))) (forall ((M tptp.rat) (K tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.dvd_dvd_rat (tptp.aa_rat_rat tptp.abs_abs_rat M)) K)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.dvd_dvd_rat M) K)))) (forall ((M tptp.real) (K tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.dvd_dvd_real M))) (= (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real tptp.abs_abs_real K))) (tptp.pp (tptp.aa_real_bool _let_1 K))))) (forall ((M tptp.int) (K tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int M))) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int tptp.abs_abs_int K))) (tptp.pp (tptp.aa_int_bool _let_1 K))))) (forall ((M tptp.code_integer) (K tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer M))) (= (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.abs_abs_Code_integer K))) (tptp.pp (tptp.aa_Code_integer_bool _let_1 K))))) (forall ((M tptp.rat) (K tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.dvd_dvd_rat M))) (= (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat tptp.abs_abs_rat K))) (tptp.pp (tptp.aa_rat_bool _let_1 K))))) (forall ((P tptp.bool)) (let ((_let_1 (tptp.zero_n3304061248610475627l_real P))) (= (tptp.aa_real_real tptp.abs_abs_real _let_1) _let_1))) (forall ((P tptp.bool)) (let ((_let_1 (tptp.zero_n2052037380579107095ol_rat P))) (= (tptp.aa_rat_rat tptp.abs_abs_rat _let_1) _let_1))) (forall ((P tptp.bool)) (let ((_let_1 (tptp.aa_bool_int tptp.zero_n2684676970156552555ol_int P))) (= (tptp.aa_int_int tptp.abs_abs_int _let_1) _let_1))) (forall ((P tptp.bool)) (let ((_let_1 (tptp.zero_n356916108424825756nteger P))) (= (tptp.abs_abs_Code_integer _let_1) _let_1))) (= (tptp.aa_complex_complex tptp.neg_nu6511756317524482435omplex tptp.one_one_complex) tptp.one_one_complex) (= (tptp.aa_real_real tptp.neg_nu6075765906172075777c_real tptp.one_one_real) tptp.one_one_real) (= (tptp.aa_rat_rat tptp.neg_nu3179335615603231917ec_rat tptp.one_one_rat) tptp.one_one_rat) (= (tptp.aa_int_int tptp.neg_nu3811975205180677377ec_int tptp.one_one_int) tptp.one_one_int) (forall ((A tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.abs_abs_Code_integer A)) tptp.zero_z3403309356797280102nteger)) (= A tptp.zero_z3403309356797280102nteger))) (forall ((A tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real A)) tptp.zero_zero_real)) (= A tptp.zero_zero_real))) (forall ((A tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat tptp.abs_abs_rat A)) tptp.zero_zero_rat)) (= A tptp.zero_zero_rat))) (forall ((A tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.abs_abs_int A)) tptp.zero_zero_int)) (= A tptp.zero_zero_int))) (forall ((A tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.abs_abs_Code_integer A)) A)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A)))) (forall ((A tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real A)) A)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) A)))) (forall ((A tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat tptp.abs_abs_rat A)) A)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) A)))) (forall ((A tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.abs_abs_int A)) A)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) A)))) (forall ((A tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A)) (= (tptp.abs_abs_Code_integer A) A))) (forall ((A tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) A)) (= (tptp.aa_real_real tptp.abs_abs_real A) A))) (forall ((A tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) A)) (= (tptp.aa_rat_rat tptp.abs_abs_rat A) A))) (forall ((A tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) A)) (= (tptp.aa_int_int tptp.abs_abs_int A) A))) (forall ((A tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (tptp.abs_abs_Code_integer A))) (not (= A tptp.zero_z3403309356797280102nteger)))) (forall ((A tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) (tptp.aa_real_real tptp.abs_abs_real A))) (not (= A tptp.zero_zero_real)))) (forall ((A tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) (tptp.aa_rat_rat tptp.abs_abs_rat A))) (not (= A tptp.zero_zero_rat)))) (forall ((A tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) (tptp.aa_int_int tptp.abs_abs_int A))) (not (= A tptp.zero_zero_int)))) (forall ((N tptp.num)) (let ((_let_1 (tptp.aa_num_real tptp.numeral_numeral_real N))) (= (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_real_real tptp.uminus_uminus_real _let_1)) _let_1))) (forall ((N tptp.num)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int N))) (= (tptp.aa_int_int tptp.abs_abs_int (tptp.aa_int_int tptp.uminus_uminus_int _let_1)) _let_1))) (forall ((N tptp.num)) (let ((_let_1 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger N))) (= (tptp.abs_abs_Code_integer (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger _let_1)) _let_1))) (forall ((N tptp.num)) (let ((_let_1 (tptp.aa_num_rat tptp.numeral_numeral_rat N))) (= (tptp.aa_rat_rat tptp.abs_abs_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat _let_1)) _let_1))) (= (tptp.aa_real_real tptp.abs_abs_real _let_57) tptp.one_one_real) (= (tptp.aa_int_int tptp.abs_abs_int _let_37) tptp.one_one_int) (= (tptp.abs_abs_Code_integer _let_83) tptp.one_one_Code_integer) (= (tptp.aa_rat_rat tptp.abs_abs_rat _let_38) tptp.one_one_rat) (forall ((A tptp.real) (N tptp.nat)) (= (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real tptp.uminus_uminus_real A)) N)) (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real A) N)))) (forall ((A tptp.int) (N tptp.nat)) (= (tptp.aa_int_int tptp.abs_abs_int (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_int_int tptp.uminus_uminus_int A)) N)) (tptp.aa_int_int tptp.abs_abs_int (tptp.aa_nat_int (tptp.power_power_int A) N)))) (forall ((A tptp.code_integer) (N tptp.nat)) (= (tptp.abs_abs_Code_integer (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A)) N)) (tptp.abs_abs_Code_integer (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger A) N)))) (forall ((A tptp.rat) (N tptp.nat)) (= (tptp.aa_rat_rat tptp.abs_abs_rat (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat A)) N)) (tptp.aa_rat_rat tptp.abs_abs_rat (tptp.aa_nat_rat (tptp.power_power_rat A) N)))) (= (tptp.aa_num_nat tptp.pred_numeral tptp.one) tptp.zero_zero_nat) (forall ((K tptp.num) (N tptp.nat)) (= (= (tptp.aa_num_nat tptp.numeral_numeral_nat K) (tptp.aa_nat_nat tptp.suc N)) (= (tptp.aa_num_nat tptp.pred_numeral K) N))) (forall ((N tptp.nat) (K tptp.num)) (= (= (tptp.aa_nat_nat tptp.suc N) (tptp.aa_num_nat tptp.numeral_numeral_nat K)) (= N (tptp.aa_num_nat tptp.pred_numeral K)))) (forall ((F tptp.fun_int_int) (A4 tptp.set_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.abs_abs_int (tptp.groups4538972089207619220nt_int F A4))) (tptp.groups4538972089207619220nt_int (tptp.aTP_Lamm_gw F) A4)))) (forall ((F tptp.fun_nat_real) (A4 tptp.set_nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real (tptp.groups6591440286371151544t_real F A4))) (tptp.groups6591440286371151544t_real (tptp.aTP_Lamm_gx F) A4)))) (forall ((A tptp.real) (B2 tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (= (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real A) (tptp.aa_real_real tptp.abs_abs_real B2)))) (or (tptp.pp (tptp.aa_real_bool _let_1 A)) (= B2 tptp.zero_zero_real))))) (forall ((A tptp.rat) (B2 tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat))) (= (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat (tptp.divide_divide_rat A) (tptp.aa_rat_rat tptp.abs_abs_rat B2)))) (or (tptp.pp (tptp.aa_rat_bool _let_1 A)) (= B2 tptp.zero_zero_rat))))) (forall ((A tptp.real) (B2 tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real A) (tptp.aa_real_real tptp.abs_abs_real B2))) tptp.zero_zero_real)) (or (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) tptp.zero_zero_real)) (= B2 tptp.zero_zero_real)))) (forall ((A tptp.rat) (B2 tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.divide_divide_rat A) (tptp.aa_rat_rat tptp.abs_abs_rat B2))) tptp.zero_zero_rat)) (or (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) tptp.zero_zero_rat)) (= B2 tptp.zero_zero_rat)))) (forall ((A tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) tptp.zero_zero_real)) (= (tptp.aa_real_real tptp.abs_abs_real A) (tptp.aa_real_real tptp.uminus_uminus_real A)))) (forall ((A tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger A) tptp.zero_z3403309356797280102nteger)) (= (tptp.abs_abs_Code_integer A) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A)))) (forall ((A tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) tptp.zero_zero_rat)) (= (tptp.aa_rat_rat tptp.abs_abs_rat A) (tptp.aa_rat_rat tptp.uminus_uminus_rat A)))) (forall ((A tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) tptp.zero_zero_int)) (= (tptp.aa_int_int tptp.abs_abs_int A) (tptp.aa_int_int tptp.uminus_uminus_int A)))) (forall ((K tptp.num) (N tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_num_nat tptp.numeral_numeral_nat K)) (tptp.aa_nat_nat tptp.suc N))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_num_nat tptp.pred_numeral K)) N)))) (forall ((N tptp.nat) (K tptp.num)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat tptp.suc N)) (tptp.aa_num_nat tptp.numeral_numeral_nat K))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N) (tptp.aa_num_nat tptp.pred_numeral K))))) (forall ((X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.abs_abs_real X)) tptp.one_one_real)) (= (tptp.aa_real_real tptp.artanh_real (tptp.aa_real_real tptp.uminus_uminus_real X)) (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_real_real tptp.artanh_real X))))) (forall ((K tptp.num)) (= (tptp.aa_num_nat tptp.pred_numeral (tptp.aa_num_num tptp.bit1 K)) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 K)))) (forall ((K tptp.num) (N tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_num_nat tptp.numeral_numeral_nat K)) (tptp.aa_nat_nat tptp.suc N))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_num_nat tptp.pred_numeral K)) N)))) (forall ((N tptp.nat) (K tptp.num)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat tptp.suc N)) (tptp.aa_num_nat tptp.numeral_numeral_nat K))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N) (tptp.aa_num_nat tptp.pred_numeral K))))) (forall ((N tptp.nat) (K tptp.num)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat tptp.suc N)) (tptp.aa_num_nat tptp.numeral_numeral_nat K)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) (tptp.aa_num_nat tptp.pred_numeral K)))) (forall ((K tptp.num) (N tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_num_nat tptp.numeral_numeral_nat K)) (tptp.aa_nat_nat tptp.suc N)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_num_nat tptp.pred_numeral K)) N))) (forall ((N tptp.nat) (K tptp.num)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat (tptp.aa_nat_nat tptp.suc N)) (tptp.aa_num_nat tptp.numeral_numeral_nat K)) (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat N) (tptp.aa_num_nat tptp.pred_numeral K))))) (forall ((K tptp.num) (N tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat (tptp.aa_num_nat tptp.numeral_numeral_nat K)) (tptp.aa_nat_nat tptp.suc N)) (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat (tptp.aa_num_nat tptp.pred_numeral K)) N)))) (forall ((F tptp.fun_int_int) (A4 tptp.set_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.groups4538972089207619220nt_int (tptp.aTP_Lamm_gw F) A4)))) (forall ((F tptp.fun_nat_real) (A4 tptp.set_nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.groups6591440286371151544t_real (tptp.aTP_Lamm_gx F) A4)))) (= (tptp.aa_real_real tptp.neg_nu6075765906172075777c_real tptp.zero_zero_real) _let_57) (= (tptp.aa_int_int tptp.neg_nu3811975205180677377ec_int tptp.zero_zero_int) _let_37) (= (tptp.aa_complex_complex tptp.neg_nu6511756317524482435omplex tptp.zero_zero_complex) _let_54) (= (tptp.neg_nu7757733837767384882nteger tptp.zero_z3403309356797280102nteger) _let_83) (= (tptp.aa_rat_rat tptp.neg_nu3179335615603231917ec_rat tptp.zero_zero_rat) _let_38) (forall ((M tptp.num) (N tptp.num)) (= (tptp.aa_int_int (tptp.divide_divide_int (tptp.aa_num_int tptp.numeral_numeral_int M)) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int N))) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.adjust_div (tptp.unique5052692396658037445od_int M N))))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.aa_int_int (tptp.divide_divide_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int M))) (tptp.aa_num_int tptp.numeral_numeral_int N)) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.adjust_div (tptp.unique5052692396658037445od_int M N))))) (forall ((A tptp.code_integer) (N tptp.nat)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger (tptp.abs_abs_Code_integer A)) N))) (or (not (= A tptp.zero_z3403309356797280102nteger)) (= N tptp.zero_zero_nat)))) (forall ((A tptp.real) (N tptp.nat)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real tptp.abs_abs_real A)) N))) (or (not (= A tptp.zero_zero_real)) (= N tptp.zero_zero_nat)))) (forall ((A tptp.rat) (N tptp.nat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_rat_rat tptp.abs_abs_rat A)) N))) (or (not (= A tptp.zero_zero_rat)) (= N tptp.zero_zero_nat)))) (forall ((A tptp.int) (N tptp.nat)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_int_int tptp.abs_abs_int A)) N))) (or (not (= A tptp.zero_zero_int)) (= N tptp.zero_zero_nat)))) (forall ((A tptp.code_integer)) (let ((_let_1 (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger A) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.abs_abs_Code_integer _let_1) _let_1))) (forall ((A tptp.rat)) (let ((_let_1 (tptp.aa_nat_rat (tptp.power_power_rat A) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.aa_rat_rat tptp.abs_abs_rat _let_1) _let_1))) (forall ((A tptp.real)) (let ((_let_1 (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real A) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.aa_real_real tptp.abs_abs_real _let_1) _let_1))) (forall ((A tptp.int)) (let ((_let_1 (tptp.aa_nat_int (tptp.power_power_int A) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.aa_int_int tptp.abs_abs_int _let_1) _let_1))) (forall ((A tptp.code_integer)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger (tptp.abs_abs_Code_integer A)) _let_1) (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger A) _let_1)))) (forall ((A tptp.rat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_rat_rat tptp.abs_abs_rat A)) _let_1) (tptp.aa_nat_rat (tptp.power_power_rat A) _let_1)))) (forall ((A tptp.real)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real tptp.abs_abs_real A)) _let_1) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real A) _let_1)))) (forall ((A tptp.int)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_int_int tptp.abs_abs_int A)) _let_1) (tptp.aa_nat_int (tptp.power_power_int A) _let_1)))) (forall ((N tptp.nat) (M tptp.nat) (G tptp.fun_nat_complex)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N))) (let ((_let_2 (tptp.groups2073611262835488442omplex G (tptp.set_or1269000886237332187st_nat M _let_1)))) (let ((_let_3 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_1) M)))) (and (=> _let_3 (= _let_2 tptp.zero_zero_complex)) (=> (not _let_3) (= _let_2 (tptp.aa_complex_complex (tptp.plus_plus_complex (tptp.groups2073611262835488442omplex G (tptp.set_or1269000886237332187st_nat M N))) (tptp.aa_nat_complex G _let_1))))))))) (forall ((N tptp.nat) (M tptp.nat) (G tptp.fun_nat_rat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N))) (let ((_let_2 (tptp.groups2906978787729119204at_rat G (tptp.set_or1269000886237332187st_nat M _let_1)))) (let ((_let_3 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_1) M)))) (and (=> _let_3 (= _let_2 tptp.zero_zero_rat)) (=> (not _let_3) (= _let_2 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.groups2906978787729119204at_rat G (tptp.set_or1269000886237332187st_nat M N))) (tptp.aa_nat_rat G _let_1))))))))) (forall ((N tptp.nat) (M tptp.nat) (G tptp.fun_nat_int)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N))) (let ((_let_2 (tptp.groups3539618377306564664at_int G (tptp.set_or1269000886237332187st_nat M _let_1)))) (let ((_let_3 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_1) M)))) (and (=> _let_3 (= _let_2 tptp.zero_zero_int)) (=> (not _let_3) (= _let_2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.groups3539618377306564664at_int G (tptp.set_or1269000886237332187st_nat M N))) (tptp.aa_nat_int G _let_1))))))))) (forall ((N tptp.nat) (M tptp.nat) (G tptp.fun_nat_nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N))) (let ((_let_2 (tptp.groups3542108847815614940at_nat G))) (let ((_let_3 (tptp.aa_set_nat_nat _let_2 (tptp.set_or1269000886237332187st_nat M _let_1)))) (let ((_let_4 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_1) M)))) (and (=> _let_4 (= _let_3 tptp.zero_zero_nat)) (=> (not _let_4) (= _let_3 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_set_nat_nat _let_2 (tptp.set_or1269000886237332187st_nat M N))) (tptp.aa_nat_nat G _let_1)))))))))) (forall ((N tptp.nat) (M tptp.nat) (G tptp.fun_nat_real)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N))) (let ((_let_2 (tptp.groups6591440286371151544t_real G (tptp.set_or1269000886237332187st_nat M _let_1)))) (let ((_let_3 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_1) M)))) (and (=> _let_3 (= _let_2 tptp.zero_zero_real)) (=> (not _let_3) (= _let_2 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.groups6591440286371151544t_real G (tptp.set_or1269000886237332187st_nat M N))) (tptp.aa_nat_real G _let_1))))))))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_num_int tptp.numeral_numeral_int M)) (tptp.aa_num_int tptp.numeral_numeral_int N))) (tptp.pp (tptp.aa_Pro4501881432599481050t_bool tptp.unique6319869463603278526ux_int (tptp.unique5052692396658037445od_int N M))))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat M)) (tptp.aa_num_nat tptp.numeral_numeral_nat N))) (tptp.pp (tptp.aa_Pro2232559814647311250t_bool tptp.unique6322359934112328802ux_nat (tptp.unique5055182867167087721od_nat N M))))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger M)) (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger N))) (tptp.unique5706413561485394159nteger (tptp.unique3479559517661332726nteger N M)))) (forall ((M tptp.num)) (= (tptp.unique5052692396658037445od_int M tptp.one) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int (tptp.aa_num_int tptp.numeral_numeral_int M)) tptp.zero_zero_int))) (forall ((M tptp.num)) (= (tptp.unique5055182867167087721od_nat M tptp.one) (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat (tptp.aa_num_nat tptp.numeral_numeral_nat M)) tptp.zero_zero_nat))) (forall ((M tptp.num)) (= (tptp.unique3479559517661332726nteger M tptp.one) (tptp.produc1086072967326762835nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger M) tptp.zero_z3403309356797280102nteger))) (forall ((A4 tptp.set_nat) (C tptp.fun_nat_complex)) (let ((_let_1 (tptp.groups2073611262835488442omplex (tptp.aTP_Lamm_gy C) A4))) (let ((_let_2 (and (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A4)) (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat tptp.zero_zero_nat) A4))))) (and (=> _let_2 (= _let_1 (tptp.aa_nat_complex C tptp.zero_zero_nat))) (=> (not _let_2) (= _let_1 tptp.zero_zero_complex)))))) (forall ((A4 tptp.set_nat) (C tptp.fun_nat_rat)) (let ((_let_1 (tptp.groups2906978787729119204at_rat (tptp.aTP_Lamm_gz C) A4))) (let ((_let_2 (and (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A4)) (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat tptp.zero_zero_nat) A4))))) (and (=> _let_2 (= _let_1 (tptp.aa_nat_rat C tptp.zero_zero_nat))) (=> (not _let_2) (= _let_1 tptp.zero_zero_rat)))))) (forall ((A4 tptp.set_nat) (C tptp.fun_nat_real)) (let ((_let_1 (tptp.groups6591440286371151544t_real (tptp.aTP_Lamm_ha C) A4))) (let ((_let_2 (and (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A4)) (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat tptp.zero_zero_nat) A4))))) (and (=> _let_2 (= _let_1 (tptp.aa_nat_real C tptp.zero_zero_nat))) (=> (not _let_2) (= _let_1 tptp.zero_zero_real)))))) (forall ((W tptp.num) (A tptp.code_integer)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat W))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) _let_1)) (= (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger (tptp.abs_abs_Code_integer A)) _let_1) (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger A) _let_1))))) (forall ((W tptp.num) (A tptp.rat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat W))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) _let_1)) (= (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_rat_rat tptp.abs_abs_rat A)) _let_1) (tptp.aa_nat_rat (tptp.power_power_rat A) _let_1))))) (forall ((W tptp.num) (A tptp.real)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat W))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) _let_1)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real tptp.abs_abs_real A)) _let_1) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real A) _let_1))))) (forall ((W tptp.num) (A tptp.int)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat W))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) _let_1)) (= (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_int_int tptp.abs_abs_int A)) _let_1) (tptp.aa_nat_int (tptp.power_power_int A) _let_1))))) (forall ((N tptp.num)) (= (tptp.unique5052692396658037445od_int tptp.one (tptp.aa_num_num tptp.bit0 N)) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int tptp.zero_zero_int) (tptp.aa_num_int tptp.numeral_numeral_int tptp.one)))) (forall ((N tptp.num)) (= (tptp.unique5055182867167087721od_nat tptp.one (tptp.aa_num_num tptp.bit0 N)) (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat tptp.zero_zero_nat) (tptp.aa_num_nat tptp.numeral_numeral_nat tptp.one)))) (forall ((N tptp.num)) (= (tptp.unique3479559517661332726nteger tptp.one (tptp.aa_num_num tptp.bit0 N)) (tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger tptp.one)))) (forall ((N tptp.num)) (= (tptp.unique5052692396658037445od_int tptp.one (tptp.aa_num_num tptp.bit1 N)) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int tptp.zero_zero_int) (tptp.aa_num_int tptp.numeral_numeral_int tptp.one)))) (forall ((N tptp.num)) (= (tptp.unique5055182867167087721od_nat tptp.one (tptp.aa_num_num tptp.bit1 N)) (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat tptp.zero_zero_nat) (tptp.aa_num_nat tptp.numeral_numeral_nat tptp.one)))) (forall ((N tptp.num)) (= (tptp.unique3479559517661332726nteger tptp.one (tptp.aa_num_num tptp.bit1 N)) (tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger tptp.one)))) (forall ((A4 tptp.set_nat) (C tptp.fun_nat_complex) (D tptp.fun_nat_complex)) (let ((_let_1 (tptp.groups2073611262835488442omplex (tptp.aa_fun2955221450537884980omplex (tptp.aTP_Lamm_hb C) D) A4))) (let ((_let_2 (and (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A4)) (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat tptp.zero_zero_nat) A4))))) (and (=> _let_2 (= _let_1 (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex (tptp.aa_nat_complex C tptp.zero_zero_nat)) (tptp.aa_nat_complex D tptp.zero_zero_nat)))) (=> (not _let_2) (= _let_1 tptp.zero_zero_complex)))))) (forall ((A4 tptp.set_nat) (C tptp.fun_nat_rat) (D tptp.fun_nat_rat)) (let ((_let_1 (tptp.groups2906978787729119204at_rat (tptp.aa_fun765758790203053448at_rat (tptp.aTP_Lamm_hc C) D) A4))) (let ((_let_2 (and (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A4)) (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat tptp.zero_zero_nat) A4))))) (and (=> _let_2 (= _let_1 (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_nat_rat C tptp.zero_zero_nat)) (tptp.aa_nat_rat D tptp.zero_zero_nat)))) (=> (not _let_2) (= _let_1 tptp.zero_zero_rat)))))) (forall ((A4 tptp.set_nat) (C tptp.fun_nat_real) (D tptp.fun_nat_real)) (let ((_let_1 (tptp.groups6591440286371151544t_real (tptp.aa_fun1839206346889086768t_real (tptp.aTP_Lamm_hd C) D) A4))) (let ((_let_2 (and (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A4)) (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat tptp.zero_zero_nat) A4))))) (and (=> _let_2 (= _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_nat_real C tptp.zero_zero_nat)) (tptp.aa_nat_real D tptp.zero_zero_nat)))) (=> (not _let_2) (= _let_1 tptp.zero_zero_real)))))) (forall ((N tptp.num)) (= (tptp.aa_int_int (tptp.divide_divide_int tptp.one_one_int) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int N))) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.adjust_div (tptp.unique5052692396658037445od_int tptp.one N))))) (forall ((N tptp.num)) (= (tptp.aa_int_int (tptp.divide_divide_int (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int)) (tptp.aa_num_int tptp.numeral_numeral_int N)) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.adjust_div (tptp.unique5052692396658037445od_int tptp.one N))))) (forall ((L tptp.num) (K tptp.num)) (= (tptp.aa_int_int (tptp.bit_ri631733984087533419it_int (tptp.aa_num_nat tptp.numeral_numeral_nat L)) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 K))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.bit_ri631733984087533419it_int (tptp.aa_num_nat tptp.pred_numeral L)) (tptp.aa_num_int tptp.numeral_numeral_int K))) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.unique5052692396658037445od_int (tptp.aa_num_num tptp.bit0 M) (tptp.aa_num_num tptp.bit0 N)) (tptp.aa_Pro6970504127699319548nt_int (tptp.produc4245557441103728435nt_int tptp.aTP_Lamm_he) (tptp.unique5052692396658037445od_int M N)))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.unique5055182867167087721od_nat (tptp.aa_num_num tptp.bit0 M) (tptp.aa_num_num tptp.bit0 N)) (tptp.aa_Pro262675715343573244at_nat (tptp.produc2626176000494625587at_nat tptp.aTP_Lamm_hf) (tptp.unique5055182867167087721od_nat M N)))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.unique3479559517661332726nteger (tptp.aa_num_num tptp.bit0 M) (tptp.aa_num_num tptp.bit0 N)) (tptp.produc6916734918728496179nteger tptp.aTP_Lamm_hg (tptp.unique3479559517661332726nteger M N)))) (forall ((L tptp.num) (K tptp.num)) (= (tptp.aa_int_int (tptp.bit_ri631733984087533419it_int (tptp.aa_num_nat tptp.numeral_numeral_nat L)) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 K)))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.bit_ri631733984087533419it_int (tptp.aa_num_nat tptp.pred_numeral L)) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int K)))) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))))) (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit1 N))) (let ((_let_2 (tptp.aa_num_num tptp.bit1 M))) (let ((_let_3 (tptp.unique5055182867167087721od_nat _let_2 _let_1))) (let ((_let_4 (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num M) N)))) (and (=> _let_4 (= _let_3 (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat tptp.zero_zero_nat) (tptp.aa_num_nat tptp.numeral_numeral_nat _let_2)))) (=> (not _let_4) (= _let_3 (tptp.unique5026877609467782581ep_nat _let_1 (tptp.unique5055182867167087721od_nat _let_2 (tptp.aa_num_num tptp.bit0 _let_1))))))))))) (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit1 N))) (let ((_let_2 (tptp.aa_num_num tptp.bit1 M))) (let ((_let_3 (tptp.unique5052692396658037445od_int _let_2 _let_1))) (let ((_let_4 (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num M) N)))) (and (=> _let_4 (= _let_3 (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int tptp.zero_zero_int) (tptp.aa_num_int tptp.numeral_numeral_int _let_2)))) (=> (not _let_4) (= _let_3 (tptp.aa_Pro6970504127699319548nt_int (tptp.unique5024387138958732305ep_int _let_1) (tptp.unique5052692396658037445od_int _let_2 (tptp.aa_num_num tptp.bit0 _let_1))))))))))) (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit1 N))) (let ((_let_2 (tptp.aa_num_num tptp.bit1 M))) (let ((_let_3 (tptp.unique3479559517661332726nteger _let_2 _let_1))) (let ((_let_4 (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num M) N)))) (and (=> _let_4 (= _let_3 (tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger _let_2)))) (=> (not _let_4) (= _let_3 (tptp.unique4921790084139445826nteger _let_1 (tptp.unique3479559517661332726nteger _let_2 (tptp.aa_num_num tptp.bit0 _let_1))))))))))) (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit1 N))) (let ((_let_2 (tptp.aa_num_num tptp.bit0 M))) (let ((_let_3 (tptp.unique5055182867167087721od_nat _let_2 _let_1))) (let ((_let_4 (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num M) N)))) (and (=> _let_4 (= _let_3 (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat tptp.zero_zero_nat) (tptp.aa_num_nat tptp.numeral_numeral_nat _let_2)))) (=> (not _let_4) (= _let_3 (tptp.unique5026877609467782581ep_nat _let_1 (tptp.unique5055182867167087721od_nat _let_2 (tptp.aa_num_num tptp.bit0 _let_1))))))))))) (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit1 N))) (let ((_let_2 (tptp.aa_num_num tptp.bit0 M))) (let ((_let_3 (tptp.unique5052692396658037445od_int _let_2 _let_1))) (let ((_let_4 (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num M) N)))) (and (=> _let_4 (= _let_3 (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int tptp.zero_zero_int) (tptp.aa_num_int tptp.numeral_numeral_int _let_2)))) (=> (not _let_4) (= _let_3 (tptp.aa_Pro6970504127699319548nt_int (tptp.unique5024387138958732305ep_int _let_1) (tptp.unique5052692396658037445od_int _let_2 (tptp.aa_num_num tptp.bit0 _let_1))))))))))) (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit1 N))) (let ((_let_2 (tptp.aa_num_num tptp.bit0 M))) (let ((_let_3 (tptp.unique3479559517661332726nteger _let_2 _let_1))) (let ((_let_4 (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num M) N)))) (and (=> _let_4 (= _let_3 (tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger _let_2)))) (=> (not _let_4) (= _let_3 (tptp.unique4921790084139445826nteger _let_1 (tptp.unique3479559517661332726nteger _let_2 (tptp.aa_num_num tptp.bit0 _let_1))))))))))) (forall ((L tptp.num) (K tptp.num)) (= (tptp.aa_int_int (tptp.bit_ri631733984087533419it_int (tptp.aa_num_nat tptp.numeral_numeral_nat L)) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit1 K))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.bit_ri631733984087533419it_int (tptp.aa_num_nat tptp.pred_numeral L)) (tptp.aa_num_int tptp.numeral_numeral_int K))) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one)))) tptp.one_one_int))) (forall ((A tptp.real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) (tptp.aa_real_real tptp.abs_abs_real A)))) (forall ((A tptp.code_integer)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger A) (tptp.abs_abs_Code_integer A)))) (forall ((A tptp.rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) (tptp.aa_rat_rat tptp.abs_abs_rat A)))) (forall ((A tptp.int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) (tptp.aa_int_int tptp.abs_abs_int A)))) (forall ((A tptp.real) (B2 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real A)) B2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) B2)))) (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.abs_abs_Code_integer A)) B2)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger A) B2)))) (forall ((A tptp.rat) (B2 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat tptp.abs_abs_rat A)) B2)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B2)))) (forall ((A tptp.int) (B2 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.abs_abs_int A)) B2)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B2)))) (forall ((A tptp.code_integer)) (= (= (tptp.abs_abs_Code_integer A) tptp.zero_z3403309356797280102nteger) (= A tptp.zero_z3403309356797280102nteger))) (forall ((A tptp.complex)) (= (= (tptp.aa_complex_complex tptp.abs_abs_complex A) tptp.zero_zero_complex) (= A tptp.zero_zero_complex))) (forall ((A tptp.real)) (= (= (tptp.aa_real_real tptp.abs_abs_real A) tptp.zero_zero_real) (= A tptp.zero_zero_real))) (forall ((A tptp.rat)) (= (= (tptp.aa_rat_rat tptp.abs_abs_rat A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))) (forall ((A tptp.int)) (= (= (tptp.aa_int_int tptp.abs_abs_int A) tptp.zero_zero_int) (= A tptp.zero_zero_int))) (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (= (tptp.abs_abs_Code_integer (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) B2)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.abs_abs_Code_integer A)) (tptp.abs_abs_Code_integer B2)))) (forall ((A tptp.real) (B2 tptp.real)) (= (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) B2)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real tptp.abs_abs_real A)) (tptp.aa_real_real tptp.abs_abs_real B2)))) (forall ((A tptp.rat) (B2 tptp.rat)) (= (tptp.aa_rat_rat tptp.abs_abs_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) B2)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat tptp.abs_abs_rat A)) (tptp.aa_rat_rat tptp.abs_abs_rat B2)))) (forall ((A tptp.int) (B2 tptp.int)) (= (tptp.aa_int_int tptp.abs_abs_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) B2)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int tptp.abs_abs_int A)) (tptp.aa_int_int tptp.abs_abs_int B2)))) _let_90 _let_89 _let_88 _let_87 (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (= (tptp.abs_abs_Code_integer (tptp.minus_8373710615458151222nteger A B2)) (tptp.abs_abs_Code_integer (tptp.minus_8373710615458151222nteger B2 A)))) (forall ((A tptp.real) (B2 tptp.real)) (= (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A) B2)) (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real B2) A)))) (forall ((A tptp.rat) (B2 tptp.rat)) (= (tptp.aa_rat_rat tptp.abs_abs_rat (tptp.aa_rat_rat (tptp.minus_minus_rat A) B2)) (tptp.aa_rat_rat tptp.abs_abs_rat (tptp.aa_rat_rat (tptp.minus_minus_rat B2) A)))) (forall ((A tptp.int) (B2 tptp.int)) (= (tptp.aa_int_int tptp.abs_abs_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) B2)) (tptp.aa_int_int tptp.abs_abs_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int B2) A)))) (forall ((X tptp.real) (Y tptp.real)) (= (= (tptp.aa_real_real tptp.abs_abs_real X) (tptp.aa_real_real tptp.abs_abs_real Y)) (or (= X Y) (= X (tptp.aa_real_real tptp.uminus_uminus_real Y))))) (forall ((X tptp.int) (Y tptp.int)) (= (= (tptp.aa_int_int tptp.abs_abs_int X) (tptp.aa_int_int tptp.abs_abs_int Y)) (or (= X Y) (= X (tptp.aa_int_int tptp.uminus_uminus_int Y))))) (forall ((X tptp.code_integer) (Y tptp.code_integer)) (= (= (tptp.abs_abs_Code_integer X) (tptp.abs_abs_Code_integer Y)) (or (= X Y) (= X (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger Y))))) (forall ((X tptp.rat) (Y tptp.rat)) (= (= (tptp.aa_rat_rat tptp.abs_abs_rat X) (tptp.aa_rat_rat tptp.abs_abs_rat Y)) (or (= X Y) (= X (tptp.aa_rat_rat tptp.uminus_uminus_rat Y))))) (forall ((A tptp.code_integer) (N tptp.nat)) (= (tptp.abs_abs_Code_integer (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger A) N)) (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger (tptp.abs_abs_Code_integer A)) N))) (forall ((A tptp.rat) (N tptp.nat)) (= (tptp.aa_rat_rat tptp.abs_abs_rat (tptp.aa_nat_rat (tptp.power_power_rat A) N)) (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_rat_rat tptp.abs_abs_rat A)) N))) (forall ((A tptp.real) (N tptp.nat)) (= (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real A) N)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real tptp.abs_abs_real A)) N))) (forall ((A tptp.int) (N tptp.nat)) (= (tptp.aa_int_int tptp.abs_abs_int (tptp.aa_nat_int (tptp.power_power_int A) N)) (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_int_int tptp.abs_abs_int A)) N))) (forall ((L tptp.real) (K tptp.real)) (=> (= (tptp.aa_real_real tptp.abs_abs_real L) (tptp.aa_real_real tptp.abs_abs_real K)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.dvd_dvd_real L) K)))) (forall ((L tptp.int) (K tptp.int)) (=> (= (tptp.aa_int_int tptp.abs_abs_int L) (tptp.aa_int_int tptp.abs_abs_int K)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int L) K)))) (forall ((L tptp.code_integer) (K tptp.code_integer)) (=> (= (tptp.abs_abs_Code_integer L) (tptp.abs_abs_Code_integer K)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer L) K)))) (forall ((L tptp.rat) (K tptp.rat)) (=> (= (tptp.aa_rat_rat tptp.abs_abs_rat L) (tptp.aa_rat_rat tptp.abs_abs_rat K)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.dvd_dvd_rat L) K)))) (forall ((Z tptp.nat) (C tptp.fun_in2630332840903238488et_nat) (P2 tptp.product_prod_int_int)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat Z) (tptp.produc4251311855443802252et_nat C P2))) (not (forall ((X4 tptp.int) (Y4 tptp.int)) (=> (= P2 (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int X4) Y4)) (not (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat Z) (tptp.aa_int_set_nat (tptp.aa_int1906528167449992217et_nat C X4) Y4))))))))) (forall ((Z tptp.real) (C tptp.fun_in6553099857819052212t_real) (P2 tptp.product_prod_int_int)) (=> (tptp.member_real Z (tptp.produc6452406959799940328t_real C P2)) (not (forall ((X4 tptp.int) (Y4 tptp.int)) (=> (= P2 (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int X4) Y4)) (not (tptp.member_real Z (tptp.aa_int_set_real (tptp.aa_int4847878404602763637t_real C X4) Y4)))))))) (forall ((Z tptp.int) (C tptp.fun_in7040156458970095540et_int) (P2 tptp.product_prod_int_int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Z) (tptp.produc73460835934605544et_int C P2))) (not (forall ((X4 tptp.int) (Y4 tptp.int)) (=> (= P2 (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int X4) Y4)) (not (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Z) (tptp.aa_int_set_int (tptp.aa_int8639817059373041269et_int C X4) Y4))))))))) (forall ((Z tptp.complex) (C tptp.fun_in230608924162954550omplex) (P2 tptp.product_prod_int_int)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex Z) (tptp.produc8580519160106071146omplex C P2))) (not (forall ((X4 tptp.int) (Y4 tptp.int)) (=> (= P2 (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int X4) Y4)) (not (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex Z) (tptp.aa_int_set_complex (tptp.aa_int6119279391169676535omplex C X4) Y4))))))))) (forall ((Z tptp.nat) (C tptp.fun_fu3482081750474265950et_nat) (P2 tptp.produc5207004643709237345nteger)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat Z) (tptp.produc3005202867389586502et_nat C P2))) (not (forall ((X4 tptp.fun_Co6545587727236015215e_term) (Y4 tptp.produc8923325533196201883nteger)) (=> (= P2 (tptp.produc4282985567423050387nteger X4 Y4)) (not (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat Z) (tptp.aa_Pro381016180347496421et_nat (tptp.aa_fun3173333638319427527et_nat C X4) Y4))))))))) (forall ((Z tptp.real) (C tptp.fun_fu8939667915452561338t_real) (P2 tptp.produc5207004643709237345nteger)) (=> (tptp.member_real Z (tptp.produc6662958528406444962t_real C P2)) (not (forall ((X4 tptp.fun_Co6545587727236015215e_term) (Y4 tptp.produc8923325533196201883nteger)) (=> (= P2 (tptp.produc4282985567423050387nteger X4 Y4)) (not (tptp.member_real Z (tptp.aa_Pro6515153133580421057t_real (tptp.aa_fun4299200212449711651t_real C X4) Y4)))))))) (forall ((Z tptp.int) (C tptp.fun_fu7891905368541123002et_int) (P2 tptp.produc5207004643709237345nteger)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Z) (tptp.produc8050723884735165602et_int C P2))) (not (forall ((X4 tptp.fun_Co6545587727236015215e_term) (Y4 tptp.produc8923325533196201883nteger)) (=> (= P2 (tptp.produc4282985567423050387nteger X4 Y4)) (not (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Z) (tptp.aa_Pro5426537197693075521et_int (tptp.aa_fun683250493387700771et_int C X4) Y4))))))))) (forall ((Z tptp.complex) (C tptp.fun_fu3393861840643144508omplex) (P2 tptp.produc5207004643709237345nteger)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex Z) (tptp.produc4085712862462845988omplex C P2))) (not (forall ((X4 tptp.fun_Co6545587727236015215e_term) (Y4 tptp.produc8923325533196201883nteger)) (=> (= P2 (tptp.produc4282985567423050387nteger X4 Y4)) (not (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex Z) (tptp.aa_Pro5605272939097928131omplex (tptp.aa_fun8289708515469319333omplex C X4) Y4))))))))) (forall ((Z tptp.nat) (C tptp.fun_fu4770337263308229357et_nat) (P2 tptp.produc6768802789813714928nt_int)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat Z) (tptp.produc2360586433946867413et_nat C P2))) (not (forall ((X4 tptp.fun_in6429348457993719614e_term) (Y4 tptp.product_prod_int_int)) (=> (= P2 (tptp.produc4852315488734385442nt_int X4 Y4)) (not (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat Z) (tptp.aa_Pro3599192995643711491et_nat (tptp.aa_fun1858489612225131606et_nat C X4) Y4))))))))) (forall ((Z tptp.real) (C tptp.fun_fu1570079290182735305t_real) (P2 tptp.produc6768802789813714928nt_int)) (=> (tptp.member_real Z (tptp.produc4003755410105663153t_real C P2)) (not (forall ((X4 tptp.fun_in6429348457993719614e_term) (Y4 tptp.product_prod_int_int)) (=> (= P2 (tptp.produc4852315488734385442nt_int X4 Y4)) (not (tptp.member_real Z (tptp.aa_Pro7989103684195733727t_real (tptp.aa_fun2257173110403687218t_real C X4) Y4)))))))) (forall ((F tptp.fun_fu6012121808138353003r_bool) (A tptp.fun_Co6545587727236015215e_term) (B2 tptp.produc8923325533196201883nteger)) (=> (tptp.pp (tptp.aa_Pro7150874649148492216r_bool (tptp.produc401098500374025047r_bool F) (tptp.produc4282985567423050387nteger A B2))) (tptp.pp (tptp.aa_Pro5843519176478241656r_bool (tptp.aa_fun5646951941296221740r_bool F A) B2)))) (forall ((F tptp.fun_fu1674507805476766837r_bool) (A tptp.fun_Pr272337284026993017e_term) (B2 tptp.produc8923325533196201883nteger)) (=> (tptp.pp (tptp.aa_Pro3640759179027349698r_bool (tptp.produc1236900166980094561r_bool F) (tptp.produc7384524951051686153nteger A B2))) (tptp.pp (tptp.aa_Pro5843519176478241656r_bool (tptp.aa_fun5449300841655810358r_bool F A) B2)))) (forall ((F tptp.fun_fu4196931294019812808t_bool) (A tptp.fun_Pr9164807099015279978e_term) (B2 tptp.product_prod_int_int)) (=> (tptp.pp (tptp.aa_Pro5031108791230793749t_bool (tptp.produc625993674133193396t_bool F) (tptp.produc1560874099174258678nt_int A B2))) (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.aa_fun5300525129335604105t_bool F A) B2)))) (forall ((F tptp.fun_fu5117548769634986908t_bool) (A tptp.fun_in6429348457993719614e_term) (B2 tptp.product_prod_int_int)) (=> (tptp.pp (tptp.aa_Pro7591400126937138665t_bool (tptp.produc6627716702706253960t_bool F) (tptp.produc4852315488734385442nt_int A B2))) (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.aa_fun4446166836006121821t_bool F A) B2)))) (forall ((F tptp.fun_int_fun_int_bool) (A tptp.int) (B2 tptp.int)) (=> (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.produc8560705615207772305t_bool F) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int A) B2))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool F A) B2)))) (forall ((C tptp.fun_fu6012121808138353003r_bool) (P2 tptp.produc5207004643709237345nteger)) (=> (tptp.pp (tptp.aa_Pro7150874649148492216r_bool (tptp.produc401098500374025047r_bool C) P2)) (not (forall ((X4 tptp.fun_Co6545587727236015215e_term) (Y4 tptp.produc8923325533196201883nteger)) (=> (= P2 (tptp.produc4282985567423050387nteger X4 Y4)) (not (tptp.pp (tptp.aa_Pro5843519176478241656r_bool (tptp.aa_fun5646951941296221740r_bool C X4) Y4)))))))) (forall ((C tptp.fun_fu1674507805476766837r_bool) (P2 tptp.produc1616345218596728535nteger)) (=> (tptp.pp (tptp.aa_Pro3640759179027349698r_bool (tptp.produc1236900166980094561r_bool C) P2)) (not (forall ((X4 tptp.fun_Pr272337284026993017e_term) (Y4 tptp.produc8923325533196201883nteger)) (=> (= P2 (tptp.produc7384524951051686153nteger X4 Y4)) (not (tptp.pp (tptp.aa_Pro5843519176478241656r_bool (tptp.aa_fun5449300841655810358r_bool C X4) Y4)))))))) (forall ((C tptp.fun_fu4196931294019812808t_bool) (P2 tptp.produc4441460161354545860nt_int)) (=> (tptp.pp (tptp.aa_Pro5031108791230793749t_bool (tptp.produc625993674133193396t_bool C) P2)) (not (forall ((X4 tptp.fun_Pr9164807099015279978e_term) (Y4 tptp.product_prod_int_int)) (=> (= P2 (tptp.produc1560874099174258678nt_int X4 Y4)) (not (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.aa_fun5300525129335604105t_bool C X4) Y4)))))))) (forall ((C tptp.fun_fu5117548769634986908t_bool) (P2 tptp.produc6768802789813714928nt_int)) (=> (tptp.pp (tptp.aa_Pro7591400126937138665t_bool (tptp.produc6627716702706253960t_bool C) P2)) (not (forall ((X4 tptp.fun_in6429348457993719614e_term) (Y4 tptp.product_prod_int_int)) (=> (= P2 (tptp.produc4852315488734385442nt_int X4 Y4)) (not (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.aa_fun4446166836006121821t_bool C X4) Y4)))))))) (forall ((C tptp.fun_int_fun_int_bool) (P2 tptp.product_prod_int_int)) (=> (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.produc8560705615207772305t_bool C) P2)) (not (forall ((X4 tptp.int) (Y4 tptp.int)) (=> (= P2 (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int X4) Y4)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool C X4) Y4)))))))) (forall ((R2 tptp.fun_na4786964484885125043t_bool) (A tptp.nat) (B2 tptp.nat) (C tptp.product_prod_nat_nat)) (=> (tptp.pp (tptp.aa_Pro2232559814647311250t_bool (tptp.aa_Pro595088089689268830t_bool (tptp.produc5023667602222594023t_bool R2) (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat A) B2)) C)) (tptp.pp (tptp.aa_Pro2232559814647311250t_bool (tptp.aa_nat4401263874371387303t_bool (tptp.aa_nat4909001760120733684t_bool R2 A) B2) C)))) (forall ((C tptp.fun_na4786964484885125043t_bool) (P2 tptp.product_prod_nat_nat) (Z tptp.product_prod_nat_nat)) (=> (tptp.pp (tptp.aa_Pro2232559814647311250t_bool (tptp.aa_Pro595088089689268830t_bool (tptp.produc5023667602222594023t_bool C) P2) Z)) (not (forall ((X4 tptp.nat) (Y4 tptp.nat)) (=> (= P2 (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat X4) Y4)) (not (tptp.pp (tptp.aa_Pro2232559814647311250t_bool (tptp.aa_nat4401263874371387303t_bool (tptp.aa_nat4909001760120733684t_bool C X4) Y4) Z)))))))) (forall ((A tptp.code_integer)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (tptp.abs_abs_Code_integer A)))) (forall ((A tptp.real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_real_real tptp.abs_abs_real A)))) (forall ((A tptp.rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_rat_rat tptp.abs_abs_rat A)))) (forall ((A tptp.int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.aa_int_int tptp.abs_abs_int A)))) (forall ((A tptp.code_integer)) (not (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.abs_abs_Code_integer A)) tptp.zero_z3403309356797280102nteger)))) (forall ((A tptp.real)) (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.abs_abs_real A)) tptp.zero_zero_real)))) (forall ((A tptp.rat)) (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat tptp.abs_abs_rat A)) tptp.zero_zero_rat)))) (forall ((A tptp.int)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int tptp.abs_abs_int A)) tptp.zero_zero_int)))) (forall ((A tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A)) (= (tptp.abs_abs_Code_integer A) A))) (forall ((A tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) A)) (= (tptp.aa_real_real tptp.abs_abs_real A) A))) (forall ((A tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) A)) (= (tptp.aa_rat_rat tptp.abs_abs_rat A) A))) (forall ((A tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) A)) (= (tptp.aa_int_int tptp.abs_abs_int A) A))) (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.abs_abs_Code_integer (tptp.plus_p5714425477246183910nteger A B2))) (tptp.plus_p5714425477246183910nteger (tptp.abs_abs_Code_integer A) (tptp.abs_abs_Code_integer B2))))) (forall ((A tptp.real) (B2 tptp.real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) B2))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real tptp.abs_abs_real A)) (tptp.aa_real_real tptp.abs_abs_real B2))))) (forall ((A tptp.rat) (B2 tptp.rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat tptp.abs_abs_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) B2))) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat tptp.abs_abs_rat A)) (tptp.aa_rat_rat tptp.abs_abs_rat B2))))) (forall ((A tptp.int) (B2 tptp.int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.abs_abs_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) B2))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int tptp.abs_abs_int A)) (tptp.aa_int_int tptp.abs_abs_int B2))))) (forall ((A tptp.code_integer) (C tptp.code_integer) (B2 tptp.code_integer) (D tptp.code_integer)) (let ((_let_1 (tptp.abs_abs_Code_integer B2))) (let ((_let_2 (tptp.abs_abs_Code_integer A))) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger _let_2) C)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger _let_1) D)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger _let_2) _let_1)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger C) D)))))))) (forall ((A tptp.real) (C tptp.real) (B2 tptp.real) (D tptp.real)) (let ((_let_1 (tptp.aa_real_real tptp.abs_abs_real B2))) (let ((_let_2 (tptp.aa_real_real tptp.abs_abs_real A))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real _let_2) C)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real _let_1) D)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real _let_2) _let_1)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real C) D)))))))) (forall ((A tptp.rat) (C tptp.rat) (B2 tptp.rat) (D tptp.rat)) (let ((_let_1 (tptp.aa_rat_rat tptp.abs_abs_rat B2))) (let ((_let_2 (tptp.aa_rat_rat tptp.abs_abs_rat A))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat _let_2) C)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat _let_1) D)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat _let_2) _let_1)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat C) D)))))))) (forall ((A tptp.int) (C tptp.int) (B2 tptp.int) (D tptp.int)) (let ((_let_1 (tptp.aa_int_int tptp.abs_abs_int B2))) (let ((_let_2 (tptp.aa_int_int tptp.abs_abs_int A))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int _let_2) C)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int _let_1) D)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int _let_2) _let_1)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int C) D)))))))) (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.minus_8373710615458151222nteger (tptp.abs_abs_Code_integer A) (tptp.abs_abs_Code_integer B2))) (tptp.abs_abs_Code_integer (tptp.minus_8373710615458151222nteger A B2))))) (forall ((A tptp.real) (B2 tptp.real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real tptp.abs_abs_real A)) (tptp.aa_real_real tptp.abs_abs_real B2))) (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A) B2))))) (forall ((A tptp.rat) (B2 tptp.rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_rat_rat tptp.abs_abs_rat A)) (tptp.aa_rat_rat tptp.abs_abs_rat B2))) (tptp.aa_rat_rat tptp.abs_abs_rat (tptp.aa_rat_rat (tptp.minus_minus_rat A) B2))))) (forall ((A tptp.int) (B2 tptp.int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_int_int tptp.abs_abs_int A)) (tptp.aa_int_int tptp.abs_abs_int B2))) (tptp.aa_int_int tptp.abs_abs_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) B2))))) (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.abs_abs_Code_integer (tptp.minus_8373710615458151222nteger (tptp.abs_abs_Code_integer A) (tptp.abs_abs_Code_integer B2)))) (tptp.abs_abs_Code_integer (tptp.minus_8373710615458151222nteger A B2))))) (forall ((A tptp.real) (B2 tptp.real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real tptp.abs_abs_real A)) (tptp.aa_real_real tptp.abs_abs_real B2)))) (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A) B2))))) (forall ((A tptp.rat) (B2 tptp.rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat tptp.abs_abs_rat (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_rat_rat tptp.abs_abs_rat A)) (tptp.aa_rat_rat tptp.abs_abs_rat B2)))) (tptp.aa_rat_rat tptp.abs_abs_rat (tptp.aa_rat_rat (tptp.minus_minus_rat A) B2))))) (forall ((A tptp.int) (B2 tptp.int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.abs_abs_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_int_int tptp.abs_abs_int A)) (tptp.aa_int_int tptp.abs_abs_int B2)))) (tptp.aa_int_int tptp.abs_abs_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) B2))))) (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.minus_8373710615458151222nteger (tptp.abs_abs_Code_integer A) (tptp.abs_abs_Code_integer B2))) (tptp.abs_abs_Code_integer (tptp.minus_8373710615458151222nteger B2 A))))) (forall ((A tptp.real) (B2 tptp.real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real tptp.abs_abs_real A)) (tptp.aa_real_real tptp.abs_abs_real B2))) (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real B2) A))))) (forall ((A tptp.rat) (B2 tptp.rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_rat_rat tptp.abs_abs_rat A)) (tptp.aa_rat_rat tptp.abs_abs_rat B2))) (tptp.aa_rat_rat tptp.abs_abs_rat (tptp.aa_rat_rat (tptp.minus_minus_rat B2) A))))) (forall ((A tptp.int) (B2 tptp.int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_int_int tptp.abs_abs_int A)) (tptp.aa_int_int tptp.abs_abs_int B2))) (tptp.aa_int_int tptp.abs_abs_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int B2) A))))) (forall ((B2 tptp.real) (A tptp.real)) (=> (not (= B2 tptp.zero_zero_real)) (= (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real A) B2)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real tptp.abs_abs_real A)) (tptp.aa_real_real tptp.abs_abs_real B2))))) (forall ((B2 tptp.rat) (A tptp.rat)) (=> (not (= B2 tptp.zero_zero_rat)) (= (tptp.aa_rat_rat tptp.abs_abs_rat (tptp.aa_rat_rat (tptp.divide_divide_rat A) B2)) (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_rat_rat tptp.abs_abs_rat A)) (tptp.aa_rat_rat tptp.abs_abs_rat B2))))) (forall ((A tptp.real) (B2 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) B2)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real A)) B2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real A)) B2))))) (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger A) B2)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A)) B2)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.abs_abs_Code_integer A)) B2))))) (forall ((A tptp.rat) (B2 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B2)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat A)) B2)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat tptp.abs_abs_rat A)) B2))))) (forall ((A tptp.int) (B2 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B2)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.uminus_uminus_int A)) B2)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.abs_abs_int A)) B2))))) (forall ((A tptp.real) (B2 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real A)) B2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real A)) B2)))) (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.abs_abs_Code_integer A)) B2)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A)) B2)))) (forall ((A tptp.rat) (B2 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat tptp.abs_abs_rat A)) B2)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat A)) B2)))) (forall ((A tptp.int) (B2 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.abs_abs_int A)) B2)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.uminus_uminus_int A)) B2)))) (forall ((A tptp.real) (B2 tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real A)) B2)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) B2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real A)) B2))))) (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.abs_abs_Code_integer A)) B2)) (and (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger A) B2)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A)) B2))))) (forall ((A tptp.rat) (B2 tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat tptp.abs_abs_rat A)) B2)) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B2)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat A)) B2))))) (forall ((A tptp.int) (B2 tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.abs_abs_int A)) B2)) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B2)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.uminus_uminus_int A)) B2))))) (forall ((A tptp.real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real A)) (tptp.aa_real_real tptp.abs_abs_real A)))) (forall ((A tptp.code_integer)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A)) (tptp.abs_abs_Code_integer A)))) (forall ((A tptp.rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat A)) (tptp.aa_rat_rat tptp.abs_abs_rat A)))) (forall ((A tptp.int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.uminus_uminus_int A)) (tptp.aa_int_int tptp.abs_abs_int A)))) (forall ((A tptp.real) (B2 tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.abs_abs_real A)) B2)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.uminus_uminus_real A)) B2))))) (forall ((A tptp.int) (B2 tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int tptp.abs_abs_int A)) B2)) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B2)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int tptp.uminus_uminus_int A)) B2))))) (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.abs_abs_Code_integer A)) B2)) (and (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger A) B2)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A)) B2))))) (forall ((A tptp.rat) (B2 tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat tptp.abs_abs_rat A)) B2)) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B2)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat A)) B2))))) (forall ((X tptp.real) (Y tptp.real) (U tptp.real) (V tptp.real)) (=> (= X Y) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real U)) V)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) U)) Y))) V))))) (forall ((K tptp.num)) (= (tptp.aa_num_nat tptp.numeral_numeral_nat K) (tptp.aa_nat_nat tptp.suc (tptp.aa_num_nat tptp.pred_numeral K)))) (forall ((A4 tptp.set_real) (G tptp.fun_real_nat) (F tptp.fun_real_nat)) (=> (forall ((X4 tptp.real)) (=> (tptp.member_real X4 A4) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_real_nat G X4)) (tptp.aa_real_nat F X4))))) (= (tptp.groups1935376822645274424al_nat (tptp.aa_fun211602392931233840al_nat (tptp.aTP_Lamm_hh G) F) A4) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.groups1935376822645274424al_nat F A4)) (tptp.groups1935376822645274424al_nat G A4))))) (forall ((A4 tptp.set_int) (G tptp.fun_int_nat) (F tptp.fun_int_nat)) (=> (forall ((X4 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X4) A4)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_int_nat G X4)) (tptp.aa_int_nat F X4))))) (= (tptp.groups4541462559716669496nt_nat (tptp.aa_fun6506752150744536624nt_nat (tptp.aTP_Lamm_hi G) F) A4) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.groups4541462559716669496nt_nat F A4)) (tptp.groups4541462559716669496nt_nat G A4))))) (forall ((A4 tptp.set_complex) (G tptp.fun_complex_nat) (F tptp.fun_complex_nat)) (=> (forall ((X4 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex X4) A4)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_complex_nat G X4)) (tptp.aa_complex_nat F X4))))) (= (tptp.groups5693394587270226106ex_nat (tptp.aa_fun2465681967280144180ex_nat (tptp.aTP_Lamm_hj G) F) A4) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.groups5693394587270226106ex_nat F A4)) (tptp.groups5693394587270226106ex_nat G A4))))) (forall ((A4 tptp.set_nat) (G tptp.fun_nat_nat) (F tptp.fun_nat_nat)) (=> (forall ((X4 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X4) A4)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat G X4)) (tptp.aa_nat_nat F X4))))) (= (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_fun5791449513213591928at_nat (tptp.aTP_Lamm_hk G) F)) A4) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat F) A4)) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat G) A4))))) (forall ((G tptp.fun_nat_nat) (M tptp.nat) (K tptp.nat) (N tptp.nat)) (= (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat G) (tptp.set_or1269000886237332187st_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) K) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N) K))) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_nat_fun_nat_nat (tptp.aTP_Lamm_hl G) K)) (tptp.set_or1269000886237332187st_nat M N)))) (forall ((G tptp.fun_nat_real) (M tptp.nat) (K tptp.nat) (N tptp.nat)) (= (tptp.groups6591440286371151544t_real G (tptp.set_or1269000886237332187st_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) K) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N) K))) (tptp.groups6591440286371151544t_real (tptp.aa_nat_fun_nat_real (tptp.aTP_Lamm_hm G) K) (tptp.set_or1269000886237332187st_nat M N)))) (forall ((X tptp.real)) (=> (forall ((E2 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) E2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real X)) E2)))) (= X tptp.zero_zero_real))) (forall ((X tptp.rat)) (=> (forall ((E2 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) E2)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat tptp.abs_abs_rat X)) E2)))) (= X tptp.zero_zero_rat))) (forall ((X tptp.code_integer) (Y tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) X)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.abs_abs_Code_integer Y)) X) (tptp.abs_abs_Code_integer (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger Y) X))))) (forall ((X tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) X)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real tptp.abs_abs_real Y)) X) (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real Y) X))))) (forall ((X tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) X)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat tptp.abs_abs_rat Y)) X) (tptp.aa_rat_rat tptp.abs_abs_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat Y) X))))) (forall ((X tptp.int) (Y tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) X)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int tptp.abs_abs_int Y)) X) (tptp.aa_int_int tptp.abs_abs_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int Y) X))))) (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (=> (and (or (tptp.pp (tptp.aa_Code_integer_bool _let_1 A)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger A) tptp.zero_z3403309356797280102nteger))) (or (tptp.pp (tptp.aa_Code_integer_bool _let_1 B2)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger B2) tptp.zero_z3403309356797280102nteger)))) (= (tptp.abs_abs_Code_integer (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) B2)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.abs_abs_Code_integer A)) (tptp.abs_abs_Code_integer B2)))))) (forall ((A tptp.real) (B2 tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (and (or (tptp.pp (tptp.aa_real_bool _let_1 A)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) tptp.zero_zero_real))) (or (tptp.pp (tptp.aa_real_bool _let_1 B2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real B2) tptp.zero_zero_real)))) (= (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) B2)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real tptp.abs_abs_real A)) (tptp.aa_real_real tptp.abs_abs_real B2)))))) (forall ((A tptp.rat) (B2 tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (and (or (tptp.pp (tptp.aa_rat_bool _let_1 A)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) tptp.zero_zero_rat))) (or (tptp.pp (tptp.aa_rat_bool _let_1 B2)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B2) tptp.zero_zero_rat)))) (= (tptp.aa_rat_rat tptp.abs_abs_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) B2)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat tptp.abs_abs_rat A)) (tptp.aa_rat_rat tptp.abs_abs_rat B2)))))) (forall ((A tptp.int) (B2 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (and (or (tptp.pp (tptp.aa_int_bool _let_1 A)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) tptp.zero_zero_int))) (or (tptp.pp (tptp.aa_int_bool _let_1 B2)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B2) tptp.zero_zero_int)))) (= (tptp.aa_int_int tptp.abs_abs_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) B2)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int tptp.abs_abs_int A)) (tptp.aa_int_int tptp.abs_abs_int B2)))))) (forall ((A tptp.real) (B2 tptp.real)) (= (= (tptp.aa_real_real tptp.abs_abs_real A) B2) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) B2)) (or (= A B2) (= A (tptp.aa_real_real tptp.uminus_uminus_real B2)))))) (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (= (= (tptp.abs_abs_Code_integer A) B2) (and (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) B2)) (or (= A B2) (= A (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger B2)))))) (forall ((A tptp.rat) (B2 tptp.rat)) (= (= (tptp.aa_rat_rat tptp.abs_abs_rat A) B2) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) B2)) (or (= A B2) (= A (tptp.aa_rat_rat tptp.uminus_uminus_rat B2)))))) (forall ((A tptp.int) (B2 tptp.int)) (= (= (tptp.aa_int_int tptp.abs_abs_int A) B2) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) B2)) (or (= A B2) (= A (tptp.aa_int_int tptp.uminus_uminus_int B2)))))) (forall ((A tptp.real) (B2 tptp.real)) (= (= A (tptp.aa_real_real tptp.abs_abs_real B2)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) A)) (or (= B2 A) (= B2 (tptp.aa_real_real tptp.uminus_uminus_real A)))))) (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (= (= A (tptp.abs_abs_Code_integer B2)) (and (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A)) (or (= B2 A) (= B2 (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A)))))) (forall ((A tptp.rat) (B2 tptp.rat)) (= (= A (tptp.aa_rat_rat tptp.abs_abs_rat B2)) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) A)) (or (= B2 A) (= B2 (tptp.aa_rat_rat tptp.uminus_uminus_rat A)))))) (forall ((A tptp.int) (B2 tptp.int)) (= (= A (tptp.aa_int_int tptp.abs_abs_int B2)) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) A)) (or (= B2 A) (= B2 (tptp.aa_int_int tptp.uminus_uminus_int A)))))) (forall ((A tptp.real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_real_real tptp.abs_abs_real A))) tptp.zero_zero_real))) (forall ((A tptp.code_integer)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.abs_abs_Code_integer A))) tptp.zero_z3403309356797280102nteger))) (forall ((A tptp.rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_rat_rat tptp.abs_abs_rat A))) tptp.zero_zero_rat))) (forall ((A tptp.int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_int_int tptp.abs_abs_int A))) tptp.zero_zero_int))) (forall ((Y tptp.real) (X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) Y)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real tptp.abs_abs_real X)) Y) (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real X) Y))))) (forall ((Y tptp.rat) (X tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) Y)) (= (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_rat_rat tptp.abs_abs_rat X)) Y) (tptp.aa_rat_rat tptp.abs_abs_rat (tptp.aa_rat_rat (tptp.divide_divide_rat X) Y))))) (forall ((A tptp.code_integer) (N tptp.nat)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger (tptp.abs_abs_Code_integer A)) N)))) (forall ((A tptp.real) (N tptp.nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real tptp.abs_abs_real A)) N)))) (forall ((A tptp.rat) (N tptp.nat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_rat_rat tptp.abs_abs_rat A)) N)))) (forall ((A tptp.int) (N tptp.nat)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_int_int tptp.abs_abs_int A)) N)))) (forall ((A tptp.real)) (let ((_let_1 (tptp.aa_real_real tptp.abs_abs_real A))) (let ((_let_2 (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) tptp.zero_zero_real)))) (and (=> _let_2 (= _let_1 (tptp.aa_real_real tptp.uminus_uminus_real A))) (=> (not _let_2) (= _let_1 A)))))) (forall ((A tptp.int)) (let ((_let_1 (tptp.aa_int_int tptp.abs_abs_int A))) (let ((_let_2 (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) tptp.zero_zero_int)))) (and (=> _let_2 (= _let_1 (tptp.aa_int_int tptp.uminus_uminus_int A))) (=> (not _let_2) (= _let_1 A)))))) (forall ((A tptp.code_integer)) (let ((_let_1 (tptp.abs_abs_Code_integer A))) (let ((_let_2 (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger A) tptp.zero_z3403309356797280102nteger)))) (and (=> _let_2 (= _let_1 (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A))) (=> (not _let_2) (= _let_1 A)))))) (forall ((A tptp.rat)) (let ((_let_1 (tptp.aa_rat_rat tptp.abs_abs_rat A))) (let ((_let_2 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) tptp.zero_zero_rat)))) (and (=> _let_2 (= _let_1 (tptp.aa_rat_rat tptp.uminus_uminus_rat A))) (=> (not _let_2) (= _let_1 A)))))) (forall ((X5 tptp.real)) (let ((_let_1 (tptp.aa_real_real tptp.abs_abs_real X5))) (let ((_let_2 (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X5) tptp.zero_zero_real)))) (and (=> _let_2 (= _let_1 (tptp.aa_real_real tptp.uminus_uminus_real X5))) (=> (not _let_2) (= _let_1 X5)))))) (forall ((X5 tptp.int)) (let ((_let_1 (tptp.aa_int_int tptp.abs_abs_int X5))) (let ((_let_2 (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X5) tptp.zero_zero_int)))) (and (=> _let_2 (= _let_1 (tptp.aa_int_int tptp.uminus_uminus_int X5))) (=> (not _let_2) (= _let_1 X5)))))) (forall ((X5 tptp.code_integer)) (let ((_let_1 (tptp.abs_abs_Code_integer X5))) (let ((_let_2 (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger X5) tptp.zero_z3403309356797280102nteger)))) (and (=> _let_2 (= _let_1 (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger X5))) (=> (not _let_2) (= _let_1 X5)))))) (forall ((X5 tptp.rat)) (let ((_let_1 (tptp.aa_rat_rat tptp.abs_abs_rat X5))) (let ((_let_2 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X5) tptp.zero_zero_rat)))) (and (=> _let_2 (= _let_1 (tptp.aa_rat_rat tptp.uminus_uminus_rat X5))) (=> (not _let_2) (= _let_1 X5)))))) (forall ((A tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) tptp.zero_zero_real)) (= (tptp.aa_real_real tptp.abs_abs_real A) (tptp.aa_real_real tptp.uminus_uminus_real A)))) (forall ((A tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) tptp.zero_zero_int)) (= (tptp.aa_int_int tptp.abs_abs_int A) (tptp.aa_int_int tptp.uminus_uminus_int A)))) (forall ((A tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger A) tptp.zero_z3403309356797280102nteger)) (= (tptp.abs_abs_Code_integer A) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A)))) (forall ((A tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) tptp.zero_zero_rat)) (= (tptp.aa_rat_rat tptp.abs_abs_rat A) (tptp.aa_rat_rat tptp.uminus_uminus_rat A)))) (forall ((X tptp.code_integer) (A tptp.code_integer) (R tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.abs_abs_Code_integer (tptp.minus_8373710615458151222nteger X A))) R)) (and (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.minus_8373710615458151222nteger A R)) X)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger X) (tptp.plus_p5714425477246183910nteger A R)))))) (forall ((X tptp.real) (A tptp.real) (R tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real X) A))) R)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A) R)) X)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) R)))))) (forall ((X tptp.rat) (A tptp.rat) (R tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat tptp.abs_abs_rat (tptp.aa_rat_rat (tptp.minus_minus_rat X) A))) R)) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.minus_minus_rat A) R)) X)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) R)))))) (forall ((X tptp.int) (A tptp.int) (R tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.abs_abs_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int X) A))) R)) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) R)) X)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) R)))))) (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.abs_abs_Code_integer (tptp.minus_8373710615458151222nteger A B2))) (tptp.plus_p5714425477246183910nteger (tptp.abs_abs_Code_integer A) (tptp.abs_abs_Code_integer B2))))) (forall ((A tptp.real) (B2 tptp.real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A) B2))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real tptp.abs_abs_real A)) (tptp.aa_real_real tptp.abs_abs_real B2))))) (forall ((A tptp.rat) (B2 tptp.rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat tptp.abs_abs_rat (tptp.aa_rat_rat (tptp.minus_minus_rat A) B2))) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat tptp.abs_abs_rat A)) (tptp.aa_rat_rat tptp.abs_abs_rat B2))))) (forall ((A tptp.int) (B2 tptp.int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.abs_abs_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) B2))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int tptp.abs_abs_int A)) (tptp.aa_int_int tptp.abs_abs_int B2))))) (forall ((A tptp.code_integer) (B2 tptp.code_integer) (C tptp.code_integer) (D tptp.code_integer)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.abs_abs_Code_integer (tptp.minus_8373710615458151222nteger (tptp.plus_p5714425477246183910nteger A B2) (tptp.plus_p5714425477246183910nteger C D)))) (tptp.plus_p5714425477246183910nteger (tptp.abs_abs_Code_integer (tptp.minus_8373710615458151222nteger A C)) (tptp.abs_abs_Code_integer (tptp.minus_8373710615458151222nteger B2 D)))))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real) (D tptp.real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) B2)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real C) D)))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A) C))) (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real B2) D)))))) (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat) (D tptp.rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat tptp.abs_abs_rat (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) B2)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat C) D)))) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat tptp.abs_abs_rat (tptp.aa_rat_rat (tptp.minus_minus_rat A) C))) (tptp.aa_rat_rat tptp.abs_abs_rat (tptp.aa_rat_rat (tptp.minus_minus_rat B2) D)))))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int) (D tptp.int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.abs_abs_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) B2)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int C) D)))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int tptp.abs_abs_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) C))) (tptp.aa_int_int tptp.abs_abs_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int B2) D)))))) (forall ((X tptp.code_integer) (A tptp.code_integer) (R tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.abs_abs_Code_integer (tptp.minus_8373710615458151222nteger X A))) R)) (and (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.minus_8373710615458151222nteger A R)) X)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger X) (tptp.plus_p5714425477246183910nteger A R)))))) (forall ((X tptp.real) (A tptp.real) (R tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real X) A))) R)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A) R)) X)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) R)))))) (forall ((X tptp.rat) (A tptp.rat) (R tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat tptp.abs_abs_rat (tptp.aa_rat_rat (tptp.minus_minus_rat X) A))) R)) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.minus_minus_rat A) R)) X)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) R)))))) (forall ((X tptp.int) (A tptp.int) (R tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int tptp.abs_abs_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int X) A))) R)) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) R)) X)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) R)))))) (forall ((F tptp.fun_nat_nat) (A4 tptp.set_nat) (N tptp.nat)) (=> (= (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat F) A4) (tptp.aa_nat_nat tptp.suc N)) (exists ((X4 tptp.nat)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X4) A4)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.aa_nat_nat F X4))))))) (forall ((A tptp.real)) (let ((_let_1 (tptp.aa_real_real tptp.abs_abs_real A))) (let ((_let_2 (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) tptp.zero_zero_real)))) (and (=> _let_2 (= _let_1 (tptp.aa_real_real tptp.uminus_uminus_real A))) (=> (not _let_2) (= _let_1 A)))))) (forall ((A tptp.real) (X tptp.real) (B2 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) B2)) (exists ((D2 tptp.real)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) D2)) (forall ((Y5 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real X) Y5))) D2)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) Y5)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y5) B2)))))))))) (forall ((X tptp.complex) (M tptp.nat) (I5 tptp.set_nat)) (let ((_let_1 (tptp.power_power_complex X))) (= (tptp.groups2073611262835488442omplex (tptp.aa_nat6454746962644518025omplex (tptp.aTP_Lamm_hn X) M) I5) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_nat_complex _let_1 M)) (tptp.groups2073611262835488442omplex _let_1 I5))))) (forall ((X tptp.rat) (M tptp.nat) (I5 tptp.set_nat)) (let ((_let_1 (tptp.power_power_rat X))) (= (tptp.groups2906978787729119204at_rat (tptp.aa_nat_fun_nat_rat (tptp.aTP_Lamm_ho X) M) I5) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat _let_1 M)) (tptp.groups2906978787729119204at_rat _let_1 I5))))) (forall ((X tptp.int) (M tptp.nat) (I5 tptp.set_nat)) (let ((_let_1 (tptp.power_power_int X))) (= (tptp.groups3539618377306564664at_int (tptp.aa_nat_fun_nat_int (tptp.aTP_Lamm_hp X) M) I5) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int _let_1 M)) (tptp.groups3539618377306564664at_int _let_1 I5))))) (forall ((X tptp.real) (M tptp.nat) (I5 tptp.set_nat)) (let ((_let_1 (tptp.aa_real_fun_nat_real tptp.power_power_real X))) (= (tptp.groups6591440286371151544t_real (tptp.aa_nat_fun_nat_real (tptp.aTP_Lamm_hq X) M) I5) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real _let_1 M)) (tptp.groups6591440286371151544t_real _let_1 I5))))) (forall ((G tptp.fun_nat_nat) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.set_or1269000886237332187st_nat N M))) (= (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat G) _let_1) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_nat_fun_nat_nat (tptp.aa_nat3783148529270815480at_nat (tptp.aTP_Lamm_hr G) N) M)) _let_1)))) (forall ((G tptp.fun_nat_real) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.set_or1269000886237332187st_nat N M))) (= (tptp.groups6591440286371151544t_real G _let_1) (tptp.groups6591440286371151544t_real (tptp.aa_nat_fun_nat_real (tptp.aa_nat4085805313368488148t_real (tptp.aTP_Lamm_hs G) N) M) _let_1)))) (forall ((K tptp.num)) (= (tptp.aa_num_nat tptp.pred_numeral K) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_num_nat tptp.numeral_numeral_nat K)) tptp.one_one_nat))) (forall ((N tptp.nat) (C tptp.complex)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.one_one_nat) N)) (= (tptp.groups7754918857620584856omplex tptp.aTP_Lamm_ai (tptp.collect_complex (tptp.aa_com1553036987509291606x_bool (tptp.aTP_Lamm_fd N) C))) tptp.zero_zero_complex))) (forall ((N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.one_one_nat) N)) (= (tptp.groups7754918857620584856omplex tptp.aTP_Lamm_ai (tptp.collect_complex (tptp.aTP_Lamm_cq N))) tptp.zero_zero_complex))) (forall ((X tptp.code_integer)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer (tptp.abs_abs_Code_integer X))))) (forall ((X tptp.real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real tptp.one_one_real) (tptp.aa_real_real tptp.abs_abs_real X))))) (forall ((X tptp.rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat tptp.one_one_rat) (tptp.aa_rat_rat tptp.abs_abs_rat X))))) (forall ((X tptp.int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int tptp.one_one_int) (tptp.aa_int_int tptp.abs_abs_int X))))) (forall ((B4 tptp.set_complex) (A4 tptp.set_complex) (F tptp.fun_complex_nat)) (=> (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex B4)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.ord_le211207098394363844omplex B4) A4)) (= (tptp.groups5693394587270226106ex_nat F (tptp.minus_811609699411566653omplex A4 B4)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.groups5693394587270226106ex_nat F A4)) (tptp.groups5693394587270226106ex_nat F B4)))))) (forall ((B4 tptp.set_int) (A4 tptp.set_int) (F tptp.fun_int_nat)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int B4)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int B4) A4)) (= (tptp.groups4541462559716669496nt_nat F (tptp.minus_minus_set_int A4 B4)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.groups4541462559716669496nt_nat F A4)) (tptp.groups4541462559716669496nt_nat F B4)))))) (forall ((B4 tptp.set_nat) (A4 tptp.set_nat) (F tptp.fun_nat_nat)) (let ((_let_1 (tptp.groups3542108847815614940at_nat F))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat B4)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat B4) A4)) (= (tptp.aa_set_nat_nat _let_1 (tptp.minus_minus_set_nat A4 B4)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_set_nat_nat _let_1 A4)) (tptp.aa_set_nat_nat _let_1 B4))))))) (forall ((G tptp.fun_nat_rat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N))) (= (tptp.groups2906978787729119204at_rat G (tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat _let_1)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.groups2906978787729119204at_rat G (tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat N))) (tptp.aa_nat_rat G _let_1))))) (forall ((G tptp.fun_nat_int) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N))) (= (tptp.groups3539618377306564664at_int G (tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat _let_1)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.groups3539618377306564664at_int G (tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat N))) (tptp.aa_nat_int G _let_1))))) (forall ((G tptp.fun_nat_nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N))) (let ((_let_2 (tptp.groups3542108847815614940at_nat G))) (= (tptp.aa_set_nat_nat _let_2 (tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat _let_1)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_set_nat_nat _let_2 (tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat N))) (tptp.aa_nat_nat G _let_1)))))) (forall ((G tptp.fun_nat_real) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N))) (= (tptp.groups6591440286371151544t_real G (tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat _let_1)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.groups6591440286371151544t_real G (tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat N))) (tptp.aa_nat_real G _let_1))))) (forall ((M tptp.nat) (N tptp.nat) (G tptp.fun_nat_rat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)) (= (tptp.groups2906978787729119204at_rat G (tptp.set_or1269000886237332187st_nat M N)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_nat_rat G M)) (tptp.groups2906978787729119204at_rat G (tptp.set_or1269000886237332187st_nat (tptp.aa_nat_nat tptp.suc M) N)))))) (forall ((M tptp.nat) (N tptp.nat) (G tptp.fun_nat_int)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)) (= (tptp.groups3539618377306564664at_int G (tptp.set_or1269000886237332187st_nat M N)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_nat_int G M)) (tptp.groups3539618377306564664at_int G (tptp.set_or1269000886237332187st_nat (tptp.aa_nat_nat tptp.suc M) N)))))) (forall ((M tptp.nat) (N tptp.nat) (G tptp.fun_nat_nat)) (let ((_let_1 (tptp.groups3542108847815614940at_nat G))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)) (= (tptp.aa_set_nat_nat _let_1 (tptp.set_or1269000886237332187st_nat M N)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat G M)) (tptp.aa_set_nat_nat _let_1 (tptp.set_or1269000886237332187st_nat (tptp.aa_nat_nat tptp.suc M) N))))))) (forall ((M tptp.nat) (N tptp.nat) (G tptp.fun_nat_real)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)) (= (tptp.groups6591440286371151544t_real G (tptp.set_or1269000886237332187st_nat M N)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real G M)) (tptp.groups6591440286371151544t_real G (tptp.set_or1269000886237332187st_nat (tptp.aa_nat_nat tptp.suc M) N)))))) (forall ((M tptp.nat) (N tptp.nat) (G tptp.fun_nat_rat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) _let_1)) (= (tptp.groups2906978787729119204at_rat G (tptp.set_or1269000886237332187st_nat M _let_1)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_nat_rat G _let_1)) (tptp.groups2906978787729119204at_rat G (tptp.set_or1269000886237332187st_nat M N))))))) (forall ((M tptp.nat) (N tptp.nat) (G tptp.fun_nat_int)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) _let_1)) (= (tptp.groups3539618377306564664at_int G (tptp.set_or1269000886237332187st_nat M _let_1)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_nat_int G _let_1)) (tptp.groups3539618377306564664at_int G (tptp.set_or1269000886237332187st_nat M N))))))) (forall ((M tptp.nat) (N tptp.nat) (G tptp.fun_nat_nat)) (let ((_let_1 (tptp.groups3542108847815614940at_nat G))) (let ((_let_2 (tptp.aa_nat_nat tptp.suc N))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) _let_2)) (= (tptp.aa_set_nat_nat _let_1 (tptp.set_or1269000886237332187st_nat M _let_2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat G _let_2)) (tptp.aa_set_nat_nat _let_1 (tptp.set_or1269000886237332187st_nat M N)))))))) (forall ((M tptp.nat) (N tptp.nat) (G tptp.fun_nat_real)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) _let_1)) (= (tptp.groups6591440286371151544t_real G (tptp.set_or1269000886237332187st_nat M _let_1)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real G _let_1)) (tptp.groups6591440286371151544t_real G (tptp.set_or1269000886237332187st_nat M N))))))) (forall ((A tptp.real) (X tptp.real) (B2 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) B2)) (exists ((D2 tptp.real)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) D2)) (forall ((Y5 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real X) Y5))) D2)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) Y5)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y5) B2)))))))))) (forall ((M tptp.nat) (N tptp.nat) (G tptp.fun_nat_rat)) (let ((_let_1 (tptp.set_or1269000886237332187st_nat M N))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.groups2906978787729119204at_rat G _let_1)) (tptp.aa_nat_rat G (tptp.aa_nat_nat tptp.suc N))) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_nat_rat G M)) (tptp.groups2906978787729119204at_rat (tptp.aTP_Lamm_ht G) _let_1)))))) (forall ((M tptp.nat) (N tptp.nat) (G tptp.fun_nat_int)) (let ((_let_1 (tptp.set_or1269000886237332187st_nat M N))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.groups3539618377306564664at_int G _let_1)) (tptp.aa_nat_int G (tptp.aa_nat_nat tptp.suc N))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_nat_int G M)) (tptp.groups3539618377306564664at_int (tptp.aTP_Lamm_hu G) _let_1)))))) (forall ((M tptp.nat) (N tptp.nat) (G tptp.fun_nat_nat)) (let ((_let_1 (tptp.set_or1269000886237332187st_nat M N))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat G) _let_1)) (tptp.aa_nat_nat G (tptp.aa_nat_nat tptp.suc N))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat G M)) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aTP_Lamm_hv G)) _let_1)))))) (forall ((M tptp.nat) (N tptp.nat) (G tptp.fun_nat_real)) (let ((_let_1 (tptp.set_or1269000886237332187st_nat M N))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.groups6591440286371151544t_real G _let_1)) (tptp.aa_nat_real G (tptp.aa_nat_nat tptp.suc N))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real G M)) (tptp.groups6591440286371151544t_real (tptp.aTP_Lamm_hw G) _let_1)))))) (forall ((M tptp.nat) (N tptp.nat) (F tptp.fun_nat_complex)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) _let_1)) (= (tptp.groups2073611262835488442omplex (tptp.aTP_Lamm_hx F) (tptp.set_or1269000886237332187st_nat M N)) (tptp.aa_complex_complex (tptp.minus_minus_complex (tptp.aa_nat_complex F _let_1)) (tptp.aa_nat_complex F M)))))) (forall ((M tptp.nat) (N tptp.nat) (F tptp.fun_nat_rat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) _let_1)) (= (tptp.groups2906978787729119204at_rat (tptp.aTP_Lamm_hy F) (tptp.set_or1269000886237332187st_nat M N)) (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_nat_rat F _let_1)) (tptp.aa_nat_rat F M)))))) (forall ((M tptp.nat) (N tptp.nat) (F tptp.fun_nat_int)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) _let_1)) (= (tptp.groups3539618377306564664at_int (tptp.aTP_Lamm_hz F) (tptp.set_or1269000886237332187st_nat M N)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_nat_int F _let_1)) (tptp.aa_nat_int F M)))))) (forall ((M tptp.nat) (N tptp.nat) (F tptp.fun_nat_real)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) _let_1)) (= (tptp.groups6591440286371151544t_real (tptp.aTP_Lamm_ia F) (tptp.set_or1269000886237332187st_nat M N)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_nat_real F _let_1)) (tptp.aa_nat_real F M)))))) (forall ((X tptp.code_integer) (Y tptp.code_integer)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.abs_abs_Code_integer X)) (tptp.abs_abs_Code_integer Y))) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger X) _let_1)) (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger Y) _let_1)))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real X)) (tptp.aa_real_real tptp.abs_abs_real Y))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) _let_1)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Y) _let_1)))))) (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat tptp.abs_abs_rat X)) (tptp.aa_rat_rat tptp.abs_abs_rat Y))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat (tptp.power_power_rat X) _let_1)) (tptp.aa_nat_rat (tptp.power_power_rat Y) _let_1)))))) (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.abs_abs_int X)) (tptp.aa_int_int tptp.abs_abs_int Y))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int (tptp.power_power_int X) _let_1)) (tptp.aa_nat_int (tptp.power_power_int Y) _let_1)))))) (forall ((X tptp.code_integer)) (= (= (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger X) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) tptp.one_one_Code_integer) (= (tptp.abs_abs_Code_integer X) tptp.one_one_Code_integer))) (forall ((X tptp.rat)) (= (= (tptp.aa_nat_rat (tptp.power_power_rat X) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) tptp.one_one_rat) (= (tptp.aa_rat_rat tptp.abs_abs_rat X) tptp.one_one_rat))) (forall ((X tptp.real)) (= (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) tptp.one_one_real) (= (tptp.aa_real_real tptp.abs_abs_real X) tptp.one_one_real))) (forall ((X tptp.int)) (= (= (tptp.aa_nat_int (tptp.power_power_int X) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) tptp.one_one_int) (= (tptp.aa_int_int tptp.abs_abs_int X) tptp.one_one_int))) (forall ((N tptp.nat) (A tptp.code_integer)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N)) (= (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger (tptp.abs_abs_Code_integer A)) N) (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger A) N)))) (forall ((N tptp.nat) (A tptp.rat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N)) (= (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_rat_rat tptp.abs_abs_rat A)) N) (tptp.aa_nat_rat (tptp.power_power_rat A) N)))) (forall ((N tptp.nat) (A tptp.real)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real tptp.abs_abs_real A)) N) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real A) N)))) (forall ((N tptp.nat) (A tptp.int)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N)) (= (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_int_int tptp.abs_abs_int A)) N) (tptp.aa_nat_int (tptp.power_power_int A) N)))) (forall ((M tptp.nat) (N tptp.nat) (G tptp.fun_nat_rat) (P2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N))) (let ((_let_2 (tptp.aa_nat_nat _let_1 P2))) (let ((_let_3 (tptp.aa_nat_nat _let_1 tptp.one_one_nat))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) _let_3)) (= (tptp.groups2906978787729119204at_rat G (tptp.set_or1269000886237332187st_nat M _let_2)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.groups2906978787729119204at_rat G (tptp.set_or1269000886237332187st_nat M N))) (tptp.groups2906978787729119204at_rat G (tptp.set_or1269000886237332187st_nat _let_3 _let_2))))))))) (forall ((M tptp.nat) (N tptp.nat) (G tptp.fun_nat_int) (P2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N))) (let ((_let_2 (tptp.aa_nat_nat _let_1 P2))) (let ((_let_3 (tptp.aa_nat_nat _let_1 tptp.one_one_nat))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) _let_3)) (= (tptp.groups3539618377306564664at_int G (tptp.set_or1269000886237332187st_nat M _let_2)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.groups3539618377306564664at_int G (tptp.set_or1269000886237332187st_nat M N))) (tptp.groups3539618377306564664at_int G (tptp.set_or1269000886237332187st_nat _let_3 _let_2))))))))) (forall ((M tptp.nat) (N tptp.nat) (G tptp.fun_nat_nat) (P2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N))) (let ((_let_2 (tptp.aa_nat_nat _let_1 P2))) (let ((_let_3 (tptp.aa_nat_nat _let_1 tptp.one_one_nat))) (let ((_let_4 (tptp.groups3542108847815614940at_nat G))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) _let_3)) (= (tptp.aa_set_nat_nat _let_4 (tptp.set_or1269000886237332187st_nat M _let_2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_set_nat_nat _let_4 (tptp.set_or1269000886237332187st_nat M N))) (tptp.aa_set_nat_nat _let_4 (tptp.set_or1269000886237332187st_nat _let_3 _let_2)))))))))) (forall ((M tptp.nat) (N tptp.nat) (G tptp.fun_nat_real) (P2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N))) (let ((_let_2 (tptp.aa_nat_nat _let_1 P2))) (let ((_let_3 (tptp.aa_nat_nat _let_1 tptp.one_one_nat))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) _let_3)) (= (tptp.groups6591440286371151544t_real G (tptp.set_or1269000886237332187st_nat M _let_2)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.groups6591440286371151544t_real G (tptp.set_or1269000886237332187st_nat M N))) (tptp.groups6591440286371151544t_real G (tptp.set_or1269000886237332187st_nat _let_3 _let_2))))))))) (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int N))) (let ((_let_2 (tptp.aa_num_int tptp.numeral_numeral_int M))) (= (tptp.unique5052692396658037445od_int M N) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int (tptp.aa_int_int (tptp.divide_divide_int _let_2) _let_1)) (tptp.aa_int_int (tptp.modulo_modulo_int _let_2) _let_1)))))) (forall ((Y tptp.code_integer) (X tptp.code_integer)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) Y)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger X) _let_1)) (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger Y) _let_1))) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.abs_abs_Code_integer X)) Y)))))) (forall ((Y tptp.real) (X tptp.real)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) Y)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) _let_1)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Y) _let_1))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real X)) Y)))))) (forall ((Y tptp.rat) (X tptp.rat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) Y)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat (tptp.power_power_rat X) _let_1)) (tptp.aa_nat_rat (tptp.power_power_rat Y) _let_1))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat tptp.abs_abs_rat X)) Y)))))) (forall ((Y tptp.int) (X tptp.int)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) Y)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int (tptp.power_power_int X) _let_1)) (tptp.aa_nat_int (tptp.power_power_int Y) _let_1))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.abs_abs_int X)) Y)))))) (forall ((P tptp.fun_Co8310303586393106575r_bool) (X tptp.code_integer)) (=> (forall ((X4 tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) X4)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool P X4) (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger X4) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))))) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool P (tptp.abs_abs_Code_integer X)) (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger X) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))))) (forall ((P tptp.fun_re1255401033344146673l_bool) (X tptp.real)) (=> (forall ((X4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) X4)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool P X4) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X4) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool P (tptp.aa_real_real tptp.abs_abs_real X)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))))) (forall ((P tptp.fun_rat_fun_rat_bool) (X tptp.rat)) (=> (forall ((X4 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) X4)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool P X4) (tptp.aa_nat_rat (tptp.power_power_rat X4) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool P (tptp.aa_rat_rat tptp.abs_abs_rat X)) (tptp.aa_nat_rat (tptp.power_power_rat X) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))))) (forall ((P tptp.fun_int_fun_int_bool) (X tptp.int)) (=> (forall ((X4 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) X4)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool P X4) (tptp.aa_nat_int (tptp.power_power_int X4) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool P (tptp.aa_int_int tptp.abs_abs_int X)) (tptp.aa_nat_int (tptp.power_power_int X) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))))) (forall ((X tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger X) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) tptp.one_one_Code_integer)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.abs_abs_Code_integer X)) tptp.one_one_Code_integer)))) (forall ((X tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) tptp.one_one_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real X)) tptp.one_one_real)))) (forall ((X tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat (tptp.power_power_rat X) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) tptp.one_one_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat tptp.abs_abs_rat X)) tptp.one_one_rat)))) (forall ((X tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int (tptp.power_power_int X) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) tptp.one_one_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.abs_abs_int X)) tptp.one_one_int)))) (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int N))) (let ((_let_2 (tptp.aa_num_int tptp.numeral_numeral_int M))) (= (tptp.unique5052692396658037445od_int M N) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int (tptp.aa_int_int (tptp.divide_divide_int _let_2) _let_1)) (tptp.aa_int_int (tptp.modulo_modulo_int _let_2) _let_1)))))) (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat N))) (let ((_let_2 (tptp.aa_num_nat tptp.numeral_numeral_nat M))) (= (tptp.unique5055182867167087721od_nat M N) (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat _let_2) _let_1)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat _let_2) _let_1)))))) (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger N))) (let ((_let_2 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger M))) (= (tptp.unique3479559517661332726nteger M N) (tptp.produc1086072967326762835nteger (tptp.divide6298287555418463151nteger _let_2 _let_1) (tptp.modulo364778990260209775nteger _let_2 _let_1)))))) (forall ((X tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger X) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) tptp.one_one_Code_integer)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.abs_abs_Code_integer X)) tptp.one_one_Code_integer)))) (forall ((X tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) tptp.one_one_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.abs_abs_real X)) tptp.one_one_real)))) (forall ((X tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_nat_rat (tptp.power_power_rat X) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) tptp.one_one_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat tptp.abs_abs_rat X)) tptp.one_one_rat)))) (forall ((X tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_nat_int (tptp.power_power_int X) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) tptp.one_one_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int tptp.abs_abs_int X)) tptp.one_one_int)))) (forall ((N tptp.nat) (A tptp.code_integer) (B2 tptp.code_integer)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.abs_abs_Code_integer A)) (tptp.abs_abs_Code_integer B2))) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger A) N)) (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger B2) N)))))) (forall ((N tptp.nat) (A tptp.real) (B2 tptp.real)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real A)) (tptp.aa_real_real tptp.abs_abs_real B2))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real A) N)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real B2) N)))))) (forall ((N tptp.nat) (A tptp.rat) (B2 tptp.rat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat tptp.abs_abs_rat A)) (tptp.aa_rat_rat tptp.abs_abs_rat B2))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat (tptp.power_power_rat A) N)) (tptp.aa_nat_rat (tptp.power_power_rat B2) N)))))) (forall ((N tptp.nat) (A tptp.int) (B2 tptp.int)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.abs_abs_int A)) (tptp.aa_int_int tptp.abs_abs_int B2))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int (tptp.power_power_int A) N)) (tptp.aa_nat_int (tptp.power_power_int B2) N)))))) (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat N))) (let ((_let_2 (tptp.aa_num_nat tptp.numeral_numeral_nat M))) (= (tptp.unique5055182867167087721od_nat M N) (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat _let_2) _let_1)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat _let_2) _let_1)))))) (forall ((I5 tptp.set_nat) (X tptp.fun_nat_Code_integer) (A tptp.fun_nat_Code_integer) (B2 tptp.code_integer) (Delta tptp.code_integer)) (=> (forall ((I3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat I3) I5)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (tptp.aa_nat_Code_integer X I3))))) (=> (= (tptp.groups7501900531339628137nteger X I5) tptp.one_one_Code_integer) (=> (forall ((I3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat I3) I5)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.abs_abs_Code_integer (tptp.minus_8373710615458151222nteger (tptp.aa_nat_Code_integer A I3) B2))) Delta)))) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.abs_abs_Code_integer (tptp.minus_8373710615458151222nteger (tptp.groups7501900531339628137nteger (tptp.aa_fun589076786913273746nteger (tptp.aTP_Lamm_ib X) A) I5) B2))) Delta)))))) (forall ((I5 tptp.set_real) (X tptp.fun_re6978948838062957830nteger) (A tptp.fun_re6978948838062957830nteger) (B2 tptp.code_integer) (Delta tptp.code_integer)) (=> (forall ((I3 tptp.real)) (=> (tptp.member_real I3 I5) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (tptp.aa_real_Code_integer X I3))))) (=> (= (tptp.groups7713935264441627589nteger X I5) tptp.one_one_Code_integer) (=> (forall ((I3 tptp.real)) (=> (tptp.member_real I3 I5) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.abs_abs_Code_integer (tptp.minus_8373710615458151222nteger (tptp.aa_real_Code_integer A I3) B2))) Delta)))) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.abs_abs_Code_integer (tptp.minus_8373710615458151222nteger (tptp.groups7713935264441627589nteger (tptp.aa_fun7923231501384339402nteger (tptp.aTP_Lamm_ic X) A) I5) B2))) Delta)))))) (forall ((I5 tptp.set_int) (X tptp.fun_int_Code_integer) (A tptp.fun_int_Code_integer) (B2 tptp.code_integer) (Delta tptp.code_integer)) (=> (forall ((I3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int I3) I5)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (tptp.aa_int_Code_integer X I3))))) (=> (= (tptp.groups7873554091576472773nteger X I5) tptp.one_one_Code_integer) (=> (forall ((I3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int I3) I5)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.abs_abs_Code_integer (tptp.minus_8373710615458151222nteger (tptp.aa_int_Code_integer A I3) B2))) Delta)))) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.abs_abs_Code_integer (tptp.minus_8373710615458151222nteger (tptp.groups7873554091576472773nteger (tptp.aa_fun5304498221708291146nteger (tptp.aTP_Lamm_id X) A) I5) B2))) Delta)))))) (forall ((I5 tptp.set_complex) (X tptp.fun_co8153928105989009288nteger) (A tptp.fun_co8153928105989009288nteger) (B2 tptp.code_integer) (Delta tptp.code_integer)) (=> (forall ((I3 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex I3) I5)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (tptp.aa_com4217951221296830281nteger X I3))))) (=> (= (tptp.groups6621422865394947399nteger X I5) tptp.one_one_Code_integer) (=> (forall ((I3 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex I3) I5)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.abs_abs_Code_integer (tptp.minus_8373710615458151222nteger (tptp.aa_com4217951221296830281nteger A I3) B2))) Delta)))) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.abs_abs_Code_integer (tptp.minus_8373710615458151222nteger (tptp.groups6621422865394947399nteger (tptp.aa_fun5267417455630836558nteger (tptp.aTP_Lamm_ie X) A) I5) B2))) Delta)))))) (forall ((I5 tptp.set_real) (X tptp.fun_real_real) (A tptp.fun_real_real) (B2 tptp.real) (Delta tptp.real)) (=> (forall ((I3 tptp.real)) (=> (tptp.member_real I3 I5) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_real_real X I3))))) (=> (= (tptp.groups8097168146408367636l_real X I5) tptp.one_one_real) (=> (forall ((I3 tptp.real)) (=> (tptp.member_real I3 I5) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real A I3)) B2))) Delta)))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.groups8097168146408367636l_real (tptp.aa_fun6946558556880649704l_real (tptp.aTP_Lamm_if X) A) I5)) B2))) Delta)))))) (forall ((I5 tptp.set_int) (X tptp.fun_int_real) (A tptp.fun_int_real) (B2 tptp.real) (Delta tptp.real)) (=> (forall ((I3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int I3) I5)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_int_real X I3))))) (=> (= (tptp.groups8778361861064173332t_real X I5) tptp.one_one_real) (=> (forall ((I3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int I3) I5)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_int_real A I3)) B2))) Delta)))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.groups8778361861064173332t_real (tptp.aa_fun3252798400008884712t_real (tptp.aTP_Lamm_ig X) A) I5)) B2))) Delta)))))) (forall ((I5 tptp.set_complex) (X tptp.fun_complex_real) (A tptp.fun_complex_real) (B2 tptp.real) (Delta tptp.real)) (=> (forall ((I3 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex I3) I5)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_complex_real X I3))))) (=> (= (tptp.groups5808333547571424918x_real X I5) tptp.one_one_real) (=> (forall ((I3 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex I3) I5)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_complex_real A I3)) B2))) Delta)))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.groups5808333547571424918x_real (tptp.aa_fun8933909628229591020x_real (tptp.aTP_Lamm_ih X) A) I5)) B2))) Delta)))))) (forall ((I5 tptp.set_nat) (X tptp.fun_nat_rat) (A tptp.fun_nat_rat) (B2 tptp.rat) (Delta tptp.rat)) (=> (forall ((I3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat I3) I5)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_nat_rat X I3))))) (=> (= (tptp.groups2906978787729119204at_rat X I5) tptp.one_one_rat) (=> (forall ((I3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat I3) I5)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat tptp.abs_abs_rat (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_nat_rat A I3)) B2))) Delta)))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat tptp.abs_abs_rat (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.groups2906978787729119204at_rat (tptp.aa_fun765758790203053448at_rat (tptp.aTP_Lamm_ii X) A) I5)) B2))) Delta)))))) (forall ((I5 tptp.set_real) (X tptp.fun_real_rat) (A tptp.fun_real_rat) (B2 tptp.rat) (Delta tptp.rat)) (=> (forall ((I3 tptp.real)) (=> (tptp.member_real I3 I5) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_real_rat X I3))))) (=> (= (tptp.groups1300246762558778688al_rat X I5) tptp.one_one_rat) (=> (forall ((I3 tptp.real)) (=> (tptp.member_real I3 I5) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat tptp.abs_abs_rat (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_real_rat A I3)) B2))) Delta)))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat tptp.abs_abs_rat (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.groups1300246762558778688al_rat (tptp.aa_fun2468082234287226944al_rat (tptp.aTP_Lamm_ij X) A) I5)) B2))) Delta)))))) (forall ((I5 tptp.set_int) (X tptp.fun_int_rat) (A tptp.fun_int_rat) (B2 tptp.rat) (Delta tptp.rat)) (=> (forall ((I3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int I3) I5)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_int_rat X I3))))) (=> (= (tptp.groups3906332499630173760nt_rat X I5) tptp.one_one_rat) (=> (forall ((I3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int I3) I5)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat tptp.abs_abs_rat (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_int_rat A I3)) B2))) Delta)))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat tptp.abs_abs_rat (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.groups3906332499630173760nt_rat (tptp.aa_fun1481061427733998144nt_rat (tptp.aTP_Lamm_ik X) A) I5)) B2))) Delta)))))) (forall ((X tptp.complex)) (= (tptp.aa_complex_complex tptp.neg_nu6511756317524482435omplex X) (tptp.aa_complex_complex (tptp.minus_minus_complex (tptp.aa_complex_complex (tptp.plus_plus_complex X) X)) tptp.one_one_complex))) (forall ((X tptp.real)) (= (tptp.aa_real_real tptp.neg_nu6075765906172075777c_real X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) X)) tptp.one_one_real))) (forall ((X tptp.rat)) (= (tptp.aa_rat_rat tptp.neg_nu3179335615603231917ec_rat X) (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat X) X)) tptp.one_one_rat))) (forall ((X tptp.int)) (= (tptp.aa_int_int tptp.neg_nu3811975205180677377ec_int X) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int X) X)) tptp.one_one_int))) (forall ((M tptp.nat) (N tptp.nat) (F tptp.fun_nat_complex)) (let ((_let_1 (tptp.groups2073611262835488442omplex (tptp.aTP_Lamm_il F) (tptp.set_or1269000886237332187st_nat M N)))) (let ((_let_2 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)))) (and (=> _let_2 (= _let_1 (tptp.aa_complex_complex (tptp.minus_minus_complex (tptp.aa_nat_complex F M)) (tptp.aa_nat_complex F (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N) tptp.one_one_nat))))) (=> (not _let_2) (= _let_1 tptp.zero_zero_complex)))))) (forall ((M tptp.nat) (N tptp.nat) (F tptp.fun_nat_rat)) (let ((_let_1 (tptp.groups2906978787729119204at_rat (tptp.aTP_Lamm_im F) (tptp.set_or1269000886237332187st_nat M N)))) (let ((_let_2 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)))) (and (=> _let_2 (= _let_1 (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_nat_rat F M)) (tptp.aa_nat_rat F (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N) tptp.one_one_nat))))) (=> (not _let_2) (= _let_1 tptp.zero_zero_rat)))))) (forall ((M tptp.nat) (N tptp.nat) (F tptp.fun_nat_int)) (let ((_let_1 (tptp.groups3539618377306564664at_int (tptp.aTP_Lamm_in F) (tptp.set_or1269000886237332187st_nat M N)))) (let ((_let_2 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)))) (and (=> _let_2 (= _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_nat_int F M)) (tptp.aa_nat_int F (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N) tptp.one_one_nat))))) (=> (not _let_2) (= _let_1 tptp.zero_zero_int)))))) (forall ((M tptp.nat) (N tptp.nat) (F tptp.fun_nat_real)) (let ((_let_1 (tptp.groups6591440286371151544t_real (tptp.aTP_Lamm_io F) (tptp.set_or1269000886237332187st_nat M N)))) (let ((_let_2 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)))) (and (=> _let_2 (= _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_nat_real F M)) (tptp.aa_nat_real F (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N) tptp.one_one_nat))))) (=> (not _let_2) (= _let_1 tptp.zero_zero_real)))))) (forall ((M tptp.nat) (N tptp.nat) (F tptp.fun_nat_complex)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)) (= (tptp.groups2073611262835488442omplex (tptp.aTP_Lamm_ip F) (tptp.set_or1269000886237332187st_nat (tptp.aa_nat_nat tptp.suc M) N)) (tptp.aa_complex_complex (tptp.minus_minus_complex (tptp.aa_nat_complex F N)) (tptp.aa_nat_complex F M))))) (forall ((M tptp.nat) (N tptp.nat) (F tptp.fun_nat_rat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)) (= (tptp.groups2906978787729119204at_rat (tptp.aTP_Lamm_iq F) (tptp.set_or1269000886237332187st_nat (tptp.aa_nat_nat tptp.suc M) N)) (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_nat_rat F N)) (tptp.aa_nat_rat F M))))) (forall ((M tptp.nat) (N tptp.nat) (F tptp.fun_nat_int)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)) (= (tptp.groups3539618377306564664at_int (tptp.aTP_Lamm_ir F) (tptp.set_or1269000886237332187st_nat (tptp.aa_nat_nat tptp.suc M) N)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_nat_int F N)) (tptp.aa_nat_int F M))))) (forall ((M tptp.nat) (N tptp.nat) (F tptp.fun_nat_real)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)) (= (tptp.groups6591440286371151544t_real (tptp.aTP_Lamm_is F) (tptp.set_or1269000886237332187st_nat (tptp.aa_nat_nat tptp.suc M) N)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_nat_real F N)) (tptp.aa_nat_real F M))))) (forall ((N tptp.nat)) (let ((_let_1 (tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_nat_int _let_1 N)) tptp.one_one_int) (tptp.groups3539618377306564664at_int _let_1 (tptp.collect_nat (tptp.aa_nat_fun_nat_bool tptp.aTP_Lamm_br N)))))) (forall ((N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat _let_1 N)) tptp.one_one_nat) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat _let_1) (tptp.collect_nat (tptp.aa_nat_fun_nat_bool tptp.aTP_Lamm_br N)))))) (forall ((M tptp.nat) (N tptp.nat) (X tptp.complex)) (let ((_let_1 (tptp.power_power_complex X))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)) (= (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_complex_complex (tptp.minus_minus_complex tptp.one_one_complex) X)) (tptp.groups2073611262835488442omplex _let_1 (tptp.set_or1269000886237332187st_nat M N))) (tptp.aa_complex_complex (tptp.minus_minus_complex (tptp.aa_nat_complex _let_1 M)) (tptp.aa_nat_complex _let_1 (tptp.aa_nat_nat tptp.suc N))))))) (forall ((M tptp.nat) (N tptp.nat) (X tptp.rat)) (let ((_let_1 (tptp.power_power_rat X))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat (tptp.minus_minus_rat tptp.one_one_rat) X)) (tptp.groups2906978787729119204at_rat _let_1 (tptp.set_or1269000886237332187st_nat M N))) (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_nat_rat _let_1 M)) (tptp.aa_nat_rat _let_1 (tptp.aa_nat_nat tptp.suc N))))))) (forall ((M tptp.nat) (N tptp.nat) (X tptp.int)) (let ((_let_1 (tptp.power_power_int X))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int tptp.one_one_int) X)) (tptp.groups3539618377306564664at_int _let_1 (tptp.set_or1269000886237332187st_nat M N))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_nat_int _let_1 M)) (tptp.aa_nat_int _let_1 (tptp.aa_nat_nat tptp.suc N))))))) (forall ((M tptp.nat) (N tptp.nat) (X tptp.real)) (let ((_let_1 (tptp.aa_real_fun_nat_real tptp.power_power_real X))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real tptp.one_one_real) X)) (tptp.groups6591440286371151544t_real _let_1 (tptp.set_or1269000886237332187st_nat M N))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_nat_real _let_1 M)) (tptp.aa_nat_real _let_1 (tptp.aa_nat_nat tptp.suc N))))))) (forall ((G tptp.fun_nat_rat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.groups2906978787729119204at_rat G (tptp.set_or1269000886237332187st_nat (tptp.aa_nat_nat _let_1 M) (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat _let_1 N)))) (tptp.groups2906978787729119204at_rat (tptp.aTP_Lamm_it G) (tptp.set_or1269000886237332187st_nat M N))))) (forall ((G tptp.fun_nat_int) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.groups3539618377306564664at_int G (tptp.set_or1269000886237332187st_nat (tptp.aa_nat_nat _let_1 M) (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat _let_1 N)))) (tptp.groups3539618377306564664at_int (tptp.aTP_Lamm_iu G) (tptp.set_or1269000886237332187st_nat M N))))) (forall ((G tptp.fun_nat_nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat G) (tptp.set_or1269000886237332187st_nat (tptp.aa_nat_nat _let_1 M) (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat _let_1 N)))) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aTP_Lamm_iv G)) (tptp.set_or1269000886237332187st_nat M N))))) (forall ((G tptp.fun_nat_real) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.groups6591440286371151544t_real G (tptp.set_or1269000886237332187st_nat (tptp.aa_nat_nat _let_1 M) (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat _let_1 N)))) (tptp.groups6591440286371151544t_real (tptp.aTP_Lamm_iw G) (tptp.set_or1269000886237332187st_nat M N))))) (forall ((N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat _let_1 N)) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat _let_1) (tptp.collect_nat (tptp.aa_nat_fun_nat_bool tptp.aTP_Lamm_br N)))))) (forall ((N tptp.nat)) (= (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat tptp.aTP_Lamm_al) (tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat N)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat N) (tptp.aa_nat_nat tptp.suc N))) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (forall ((A tptp.nat) (D tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_nat_fun_nat_nat (tptp.aTP_Lamm_ix A) D)) (tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat N)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat tptp.suc N)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat _let_1) A)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat N) D)))) _let_1)))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat tptp.aTP_Lamm_al) (tptp.set_or1269000886237332187st_nat M N)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat N) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N) tptp.one_one_nat))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat M) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) tptp.one_one_nat)))) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (tptp.unique5055182867167087721od_nat M N))) (let ((_let_2 (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num M) N)))) (and (=> _let_2 (= _let_1 (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat tptp.zero_zero_nat) (tptp.aa_num_nat tptp.numeral_numeral_nat M)))) (=> (not _let_2) (= _let_1 (tptp.unique5026877609467782581ep_nat N (tptp.unique5055182867167087721od_nat M (tptp.aa_num_num tptp.bit0 N))))))))) (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (tptp.unique5052692396658037445od_int M N))) (let ((_let_2 (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num M) N)))) (and (=> _let_2 (= _let_1 (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int tptp.zero_zero_int) (tptp.aa_num_int tptp.numeral_numeral_int M)))) (=> (not _let_2) (= _let_1 (tptp.aa_Pro6970504127699319548nt_int (tptp.unique5024387138958732305ep_int N) (tptp.unique5052692396658037445od_int M (tptp.aa_num_num tptp.bit0 N))))))))) (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (tptp.unique3479559517661332726nteger M N))) (let ((_let_2 (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num M) N)))) (and (=> _let_2 (= _let_1 (tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger M)))) (=> (not _let_2) (= _let_1 (tptp.unique4921790084139445826nteger N (tptp.unique3479559517661332726nteger M (tptp.aa_num_num tptp.bit0 N))))))))) (forall ((X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) tptp.one_one_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real tptp.ln_ln_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real tptp.one_one_real) X))) X))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))))))) (forall ((X tptp.real)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (let ((_let_2 (tptp.aa_num_real tptp.numeral_numeral_real _let_1))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real X)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.one_one_real) _let_2))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real tptp.ln_ln_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real tptp.one_one_real) X))) X))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real _let_2) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1))))))))) (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.divmod_nat M N))) (let ((_let_2 (or (= N tptp.zero_zero_nat) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N))))) (and (=> _let_2 (= _let_1 (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat tptp.zero_zero_nat) M))) (=> (not _let_2) (= _let_1 (tptp.aa_Pro262675715343573244at_nat (tptp.produc2626176000494625587at_nat tptp.aTP_Lamm_iy) (tptp.divmod_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) N) N)))))))) (forall ((X tptp.real)) (let ((_let_1 (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) X)) (= (tptp.aa_real_real tptp.tanh_real (tptp.aa_real_real tptp.ln_ln_real X)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real _let_1) tptp.one_one_real)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real _let_1) tptp.one_one_real)))))) (forall ((X tptp.real)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (let ((_let_2 (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_num_real tptp.numeral_numeral_real _let_1)))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.abs_abs_real X)) tptp.one_one_real)) (= (tptp.aa_real_real _let_2 (tptp.aa_real_real tptp.arctan X)) (tptp.aa_real_real tptp.arctan (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real _let_2 X)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real tptp.one_one_real) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1)))))))))) (= (tptp.aa_complex_complex tptp.neg_nu8557863876264182079omplex tptp.one_one_complex) _let_86) (= (tptp.aa_real_real tptp.neg_nu8295874005876285629c_real tptp.one_one_real) _let_59) (= (tptp.aa_rat_rat tptp.neg_nu5219082963157363817nc_rat tptp.one_one_rat) _let_85) (= (tptp.aa_int_int tptp.neg_nu5851722552734809277nc_int tptp.one_one_int) _let_84) (forall ((N tptp.nat) (M tptp.nat) (X tptp.complex)) (let ((_let_1 (tptp.power_power_complex X))) (let ((_let_2 (tptp.groups2073611262835488442omplex _let_1 (tptp.set_or1269000886237332187st_nat M N)))) (let ((_let_3 (= X tptp.one_one_complex))) (let ((_let_4 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N) M)))) (and (=> _let_4 (= _let_2 tptp.zero_zero_complex)) (=> (not _let_4) (and (=> _let_3 (= _let_2 (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N) tptp.one_one_nat)) M)))) (=> (not _let_3) (= _let_2 (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex (tptp.aa_complex_complex (tptp.minus_minus_complex (tptp.aa_nat_complex _let_1 M)) (tptp.aa_nat_complex _let_1 (tptp.aa_nat_nat tptp.suc N)))) (tptp.aa_complex_complex (tptp.minus_minus_complex tptp.one_one_complex) X)))))))))))) (forall ((N tptp.nat) (M tptp.nat) (X tptp.rat)) (let ((_let_1 (tptp.power_power_rat X))) (let ((_let_2 (tptp.groups2906978787729119204at_rat _let_1 (tptp.set_or1269000886237332187st_nat M N)))) (let ((_let_3 (= X tptp.one_one_rat))) (let ((_let_4 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N) M)))) (and (=> _let_4 (= _let_2 tptp.zero_zero_rat)) (=> (not _let_4) (and (=> _let_3 (= _let_2 (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N) tptp.one_one_nat)) M)))) (=> (not _let_3) (= _let_2 (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_nat_rat _let_1 M)) (tptp.aa_nat_rat _let_1 (tptp.aa_nat_nat tptp.suc N)))) (tptp.aa_rat_rat (tptp.minus_minus_rat tptp.one_one_rat) X)))))))))))) (forall ((N tptp.nat) (M tptp.nat) (X tptp.real)) (let ((_let_1 (tptp.aa_real_fun_nat_real tptp.power_power_real X))) (let ((_let_2 (tptp.groups6591440286371151544t_real _let_1 (tptp.set_or1269000886237332187st_nat M N)))) (let ((_let_3 (= X tptp.one_one_real))) (let ((_let_4 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N) M)))) (and (=> _let_4 (= _let_2 tptp.zero_zero_real)) (=> (not _let_4) (and (=> _let_3 (= _let_2 (tptp.aa_nat_real tptp.semiri5074537144036343181t_real (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N) tptp.one_one_nat)) M)))) (=> (not _let_3) (= _let_2 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_nat_real _let_1 M)) (tptp.aa_nat_real _let_1 (tptp.aa_nat_nat tptp.suc N)))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real tptp.one_one_real) X)))))))))))) (forall ((M tptp.nat) (N tptp.nat)) (= (= (tptp.aa_nat_int tptp.semiri1314217659103216013at_int M) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N)) (= M N))) (forall ((M tptp.nat) (N tptp.nat)) (= (= (tptp.aa_nat_real tptp.semiri5074537144036343181t_real M) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N)) (= M N))) (forall ((M tptp.nat) (N tptp.nat)) (= (= (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat M) (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat N)) (= M N))) (forall ((M tptp.nat) (V tptp.num)) (= (= (tptp.aa_nat_int tptp.semiri1314217659103216013at_int M) (tptp.aa_num_int tptp.numeral_numeral_int V)) (= M (tptp.aa_num_nat tptp.numeral_numeral_nat V)))) (forall ((N tptp.nat)) (let ((_let_1 (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger N))) (= (tptp.abs_abs_Code_integer _let_1) _let_1))) (forall ((N tptp.nat)) (let ((_let_1 (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat N))) (= (tptp.aa_rat_rat tptp.abs_abs_rat _let_1) _let_1))) (forall ((N tptp.nat)) (let ((_let_1 (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N))) (= (tptp.aa_int_int tptp.abs_abs_int _let_1) _let_1))) (forall ((N tptp.nat)) (let ((_let_1 (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N))) (= (tptp.aa_real_real tptp.abs_abs_real _let_1) _let_1))) (forall ((N tptp.nat) (M tptp.nat)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N))) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int M)))) (forall ((X tptp.real) (Y tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.tanh_real X)) (tptp.aa_real_real tptp.tanh_real Y))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Y)))) (forall ((X tptp.real) (Y tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.tanh_real X)) (tptp.aa_real_real tptp.tanh_real Y))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) Y)))) (forall ((M tptp.nat)) (= (= (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex M) tptp.zero_zero_complex) (= M tptp.zero_zero_nat))) (forall ((M tptp.nat)) (= (= (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat M) tptp.zero_zero_rat) (= M tptp.zero_zero_nat))) (forall ((M tptp.nat)) (= (= (tptp.aa_nat_int tptp.semiri1314217659103216013at_int M) tptp.zero_zero_int) (= M tptp.zero_zero_nat))) (forall ((M tptp.nat)) (= (= (tptp.aa_nat_real tptp.semiri5074537144036343181t_real M) tptp.zero_zero_real) (= M tptp.zero_zero_nat))) (forall ((M tptp.nat)) (= (= (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat M) tptp.zero_zero_nat) (= M tptp.zero_zero_nat))) (forall ((N tptp.nat)) (= (= tptp.zero_zero_complex (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex N)) (= tptp.zero_zero_nat N))) (forall ((N tptp.nat)) (= (= tptp.zero_zero_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat N)) (= tptp.zero_zero_nat N))) (forall ((N tptp.nat)) (= (= tptp.zero_zero_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N)) (= tptp.zero_zero_nat N))) (forall ((N tptp.nat)) (= (= tptp.zero_zero_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N)) (= tptp.zero_zero_nat N))) (forall ((N tptp.nat)) (= (= tptp.zero_zero_nat (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat N)) (= tptp.zero_zero_nat N))) (= (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex tptp.zero_zero_nat) tptp.zero_zero_complex) (= (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat tptp.zero_zero_nat) tptp.zero_zero_rat) _let_82 (= (tptp.aa_nat_real tptp.semiri5074537144036343181t_real tptp.zero_zero_nat) tptp.zero_zero_real) (= (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat tptp.zero_zero_nat) tptp.zero_zero_nat) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat M)) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat N))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N)))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int M)) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N)))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real M)) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N)))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat M)) (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat N))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N)))) (forall ((N tptp.num)) (= (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex (tptp.aa_num_nat tptp.numeral_numeral_nat N)) (tptp.numera6690914467698888265omplex N))) (forall ((N tptp.num)) (= (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat (tptp.aa_num_nat tptp.numeral_numeral_nat N)) (tptp.aa_num_rat tptp.numeral_numeral_rat N))) (forall ((N tptp.num)) (= (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_num_nat tptp.numeral_numeral_nat N)) (tptp.aa_num_int tptp.numeral_numeral_int N))) (forall ((N tptp.num)) (= (tptp.aa_nat_real tptp.semiri5074537144036343181t_real (tptp.aa_num_nat tptp.numeral_numeral_nat N)) (tptp.aa_num_real tptp.numeral_numeral_real N))) (forall ((N tptp.num)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat N))) (= (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat _let_1) _let_1))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real M)) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat M)) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat N))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat M)) (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat N))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int M)) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) N)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat M)) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat N)))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) N)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int M)) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N)))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.aa_nat_real tptp.semiri5074537144036343181t_real (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) N)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real M)) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N)))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) N)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat M)) (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat N)))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat M) N)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat M)) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat N)))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat M) N)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int M)) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N)))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.aa_nat_real tptp.semiri5074537144036343181t_real (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat M) N)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real M)) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N)))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat M) N)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat M)) (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat N)))) (forall ((N tptp.nat)) (= (= (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex N) tptp.one_one_complex) (= N tptp.one_one_nat))) (forall ((N tptp.nat)) (= (= (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat N) tptp.one_one_rat) (= N tptp.one_one_nat))) (forall ((N tptp.nat)) (= (= (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N) tptp.one_one_int) (= N tptp.one_one_nat))) (forall ((N tptp.nat)) (= (= (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N) tptp.one_one_real) (= N tptp.one_one_nat))) (forall ((N tptp.nat)) (= (= (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat N) tptp.one_one_nat) (= N tptp.one_one_nat))) (forall ((N tptp.nat)) (= (= tptp.one_one_complex (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex N)) (= N tptp.one_one_nat))) (forall ((N tptp.nat)) (= (= tptp.one_one_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat N)) (= N tptp.one_one_nat))) (forall ((N tptp.nat)) (= (= tptp.one_one_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N)) (= N tptp.one_one_nat))) (forall ((N tptp.nat)) (= (= tptp.one_one_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N)) (= N tptp.one_one_nat))) (forall ((N tptp.nat)) (= (= tptp.one_one_nat (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat N)) (= N tptp.one_one_nat))) (= (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex tptp.one_one_nat) tptp.one_one_complex) (= (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat tptp.one_one_nat) tptp.one_one_rat) _let_81 (= (tptp.aa_nat_real tptp.semiri5074537144036343181t_real tptp.one_one_nat) tptp.one_one_real) (= (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat tptp.one_one_nat) tptp.one_one_nat) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat M) N)) (tptp.aa_nat_complex (tptp.power_power_complex (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex M)) N))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat M) N)) (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int M)) N))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.aa_nat_real tptp.semiri5074537144036343181t_real (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat M) N)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real M)) N))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat M) N)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat M)) N))) (forall ((B2 tptp.nat) (W tptp.nat) (X tptp.nat)) (= (= (tptp.aa_nat_complex (tptp.power_power_complex (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex B2)) W) (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex X)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat B2) W) X))) (forall ((B2 tptp.nat) (W tptp.nat) (X tptp.nat)) (= (= (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int B2)) W) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int X)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat B2) W) X))) (forall ((B2 tptp.nat) (W tptp.nat) (X tptp.nat)) (= (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real B2)) W) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real X)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat B2) W) X))) (forall ((B2 tptp.nat) (W tptp.nat) (X tptp.nat)) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat B2)) W) (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat X)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat B2) W) X))) (forall ((X tptp.nat) (B2 tptp.nat) (W tptp.nat)) (= (= (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex X) (tptp.aa_nat_complex (tptp.power_power_complex (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex B2)) W)) (= X (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat B2) W)))) (forall ((X tptp.nat) (B2 tptp.nat) (W tptp.nat)) (= (= (tptp.aa_nat_int tptp.semiri1314217659103216013at_int X) (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int B2)) W)) (= X (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat B2) W)))) (forall ((X tptp.nat) (B2 tptp.nat) (W tptp.nat)) (= (= (tptp.aa_nat_real tptp.semiri5074537144036343181t_real X) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real B2)) W)) (= X (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat B2) W)))) (forall ((X tptp.nat) (B2 tptp.nat) (W tptp.nat)) (= (= (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat X) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat B2)) W)) (= X (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat B2) W)))) (forall ((N tptp.nat) (M tptp.nat)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_nat tptp.suc N)))) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int M)))) (forall ((Z tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int tptp.abs_abs_int Z)) tptp.one_one_int)) (= Z tptp.zero_zero_int))) (forall ((X tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real))) (= (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real tptp.arctan X))) (tptp.pp (tptp.aa_real_bool _let_1 X))))) (forall ((X tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.arctan X)) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) tptp.zero_zero_real)))) (forall ((X tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (= (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real tptp.arctan X))) (tptp.pp (tptp.aa_real_bool _let_1 X))))) (forall ((X tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.arctan X)) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) tptp.zero_zero_real)))) (forall ((X tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real))) (= (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real tptp.tanh_real X))) (tptp.pp (tptp.aa_real_bool _let_1 X))))) (forall ((X tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.tanh_real X)) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) tptp.zero_zero_real)))) (forall ((X tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.tanh_real X)) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) tptp.zero_zero_real)))) (forall ((X tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (= (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real tptp.tanh_real X))) (tptp.pp (tptp.aa_real_bool _let_1 X))))) (= (tptp.aa_complex_complex tptp.neg_nu8557863876264182079omplex tptp.zero_zero_complex) tptp.one_one_complex) (= (tptp.aa_real_real tptp.neg_nu8295874005876285629c_real tptp.zero_zero_real) tptp.one_one_real) (= (tptp.aa_rat_rat tptp.neg_nu5219082963157363817nc_rat tptp.zero_zero_rat) tptp.one_one_rat) (= (tptp.aa_int_int tptp.neg_nu5851722552734809277nc_int tptp.zero_zero_int) tptp.one_one_int) (forall ((P tptp.bool)) (= (tptp.aa_nat_real tptp.semiri5074537144036343181t_real (tptp.zero_n2687167440665602831ol_nat P)) (tptp.zero_n3304061248610475627l_real P))) (forall ((P tptp.bool)) (let ((_let_1 (tptp.zero_n2687167440665602831ol_nat P))) (= (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat _let_1) _let_1))) (forall ((P tptp.bool)) (= (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.zero_n2687167440665602831ol_nat P)) (tptp.aa_bool_int tptp.zero_n2684676970156552555ol_int P))) (forall ((P tptp.bool)) (= (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger (tptp.zero_n2687167440665602831ol_nat P)) (tptp.zero_n356916108424825756nteger P))) (= (tptp.aa_real_real tptp.neg_nu8295874005876285629c_real _let_57) _let_57) (= (tptp.aa_int_int tptp.neg_nu5851722552734809277nc_int _let_37) _let_37) (= (tptp.aa_complex_complex tptp.neg_nu8557863876264182079omplex _let_54) _let_54) (= (tptp.neg_nu5831290666863070958nteger _let_83) _let_83) (= (tptp.aa_rat_rat tptp.neg_nu5219082963157363817nc_rat _let_38) _let_38) (forall ((K tptp.num)) (= (tptp.aa_complex_complex tptp.neg_nu8557863876264182079omplex (tptp.numera6690914467698888265omplex K)) (tptp.numera6690914467698888265omplex (tptp.aa_num_num tptp.bit1 K)))) (forall ((K tptp.num)) (= (tptp.aa_real_real tptp.neg_nu8295874005876285629c_real (tptp.aa_num_real tptp.numeral_numeral_real K)) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit1 K)))) (forall ((K tptp.num)) (= (tptp.aa_rat_rat tptp.neg_nu5219082963157363817nc_rat (tptp.aa_num_rat tptp.numeral_numeral_rat K)) (tptp.aa_num_rat tptp.numeral_numeral_rat (tptp.aa_num_num tptp.bit1 K)))) (forall ((K tptp.num)) (= (tptp.aa_int_int tptp.neg_nu5851722552734809277nc_int (tptp.aa_num_int tptp.numeral_numeral_int K)) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit1 K)))) (forall ((M tptp.nat)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real M)) tptp.zero_zero_real)) (= M tptp.zero_zero_nat))) (forall ((M tptp.nat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat M)) tptp.zero_zero_rat)) (= M tptp.zero_zero_nat))) (forall ((M tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat M)) tptp.zero_zero_nat)) (= M tptp.zero_zero_nat))) (forall ((M tptp.nat)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int M)) tptp.zero_zero_int)) (= M tptp.zero_zero_nat))) (forall ((M tptp.nat)) (= (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex (tptp.aa_nat_nat tptp.suc M)) (tptp.aa_complex_complex (tptp.plus_plus_complex tptp.one_one_complex) (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex M)))) (forall ((M tptp.nat)) (= (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat (tptp.aa_nat_nat tptp.suc M)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat tptp.one_one_rat) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat M)))) (forall ((M tptp.nat)) (= (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_nat tptp.suc M)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int tptp.one_one_int) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int M)))) (forall ((M tptp.nat)) (= (tptp.aa_nat_real tptp.semiri5074537144036343181t_real (tptp.aa_nat_nat tptp.suc M)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real tptp.one_one_real) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real M)))) (forall ((M tptp.nat)) (= (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat (tptp.aa_nat_nat tptp.suc M)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat tptp.one_one_nat) (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat M)))) (forall ((W tptp.num) (N tptp.nat)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_num_real tptp.numeral_numeral_real W)) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_num_nat tptp.numeral_numeral_nat W)) N)))) (forall ((N tptp.nat) (W tptp.num)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N)) (tptp.aa_num_real tptp.numeral_numeral_real W))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N) (tptp.aa_num_nat tptp.numeral_numeral_nat W))))) (forall ((N tptp.num) (M tptp.nat)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_num_real tptp.numeral_numeral_real N)) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real M))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_num_nat tptp.numeral_numeral_nat N)) M)))) (forall ((N tptp.nat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat N))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)))) (forall ((N tptp.nat)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)))) (forall ((N tptp.nat)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)))) (forall ((N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat))) (= (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat N))) (tptp.pp (tptp.aa_nat_bool _let_1 N))))) (forall ((K tptp.num)) (let ((_let_1 (tptp.aa_num_real tptp.numeral_numeral_real K))) (= (tptp.aa_real_real tptp.neg_nu8295874005876285629c_real (tptp.aa_real_real tptp.uminus_uminus_real _let_1)) (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_real_real tptp.neg_nu6075765906172075777c_real _let_1))))) (forall ((K tptp.num)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int K))) (= (tptp.aa_int_int tptp.neg_nu5851722552734809277nc_int (tptp.aa_int_int tptp.uminus_uminus_int _let_1)) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_int_int tptp.neg_nu3811975205180677377ec_int _let_1))))) (forall ((K tptp.num)) (let ((_let_1 (tptp.numera6690914467698888265omplex K))) (= (tptp.aa_complex_complex tptp.neg_nu8557863876264182079omplex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex _let_1)) (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.aa_complex_complex tptp.neg_nu6511756317524482435omplex _let_1))))) (forall ((K tptp.num)) (let ((_let_1 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger K))) (= (tptp.neg_nu5831290666863070958nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger _let_1)) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.neg_nu7757733837767384882nteger _let_1))))) (forall ((K tptp.num)) (let ((_let_1 (tptp.aa_num_rat tptp.numeral_numeral_rat K))) (= (tptp.aa_rat_rat tptp.neg_nu5219082963157363817nc_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat _let_1)) (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_rat_rat tptp.neg_nu3179335615603231917ec_rat _let_1))))) (forall ((K tptp.num)) (let ((_let_1 (tptp.aa_num_real tptp.numeral_numeral_real K))) (= (tptp.aa_real_real tptp.neg_nu6075765906172075777c_real (tptp.aa_real_real tptp.uminus_uminus_real _let_1)) (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_real_real tptp.neg_nu8295874005876285629c_real _let_1))))) (forall ((K tptp.num)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int K))) (= (tptp.aa_int_int tptp.neg_nu3811975205180677377ec_int (tptp.aa_int_int tptp.uminus_uminus_int _let_1)) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_int_int tptp.neg_nu5851722552734809277nc_int _let_1))))) (forall ((K tptp.num)) (let ((_let_1 (tptp.numera6690914467698888265omplex K))) (= (tptp.aa_complex_complex tptp.neg_nu6511756317524482435omplex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex _let_1)) (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.aa_complex_complex tptp.neg_nu8557863876264182079omplex _let_1))))) (forall ((K tptp.num)) (let ((_let_1 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger K))) (= (tptp.neg_nu7757733837767384882nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger _let_1)) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.neg_nu5831290666863070958nteger _let_1))))) (forall ((K tptp.num)) (let ((_let_1 (tptp.aa_num_rat tptp.numeral_numeral_rat K))) (= (tptp.aa_rat_rat tptp.neg_nu3179335615603231917ec_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat _let_1)) (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_rat_rat tptp.neg_nu5219082963157363817nc_rat _let_1))))) (forall ((B2 tptp.nat) (W tptp.nat) (X tptp.nat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat B2)) W)) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat X))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat B2) W)) X)))) (forall ((B2 tptp.nat) (W tptp.nat) (X tptp.nat)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int B2)) W)) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int X))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat B2) W)) X)))) (forall ((B2 tptp.nat) (W tptp.nat) (X tptp.nat)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real B2)) W)) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real X))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat B2) W)) X)))) (forall ((B2 tptp.nat) (W tptp.nat) (X tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat B2)) W)) (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat X))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat B2) W)) X)))) (forall ((X tptp.nat) (B2 tptp.nat) (W tptp.nat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat X)) (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat B2)) W))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat B2) W))))) (forall ((X tptp.nat) (B2 tptp.nat) (W tptp.nat)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int X)) (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int B2)) W))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat B2) W))))) (forall ((X tptp.nat) (B2 tptp.nat) (W tptp.nat)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real X)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real B2)) W))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat B2) W))))) (forall ((X tptp.nat) (B2 tptp.nat) (W tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat X)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat B2)) W))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat B2) W))))) (forall ((Y tptp.nat) (X tptp.num) (N tptp.nat)) (= (= (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex Y) (tptp.aa_nat_complex (tptp.power_power_complex (tptp.numera6690914467698888265omplex X)) N)) (= Y (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat X)) N)))) (forall ((Y tptp.nat) (X tptp.num) (N tptp.nat)) (= (= (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat Y) (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_num_rat tptp.numeral_numeral_rat X)) N)) (= Y (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat X)) N)))) (forall ((Y tptp.nat) (X tptp.num) (N tptp.nat)) (= (= (tptp.aa_nat_int tptp.semiri1314217659103216013at_int Y) (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int X)) N)) (= Y (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat X)) N)))) (forall ((Y tptp.nat) (X tptp.num) (N tptp.nat)) (= (= (tptp.aa_nat_real tptp.semiri5074537144036343181t_real Y) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_num_real tptp.numeral_numeral_real X)) N)) (= Y (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat X)) N)))) (forall ((Y tptp.nat) (X tptp.num) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat X)) N))) (= (= (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat Y) _let_1) (= Y _let_1)))) (forall ((X tptp.num) (N tptp.nat) (Y tptp.nat)) (= (= (tptp.aa_nat_complex (tptp.power_power_complex (tptp.numera6690914467698888265omplex X)) N) (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex Y)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat X)) N) Y))) (forall ((X tptp.num) (N tptp.nat) (Y tptp.nat)) (= (= (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_num_rat tptp.numeral_numeral_rat X)) N) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat Y)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat X)) N) Y))) (forall ((X tptp.num) (N tptp.nat) (Y tptp.nat)) (= (= (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int X)) N) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int Y)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat X)) N) Y))) (forall ((X tptp.num) (N tptp.nat) (Y tptp.nat)) (= (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_num_real tptp.numeral_numeral_real X)) N) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real Y)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat X)) N) Y))) (forall ((X tptp.num) (N tptp.nat) (Y tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat X)) N))) (= (= _let_1 (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat Y)) (= _let_1 Y)))) (forall ((B2 tptp.nat) (W tptp.nat) (X tptp.nat)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real B2)) W)) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real X))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat B2) W)) X)))) (forall ((B2 tptp.nat) (W tptp.nat) (X tptp.nat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat B2)) W)) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat X))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat B2) W)) X)))) (forall ((B2 tptp.nat) (W tptp.nat) (X tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat B2)) W)) (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat X))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat B2) W)) X)))) (forall ((B2 tptp.nat) (W tptp.nat) (X tptp.nat)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int B2)) W)) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int X))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat B2) W)) X)))) (forall ((X tptp.nat) (B2 tptp.nat) (W tptp.nat)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real X)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real B2)) W))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat B2) W))))) (forall ((X tptp.nat) (B2 tptp.nat) (W tptp.nat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat X)) (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat B2)) W))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat B2) W))))) (forall ((X tptp.nat) (B2 tptp.nat) (W tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat X)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat B2)) W))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat B2) W))))) (forall ((X tptp.nat) (B2 tptp.nat) (W tptp.nat)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int X)) (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int B2)) W))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat B2) W))))) (forall ((X tptp.nat) (N tptp.nat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat X)) N))) (or (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) X)) (= N tptp.zero_zero_nat)))) (forall ((X tptp.nat) (N tptp.nat)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int X)) N))) (or (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) X)) (= N tptp.zero_zero_nat)))) (forall ((X tptp.nat) (N tptp.nat)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real X)) N))) (or (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) X)) (= N tptp.zero_zero_nat)))) (forall ((X tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat))) (= (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat X)) N))) (or (tptp.pp (tptp.aa_nat_bool _let_1 X)) (= N tptp.zero_zero_nat))))) (forall ((N tptp.nat)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger _let_1)) (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger N))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1)) N))))) (forall ((N tptp.nat)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_num_int tptp.numeral_numeral_int _let_1)) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1)) N))))) (forall ((N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat N))) (tptp.pp (tptp.aa_nat_bool _let_1 N))))) (forall ((I tptp.num) (N tptp.nat) (X tptp.nat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_num_rat tptp.numeral_numeral_rat I)) N)) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat X))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat I)) N)) X)))) (forall ((I tptp.num) (N tptp.nat) (X tptp.nat)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int I)) N)) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int X))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat I)) N)) X)))) (forall ((I tptp.num) (N tptp.nat) (X tptp.nat)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_num_real tptp.numeral_numeral_real I)) N)) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real X))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat I)) N)) X)))) (forall ((I tptp.num) (N tptp.nat) (X tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat I)) N)))) (= (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat X))) (tptp.pp (tptp.aa_nat_bool _let_1 X))))) (forall ((X tptp.nat) (I tptp.num) (N tptp.nat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat X)) (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_num_rat tptp.numeral_numeral_rat I)) N))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat I)) N))))) (forall ((X tptp.nat) (I tptp.num) (N tptp.nat)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int X)) (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int I)) N))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat I)) N))))) (forall ((X tptp.nat) (I tptp.num) (N tptp.nat)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real X)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_num_real tptp.numeral_numeral_real I)) N))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat I)) N))))) (forall ((X tptp.nat) (I tptp.num) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat I)) N))) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat X)) _let_1)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) _let_1))))) (forall ((I tptp.num) (N tptp.nat) (X tptp.nat)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_num_real tptp.numeral_numeral_real I)) N)) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real X))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat I)) N)) X)))) (forall ((I tptp.num) (N tptp.nat) (X tptp.nat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_num_rat tptp.numeral_numeral_rat I)) N)) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat X))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat I)) N)) X)))) (forall ((I tptp.num) (N tptp.nat) (X tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat I)) N)))) (= (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat X))) (tptp.pp (tptp.aa_nat_bool _let_1 X))))) (forall ((I tptp.num) (N tptp.nat) (X tptp.nat)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int I)) N)) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int X))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat I)) N)) X)))) (forall ((X tptp.nat) (I tptp.num) (N tptp.nat)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real X)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_num_real tptp.numeral_numeral_real I)) N))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat I)) N))))) (forall ((X tptp.nat) (I tptp.num) (N tptp.nat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat X)) (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_num_rat tptp.numeral_numeral_rat I)) N))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat I)) N))))) (forall ((X tptp.nat) (I tptp.num) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat I)) N))) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat X)) _let_1)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X) _let_1))))) (forall ((X tptp.nat) (I tptp.num) (N tptp.nat)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int X)) (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int I)) N))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat I)) N))))) (forall ((A4 tptp.fun_int_fun_int_bool) (B4 tptp.fun_int_fun_int_bool)) (=> (tptp.ord_le4546832483993983377t_bool A4 B4) (tptp.ord_le2843351958646193337nt_int (tptp.collec213857154873943460nt_int (tptp.produc8560705615207772305t_bool A4)) (tptp.collec213857154873943460nt_int (tptp.produc8560705615207772305t_bool B4))))) (forall ((X tptp.nat) (Y tptp.rat)) (let ((_let_1 (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat X))) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat _let_1) Y) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat Y) _let_1)))) (forall ((X tptp.nat) (Y tptp.int)) (let ((_let_1 (tptp.aa_nat_int tptp.semiri1314217659103216013at_int X))) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int _let_1) Y) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int Y) _let_1)))) (forall ((X tptp.nat) (Y tptp.real)) (let ((_let_1 (tptp.aa_nat_real tptp.semiri5074537144036343181t_real X))) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real _let_1) Y) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real Y) _let_1)))) (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat X))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat _let_1) Y) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat Y) _let_1)))) (forall ((X tptp.real) (Y tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.arctan X)) (tptp.aa_real_real tptp.arctan Y))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Y)))) (forall ((X tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Y)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.arctan X)) (tptp.aa_real_real tptp.arctan Y))))) (forall ((X tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) Y)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.arctan X)) (tptp.aa_real_real tptp.arctan Y))))) (forall ((X tptp.real) (Y tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.arctan X)) (tptp.aa_real_real tptp.arctan Y))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) Y)))) (forall ((N tptp.nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N)))) (forall ((N tptp.nat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat N)))) (forall ((N tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat N)))) (forall ((N tptp.nat)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N)))) (forall ((M tptp.nat)) (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat M)) tptp.zero_zero_rat)))) (forall ((M tptp.nat)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int M)) tptp.zero_zero_int)))) (forall ((M tptp.nat)) (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real M)) tptp.zero_zero_real)))) (forall ((M tptp.nat)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat M)) tptp.zero_zero_nat)))) (forall ((N tptp.nat)) (not (= (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex (tptp.aa_nat_nat tptp.suc N)) tptp.zero_zero_complex))) (forall ((N tptp.nat)) (not (= (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat (tptp.aa_nat_nat tptp.suc N)) tptp.zero_zero_rat))) (forall ((N tptp.nat)) (not (= (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_nat tptp.suc N)) tptp.zero_zero_int))) (forall ((N tptp.nat)) (not (= (tptp.aa_nat_real tptp.semiri5074537144036343181t_real (tptp.aa_nat_nat tptp.suc N)) tptp.zero_zero_real))) (forall ((N tptp.nat)) (not (= (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat (tptp.aa_nat_nat tptp.suc N)) tptp.zero_zero_nat))) (forall ((A tptp.int) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N))) (let ((_let_2 (tptp.aa_nat_int tptp.semiri1314217659103216013at_int M))) (let ((_let_3 (tptp.divide_divide_int A))) (= (tptp.aa_int_int _let_3 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int _let_2) _let_1)) (tptp.aa_int_int (tptp.divide_divide_int (tptp.aa_int_int _let_3 _let_2)) _let_1)))))) (forall ((A tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat N))) (let ((_let_2 (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat M))) (let ((_let_3 (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A))) (= (tptp.aa_nat_nat _let_3 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat _let_2) _let_1)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat _let_3 _let_2)) _let_1)))))) (forall ((M tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat M)) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat N))))) (forall ((M tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int M)) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N))))) (forall ((M tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real M)) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N))))) (forall ((M tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat M)) (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat N))))) (forall ((M tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat M)) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat N))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N)))) (forall ((M tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int M)) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N)))) (forall ((M tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real M)) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N)))) (forall ((M tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat M)) (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat N))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N)))) (forall ((I tptp.nat) (J tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I) J)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real I)) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real J))))) (forall ((I tptp.nat) (J tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I) J)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat I)) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat J))))) (forall ((I tptp.nat) (J tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I) J)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat I)) (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat J))))) (forall ((I tptp.nat) (J tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I) J)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int I)) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int J))))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat M) N)) (tptp.aa_int_int (tptp.divide_divide_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int M)) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N)))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat M) N)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat M)) (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat N)))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger M)) (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger N))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat M) N)))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int M)) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat M) N)))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat M)) (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat N))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat M) N)))) _let_82 (forall ((N tptp.num)) (= (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_num_nat tptp.numeral_numeral_nat N)) (tptp.aa_num_int tptp.numeral_numeral_int N))) (forall ((M tptp.int) (N tptp.int)) (=> (= (tptp.aa_int_int tptp.abs_abs_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int M) N)) tptp.one_one_int) (= (tptp.aa_int_int tptp.abs_abs_int M) tptp.one_one_int))) (forall ((A tptp.nat) (B2 tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) B2)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int A)) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int B2))))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int M)) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)))) (forall ((A tptp.nat) (B2 tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B2)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int A)) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int B2))))) (forall ((K tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) K)) (not (forall ((N2 tptp.nat)) (not (= K (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N2))))))) (forall ((K tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) K)) (exists ((N2 tptp.nat)) (= K (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N2))))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat M) N)) (tptp.modulo364778990260209775nteger (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger M) (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger N)))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat M) N)) (tptp.aa_int_int (tptp.modulo_modulo_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int M)) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N)))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat M) N)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat M)) (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat N)))) (forall ((M tptp.nat) (N tptp.nat) (Z tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int M)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N)) Z)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) N))) Z))) (forall ((N tptp.nat) (M tptp.nat)) (= (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N) M)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N)) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int M)))) (forall ((A tptp.nat) (B2 tptp.nat)) (= (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) B2)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int A)) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int B2)))) _let_81 (forall ((A tptp.nat) (B2 tptp.nat)) (= (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) B2)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int A)) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int B2)))) (forall ((W tptp.int) (Z tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int W) Z)) (exists ((N5 tptp.nat)) (= Z (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int W) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N5)))))) (forall ((N tptp.nat) (M tptp.nat)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N)) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int M)))))) (forall ((A tptp.nat) (B2 tptp.nat)) (= (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) B2)) (tptp.aa_int_int (tptp.divide_divide_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int A)) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int B2)))) (forall ((X tptp.nat) (Y tptp.nat)) (= (tptp.semiri4216267220026989637d_enat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat X) Y)) (tptp.aa_Ext7969882492699152700d_enat (tptp.aa_Ext3475206891998675565d_enat tptp.ord_ma741700101516333627d_enat (tptp.semiri4216267220026989637d_enat X)) (tptp.semiri4216267220026989637d_enat Y)))) (forall ((X tptp.nat) (Y tptp.nat)) (= (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat X) Y)) (tptp.aa_int_int (tptp.ord_max_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int X)) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int Y)))) (forall ((X tptp.nat) (Y tptp.nat)) (= (tptp.aa_nat_real tptp.semiri5074537144036343181t_real (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat X) Y)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.ord_max_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real X)) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real Y)))) (forall ((X tptp.nat) (Y tptp.nat)) (= (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat X) Y)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat X)) (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat Y)))) (forall ((X tptp.real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.tanh_real X)) tptp.one_one_real))) (forall ((X5 tptp.nat) (Xa tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X5) Xa)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int X5)) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int Xa))))) (forall ((X5 tptp.nat) (Xa tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X5) Xa)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int X5)) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int Xa))))) (forall ((N tptp.nat) (M tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N) M)) (= (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) N)) (tptp.aa_complex_complex (tptp.minus_minus_complex (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex M)) (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex N))))) (forall ((N tptp.nat) (M tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N) M)) (= (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) N)) (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat M)) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat N))))) (forall ((N tptp.nat) (M tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N) M)) (= (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) N)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int M)) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N))))) (forall ((N tptp.nat) (M tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N) M)) (= (tptp.aa_nat_real tptp.semiri5074537144036343181t_real (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) N)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real M)) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N))))) (forall ((N tptp.nat) (M tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N) M)) (= (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) N)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat M)) (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat N))))) (forall ((I tptp.int)) (let ((_let_1 (tptp.aa_int_int tptp.abs_abs_int I))) (let ((_let_2 (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int I) tptp.zero_zero_int)))) (and (=> _let_2 (= _let_1 (tptp.aa_int_int tptp.uminus_uminus_int I))) (=> (not _let_2) (= _let_1 I)))))) (forall ((X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) X)) (forall ((Y5 tptp.real)) (exists ((N2 tptp.nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y5) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N2)) X))))))) (forall ((M tptp.int)) (=> (forall ((N2 tptp.nat)) (not (= M (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N2)))) (not (forall ((N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)) (not (= M (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N2))))))))) (forall ((I tptp.int) (D tptp.int)) (=> (not (= I tptp.zero_zero_int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int D) I)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.abs_abs_int D)) (tptp.aa_int_int tptp.abs_abs_int I)))))) (forall ((N tptp.nat) (X tptp.nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat N) X))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N)) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real X))))) (forall ((N tptp.nat) (M tptp.nat)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N)) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int M)))) (and (= N tptp.zero_zero_nat) (= M tptp.zero_zero_nat)))) (forall ((A tptp.nat)) (= (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_nat tptp.suc A)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int A)) tptp.one_one_int))) (forall ((N tptp.nat)) (= (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_nat tptp.suc N)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N)) tptp.one_one_int))) (forall ((W tptp.int) (Z tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int W) Z)) (exists ((N5 tptp.nat)) (= Z (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int W) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_nat tptp.suc N5))))))) (forall ((L tptp.int) (K tptp.int)) (=> (not (= L tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int tptp.abs_abs_int (tptp.aa_int_int (tptp.modulo_modulo_int K) L))) (tptp.aa_int_int tptp.abs_abs_int L))))) (forall ((N tptp.nat)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N))) tptp.zero_zero_int))) (forall ((K tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int K) tptp.zero_zero_int)) (not (forall ((N2 tptp.nat)) (not (= K (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N2)))))))) (forall ((D tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat D) N)) (= (tptp.aa_nat_real tptp.semiri5074537144036343181t_real (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat N) D)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N)) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real D))))) (forall ((X tptp.real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)) (tptp.aa_real_real tptp.tanh_real X)))) (forall ((A tptp.code_integer) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger M))) (let ((_let_2 (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger N))) (let ((_let_3 (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger _let_1))) (= (tptp.modulo364778990260209775nteger A (tptp.aa_Cod1783974652533396728nteger _let_3 _let_2)) (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger _let_3 (tptp.modulo364778990260209775nteger (tptp.divide6298287555418463151nteger A _let_1) _let_2)) (tptp.modulo364778990260209775nteger A _let_1))))))) (forall ((A tptp.int) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_int tptp.semiri1314217659103216013at_int M))) (let ((_let_2 (tptp.modulo_modulo_int A))) (let ((_let_3 (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N))) (let ((_let_4 (tptp.aa_int_fun_int_int tptp.times_times_int _let_1))) (= (tptp.aa_int_int _let_2 (tptp.aa_int_int _let_4 _let_3)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int _let_4 (tptp.aa_int_int (tptp.modulo_modulo_int (tptp.aa_int_int (tptp.divide_divide_int A) _let_1)) _let_3))) (tptp.aa_int_int _let_2 _let_1)))))))) (forall ((A tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat M))) (let ((_let_2 (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A))) (let ((_let_3 (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat N))) (let ((_let_4 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat _let_1))) (= (tptp.aa_nat_nat _let_2 (tptp.aa_nat_nat _let_4 _let_3)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat _let_4 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) _let_1)) _let_3))) (tptp.aa_nat_nat _let_2 _let_1)))))))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat M) N)) (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex (tptp.aa_complex_complex (tptp.minus_minus_complex (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex M)) (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat M) N)))) (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex N)))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat M) N)) (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat M)) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat M) N)))) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat N)))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.aa_nat_real tptp.semiri5074537144036343181t_real (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat M) N)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real M)) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat M) N)))) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N)))) (forall ((K tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) K)) (not (forall ((N2 tptp.nat)) (=> (= K (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N2)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)))))))) (forall ((K tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) K)) (exists ((N2 tptp.nat)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)) (= K (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N2)))))) (forall ((K tptp.int)) (=> (not (= K tptp.zero_zero_int)) (=> (forall ((N2 tptp.nat)) (=> (= K (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N2)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2))))) (not (forall ((N2 tptp.nat)) (=> (= K (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N2))) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2))))))))) (forall ((N tptp.nat) (M tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N) M)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N)) tptp.one_one_real)) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real M))))) (forall ((N tptp.nat) (M tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N) M)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real M)) tptp.one_one_real))))) (forall ((I tptp.int) (J tptp.int) (K tptp.nat)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int K)))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int I) J)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) K)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int _let_1 I)) (tptp.aa_int_int _let_1 J))))))) (forall ((M tptp.int) (N tptp.int)) (=> (not (= M tptp.zero_zero_int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int M) N)) M)) (= (tptp.aa_int_int tptp.abs_abs_int N) tptp.one_one_int)))) (forall ((N tptp.nat)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_nat tptp.suc N))))))) (forall ((X tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) tptp.zero_zero_int)) (exists ((N2 tptp.nat)) (= X (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_nat tptp.suc N2))))))) (forall ((N tptp.nat)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_nat tptp.suc N)))) tptp.zero_zero_int))) (forall ((X tptp.complex)) (= (tptp.aa_complex_complex tptp.neg_nu8557863876264182079omplex X) (tptp.aa_complex_complex (tptp.plus_plus_complex (tptp.aa_complex_complex (tptp.plus_plus_complex X) X)) tptp.one_one_complex))) (forall ((X tptp.real)) (= (tptp.aa_real_real tptp.neg_nu8295874005876285629c_real X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) X)) tptp.one_one_real))) (forall ((X tptp.rat)) (= (tptp.aa_rat_rat tptp.neg_nu5219082963157363817nc_rat X) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat X) X)) tptp.one_one_rat))) (forall ((X tptp.int)) (= (tptp.aa_int_int tptp.neg_nu5851722552734809277nc_int X) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int X) X)) tptp.one_one_int))) (forall ((A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_int tptp.semiri1314217659103216013at_int B2))) (let ((_let_2 (tptp.aa_nat_int tptp.semiri1314217659103216013at_int A))) (let ((_let_3 (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat A) B2)))) (let ((_let_4 (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int _let_2) _let_1)))) (and (=> _let_4 (= _let_3 tptp.zero_zero_int)) (=> (not _let_4) (= _let_3 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int _let_2) _let_1))))))))) (forall ((X tptp.nat) (D tptp.nat)) (let ((_let_1 (tptp.aa_nat_real tptp.semiri5074537144036343181t_real D))) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real X)) _let_1) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat X) D))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat X) D))) _let_1))))) (forall ((N tptp.nat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat N)) (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_num_rat tptp.numeral_numeral_rat (tptp.aa_num_num tptp.bit0 tptp.one))) N)))) (forall ((N tptp.nat)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N)) (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) N)))) (forall ((N tptp.nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))) N)))) (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.one_one_real))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N) M)) (=> (not (= N tptp.zero_zero_nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real _let_1 (tptp.aa_nat_real tptp.semiri5074537144036343181t_real M))) (tptp.aa_real_real _let_1 (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N)))))))) (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.divide_divide_rat tptp.one_one_rat))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N) M)) (=> (not (= N tptp.zero_zero_nat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat _let_1 (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat M))) (tptp.aa_rat_rat _let_1 (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat N)))))))) (forall ((K tptp.int) (L tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int tptp.abs_abs_int K)) L))) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int K) L)))))) (forall ((K tptp.int) (L tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.plus_plus_int K))) (let ((_let_2 (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.pp (tptp.aa_int_bool _let_2 (tptp.aa_int_int _let_1 (tptp.aa_int_int tptp.abs_abs_int L)))) (tptp.pp (tptp.aa_int_bool _let_2 (tptp.aa_int_int _let_1 L))))))) (forall ((X tptp.real) (C tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool _let_1 X)) (=> (tptp.pp (tptp.aa_real_bool _let_1 C)) (=> (forall ((M3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) M3)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real M3)) X)) C)))) (= X tptp.zero_zero_real)))))) (forall ((K tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int K) tptp.zero_zero_int)) (not (forall ((N2 tptp.nat)) (=> (= K (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N2))) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)))))))) (forall ((P tptp.fun_int_bool) (X tptp.nat) (Y tptp.nat)) (= (tptp.pp (tptp.aa_int_bool P (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat X) Y)))) (and (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Y) X)) (tptp.pp (tptp.aa_int_bool P (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int X)) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int Y))))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Y)) (tptp.pp (tptp.aa_int_bool P tptp.zero_zero_int)))))) (forall ((N tptp.nat) (X tptp.nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N)) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real X))) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat N) X)))))) (forall ((N tptp.nat) (X tptp.nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N)) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real X))) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat N) X)))) tptp.one_one_real))) (forall ((X tptp.real) (N tptp.nat)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) X)) (= (tptp.aa_real_real tptp.ln_ln_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) N)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N)) (tptp.aa_real_real tptp.ln_ln_real X))))) (forall ((M tptp.nat) (N tptp.nat) (F tptp.fun_nat_int) (K tptp.int)) (=> (forall ((I3 tptp.nat)) (=> (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) I3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I3) N))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.abs_abs_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_nat_int F (tptp.aa_nat_nat tptp.suc I3))) (tptp.aa_nat_int F I3)))) tptp.one_one_int)))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int F M)) K)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int K) (tptp.aa_nat_int F N))) (exists ((I3 tptp.nat)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) I3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I3) N)) (= (tptp.aa_nat_int F I3) K)))))))) (forall ((D tptp.int) (Z tptp.int) (X tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) D)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Z) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int X) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int tptp.abs_abs_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int X) Z))) tptp.one_one_int)) D)))))) (forall ((D tptp.int) (X tptp.int) (Z tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.minus_minus_int X))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) D)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int tptp.abs_abs_int (tptp.aa_int_int _let_1 Z))) tptp.one_one_int)) D))) Z))))) (forall ((X tptp.real) (N tptp.nat)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) X)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N)) X)) tptp.one_one_real)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) tptp.one_one_real)) N))))) (forall ((X tptp.real) (N tptp.nat)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real tptp.one_one_real))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)) X)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N)) X))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real _let_1 X)) N)))))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.divmod_nat M N) (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat M) N)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat M) N)))) (forall ((N tptp.nat) (F tptp.fun_nat_int) (K tptp.int)) (=> (forall ((I3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I3) N)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.abs_abs_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_nat_int F (tptp.aa_nat_nat tptp.suc I3))) (tptp.aa_nat_int F I3)))) tptp.one_one_int)))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int F tptp.zero_zero_nat)) K)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int K) (tptp.aa_nat_int F N))) (exists ((I3 tptp.nat)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I3) N)) (= (tptp.aa_nat_int F I3) K))))))) (forall ((N tptp.nat) (F tptp.fun_nat_int) (K tptp.int)) (=> (forall ((I3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I3) N)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.abs_abs_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_nat_int F (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat I3) tptp.one_one_nat))) (tptp.aa_nat_int F I3)))) tptp.one_one_int)))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int F tptp.zero_zero_nat)) K)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int K) (tptp.aa_nat_int F N))) (exists ((I3 tptp.nat)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I3) N)) (= (tptp.aa_nat_int F I3) K))))))) (forall ((A tptp.complex) (D tptp.complex) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex N))) (let ((_let_2 (tptp.times_times_complex (tptp.numera6690914467698888265omplex (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.aa_complex_complex _let_2 (tptp.groups2073611262835488442omplex (tptp.aa_com8181001469867462503omplex (tptp.aTP_Lamm_iz A) D) (tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat N))) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_complex_complex (tptp.plus_plus_complex _let_1) tptp.one_one_complex)) (tptp.aa_complex_complex (tptp.plus_plus_complex (tptp.aa_complex_complex _let_2 A)) (tptp.aa_complex_complex (tptp.times_times_complex _let_1) D))))))) (forall ((A tptp.rat) (D tptp.rat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat N))) (let ((_let_2 (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_num_rat tptp.numeral_numeral_rat (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.aa_rat_rat _let_2 (tptp.groups2906978787729119204at_rat (tptp.aa_rat_fun_nat_rat (tptp.aTP_Lamm_ja A) D) (tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat N))) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat _let_1) tptp.one_one_rat)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat _let_2 A)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat _let_1) D))))))) (forall ((A tptp.int) (D tptp.int) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N))) (let ((_let_2 (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.aa_int_int _let_2 (tptp.groups3539618377306564664at_int (tptp.aa_int_fun_nat_int (tptp.aTP_Lamm_jb A) D) (tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat N))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int _let_1) tptp.one_one_int)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int _let_2 A)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int _let_1) D))))))) (forall ((A tptp.nat) (D tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat N))) (let ((_let_2 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.aa_nat_nat _let_2 (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_nat_fun_nat_nat (tptp.aTP_Lamm_jc A) D)) (tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat N))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat _let_1) tptp.one_one_nat)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat _let_2 A)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat _let_1) D))))))) (forall ((A tptp.real) (D tptp.real) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N))) (let ((_let_2 (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.aa_real_real _let_2 (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_jd A) D) (tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat N))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real _let_1) tptp.one_one_real)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real _let_2 A)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real _let_1) D))))))) (forall ((N tptp.nat)) (let ((_let_1 (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex N))) (= (tptp.aa_complex_complex (tptp.times_times_complex (tptp.numera6690914467698888265omplex (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.groups2073611262835488442omplex tptp.semiri8010041392384452111omplex (tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat N))) (tptp.aa_complex_complex (tptp.times_times_complex _let_1) (tptp.aa_complex_complex (tptp.plus_plus_complex _let_1) tptp.one_one_complex))))) (forall ((N tptp.nat)) (let ((_let_1 (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat N))) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_num_rat tptp.numeral_numeral_rat (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.groups2906978787729119204at_rat tptp.semiri681578069525770553at_rat (tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat N))) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat _let_1) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat _let_1) tptp.one_one_rat))))) (forall ((N tptp.nat)) (let ((_let_1 (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N))) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.groups3539618377306564664at_int tptp.semiri1314217659103216013at_int (tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat N))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int _let_1) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int _let_1) tptp.one_one_int))))) (forall ((N tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat N))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat tptp.semiri1316708129612266289at_nat) (tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat N))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat _let_1) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat _let_1) tptp.one_one_nat))))) (forall ((N tptp.nat)) (let ((_let_1 (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N))) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.groups6591440286371151544t_real tptp.semiri5074537144036343181t_real (tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat N))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real _let_1) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real _let_1) tptp.one_one_real))))) (forall ((X tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real X)) tptp.one_one_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.abs_abs_real Y)) tptp.one_one_real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real tptp.arctan X)) (tptp.aa_real_real tptp.arctan Y)) (tptp.aa_real_real tptp.arctan (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) Y)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real tptp.one_one_real) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real X) Y)))))))) (forall ((A tptp.int) (D tptp.int) (N tptp.nat)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N))) (= (tptp.groups3539618377306564664at_int (tptp.aa_int_fun_nat_int (tptp.aTP_Lamm_jb A) D) (tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat N)) (tptp.aa_int_int (tptp.divide_divide_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int _let_2) tptp.one_one_int)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int _let_1) A)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int _let_2) D)))) _let_1))))) (forall ((A tptp.nat) (D tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat N))) (= (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_nat_fun_nat_nat (tptp.aTP_Lamm_jc A) D)) (tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat N)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat _let_2) tptp.one_one_nat)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat _let_1) A)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat _let_2) D)))) _let_1))))) (forall ((N tptp.nat)) (let ((_let_1 (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N))) (= (tptp.groups3539618377306564664at_int tptp.semiri1314217659103216013at_int (tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat N)) (tptp.aa_int_int (tptp.divide_divide_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int _let_1) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int _let_1) tptp.one_one_int))) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one)))))) (forall ((N tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat N))) (= (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat tptp.semiri1316708129612266289at_nat) (tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat N)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat _let_1) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat _let_1) tptp.one_one_nat))) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))))) (forall ((N tptp.nat)) (let ((_let_1 (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex N))) (= (tptp.aa_complex_complex (tptp.times_times_complex (tptp.numera6690914467698888265omplex (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.groups2073611262835488442omplex tptp.semiri8010041392384452111omplex (tptp.set_or1269000886237332187st_nat (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat) N))) (tptp.aa_complex_complex (tptp.times_times_complex _let_1) (tptp.aa_complex_complex (tptp.plus_plus_complex _let_1) tptp.one_one_complex))))) (forall ((N tptp.nat)) (let ((_let_1 (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat N))) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_num_rat tptp.numeral_numeral_rat (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.groups2906978787729119204at_rat tptp.semiri681578069525770553at_rat (tptp.set_or1269000886237332187st_nat (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat) N))) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat _let_1) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat _let_1) tptp.one_one_rat))))) (forall ((N tptp.nat)) (let ((_let_1 (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N))) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.groups3539618377306564664at_int tptp.semiri1314217659103216013at_int (tptp.set_or1269000886237332187st_nat (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat) N))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int _let_1) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int _let_1) tptp.one_one_int))))) (forall ((N tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat N))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat tptp.semiri1316708129612266289at_nat) (tptp.set_or1269000886237332187st_nat (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat) N))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat _let_1) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat _let_1) tptp.one_one_nat))))) (forall ((N tptp.nat)) (let ((_let_1 (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N))) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.groups6591440286371151544t_real tptp.semiri5074537144036343181t_real (tptp.set_or1269000886237332187st_nat (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat) N))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real _let_1) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real _let_1) tptp.one_one_real))))) (forall ((N tptp.nat) (X tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real tptp.one_one_real))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N)) X))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real _let_1 X)) N)))))) (forall ((X tptp.complex) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.minus_minus_complex tptp.one_one_complex))) (let ((_let_2 (tptp.power_power_complex X))) (let ((_let_3 (tptp.groups2073611262835488442omplex _let_2 (tptp.set_or1269000886237332187st_nat M (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) N))))) (let ((_let_4 (= X tptp.one_one_complex))) (and (=> _let_4 (= _let_3 (tptp.aa_complex_complex (tptp.plus_plus_complex (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex N)) tptp.one_one_complex))) (=> (not _let_4) (= _let_3 (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_nat_complex _let_2 M)) (tptp.aa_complex_complex _let_1 (tptp.aa_nat_complex _let_2 (tptp.aa_nat_nat tptp.suc N))))) (tptp.aa_complex_complex _let_1 X)))))))))) (forall ((X tptp.rat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.minus_minus_rat tptp.one_one_rat))) (let ((_let_2 (tptp.power_power_rat X))) (let ((_let_3 (tptp.groups2906978787729119204at_rat _let_2 (tptp.set_or1269000886237332187st_nat M (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) N))))) (let ((_let_4 (= X tptp.one_one_rat))) (and (=> _let_4 (= _let_3 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat N)) tptp.one_one_rat))) (=> (not _let_4) (= _let_3 (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat _let_2 M)) (tptp.aa_rat_rat _let_1 (tptp.aa_nat_rat _let_2 (tptp.aa_nat_nat tptp.suc N))))) (tptp.aa_rat_rat _let_1 X)))))))))) (forall ((X tptp.real) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real tptp.one_one_real))) (let ((_let_2 (tptp.aa_real_fun_nat_real tptp.power_power_real X))) (let ((_let_3 (tptp.groups6591440286371151544t_real _let_2 (tptp.set_or1269000886237332187st_nat M (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) N))))) (let ((_let_4 (= X tptp.one_one_real))) (and (=> _let_4 (= _let_3 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N)) tptp.one_one_real))) (=> (not _let_4) (= _let_3 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real _let_2 M)) (tptp.aa_real_real _let_1 (tptp.aa_nat_real _let_2 (tptp.aa_nat_nat tptp.suc N))))) (tptp.aa_real_real _let_1 X)))))))))) (forall ((N tptp.nat)) (let ((_let_1 (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N))) (= (tptp.groups3539618377306564664at_int tptp.semiri1314217659103216013at_int (tptp.set_or1269000886237332187st_nat (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat) N)) (tptp.aa_int_int (tptp.divide_divide_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int _let_1) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int _let_1) tptp.one_one_int))) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one)))))) (forall ((N tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat N))) (= (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat tptp.semiri1316708129612266289at_nat) (tptp.set_or1269000886237332187st_nat (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat) N)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat _let_1) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat _let_1) tptp.one_one_nat))) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))))) (forall ((N tptp.nat)) (let ((_let_1 (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex N))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.zero_zero_complex)) (=> (not _let_2) (= _let_1 (tptp.produc1917071388513777916omplex tptp.aTP_Lamm_je (tptp.divmod_nat N (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))))))))) (forall ((N tptp.nat)) (let ((_let_1 (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat N))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.zero_zero_rat)) (=> (not _let_2) (= _let_1 (tptp.produc6207742614233964070at_rat tptp.aTP_Lamm_jf (tptp.divmod_nat N (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))))))))) (forall ((N tptp.nat)) (let ((_let_1 (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.zero_zero_int)) (=> (not _let_2) (= _let_1 (tptp.aa_Pro4240683299535347697at_int (tptp.produc6840382203811409530at_int tptp.aTP_Lamm_jg) (tptp.divmod_nat N (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))))))))) (forall ((N tptp.nat)) (let ((_let_1 (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.zero_zero_real)) (=> (not _let_2) (= _let_1 (tptp.aa_Pro6168199777849092593t_real (tptp.produc1703576794950452218t_real tptp.aTP_Lamm_jh) (tptp.divmod_nat N (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))))))))) (forall ((N tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat N))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.zero_zero_nat)) (=> (not _let_2) (= _let_1 (tptp.aa_Pro4243173770044397973at_nat (tptp.produc6842872674320459806at_nat tptp.aTP_Lamm_ji) (tptp.divmod_nat N (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))))))))) (forall ((E tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) E)) (not (forall ((N2 tptp.nat)) (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.divide_divide_rat tptp.one_one_rat) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat (tptp.aa_nat_nat tptp.suc N2)))) E))))))) (forall ((E tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) E)) (not (forall ((N2 tptp.nat)) (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.one_one_real) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real (tptp.aa_nat_nat tptp.suc N2)))) E))))))) (forall ((X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real X)) tptp.one_one_real)) (tptp.topolo6980174941875973593q_real (tptp.aa_real_fun_nat_real tptp.aTP_Lamm_jj X)))) (forall ((H tptp.real) (Z tptp.real) (K5 tptp.real) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N))) (let ((_let_2 (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)))) (let ((_let_3 (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N)))) (let ((_let_4 (tptp.aa_real_fun_nat_real tptp.power_power_real Z))) (let ((_let_5 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real Z) H))) (=> (not (= H tptp.zero_zero_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real Z)) K5)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real _let_5)) K5)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real _let_5) N)) (tptp.aa_nat_real _let_4 N))) H)) (tptp.aa_real_real _let_3 (tptp.aa_nat_real _let_4 _let_2))))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real _let_3 (tptp.aa_nat_real tptp.semiri5074537144036343181t_real _let_2))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real K5) (tptp.aa_nat_nat _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))))) (tptp.aa_real_real tptp.real_V7735802525324610683m_real H))))))))))))) (forall ((H tptp.complex) (Z tptp.complex) (K5 tptp.real) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N))) (let ((_let_2 (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)))) (let ((_let_3 (tptp.power_power_complex Z))) (let ((_let_4 (tptp.aa_complex_complex (tptp.plus_plus_complex Z) H))) (=> (not (= H tptp.zero_zero_complex)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex Z)) K5)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex _let_4)) K5)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.aa_complex_complex (tptp.minus_minus_complex (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex (tptp.aa_complex_complex (tptp.minus_minus_complex (tptp.aa_nat_complex (tptp.power_power_complex _let_4) N)) (tptp.aa_nat_complex _let_3 N))) H)) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex N)) (tptp.aa_nat_complex _let_3 _let_2))))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N)) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real _let_2))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real K5) (tptp.aa_nat_nat _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))))) (tptp.aa_complex_real tptp.real_V1022390504157884413omplex H)))))))))))) (forall ((X tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) X)) (exists ((N2 tptp.nat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Y) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat N2)) X)))))) (forall ((X tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) X)) (exists ((N2 tptp.nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N2)) X)))))) (forall ((X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.aa_real_real tptp.ln_ln_real X) (tptp.suminf_real (tptp.aa_real_fun_nat_real tptp.aTP_Lamm_jk X)))))) (forall ((F tptp.fun_nat_complex)) (= (tptp.suminf_complex (tptp.aTP_Lamm_gy F)) (tptp.aa_nat_complex F tptp.zero_zero_nat))) (forall ((F tptp.fun_nat_real)) (= (tptp.suminf_real (tptp.aTP_Lamm_ha F)) (tptp.aa_nat_real F tptp.zero_zero_nat))) (forall ((P tptp.bool) (A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.if_nat P) A) B2)))) (let ((_let_2 (tptp.pp P))) (and (=> _let_2 (= _let_1 (tptp.aa_nat_int tptp.semiri1314217659103216013at_int A))) (=> (not _let_2) (= _let_1 (tptp.aa_nat_int tptp.semiri1314217659103216013at_int B2))))))) (forall ((A tptp.nat) (B2 tptp.nat)) (= (= A B2) (= (tptp.aa_nat_int tptp.semiri1314217659103216013at_int A) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int B2)))) (forall ((X tptp.complex)) (let ((_let_1 (tptp.aa_complex_real tptp.real_V1022390504157884413omplex X))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real _let_1)) _let_1)))) (forall ((B2 tptp.complex) (A tptp.complex)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.aa_complex_complex (tptp.plus_plus_complex B2) A))) (tptp.aa_complex_real tptp.real_V1022390504157884413omplex B2))) (tptp.aa_complex_real tptp.real_V1022390504157884413omplex A)))) (forall ((X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) tptp.one_one_real)) (tptp.topolo6980174941875973593q_real (tptp.aa_real_fun_nat_real tptp.power_power_real X))))) (forall ((X tptp.real)) (exists ((N2 tptp.nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N2))))) (forall ((X tptp.rat)) (exists ((N2 tptp.nat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat N2))))) (forall ((X tptp.rat)) (exists ((N2 tptp.nat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat N2))))) (forall ((X tptp.real)) (exists ((N2 tptp.nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N2))))) (forall ((X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real X)) tptp.one_one_real)) (= (tptp.aa_real_real tptp.arctan X) (tptp.suminf_real (tptp.aa_real_fun_nat_real tptp.aTP_Lamm_jl X))))) (forall ((A tptp.real) (W tptp.num)) (let ((_let_1 (tptp.aa_num_real tptp.numeral_numeral_real W))) (= (tptp.aa_real_real tptp.real_V7735802525324610683m_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real A) _let_1)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real A)) _let_1)))) (forall ((A tptp.complex) (W tptp.num)) (= (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex A) (tptp.numera6690914467698888265omplex W))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex A)) (tptp.aa_num_real tptp.numeral_numeral_real W)))) (forall ((W tptp.num) (A tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_num_real tptp.numeral_numeral_real W)))) (= (tptp.aa_real_real tptp.real_V7735802525324610683m_real (tptp.aa_real_real _let_1 A)) (tptp.aa_real_real _let_1 (tptp.aa_real_real tptp.real_V7735802525324610683m_real A))))) (forall ((W tptp.num) (A tptp.complex)) (= (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.aa_complex_complex (tptp.times_times_complex (tptp.numera6690914467698888265omplex W)) A)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_num_real tptp.numeral_numeral_real W)) (tptp.aa_complex_real tptp.real_V1022390504157884413omplex A)))) (forall ((A tptp.real) (W tptp.num)) (let ((_let_1 (tptp.aa_num_real tptp.numeral_numeral_real W))) (= (tptp.aa_real_real tptp.real_V7735802525324610683m_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) _let_1)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real A)) _let_1)))) (forall ((A tptp.complex) (W tptp.num)) (= (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.aa_complex_complex (tptp.times_times_complex A) (tptp.numera6690914467698888265omplex W))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex A)) (tptp.aa_num_real tptp.numeral_numeral_real W)))) (forall ((W tptp.num)) (let ((_let_1 (tptp.aa_num_real tptp.numeral_numeral_real W))) (= (tptp.aa_real_real tptp.real_V7735802525324610683m_real (tptp.aa_real_real tptp.uminus_uminus_real _let_1)) _let_1))) (forall ((W tptp.num)) (= (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.numera6690914467698888265omplex W))) (tptp.aa_num_real tptp.numeral_numeral_real W))) (forall ((X tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real X)) tptp.zero_zero_real)) (= X tptp.zero_zero_real))) (forall ((X tptp.complex)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex X)) tptp.zero_zero_real)) (= X tptp.zero_zero_complex))) (forall ((X tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) (tptp.aa_real_real tptp.real_V7735802525324610683m_real X))) (not (= X tptp.zero_zero_real)))) (forall ((X tptp.complex)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) (tptp.aa_complex_real tptp.real_V1022390504157884413omplex X))) (not (= X tptp.zero_zero_complex)))) (forall ((W tptp.num)) (let ((_let_1 (tptp.aa_num_real tptp.numeral_numeral_real W))) (= (tptp.aa_real_real tptp.real_V7735802525324610683m_real _let_1) _let_1))) (forall ((W tptp.num)) (= (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.numera6690914467698888265omplex W)) (tptp.aa_num_real tptp.numeral_numeral_real W))) (forall ((A tptp.real) (B2 tptp.real)) (= (tptp.aa_real_real tptp.real_V7735802525324610683m_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A) B2)) (tptp.aa_real_real tptp.real_V7735802525324610683m_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real B2) A)))) (forall ((A tptp.complex) (B2 tptp.complex)) (= (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.aa_complex_complex (tptp.minus_minus_complex A) B2)) (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.aa_complex_complex (tptp.minus_minus_complex B2) A)))) (forall ((X tptp.complex)) (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex X)) tptp.zero_zero_real)))) (forall ((X tptp.complex)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_complex_real tptp.real_V1022390504157884413omplex X)))) (forall ((X tptp.real) (Y tptp.real)) (= (tptp.aa_real_real tptp.real_V7735802525324610683m_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real X) Y)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real X)) (tptp.aa_real_real tptp.real_V7735802525324610683m_real Y)))) (forall ((X tptp.complex) (Y tptp.complex)) (= (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.aa_complex_complex (tptp.times_times_complex X) Y)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex X)) (tptp.aa_complex_real tptp.real_V1022390504157884413omplex Y)))) (forall ((S2 tptp.set_real) (F tptp.fun_real_complex) (G tptp.fun_real_real)) (=> (forall ((X4 tptp.real)) (=> (tptp.member_real X4 S2) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.aa_real_complex F X4))) (tptp.aa_real_real G X4))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.groups5754745047067104278omplex F S2))) (tptp.groups8097168146408367636l_real G S2))))) (forall ((S2 tptp.set_int) (F tptp.fun_int_complex) (G tptp.fun_int_real)) (=> (forall ((X4 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X4) S2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.aa_int_complex F X4))) (tptp.aa_int_real G X4))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.groups3049146728041665814omplex F S2))) (tptp.groups8778361861064173332t_real G S2))))) (forall ((S2 tptp.set_nat) (F tptp.fun_nat_complex) (G tptp.fun_nat_real)) (=> (forall ((X4 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X4) S2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.aa_nat_complex F X4))) (tptp.aa_nat_real G X4))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.groups2073611262835488442omplex F S2))) (tptp.groups6591440286371151544t_real G S2))))) (forall ((S2 tptp.set_complex) (F tptp.fun_complex_complex) (G tptp.fun_complex_real)) (=> (forall ((X4 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex X4) S2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.aa_complex_complex F X4))) (tptp.aa_complex_real G X4))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.groups7754918857620584856omplex F S2))) (tptp.groups5808333547571424918x_real G S2))))) (forall ((S2 tptp.set_nat) (F tptp.fun_nat_real) (G tptp.fun_nat_real)) (=> (forall ((X4 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X4) S2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real (tptp.aa_nat_real F X4))) (tptp.aa_nat_real G X4))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real (tptp.groups6591440286371151544t_real F S2))) (tptp.groups6591440286371151544t_real G S2))))) (forall ((A tptp.real) (B2 tptp.real)) (= (tptp.aa_real_real tptp.real_V7735802525324610683m_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real A) B2)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real A)) (tptp.aa_real_real tptp.real_V7735802525324610683m_real B2)))) (forall ((A tptp.complex) (B2 tptp.complex)) (= (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex A) B2)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex A)) (tptp.aa_complex_real tptp.real_V1022390504157884413omplex B2)))) (forall ((X tptp.real) (N tptp.nat)) (= (tptp.aa_real_real tptp.real_V7735802525324610683m_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) N)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real X)) N))) (forall ((X tptp.complex) (N tptp.nat)) (= (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.aa_nat_complex (tptp.power_power_complex X) N)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex X)) N))) (forall ((F tptp.fun_nat_complex) (A4 tptp.set_nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.groups2073611262835488442omplex F A4))) (tptp.groups6591440286371151544t_real (tptp.aTP_Lamm_jm F) A4)))) (forall ((F tptp.fun_complex_complex) (A4 tptp.set_complex)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.groups7754918857620584856omplex F A4))) (tptp.groups5808333547571424918x_real (tptp.aTP_Lamm_jn F) A4)))) (forall ((F tptp.fun_nat_real) (A4 tptp.set_nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real (tptp.groups6591440286371151544t_real F A4))) (tptp.groups6591440286371151544t_real (tptp.aTP_Lamm_jo F) A4)))) (forall ((X tptp.real) (Y tptp.real)) (= (tptp.aa_real_real tptp.real_V7735802525324610683m_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real tptp.uminus_uminus_real X)) Y)) (tptp.aa_real_real tptp.real_V7735802525324610683m_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) Y)))) (forall ((X tptp.complex) (Y tptp.complex)) (= (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.aa_complex_complex (tptp.minus_minus_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex X)) Y)) (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.aa_complex_complex (tptp.plus_plus_complex X) Y)))) (forall ((B2 tptp.real) (A tptp.real)) (=> (not (= B2 tptp.zero_zero_real)) (= (tptp.aa_real_real tptp.real_V7735802525324610683m_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real A) B2)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real A)) (tptp.aa_real_real tptp.real_V7735802525324610683m_real B2))))) (forall ((B2 tptp.complex) (A tptp.complex)) (=> (not (= B2 tptp.zero_zero_complex)) (= (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex A) B2)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex A)) (tptp.aa_complex_real tptp.real_V1022390504157884413omplex B2))))) (forall ((W tptp.real) (N tptp.nat) (Z tptp.real)) (=> (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real W) N) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Z) N)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (= (tptp.aa_real_real tptp.real_V7735802525324610683m_real W) (tptp.aa_real_real tptp.real_V7735802525324610683m_real Z))))) (forall ((W tptp.complex) (N tptp.nat) (Z tptp.complex)) (=> (= (tptp.aa_nat_complex (tptp.power_power_complex W) N) (tptp.aa_nat_complex (tptp.power_power_complex Z) N)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (= (tptp.aa_complex_real tptp.real_V1022390504157884413omplex W) (tptp.aa_complex_real tptp.real_V1022390504157884413omplex Z))))) (forall ((X tptp.real) (R tptp.real) (Y tptp.real) (S tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real X)) R)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real Y)) S)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real X) Y))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real R) S)))))) (forall ((X tptp.complex) (R tptp.real) (Y tptp.complex) (S tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex X)) R)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex Y)) S)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.aa_complex_complex (tptp.times_times_complex X) Y))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real R) S)))))) (forall ((X tptp.real) (Y tptp.real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real X) Y))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real X)) (tptp.aa_real_real tptp.real_V7735802525324610683m_real Y))))) (forall ((X tptp.complex) (Y tptp.complex)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.aa_complex_complex (tptp.times_times_complex X) Y))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex X)) (tptp.aa_complex_real tptp.real_V1022390504157884413omplex Y))))) (forall ((X tptp.real) (Y tptp.real) (E tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real X)) (tptp.aa_real_real tptp.real_V7735802525324610683m_real Y))) E)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) Y))) E)))) (forall ((X tptp.complex) (Y tptp.complex) (E tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex X)) (tptp.aa_complex_real tptp.real_V1022390504157884413omplex Y))) E)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.aa_complex_complex (tptp.plus_plus_complex X) Y))) E)))) (forall ((X tptp.real) (R tptp.real) (Y tptp.real) (S tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real X)) R)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real Y)) S)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) Y))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real R) S)))))) (forall ((X tptp.complex) (R tptp.real) (Y tptp.complex) (S tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex X)) R)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex Y)) S)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.aa_complex_complex (tptp.plus_plus_complex X) Y))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real R) S)))))) (forall ((X tptp.real) (N tptp.nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) N))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real X)) N)))) (forall ((X tptp.complex) (N tptp.nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.aa_nat_complex (tptp.power_power_complex X) N))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex X)) N)))) (forall ((A tptp.real) (R tptp.real) (B2 tptp.real) (S tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real A)) R)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real B2)) S)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) B2))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real R) S)))))) (forall ((A tptp.complex) (R tptp.real) (B2 tptp.complex) (S tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex A)) R)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex B2)) S)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.aa_complex_complex (tptp.plus_plus_complex A) B2))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real R) S)))))) (forall ((X tptp.real) (Y tptp.real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) Y))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real X)) (tptp.aa_real_real tptp.real_V7735802525324610683m_real Y))))) (forall ((X tptp.complex) (Y tptp.complex)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.aa_complex_complex (tptp.plus_plus_complex X) Y))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex X)) (tptp.aa_complex_real tptp.real_V1022390504157884413omplex Y))))) (forall ((X tptp.real) (Y tptp.real) (E tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real X)) (tptp.aa_real_real tptp.real_V7735802525324610683m_real Y))) E)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) Y))) E)))) (forall ((X tptp.complex) (Y tptp.complex) (E tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex X)) (tptp.aa_complex_real tptp.real_V1022390504157884413omplex Y))) E)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.aa_complex_complex (tptp.plus_plus_complex X) Y))) E)))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) B2))) C)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real B2)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real A)) C))))) (forall ((A tptp.complex) (B2 tptp.complex) (C tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.aa_complex_complex (tptp.plus_plus_complex A) B2))) C)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex B2)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex A)) C))))) (forall ((X tptp.real) (Y tptp.real) (E1 tptp.real) (Z tptp.real) (E22 tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real X))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real (tptp.aa_real_real _let_1 Y))) E1)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real Y) Z))) E22)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real (tptp.aa_real_real _let_1 Z))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real E1) E22))))))) (forall ((X tptp.complex) (Y tptp.complex) (E1 tptp.real) (Z tptp.complex) (E22 tptp.real)) (let ((_let_1 (tptp.minus_minus_complex X))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.aa_complex_complex _let_1 Y))) E1)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.aa_complex_complex (tptp.minus_minus_complex Y) Z))) E22)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.aa_complex_complex _let_1 Z))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real E1) E22))))))) (forall ((X tptp.real) (Y tptp.real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real X)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real Y)) (tptp.aa_real_real tptp.real_V7735802525324610683m_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real X) Y)))))) (forall ((X tptp.complex) (Y tptp.complex)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex X)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex Y)) (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.aa_complex_complex (tptp.minus_minus_complex X) Y)))))) (forall ((A tptp.real) (B2 tptp.real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A) B2))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real A)) (tptp.aa_real_real tptp.real_V7735802525324610683m_real B2))))) (forall ((A tptp.complex) (B2 tptp.complex)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.aa_complex_complex (tptp.minus_minus_complex A) B2))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex A)) (tptp.aa_complex_real tptp.real_V1022390504157884413omplex B2))))) (forall ((X tptp.real) (Y tptp.real) (E1 tptp.real) (Z tptp.real) (E22 tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real X))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real (tptp.aa_real_real _let_1 Y))) E1)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real Y) Z))) E22)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real (tptp.aa_real_real _let_1 Z))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real E1) E22))))))) (forall ((X tptp.complex) (Y tptp.complex) (E1 tptp.real) (Z tptp.complex) (E22 tptp.real)) (let ((_let_1 (tptp.minus_minus_complex X))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.aa_complex_complex _let_1 Y))) E1)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.aa_complex_complex (tptp.minus_minus_complex Y) Z))) E22)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.aa_complex_complex _let_1 Z))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real E1) E22))))))) (forall ((X tptp.real) (Y tptp.real) (E tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real X)) (tptp.aa_real_real tptp.real_V7735802525324610683m_real Y))) E)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real X) Y))) E)))) (forall ((X tptp.complex) (Y tptp.complex) (E tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex X)) (tptp.aa_complex_real tptp.real_V1022390504157884413omplex Y))) E)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.aa_complex_complex (tptp.minus_minus_complex X) Y))) E)))) (forall ((A tptp.real) (B2 tptp.real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real A)) (tptp.aa_real_real tptp.real_V7735802525324610683m_real B2))) (tptp.aa_real_real tptp.real_V7735802525324610683m_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) B2))))) (forall ((A tptp.complex) (B2 tptp.complex)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex A)) (tptp.aa_complex_real tptp.real_V1022390504157884413omplex B2))) (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.aa_complex_complex (tptp.plus_plus_complex A) B2))))) (forall ((A tptp.real) (B2 tptp.real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real A)) (tptp.aa_real_real tptp.real_V7735802525324610683m_real B2))) (tptp.aa_real_real tptp.real_V7735802525324610683m_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A) B2))))) (forall ((A tptp.complex) (B2 tptp.complex)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex A)) (tptp.aa_complex_real tptp.real_V1022390504157884413omplex B2))) (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.aa_complex_complex (tptp.minus_minus_complex A) B2))))) (forall ((W tptp.real) (N tptp.nat)) (=> (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real W) N) tptp.one_one_real) (or (= (tptp.aa_real_real tptp.real_V7735802525324610683m_real W) tptp.one_one_real) (= N tptp.zero_zero_nat)))) (forall ((W tptp.complex) (N tptp.nat)) (=> (= (tptp.aa_nat_complex (tptp.power_power_complex W) N) tptp.one_one_complex) (or (= (tptp.aa_complex_real tptp.real_V1022390504157884413omplex W) tptp.one_one_real) (= N tptp.zero_zero_nat)))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real) (D tptp.real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) B2)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real C) D)))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A) C))) (tptp.aa_real_real tptp.real_V7735802525324610683m_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real B2) D)))))) (forall ((A tptp.complex) (B2 tptp.complex) (C tptp.complex) (D tptp.complex)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.aa_complex_complex (tptp.minus_minus_complex (tptp.aa_complex_complex (tptp.plus_plus_complex A) B2)) (tptp.aa_complex_complex (tptp.plus_plus_complex C) D)))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.aa_complex_complex (tptp.minus_minus_complex A) C))) (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.aa_complex_complex (tptp.minus_minus_complex B2) D)))))) (forall ((A tptp.real) (B2 tptp.real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real A)) (tptp.aa_real_real tptp.real_V7735802525324610683m_real B2)))) (tptp.aa_real_real tptp.real_V7735802525324610683m_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A) B2))))) (forall ((A tptp.complex) (B2 tptp.complex)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex A)) (tptp.aa_complex_real tptp.real_V1022390504157884413omplex B2)))) (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.aa_complex_complex (tptp.minus_minus_complex A) B2))))) (forall ((X tptp.real)) (=> (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) tptp.one_one_real) (= (tptp.aa_real_real tptp.real_V7735802525324610683m_real X) tptp.one_one_real))) (forall ((X tptp.complex)) (=> (= (tptp.aa_nat_complex (tptp.power_power_complex X) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) tptp.one_one_complex) (= (tptp.aa_complex_real tptp.real_V1022390504157884413omplex X) tptp.one_one_real))) (forall ((Z tptp.real) (W tptp.real) (M tptp.nat)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real Z)) tptp.one_one_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real W)) tptp.one_one_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Z) M)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real W) M)))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real M)) (tptp.aa_real_real tptp.real_V7735802525324610683m_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real Z) W)))))))) (forall ((Z tptp.complex) (W tptp.complex) (M tptp.nat)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex Z)) tptp.one_one_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex W)) tptp.one_one_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.aa_complex_complex (tptp.minus_minus_complex (tptp.aa_nat_complex (tptp.power_power_complex Z) M)) (tptp.aa_nat_complex (tptp.power_power_complex W) M)))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real M)) (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.aa_complex_complex (tptp.minus_minus_complex Z) W)))))))) (forall ((C tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real C)) tptp.one_one_real)) (= (tptp.suminf_real (tptp.aa_real_fun_nat_real tptp.power_power_real C)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.one_one_real) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real tptp.one_one_real) C))))) (forall ((C tptp.complex)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex C)) tptp.one_one_real)) (= (tptp.suminf_complex (tptp.power_power_complex C)) (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex tptp.one_one_complex) (tptp.aa_complex_complex (tptp.minus_minus_complex tptp.one_one_complex) C))))) (= _let_67 (tptp.suminf_real tptp.aTP_Lamm_jp)) (forall ((H tptp.complex) (Z tptp.complex) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)))) (let ((_let_2 (tptp.power_power_complex Z))) (=> (not (= H tptp.zero_zero_complex)) (= (tptp.aa_complex_complex (tptp.minus_minus_complex (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex (tptp.aa_complex_complex (tptp.minus_minus_complex (tptp.aa_nat_complex (tptp.power_power_complex (tptp.aa_complex_complex (tptp.plus_plus_complex Z) H)) N)) (tptp.aa_nat_complex _let_2 N))) H)) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex N)) (tptp.aa_nat_complex _let_2 _let_1))) (tptp.aa_complex_complex (tptp.times_times_complex H) (tptp.groups2073611262835488442omplex (tptp.aa_nat6454746962644518025omplex (tptp.aa_com4347742694490471604omplex (tptp.aTP_Lamm_jr H) Z) N) (tptp.set_ord_lessThan_nat _let_1)))))))) (forall ((H tptp.rat) (Z tptp.rat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)))) (let ((_let_2 (tptp.power_power_rat Z))) (=> (not (= H tptp.zero_zero_rat)) (= (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat Z) H)) N)) (tptp.aa_nat_rat _let_2 N))) H)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat N)) (tptp.aa_nat_rat _let_2 _let_1))) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat H) (tptp.groups2906978787729119204at_rat (tptp.aa_nat_fun_nat_rat (tptp.aa_rat250263598611652360at_rat (tptp.aTP_Lamm_jt H) Z) N) (tptp.set_ord_lessThan_nat _let_1)))))))) (forall ((H tptp.real) (Z tptp.real) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)))) (let ((_let_2 (tptp.aa_real_fun_nat_real tptp.power_power_real Z))) (=> (not (= H tptp.zero_zero_real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real Z) H)) N)) (tptp.aa_nat_real _let_2 N))) H)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N)) (tptp.aa_nat_real _let_2 _let_1))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real H) (tptp.groups6591440286371151544t_real (tptp.aa_nat_fun_nat_real (tptp.aa_rea6853821027689443120t_real (tptp.aTP_Lamm_jv H) Z) N) (tptp.set_ord_lessThan_nat _let_1)))))))) (forall ((X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real X)) tptp.one_one_real)) (tptp.summable_real (tptp.aa_real_fun_nat_real tptp.aTP_Lamm_jl X)))) (forall ((R2 tptp.set_Pr958786334691620121nt_int) (S2 tptp.set_Pr958786334691620121nt_int)) (= (tptp.ord_le4546832483993983377t_bool (tptp.aTP_Lamm_jw R2) (tptp.aTP_Lamm_jw S2)) (tptp.ord_le2843351958646193337nt_int R2 S2))) (forall ((R2 tptp.set_Pr7592006421409863191nteger) (S2 tptp.set_Pr7592006421409863191nteger)) (= (tptp.ord_le7456723041722595787r_bool (tptp.aTP_Lamm_jx R2) (tptp.aTP_Lamm_jx S2)) (tptp.ord_le5347933966117430903nteger R2 S2))) (forall ((R2 tptp.set_Pr5663546166630115725nteger) (S2 tptp.set_Pr5663546166630115725nteger)) (= (tptp.ord_le1120571524945282261r_bool (tptp.aTP_Lamm_jy R2) (tptp.aTP_Lamm_jy S2)) (tptp.ord_le3337582088779512301nteger R2 S2))) (forall ((R2 tptp.set_Pr233528076387193594nt_int) (S2 tptp.set_Pr233528076387193594nt_int)) (= (tptp.ord_le1486933126236225064t_bool (tptp.aTP_Lamm_jz R2) (tptp.aTP_Lamm_jz S2)) (tptp.ord_le5172437211506631514nt_int R2 S2))) (forall ((R2 tptp.set_Pr5033440245338114598nt_int) (S2 tptp.set_Pr5033440245338114598nt_int)) (= (tptp.ord_le4148652360786930684t_bool (tptp.aTP_Lamm_ka R2) (tptp.aTP_Lamm_ka S2)) (tptp.ord_le172202941055982214nt_int R2 S2))) (forall ((S2 tptp.set_int)) (= (not (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int S2))) (forall ((M6 tptp.int)) (exists ((N5 tptp.int)) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int M6) (tptp.aa_int_int tptp.abs_abs_int N5))) (tptp.pp (tptp.aa_set_int_bool (tptp.member_int N5) S2))))))) (forall ((I tptp.rat) (K tptp.rat)) (= (tptp.member_rat I (tptp.set_ord_lessThan_rat K)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat I) K)))) (forall ((I tptp.num) (K tptp.num)) (= (tptp.member_num I (tptp.set_ord_lessThan_num K)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num I) K)))) (forall ((I tptp.nat) (K tptp.nat)) (= (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat I) (tptp.set_ord_lessThan_nat K))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I) K)))) (forall ((I tptp.int) (K tptp.int)) (= (tptp.pp (tptp.aa_set_int_bool (tptp.member_int I) (tptp.set_ord_lessThan_int K))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int I) K)))) (forall ((I tptp.real) (K tptp.real)) (= (tptp.member_real I (tptp.set_or5984915006950818249n_real K)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real I) K)))) (forall ((F tptp.fun_nat_real) (K tptp.nat)) (= (tptp.summable_real (tptp.aa_nat_fun_nat_real (tptp.aTP_Lamm_hm F) K)) (tptp.summable_real F))) (forall ((X tptp.rat) (Y tptp.rat)) (= (tptp.ord_less_eq_set_rat (tptp.set_ord_lessThan_rat X) (tptp.set_ord_lessThan_rat Y)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) Y)))) (forall ((X tptp.num) (Y tptp.num)) (= (tptp.ord_less_eq_set_num (tptp.set_ord_lessThan_num X) (tptp.set_ord_lessThan_num Y)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X) Y)))) (forall ((X tptp.nat) (Y tptp.nat)) (= (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat (tptp.set_ord_lessThan_nat X)) (tptp.set_ord_lessThan_nat Y))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X) Y)))) (forall ((X tptp.int) (Y tptp.int)) (= (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int (tptp.set_ord_lessThan_int X)) (tptp.set_ord_lessThan_int Y))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X) Y)))) (forall ((X tptp.real) (Y tptp.real)) (= (tptp.ord_less_eq_set_real (tptp.set_or5984915006950818249n_real X) (tptp.set_or5984915006950818249n_real Y)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) Y)))) (forall ((C tptp.complex) (F tptp.fun_nat_complex)) (= (tptp.summable_complex (tptp.aa_fun2955221450537884980omplex (tptp.aTP_Lamm_kb C) F)) (or (= C tptp.zero_zero_complex) (tptp.summable_complex F)))) (forall ((C tptp.real) (F tptp.fun_nat_real)) (= (tptp.summable_real (tptp.aa_fun1839206346889086768t_real (tptp.aTP_Lamm_gc C) F)) (or (= C tptp.zero_zero_real) (tptp.summable_real F)))) (forall ((F tptp.fun_nat_complex) (C tptp.complex)) (= (tptp.summable_complex (tptp.aa_com8181001469867462503omplex (tptp.aTP_Lamm_kc F) C)) (or (= C tptp.zero_zero_complex) (tptp.summable_complex F)))) (forall ((F tptp.fun_nat_real) (C tptp.real)) (= (tptp.summable_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_gl F) C)) (or (= C tptp.zero_zero_real) (tptp.summable_real F)))) (forall ((G tptp.fun_nat_rat) (N tptp.nat)) (= (tptp.groups2906978787729119204at_rat G (tptp.set_ord_lessThan_nat (tptp.aa_nat_nat tptp.suc N))) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.groups2906978787729119204at_rat G (tptp.set_ord_lessThan_nat N))) (tptp.aa_nat_rat G N)))) (forall ((G tptp.fun_nat_int) (N tptp.nat)) (= (tptp.groups3539618377306564664at_int G (tptp.set_ord_lessThan_nat (tptp.aa_nat_nat tptp.suc N))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.groups3539618377306564664at_int G (tptp.set_ord_lessThan_nat N))) (tptp.aa_nat_int G N)))) (forall ((G tptp.fun_nat_nat) (N tptp.nat)) (let ((_let_1 (tptp.groups3542108847815614940at_nat G))) (= (tptp.aa_set_nat_nat _let_1 (tptp.set_ord_lessThan_nat (tptp.aa_nat_nat tptp.suc N))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_set_nat_nat _let_1 (tptp.set_ord_lessThan_nat N))) (tptp.aa_nat_nat G N))))) (forall ((G tptp.fun_nat_real) (N tptp.nat)) (= (tptp.groups6591440286371151544t_real G (tptp.set_ord_lessThan_nat (tptp.aa_nat_nat tptp.suc N))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.groups6591440286371151544t_real G (tptp.set_ord_lessThan_nat N))) (tptp.aa_nat_real G N)))) (forall ((C tptp.real)) (= (tptp.summable_real (tptp.aa_real_fun_nat_real tptp.power_power_real C)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real C)) tptp.one_one_real)))) (forall ((C tptp.complex)) (= (tptp.summable_complex (tptp.power_power_complex C)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex C)) tptp.one_one_real)))) (forall ((G tptp.fun_nat_real) (N3 tptp.nat) (F tptp.fun_nat_real)) (=> (tptp.summable_real G) (=> (forall ((N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N3) N2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real (tptp.aa_nat_real F N2))) (tptp.aa_nat_real G N2))))) (tptp.summable_real F)))) (forall ((G tptp.fun_nat_real) (N3 tptp.nat) (F tptp.fun_nat_complex)) (=> (tptp.summable_real G) (=> (forall ((N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N3) N2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.aa_nat_complex F N2))) (tptp.aa_nat_real G N2))))) (tptp.summable_complex F)))) (forall ((F tptp.fun_nat_real) (G tptp.fun_nat_real)) (=> (exists ((N6 tptp.nat)) (forall ((N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N6) N2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real (tptp.aa_nat_real F N2))) (tptp.aa_nat_real G N2)))))) (=> (tptp.summable_real G) (tptp.summable_real F)))) (forall ((F tptp.fun_nat_complex) (G tptp.fun_nat_real)) (=> (exists ((N6 tptp.nat)) (forall ((N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N6) N2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.aa_nat_complex F N2))) (tptp.aa_nat_real G N2)))))) (=> (tptp.summable_real G) (tptp.summable_complex F)))) (forall ((F tptp.fun_nat_real) (K tptp.nat)) (=> (tptp.summable_real F) (tptp.summable_real (tptp.aa_nat_fun_nat_real (tptp.aTP_Lamm_hm F) K)))) (forall ((F tptp.fun_nat_real) (G tptp.fun_nat_real)) (=> (tptp.summable_real F) (=> (tptp.summable_real G) (tptp.summable_real (tptp.aa_fun1839206346889086768t_real (tptp.aTP_Lamm_gg F) G))))) (forall ((F tptp.fun_nat_nat) (G tptp.fun_nat_nat)) (=> (tptp.summable_nat F) (=> (tptp.summable_nat G) (tptp.summable_nat (tptp.aa_fun5791449513213591928at_nat (tptp.aTP_Lamm_gf F) G))))) (forall ((F tptp.fun_nat_int) (G tptp.fun_nat_int)) (=> (tptp.summable_int F) (=> (tptp.summable_int G) (tptp.summable_int (tptp.aa_fun5565043122120104496at_int (tptp.aTP_Lamm_kd F) G))))) (forall ((F tptp.fun_nat_complex) (G tptp.fun_nat_complex)) (=> (tptp.summable_complex F) (=> (tptp.summable_complex G) (tptp.summable_complex (tptp.aa_fun2955221450537884980omplex (tptp.aTP_Lamm_ke F) G))))) (forall ((F tptp.fun_nat_real) (G tptp.fun_nat_real)) (=> (tptp.summable_real F) (=> (tptp.summable_real G) (tptp.summable_real (tptp.aa_fun1839206346889086768t_real (tptp.aTP_Lamm_gj F) G))))) (forall ((F tptp.fun_nat_complex) (C tptp.complex)) (=> (tptp.summable_complex F) (tptp.summable_complex (tptp.aa_com8181001469867462503omplex (tptp.aTP_Lamm_kc F) C)))) (forall ((F tptp.fun_nat_real) (C tptp.real)) (=> (tptp.summable_real F) (tptp.summable_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_gl F) C)))) (forall ((F tptp.fun_nat_real) (C tptp.real)) (=> (tptp.summable_real F) (tptp.summable_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_fy F) C)))) (forall ((F tptp.fun_nat_real) (C tptp.real)) (=> (tptp.summable_real F) (tptp.summable_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_kf F) C)))) (forall ((F tptp.fun_nat_int) (X tptp.int)) (=> (tptp.summable_int F) (=> (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.groups3539618377306564664at_int F (tptp.set_ord_lessThan_nat N2))) X))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.suminf_int F)) X))))) (forall ((F tptp.fun_nat_nat) (X tptp.nat)) (=> (tptp.summable_nat F) (=> (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat F) (tptp.set_ord_lessThan_nat N2))) X))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.suminf_nat F)) X))))) (forall ((F tptp.fun_nat_real) (X tptp.real)) (=> (tptp.summable_real F) (=> (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.groups6591440286371151544t_real F (tptp.set_ord_lessThan_nat N2))) X))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.suminf_real F)) X))))) (forall ((F tptp.fun_nat_int) (X tptp.int)) (=> (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.aa_nat_int F N2)))) (=> (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.groups3539618377306564664at_int F (tptp.set_ord_lessThan_nat N2))) X))) (tptp.summable_int F)))) (forall ((F tptp.fun_nat_nat) (X tptp.nat)) (=> (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) (tptp.aa_nat_nat F N2)))) (=> (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat F) (tptp.set_ord_lessThan_nat N2))) X))) (tptp.summable_nat F)))) (forall ((F tptp.fun_nat_real) (X tptp.real)) (=> (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_nat_real F N2)))) (=> (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.groups6591440286371151544t_real F (tptp.set_ord_lessThan_nat N2))) X))) (tptp.summable_real F)))) (forall ((F tptp.fun_nat_real) (G tptp.fun_nat_real)) (=> (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_nat_real F N2)) (tptp.aa_nat_real G N2)))) (=> (tptp.summable_real F) (=> (tptp.summable_real G) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.suminf_real F)) (tptp.suminf_real G))))))) (forall ((F tptp.fun_nat_nat) (G tptp.fun_nat_nat)) (=> (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat F N2)) (tptp.aa_nat_nat G N2)))) (=> (tptp.summable_nat F) (=> (tptp.summable_nat G) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.suminf_nat F)) (tptp.suminf_nat G))))))) (forall ((F tptp.fun_nat_int) (G tptp.fun_nat_int)) (=> (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int F N2)) (tptp.aa_nat_int G N2)))) (=> (tptp.summable_int F) (=> (tptp.summable_int G) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.suminf_int F)) (tptp.suminf_int G))))))) (forall ((C tptp.complex) (F tptp.fun_nat_complex)) (=> (tptp.summable_complex (tptp.aa_fun2955221450537884980omplex (tptp.aTP_Lamm_kb C) F)) (=> (not (= C tptp.zero_zero_complex)) (tptp.summable_complex F)))) (forall ((C tptp.real) (F tptp.fun_nat_real)) (=> (tptp.summable_real (tptp.aa_fun1839206346889086768t_real (tptp.aTP_Lamm_gc C) F)) (=> (not (= C tptp.zero_zero_real)) (tptp.summable_real F)))) (tptp.summable_real _let_80) (tptp.summable_int _let_79) (tptp.summable_complex _let_78) (forall ((U tptp.rat)) (= (tptp.set_ord_lessThan_rat U) (tptp.collect_rat (tptp.aa_rat_fun_rat_bool tptp.aTP_Lamm_kg U)))) (forall ((U tptp.num)) (= (tptp.set_ord_lessThan_num U) (tptp.collect_num (tptp.aa_num_fun_num_bool tptp.aTP_Lamm_kh U)))) (forall ((U tptp.nat)) (= (tptp.set_ord_lessThan_nat U) (tptp.collect_nat (tptp.aa_nat_fun_nat_bool tptp.aTP_Lamm_br U)))) (forall ((U tptp.int)) (= (tptp.set_ord_lessThan_int U) (tptp.collect_int (tptp.aa_int_fun_int_bool tptp.aTP_Lamm_ki U)))) (forall ((U tptp.real)) (= (tptp.set_or5984915006950818249n_real U) (tptp.collect_real (tptp.aa_rea7809428808904475482l_bool tptp.aTP_Lamm_kj U)))) (forall ((F tptp.fun_nat_real) (C tptp.real)) (=> (tptp.summable_real F) (= (tptp.suminf_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_kf F) C)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real C) (tptp.suminf_real F))))) (forall ((F tptp.fun_nat_real) (C tptp.real)) (=> (tptp.summable_real F) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.suminf_real F)) C) (tptp.suminf_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_fy F) C))))) (forall ((F tptp.fun_nat_real) (G tptp.fun_nat_real)) (=> (tptp.summable_real F) (=> (tptp.summable_real G) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.suminf_real F)) (tptp.suminf_real G)) (tptp.suminf_real (tptp.aa_fun1839206346889086768t_real (tptp.aTP_Lamm_gg F) G)))))) (forall ((F tptp.fun_nat_nat) (G tptp.fun_nat_nat)) (=> (tptp.summable_nat F) (=> (tptp.summable_nat G) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.suminf_nat F)) (tptp.suminf_nat G)) (tptp.suminf_nat (tptp.aa_fun5791449513213591928at_nat (tptp.aTP_Lamm_gf F) G)))))) (forall ((F tptp.fun_nat_int) (G tptp.fun_nat_int)) (=> (tptp.summable_int F) (=> (tptp.summable_int G) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.suminf_int F)) (tptp.suminf_int G)) (tptp.suminf_int (tptp.aa_fun5565043122120104496at_int (tptp.aTP_Lamm_kd F) G)))))) (forall ((F tptp.fun_nat_complex) (G tptp.fun_nat_complex)) (=> (tptp.summable_complex F) (=> (tptp.summable_complex G) (= (tptp.aa_complex_complex (tptp.minus_minus_complex (tptp.suminf_complex F)) (tptp.suminf_complex G)) (tptp.suminf_complex (tptp.aa_fun2955221450537884980omplex (tptp.aTP_Lamm_ke F) G)))))) (forall ((F tptp.fun_nat_real) (G tptp.fun_nat_real)) (=> (tptp.summable_real F) (=> (tptp.summable_real G) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.suminf_real F)) (tptp.suminf_real G)) (tptp.suminf_real (tptp.aa_fun1839206346889086768t_real (tptp.aTP_Lamm_gj F) G)))))) (forall ((F tptp.fun_nat_complex) (C tptp.complex)) (=> (tptp.summable_complex F) (= (tptp.suminf_complex (tptp.aa_com8181001469867462503omplex (tptp.aTP_Lamm_kc F) C)) (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex (tptp.suminf_complex F)) C)))) (forall ((F tptp.fun_nat_real) (C tptp.real)) (=> (tptp.summable_real F) (= (tptp.suminf_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_gl F) C)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.suminf_real F)) C)))) (forall ((F tptp.fun_nat_real) (K tptp.nat)) (=> (tptp.summable_real F) (= (tptp.suminf_real F) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.suminf_real (tptp.aa_nat_fun_nat_real (tptp.aTP_Lamm_hm F) K))) (tptp.groups6591440286371151544t_real F (tptp.set_ord_lessThan_nat K)))))) (forall ((F tptp.fun_nat_complex) (K tptp.nat)) (=> (tptp.summable_complex F) (= (tptp.suminf_complex (tptp.aa_nat6454746962644518025omplex (tptp.aTP_Lamm_kk F) K)) (tptp.aa_complex_complex (tptp.minus_minus_complex (tptp.suminf_complex F)) (tptp.groups2073611262835488442omplex F (tptp.set_ord_lessThan_nat K)))))) (forall ((F tptp.fun_nat_real) (K tptp.nat)) (=> (tptp.summable_real F) (= (tptp.suminf_real (tptp.aa_nat_fun_nat_real (tptp.aTP_Lamm_hm F) K)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.suminf_real F)) (tptp.groups6591440286371151544t_real F (tptp.set_ord_lessThan_nat K)))))) (forall ((S2 tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat S2)) (exists ((K3 tptp.nat)) (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat S2) (tptp.set_ord_lessThan_nat K3)))))) (forall ((S2 tptp.set_nat)) (= (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat S2)) (exists ((K2 tptp.nat)) (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat S2) (tptp.set_ord_lessThan_nat K2)))))) (forall ((F tptp.fun_nat_int) (N tptp.nat)) (=> (tptp.summable_int F) (=> (forall ((M3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N) M3)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) (tptp.aa_nat_int F M3))))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.groups3539618377306564664at_int F (tptp.set_ord_lessThan_nat N))) (tptp.suminf_int F)))))) (forall ((F tptp.fun_nat_nat) (N tptp.nat)) (=> (tptp.summable_nat F) (=> (forall ((M3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N) M3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.aa_nat_nat F M3))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat F) (tptp.set_ord_lessThan_nat N))) (tptp.suminf_nat F)))))) (forall ((F tptp.fun_nat_real) (N tptp.nat)) (=> (tptp.summable_real F) (=> (forall ((M3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N) M3)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) (tptp.aa_nat_real F M3))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.groups6591440286371151544t_real F (tptp.set_ord_lessThan_nat N))) (tptp.suminf_real F)))))) (forall ((F tptp.fun_nat_real) (X tptp.real) (Z tptp.real)) (=> (tptp.summable_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_kl F) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real Z)) (tptp.aa_real_real tptp.real_V7735802525324610683m_real X))) (tptp.summable_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_km F) Z))))) (forall ((F tptp.fun_nat_complex) (X tptp.complex) (Z tptp.complex)) (=> (tptp.summable_complex (tptp.aa_com8181001469867462503omplex (tptp.aTP_Lamm_kn F) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex Z)) (tptp.aa_complex_real tptp.real_V1022390504157884413omplex X))) (tptp.summable_real (tptp.aa_com20334259897932645t_real (tptp.aTP_Lamm_ko F) Z))))) (forall ((F tptp.fun_nat_real)) (=> (tptp.summable_real F) (=> (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_nat_real F N2)))) (= (= (tptp.suminf_real F) tptp.zero_zero_real) (forall ((N5 tptp.nat)) (= (tptp.aa_nat_real F N5) tptp.zero_zero_real)))))) (forall ((F tptp.fun_nat_nat)) (=> (tptp.summable_nat F) (=> (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) (tptp.aa_nat_nat F N2)))) (= (= (tptp.suminf_nat F) tptp.zero_zero_nat) (forall ((N5 tptp.nat)) (= (tptp.aa_nat_nat F N5) tptp.zero_zero_nat)))))) (forall ((F tptp.fun_nat_int)) (=> (tptp.summable_int F) (=> (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.aa_nat_int F N2)))) (= (= (tptp.suminf_int F) tptp.zero_zero_int) (forall ((N5 tptp.nat)) (= (tptp.aa_nat_int F N5) tptp.zero_zero_int)))))) (forall ((F tptp.fun_nat_real)) (=> (tptp.summable_real F) (=> (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_nat_real F N2)))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.suminf_real F)))))) (forall ((F tptp.fun_nat_nat)) (=> (tptp.summable_nat F) (=> (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) (tptp.aa_nat_nat F N2)))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) (tptp.suminf_nat F)))))) (forall ((F tptp.fun_nat_int)) (=> (tptp.summable_int F) (=> (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.aa_nat_int F N2)))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.suminf_int F)))))) (forall ((F tptp.fun_nat_real)) (=> (tptp.summable_real F) (=> (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) (tptp.aa_nat_real F N2)))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) (tptp.suminf_real F)))))) (forall ((F tptp.fun_nat_nat)) (=> (tptp.summable_nat F) (=> (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.aa_nat_nat F N2)))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.suminf_nat F)))))) (forall ((F tptp.fun_nat_int)) (=> (tptp.summable_int F) (=> (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) (tptp.aa_nat_int F N2)))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) (tptp.suminf_int F)))))) (forall ((M tptp.rat) (N tptp.rat)) (= (tptp.ord_less_set_rat (tptp.set_ord_lessThan_rat M) (tptp.set_ord_lessThan_rat N)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat M) N)))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.ord_less_set_num (tptp.set_ord_lessThan_num M) (tptp.set_ord_lessThan_num N)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num M) N)))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_set_nat (tptp.set_ord_lessThan_nat M)) (tptp.set_ord_lessThan_nat N))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N)))) (forall ((M tptp.int) (N tptp.int)) (= (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_set_int (tptp.set_ord_lessThan_int M)) (tptp.set_ord_lessThan_int N))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int M) N)))) (forall ((M tptp.real) (N tptp.real)) (= (tptp.ord_less_set_real (tptp.set_or5984915006950818249n_real M) (tptp.set_or5984915006950818249n_real N)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real M) N)))) (forall ((F tptp.fun_nat_complex)) (tptp.summable_complex (tptp.aTP_Lamm_gy F))) (forall ((F tptp.fun_nat_real)) (tptp.summable_real (tptp.aTP_Lamm_ha F))) (forall ((F tptp.fun_nat_complex)) (tptp.summable_complex (tptp.aTP_Lamm_gy F))) (forall ((F tptp.fun_nat_real)) (tptp.summable_real (tptp.aTP_Lamm_ha F))) (forall ((F tptp.fun_nat_int)) (tptp.summable_int (tptp.aTP_Lamm_kp F))) (forall ((F tptp.fun_nat_complex) (Z tptp.complex)) (=> (tptp.summable_complex (tptp.aa_com8181001469867462503omplex (tptp.aTP_Lamm_kn F) Z)) (tptp.summable_complex (tptp.aa_com8181001469867462503omplex (tptp.aTP_Lamm_kq F) Z)))) (forall ((F tptp.fun_nat_real) (Z tptp.real)) (=> (tptp.summable_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_kl F) Z)) (tptp.summable_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_kr F) Z)))) (forall ((F tptp.fun_nat_complex) (Z tptp.complex)) (= (tptp.summable_complex (tptp.aa_com8181001469867462503omplex (tptp.aTP_Lamm_kq F) Z)) (tptp.summable_complex (tptp.aa_com8181001469867462503omplex (tptp.aTP_Lamm_kn F) Z)))) (forall ((F tptp.fun_nat_real) (Z tptp.real)) (= (tptp.summable_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_kr F) Z)) (tptp.summable_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_kl F) Z)))) (forall ((F tptp.fun_nat_complex) (M tptp.nat) (Z tptp.complex)) (= (tptp.summable_complex (tptp.aa_com8181001469867462503omplex (tptp.aa_nat2301396582920332468omplex (tptp.aTP_Lamm_ks F) M) Z)) (tptp.summable_complex (tptp.aa_com8181001469867462503omplex (tptp.aTP_Lamm_kn F) Z)))) (forall ((F tptp.fun_nat_real) (M tptp.nat) (Z tptp.real)) (= (tptp.summable_real (tptp.aa_real_fun_nat_real (tptp.aa_nat1308781354268537904t_real (tptp.aTP_Lamm_kt F) M) Z)) (tptp.summable_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_kl F) Z)))) (not (tptp.pp (tptp.aa_real_bool _let_77 tptp.zero_zero_real))) (tptp.pp (tptp.aa_real_bool _let_76 tptp.pi)) (tptp.pp (tptp.aa_real_bool _let_75 tptp.pi)) (forall ((F tptp.fun_nat_int) (N tptp.nat) (I tptp.nat)) (=> (tptp.summable_int F) (=> (forall ((M3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N) M3)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.aa_nat_int F M3))))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N) I)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) (tptp.aa_nat_int F I))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.groups3539618377306564664at_int F (tptp.set_ord_lessThan_nat N))) (tptp.suminf_int F)))))))) (forall ((F tptp.fun_nat_nat) (N tptp.nat) (I tptp.nat)) (=> (tptp.summable_nat F) (=> (forall ((M3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N) M3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) (tptp.aa_nat_nat F M3))))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N) I)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.aa_nat_nat F I))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat F) (tptp.set_ord_lessThan_nat N))) (tptp.suminf_nat F)))))))) (forall ((F tptp.fun_nat_real) (N tptp.nat) (I tptp.nat)) (=> (tptp.summable_real F) (=> (forall ((M3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N) M3)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_nat_real F M3))))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N) I)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) (tptp.aa_nat_real F I))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.groups6591440286371151544t_real F (tptp.set_ord_lessThan_nat N))) (tptp.suminf_real F)))))))) (forall ((F tptp.fun_nat_complex) (G tptp.fun_nat_real)) (=> (exists ((N6 tptp.nat)) (forall ((N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N6) N2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.aa_nat_complex F N2))) (tptp.aa_nat_real G N2)))))) (=> (tptp.summable_real G) (tptp.summable_real (tptp.aTP_Lamm_jm F))))) (forall ((F tptp.fun_nat_real) (G tptp.fun_nat_real)) (=> (exists ((N6 tptp.nat)) (forall ((N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N6) N2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_nat_real F N2))) (tptp.aa_nat_real G N2)))))) (=> (tptp.summable_real G) (tptp.summable_real (tptp.aTP_Lamm_gx F))))) (forall ((F tptp.fun_nat_real)) (let ((_let_1 (tptp.aTP_Lamm_gx F))) (=> (tptp.summable_real _let_1) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real (tptp.suminf_real F))) (tptp.suminf_real _let_1)))))) (forall ((F tptp.fun_nat_real) (I tptp.nat)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real))) (=> (tptp.summable_real F) (=> (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_nat_real F N2)))) (=> (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_nat_real F I))) (tptp.pp (tptp.aa_real_bool _let_1 (tptp.suminf_real F)))))))) (forall ((F tptp.fun_nat_nat) (I tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat))) (=> (tptp.summable_nat F) (=> (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) (tptp.aa_nat_nat F N2)))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat F I))) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.suminf_nat F)))))))) (forall ((F tptp.fun_nat_int) (I tptp.nat)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int))) (=> (tptp.summable_int F) (=> (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.aa_nat_int F N2)))) (=> (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_nat_int F I))) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.suminf_int F)))))))) (forall ((F tptp.fun_nat_real)) (=> (tptp.summable_real F) (=> (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_nat_real F N2)))) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) (tptp.suminf_real F))) (exists ((I4 tptp.nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) (tptp.aa_nat_real F I4)))))))) (forall ((F tptp.fun_nat_nat)) (=> (tptp.summable_nat F) (=> (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) (tptp.aa_nat_nat F N2)))) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.suminf_nat F))) (exists ((I4 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.aa_nat_nat F I4)))))))) (forall ((F tptp.fun_nat_int)) (=> (tptp.summable_int F) (=> (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.aa_nat_int F N2)))) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) (tptp.suminf_int F))) (exists ((I4 tptp.nat)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) (tptp.aa_nat_int F I4)))))))) (forall ((C tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real C)) tptp.one_one_real)) (tptp.summable_real (tptp.aa_real_fun_nat_real tptp.power_power_real C)))) (forall ((C tptp.complex)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex C)) tptp.one_one_real)) (tptp.summable_complex (tptp.power_power_complex C)))) (forall ((X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real X)) tptp.one_one_real)) (tptp.summable_real (tptp.aa_real_fun_nat_real tptp.power_power_real X)))) (forall ((X tptp.complex)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex X)) tptp.one_one_real)) (tptp.summable_complex (tptp.power_power_complex X)))) (forall ((F tptp.fun_nat_complex)) (=> (tptp.summable_complex F) (= (tptp.suminf_complex (tptp.aTP_Lamm_ku F)) (tptp.aa_complex_complex (tptp.minus_minus_complex (tptp.suminf_complex F)) (tptp.aa_nat_complex F tptp.zero_zero_nat))))) (forall ((F tptp.fun_nat_real)) (=> (tptp.summable_real F) (= (tptp.suminf_real (tptp.aTP_Lamm_hw F)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.suminf_real F)) (tptp.aa_nat_real F tptp.zero_zero_nat))))) (forall ((F tptp.fun_nat_real)) (let ((_let_1 (tptp.aTP_Lamm_jo F))) (=> (tptp.summable_real _let_1) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real (tptp.suminf_real F))) (tptp.suminf_real _let_1)))))) (forall ((F tptp.fun_nat_complex)) (let ((_let_1 (tptp.aTP_Lamm_jm F))) (=> (tptp.summable_real _let_1) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.suminf_complex F))) (tptp.suminf_real _let_1)))))) (forall ((G tptp.fun_nat_nat) (N tptp.nat)) (let ((_let_1 (tptp.set_ord_lessThan_nat N))) (= (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_nat_fun_nat_nat (tptp.aTP_Lamm_kv G) N)) _let_1) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat G) _let_1)))) (forall ((G tptp.fun_nat_real) (N tptp.nat)) (let ((_let_1 (tptp.set_ord_lessThan_nat N))) (= (tptp.groups6591440286371151544t_real (tptp.aa_nat_fun_nat_real (tptp.aTP_Lamm_kw G) N) _let_1) (tptp.groups6591440286371151544t_real G _let_1)))) (forall ((F tptp.fun_nat_int) (I5 tptp.set_nat)) (=> (tptp.summable_int F) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat I5)) (=> (forall ((N2 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat N2) (tptp.uminus5710092332889474511et_nat I5))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.aa_nat_int F N2))))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.groups3539618377306564664at_int F I5)) (tptp.suminf_int F))))))) (forall ((F tptp.fun_nat_nat) (I5 tptp.set_nat)) (=> (tptp.summable_nat F) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat I5)) (=> (forall ((N2 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat N2) (tptp.uminus5710092332889474511et_nat I5))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) (tptp.aa_nat_nat F N2))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat F) I5)) (tptp.suminf_nat F))))))) (forall ((F tptp.fun_nat_real) (I5 tptp.set_nat)) (=> (tptp.summable_real F) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat I5)) (=> (forall ((N2 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat N2) (tptp.uminus5710092332889474511et_nat I5))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_nat_real F N2))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.groups6591440286371151544t_real F I5)) (tptp.suminf_real F))))))) (forall ((Q tptp.fun_int_nat) (P tptp.fun_int_nat) (N tptp.int)) (let ((_let_1 (tptp.set_ord_lessThan_int N))) (=> (forall ((X4 tptp.int)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_int_nat Q X4)) (tptp.aa_int_nat P X4)))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.groups4541462559716669496nt_nat P _let_1)) (tptp.groups4541462559716669496nt_nat Q _let_1)) (tptp.groups4541462559716669496nt_nat (tptp.aa_fun6506752150744536624nt_nat (tptp.aTP_Lamm_hi Q) P) _let_1))))) (forall ((Q tptp.fun_real_nat) (P tptp.fun_real_nat) (N tptp.real)) (let ((_let_1 (tptp.set_or5984915006950818249n_real N))) (=> (forall ((X4 tptp.real)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_real_nat Q X4)) (tptp.aa_real_nat P X4)))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.groups1935376822645274424al_nat P _let_1)) (tptp.groups1935376822645274424al_nat Q _let_1)) (tptp.groups1935376822645274424al_nat (tptp.aa_fun211602392931233840al_nat (tptp.aTP_Lamm_hh Q) P) _let_1))))) (forall ((Q tptp.fun_nat_nat) (P tptp.fun_nat_nat) (N tptp.nat)) (let ((_let_1 (tptp.set_ord_lessThan_nat N))) (=> (forall ((X4 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat Q X4)) (tptp.aa_nat_nat P X4)))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat P) _let_1)) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat Q) _let_1)) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_fun5791449513213591928at_nat (tptp.aTP_Lamm_hk Q) P)) _let_1))))) (forall ((F tptp.fun_nat_real) (X tptp.real) (Z tptp.real)) (let ((_let_1 (tptp.aTP_Lamm_kl F))) (=> (tptp.summable_real (tptp.aa_real_fun_nat_real _let_1 X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real Z)) (tptp.aa_real_real tptp.real_V7735802525324610683m_real X))) (tptp.summable_real (tptp.aa_real_fun_nat_real _let_1 Z)))))) (forall ((F tptp.fun_nat_complex) (X tptp.complex) (Z tptp.complex)) (let ((_let_1 (tptp.aTP_Lamm_kn F))) (=> (tptp.summable_complex (tptp.aa_com8181001469867462503omplex _let_1 X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex Z)) (tptp.aa_complex_real tptp.real_V1022390504157884413omplex X))) (tptp.summable_complex (tptp.aa_com8181001469867462503omplex _let_1 Z)))))) (tptp.pp (tptp.aa_real_bool _let_77 _let_66)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real _let_28) tptp.pi)) (not (= _let_30 _let_28)) (forall ((F tptp.fun_nat_real) (K tptp.nat)) (=> (tptp.summable_real F) (=> (forall ((D2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat))) D2))) (let ((_let_2 (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat K))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real F (tptp.aa_nat_nat _let_2 _let_1))) (tptp.aa_nat_real F (tptp.aa_nat_nat _let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat _let_1) tptp.one_one_nat))))))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.groups6591440286371151544t_real F (tptp.set_ord_lessThan_nat K))) (tptp.suminf_real F)))))) (forall ((F tptp.fun_nat_complex) (Z tptp.complex)) (let ((_let_1 (tptp.aa_com8181001469867462503omplex (tptp.aTP_Lamm_kn F) Z))) (=> (tptp.summable_complex _let_1) (= (tptp.suminf_complex _let_1) (tptp.aa_complex_complex (tptp.plus_plus_complex (tptp.aa_nat_complex F tptp.zero_zero_nat)) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.suminf_complex (tptp.aa_com8181001469867462503omplex (tptp.aTP_Lamm_kq F) Z))) Z)))))) (forall ((F tptp.fun_nat_real) (Z tptp.real)) (let ((_let_1 (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_kl F) Z))) (=> (tptp.summable_real _let_1) (= (tptp.suminf_real _let_1) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real F tptp.zero_zero_nat)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.suminf_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_kr F) Z))) Z)))))) (forall ((G tptp.fun_nat_rat) (N tptp.nat)) (= (tptp.groups2906978787729119204at_rat G (tptp.set_ord_lessThan_nat (tptp.aa_nat_nat tptp.suc N))) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_nat_rat G tptp.zero_zero_nat)) (tptp.groups2906978787729119204at_rat (tptp.aTP_Lamm_ht G) (tptp.set_ord_lessThan_nat N))))) (forall ((G tptp.fun_nat_int) (N tptp.nat)) (= (tptp.groups3539618377306564664at_int G (tptp.set_ord_lessThan_nat (tptp.aa_nat_nat tptp.suc N))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_nat_int G tptp.zero_zero_nat)) (tptp.groups3539618377306564664at_int (tptp.aTP_Lamm_hu G) (tptp.set_ord_lessThan_nat N))))) (forall ((G tptp.fun_nat_nat) (N tptp.nat)) (= (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat G) (tptp.set_ord_lessThan_nat (tptp.aa_nat_nat tptp.suc N))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat G tptp.zero_zero_nat)) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aTP_Lamm_hv G)) (tptp.set_ord_lessThan_nat N))))) (forall ((G tptp.fun_nat_real) (N tptp.nat)) (= (tptp.groups6591440286371151544t_real G (tptp.set_ord_lessThan_nat (tptp.aa_nat_nat tptp.suc N))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real G tptp.zero_zero_nat)) (tptp.groups6591440286371151544t_real (tptp.aTP_Lamm_hw G) (tptp.set_ord_lessThan_nat N))))) (forall ((F tptp.fun_nat_complex) (Z tptp.complex)) (let ((_let_1 (tptp.aa_com8181001469867462503omplex (tptp.aTP_Lamm_kn F) Z))) (=> (tptp.summable_complex _let_1) (= (tptp.aa_complex_complex (tptp.times_times_complex (tptp.suminf_complex (tptp.aa_com8181001469867462503omplex (tptp.aTP_Lamm_kq F) Z))) Z) (tptp.aa_complex_complex (tptp.minus_minus_complex (tptp.suminf_complex _let_1)) (tptp.aa_nat_complex F tptp.zero_zero_nat)))))) (forall ((F tptp.fun_nat_real) (Z tptp.real)) (let ((_let_1 (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_kl F) Z))) (=> (tptp.summable_real _let_1) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.suminf_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_kr F) Z))) Z) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.suminf_real _let_1)) (tptp.aa_nat_real F tptp.zero_zero_nat)))))) (forall ((F tptp.fun_nat_complex) (N tptp.nat) (R tptp.complex)) (let ((_let_1 (tptp.set_ord_lessThan_nat N))) (= (tptp.aa_complex_complex (tptp.minus_minus_complex (tptp.groups2073611262835488442omplex F _let_1)) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex N)) R)) (tptp.groups2073611262835488442omplex (tptp.aa_com8181001469867462503omplex (tptp.aTP_Lamm_kx F) R) _let_1)))) (forall ((F tptp.fun_nat_rat) (N tptp.nat) (R tptp.rat)) (let ((_let_1 (tptp.set_ord_lessThan_nat N))) (= (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.groups2906978787729119204at_rat F _let_1)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat N)) R)) (tptp.groups2906978787729119204at_rat (tptp.aa_rat_fun_nat_rat (tptp.aTP_Lamm_ky F) R) _let_1)))) (forall ((F tptp.fun_nat_int) (N tptp.nat) (R tptp.int)) (let ((_let_1 (tptp.set_ord_lessThan_nat N))) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.groups3539618377306564664at_int F _let_1)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N)) R)) (tptp.groups3539618377306564664at_int (tptp.aa_int_fun_nat_int (tptp.aTP_Lamm_kz F) R) _let_1)))) (forall ((F tptp.fun_nat_real) (N tptp.nat) (R tptp.real)) (let ((_let_1 (tptp.set_ord_lessThan_nat N))) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.groups6591440286371151544t_real F _let_1)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N)) R)) (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_la F) R) _let_1)))) (forall ((F tptp.fun_nat_complex) (M tptp.nat)) (= (tptp.groups2073611262835488442omplex (tptp.aTP_Lamm_hx F) (tptp.set_ord_lessThan_nat M)) (tptp.aa_complex_complex (tptp.minus_minus_complex (tptp.aa_nat_complex F M)) (tptp.aa_nat_complex F tptp.zero_zero_nat)))) (forall ((F tptp.fun_nat_rat) (M tptp.nat)) (= (tptp.groups2906978787729119204at_rat (tptp.aTP_Lamm_hy F) (tptp.set_ord_lessThan_nat M)) (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_nat_rat F M)) (tptp.aa_nat_rat F tptp.zero_zero_nat)))) (forall ((F tptp.fun_nat_int) (M tptp.nat)) (= (tptp.groups3539618377306564664at_int (tptp.aTP_Lamm_hz F) (tptp.set_ord_lessThan_nat M)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_nat_int F M)) (tptp.aa_nat_int F tptp.zero_zero_nat)))) (forall ((F tptp.fun_nat_real) (M tptp.nat)) (= (tptp.groups6591440286371151544t_real (tptp.aTP_Lamm_ia F) (tptp.set_ord_lessThan_nat M)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_nat_real F M)) (tptp.aa_nat_real F tptp.zero_zero_nat)))) (forall ((F tptp.fun_nat_complex) (M tptp.nat)) (= (tptp.groups2073611262835488442omplex (tptp.aTP_Lamm_lb F) (tptp.set_ord_lessThan_nat M)) (tptp.aa_complex_complex (tptp.minus_minus_complex (tptp.aa_nat_complex F tptp.zero_zero_nat)) (tptp.aa_nat_complex F M)))) (forall ((F tptp.fun_nat_rat) (M tptp.nat)) (= (tptp.groups2906978787729119204at_rat (tptp.aTP_Lamm_lc F) (tptp.set_ord_lessThan_nat M)) (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_nat_rat F tptp.zero_zero_nat)) (tptp.aa_nat_rat F M)))) (forall ((F tptp.fun_nat_int) (M tptp.nat)) (= (tptp.groups3539618377306564664at_int (tptp.aTP_Lamm_ld F) (tptp.set_ord_lessThan_nat M)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_nat_int F tptp.zero_zero_nat)) (tptp.aa_nat_int F M)))) (forall ((F tptp.fun_nat_real) (M tptp.nat)) (= (tptp.groups6591440286371151544t_real (tptp.aTP_Lamm_le F) (tptp.set_ord_lessThan_nat M)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_nat_real F tptp.zero_zero_nat)) (tptp.aa_nat_real F M)))) (forall ((F tptp.fun_nat_complex) (E tptp.real)) (=> (tptp.summable_complex F) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) E)) (not (forall ((N7 tptp.nat)) (not (forall ((M2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N7) M2)) (forall ((N8 tptp.nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.groups2073611262835488442omplex F (tptp.set_or1269000886237332187st_nat M2 N8)))) E))))))))))) (forall ((F tptp.fun_nat_real) (E tptp.real)) (=> (tptp.summable_real F) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) E)) (not (forall ((N7 tptp.nat)) (not (forall ((M2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N7) M2)) (forall ((N8 tptp.nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real (tptp.groups6591440286371151544t_real F (tptp.set_or1269000886237332187st_nat M2 N8)))) E))))))))))) (forall ((R tptp.real) (F tptp.fun_nat_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) R)) (=> (tptp.summable_real F) (exists ((N7 tptp.nat)) (forall ((N8 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N7) N8)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real (tptp.suminf_real (tptp.aa_nat_fun_nat_real (tptp.aTP_Lamm_hm F) N8)))) R)))))))) (forall ((R tptp.real) (F tptp.fun_nat_complex)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) R)) (=> (tptp.summable_complex F) (exists ((N7 tptp.nat)) (forall ((N8 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N7) N8)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.suminf_complex (tptp.aa_nat6454746962644518025omplex (tptp.aTP_Lamm_kk F) N8)))) R)))))))) (forall ((F tptp.fun_nat_real) (Z tptp.real)) (=> (forall ((I3 tptp.nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_nat_real F I3)) tptp.one_one_real))) (=> (forall ((I3 tptp.nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_nat_real F I3)))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) Z)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Z) tptp.one_one_real)) (tptp.summable_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_kl F) Z))))))) (forall ((R tptp.real) (R0 tptp.real) (A tptp.fun_nat_complex) (M7 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) R)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real R) R0)) (=> (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.aa_nat_complex A N2))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real R0) N2))) M7))) (tptp.summable_real (tptp.aa_fun7054779078796324018t_real (tptp.aTP_Lamm_lf R) A)))))) (forall ((X5 tptp.int) (Xa tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.bot_bo6207810721336151133t_bool X5) Xa)) (tptp.member5262025264175285858nt_int (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int X5) Xa) tptp.bot_bo1796632182523588997nt_int))) (forall ((X5 tptp.fun_Co6545587727236015215e_term) (Xa tptp.produc8923325533196201883nteger)) (= (tptp.pp (tptp.aa_Pro5843519176478241656r_bool (tptp.aa_fun5646951941296221740r_bool tptp.bot_bo1209944405316066303r_bool X5) Xa)) (tptp.member4581088367259704696nteger (tptp.produc4282985567423050387nteger X5 Xa) tptp.bot_bo360956144901883563nteger))) (forall ((X5 tptp.fun_Pr272337284026993017e_term) (Xa tptp.produc8923325533196201883nteger)) (= (tptp.pp (tptp.aa_Pro5843519176478241656r_bool (tptp.aa_fun5449300841655810358r_bool tptp.bot_bo7238443650746976009r_bool X5) Xa)) (tptp.member6423679177046879214nteger (tptp.produc7384524951051686153nteger X5 Xa) tptp.bot_bo5920137642514184737nteger))) (forall ((X5 tptp.fun_Pr9164807099015279978e_term) (Xa tptp.product_prod_int_int)) (= (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.aa_fun5300525129335604105t_bool tptp.bot_bo9220524098407837788t_bool X5) Xa)) (tptp.member690604328116145115nt_int (tptp.produc1560874099174258678nt_int X5 Xa) tptp.bot_bo5853814528170464142nt_int))) (forall ((X5 tptp.fun_in6429348457993719614e_term) (Xa tptp.product_prod_int_int)) (= (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.aa_fun4446166836006121821t_bool tptp.bot_bo6140462223577857584t_bool X5) Xa)) (tptp.member500491123954006279nt_int (tptp.produc4852315488734385442nt_int X5 Xa) tptp.bot_bo1891714543702108858nt_int))) (forall ((R2 tptp.set_Pr958786334691620121nt_int) (S2 tptp.set_Pr958786334691620121nt_int)) (= (forall ((X3 tptp.int) (Xa4 tptp.int)) (let ((_let_1 (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int X3) Xa4))) (= (tptp.member5262025264175285858nt_int _let_1 R2) (tptp.member5262025264175285858nt_int _let_1 S2)))) (= R2 S2))) (forall ((R2 tptp.set_Pr7592006421409863191nteger) (S2 tptp.set_Pr7592006421409863191nteger)) (= (forall ((X3 tptp.fun_Co6545587727236015215e_term) (Xa4 tptp.produc8923325533196201883nteger)) (let ((_let_1 (tptp.produc4282985567423050387nteger X3 Xa4))) (= (tptp.member4581088367259704696nteger _let_1 R2) (tptp.member4581088367259704696nteger _let_1 S2)))) (= R2 S2))) (forall ((R2 tptp.set_Pr5663546166630115725nteger) (S2 tptp.set_Pr5663546166630115725nteger)) (= (forall ((X3 tptp.fun_Pr272337284026993017e_term) (Xa4 tptp.produc8923325533196201883nteger)) (let ((_let_1 (tptp.produc7384524951051686153nteger X3 Xa4))) (= (tptp.member6423679177046879214nteger _let_1 R2) (tptp.member6423679177046879214nteger _let_1 S2)))) (= R2 S2))) (forall ((R2 tptp.set_Pr233528076387193594nt_int) (S2 tptp.set_Pr233528076387193594nt_int)) (= (forall ((X3 tptp.fun_Pr9164807099015279978e_term) (Xa4 tptp.product_prod_int_int)) (let ((_let_1 (tptp.produc1560874099174258678nt_int X3 Xa4))) (= (tptp.member690604328116145115nt_int _let_1 R2) (tptp.member690604328116145115nt_int _let_1 S2)))) (= R2 S2))) (forall ((R2 tptp.set_Pr5033440245338114598nt_int) (S2 tptp.set_Pr5033440245338114598nt_int)) (= (forall ((X3 tptp.fun_in6429348457993719614e_term) (Xa4 tptp.product_prod_int_int)) (let ((_let_1 (tptp.produc4852315488734385442nt_int X3 Xa4))) (= (tptp.member500491123954006279nt_int _let_1 R2) (tptp.member500491123954006279nt_int _let_1 S2)))) (= R2 S2))) (forall ((C tptp.real) (N3 tptp.nat) (F tptp.fun_nat_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real C) tptp.one_one_real)) (=> (forall ((N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N3) N2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real (tptp.aa_nat_real F (tptp.aa_nat_nat tptp.suc N2)))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real C) (tptp.aa_real_real tptp.real_V7735802525324610683m_real (tptp.aa_nat_real F N2))))))) (tptp.summable_real F)))) (forall ((C tptp.real) (N3 tptp.nat) (F tptp.fun_nat_complex)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real C) tptp.one_one_real)) (=> (forall ((N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N3) N2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.aa_nat_complex F (tptp.aa_nat_nat tptp.suc N2)))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real C) (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.aa_nat_complex F N2))))))) (tptp.summable_complex F)))) (not (= _let_30 tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real _let_30) _let_28)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real _let_30) _let_28)) (forall ((X tptp.complex) (N tptp.nat)) (let ((_let_1 (tptp.power_power_complex X))) (= (tptp.aa_complex_complex (tptp.minus_minus_complex (tptp.aa_nat_complex _let_1 N)) tptp.one_one_complex) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_complex_complex (tptp.minus_minus_complex X) tptp.one_one_complex)) (tptp.groups2073611262835488442omplex _let_1 (tptp.set_ord_lessThan_nat N)))))) (forall ((X tptp.rat) (N tptp.nat)) (let ((_let_1 (tptp.power_power_rat X))) (= (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_nat_rat _let_1 N)) tptp.one_one_rat) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat (tptp.minus_minus_rat X) tptp.one_one_rat)) (tptp.groups2906978787729119204at_rat _let_1 (tptp.set_ord_lessThan_nat N)))))) (forall ((X tptp.int) (N tptp.nat)) (let ((_let_1 (tptp.power_power_int X))) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_nat_int _let_1 N)) tptp.one_one_int) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int X) tptp.one_one_int)) (tptp.groups3539618377306564664at_int _let_1 (tptp.set_ord_lessThan_nat N)))))) (forall ((X tptp.real) (N tptp.nat)) (let ((_let_1 (tptp.aa_real_fun_nat_real tptp.power_power_real X))) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_nat_real _let_1 N)) tptp.one_one_real) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real X) tptp.one_one_real)) (tptp.groups6591440286371151544t_real _let_1 (tptp.set_ord_lessThan_nat N)))))) (forall ((X tptp.complex) (N tptp.nat)) (let ((_let_1 (tptp.power_power_complex X))) (let ((_let_2 (tptp.minus_minus_complex tptp.one_one_complex))) (= (tptp.aa_complex_complex _let_2 (tptp.aa_nat_complex _let_1 N)) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_complex_complex _let_2 X)) (tptp.groups2073611262835488442omplex _let_1 (tptp.set_ord_lessThan_nat N))))))) (forall ((X tptp.rat) (N tptp.nat)) (let ((_let_1 (tptp.power_power_rat X))) (let ((_let_2 (tptp.minus_minus_rat tptp.one_one_rat))) (= (tptp.aa_rat_rat _let_2 (tptp.aa_nat_rat _let_1 N)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat _let_2 X)) (tptp.groups2906978787729119204at_rat _let_1 (tptp.set_ord_lessThan_nat N))))))) (forall ((X tptp.int) (N tptp.nat)) (let ((_let_1 (tptp.power_power_int X))) (let ((_let_2 (tptp.aa_int_fun_int_int tptp.minus_minus_int tptp.one_one_int))) (= (tptp.aa_int_int _let_2 (tptp.aa_nat_int _let_1 N)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int _let_2 X)) (tptp.groups3539618377306564664at_int _let_1 (tptp.set_ord_lessThan_nat N))))))) (forall ((X tptp.real) (N tptp.nat)) (let ((_let_1 (tptp.aa_real_fun_nat_real tptp.power_power_real X))) (let ((_let_2 (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real tptp.one_one_real))) (= (tptp.aa_real_real _let_2 (tptp.aa_nat_real _let_1 N)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real _let_2 X)) (tptp.groups6591440286371151544t_real _let_1 (tptp.set_ord_lessThan_nat N))))))) (forall ((X tptp.complex) (N tptp.nat)) (let ((_let_1 (tptp.power_power_complex X))) (=> (not (= X tptp.one_one_complex)) (= (tptp.groups2073611262835488442omplex _let_1 (tptp.set_ord_lessThan_nat N)) (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex (tptp.aa_complex_complex (tptp.minus_minus_complex (tptp.aa_nat_complex _let_1 N)) tptp.one_one_complex)) (tptp.aa_complex_complex (tptp.minus_minus_complex X) tptp.one_one_complex)))))) (forall ((X tptp.rat) (N tptp.nat)) (let ((_let_1 (tptp.power_power_rat X))) (=> (not (= X tptp.one_one_rat)) (= (tptp.groups2906978787729119204at_rat _let_1 (tptp.set_ord_lessThan_nat N)) (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_nat_rat _let_1 N)) tptp.one_one_rat)) (tptp.aa_rat_rat (tptp.minus_minus_rat X) tptp.one_one_rat)))))) (forall ((X tptp.real) (N tptp.nat)) (let ((_let_1 (tptp.aa_real_fun_nat_real tptp.power_power_real X))) (=> (not (= X tptp.one_one_real)) (= (tptp.groups6591440286371151544t_real _let_1 (tptp.set_ord_lessThan_nat N)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_nat_real _let_1 N)) tptp.one_one_real)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real X) tptp.one_one_real)))))) (forall ((X tptp.complex) (N tptp.nat)) (let ((_let_1 (tptp.minus_minus_complex tptp.one_one_complex))) (let ((_let_2 (tptp.power_power_complex X))) (let ((_let_3 (tptp.groups2073611262835488442omplex _let_2 (tptp.set_ord_lessThan_nat N)))) (let ((_let_4 (= X tptp.one_one_complex))) (and (=> _let_4 (= _let_3 (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex N))) (=> (not _let_4) (= _let_3 (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex (tptp.aa_complex_complex _let_1 (tptp.aa_nat_complex _let_2 N))) (tptp.aa_complex_complex _let_1 X)))))))))) (forall ((X tptp.rat) (N tptp.nat)) (let ((_let_1 (tptp.minus_minus_rat tptp.one_one_rat))) (let ((_let_2 (tptp.power_power_rat X))) (let ((_let_3 (tptp.groups2906978787729119204at_rat _let_2 (tptp.set_ord_lessThan_nat N)))) (let ((_let_4 (= X tptp.one_one_rat))) (and (=> _let_4 (= _let_3 (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat N))) (=> (not _let_4) (= _let_3 (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_rat_rat _let_1 (tptp.aa_nat_rat _let_2 N))) (tptp.aa_rat_rat _let_1 X)))))))))) (forall ((X tptp.real) (N tptp.nat)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real tptp.one_one_real))) (let ((_let_2 (tptp.aa_real_fun_nat_real tptp.power_power_real X))) (let ((_let_3 (tptp.groups6591440286371151544t_real _let_2 (tptp.set_ord_lessThan_nat N)))) (let ((_let_4 (= X tptp.one_one_real))) (and (=> _let_4 (= _let_3 (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N))) (=> (not _let_4) (= _let_3 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real _let_1 (tptp.aa_nat_real _let_2 N))) (tptp.aa_real_real _let_1 X)))))))))) (forall ((Z tptp.complex) (H tptp.complex) (M tptp.nat)) (let ((_let_1 (tptp.set_ord_lessThan_nat M))) (= (tptp.groups2073611262835488442omplex (tptp.aa_nat6454746962644518025omplex (tptp.aa_com4347742694490471604omplex (tptp.aTP_Lamm_lg Z) H) M) _let_1) (tptp.groups2073611262835488442omplex (tptp.aa_nat6454746962644518025omplex (tptp.aa_com4347742694490471604omplex (tptp.aTP_Lamm_lh Z) H) M) _let_1)))) (forall ((Z tptp.rat) (H tptp.rat) (M tptp.nat)) (let ((_let_1 (tptp.set_ord_lessThan_nat M))) (= (tptp.groups2906978787729119204at_rat (tptp.aa_nat_fun_nat_rat (tptp.aa_rat250263598611652360at_rat (tptp.aTP_Lamm_li Z) H) M) _let_1) (tptp.groups2906978787729119204at_rat (tptp.aa_nat_fun_nat_rat (tptp.aa_rat250263598611652360at_rat (tptp.aTP_Lamm_lj Z) H) M) _let_1)))) (forall ((Z tptp.int) (H tptp.int) (M tptp.nat)) (let ((_let_1 (tptp.set_ord_lessThan_nat M))) (= (tptp.groups3539618377306564664at_int (tptp.aa_nat_fun_nat_int (tptp.aa_int431785320988601264at_int (tptp.aTP_Lamm_lk Z) H) M) _let_1) (tptp.groups3539618377306564664at_int (tptp.aa_nat_fun_nat_int (tptp.aa_int431785320988601264at_int (tptp.aTP_Lamm_ll Z) H) M) _let_1)))) (forall ((Z tptp.real) (H tptp.real) (M tptp.nat)) (let ((_let_1 (tptp.set_ord_lessThan_nat M))) (= (tptp.groups6591440286371151544t_real (tptp.aa_nat_fun_nat_real (tptp.aa_rea6853821027689443120t_real (tptp.aTP_Lamm_lm Z) H) M) _let_1) (tptp.groups6591440286371151544t_real (tptp.aa_nat_fun_nat_real (tptp.aa_rea6853821027689443120t_real (tptp.aTP_Lamm_ln Z) H) M) _let_1)))) (tptp.pp (tptp.aa_real_bool _let_76 _let_30)) (forall ((X tptp.complex) (N tptp.nat) (Y tptp.complex)) (= (tptp.aa_complex_complex (tptp.minus_minus_complex (tptp.aa_nat_complex (tptp.power_power_complex X) N)) (tptp.aa_nat_complex (tptp.power_power_complex Y) N)) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_complex_complex (tptp.minus_minus_complex X) Y)) (tptp.groups2073611262835488442omplex (tptp.aa_com8181001469867462503omplex (tptp.aa_nat2301396582920332468omplex (tptp.aTP_Lamm_lo X) N) Y) (tptp.set_ord_lessThan_nat N))))) (forall ((X tptp.rat) (N tptp.nat) (Y tptp.rat)) (= (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_nat_rat (tptp.power_power_rat X) N)) (tptp.aa_nat_rat (tptp.power_power_rat Y) N)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat (tptp.minus_minus_rat X) Y)) (tptp.groups2906978787729119204at_rat (tptp.aa_rat_fun_nat_rat (tptp.aa_nat298952458717073160at_rat (tptp.aTP_Lamm_lp X) N) Y) (tptp.set_ord_lessThan_nat N))))) (forall ((X tptp.int) (N tptp.nat) (Y tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_nat_int (tptp.power_power_int X) N)) (tptp.aa_nat_int (tptp.power_power_int Y) N)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int X) Y)) (tptp.groups3539618377306564664at_int (tptp.aa_int_fun_nat_int (tptp.aa_nat6704147566042551216at_int (tptp.aTP_Lamm_lq X) N) Y) (tptp.set_ord_lessThan_nat N))))) (forall ((X tptp.real) (N tptp.nat) (Y tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) N)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Y) N)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real X) Y)) (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real (tptp.aa_nat1308781354268537904t_real (tptp.aTP_Lamm_lr X) N) Y) (tptp.set_ord_lessThan_nat N))))) (forall ((X tptp.complex) (N tptp.nat) (Y tptp.complex)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N))) (= (tptp.aa_complex_complex (tptp.minus_minus_complex (tptp.aa_nat_complex (tptp.power_power_complex X) _let_1)) (tptp.aa_nat_complex (tptp.power_power_complex Y) _let_1)) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_complex_complex (tptp.minus_minus_complex X) Y)) (tptp.groups2073611262835488442omplex (tptp.aa_com8181001469867462503omplex (tptp.aa_nat2301396582920332468omplex (tptp.aTP_Lamm_ls X) N) Y) (tptp.set_ord_lessThan_nat _let_1)))))) (forall ((X tptp.rat) (N tptp.nat) (Y tptp.rat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N))) (= (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_nat_rat (tptp.power_power_rat X) _let_1)) (tptp.aa_nat_rat (tptp.power_power_rat Y) _let_1)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat (tptp.minus_minus_rat X) Y)) (tptp.groups2906978787729119204at_rat (tptp.aa_rat_fun_nat_rat (tptp.aa_nat298952458717073160at_rat (tptp.aTP_Lamm_lt X) N) Y) (tptp.set_ord_lessThan_nat _let_1)))))) (forall ((X tptp.int) (N tptp.nat) (Y tptp.int)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N))) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_nat_int (tptp.power_power_int X) _let_1)) (tptp.aa_nat_int (tptp.power_power_int Y) _let_1)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int X) Y)) (tptp.groups3539618377306564664at_int (tptp.aa_int_fun_nat_int (tptp.aa_nat6704147566042551216at_int (tptp.aTP_Lamm_lu X) N) Y) (tptp.set_ord_lessThan_nat _let_1)))))) (forall ((X tptp.real) (N tptp.nat) (Y tptp.real)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N))) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) _let_1)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Y) _let_1)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real X) Y)) (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real (tptp.aa_nat1308781354268537904t_real (tptp.aTP_Lamm_lv X) N) Y) (tptp.set_ord_lessThan_nat _let_1)))))) (tptp.pp (tptp.aa_real_bool _let_75 _let_30)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.uminus_uminus_real _let_55)) tptp.pi)) (forall ((Y tptp.real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.arctan Y)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))))) (= (tptp.aa_real_real tptp.arctan tptp.one_one_real) _let_67) (forall ((N tptp.nat) (F tptp.fun_nat_rat) (K5 tptp.rat) (K tptp.nat)) (=> (forall ((P4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat P4) N)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat F P4)) K5)))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) K5)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.groups2906978787729119204at_rat F (tptp.set_ord_lessThan_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) K)))) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat N)) K5)))))) (forall ((N tptp.nat) (F tptp.fun_nat_int) (K5 tptp.int) (K tptp.nat)) (=> (forall ((P4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat P4) N)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int F P4)) K5)))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) K5)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.groups3539618377306564664at_int F (tptp.set_ord_lessThan_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) K)))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N)) K5)))))) (forall ((N tptp.nat) (F tptp.fun_nat_nat) (K5 tptp.nat) (K tptp.nat)) (=> (forall ((P4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat P4) N)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat F P4)) K5)))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) K5)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat F) (tptp.set_ord_lessThan_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) K)))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat N)) K5)))))) (forall ((N tptp.nat) (F tptp.fun_nat_real) (K5 tptp.real) (K tptp.nat)) (=> (forall ((P4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat P4) N)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_nat_real F P4)) K5)))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) K5)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.groups6591440286371151544t_real F (tptp.set_ord_lessThan_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) K)))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N)) K5)))))) (forall ((X tptp.complex) (N tptp.nat)) (let ((_let_1 (tptp.minus_minus_complex tptp.one_one_complex))) (= (tptp.aa_complex_complex _let_1 (tptp.aa_nat_complex (tptp.power_power_complex X) N)) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_complex_complex _let_1 X)) (tptp.groups2073611262835488442omplex (tptp.aa_nat6454746962644518025omplex (tptp.aTP_Lamm_lw X) N) (tptp.set_ord_lessThan_nat N)))))) (forall ((X tptp.rat) (N tptp.nat)) (let ((_let_1 (tptp.minus_minus_rat tptp.one_one_rat))) (= (tptp.aa_rat_rat _let_1 (tptp.aa_nat_rat (tptp.power_power_rat X) N)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat _let_1 X)) (tptp.groups2906978787729119204at_rat (tptp.aa_nat_fun_nat_rat (tptp.aTP_Lamm_lx X) N) (tptp.set_ord_lessThan_nat N)))))) (forall ((X tptp.int) (N tptp.nat)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.minus_minus_int tptp.one_one_int))) (= (tptp.aa_int_int _let_1 (tptp.aa_nat_int (tptp.power_power_int X) N)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int _let_1 X)) (tptp.groups3539618377306564664at_int (tptp.aa_nat_fun_nat_int (tptp.aTP_Lamm_ly X) N) (tptp.set_ord_lessThan_nat N)))))) (forall ((X tptp.real) (N tptp.nat)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real tptp.one_one_real))) (= (tptp.aa_real_real _let_1 (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) N)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real _let_1 X)) (tptp.groups6591440286371151544t_real (tptp.aa_nat_fun_nat_real (tptp.aTP_Lamm_lz X) N) (tptp.set_ord_lessThan_nat N)))))) (forall ((R tptp.set_Pr958786334691620121nt_int) (S tptp.set_Pr958786334691620121nt_int)) (=> (forall ((X4 tptp.int) (Y4 tptp.int)) (let ((_let_1 (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int X4) Y4))) (=> (tptp.member5262025264175285858nt_int _let_1 R) (tptp.member5262025264175285858nt_int _let_1 S)))) (tptp.ord_le2843351958646193337nt_int R S))) (forall ((R tptp.set_Pr7592006421409863191nteger) (S tptp.set_Pr7592006421409863191nteger)) (=> (forall ((X4 tptp.fun_Co6545587727236015215e_term) (Y4 tptp.produc8923325533196201883nteger)) (let ((_let_1 (tptp.produc4282985567423050387nteger X4 Y4))) (=> (tptp.member4581088367259704696nteger _let_1 R) (tptp.member4581088367259704696nteger _let_1 S)))) (tptp.ord_le5347933966117430903nteger R S))) (forall ((R tptp.set_Pr5663546166630115725nteger) (S tptp.set_Pr5663546166630115725nteger)) (=> (forall ((X4 tptp.fun_Pr272337284026993017e_term) (Y4 tptp.produc8923325533196201883nteger)) (let ((_let_1 (tptp.produc7384524951051686153nteger X4 Y4))) (=> (tptp.member6423679177046879214nteger _let_1 R) (tptp.member6423679177046879214nteger _let_1 S)))) (tptp.ord_le3337582088779512301nteger R S))) (forall ((R tptp.set_Pr233528076387193594nt_int) (S tptp.set_Pr233528076387193594nt_int)) (=> (forall ((X4 tptp.fun_Pr9164807099015279978e_term) (Y4 tptp.product_prod_int_int)) (let ((_let_1 (tptp.produc1560874099174258678nt_int X4 Y4))) (=> (tptp.member690604328116145115nt_int _let_1 R) (tptp.member690604328116145115nt_int _let_1 S)))) (tptp.ord_le5172437211506631514nt_int R S))) (forall ((R tptp.set_Pr5033440245338114598nt_int) (S tptp.set_Pr5033440245338114598nt_int)) (=> (forall ((X4 tptp.fun_in6429348457993719614e_term) (Y4 tptp.product_prod_int_int)) (let ((_let_1 (tptp.produc4852315488734385442nt_int X4 Y4))) (=> (tptp.member500491123954006279nt_int _let_1 R) (tptp.member500491123954006279nt_int _let_1 S)))) (tptp.ord_le172202941055982214nt_int R S))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real _let_31) tptp.zero_zero_real)) (forall ((Y tptp.real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))))) (tptp.aa_real_real tptp.arctan Y)))) (forall ((Y tptp.real)) (let ((_let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_2 (tptp.aa_real_real tptp.arctan Y))) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.uminus_uminus_real _let_1)) _let_2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real _let_2) _let_1)))))) (forall ((K tptp.nat) (S2 tptp.set_nat)) (=> (forall ((M3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat K) M3)) (exists ((N8 tptp.nat)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M3) N8)) (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat N8) S2)))))) (not (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat S2))))) (forall ((S2 tptp.set_nat)) (= (not (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat S2))) (forall ((M6 tptp.nat)) (exists ((N5 tptp.nat)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M6) N5)) (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat N5) S2))))))) (forall ((S2 tptp.set_nat)) (= (not (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat S2))) (forall ((M6 tptp.nat)) (exists ((N5 tptp.nat)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M6) N5)) (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat N5) S2))))))) (forall ((F tptp.fun_nat_real) (G tptp.fun_nat_real) (N tptp.nat)) (let ((_let_1 (tptp.set_ord_lessThan_nat N))) (= (tptp.groups6591440286371151544t_real (tptp.aa_fun1839206346889086768t_real (tptp.aTP_Lamm_ma F) G) (tptp.set_ord_lessThan_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.groups6591440286371151544t_real (tptp.aTP_Lamm_mb F) _let_1)) (tptp.groups6591440286371151544t_real (tptp.aTP_Lamm_mc G) _let_1))))) (forall ((R2 tptp.set_nat) (S2 tptp.set_nat)) (= (tptp.ord_le8840051076831633728t_bool (tptp.aTP_Lamm_ac R2) (tptp.aTP_Lamm_ac S2)) (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat R2) S2)))) (forall ((R2 tptp.set_real) (S2 tptp.set_real)) (= (tptp.ord_le5573776112191778788l_bool (tptp.aTP_Lamm_aa R2) (tptp.aTP_Lamm_aa S2)) (tptp.ord_less_eq_set_real R2 S2))) (forall ((R2 tptp.set_complex) (S2 tptp.set_complex)) (= (tptp.ord_le4633831435867229666x_bool (tptp.aTP_Lamm_a R2) (tptp.aTP_Lamm_a S2)) (tptp.pp (tptp.aa_set_complex_bool (tptp.ord_le211207098394363844omplex R2) S2)))) (forall ((R2 tptp.set_int) (S2 tptp.set_int)) (= (tptp.ord_le5715760110363009508t_bool (tptp.aTP_Lamm_ad R2) (tptp.aTP_Lamm_ad S2)) (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int R2) S2)))) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real _let_74) (tptp.aa_real_real tptp.arctan (tptp.aa_real_real _let_64 (tptp.aa_num_real tptp.numeral_numeral_real _let_73))))) (tptp.aa_real_real _let_46 (tptp.aa_real_real tptp.arctan (tptp.aa_real_real _let_71 (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit1 _let_25))))))))) _let_67) (= _let_67 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real _let_66) (tptp.aa_real_real tptp.arctan (tptp.aa_real_real _let_64 _let_74)))) (tptp.aa_real_real tptp.arctan (tptp.aa_real_real _let_64 (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit0 _let_73)))))))))) (forall ((S2 tptp.set_int)) (= (not (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int S2))) (forall ((M6 tptp.int)) (exists ((N5 tptp.int)) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int M6) (tptp.aa_int_int tptp.abs_abs_int N5))) (tptp.pp (tptp.aa_set_int_bool (tptp.member_int N5) S2))))))) (forall ((N tptp.nat)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (= (tptp.aa_real_real tptp.sin_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1)) N)))) tptp.pi)) (tptp.aa_num_real tptp.numeral_numeral_real _let_1))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)) N)))) (forall ((N tptp.nat)) (= (tptp.groups6591440286371151544t_real tptp.aTP_Lamm_md (tptp.set_ord_lessThan_nat (tptp.aa_nat_nat tptp.suc N))) tptp.one_one_real)) (forall ((M tptp.nat)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (= (tptp.aa_real_real tptp.cos_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real tptp.pi) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1)) M))))) (tptp.aa_num_real tptp.numeral_numeral_real _let_1))) tptp.zero_zero_real))) (forall ((R1 tptp.fun_Pr5837708615769641901m_bool) (R22 tptp.fun_Pr5837708615769641901m_bool)) (=> (tptp.ord_le7676714441581034317m_bool R1 R22) (tptp.ord_le998981803562422117m_bool (tptp.accp_P3113834385874906142um_num R22) (tptp.accp_P3113834385874906142um_num R1)))) (forall ((R1 tptp.fun_Pr248683899324676269t_bool) (R22 tptp.fun_Pr248683899324676269t_bool)) (=> (tptp.ord_le2087689725136068685t_bool R1 R22) (tptp.pp (tptp.aa_fun8663595511526100224l_bool (tptp.ord_le2468614981408567801t_bool (tptp.accp_P4275260045618599050at_nat R22)) (tptp.accp_P4275260045618599050at_nat R1))))) (forall ((R1 tptp.fun_Pr3099820731930151597t_bool) (R22 tptp.fun_Pr3099820731930151597t_bool)) (=> (tptp.ord_le4938826557741544013t_bool R1 R22) (tptp.ord_le4737936599360737601t_bool (tptp.accp_P1096762738010456898nt_int R22) (tptp.accp_P1096762738010456898nt_int R1)))) (forall ((R1 tptp.fun_li8598321315282354825t_bool) (R22 tptp.fun_li8598321315282354825t_bool)) (=> (tptp.ord_le4434192926011882025t_bool R1 R22) (tptp.ord_le2936377143570524336t_bool (tptp.accp_list_nat R22) (tptp.accp_list_nat R1)))) (forall ((R1 tptp.fun_nat_fun_nat_bool) (R22 tptp.fun_nat_fun_nat_bool)) (=> (tptp.ord_le4899916226251588169t_bool R1 R22) (tptp.ord_le8840051076831633728t_bool (tptp.accp_nat R22) (tptp.accp_nat R1)))) (forall ((Z tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real Z)) tptp.one_one_real)) (tptp.pp (tptp.aa_real_bool (tptp.sums_real (tptp.aa_real_fun_nat_real tptp.aTP_Lamm_me Z)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.one_one_real) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real tptp.one_one_real) Z)) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))))))) (forall ((Z tptp.complex)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex Z)) tptp.one_one_real)) (tptp.pp (tptp.aa_complex_bool (tptp.sums_complex (tptp.aTP_Lamm_mf Z)) (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex tptp.one_one_complex) (tptp.aa_nat_complex (tptp.power_power_complex (tptp.aa_complex_complex (tptp.minus_minus_complex tptp.one_one_complex) Z)) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))))))) (forall ((X7 tptp.fun_nat_real)) (= (tptp.topolo6980174941875973593q_real X7) (or (forall ((M6 tptp.nat) (N5 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M6) N5)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_nat_real X7 M6)) (tptp.aa_nat_real X7 N5))))) (forall ((M6 tptp.nat) (N5 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M6) N5)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_nat_real X7 N5)) (tptp.aa_nat_real X7 M6)))))))) (forall ((X7 tptp.fun_nat_set_int)) (= (tptp.topolo3100542954746470799et_int X7) (or (forall ((M6 tptp.nat) (N5 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M6) N5)) (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int (tptp.aa_nat_set_int X7 M6)) (tptp.aa_nat_set_int X7 N5))))) (forall ((M6 tptp.nat) (N5 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M6) N5)) (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int (tptp.aa_nat_set_int X7 N5)) (tptp.aa_nat_set_int X7 M6)))))))) (forall ((X7 tptp.fun_nat_rat)) (= (tptp.topolo4267028734544971653eq_rat X7) (or (forall ((M6 tptp.nat) (N5 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M6) N5)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat X7 M6)) (tptp.aa_nat_rat X7 N5))))) (forall ((M6 tptp.nat) (N5 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M6) N5)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat X7 N5)) (tptp.aa_nat_rat X7 M6)))))))) (forall ((X7 tptp.fun_nat_num)) (= (tptp.topolo1459490580787246023eq_num X7) (or (forall ((M6 tptp.nat) (N5 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M6) N5)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_nat_num X7 M6)) (tptp.aa_nat_num X7 N5))))) (forall ((M6 tptp.nat) (N5 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M6) N5)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_nat_num X7 N5)) (tptp.aa_nat_num X7 M6)))))))) (forall ((X7 tptp.fun_nat_nat)) (= (tptp.topolo4902158794631467389eq_nat X7) (or (forall ((M6 tptp.nat) (N5 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M6) N5)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat X7 M6)) (tptp.aa_nat_nat X7 N5))))) (forall ((M6 tptp.nat) (N5 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M6) N5)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat X7 N5)) (tptp.aa_nat_nat X7 M6)))))))) (forall ((X7 tptp.fun_nat_int)) (= (tptp.topolo4899668324122417113eq_int X7) (or (forall ((M6 tptp.nat) (N5 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M6) N5)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int X7 M6)) (tptp.aa_nat_int X7 N5))))) (forall ((M6 tptp.nat) (N5 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M6) N5)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int X7 N5)) (tptp.aa_nat_int X7 M6)))))))) (forall ((X tptp.complex)) (let ((_let_1 (tptp.aa_complex_complex tptp.sin_complex X))) (let ((_let_2 (tptp.aa_complex_complex tptp.cos_complex X))) (= (tptp.aa_complex_complex (tptp.plus_plus_complex (tptp.aa_complex_complex (tptp.times_times_complex _let_2) _let_2)) (tptp.aa_complex_complex (tptp.times_times_complex _let_1) _let_1)) tptp.one_one_complex)))) (forall ((X tptp.real)) (let ((_let_1 (tptp.aa_real_real tptp.sin_real X))) (let ((_let_2 (tptp.aa_real_real tptp.cos_real X))) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real _let_2) _let_2)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real _let_1) _let_1)) tptp.one_one_real)))) (forall ((N tptp.nat)) (= (tptp.aa_real_real tptp.sin_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real tptp.pi) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N))) tptp.zero_zero_real)) (forall ((N tptp.nat)) (= (tptp.aa_real_real tptp.sin_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N)) tptp.pi)) tptp.zero_zero_real)) (forall ((A tptp.fun_nat_complex) (X tptp.complex)) (= (tptp.pp (tptp.aa_complex_bool (tptp.sums_complex (tptp.aTP_Lamm_gy A)) X)) (= (tptp.aa_nat_complex A tptp.zero_zero_nat) X))) (forall ((A tptp.fun_nat_real) (X tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.sums_real (tptp.aTP_Lamm_ha A)) X)) (= (tptp.aa_nat_real A tptp.zero_zero_nat) X))) (= (tptp.aa_real_real tptp.cos_real _let_30) tptp.zero_zero_real) (= (tptp.aa_real_real tptp.sin_real _let_55) tptp.zero_zero_real) (= (tptp.aa_real_real tptp.sin_real _let_30) tptp.one_one_real) (= (tptp.aa_real_real tptp.cos_real _let_55) tptp.one_one_real) (forall ((X tptp.real)) (= (tptp.aa_real_real tptp.cos_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))) tptp.pi))) (tptp.aa_real_real tptp.cos_real X))) (forall ((X tptp.real)) (= (tptp.aa_real_real tptp.sin_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))) tptp.pi))) (tptp.aa_real_real tptp.sin_real X))) (forall ((X tptp.real)) (= (tptp.aa_real_real tptp.cos_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))) tptp.pi)) X)) (tptp.aa_real_real tptp.cos_real X))) (forall ((N tptp.nat)) (= (tptp.aa_real_real tptp.cos_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real tptp.pi) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)) N))) (forall ((N tptp.nat)) (= (tptp.aa_real_real tptp.cos_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N)) tptp.pi)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)) N))) (forall ((X tptp.real)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real tptp.sin_real X)) _let_1)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real tptp.cos_real X)) _let_1)) tptp.one_one_real))) (forall ((X tptp.complex)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.aa_complex_complex (tptp.plus_plus_complex (tptp.aa_nat_complex (tptp.power_power_complex (tptp.aa_complex_complex tptp.sin_complex X)) _let_1)) (tptp.aa_nat_complex (tptp.power_power_complex (tptp.aa_complex_complex tptp.cos_complex X)) _let_1)) tptp.one_one_complex))) (forall ((X tptp.real)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real tptp.cos_real X)) _let_1)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real tptp.sin_real X)) _let_1)) tptp.one_one_real))) (forall ((X tptp.complex)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.aa_complex_complex (tptp.plus_plus_complex (tptp.aa_nat_complex (tptp.power_power_complex (tptp.aa_complex_complex tptp.cos_complex X)) _let_1)) (tptp.aa_nat_complex (tptp.power_power_complex (tptp.aa_complex_complex tptp.sin_complex X)) _let_1)) tptp.one_one_complex))) (forall ((N tptp.nat)) (= (tptp.aa_real_real tptp.sin_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N))) tptp.pi)) tptp.zero_zero_real)) (forall ((N tptp.nat)) (= (tptp.aa_real_real tptp.cos_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N))) tptp.pi)) tptp.one_one_real)) (forall ((X tptp.real)) (= (tptp.aa_real_real tptp.sin_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))) tptp.pi)) X)) (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_real_real tptp.sin_real X)))) (= (tptp.aa_real_real tptp.cos_real _let_72) tptp.zero_zero_real) (= (tptp.aa_real_real tptp.sin_real _let_72) _let_57) (forall ((F tptp.fun_nat_real) (G tptp.fun_nat_real) (S tptp.real) (T tptp.real)) (=> (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_nat_real F N2)) (tptp.aa_nat_real G N2)))) (=> (tptp.pp (tptp.aa_real_bool (tptp.sums_real F) S)) (=> (tptp.pp (tptp.aa_real_bool (tptp.sums_real G) T)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real S) T)))))) (forall ((F tptp.fun_nat_nat) (G tptp.fun_nat_nat) (S tptp.nat) (T tptp.nat)) (=> (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat F N2)) (tptp.aa_nat_nat G N2)))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.sums_nat F) S)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.sums_nat G) T)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat S) T)))))) (forall ((F tptp.fun_nat_int) (G tptp.fun_nat_int) (S tptp.int) (T tptp.int)) (=> (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int F N2)) (tptp.aa_nat_int G N2)))) (=> (tptp.pp (tptp.aa_int_bool (tptp.sums_int F) S)) (=> (tptp.pp (tptp.aa_int_bool (tptp.sums_int G) T)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int S) T)))))) (forall ((X tptp.real) (Y tptp.real)) (exists ((R3 tptp.real) (A3 tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.times_times_real R3))) (and (= X (tptp.aa_real_real _let_1 (tptp.aa_real_real tptp.cos_real A3))) (= Y (tptp.aa_real_real _let_1 (tptp.aa_real_real tptp.sin_real A3))))))) (forall ((X tptp.complex) (Y tptp.complex)) (= (tptp.aa_complex_complex tptp.sin_complex (tptp.aa_complex_complex (tptp.minus_minus_complex X) Y)) (tptp.aa_complex_complex (tptp.minus_minus_complex (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_complex_complex tptp.sin_complex X)) (tptp.aa_complex_complex tptp.cos_complex Y))) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_complex_complex tptp.cos_complex X)) (tptp.aa_complex_complex tptp.sin_complex Y))))) (forall ((X tptp.real) (Y tptp.real)) (= (tptp.aa_real_real tptp.sin_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real X) Y)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real tptp.sin_real X)) (tptp.aa_real_real tptp.cos_real Y))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real tptp.cos_real X)) (tptp.aa_real_real tptp.sin_real Y))))) (forall ((X tptp.real) (Y tptp.real)) (= (tptp.aa_real_real tptp.sin_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) Y)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real tptp.sin_real X)) (tptp.aa_real_real tptp.cos_real Y))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real tptp.cos_real X)) (tptp.aa_real_real tptp.sin_real Y))))) (forall ((F tptp.fun_nat_real) (A tptp.real) (C tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.sums_real F) A)) (tptp.pp (tptp.aa_real_bool (tptp.sums_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_kf F) C)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real C) A))))) (forall ((F tptp.fun_nat_real) (A tptp.real) (C tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.sums_real F) A)) (tptp.pp (tptp.aa_real_bool (tptp.sums_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_fy F) C)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) C))))) (forall ((F tptp.fun_nat_real) (A tptp.real) (G tptp.fun_nat_real) (B2 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.sums_real F) A)) (=> (tptp.pp (tptp.aa_real_bool (tptp.sums_real G) B2)) (tptp.pp (tptp.aa_real_bool (tptp.sums_real (tptp.aa_fun1839206346889086768t_real (tptp.aTP_Lamm_gg F) G)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) B2)))))) (forall ((F tptp.fun_nat_nat) (A tptp.nat) (G tptp.fun_nat_nat) (B2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.sums_nat F) A)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.sums_nat G) B2)) (tptp.pp (tptp.aa_nat_bool (tptp.sums_nat (tptp.aa_fun5791449513213591928at_nat (tptp.aTP_Lamm_gf F) G)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) B2)))))) (forall ((F tptp.fun_nat_int) (A tptp.int) (G tptp.fun_nat_int) (B2 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.sums_int F) A)) (=> (tptp.pp (tptp.aa_int_bool (tptp.sums_int G) B2)) (tptp.pp (tptp.aa_int_bool (tptp.sums_int (tptp.aa_fun5565043122120104496at_int (tptp.aTP_Lamm_kd F) G)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) B2)))))) (forall ((F tptp.fun_nat_complex) (A tptp.complex) (G tptp.fun_nat_complex) (B2 tptp.complex)) (=> (tptp.pp (tptp.aa_complex_bool (tptp.sums_complex F) A)) (=> (tptp.pp (tptp.aa_complex_bool (tptp.sums_complex G) B2)) (tptp.pp (tptp.aa_complex_bool (tptp.sums_complex (tptp.aa_fun2955221450537884980omplex (tptp.aTP_Lamm_ke F) G)) (tptp.aa_complex_complex (tptp.minus_minus_complex A) B2)))))) (forall ((F tptp.fun_nat_real) (A tptp.real) (G tptp.fun_nat_real) (B2 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.sums_real F) A)) (=> (tptp.pp (tptp.aa_real_bool (tptp.sums_real G) B2)) (tptp.pp (tptp.aa_real_bool (tptp.sums_real (tptp.aa_fun1839206346889086768t_real (tptp.aTP_Lamm_gj F) G)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A) B2)))))) (forall ((F tptp.fun_nat_complex) (A tptp.complex) (C tptp.complex)) (=> (tptp.pp (tptp.aa_complex_bool (tptp.sums_complex F) A)) (tptp.pp (tptp.aa_complex_bool (tptp.sums_complex (tptp.aa_com8181001469867462503omplex (tptp.aTP_Lamm_kc F) C)) (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex A) C))))) (forall ((F tptp.fun_nat_real) (A tptp.real) (C tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.sums_real F) A)) (tptp.pp (tptp.aa_real_bool (tptp.sums_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_gl F) C)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real A) C))))) (forall ((X tptp.complex) (Y tptp.complex)) (= (tptp.aa_complex_complex tptp.cos_complex (tptp.aa_complex_complex (tptp.plus_plus_complex X) Y)) (tptp.aa_complex_complex (tptp.minus_minus_complex (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_complex_complex tptp.cos_complex X)) (tptp.aa_complex_complex tptp.cos_complex Y))) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_complex_complex tptp.sin_complex X)) (tptp.aa_complex_complex tptp.sin_complex Y))))) (forall ((X tptp.real) (Y tptp.real)) (= (tptp.aa_real_real tptp.cos_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) Y)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real tptp.cos_real X)) (tptp.aa_real_real tptp.cos_real Y))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real tptp.sin_real X)) (tptp.aa_real_real tptp.sin_real Y))))) (forall ((X tptp.complex) (Y tptp.complex)) (= (tptp.aa_complex_complex tptp.cos_complex (tptp.aa_complex_complex (tptp.minus_minus_complex X) Y)) (tptp.aa_complex_complex (tptp.plus_plus_complex (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_complex_complex tptp.cos_complex X)) (tptp.aa_complex_complex tptp.cos_complex Y))) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_complex_complex tptp.sin_complex X)) (tptp.aa_complex_complex tptp.sin_complex Y))))) (forall ((X tptp.real) (Y tptp.real)) (= (tptp.aa_real_real tptp.cos_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real X) Y)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real tptp.cos_real X)) (tptp.aa_real_real tptp.cos_real Y))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real tptp.sin_real X)) (tptp.aa_real_real tptp.sin_real Y))))) (forall ((X tptp.complex)) (let ((_let_1 (tptp.times_times_complex (tptp.numera6690914467698888265omplex (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.aa_complex_complex tptp.sin_complex (tptp.aa_complex_complex _let_1 X)) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_complex_complex _let_1 (tptp.aa_complex_complex tptp.sin_complex X))) (tptp.aa_complex_complex tptp.cos_complex X))))) (forall ((X tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.aa_real_real tptp.sin_real (tptp.aa_real_real _let_1 X)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real _let_1 (tptp.aa_real_real tptp.sin_real X))) (tptp.aa_real_real tptp.cos_real X))))) (forall ((X tptp.real)) (exists ((Y4 tptp.real)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.pi)) Y4)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y4) tptp.pi)) (= (tptp.aa_real_real tptp.sin_real Y4) (tptp.aa_real_real tptp.sin_real X)) (= (tptp.aa_real_real tptp.cos_real Y4) (tptp.aa_real_real tptp.cos_real X))))) (forall ((X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) X)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.sin_real X)) X)))) (forall ((X tptp.real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.sin_real X)) tptp.one_one_real))) (forall ((X tptp.real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.cos_real X)) tptp.one_one_real))) (forall ((X tptp.real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_real_real tptp.sin_real X))) (tptp.aa_real_real tptp.abs_abs_real X)))) (forall ((C tptp.complex) (F tptp.fun_nat_complex) (D tptp.complex)) (=> (not (= C tptp.zero_zero_complex)) (= (tptp.pp (tptp.aa_complex_bool (tptp.sums_complex (tptp.aa_fun2955221450537884980omplex (tptp.aTP_Lamm_kb C) F)) (tptp.aa_complex_complex (tptp.times_times_complex C) D))) (tptp.pp (tptp.aa_complex_bool (tptp.sums_complex F) D))))) (forall ((C tptp.real) (F tptp.fun_nat_real) (D tptp.real)) (=> (not (= C tptp.zero_zero_real)) (= (tptp.pp (tptp.aa_real_bool (tptp.sums_real (tptp.aa_fun1839206346889086768t_real (tptp.aTP_Lamm_gc C) F)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real C) D))) (tptp.pp (tptp.aa_real_bool (tptp.sums_real F) D))))) (forall ((C tptp.complex) (F tptp.fun_nat_complex) (D tptp.complex)) (=> (not (= C tptp.zero_zero_complex)) (= (tptp.pp (tptp.aa_complex_bool (tptp.sums_complex (tptp.aa_fun2955221450537884980omplex (tptp.aTP_Lamm_mg C) F)) (tptp.aa_complex_complex (tptp.times_times_complex D) C))) (tptp.pp (tptp.aa_complex_bool (tptp.sums_complex F) D))))) (forall ((C tptp.real) (F tptp.fun_nat_real) (D tptp.real)) (=> (not (= C tptp.zero_zero_real)) (= (tptp.pp (tptp.aa_real_bool (tptp.sums_real (tptp.aa_fun1839206346889086768t_real (tptp.aTP_Lamm_mh C) F)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real D) C))) (tptp.pp (tptp.aa_real_bool (tptp.sums_real F) D))))) (forall ((X tptp.real) (Y tptp.real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real tptp.sin_real X)) (tptp.aa_real_real tptp.sin_real Y))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real tptp.cos_real X)) (tptp.aa_real_real tptp.cos_real Y))))) tptp.one_one_real))) (forall ((X tptp.complex)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.aa_nat_complex (tptp.power_power_complex (tptp.aa_complex_complex tptp.cos_complex X)) _let_1) (tptp.aa_complex_complex (tptp.minus_minus_complex tptp.one_one_complex) (tptp.aa_nat_complex (tptp.power_power_complex (tptp.aa_complex_complex tptp.sin_complex X)) _let_1))))) (forall ((X tptp.real)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real tptp.cos_real X)) _let_1) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real tptp.one_one_real) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real tptp.sin_real X)) _let_1))))) (forall ((X tptp.complex)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.aa_nat_complex (tptp.power_power_complex (tptp.aa_complex_complex tptp.sin_complex X)) _let_1) (tptp.aa_complex_complex (tptp.minus_minus_complex tptp.one_one_complex) (tptp.aa_nat_complex (tptp.power_power_complex (tptp.aa_complex_complex tptp.cos_complex X)) _let_1))))) (forall ((X tptp.real)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real tptp.sin_real X)) _let_1) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real tptp.one_one_real) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real tptp.cos_real X)) _let_1))))) (forall ((C tptp.complex) (F tptp.fun_nat_complex) (A tptp.complex)) (=> (tptp.pp (tptp.aa_complex_bool (tptp.sums_complex (tptp.aa_fun2955221450537884980omplex (tptp.aTP_Lamm_kb C) F)) A)) (=> (not (= C tptp.zero_zero_complex)) (tptp.pp (tptp.aa_complex_bool (tptp.sums_complex F) (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex A) C)))))) (forall ((C tptp.real) (F tptp.fun_nat_real) (A tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.sums_real (tptp.aa_fun1839206346889086768t_real (tptp.aTP_Lamm_gc C) F)) A)) (=> (not (= C tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.sums_real F) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real A) C)))))) (forall ((F tptp.fun_nat_real) (S tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.sums_real (tptp.aTP_Lamm_hw F)) S)) (tptp.pp (tptp.aa_real_bool (tptp.sums_real F) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real S) (tptp.aa_nat_real F tptp.zero_zero_nat)))))) (forall ((F tptp.fun_nat_real) (L tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.sums_real (tptp.aTP_Lamm_hw F)) L)) (tptp.pp (tptp.aa_real_bool (tptp.sums_real F) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real L) (tptp.aa_nat_real F tptp.zero_zero_nat)))))) (forall ((F tptp.fun_nat_nat) (L tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.sums_nat (tptp.aTP_Lamm_hv F)) L)) (tptp.pp (tptp.aa_nat_bool (tptp.sums_nat F) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat L) (tptp.aa_nat_nat F tptp.zero_zero_nat)))))) (forall ((F tptp.fun_nat_int) (L tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.sums_int (tptp.aTP_Lamm_hu F)) L)) (tptp.pp (tptp.aa_int_bool (tptp.sums_int F) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int L) (tptp.aa_nat_int F tptp.zero_zero_nat)))))) (forall ((X tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool _let_1 X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) tptp.pi)) (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real tptp.sin_real X))))))) (forall ((X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) X)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real X)) (tptp.aa_real_real tptp.sin_real X))))) (forall ((X tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool _let_1 X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) tptp.pi)) (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real tptp.sin_real X))))))) (forall ((N tptp.nat) (F tptp.fun_nat_complex) (S tptp.complex)) (=> (forall ((I3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I3) N)) (= (tptp.aa_nat_complex F I3) tptp.zero_zero_complex))) (= (tptp.pp (tptp.aa_complex_bool (tptp.sums_complex (tptp.aa_fun2955221450537884980omplex (tptp.aTP_Lamm_mi N) F)) S)) (tptp.pp (tptp.aa_complex_bool (tptp.sums_complex F) S))))) (forall ((N tptp.nat) (F tptp.fun_nat_real) (S tptp.real)) (=> (forall ((I3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I3) N)) (= (tptp.aa_nat_real F I3) tptp.zero_zero_real))) (= (tptp.pp (tptp.aa_real_bool (tptp.sums_real (tptp.aa_fun1839206346889086768t_real (tptp.aTP_Lamm_mj N) F)) S)) (tptp.pp (tptp.aa_real_bool (tptp.sums_real F) S))))) (forall ((X tptp.real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)) (tptp.aa_real_real tptp.sin_real X)))) (forall ((Y tptp.real) (X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) Y)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) tptp.pi)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.cos_real X)) (tptp.aa_real_real tptp.cos_real Y))))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y))) (let ((_let_2 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool _let_2 X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) tptp.pi)) (=> (tptp.pp (tptp.aa_real_bool _let_2 Y)) (=> (tptp.pp (tptp.aa_real_bool _let_1 tptp.pi)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.cos_real X)) (tptp.aa_real_real tptp.cos_real Y))) (tptp.pp (tptp.aa_real_bool _let_1 X)))))))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool _let_1 X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) tptp.pi)) (=> (tptp.pp (tptp.aa_real_bool _let_1 Y)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y) tptp.pi)) (=> (= (tptp.aa_real_real tptp.cos_real X) (tptp.aa_real_real tptp.cos_real Y)) (= X Y)))))))) (forall ((X tptp.real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)) (tptp.aa_real_real tptp.cos_real X)))) (forall ((X tptp.real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_real_real tptp.sin_real X))) tptp.one_one_real))) (forall ((X tptp.real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_real_real tptp.cos_real X))) tptp.one_one_real))) (forall ((W tptp.complex) (Z tptp.complex)) (= (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_complex_complex tptp.sin_complex W)) (tptp.aa_complex_complex tptp.sin_complex Z)) (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex (tptp.aa_complex_complex (tptp.minus_minus_complex (tptp.aa_complex_complex tptp.cos_complex (tptp.aa_complex_complex (tptp.minus_minus_complex W) Z))) (tptp.aa_complex_complex tptp.cos_complex (tptp.aa_complex_complex (tptp.plus_plus_complex W) Z)))) (tptp.numera6690914467698888265omplex (tptp.aa_num_num tptp.bit0 tptp.one))))) (forall ((W tptp.real) (Z tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real tptp.sin_real W)) (tptp.aa_real_real tptp.sin_real Z)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real tptp.cos_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real W) Z))) (tptp.aa_real_real tptp.cos_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real W) Z)))) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))))) (forall ((W tptp.complex) (Z tptp.complex)) (= (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_complex_complex tptp.sin_complex W)) (tptp.aa_complex_complex tptp.cos_complex Z)) (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex (tptp.aa_complex_complex (tptp.plus_plus_complex (tptp.aa_complex_complex tptp.sin_complex (tptp.aa_complex_complex (tptp.plus_plus_complex W) Z))) (tptp.aa_complex_complex tptp.sin_complex (tptp.aa_complex_complex (tptp.minus_minus_complex W) Z)))) (tptp.numera6690914467698888265omplex (tptp.aa_num_num tptp.bit0 tptp.one))))) (forall ((W tptp.real) (Z tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real tptp.sin_real W)) (tptp.aa_real_real tptp.cos_real Z)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real tptp.sin_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real W) Z))) (tptp.aa_real_real tptp.sin_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real W) Z)))) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))))) (forall ((W tptp.complex) (Z tptp.complex)) (= (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_complex_complex tptp.cos_complex W)) (tptp.aa_complex_complex tptp.sin_complex Z)) (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex (tptp.aa_complex_complex (tptp.minus_minus_complex (tptp.aa_complex_complex tptp.sin_complex (tptp.aa_complex_complex (tptp.plus_plus_complex W) Z))) (tptp.aa_complex_complex tptp.sin_complex (tptp.aa_complex_complex (tptp.minus_minus_complex W) Z)))) (tptp.numera6690914467698888265omplex (tptp.aa_num_num tptp.bit0 tptp.one))))) (forall ((W tptp.real) (Z tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real tptp.cos_real W)) (tptp.aa_real_real tptp.sin_real Z)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real tptp.sin_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real W) Z))) (tptp.aa_real_real tptp.sin_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real W) Z)))) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))))) (forall ((W tptp.complex) (Z tptp.complex)) (let ((_let_1 (tptp.numera6690914467698888265omplex (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.aa_complex_complex (tptp.plus_plus_complex (tptp.aa_complex_complex tptp.sin_complex W)) (tptp.aa_complex_complex tptp.sin_complex Z)) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_complex_complex (tptp.times_times_complex _let_1) (tptp.aa_complex_complex tptp.sin_complex (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex (tptp.aa_complex_complex (tptp.plus_plus_complex W) Z)) _let_1)))) (tptp.aa_complex_complex tptp.cos_complex (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex (tptp.aa_complex_complex (tptp.minus_minus_complex W) Z)) _let_1)))))) (forall ((W tptp.real) (Z tptp.real)) (let ((_let_1 (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real tptp.sin_real W)) (tptp.aa_real_real tptp.sin_real Z)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real _let_1) (tptp.aa_real_real tptp.sin_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real W) Z)) _let_1)))) (tptp.aa_real_real tptp.cos_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real W) Z)) _let_1)))))) (forall ((W tptp.complex) (Z tptp.complex)) (let ((_let_1 (tptp.numera6690914467698888265omplex (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.aa_complex_complex (tptp.minus_minus_complex (tptp.aa_complex_complex tptp.sin_complex W)) (tptp.aa_complex_complex tptp.sin_complex Z)) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_complex_complex (tptp.times_times_complex _let_1) (tptp.aa_complex_complex tptp.sin_complex (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex (tptp.aa_complex_complex (tptp.minus_minus_complex W) Z)) _let_1)))) (tptp.aa_complex_complex tptp.cos_complex (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex (tptp.aa_complex_complex (tptp.plus_plus_complex W) Z)) _let_1)))))) (forall ((W tptp.real) (Z tptp.real)) (let ((_let_1 (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real tptp.sin_real W)) (tptp.aa_real_real tptp.sin_real Z)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real _let_1) (tptp.aa_real_real tptp.sin_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real W) Z)) _let_1)))) (tptp.aa_real_real tptp.cos_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real W) Z)) _let_1)))))) (forall ((W tptp.complex) (Z tptp.complex)) (let ((_let_1 (tptp.numera6690914467698888265omplex (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.aa_complex_complex (tptp.minus_minus_complex (tptp.aa_complex_complex tptp.cos_complex W)) (tptp.aa_complex_complex tptp.cos_complex Z)) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_complex_complex (tptp.times_times_complex _let_1) (tptp.aa_complex_complex tptp.sin_complex (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex (tptp.aa_complex_complex (tptp.plus_plus_complex W) Z)) _let_1)))) (tptp.aa_complex_complex tptp.sin_complex (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex (tptp.aa_complex_complex (tptp.minus_minus_complex Z) W)) _let_1)))))) (forall ((W tptp.real) (Z tptp.real)) (let ((_let_1 (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real tptp.cos_real W)) (tptp.aa_real_real tptp.cos_real Z)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real _let_1) (tptp.aa_real_real tptp.sin_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real W) Z)) _let_1)))) (tptp.aa_real_real tptp.sin_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real Z) W)) _let_1)))))) (forall ((X tptp.complex)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (let ((_let_2 (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1))) (= (tptp.aa_complex_complex tptp.cos_complex (tptp.aa_complex_complex (tptp.times_times_complex (tptp.numera6690914467698888265omplex _let_1)) X)) (tptp.aa_complex_complex (tptp.minus_minus_complex (tptp.aa_nat_complex (tptp.power_power_complex (tptp.aa_complex_complex tptp.cos_complex X)) _let_2)) (tptp.aa_nat_complex (tptp.power_power_complex (tptp.aa_complex_complex tptp.sin_complex X)) _let_2)))))) (forall ((X tptp.real)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (let ((_let_2 (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1))) (= (tptp.aa_real_real tptp.cos_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_num_real tptp.numeral_numeral_real _let_1)) X)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real tptp.cos_real X)) _let_2)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real tptp.sin_real X)) _let_2)))))) (forall ((W tptp.complex)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (let ((_let_2 (tptp.times_times_complex (tptp.numera6690914467698888265omplex _let_1)))) (= (tptp.aa_complex_complex tptp.cos_complex (tptp.aa_complex_complex _let_2 W)) (tptp.aa_complex_complex (tptp.minus_minus_complex tptp.one_one_complex) (tptp.aa_complex_complex _let_2 (tptp.aa_nat_complex (tptp.power_power_complex (tptp.aa_complex_complex tptp.sin_complex W)) (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1)))))))) (forall ((W tptp.real)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (let ((_let_2 (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_num_real tptp.numeral_numeral_real _let_1)))) (= (tptp.aa_real_real tptp.cos_real (tptp.aa_real_real _let_2 W)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real tptp.one_one_real) (tptp.aa_real_real _let_2 (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real tptp.sin_real W)) (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1)))))))) (forall ((M tptp.nat) (Z tptp.complex)) (tptp.pp (tptp.aa_complex_bool (tptp.sums_complex (tptp.aa_com8181001469867462503omplex (tptp.aTP_Lamm_mk M) Z)) (tptp.aa_nat_complex (tptp.power_power_complex Z) M)))) (forall ((M tptp.nat) (Z tptp.real)) (tptp.pp (tptp.aa_real_bool (tptp.sums_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_ml M) Z)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Z) M)))) (forall ((M tptp.nat) (Z tptp.int)) (tptp.pp (tptp.aa_int_bool (tptp.sums_int (tptp.aa_int_fun_nat_int (tptp.aTP_Lamm_mm M) Z)) (tptp.aa_nat_int (tptp.power_power_int Z) M)))) (forall ((A tptp.fun_nat_complex)) (tptp.pp (tptp.aa_complex_bool (tptp.sums_complex (tptp.aTP_Lamm_gy A)) (tptp.aa_nat_complex A tptp.zero_zero_nat)))) (forall ((A tptp.fun_nat_real)) (tptp.pp (tptp.aa_real_bool (tptp.sums_real (tptp.aTP_Lamm_ha A)) (tptp.aa_nat_real A tptp.zero_zero_nat)))) (not (= _let_70 tptp.zero_zero_real)) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool _let_1 X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) tptp.pi)) (=> (tptp.pp (tptp.aa_real_bool _let_1 Y)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y) tptp.pi)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.cos_real X)) (tptp.aa_real_real tptp.cos_real Y))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y) X))))))))) (forall ((Y tptp.real) (X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) Y)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) tptp.pi)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.cos_real X)) (tptp.aa_real_real tptp.cos_real Y))))))) (forall ((X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.pi)) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) tptp.pi)) (=> (= (tptp.aa_real_real tptp.sin_real X) tptp.zero_zero_real) (= X tptp.zero_zero_real))))) (forall ((F tptp.fun_nat_real) (N tptp.nat) (S tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.sums_real (tptp.aa_nat_fun_nat_real (tptp.aTP_Lamm_hm F) N)) S)) (tptp.pp (tptp.aa_real_bool (tptp.sums_real F) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real S) (tptp.groups6591440286371151544t_real F (tptp.set_ord_lessThan_nat N))))))) (forall ((F tptp.fun_nat_complex) (S tptp.complex) (N tptp.nat)) (=> (tptp.pp (tptp.aa_complex_bool (tptp.sums_complex F) S)) (tptp.pp (tptp.aa_complex_bool (tptp.sums_complex (tptp.aa_nat6454746962644518025omplex (tptp.aTP_Lamm_kk F) N)) (tptp.aa_complex_complex (tptp.minus_minus_complex S) (tptp.groups2073611262835488442omplex F (tptp.set_ord_lessThan_nat N))))))) (forall ((F tptp.fun_nat_real) (S tptp.real) (N tptp.nat)) (=> (tptp.pp (tptp.aa_real_bool (tptp.sums_real F) S)) (tptp.pp (tptp.aa_real_bool (tptp.sums_real (tptp.aa_nat_fun_nat_real (tptp.aTP_Lamm_hm F) N)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real S) (tptp.groups6591440286371151544t_real F (tptp.set_ord_lessThan_nat N))))))) (forall ((F tptp.fun_nat_complex) (N tptp.nat) (S tptp.complex)) (= (tptp.pp (tptp.aa_complex_bool (tptp.sums_complex (tptp.aa_nat6454746962644518025omplex (tptp.aTP_Lamm_kk F) N)) (tptp.aa_complex_complex (tptp.minus_minus_complex S) (tptp.groups2073611262835488442omplex F (tptp.set_ord_lessThan_nat N))))) (tptp.pp (tptp.aa_complex_bool (tptp.sums_complex F) S)))) (forall ((F tptp.fun_nat_real) (N tptp.nat) (S tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.sums_real (tptp.aa_nat_fun_nat_real (tptp.aTP_Lamm_hm F) N)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real S) (tptp.groups6591440286371151544t_real F (tptp.set_ord_lessThan_nat N))))) (tptp.pp (tptp.aa_real_bool (tptp.sums_real F) S)))) (forall ((X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.abs_abs_real X)) tptp.pi)) (= (= (tptp.aa_real_real tptp.sin_real X) tptp.zero_zero_real) (= X tptp.zero_zero_real)))) (forall ((Y tptp.real) (X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.pi)) Y)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.cos_real Y)) (tptp.aa_real_real tptp.cos_real X))))))) (forall ((G tptp.fun_nat_complex) (S2 tptp.complex) (A4 tptp.set_nat) (S4 tptp.complex) (F tptp.fun_nat_complex)) (=> (tptp.pp (tptp.aa_complex_bool (tptp.sums_complex G) S2)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A4)) (=> (= S4 (tptp.aa_complex_complex (tptp.plus_plus_complex S2) (tptp.groups2073611262835488442omplex (tptp.aa_fun2955221450537884980omplex (tptp.aTP_Lamm_mn G) F) A4))) (tptp.pp (tptp.aa_complex_bool (tptp.sums_complex (tptp.aa_fun2955221450537884980omplex (tptp.aa_set5115289136882354743omplex (tptp.aTP_Lamm_mo G) A4) F)) S4)))))) (forall ((G tptp.fun_nat_real) (S2 tptp.real) (A4 tptp.set_nat) (S4 tptp.real) (F tptp.fun_nat_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.sums_real G) S2)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A4)) (=> (= S4 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real S2) (tptp.groups6591440286371151544t_real (tptp.aa_fun1839206346889086768t_real (tptp.aTP_Lamm_mp G) F) A4))) (tptp.pp (tptp.aa_real_bool (tptp.sums_real (tptp.aa_fun1839206346889086768t_real (tptp.aa_set1316517696749040435t_real (tptp.aTP_Lamm_mq G) A4) F)) S4)))))) (forall ((Y tptp.real) (X tptp.real)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) Y)) (=> (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) _let_1)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Y) _let_1)) tptp.one_one_real) (exists ((T4 tptp.real)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) T4)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real T4) tptp.pi)) (= X (tptp.aa_real_real tptp.cos_real T4)) (= Y (tptp.aa_real_real tptp.sin_real T4)))))))) (forall ((X tptp.real) (M tptp.nat)) (let ((_let_1 (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X))) (= (tptp.aa_real_real tptp.sin_real (tptp.aa_real_real _let_2 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real (tptp.aa_nat_nat tptp.suc M))) tptp.pi)) _let_1))) (tptp.aa_real_real tptp.cos_real (tptp.aa_real_real _let_2 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real M)) tptp.pi)) _let_1))))))) (forall ((X tptp.real) (M tptp.nat)) (let ((_let_1 (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X))) (= (tptp.aa_real_real tptp.cos_real (tptp.aa_real_real _let_2 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real (tptp.aa_nat_nat tptp.suc M))) tptp.pi)) _let_1))) (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_real_real tptp.sin_real (tptp.aa_real_real _let_2 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real M)) tptp.pi)) _let_1)))))))) (forall ((X tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool _let_1 X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))) (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real tptp.sin_real X))))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real _let_70) tptp.zero_zero_real)) (exists ((X4 tptp.real)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) X4)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X4) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.aa_real_real tptp.cos_real X4) tptp.zero_zero_real) (forall ((Y5 tptp.real)) (=> (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) Y5)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y5) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.aa_real_real tptp.cos_real Y5) tptp.zero_zero_real)) (= Y5 X4))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real _let_70) tptp.zero_zero_real)) (forall ((Y tptp.real) (X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.pi)) Y)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.cos_real Y)) (tptp.aa_real_real tptp.cos_real X))))))) (forall ((Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)) Y)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y) tptp.one_one_real)) (exists ((X4 tptp.real)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) X4)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X4) tptp.pi)) (= (tptp.aa_real_real tptp.cos_real X4) Y) (forall ((Y5 tptp.real)) (=> (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) Y5)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y5) tptp.pi)) (= (tptp.aa_real_real tptp.cos_real Y5) Y)) (= Y5 X4)))))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool _let_2 X)) (=> (tptp.pp (tptp.aa_real_bool _let_2 Y)) (=> (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) _let_1)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Y) _let_1)) tptp.one_one_real) (exists ((T4 tptp.real)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) T4)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real T4) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))))) (= X (tptp.aa_real_real tptp.cos_real T4)) (= Y (tptp.aa_real_real tptp.sin_real T4)))))))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) _let_1)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Y) _let_1)) tptp.one_one_real) (exists ((T4 tptp.real)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) T4)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real T4) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))) tptp.pi))) (= X (tptp.aa_real_real tptp.cos_real T4)) (= Y (tptp.aa_real_real tptp.sin_real T4))))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) _let_1)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Y) _let_1)) tptp.one_one_real) (not (forall ((T4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) T4)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real T4) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))) tptp.pi))) (=> (= X (tptp.aa_real_real tptp.cos_real T4)) (not (= Y (tptp.aa_real_real tptp.sin_real T4))))))))))) (forall ((N tptp.nat)) (=> (not (= N tptp.zero_zero_nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_real_real tptp.sin_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N))))))) (forall ((W tptp.complex) (Z tptp.complex)) (= (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_complex_complex tptp.cos_complex W)) (tptp.aa_complex_complex tptp.cos_complex Z)) (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex (tptp.aa_complex_complex (tptp.plus_plus_complex (tptp.aa_complex_complex tptp.cos_complex (tptp.aa_complex_complex (tptp.minus_minus_complex W) Z))) (tptp.aa_complex_complex tptp.cos_complex (tptp.aa_complex_complex (tptp.plus_plus_complex W) Z)))) (tptp.numera6690914467698888265omplex (tptp.aa_num_num tptp.bit0 tptp.one))))) (forall ((W tptp.real) (Z tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real tptp.cos_real W)) (tptp.aa_real_real tptp.cos_real Z)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real tptp.cos_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real W) Z))) (tptp.aa_real_real tptp.cos_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real W) Z)))) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))))) (forall ((W tptp.complex) (Z tptp.complex)) (let ((_let_1 (tptp.numera6690914467698888265omplex (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.aa_complex_complex (tptp.plus_plus_complex (tptp.aa_complex_complex tptp.cos_complex W)) (tptp.aa_complex_complex tptp.cos_complex Z)) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_complex_complex (tptp.times_times_complex _let_1) (tptp.aa_complex_complex tptp.cos_complex (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex (tptp.aa_complex_complex (tptp.plus_plus_complex W) Z)) _let_1)))) (tptp.aa_complex_complex tptp.cos_complex (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex (tptp.aa_complex_complex (tptp.minus_minus_complex W) Z)) _let_1)))))) (forall ((W tptp.real) (Z tptp.real)) (let ((_let_1 (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real tptp.cos_real W)) (tptp.aa_real_real tptp.cos_real Z)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real _let_1) (tptp.aa_real_real tptp.cos_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real W) Z)) _let_1)))) (tptp.aa_real_real tptp.cos_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real W) Z)) _let_1)))))) (forall ((C tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real C)) tptp.one_one_real)) (tptp.pp (tptp.aa_real_bool (tptp.sums_real (tptp.aa_real_fun_nat_real tptp.power_power_real C)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.one_one_real) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real tptp.one_one_real) C)))))) (forall ((C tptp.complex)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex C)) tptp.one_one_real)) (tptp.pp (tptp.aa_complex_bool (tptp.sums_complex (tptp.power_power_complex C)) (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex tptp.one_one_complex) (tptp.aa_complex_complex (tptp.minus_minus_complex tptp.one_one_complex) C)))))) (tptp.pp (tptp.aa_real_bool (tptp.sums_real tptp.aTP_Lamm_mr) tptp.one_one_real)) (forall ((X tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool _let_1 X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))))) (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real tptp.sin_real X))))))) (forall ((X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.pi) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))) tptp.pi))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.sin_real X)) tptp.zero_zero_real))))) (forall ((X tptp.real)) (let ((_let_1 (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) _let_1)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.cos_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real _let_1) X))) tptp.one_one_real)))))) (= (tptp.aa_real_real tptp.sin_real _let_63) _let_68) (forall ((X tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool _let_1 X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))))) (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real tptp.cos_real X))))))) (forall ((Y tptp.real) (X tptp.real)) (let ((_let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real _let_1)) Y)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) _let_1)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.sin_real Y)) (tptp.aa_real_real tptp.sin_real X)))))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X))) (let ((_let_2 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_3 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real _let_2)))) (=> (tptp.pp (tptp.aa_real_bool _let_3 X)) (=> (tptp.pp (tptp.aa_real_bool _let_1 _let_2)) (=> (tptp.pp (tptp.aa_real_bool _let_3 Y)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y) _let_2)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.sin_real X)) (tptp.aa_real_real tptp.sin_real Y))) (tptp.pp (tptp.aa_real_bool _let_1 Y))))))))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_2 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real _let_1)))) (=> (tptp.pp (tptp.aa_real_bool _let_2 X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) _let_1)) (=> (tptp.pp (tptp.aa_real_bool _let_2 Y)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y) _let_1)) (=> (= (tptp.aa_real_real tptp.sin_real X) (tptp.aa_real_real tptp.sin_real Y)) (= X Y))))))))) (= (tptp.aa_real_real tptp.cos_real _let_62) _let_68) (forall ((W tptp.complex)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (let ((_let_2 (tptp.times_times_complex (tptp.numera6690914467698888265omplex _let_1)))) (= (tptp.aa_complex_complex tptp.cos_complex (tptp.aa_complex_complex _let_2 W)) (tptp.aa_complex_complex (tptp.minus_minus_complex (tptp.aa_complex_complex _let_2 (tptp.aa_nat_complex (tptp.power_power_complex (tptp.aa_complex_complex tptp.cos_complex W)) (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1)))) tptp.one_one_complex))))) (forall ((W tptp.real)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (let ((_let_2 (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_num_real tptp.numeral_numeral_real _let_1)))) (= (tptp.aa_real_real tptp.cos_real (tptp.aa_real_real _let_2 W)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real _let_2 (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real tptp.cos_real W)) (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1)))) tptp.one_one_real))))) (forall ((X tptp.complex)) (let ((_let_1 (tptp.aa_complex_complex tptp.cos_complex X))) (let ((_let_2 (tptp.aa_num_num tptp.bit1 tptp.one))) (let ((_let_3 (tptp.times_times_complex (tptp.numera6690914467698888265omplex _let_2)))) (= (tptp.aa_complex_complex tptp.cos_complex (tptp.aa_complex_complex _let_3 X)) (tptp.aa_complex_complex (tptp.minus_minus_complex (tptp.aa_complex_complex (tptp.times_times_complex (tptp.numera6690914467698888265omplex (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit0 tptp.one)))) (tptp.aa_nat_complex (tptp.power_power_complex _let_1) (tptp.aa_num_nat tptp.numeral_numeral_nat _let_2)))) (tptp.aa_complex_complex _let_3 _let_1))))))) (forall ((X tptp.real)) (let ((_let_1 (tptp.aa_real_real tptp.cos_real X))) (let ((_let_2 (tptp.aa_num_num tptp.bit1 tptp.one))) (let ((_let_3 (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_num_real tptp.numeral_numeral_real _let_2)))) (= (tptp.aa_real_real tptp.cos_real (tptp.aa_real_real _let_3 X)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit0 tptp.one)))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real _let_1) (tptp.aa_num_nat tptp.numeral_numeral_nat _let_2)))) (tptp.aa_real_real _let_3 _let_1))))))) (forall ((G tptp.fun_nat_real) (X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.sums_real G) X)) (tptp.pp (tptp.aa_real_bool (tptp.sums_real (tptp.aTP_Lamm_ms G)) X)))) (forall ((G tptp.fun_nat_real) (X tptp.real) (F tptp.fun_nat_real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.sums_real G) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.sums_real F) Y)) (tptp.pp (tptp.aa_real_bool (tptp.sums_real (tptp.aa_fun1839206346889086768t_real (tptp.aTP_Lamm_mt G) F)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) Y)))))) (forall ((X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.pi) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))) tptp.pi))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.sin_real X)) tptp.zero_zero_real))))) (forall ((X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.pi)) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.sin_real X)) tptp.zero_zero_real))))) (forall ((Y tptp.real) (X tptp.real)) (let ((_let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real _let_1)) Y)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) _let_1)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.sin_real Y)) (tptp.aa_real_real tptp.sin_real X)))))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_2 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real _let_1)))) (=> (tptp.pp (tptp.aa_real_bool _let_2 X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) _let_1)) (=> (tptp.pp (tptp.aa_real_bool _let_2 Y)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y) _let_1)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.sin_real X)) (tptp.aa_real_real tptp.sin_real Y))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Y)))))))))) (forall ((Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)) Y)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y) tptp.one_one_real)) (exists ((X4 tptp.real)) (let ((_let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))))) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real _let_1)) X4)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X4) _let_1)) (= (tptp.aa_real_real tptp.sin_real X4) Y) (forall ((Y5 tptp.real)) (let ((_let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))))) (=> (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real _let_1)) Y5)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y5) _let_1)) (= (tptp.aa_real_real tptp.sin_real Y5) Y)) (= Y5 X4)))))))))) (forall ((X tptp.real)) (let ((_let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.uminus_uminus_real _let_1)) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) _let_1)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) (tptp.aa_real_real tptp.cos_real X))))))) (forall ((X tptp.real)) (let ((_let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real _let_1)) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) _let_1)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_real_real tptp.cos_real X))))))) (forall ((X tptp.real)) (= (= (tptp.aa_real_real tptp.cos_real X) tptp.one_one_real) (or (exists ((X3 tptp.nat)) (= X (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real X3)) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))) tptp.pi))) (exists ((X3 tptp.nat)) (= X (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real X3)) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))) tptp.pi))))))) (forall ((D4 tptp.fun_Pr6287530515171585797m_bool) (R2 tptp.fun_Pr5837708615769641901m_bool) (X tptp.product_prod_num_num) (P tptp.fun_Pr6287530515171585797m_bool)) (=> (tptp.ord_le998981803562422117m_bool D4 (tptp.accp_P3113834385874906142um_num R2)) (=> (forall ((X4 tptp.product_prod_num_num) (Z4 tptp.product_prod_num_num)) (=> (tptp.pp (tptp.aa_Pro762926636801165566m_bool D4 X4)) (=> (tptp.pp (tptp.aa_Pro762926636801165566m_bool (tptp.aa_Pro2164613399825298270m_bool R2 Z4) X4)) (tptp.pp (tptp.aa_Pro762926636801165566m_bool D4 Z4))))) (=> (tptp.pp (tptp.aa_Pro762926636801165566m_bool D4 X)) (=> (forall ((X4 tptp.product_prod_num_num)) (=> (tptp.pp (tptp.aa_Pro762926636801165566m_bool D4 X4)) (=> (forall ((Z3 tptp.product_prod_num_num)) (=> (tptp.pp (tptp.aa_Pro762926636801165566m_bool (tptp.aa_Pro2164613399825298270m_bool R2 Z3) X4)) (tptp.pp (tptp.aa_Pro762926636801165566m_bool P Z3)))) (tptp.pp (tptp.aa_Pro762926636801165566m_bool P X4))))) (tptp.pp (tptp.aa_Pro762926636801165566m_bool P X))))))) (forall ((D4 tptp.fun_Pr7757163693017731481t_bool) (R2 tptp.fun_Pr248683899324676269t_bool) (X tptp.product_prod_nat_nat) (P tptp.fun_Pr7757163693017731481t_bool)) (=> (tptp.pp (tptp.aa_fun8663595511526100224l_bool (tptp.ord_le2468614981408567801t_bool D4) (tptp.accp_P4275260045618599050at_nat R2))) (=> (forall ((X4 tptp.product_prod_nat_nat) (Z4 tptp.product_prod_nat_nat)) (=> (tptp.pp (tptp.aa_Pro2232559814647311250t_bool D4 X4)) (=> (tptp.pp (tptp.aa_Pro2232559814647311250t_bool (tptp.aa_Pro595088089689268830t_bool R2 Z4) X4)) (tptp.pp (tptp.aa_Pro2232559814647311250t_bool D4 Z4))))) (=> (tptp.pp (tptp.aa_Pro2232559814647311250t_bool D4 X)) (=> (forall ((X4 tptp.product_prod_nat_nat)) (=> (tptp.pp (tptp.aa_Pro2232559814647311250t_bool D4 X4)) (=> (forall ((Z3 tptp.product_prod_nat_nat)) (=> (tptp.pp (tptp.aa_Pro2232559814647311250t_bool (tptp.aa_Pro595088089689268830t_bool R2 Z3) X4)) (tptp.pp (tptp.aa_Pro2232559814647311250t_bool P Z3)))) (tptp.pp (tptp.aa_Pro2232559814647311250t_bool P X4))))) (tptp.pp (tptp.aa_Pro2232559814647311250t_bool P X))))))) (forall ((D4 tptp.fun_Pr803113274115125473t_bool) (R2 tptp.fun_Pr3099820731930151597t_bool) (X tptp.product_prod_int_int) (P tptp.fun_Pr803113274115125473t_bool)) (=> (tptp.ord_le4737936599360737601t_bool D4 (tptp.accp_P1096762738010456898nt_int R2)) (=> (forall ((X4 tptp.product_prod_int_int) (Z4 tptp.product_prod_int_int)) (=> (tptp.pp (tptp.aa_Pro4501881432599481050t_bool D4 X4)) (=> (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.aa_Pro1534211998248933470t_bool R2 Z4) X4)) (tptp.pp (tptp.aa_Pro4501881432599481050t_bool D4 Z4))))) (=> (tptp.pp (tptp.aa_Pro4501881432599481050t_bool D4 X)) (=> (forall ((X4 tptp.product_prod_int_int)) (=> (tptp.pp (tptp.aa_Pro4501881432599481050t_bool D4 X4)) (=> (forall ((Z3 tptp.product_prod_int_int)) (=> (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.aa_Pro1534211998248933470t_bool R2 Z3) X4)) (tptp.pp (tptp.aa_Pro4501881432599481050t_bool P Z3)))) (tptp.pp (tptp.aa_Pro4501881432599481050t_bool P X4))))) (tptp.pp (tptp.aa_Pro4501881432599481050t_bool P X))))))) (forall ((D4 tptp.fun_list_nat_bool) (R2 tptp.fun_li8598321315282354825t_bool) (X tptp.list_nat) (P tptp.fun_list_nat_bool)) (=> (tptp.ord_le2936377143570524336t_bool D4 (tptp.accp_list_nat R2)) (=> (forall ((X4 tptp.list_nat) (Z4 tptp.list_nat)) (=> (tptp.pp (tptp.aa_list_nat_bool D4 X4)) (=> (tptp.pp (tptp.aa_list_nat_bool (tptp.aa_lis4768068104879709938t_bool R2 Z4) X4)) (tptp.pp (tptp.aa_list_nat_bool D4 Z4))))) (=> (tptp.pp (tptp.aa_list_nat_bool D4 X)) (=> (forall ((X4 tptp.list_nat)) (=> (tptp.pp (tptp.aa_list_nat_bool D4 X4)) (=> (forall ((Z3 tptp.list_nat)) (=> (tptp.pp (tptp.aa_list_nat_bool (tptp.aa_lis4768068104879709938t_bool R2 Z3) X4)) (tptp.pp (tptp.aa_list_nat_bool P Z3)))) (tptp.pp (tptp.aa_list_nat_bool P X4))))) (tptp.pp (tptp.aa_list_nat_bool P X))))))) (forall ((D4 tptp.fun_nat_bool) (R2 tptp.fun_nat_fun_nat_bool) (X tptp.nat) (P tptp.fun_nat_bool)) (=> (tptp.ord_le8840051076831633728t_bool D4 (tptp.accp_nat R2)) (=> (forall ((X4 tptp.nat) (Z4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool D4 X4)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool R2 Z4) X4)) (tptp.pp (tptp.aa_nat_bool D4 Z4))))) (=> (tptp.pp (tptp.aa_nat_bool D4 X)) (=> (forall ((X4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool D4 X4)) (=> (forall ((Z3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool R2 Z3) X4)) (tptp.pp (tptp.aa_nat_bool P Z3)))) (tptp.pp (tptp.aa_nat_bool P X4))))) (tptp.pp (tptp.aa_nat_bool P X))))))) (forall ((N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) (tptp.aa_real_real tptp.sin_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N))))))) (forall ((X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) X)) (=> (= (tptp.aa_real_real tptp.sin_real X) tptp.zero_zero_real) (exists ((N2 tptp.nat)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1)) N2)) (= X (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N2)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) (tptp.aa_num_real tptp.numeral_numeral_real _let_1)))))))))) (forall ((X tptp.real)) (= (= (tptp.aa_real_real tptp.sin_real X) tptp.zero_zero_real) (or (exists ((N5 tptp.nat)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1)) N5)) (= X (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N5)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) (tptp.aa_num_real tptp.numeral_numeral_real _let_1))))))) (exists ((N5 tptp.nat)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1)) N5)) (= X (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N5)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) (tptp.aa_num_real tptp.numeral_numeral_real _let_1))))))))))) (forall ((X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) X)) (=> (= (tptp.aa_real_real tptp.cos_real X) tptp.zero_zero_real) (exists ((N2 tptp.nat)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (and (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1)) N2))) (= X (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N2)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) (tptp.aa_num_real tptp.numeral_numeral_real _let_1)))))))))) (forall ((X tptp.real)) (= (= (tptp.aa_real_real tptp.cos_real X) tptp.zero_zero_real) (or (exists ((N5 tptp.nat)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (and (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1)) N5))) (= X (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N5)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) (tptp.aa_num_real tptp.numeral_numeral_real _let_1))))))) (exists ((N5 tptp.nat)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (and (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1)) N5))) (= X (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N5)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) (tptp.aa_num_real tptp.numeral_numeral_real _let_1))))))))))) (forall ((X7 tptp.fun_nat_real)) (=> (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_nat_real X7 N2)) (tptp.aa_nat_real X7 (tptp.aa_nat_nat tptp.suc N2))))) (tptp.topolo6980174941875973593q_real X7))) (forall ((X7 tptp.fun_nat_set_int)) (=> (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int (tptp.aa_nat_set_int X7 N2)) (tptp.aa_nat_set_int X7 (tptp.aa_nat_nat tptp.suc N2))))) (tptp.topolo3100542954746470799et_int X7))) (forall ((X7 tptp.fun_nat_rat)) (=> (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat X7 N2)) (tptp.aa_nat_rat X7 (tptp.aa_nat_nat tptp.suc N2))))) (tptp.topolo4267028734544971653eq_rat X7))) (forall ((X7 tptp.fun_nat_num)) (=> (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_nat_num X7 N2)) (tptp.aa_nat_num X7 (tptp.aa_nat_nat tptp.suc N2))))) (tptp.topolo1459490580787246023eq_num X7))) (forall ((X7 tptp.fun_nat_nat)) (=> (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat X7 N2)) (tptp.aa_nat_nat X7 (tptp.aa_nat_nat tptp.suc N2))))) (tptp.topolo4902158794631467389eq_nat X7))) (forall ((X7 tptp.fun_nat_int)) (=> (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int X7 N2)) (tptp.aa_nat_int X7 (tptp.aa_nat_nat tptp.suc N2))))) (tptp.topolo4899668324122417113eq_int X7))) (forall ((X7 tptp.fun_nat_real)) (=> (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_nat_real X7 (tptp.aa_nat_nat tptp.suc N2))) (tptp.aa_nat_real X7 N2)))) (tptp.topolo6980174941875973593q_real X7))) (forall ((X7 tptp.fun_nat_set_int)) (=> (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int (tptp.aa_nat_set_int X7 (tptp.aa_nat_nat tptp.suc N2))) (tptp.aa_nat_set_int X7 N2)))) (tptp.topolo3100542954746470799et_int X7))) (forall ((X7 tptp.fun_nat_rat)) (=> (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat X7 (tptp.aa_nat_nat tptp.suc N2))) (tptp.aa_nat_rat X7 N2)))) (tptp.topolo4267028734544971653eq_rat X7))) (forall ((X7 tptp.fun_nat_num)) (=> (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_nat_num X7 (tptp.aa_nat_nat tptp.suc N2))) (tptp.aa_nat_num X7 N2)))) (tptp.topolo1459490580787246023eq_num X7))) (forall ((X7 tptp.fun_nat_nat)) (=> (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat X7 (tptp.aa_nat_nat tptp.suc N2))) (tptp.aa_nat_nat X7 N2)))) (tptp.topolo4902158794631467389eq_nat X7))) (forall ((X7 tptp.fun_nat_int)) (=> (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int X7 (tptp.aa_nat_nat tptp.suc N2))) (tptp.aa_nat_int X7 N2)))) (tptp.topolo4899668324122417113eq_int X7))) (forall ((X7 tptp.fun_nat_real)) (= (tptp.topolo6980174941875973593q_real X7) (or (forall ((N5 tptp.nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_nat_real X7 N5)) (tptp.aa_nat_real X7 (tptp.aa_nat_nat tptp.suc N5))))) (forall ((N5 tptp.nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_nat_real X7 (tptp.aa_nat_nat tptp.suc N5))) (tptp.aa_nat_real X7 N5))))))) (forall ((X7 tptp.fun_nat_set_int)) (= (tptp.topolo3100542954746470799et_int X7) (or (forall ((N5 tptp.nat)) (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int (tptp.aa_nat_set_int X7 N5)) (tptp.aa_nat_set_int X7 (tptp.aa_nat_nat tptp.suc N5))))) (forall ((N5 tptp.nat)) (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int (tptp.aa_nat_set_int X7 (tptp.aa_nat_nat tptp.suc N5))) (tptp.aa_nat_set_int X7 N5))))))) (forall ((X7 tptp.fun_nat_rat)) (= (tptp.topolo4267028734544971653eq_rat X7) (or (forall ((N5 tptp.nat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat X7 N5)) (tptp.aa_nat_rat X7 (tptp.aa_nat_nat tptp.suc N5))))) (forall ((N5 tptp.nat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat X7 (tptp.aa_nat_nat tptp.suc N5))) (tptp.aa_nat_rat X7 N5))))))) (forall ((X7 tptp.fun_nat_num)) (= (tptp.topolo1459490580787246023eq_num X7) (or (forall ((N5 tptp.nat)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_nat_num X7 N5)) (tptp.aa_nat_num X7 (tptp.aa_nat_nat tptp.suc N5))))) (forall ((N5 tptp.nat)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_nat_num X7 (tptp.aa_nat_nat tptp.suc N5))) (tptp.aa_nat_num X7 N5))))))) (forall ((X7 tptp.fun_nat_nat)) (= (tptp.topolo4902158794631467389eq_nat X7) (or (forall ((N5 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat X7 N5)) (tptp.aa_nat_nat X7 (tptp.aa_nat_nat tptp.suc N5))))) (forall ((N5 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat X7 (tptp.aa_nat_nat tptp.suc N5))) (tptp.aa_nat_nat X7 N5))))))) (forall ((X7 tptp.fun_nat_int)) (= (tptp.topolo4899668324122417113eq_int X7) (or (forall ((N5 tptp.nat)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int X7 N5)) (tptp.aa_nat_int X7 (tptp.aa_nat_nat tptp.suc N5))))) (forall ((N5 tptp.nat)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int X7 (tptp.aa_nat_nat tptp.suc N5))) (tptp.aa_nat_int X7 N5))))))) (forall ((X7 tptp.fun_nat_real)) (=> (forall ((M3 tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M3) N2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_nat_real X7 M3)) (tptp.aa_nat_real X7 N2))))) (tptp.topolo6980174941875973593q_real X7))) (forall ((X7 tptp.fun_nat_set_int)) (=> (forall ((M3 tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M3) N2)) (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int (tptp.aa_nat_set_int X7 M3)) (tptp.aa_nat_set_int X7 N2))))) (tptp.topolo3100542954746470799et_int X7))) (forall ((X7 tptp.fun_nat_rat)) (=> (forall ((M3 tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M3) N2)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat X7 M3)) (tptp.aa_nat_rat X7 N2))))) (tptp.topolo4267028734544971653eq_rat X7))) (forall ((X7 tptp.fun_nat_num)) (=> (forall ((M3 tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M3) N2)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_nat_num X7 M3)) (tptp.aa_nat_num X7 N2))))) (tptp.topolo1459490580787246023eq_num X7))) (forall ((X7 tptp.fun_nat_nat)) (=> (forall ((M3 tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M3) N2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat X7 M3)) (tptp.aa_nat_nat X7 N2))))) (tptp.topolo4902158794631467389eq_nat X7))) (forall ((X7 tptp.fun_nat_int)) (=> (forall ((M3 tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M3) N2)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int X7 M3)) (tptp.aa_nat_int X7 N2))))) (tptp.topolo4899668324122417113eq_int X7))) (forall ((X7 tptp.fun_nat_real)) (=> (forall ((M3 tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M3) N2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_nat_real X7 N2)) (tptp.aa_nat_real X7 M3))))) (tptp.topolo6980174941875973593q_real X7))) (forall ((X7 tptp.fun_nat_set_int)) (=> (forall ((M3 tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M3) N2)) (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int (tptp.aa_nat_set_int X7 N2)) (tptp.aa_nat_set_int X7 M3))))) (tptp.topolo3100542954746470799et_int X7))) (forall ((X7 tptp.fun_nat_rat)) (=> (forall ((M3 tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M3) N2)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat X7 N2)) (tptp.aa_nat_rat X7 M3))))) (tptp.topolo4267028734544971653eq_rat X7))) (forall ((X7 tptp.fun_nat_num)) (=> (forall ((M3 tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M3) N2)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_nat_num X7 N2)) (tptp.aa_nat_num X7 M3))))) (tptp.topolo1459490580787246023eq_num X7))) (forall ((X7 tptp.fun_nat_nat)) (=> (forall ((M3 tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M3) N2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat X7 N2)) (tptp.aa_nat_nat X7 M3))))) (tptp.topolo4902158794631467389eq_nat X7))) (forall ((X7 tptp.fun_nat_int)) (=> (forall ((M3 tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M3) N2)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int X7 N2)) (tptp.aa_nat_int X7 M3))))) (tptp.topolo4899668324122417113eq_int X7))) (forall ((X tptp.vEBT_VEBT) (Y tptp.option_nat)) (=> (= (tptp.vEBT_vebt_maxt X) Y) (=> (tptp.pp (tptp.aa_VEBT_VEBT_bool (tptp.accp_VEBT_VEBT tptp.vEBT_vebt_maxt_rel) X)) (=> (forall ((A3 tptp.bool) (B3 tptp.bool)) (let ((_let_1 (tptp.vEBT_Leaf A3 B3))) (let ((_let_2 (tptp.pp A3))) (let ((_let_3 (tptp.pp B3))) (=> (= X _let_1) (=> (and (=> _let_3 (= Y (tptp.some_nat tptp.one_one_nat))) (=> (not _let_3) (and (=> _let_2 (= Y (tptp.some_nat tptp.zero_zero_nat))) (=> (not _let_2) (= Y tptp.none_nat))))) (not (tptp.pp (tptp.aa_VEBT_VEBT_bool (tptp.accp_VEBT_VEBT tptp.vEBT_vebt_maxt_rel) _let_1))))))))) (=> (forall ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (let ((_let_1 (tptp.vEBT_Node tptp.none_P5556105721700978146at_nat Uu2 Uv2 Uw2))) (=> (= X _let_1) (=> (= Y tptp.none_nat) (not (tptp.pp (tptp.aa_VEBT_VEBT_bool (tptp.accp_VEBT_VEBT tptp.vEBT_vebt_maxt_rel) _let_1))))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Ux2 tptp.nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (let ((_let_1 (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Mi2) Ma2)) Ux2 Uy2 Uz2))) (=> (= X _let_1) (=> (= Y (tptp.some_nat Ma2)) (not (tptp.pp (tptp.aa_VEBT_VEBT_bool (tptp.accp_VEBT_VEBT tptp.vEBT_vebt_maxt_rel) _let_1))))))))))))) (forall ((X tptp.vEBT_VEBT) (Y tptp.option_nat)) (=> (= (tptp.vEBT_vebt_mint X) Y) (=> (tptp.pp (tptp.aa_VEBT_VEBT_bool (tptp.accp_VEBT_VEBT tptp.vEBT_vebt_mint_rel) X)) (=> (forall ((A3 tptp.bool) (B3 tptp.bool)) (let ((_let_1 (tptp.vEBT_Leaf A3 B3))) (let ((_let_2 (tptp.pp B3))) (let ((_let_3 (tptp.pp A3))) (=> (= X _let_1) (=> (and (=> _let_3 (= Y (tptp.some_nat tptp.zero_zero_nat))) (=> (not _let_3) (and (=> _let_2 (= Y (tptp.some_nat tptp.one_one_nat))) (=> (not _let_2) (= Y tptp.none_nat))))) (not (tptp.pp (tptp.aa_VEBT_VEBT_bool (tptp.accp_VEBT_VEBT tptp.vEBT_vebt_mint_rel) _let_1))))))))) (=> (forall ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (let ((_let_1 (tptp.vEBT_Node tptp.none_P5556105721700978146at_nat Uu2 Uv2 Uw2))) (=> (= X _let_1) (=> (= Y tptp.none_nat) (not (tptp.pp (tptp.aa_VEBT_VEBT_bool (tptp.accp_VEBT_VEBT tptp.vEBT_vebt_mint_rel) _let_1))))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Ux2 tptp.nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (let ((_let_1 (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Mi2) Ma2)) Ux2 Uy2 Uz2))) (=> (= X _let_1) (=> (= Y (tptp.some_nat Mi2)) (not (tptp.pp (tptp.aa_VEBT_VEBT_bool (tptp.accp_VEBT_VEBT tptp.vEBT_vebt_mint_rel) _let_1))))))))))))) (forall ((X tptp.real) (N tptp.nat)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) X)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (exists ((T4 tptp.real)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) T4)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real T4) X)) (= (tptp.aa_real_real tptp.cos_real X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real tptp.aTP_Lamm_mu X) (tptp.set_ord_lessThan_nat N))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real tptp.cos_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real T4) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.one_one_real) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N))) tptp.pi)))) (tptp.aa_nat_real tptp.semiri2265585572941072030t_real N))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) N))))))))) (forall ((N tptp.nat) (X tptp.real)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) tptp.zero_zero_real)) (exists ((T4 tptp.real)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) T4)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real T4) tptp.zero_zero_real)) (= (tptp.aa_real_real tptp.cos_real X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real tptp.aTP_Lamm_mu X) (tptp.set_ord_lessThan_nat N))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real tptp.cos_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real T4) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.one_one_real) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N))) tptp.pi)))) (tptp.aa_nat_real tptp.semiri2265585572941072030t_real N))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) N))))))))) (forall ((N tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N))) (= (tptp.aa_nat_rat tptp.semiri773545260158071498ct_rat _let_1) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat _let_1)) (tptp.aa_nat_rat tptp.semiri773545260158071498ct_rat N))))) (forall ((N tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N))) (= (tptp.aa_nat_int tptp.semiri1406184849735516958ct_int _let_1) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int _let_1)) (tptp.aa_nat_int tptp.semiri1406184849735516958ct_int N))))) (forall ((N tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N))) (= (tptp.aa_nat_real tptp.semiri2265585572941072030t_real _let_1) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real _let_1)) (tptp.aa_nat_real tptp.semiri2265585572941072030t_real N))))) (forall ((N tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N))) (= (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat _let_1) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat _let_1)) (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat N))))) (= (tptp.aa_nat_complex tptp.semiri5044797733671781792omplex _let_33) _let_50) (= (tptp.aa_nat_rat tptp.semiri773545260158071498ct_rat _let_33) _let_69) (= (tptp.aa_nat_int tptp.semiri1406184849735516958ct_int _let_33) _let_44) (= (tptp.aa_nat_real tptp.semiri2265585572941072030t_real _let_33) _let_28) (= (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat _let_33) _let_33) (forall ((N tptp.nat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_nat_rat tptp.semiri773545260158071498ct_rat N)))) (forall ((N tptp.nat)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.aa_nat_int tptp.semiri1406184849735516958ct_int N)))) (forall ((N tptp.nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_nat_real tptp.semiri2265585572941072030t_real N)))) (forall ((N tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat N)))) (forall ((N tptp.nat)) (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_nat_rat tptp.semiri773545260158071498ct_rat N)) tptp.zero_zero_rat)))) (forall ((N tptp.nat)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_nat_int tptp.semiri1406184849735516958ct_int N)) tptp.zero_zero_int)))) (forall ((N tptp.nat)) (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_nat_real tptp.semiri2265585572941072030t_real N)) tptp.zero_zero_real)))) (forall ((N tptp.nat)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat N)) tptp.zero_zero_nat)))) (forall ((N tptp.nat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) (tptp.aa_nat_rat tptp.semiri773545260158071498ct_rat N)))) (forall ((N tptp.nat)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) (tptp.aa_nat_int tptp.semiri1406184849735516958ct_int N)))) (forall ((N tptp.nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) (tptp.aa_nat_real tptp.semiri2265585572941072030t_real N)))) (forall ((N tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat N)))) (forall ((N tptp.nat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.one_one_rat) (tptp.aa_nat_rat tptp.semiri773545260158071498ct_rat N)))) (forall ((N tptp.nat)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.one_one_int) (tptp.aa_nat_int tptp.semiri1406184849735516958ct_int N)))) (forall ((N tptp.nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.one_one_real) (tptp.aa_nat_real tptp.semiri2265585572941072030t_real N)))) (forall ((N tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.one_one_nat) (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat N)))) (forall ((M tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat tptp.semiri773545260158071498ct_rat M)) (tptp.aa_nat_rat tptp.semiri773545260158071498ct_rat N))))) (forall ((M tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int tptp.semiri1406184849735516958ct_int M)) (tptp.aa_nat_int tptp.semiri1406184849735516958ct_int N))))) (forall ((M tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_nat_real tptp.semiri2265585572941072030t_real M)) (tptp.aa_nat_real tptp.semiri2265585572941072030t_real N))))) (forall ((M tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat M)) (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat N))))) (forall ((N tptp.nat) (M tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N) M)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_nat_int tptp.semiri1406184849735516958ct_int N)) (tptp.aa_nat_int tptp.semiri1406184849735516958ct_int M))))) (forall ((N tptp.nat) (M tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N) M)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.aa_nat_Code_integer tptp.semiri3624122377584611663nteger N)) (tptp.aa_nat_Code_integer tptp.semiri3624122377584611663nteger M))))) (forall ((N tptp.nat) (M tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N) M)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.dvd_dvd_real (tptp.aa_nat_real tptp.semiri2265585572941072030t_real N)) (tptp.aa_nat_real tptp.semiri2265585572941072030t_real M))))) (forall ((N tptp.nat) (M tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N) M)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat N)) (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat M))))) (forall ((M tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) M)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_nat_rat tptp.semiri773545260158071498ct_rat M)) (tptp.aa_nat_rat tptp.semiri773545260158071498ct_rat N)))))) (forall ((M tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) M)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_nat_int tptp.semiri1406184849735516958ct_int M)) (tptp.aa_nat_int tptp.semiri1406184849735516958ct_int N)))))) (forall ((M tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) M)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_nat_real tptp.semiri2265585572941072030t_real M)) (tptp.aa_nat_real tptp.semiri2265585572941072030t_real N)))))) (forall ((M tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) M)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat M)) (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat N)))))) (forall ((M tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)) (= (tptp.aa_int_int (tptp.modulo_modulo_int (tptp.aa_nat_int tptp.semiri1406184849735516958ct_int N)) (tptp.aa_nat_int tptp.semiri1406184849735516958ct_int M)) tptp.zero_zero_int))) (forall ((M tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)) (= (tptp.modulo364778990260209775nteger (tptp.aa_nat_Code_integer tptp.semiri3624122377584611663nteger N) (tptp.aa_nat_Code_integer tptp.semiri3624122377584611663nteger M)) tptp.zero_z3403309356797280102nteger))) (forall ((M tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat N)) (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat M)) tptp.zero_zero_nat))) (forall ((N tptp.nat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat tptp.semiri773545260158071498ct_rat N)) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat N) N))))) (forall ((N tptp.nat)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int tptp.semiri1406184849735516958ct_int N)) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat N) N))))) (forall ((N tptp.nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_nat_real tptp.semiri2265585572941072030t_real N)) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat N) N))))) (forall ((N tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat N)) (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat N) N))))) (forall ((K tptp.num)) (= (tptp.aa_nat_complex tptp.semiri5044797733671781792omplex (tptp.aa_num_nat tptp.numeral_numeral_nat K)) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.numera6690914467698888265omplex K)) (tptp.aa_nat_complex tptp.semiri5044797733671781792omplex (tptp.aa_num_nat tptp.pred_numeral K))))) (forall ((K tptp.num)) (= (tptp.aa_nat_rat tptp.semiri773545260158071498ct_rat (tptp.aa_num_nat tptp.numeral_numeral_nat K)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_num_rat tptp.numeral_numeral_rat K)) (tptp.aa_nat_rat tptp.semiri773545260158071498ct_rat (tptp.aa_num_nat tptp.pred_numeral K))))) (forall ((K tptp.num)) (= (tptp.aa_nat_int tptp.semiri1406184849735516958ct_int (tptp.aa_num_nat tptp.numeral_numeral_nat K)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_num_int tptp.numeral_numeral_int K)) (tptp.aa_nat_int tptp.semiri1406184849735516958ct_int (tptp.aa_num_nat tptp.pred_numeral K))))) (forall ((K tptp.num)) (= (tptp.aa_nat_real tptp.semiri2265585572941072030t_real (tptp.aa_num_nat tptp.numeral_numeral_nat K)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_num_real tptp.numeral_numeral_real K)) (tptp.aa_nat_real tptp.semiri2265585572941072030t_real (tptp.aa_num_nat tptp.pred_numeral K))))) (forall ((K tptp.num)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat K))) (= (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat _let_1) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat _let_1) (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat (tptp.aa_num_nat tptp.pred_numeral K)))))) (forall ((N tptp.nat)) (let ((_let_1 (tptp.aa_nat_real tptp.semiri2265585572941072030t_real N))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real _let_1) _let_1)) (tptp.aa_nat_real tptp.semiri2265585572941072030t_real (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N)))))) (forall ((M tptp.nat)) (let ((_let_1 (tptp.aa_nat_complex tptp.semiri5044797733671781792omplex M))) (let ((_let_2 (= M tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_complex)) (=> (not _let_2) (= _let_1 (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex M)) (tptp.aa_nat_complex tptp.semiri5044797733671781792omplex (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) tptp.one_one_nat))))))))) (forall ((M tptp.nat)) (let ((_let_1 (tptp.aa_nat_rat tptp.semiri773545260158071498ct_rat M))) (let ((_let_2 (= M tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_rat)) (=> (not _let_2) (= _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat M)) (tptp.aa_nat_rat tptp.semiri773545260158071498ct_rat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) tptp.one_one_nat))))))))) (forall ((M tptp.nat)) (let ((_let_1 (tptp.aa_nat_int tptp.semiri1406184849735516958ct_int M))) (let ((_let_2 (= M tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_int)) (=> (not _let_2) (= _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int M)) (tptp.aa_nat_int tptp.semiri1406184849735516958ct_int (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) tptp.one_one_nat))))))))) (forall ((M tptp.nat)) (let ((_let_1 (tptp.aa_nat_real tptp.semiri2265585572941072030t_real M))) (let ((_let_2 (= M tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_real)) (=> (not _let_2) (= _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real M)) (tptp.aa_nat_real tptp.semiri2265585572941072030t_real (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) tptp.one_one_nat))))))))) (forall ((M tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_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.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat M)) (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) tptp.one_one_nat))))))))) (forall ((N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (= (tptp.aa_nat_rat tptp.semiri773545260158071498ct_rat N) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat N)) (tptp.aa_nat_rat tptp.semiri773545260158071498ct_rat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) tptp.one_one_nat)))))) (forall ((N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (= (tptp.aa_nat_int tptp.semiri1406184849735516958ct_int N) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N)) (tptp.aa_nat_int tptp.semiri1406184849735516958ct_int (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) tptp.one_one_nat)))))) (forall ((N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (= (tptp.aa_nat_real tptp.semiri2265585572941072030t_real N) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N)) (tptp.aa_nat_real tptp.semiri2265585572941072030t_real (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) tptp.one_one_nat)))))) (forall ((N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (= (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat N) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat N)) (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) tptp.one_one_nat)))))) (forall ((X tptp.real) (N tptp.nat) (Diff tptp.fun_na5723442673449079972x_real)) (=> (= X tptp.zero_zero_real) (=> (not (= N tptp.zero_zero_nat)) (= (tptp.groups6591440286371151544t_real (tptp.aa_fun5746040925223427547t_real (tptp.aTP_Lamm_mv X) Diff) (tptp.set_ord_lessThan_nat N)) (tptp.aa_complex_real (tptp.aa_nat480766339200631653x_real Diff tptp.zero_zero_nat) tptp.zero_zero_complex))))) (forall ((X tptp.real) (N tptp.nat) (Diff tptp.fun_na6724076748692969250l_real)) (=> (= X tptp.zero_zero_real) (=> (not (= N tptp.zero_zero_nat)) (= (tptp.groups6591440286371151544t_real (tptp.aa_fun1113820866546176217t_real (tptp.aTP_Lamm_mw X) Diff) (tptp.set_ord_lessThan_nat N)) (tptp.aa_real_real (tptp.aa_nat_fun_real_real Diff tptp.zero_zero_nat) tptp.zero_zero_real))))) (forall ((X tptp.real) (N tptp.nat) (Diff tptp.fun_nat_fun_rat_real)) (=> (= X tptp.zero_zero_real) (=> (not (= N tptp.zero_zero_nat)) (= (tptp.groups6591440286371151544t_real (tptp.aa_fun507281639146497029t_real (tptp.aTP_Lamm_mx X) Diff) (tptp.set_ord_lessThan_nat N)) (tptp.aa_rat_real (tptp.aa_nat_fun_rat_real Diff tptp.zero_zero_nat) tptp.zero_zero_rat))))) (forall ((X tptp.real) (N tptp.nat) (Diff tptp.fun_nat_fun_nat_real)) (=> (= X tptp.zero_zero_real) (=> (not (= N tptp.zero_zero_nat)) (= (tptp.groups6591440286371151544t_real (tptp.aa_fun7039663905532832253t_real (tptp.aTP_Lamm_my X) Diff) (tptp.set_ord_lessThan_nat N)) (tptp.aa_nat_real (tptp.aa_nat_fun_nat_real Diff tptp.zero_zero_nat) tptp.zero_zero_nat))))) (forall ((X tptp.real) (N tptp.nat) (Diff tptp.fun_nat_fun_int_real)) (=> (= X tptp.zero_zero_real) (=> (not (= N tptp.zero_zero_nat)) (= (tptp.groups6591440286371151544t_real (tptp.aa_fun241848180832411225t_real (tptp.aTP_Lamm_mz X) Diff) (tptp.set_ord_lessThan_nat N)) (tptp.aa_int_real (tptp.aa_nat_fun_int_real Diff tptp.zero_zero_nat) tptp.zero_zero_int))))) (forall ((H tptp.real) (F tptp.fun_real_real) (J tptp.fun_nat_real) (N tptp.nat)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) H)) (exists ((B8 tptp.real)) (= (tptp.aa_real_real F H) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.groups6591440286371151544t_real (tptp.aa_fun1839206346889086768t_real (tptp.aTP_Lamm_na H) J) (tptp.set_ord_lessThan_nat N))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real B8) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real H) N)) (tptp.aa_nat_real tptp.semiri2265585572941072030t_real N)))))))) (forall ((X tptp.real)) (tptp.pp (tptp.aa_real_bool (tptp.sums_real (tptp.aa_real_fun_nat_real tptp.aTP_Lamm_nb X)) (tptp.aa_real_real tptp.cos_real X)))) (forall ((X5 tptp.nat)) (let ((_let_1 (tptp.aa_nat_real tptp.cos_coeff X5))) (let ((_let_2 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_3 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat _let_2) X5)))) (and (=> _let_3 (= _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat X5) _let_2))) (tptp.aa_nat_real tptp.semiri2265585572941072030t_real X5)))) (=> (not _let_3) (= _let_1 tptp.zero_zero_real))))))) (forall ((X tptp.real)) (tptp.pp (tptp.aa_real_bool (tptp.sums_real (tptp.aa_real_fun_nat_real tptp.aTP_Lamm_nc X)) (tptp.aa_real_real tptp.sin_real X)))) (forall ((X tptp.real) (N tptp.nat)) (exists ((T4 tptp.real)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real T4)) (tptp.aa_real_real tptp.abs_abs_real X))) (= (tptp.aa_real_real tptp.cos_real X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real tptp.aTP_Lamm_mu X) (tptp.set_ord_lessThan_nat N))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real tptp.cos_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real T4) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.one_one_real) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N))) tptp.pi)))) (tptp.aa_nat_real tptp.semiri2265585572941072030t_real N))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) N))))))) (forall ((N tptp.nat) (X tptp.real)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) X)) (exists ((T4 tptp.real)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) T4)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real T4) X)) (= (tptp.aa_real_real tptp.sin_real X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real tptp.aTP_Lamm_nd X) (tptp.set_ord_lessThan_nat N))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real tptp.sin_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real T4) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.one_one_real) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N))) tptp.pi)))) (tptp.aa_nat_real tptp.semiri2265585572941072030t_real N))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) N))))))))) (forall ((X tptp.real) (N tptp.nat)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) X)) (exists ((T4 tptp.real)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) T4)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real T4) X)) (= (tptp.aa_real_real tptp.sin_real X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real tptp.aTP_Lamm_nd X) (tptp.set_ord_lessThan_nat N))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real tptp.sin_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real T4) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.one_one_real) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N))) tptp.pi)))) (tptp.aa_nat_real tptp.semiri2265585572941072030t_real N))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) N)))))))) (forall ((X tptp.real) (N tptp.nat)) (exists ((T4 tptp.real)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real T4)) (tptp.aa_real_real tptp.abs_abs_real X))) (= (tptp.aa_real_real tptp.sin_real X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real tptp.aTP_Lamm_nd X) (tptp.set_ord_lessThan_nat N))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real tptp.sin_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real T4) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.one_one_real) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N))) tptp.pi)))) (tptp.aa_nat_real tptp.semiri2265585572941072030t_real N))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) N))))))) (forall ((X tptp.real) (N tptp.nat)) (exists ((T4 tptp.real)) (= (tptp.aa_real_real tptp.sin_real X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real tptp.aTP_Lamm_nd X) (tptp.set_ord_lessThan_nat N))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real tptp.sin_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real T4) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.one_one_real) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N))) tptp.pi)))) (tptp.aa_nat_real tptp.semiri2265585572941072030t_real N))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) N)))))) (forall ((X5 tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_nat_real tptp.sin_coeff X5))) (let ((_let_3 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat _let_1) X5)))) (and (=> _let_3 (= _let_2 tptp.zero_zero_real)) (=> (not _let_3) (= _let_2 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat X5) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat))) _let_1))) (tptp.aa_nat_real tptp.semiri2265585572941072030t_real X5))))))))) (forall ((N tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N) (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat N)))) (forall ((M tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat M)) (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat N))))) (forall ((M tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) M)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat M)) (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat N)))))) (forall ((N tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)) (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat N)))) (forall ((M tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.one_one_nat) M)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat M) (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat N)))))) (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc M))) (let ((_let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat _let_1) N))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N) _let_1)) (= (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat _let_2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat _let_2) (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) N)))))))) (forall ((R tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat R) N)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat N)) (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) R)))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat N) R))))) (forall ((K tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) N)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_nat_Code_integer tptp.semiri3624122377584611663nteger K)) (tptp.aa_nat_Code_integer tptp.semiri3624122377584611663nteger (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) K)))) (tptp.aa_nat_Code_integer tptp.semiri3624122377584611663nteger N))))) (forall ((K tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) N)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.dvd_dvd_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat tptp.semiri773545260158071498ct_rat K)) (tptp.aa_nat_rat tptp.semiri773545260158071498ct_rat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) K)))) (tptp.aa_nat_rat tptp.semiri773545260158071498ct_rat N))))) (forall ((K tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) N)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int tptp.semiri1406184849735516958ct_int K)) (tptp.aa_nat_int tptp.semiri1406184849735516958ct_int (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) K)))) (tptp.aa_nat_int tptp.semiri1406184849735516958ct_int N))))) (forall ((K tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) N)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.dvd_dvd_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real tptp.semiri2265585572941072030t_real K)) (tptp.aa_nat_real tptp.semiri2265585572941072030t_real (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) K)))) (tptp.aa_nat_real tptp.semiri2265585572941072030t_real N))))) (forall ((K tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) N)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat K)) (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) K)))) (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat N))))) (forall ((F tptp.fun_nat_fun_nat_nat) (A tptp.nat) (B2 tptp.nat) (Acc tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.set_fo2584398358068434914at_nat F A) B2) Acc))) (let ((_let_2 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat B2) A)))) (=> (tptp.accp_P4694664897847628410at_nat tptp.set_fo3699595496184130361el_nat (tptp.produc2818902965508115497at_nat F (tptp.produc487386426758144856at_nat A (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat B2) Acc)))) (and (=> _let_2 (= _let_1 Acc)) (=> (not _let_2) (= _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.set_fo2584398358068434914at_nat F (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) tptp.one_one_nat)) B2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat F A) Acc))))))))) (forall ((X tptp.fun_nat_fun_nat_nat) (Xa2 tptp.nat) (Xb2 tptp.nat) (Xc tptp.nat) (Y tptp.nat)) (let ((_let_1 (tptp.accp_P4694664897847628410at_nat tptp.set_fo3699595496184130361el_nat (tptp.produc2818902965508115497at_nat X (tptp.produc487386426758144856at_nat Xa2 (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Xb2) Xc)))))) (let ((_let_2 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Xb2) Xa2)))) (=> (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.set_fo2584398358068434914at_nat X Xa2) Xb2) Xc) Y) (=> _let_1 (not (=> (and (=> _let_2 (= Y Xc)) (=> (not _let_2) (= Y (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.set_fo2584398358068434914at_nat X (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Xa2) tptp.one_one_nat)) Xb2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat X Xa2) Xc))))) (not _let_1)))))))) (forall ((X tptp.fun_Pr2477239776880934807at_nat) (Xa2 tptp.option4927543243414619207at_nat) (Xb2 tptp.option4927543243414619207at_nat) (Y tptp.option4927543243414619207at_nat)) (=> (= (tptp.vEBT_V1502963449132264192at_nat X Xa2 Xb2) Y) (=> (tptp.accp_P4760198183577772864at_nat tptp.vEBT_V7235779383477046023at_nat (tptp.produc7814092408141220007at_nat X (tptp.produc488173922507101015at_nat Xa2 Xb2))) (=> (=> (= Xa2 tptp.none_P5556105721700978146at_nat) (=> (= Y tptp.none_P5556105721700978146at_nat) (not (tptp.accp_P4760198183577772864at_nat tptp.vEBT_V7235779383477046023at_nat (tptp.produc7814092408141220007at_nat X (tptp.produc488173922507101015at_nat tptp.none_P5556105721700978146at_nat Xb2)))))) (=> (forall ((V2 tptp.product_prod_nat_nat)) (let ((_let_1 (tptp.some_P7363390416028606310at_nat V2))) (=> (= Xa2 _let_1) (=> (= Xb2 tptp.none_P5556105721700978146at_nat) (=> (= Y tptp.none_P5556105721700978146at_nat) (not (tptp.accp_P4760198183577772864at_nat tptp.vEBT_V7235779383477046023at_nat (tptp.produc7814092408141220007at_nat X (tptp.produc488173922507101015at_nat _let_1 tptp.none_P5556105721700978146at_nat))))))))) (not (forall ((A3 tptp.product_prod_nat_nat)) (=> (= Xa2 (tptp.some_P7363390416028606310at_nat A3)) (forall ((B3 tptp.product_prod_nat_nat)) (let ((_let_1 (tptp.some_P7363390416028606310at_nat B3))) (=> (= Xb2 _let_1) (=> (= Y (tptp.some_P7363390416028606310at_nat (tptp.aa_Pro262675715343573244at_nat (tptp.aa_Pro8023792847356852296at_nat X A3) B3))) (not (tptp.accp_P4760198183577772864at_nat tptp.vEBT_V7235779383477046023at_nat (tptp.produc7814092408141220007at_nat X (tptp.produc488173922507101015at_nat (tptp.some_P7363390416028606310at_nat A3) _let_1)))))))))))))))) (forall ((X tptp.fun_num_fun_num_num) (Xa2 tptp.option_num) (Xb2 tptp.option_num) (Y tptp.option_num)) (=> (= (tptp.vEBT_V819420779217536731ft_num X Xa2 Xb2) Y) (=> (tptp.accp_P1225658569124232473on_num tptp.vEBT_V452583751252753300el_num (tptp.produc6360833703471310868on_num X (tptp.produc8585076106096196333on_num Xa2 Xb2))) (=> (=> (= Xa2 tptp.none_num) (=> (= Y tptp.none_num) (not (tptp.accp_P1225658569124232473on_num tptp.vEBT_V452583751252753300el_num (tptp.produc6360833703471310868on_num X (tptp.produc8585076106096196333on_num tptp.none_num Xb2)))))) (=> (forall ((V2 tptp.num)) (let ((_let_1 (tptp.some_num V2))) (=> (= Xa2 _let_1) (=> (= Xb2 tptp.none_num) (=> (= Y tptp.none_num) (not (tptp.accp_P1225658569124232473on_num tptp.vEBT_V452583751252753300el_num (tptp.produc6360833703471310868on_num X (tptp.produc8585076106096196333on_num _let_1 tptp.none_num))))))))) (not (forall ((A3 tptp.num)) (=> (= Xa2 (tptp.some_num A3)) (forall ((B3 tptp.num)) (let ((_let_1 (tptp.some_num B3))) (=> (= Xb2 _let_1) (=> (= Y (tptp.some_num (tptp.aa_num_num (tptp.aa_num_fun_num_num X A3) B3))) (not (tptp.accp_P1225658569124232473on_num tptp.vEBT_V452583751252753300el_num (tptp.produc6360833703471310868on_num X (tptp.produc8585076106096196333on_num (tptp.some_num A3) _let_1)))))))))))))))) (forall ((X tptp.fun_nat_fun_nat_nat) (Xa2 tptp.option_nat) (Xb2 tptp.option_nat) (Y tptp.option_nat)) (=> (= (tptp.aa_opt1882420858203594238on_nat (tptp.aa_opt7711074727033721499on_nat (tptp.vEBT_V4262088993061758097ft_nat X) Xa2) Xb2) Y) (=> (tptp.accp_P5526603486790338531on_nat tptp.vEBT_V3895251965096974666el_nat (tptp.produc6699827698519632094on_nat X (tptp.produc5098337634421038937on_nat Xa2 Xb2))) (=> (=> (= Xa2 tptp.none_nat) (=> (= Y tptp.none_nat) (not (tptp.accp_P5526603486790338531on_nat tptp.vEBT_V3895251965096974666el_nat (tptp.produc6699827698519632094on_nat X (tptp.produc5098337634421038937on_nat tptp.none_nat Xb2)))))) (=> (forall ((V2 tptp.nat)) (let ((_let_1 (tptp.some_nat V2))) (=> (= Xa2 _let_1) (=> (= Xb2 tptp.none_nat) (=> (= Y tptp.none_nat) (not (tptp.accp_P5526603486790338531on_nat tptp.vEBT_V3895251965096974666el_nat (tptp.produc6699827698519632094on_nat X (tptp.produc5098337634421038937on_nat _let_1 tptp.none_nat))))))))) (not (forall ((A3 tptp.nat)) (=> (= Xa2 (tptp.some_nat A3)) (forall ((B3 tptp.nat)) (let ((_let_1 (tptp.some_nat B3))) (=> (= Xb2 _let_1) (=> (= Y (tptp.some_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat X A3) B3))) (not (tptp.accp_P5526603486790338531on_nat tptp.vEBT_V3895251965096974666el_nat (tptp.produc6699827698519632094on_nat X (tptp.produc5098337634421038937on_nat (tptp.some_nat A3) _let_1)))))))))))))))) (forall ((K tptp.nat) (N tptp.nat)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_nat_Code_integer tptp.semiri3624122377584611663nteger K)) (tptp.aa_nat_Code_integer tptp.semiri3624122377584611663nteger N))) (tptp.aa_nat_Code_integer tptp.semiri3624122377584611663nteger (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat K) N))))) (forall ((K tptp.nat) (N tptp.nat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.dvd_dvd_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat tptp.semiri773545260158071498ct_rat K)) (tptp.aa_nat_rat tptp.semiri773545260158071498ct_rat N))) (tptp.aa_nat_rat tptp.semiri773545260158071498ct_rat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat K) N))))) (forall ((K tptp.nat) (N tptp.nat)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int tptp.semiri1406184849735516958ct_int K)) (tptp.aa_nat_int tptp.semiri1406184849735516958ct_int N))) (tptp.aa_nat_int tptp.semiri1406184849735516958ct_int (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat K) N))))) (forall ((K tptp.nat) (N tptp.nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.dvd_dvd_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real tptp.semiri2265585572941072030t_real K)) (tptp.aa_nat_real tptp.semiri2265585572941072030t_real N))) (tptp.aa_nat_real tptp.semiri2265585572941072030t_real (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat K) N))))) (forall ((K tptp.nat) (N tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat K)) (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat N))) (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat K) N))))) (forall ((X tptp.fun_nat_fun_nat_nat) (Xa2 tptp.nat) (Xb2 tptp.nat) (Xc tptp.nat) (Y tptp.nat)) (let ((_let_1 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Xb2) Xa2)))) (=> (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.set_fo2584398358068434914at_nat X Xa2) Xb2) Xc) Y) (and (=> _let_1 (= Y Xc)) (=> (not _let_1) (= Y (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.set_fo2584398358068434914at_nat X (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Xa2) tptp.one_one_nat)) Xb2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat X Xa2) Xc)))))))) (forall ((B2 tptp.nat) (A tptp.nat) (F tptp.fun_nat_fun_nat_nat) (Acc tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.set_fo2584398358068434914at_nat F A) B2) Acc))) (let ((_let_2 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat B2) A)))) (and (=> _let_2 (= _let_1 Acc)) (=> (not _let_2) (= _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.set_fo2584398358068434914at_nat F (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) tptp.one_one_nat)) B2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat F A) Acc)))))))) (forall ((F tptp.fun_nat_complex) (A tptp.nat) (B2 tptp.nat)) (= (tptp.groups2073611262835488442omplex F (tptp.set_or1269000886237332187st_nat A B2)) (tptp.aa_complex_complex (tptp.set_fo1517530859248394432omplex (tptp.aTP_Lamm_ne F) A B2) tptp.zero_zero_complex))) (forall ((F tptp.fun_nat_rat) (A tptp.nat) (B2 tptp.nat)) (= (tptp.groups2906978787729119204at_rat F (tptp.set_or1269000886237332187st_nat A B2)) (tptp.aa_rat_rat (tptp.set_fo1949268297981939178at_rat (tptp.aTP_Lamm_nf F) A B2) tptp.zero_zero_rat))) (forall ((F tptp.fun_nat_int) (A tptp.nat) (B2 tptp.nat)) (= (tptp.groups3539618377306564664at_int F (tptp.set_or1269000886237332187st_nat A B2)) (tptp.aa_int_int (tptp.set_fo2581907887559384638at_int (tptp.aTP_Lamm_ng F) A B2) tptp.zero_zero_int))) (forall ((F tptp.fun_nat_nat) (A tptp.nat) (B2 tptp.nat)) (= (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat F) (tptp.set_or1269000886237332187st_nat A B2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.set_fo2584398358068434914at_nat (tptp.aTP_Lamm_nh F) A) B2) tptp.zero_zero_nat))) (forall ((F tptp.fun_nat_real) (A tptp.nat) (B2 tptp.nat)) (= (tptp.groups6591440286371151544t_real F (tptp.set_or1269000886237332187st_nat A B2)) (tptp.aa_real_real (tptp.aa_nat_fun_real_real (tptp.set_fo3111899725591712190t_real (tptp.aTP_Lamm_ni F) A) B2) tptp.zero_zero_real))) (forall ((N tptp.nat)) (= (tptp.aa_nat_int tptp.semiri1406184849735516958ct_int N) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.set_fo2584398358068434914at_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N) tptp.one_one_nat)))) (forall ((N tptp.nat)) (= (tptp.aa_nat_real tptp.semiri2265585572941072030t_real N) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.set_fo2584398358068434914at_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N) tptp.one_one_nat)))) (forall ((N tptp.nat)) (= (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat N) (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.set_fo2584398358068434914at_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N) tptp.one_one_nat)))) (forall ((C tptp.fun_nat_complex) (X tptp.complex)) (let ((_let_1 (tptp.aa_com8181001469867462503omplex (tptp.aTP_Lamm_nj C) X))) (=> (tptp.summable_complex _let_1) (tptp.pp (tptp.aa_complex_bool (tptp.sums_complex (tptp.aa_com8181001469867462503omplex (tptp.aTP_Lamm_nk C) X)) (tptp.suminf_complex _let_1)))))) (forall ((C tptp.fun_nat_real) (X tptp.real)) (let ((_let_1 (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_nl C) X))) (=> (tptp.summable_real _let_1) (tptp.pp (tptp.aa_real_bool (tptp.sums_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_nm C) X)) (tptp.suminf_real _let_1)))))) (forall ((X tptp.complex)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (let ((_let_2 (tptp.aa_complex_complex tptp.tan_complex X))) (let ((_let_3 (tptp.times_times_complex (tptp.numera6690914467698888265omplex _let_1)))) (let ((_let_4 (tptp.aa_complex_complex _let_3 X))) (=> (not (= (tptp.aa_complex_complex tptp.cos_complex X) tptp.zero_zero_complex)) (=> (not (= (tptp.aa_complex_complex tptp.cos_complex _let_4) tptp.zero_zero_complex)) (= (tptp.aa_complex_complex tptp.tan_complex _let_4) (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex (tptp.aa_complex_complex _let_3 _let_2)) (tptp.aa_complex_complex (tptp.minus_minus_complex tptp.one_one_complex) (tptp.aa_nat_complex (tptp.power_power_complex _let_2) (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1)))))))))))) (forall ((X tptp.real)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (let ((_let_2 (tptp.aa_real_real tptp.tan_real X))) (let ((_let_3 (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_num_real tptp.numeral_numeral_real _let_1)))) (let ((_let_4 (tptp.aa_real_real _let_3 X))) (=> (not (= (tptp.aa_real_real tptp.cos_real X) tptp.zero_zero_real)) (=> (not (= (tptp.aa_real_real tptp.cos_real _let_4) tptp.zero_zero_real)) (= (tptp.aa_real_real tptp.tan_real _let_4) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real _let_3 _let_2)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real tptp.one_one_real) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real _let_2) (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1)))))))))))) (forall ((X tptp.int) (Y tptp.int) (F tptp.fun_int_nat)) (= (tptp.member5262025264175285858nt_int (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int X) Y) (tptp.measure_int F)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_int_nat F X)) (tptp.aa_int_nat F Y))))) (forall ((Z tptp.complex)) (=> (= (tptp.aa_complex_real tptp.real_V1022390504157884413omplex Z) tptp.one_one_real) (not (forall ((T4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) T4)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real T4) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))) tptp.pi))) (not (= Z (tptp.aa_real_complex (tptp.aa_rea2649881322057434177omplex tptp.complex2 (tptp.aa_real_real tptp.cos_real T4)) (tptp.aa_real_real tptp.sin_real T4)))))))))) (forall ((X tptp.real) (N tptp.nat)) (=> (not (= X tptp.zero_zero_real)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (exists ((T4 tptp.real)) (let ((_let_1 (tptp.aa_real_real tptp.abs_abs_real T4))) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) _let_1)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real _let_1) (tptp.aa_real_real tptp.abs_abs_real X))) (= (tptp.aa_real_real tptp.exp_real X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real tptp.aTP_Lamm_nn X) (tptp.set_ord_lessThan_nat N))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real tptp.exp_real T4)) (tptp.aa_nat_real tptp.semiri2265585572941072030t_real N))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) N)))))))))) (forall ((X tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Y)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.exp_real X)) (tptp.aa_real_real tptp.exp_real Y))))) (forall ((X tptp.real) (Y tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.exp_real X)) (tptp.aa_real_real tptp.exp_real Y))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Y)))) (forall ((X tptp.real) (Y tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.exp_real X)) (tptp.aa_real_real tptp.exp_real Y))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) Y)))) (forall ((N tptp.nat)) (= (tptp.aa_real_real tptp.tan_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N)) tptp.pi)) tptp.zero_zero_real)) (forall ((X tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real) (tptp.aa_real_real tptp.exp_real X))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) X)))) (forall ((X tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.exp_real X)) tptp.one_one_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) tptp.zero_zero_real)))) (forall ((X tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.one_one_real) (tptp.aa_real_real tptp.exp_real X))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) X)))) (forall ((X tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.exp_real X)) tptp.one_one_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) tptp.zero_zero_real)))) (forall ((X tptp.real) (N tptp.num)) (= (tptp.aa_real_real tptp.tan_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_num_real tptp.numeral_numeral_real N)) tptp.pi))) (tptp.aa_real_real tptp.tan_real X))) (forall ((X tptp.real) (N tptp.nat)) (= (tptp.aa_real_real tptp.tan_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N)) tptp.pi))) (tptp.aa_real_real tptp.tan_real X))) (forall ((X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) X)) (= (tptp.aa_real_real tptp.exp_real (tptp.aa_real_real tptp.ln_ln_real X)) X))) (forall ((X tptp.real)) (= (= (tptp.aa_real_real tptp.exp_real (tptp.aa_real_real tptp.ln_ln_real X)) X) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) X)))) (forall ((X tptp.real)) (= (tptp.aa_real_real tptp.tan_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))) tptp.pi))) (tptp.aa_real_real tptp.tan_real X))) (forall ((X tptp.real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real (tptp.aa_real_real tptp.exp_real X))) (tptp.aa_real_real tptp.exp_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real X))))) (forall ((X tptp.complex)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.aa_complex_complex tptp.exp_complex X))) (tptp.aa_real_real tptp.exp_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex X))))) (forall ((X tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.exp_real X)) (tptp.aa_real_real tptp.exp_real Y))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Y)))) (forall ((A4 tptp.complex)) (let ((_let_1 (tptp.aa_complex_complex tptp.exp_complex A4))) (= (tptp.aa_complex_complex (tptp.times_times_complex _let_1) A4) (tptp.aa_complex_complex (tptp.times_times_complex A4) _let_1)))) (forall ((A4 tptp.real)) (let ((_let_1 (tptp.aa_real_real tptp.exp_real A4))) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real _let_1) A4) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A4) _let_1)))) (forall ((Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) Y)) (exists ((X4 tptp.real)) (= (tptp.aa_real_real tptp.exp_real X4) Y)))) (forall ((X tptp.real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) (tptp.aa_real_real tptp.exp_real X)))) (forall ((X tptp.real)) (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.exp_real X)) tptp.zero_zero_real)))) (forall ((X tptp.real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_real_real tptp.exp_real X)))) (forall ((X tptp.real)) (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.exp_real X)) tptp.zero_zero_real)))) (forall ((X tptp.complex) (Y tptp.complex)) (= (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_complex_complex tptp.exp_complex X)) (tptp.aa_complex_complex tptp.exp_complex Y)) (tptp.aa_complex_complex tptp.exp_complex (tptp.aa_complex_complex (tptp.plus_plus_complex X) Y)))) (forall ((X tptp.real) (Y tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real tptp.exp_real X)) (tptp.aa_real_real tptp.exp_real Y)) (tptp.aa_real_real tptp.exp_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) Y)))) (forall ((X tptp.complex) (Y tptp.complex)) (=> (= (tptp.aa_complex_complex (tptp.times_times_complex X) Y) (tptp.aa_complex_complex (tptp.times_times_complex Y) X)) (= (tptp.aa_complex_complex tptp.exp_complex (tptp.aa_complex_complex (tptp.plus_plus_complex X) Y)) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_complex_complex tptp.exp_complex X)) (tptp.aa_complex_complex tptp.exp_complex Y))))) (forall ((X tptp.real) (Y tptp.real)) (=> (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real X) Y) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real Y) X)) (= (tptp.aa_real_real tptp.exp_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) Y)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real tptp.exp_real X)) (tptp.aa_real_real tptp.exp_real Y))))) (forall ((X tptp.complex) (Y tptp.complex)) (= (tptp.aa_complex_complex tptp.exp_complex (tptp.aa_complex_complex (tptp.minus_minus_complex X) Y)) (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex (tptp.aa_complex_complex tptp.exp_complex X)) (tptp.aa_complex_complex tptp.exp_complex Y)))) (forall ((X tptp.real) (Y tptp.real)) (= (tptp.aa_real_real tptp.exp_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real X) Y)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real tptp.exp_real X)) (tptp.aa_real_real tptp.exp_real Y)))) (forall ((A tptp.real) (B2 tptp.real) (W tptp.num)) (= (= (tptp.aa_real_complex (tptp.aa_rea2649881322057434177omplex tptp.complex2 A) B2) (tptp.numera6690914467698888265omplex W)) (and (= A (tptp.aa_num_real tptp.numeral_numeral_real W)) (= B2 tptp.zero_zero_real)))) (forall ((X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) X)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real) (tptp.aa_real_real tptp.exp_real X))))) (forall ((X tptp.real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real tptp.one_one_real) X)) (tptp.aa_real_real tptp.exp_real X)))) (forall ((X tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real tptp.exp_real X)) (tptp.aa_real_real tptp.exp_real (tptp.aa_real_real tptp.uminus_uminus_real X))) tptp.one_one_real)) (forall ((X tptp.complex)) (= (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_complex_complex tptp.exp_complex X)) (tptp.aa_complex_complex tptp.exp_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex X))) tptp.one_one_complex)) (forall ((X tptp.complex) (N tptp.nat)) (= (tptp.aa_complex_complex tptp.exp_complex (tptp.aa_complex_complex (tptp.times_times_complex X) (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex N))) (tptp.aa_nat_complex (tptp.power_power_complex (tptp.aa_complex_complex tptp.exp_complex X)) N))) (forall ((X tptp.real) (N tptp.nat)) (= (tptp.aa_real_real tptp.exp_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real X) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real tptp.exp_real X)) N))) (forall ((N tptp.nat) (X tptp.complex)) (= (tptp.aa_complex_complex tptp.exp_complex (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex N)) X)) (tptp.aa_nat_complex (tptp.power_power_complex (tptp.aa_complex_complex tptp.exp_complex X)) N))) (forall ((N tptp.nat) (X tptp.real)) (= (tptp.aa_real_real tptp.exp_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N)) X)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real tptp.exp_real X)) N))) (forall ((A tptp.real) (B2 tptp.real) (W tptp.num)) (= (= (tptp.aa_real_complex (tptp.aa_rea2649881322057434177omplex tptp.complex2 A) B2) (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.numera6690914467698888265omplex W))) (and (= A (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real W))) (= B2 tptp.zero_zero_real)))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real) (D tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.times_times_real B2))) (let ((_let_2 (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A))) (= (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_real_complex (tptp.aa_rea2649881322057434177omplex tptp.complex2 A) B2)) (tptp.aa_real_complex (tptp.aa_rea2649881322057434177omplex tptp.complex2 C) D)) (tptp.aa_real_complex (tptp.aa_rea2649881322057434177omplex tptp.complex2 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real _let_2 C)) (tptp.aa_real_real _let_1 D))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real _let_2 D)) (tptp.aa_real_real _let_1 C))))))) (forall ((X5 tptp.complex)) (= (tptp.aa_complex_complex tptp.tan_complex X5) (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex (tptp.aa_complex_complex tptp.sin_complex X5)) (tptp.aa_complex_complex tptp.cos_complex X5)))) (forall ((X5 tptp.real)) (= (tptp.aa_real_real tptp.tan_real X5) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real tptp.sin_real X5)) (tptp.aa_real_real tptp.cos_real X5)))) (forall ((X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) X)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real tptp.one_one_real) X)) (tptp.aa_real_real tptp.exp_real X))))) (forall ((Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.one_one_real) Y)) (exists ((X4 tptp.real)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) X4)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X4) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real Y) tptp.one_one_real))) (= (tptp.aa_real_real tptp.exp_real X4) Y))))) (forall ((X tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) X)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y) (tptp.aa_real_real tptp.ln_ln_real X))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.exp_real Y)) X))))) (forall ((X tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.exp_real tptp.one_one_real)) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) Y)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real tptp.ln_ln_real Y)) Y)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real tptp.ln_ln_real X)) X)))))) (forall ((C tptp.fun_nat_rat) (X5 tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc X5))) (= (tptp.aa_nat_rat (tptp.diffs_rat C) X5) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat _let_1)) (tptp.aa_nat_rat C _let_1))))) (forall ((C tptp.fun_nat_int) (X5 tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc X5))) (= (tptp.aa_nat_int (tptp.diffs_int C) X5) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int _let_1)) (tptp.aa_nat_int C _let_1))))) (forall ((C tptp.fun_nat_real) (X5 tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc X5))) (= (tptp.aa_nat_real (tptp.diffs_real C) X5) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real _let_1)) (tptp.aa_nat_real C _let_1))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.exp_real tptp.one_one_real)) _let_59)) (forall ((C tptp.fun_nat_complex) (X tptp.complex)) (=> (forall ((X4 tptp.complex)) (tptp.summable_complex (tptp.aa_com8181001469867462503omplex (tptp.aTP_Lamm_kn C) X4))) (tptp.summable_complex (tptp.aa_com8181001469867462503omplex (tptp.aTP_Lamm_nj C) X)))) (forall ((C tptp.fun_nat_real) (X tptp.real)) (=> (forall ((X4 tptp.real)) (tptp.summable_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_kl C) X4))) (tptp.summable_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_nl C) X)))) (forall ((N tptp.nat) (X tptp.complex)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (= (tptp.aa_nat_complex (tptp.power_power_complex (tptp.aa_complex_complex tptp.exp_complex (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex X) (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex N)))) N) (tptp.aa_complex_complex tptp.exp_complex X)))) (forall ((N tptp.nat) (X tptp.real)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real tptp.exp_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real X) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N)))) N) (tptp.aa_real_real tptp.exp_real X)))) (forall ((X tptp.real)) (let ((_let_1 (tptp.aa_real_real tptp.exp_real (tptp.aa_real_real tptp.uminus_uminus_real X)))) (let ((_let_2 (tptp.aa_real_real tptp.exp_real X))) (= (tptp.aa_real_real tptp.tanh_real X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real _let_2) _let_1)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real _let_2) _let_1)))))) (forall ((X tptp.complex)) (let ((_let_1 (tptp.aa_complex_complex tptp.exp_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex X)))) (let ((_let_2 (tptp.aa_complex_complex tptp.exp_complex X))) (= (tptp.aa_complex_complex tptp.tanh_complex X) (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex (tptp.aa_complex_complex (tptp.minus_minus_complex _let_2) _let_1)) (tptp.aa_complex_complex (tptp.plus_plus_complex _let_2) _let_1)))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.exp_real _let_68)) _let_28)) (= (tptp.aa_real_real tptp.tan_real _let_67) tptp.one_one_real) (forall ((Z tptp.complex)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (= (tptp.aa_complex_complex tptp.exp_complex (tptp.aa_complex_complex (tptp.times_times_complex (tptp.numera6690914467698888265omplex _let_1)) Z)) (tptp.aa_nat_complex (tptp.power_power_complex (tptp.aa_complex_complex tptp.exp_complex Z)) (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1))))) (forall ((Z tptp.real)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (= (tptp.aa_real_real tptp.exp_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_num_real tptp.numeral_numeral_real _let_1)) Z)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real tptp.exp_real Z)) (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1))))) (forall ((Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) Y)) (exists ((X4 tptp.real)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) X4)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X4) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y) (tptp.aa_real_real tptp.tan_real X4))))))) (forall ((X tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool _let_1 X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))))) (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real tptp.tan_real X))))))) (forall ((Y tptp.real)) (exists ((X4 tptp.real)) (let ((_let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))))) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.uminus_uminus_real _let_1)) X4)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X4) _let_1)) (= (tptp.aa_real_real tptp.tan_real X4) Y))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X))) (let ((_let_2 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_3 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.uminus_uminus_real _let_2)))) (=> (tptp.pp (tptp.aa_real_bool _let_3 X)) (=> (tptp.pp (tptp.aa_real_bool _let_1 _let_2)) (=> (tptp.pp (tptp.aa_real_bool _let_3 Y)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y) _let_2)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.tan_real X)) (tptp.aa_real_real tptp.tan_real Y))) (tptp.pp (tptp.aa_real_bool _let_1 Y))))))))))) (forall ((Y tptp.real) (X tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y))) (let ((_let_2 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_3 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.uminus_uminus_real _let_2)))) (=> (tptp.pp (tptp.aa_real_bool _let_3 Y)) (=> (tptp.pp (tptp.aa_real_bool _let_1 _let_2)) (=> (tptp.pp (tptp.aa_real_bool _let_3 X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) _let_2)) (= (tptp.pp (tptp.aa_real_bool _let_1 X)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.tan_real Y)) (tptp.aa_real_real tptp.tan_real X)))))))))))) (forall ((Y tptp.real) (X tptp.real)) (let ((_let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.uminus_uminus_real _let_1)) Y)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) _let_1)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.tan_real Y)) (tptp.aa_real_real tptp.tan_real X)))))))) (forall ((Y tptp.real)) (exists ((X4 tptp.real)) (let ((_let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))))) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.uminus_uminus_real _let_1)) X4)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X4) _let_1)) (= (tptp.aa_real_real tptp.tan_real X4) Y) (forall ((Y5 tptp.real)) (let ((_let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))))) (=> (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.uminus_uminus_real _let_1)) Y5)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y5) _let_1)) (= (tptp.aa_real_real tptp.tan_real Y5) Y)) (= Y5 X4)))))))) (= (tptp.aa_real_real tptp.tan_real (tptp.aa_real_real tptp.uminus_uminus_real _let_67)) _let_57) (forall ((Y tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.one_one_real) (tptp.aa_real_real tptp.tan_real Y)) (tptp.aa_real_real tptp.tan_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))) Y)))) (forall ((Z tptp.real)) (let ((_let_1 (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real Z)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.one_one_real) _let_1))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real (tptp.aa_real_real tptp.exp_real Z))) _let_1))))) (forall ((Z tptp.complex)) (let ((_let_1 (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex Z)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.one_one_real) _let_1))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.aa_complex_complex tptp.exp_complex Z))) _let_1))))) (forall ((X tptp.complex) (Y tptp.complex)) (let ((_let_1 (tptp.aa_complex_complex tptp.cos_complex Y))) (let ((_let_2 (tptp.aa_complex_complex tptp.cos_complex X))) (=> (not (= _let_2 tptp.zero_zero_complex)) (=> (not (= _let_1 tptp.zero_zero_complex)) (= (tptp.aa_complex_complex (tptp.plus_plus_complex (tptp.aa_complex_complex tptp.tan_complex X)) (tptp.aa_complex_complex tptp.tan_complex Y)) (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex (tptp.aa_complex_complex tptp.sin_complex (tptp.aa_complex_complex (tptp.plus_plus_complex X) Y))) (tptp.aa_complex_complex (tptp.times_times_complex _let_2) _let_1)))))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_real_real tptp.cos_real Y))) (let ((_let_2 (tptp.aa_real_real tptp.cos_real X))) (=> (not (= _let_2 tptp.zero_zero_real)) (=> (not (= _let_1 tptp.zero_zero_real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real tptp.tan_real X)) (tptp.aa_real_real tptp.tan_real Y)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real tptp.sin_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) Y))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real _let_2) _let_1)))))))) (forall ((X tptp.real) (K5 tptp.real) (C tptp.fun_nat_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real X)) K5)) (=> (forall ((X4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real X4)) K5)) (tptp.summable_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_kl C) X4)))) (tptp.summable_real (tptp.aa_fun1839206346889086768t_real (tptp.aTP_Lamm_no X) C))))) (forall ((X tptp.complex) (K5 tptp.real) (C tptp.fun_nat_complex)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex X)) K5)) (=> (forall ((X4 tptp.complex)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex X4)) K5)) (tptp.summable_complex (tptp.aa_com8181001469867462503omplex (tptp.aTP_Lamm_kn C) X4)))) (tptp.summable_complex (tptp.aa_fun2955221450537884980omplex (tptp.aTP_Lamm_np X) C))))) (forall ((X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) tptp.one_one_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.exp_real X)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real tptp.one_one_real) X)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))))))) (forall ((X tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool _let_1 X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))))) (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real tptp.tan_real X))))))) (forall ((Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) Y)) (exists ((X4 tptp.real)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) X4)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X4) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.aa_real_real tptp.tan_real X4) Y))))) (forall ((X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.pi)) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.tan_real X)) tptp.zero_zero_real))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_2 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.uminus_uminus_real _let_1)))) (=> (tptp.pp (tptp.aa_real_bool _let_2 X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) _let_1)) (=> (tptp.pp (tptp.aa_real_bool _let_2 Y)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y) _let_1)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.tan_real X)) (tptp.aa_real_real tptp.tan_real Y))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) Y)))))))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.uminus_uminus_real _let_1)) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) Y)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y) _let_1)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.tan_real X)) (tptp.aa_real_real tptp.tan_real Y)))))))) (forall ((X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.abs_abs_real X)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit0 tptp.one)))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_real_real tptp.tan_real X))) tptp.one_one_real)))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.uminus_uminus_real _let_1)) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) _let_1)) (=> (= (tptp.aa_real_real tptp.tan_real X) Y) (= (tptp.aa_real_real tptp.arctan Y) X)))))) (forall ((X tptp.real)) (let ((_let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.uminus_uminus_real _let_1)) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) _let_1)) (= (tptp.aa_real_real tptp.arctan (tptp.aa_real_real tptp.tan_real X)) X))))) (forall ((Y tptp.real)) (let ((_let_1 (tptp.aa_real_real tptp.arctan Y))) (let ((_let_2 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))))) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.uminus_uminus_real _let_2)) _let_1)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real _let_1) _let_2)) (= (tptp.aa_real_real tptp.tan_real _let_1) Y))))) (forall ((X tptp.complex) (Y tptp.complex)) (let ((_let_1 (tptp.aa_complex_complex tptp.cos_complex Y))) (let ((_let_2 (tptp.aa_complex_complex tptp.cos_complex X))) (=> (not (= _let_2 tptp.zero_zero_complex)) (=> (not (= _let_1 tptp.zero_zero_complex)) (= (tptp.aa_complex_complex (tptp.minus_minus_complex tptp.one_one_complex) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_complex_complex tptp.tan_complex X)) (tptp.aa_complex_complex tptp.tan_complex Y))) (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex (tptp.aa_complex_complex tptp.cos_complex (tptp.aa_complex_complex (tptp.plus_plus_complex X) Y))) (tptp.aa_complex_complex (tptp.times_times_complex _let_2) _let_1)))))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_real_real tptp.cos_real Y))) (let ((_let_2 (tptp.aa_real_real tptp.cos_real X))) (=> (not (= _let_2 tptp.zero_zero_real)) (=> (not (= _let_1 tptp.zero_zero_real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real tptp.one_one_real) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real tptp.tan_real X)) (tptp.aa_real_real tptp.tan_real Y))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real tptp.cos_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) Y))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real _let_2) _let_1)))))))) (forall ((X tptp.complex) (Y tptp.complex)) (let ((_let_1 (tptp.aa_complex_complex tptp.tan_complex Y))) (let ((_let_2 (tptp.aa_complex_complex tptp.tan_complex X))) (let ((_let_3 (tptp.aa_complex_complex (tptp.minus_minus_complex X) Y))) (=> (not (= (tptp.aa_complex_complex tptp.cos_complex X) tptp.zero_zero_complex)) (=> (not (= (tptp.aa_complex_complex tptp.cos_complex Y) tptp.zero_zero_complex)) (=> (not (= (tptp.aa_complex_complex tptp.cos_complex _let_3) tptp.zero_zero_complex)) (= (tptp.aa_complex_complex tptp.tan_complex _let_3) (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex (tptp.aa_complex_complex (tptp.minus_minus_complex _let_2) _let_1)) (tptp.aa_complex_complex (tptp.plus_plus_complex tptp.one_one_complex) (tptp.aa_complex_complex (tptp.times_times_complex _let_2) _let_1))))))))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_real_real tptp.tan_real Y))) (let ((_let_2 (tptp.aa_real_real tptp.tan_real X))) (let ((_let_3 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real X) Y))) (=> (not (= (tptp.aa_real_real tptp.cos_real X) tptp.zero_zero_real)) (=> (not (= (tptp.aa_real_real tptp.cos_real Y) tptp.zero_zero_real)) (=> (not (= (tptp.aa_real_real tptp.cos_real _let_3) tptp.zero_zero_real)) (= (tptp.aa_real_real tptp.tan_real _let_3) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real _let_2) _let_1)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real tptp.one_one_real) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real _let_2) _let_1))))))))))) (forall ((X tptp.complex) (Y tptp.complex)) (let ((_let_1 (tptp.aa_complex_complex tptp.tan_complex Y))) (let ((_let_2 (tptp.aa_complex_complex tptp.tan_complex X))) (let ((_let_3 (tptp.aa_complex_complex (tptp.plus_plus_complex X) Y))) (=> (not (= (tptp.aa_complex_complex tptp.cos_complex X) tptp.zero_zero_complex)) (=> (not (= (tptp.aa_complex_complex tptp.cos_complex Y) tptp.zero_zero_complex)) (=> (not (= (tptp.aa_complex_complex tptp.cos_complex _let_3) tptp.zero_zero_complex)) (= (tptp.aa_complex_complex tptp.tan_complex _let_3) (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex (tptp.aa_complex_complex (tptp.plus_plus_complex _let_2) _let_1)) (tptp.aa_complex_complex (tptp.minus_minus_complex tptp.one_one_complex) (tptp.aa_complex_complex (tptp.times_times_complex _let_2) _let_1))))))))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_real_real tptp.tan_real Y))) (let ((_let_2 (tptp.aa_real_real tptp.tan_real X))) (let ((_let_3 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) Y))) (=> (not (= (tptp.aa_real_real tptp.cos_real X) tptp.zero_zero_real)) (=> (not (= (tptp.aa_real_real tptp.cos_real Y) tptp.zero_zero_real)) (=> (not (= (tptp.aa_real_real tptp.cos_real _let_3) tptp.zero_zero_real)) (= (tptp.aa_real_real tptp.tan_real _let_3) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real _let_2) _let_1)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real tptp.one_one_real) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real _let_2) _let_1))))))))))) (forall ((X tptp.real)) (let ((_let_1 (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.one_one_real) _let_1))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.exp_real X)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real tptp.one_one_real) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real _let_1) X)))))))) (forall ((N tptp.nat) (X tptp.real)) (let ((_let_1 (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real _let_1)) X)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real tptp.one_one_real) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real X) _let_1))) N)) (tptp.aa_real_real tptp.exp_real X))))))) (forall ((X tptp.real) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) _let_1)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real tptp.one_one_real) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real X) _let_1))) N)) (tptp.aa_real_real tptp.exp_real (tptp.aa_real_real tptp.uminus_uminus_real X)))))))) (forall ((X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.abs_abs_real X)) tptp.one_one_real)) (exists ((Z4 tptp.real)) (let ((_let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit0 tptp.one)))))) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.uminus_uminus_real _let_1)) Z4)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Z4) _let_1)) (= (tptp.aa_real_real tptp.tan_real Z4) X)))))) (forall ((Z tptp.real)) (let ((_let_1 (tptp.aa_real_real tptp.real_V7735802525324610683m_real Z))) (let ((_let_2 (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real _let_1) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.one_one_real) _let_2))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real (tptp.aa_real_real tptp.exp_real Z))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real tptp.one_one_real) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real _let_2) _let_1)))))))) (forall ((Z tptp.complex)) (let ((_let_1 (tptp.aa_complex_real tptp.real_V1022390504157884413omplex Z))) (let ((_let_2 (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real _let_1) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.one_one_real) _let_2))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.aa_complex_complex tptp.exp_complex Z))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real tptp.one_one_real) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real _let_2) _let_1)))))))) (forall ((X tptp.real) (N tptp.nat)) (exists ((T4 tptp.real)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real T4)) (tptp.aa_real_real tptp.abs_abs_real X))) (= (tptp.aa_real_real tptp.exp_real X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real tptp.aTP_Lamm_nn X) (tptp.set_ord_lessThan_nat N))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real tptp.exp_real T4)) (tptp.aa_nat_real tptp.semiri2265585572941072030t_real N))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) N))))))) (forall ((X tptp.real)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) X)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real tptp.one_one_real) X)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1))) (tptp.aa_num_real tptp.numeral_numeral_real _let_1)))) (tptp.aa_real_real tptp.exp_real X)))))) (forall ((X tptp.real)) (let ((_let_1 (tptp.aa_real_real tptp.exp_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))) X)))) (= (tptp.aa_real_real tptp.tanh_real X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real tptp.one_one_real) _let_1)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real tptp.one_one_real) _let_1))))) (forall ((X tptp.complex)) (let ((_let_1 (tptp.aa_complex_complex (tptp.times_times_complex (tptp.numera6690914467698888265omplex (tptp.aa_num_num tptp.bit0 tptp.one))) X))) (= (tptp.aa_complex_complex tptp.tan_complex X) (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex (tptp.aa_complex_complex tptp.sin_complex _let_1)) (tptp.aa_complex_complex (tptp.plus_plus_complex (tptp.aa_complex_complex tptp.cos_complex _let_1)) tptp.one_one_complex))))) (forall ((X tptp.real)) (let ((_let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))) X))) (= (tptp.aa_real_real tptp.tan_real X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real tptp.sin_real _let_1)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real tptp.cos_real _let_1)) tptp.one_one_real))))) (forall ((N tptp.nat) (K tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) K))) (let ((_let_2 (tptp.aa_nat_fun_nat_nat tptp.binomial N))) (let ((_let_3 (tptp.aa_nat_nat _let_2 K))) (let ((_let_4 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N))) (let ((_let_5 (tptp.pp (tptp.aa_nat_bool _let_4 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) K))))) (let ((_let_6 (tptp.pp (tptp.aa_nat_bool _let_4 K)))) (and (=> _let_6 (= _let_3 tptp.zero_zero_nat)) (=> (not _let_6) (and (=> _let_5 (= _let_3 (tptp.aa_nat_nat _let_2 _let_1))) (=> (not _let_5) (= _let_3 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.set_fo2584398358068434914at_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat _let_1) tptp.one_one_nat)) N) tptp.one_one_nat)) (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat K)))))))))))))) (forall ((A4 tptp.set_nat) (B4 tptp.set_nat)) (= (tptp.member8277197624267554838et_nat (tptp.produc4532415448927165861et_nat A4 B4) tptp.finite_psubset_nat) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_set_nat A4) B4)) (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat B4))))) (forall ((A4 tptp.set_int) (B4 tptp.set_int)) (= (tptp.member2572552093476627150et_int (tptp.produc6363374080413544029et_int A4 B4) tptp.finite_psubset_int) (and (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_set_int A4) B4)) (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int B4))))) (forall ((A4 tptp.set_complex) (B4 tptp.set_complex)) (= (tptp.member351165363924911826omplex (tptp.produc3790773574474814305omplex A4 B4) tptp.finite8643634255014194347omplex) (and (tptp.pp (tptp.aa_set_complex_bool (tptp.ord_less_set_complex A4) B4)) (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex B4))))) (forall ((X tptp.real)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (let ((_let_2 (tptp.aa_real_real tptp.tan_real X))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.abs_abs_real X)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) (tptp.aa_num_real tptp.numeral_numeral_real _let_1)))) (= (tptp.aa_real_real tptp.sin_real X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real _let_2) (tptp.aa_real_real tptp.sqrt (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real tptp.one_one_real) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real _let_2) (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1)))))))))) (forall ((X tptp.real)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.abs_abs_real X)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) (tptp.aa_num_real tptp.numeral_numeral_real _let_1)))) (= (tptp.aa_real_real tptp.cos_real X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.one_one_real) (tptp.aa_real_real tptp.sqrt (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real tptp.one_one_real) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real tptp.tan_real X)) (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1))))))))) (forall ((Z tptp.complex) (N tptp.nat)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (let ((_let_2 (tptp.numera6690914467698888265omplex _let_1))) (let ((_let_3 (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1))) (let ((_let_4 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat _let_3) N))) (= (tptp.aa_nat_complex (tptp.comm_s2602460028002588243omplex (tptp.aa_complex_complex (tptp.times_times_complex _let_2) Z)) _let_4) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat _let_3) _let_4))) (tptp.aa_nat_complex (tptp.comm_s2602460028002588243omplex Z) N))) (tptp.aa_nat_complex (tptp.comm_s2602460028002588243omplex (tptp.aa_complex_complex (tptp.plus_plus_complex Z) (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex tptp.one_one_complex) _let_2))) N)))))))) (forall ((Z tptp.rat) (N tptp.nat)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (let ((_let_2 (tptp.aa_num_rat tptp.numeral_numeral_rat _let_1))) (let ((_let_3 (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1))) (let ((_let_4 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat _let_3) N))) (= (tptp.aa_nat_rat (tptp.comm_s4028243227959126397er_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat _let_2) Z)) _let_4) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat _let_3) _let_4))) (tptp.aa_nat_rat (tptp.comm_s4028243227959126397er_rat Z) N))) (tptp.aa_nat_rat (tptp.comm_s4028243227959126397er_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat Z) (tptp.aa_rat_rat (tptp.divide_divide_rat tptp.one_one_rat) _let_2))) N)))))))) (forall ((Z tptp.real) (N tptp.nat)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (let ((_let_2 (tptp.aa_num_real tptp.numeral_numeral_real _let_1))) (let ((_let_3 (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1))) (let ((_let_4 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat _let_3) N))) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.comm_s7457072308508201937r_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real _let_2) Z)) _let_4) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat _let_3) _let_4))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.comm_s7457072308508201937r_real Z) N))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.comm_s7457072308508201937r_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real Z) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.one_one_real) _let_2))) N)))))))) (forall ((X tptp.real) (Y tptp.real)) (= (= (tptp.aa_real_real tptp.sqrt X) (tptp.aa_real_real tptp.sqrt Y)) (= X Y))) (= (tptp.aa_real_real tptp.sqrt tptp.zero_zero_real) tptp.zero_zero_real) (forall ((X tptp.real)) (= (= (tptp.aa_real_real tptp.sqrt X) tptp.zero_zero_real) (= X tptp.zero_zero_real))) (forall ((X tptp.real) (Y tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.sqrt X)) (tptp.aa_real_real tptp.sqrt Y))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Y)))) (forall ((X tptp.real) (Y tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.sqrt X)) (tptp.aa_real_real tptp.sqrt Y))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) Y)))) (= (tptp.aa_real_real tptp.sqrt tptp.one_one_real) tptp.one_one_real) (forall ((X tptp.real)) (= (= (tptp.aa_real_real tptp.sqrt X) tptp.one_one_real) (= X tptp.one_one_real))) (forall ((Y tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real))) (= (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real tptp.sqrt Y))) (tptp.pp (tptp.aa_real_bool _let_1 Y))))) (forall ((X tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.sqrt X)) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) tptp.zero_zero_real)))) (forall ((Y tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (= (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real tptp.sqrt Y))) (tptp.pp (tptp.aa_real_bool _let_1 Y))))) (forall ((X tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.sqrt X)) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) tptp.zero_zero_real)))) (forall ((N tptp.nat) (K tptp.nat)) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial N) K) tptp.zero_zero_nat) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N) K)))) (forall ((N tptp.nat) (K tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc K))) (let ((_let_2 (tptp.aa_nat_fun_nat_nat tptp.binomial N))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial (tptp.aa_nat_nat tptp.suc N)) _let_1) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat _let_2 K)) (tptp.aa_nat_nat _let_2 _let_1)))))) (forall ((X tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.sqrt X)) tptp.one_one_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) tptp.one_one_real)))) (forall ((Y tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real))) (= (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real tptp.sqrt Y))) (tptp.pp (tptp.aa_real_bool _let_1 Y))))) (forall ((Y tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.one_one_real))) (= (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real tptp.sqrt Y))) (tptp.pp (tptp.aa_real_bool _let_1 Y))))) (forall ((X tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.sqrt X)) tptp.one_one_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) tptp.one_one_real)))) (forall ((A tptp.real)) (let ((_let_1 (tptp.aa_real_real tptp.sqrt A))) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real _let_1) _let_1) (tptp.aa_real_real tptp.abs_abs_real A)))) (forall ((X tptp.real)) (= (tptp.aa_real_real tptp.sqrt (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real X) X)) (tptp.aa_real_real tptp.abs_abs_real X))) (= (tptp.aa_real_real tptp.sqrt _let_66) _let_28) (forall ((N tptp.nat) (K tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial N) K))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) N)))) (forall ((X tptp.real)) (= (tptp.aa_real_real tptp.sqrt (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (tptp.aa_real_real tptp.abs_abs_real X))) (forall ((X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) X)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real tptp.sqrt X)) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) X))) (forall ((X tptp.real)) (= (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real tptp.sqrt X)) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) X) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) X)))) (forall ((X tptp.real) (Y tptp.real) (Xa2 tptp.real) (Ya tptp.real)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) _let_1)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Y) _let_1))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Xa2) _let_1)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Ya) _let_1))))) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real tptp.sqrt _let_2)) _let_1) _let_2)))) (forall ((X tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Y)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.sqrt X)) (tptp.aa_real_real tptp.sqrt Y))))) (forall ((X tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) Y)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.sqrt X)) (tptp.aa_real_real tptp.sqrt Y))))) (forall ((X tptp.real)) (= (tptp.aa_real_real tptp.sqrt (tptp.aa_real_real tptp.uminus_uminus_real X)) (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_real_real tptp.sqrt X)))) (forall ((X tptp.real) (K tptp.nat)) (= (tptp.aa_real_real tptp.sqrt (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) K)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real tptp.sqrt X)) K))) (forall ((X tptp.real) (Y tptp.real)) (= (tptp.aa_real_real tptp.sqrt (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real X) Y)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real tptp.sqrt X)) (tptp.aa_real_real tptp.sqrt Y)))) (forall ((X tptp.real) (Y tptp.real)) (= (tptp.aa_real_real tptp.sqrt (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real X) Y)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real tptp.sqrt X)) (tptp.aa_real_real tptp.sqrt Y)))) (forall ((N tptp.nat) (K tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N) K)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial N) K) tptp.zero_zero_nat))) (forall ((K tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N))) (let ((_let_2 (tptp.aa_nat_nat tptp.suc K))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat _let_2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial _let_1) _let_2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat _let_1) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial N) K)))))) (forall ((N tptp.nat) (K tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc K))) (let ((_let_2 (tptp.aa_nat_nat tptp.suc N))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat _let_2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial N) K)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial _let_2) _let_1)) _let_1))))) (forall ((K tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.binomial N))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) N)) (= (tptp.aa_nat_nat _let_1 K) (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) K)))))) (forall ((X tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool _let_1 X)) (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real tptp.sqrt X)))))) (forall ((X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) X)) (=> (= (tptp.aa_real_real tptp.sqrt X) tptp.zero_zero_real) (= X tptp.zero_zero_real)))) (forall ((X tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool _let_1 X)) (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real tptp.sqrt X)))))) (forall ((M tptp.nat) (R tptp.nat) (K tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M))) (let ((_let_2 (tptp.aa_nat_nat _let_1 R))) (let ((_let_3 (tptp.aa_nat_fun_nat_nat tptp.binomial (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat _let_2) K)))) (let ((_let_4 (tptp.aa_nat_nat _let_1 K))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat _let_3 _let_4)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial _let_4) K)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat _let_3 K)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial _let_2) M)))))))) (forall ((X tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.one_one_real))) (=> (tptp.pp (tptp.aa_real_bool _let_1 X)) (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real tptp.sqrt X)))))) (forall ((R tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat R) N)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial N) R)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat N) R))))) (forall ((X tptp.real) (N tptp.nat)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool _let_1 X)) (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.comm_s7457072308508201937r_real X) N)))))) (forall ((X tptp.rat) (N tptp.nat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 X)) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_nat_rat (tptp.comm_s4028243227959126397er_rat X) N)))))) (forall ((X tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 X)) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.comm_s4663373288045622133er_nat X) N)))))) (forall ((X tptp.int) (N tptp.nat)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int))) (=> (tptp.pp (tptp.aa_int_bool _let_1 X)) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_nat_int (tptp.comm_s4660882817536571857er_int X) N)))))) (forall ((A tptp.complex) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.comm_s2602460028002588243omplex A))) (=> (not (= (tptp.aa_nat_complex _let_1 M) tptp.zero_zero_complex)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N) M)) (not (= (tptp.aa_nat_complex _let_1 N) tptp.zero_zero_complex)))))) (forall ((A tptp.real) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_real_fun_nat_real tptp.comm_s7457072308508201937r_real A))) (=> (not (= (tptp.aa_nat_real _let_1 M) tptp.zero_zero_real)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N) M)) (not (= (tptp.aa_nat_real _let_1 N) tptp.zero_zero_real)))))) (forall ((A tptp.rat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.comm_s4028243227959126397er_rat A))) (=> (not (= (tptp.aa_nat_rat _let_1 M) tptp.zero_zero_rat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N) M)) (not (= (tptp.aa_nat_rat _let_1 N) tptp.zero_zero_rat)))))) (forall ((A tptp.complex) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.comm_s2602460028002588243omplex A))) (=> (= (tptp.aa_nat_complex _let_1 N) tptp.zero_zero_complex) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N) M)) (= (tptp.aa_nat_complex _let_1 M) tptp.zero_zero_complex))))) (forall ((A tptp.real) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.aa_real_fun_nat_real tptp.comm_s7457072308508201937r_real A))) (=> (= (tptp.aa_nat_real _let_1 N) tptp.zero_zero_real) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N) M)) (= (tptp.aa_nat_real _let_1 M) tptp.zero_zero_real))))) (forall ((A tptp.rat) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.comm_s4028243227959126397er_rat A))) (=> (= (tptp.aa_nat_rat _let_1 N) tptp.zero_zero_rat) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N) M)) (= (tptp.aa_nat_rat _let_1 M) tptp.zero_zero_rat))))) (forall ((K tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) N)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial N) K))))) (forall ((A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.binomial (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) B2))))) (let ((_let_2 (tptp.aa_nat_nat tptp.suc A))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat _let_2) (tptp.aa_nat_nat _let_1 _let_2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat tptp.suc B2)) (tptp.aa_nat_nat _let_1 A)))))) (forall ((N tptp.nat) (K tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc K))) (let ((_let_2 (tptp.aa_nat_nat tptp.suc N))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial _let_2) _let_1) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat _let_2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial N) K))) _let_1))))) (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.binomial N))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) M)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat _let_1 M)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial M) K)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat _let_1 K)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) K)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) K)))))))) (forall ((X tptp.real)) (let ((_let_1 (tptp.aa_real_real tptp.sqrt X))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) X)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real X) _let_1) _let_1)))) (forall ((N tptp.nat) (K tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat _let_1 K)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial N) K)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat N) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial (tptp.aa_nat_nat _let_1 tptp.one_one_nat)) K))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool _let_1 X)) (=> (tptp.pp (tptp.aa_real_bool _let_1 Y)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.sqrt (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) Y))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real tptp.sqrt X)) (tptp.aa_real_real tptp.sqrt Y)))))))) (forall ((X tptp.real) (Y tptp.real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) (tptp.aa_real_real tptp.sqrt (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real X) X)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real Y) Y)))))) (forall ((X tptp.real) (N tptp.nat)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) X)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.comm_s7457072308508201937r_real X) N))))) (forall ((X tptp.rat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) X)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_nat_rat (tptp.comm_s4028243227959126397er_rat X) N))))) (forall ((X tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) X)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.comm_s4663373288045622133er_nat X) N))))) (forall ((X tptp.int) (N tptp.nat)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) X)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.aa_nat_int (tptp.comm_s4660882817536571857er_int X) N))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real _let_48) _let_28)) (forall ((K tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc K))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat _let_1) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial N) _let_1)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat N) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) tptp.one_one_nat)) K))))) (forall ((K tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) N)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat K)) (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) K)))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial N) K)) (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat N)))) (forall ((A tptp.complex) (N tptp.nat)) (= (tptp.aa_nat_complex (tptp.comm_s2602460028002588243omplex A) (tptp.aa_nat_nat tptp.suc N)) (tptp.aa_complex_complex (tptp.times_times_complex A) (tptp.aa_nat_complex (tptp.comm_s2602460028002588243omplex (tptp.aa_complex_complex (tptp.plus_plus_complex A) tptp.one_one_complex)) N)))) (forall ((A tptp.real) (N tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.comm_s7457072308508201937r_real A) (tptp.aa_nat_nat tptp.suc N)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.comm_s7457072308508201937r_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) tptp.one_one_real)) N)))) (forall ((A tptp.rat) (N tptp.nat)) (= (tptp.aa_nat_rat (tptp.comm_s4028243227959126397er_rat A) (tptp.aa_nat_nat tptp.suc N)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) (tptp.aa_nat_rat (tptp.comm_s4028243227959126397er_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) tptp.one_one_rat)) N)))) (forall ((A tptp.nat) (N tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.comm_s4663373288045622133er_nat A) (tptp.aa_nat_nat tptp.suc N)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.comm_s4663373288045622133er_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) tptp.one_one_nat)) N)))) (forall ((A tptp.int) (N tptp.nat)) (= (tptp.aa_nat_int (tptp.comm_s4660882817536571857er_int A) (tptp.aa_nat_nat tptp.suc N)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) (tptp.aa_nat_int (tptp.comm_s4660882817536571857er_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) tptp.one_one_int)) N)))) (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (tptp.comm_s4028243227959126397er_rat A))) (= (tptp.aa_nat_rat _let_1 (tptp.aa_nat_nat tptp.suc N)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat _let_1 N)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat N)))))) (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (tptp.comm_s4660882817536571857er_int A))) (= (tptp.aa_nat_int _let_1 (tptp.aa_nat_nat tptp.suc N)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int _let_1 N)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N)))))) (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (tptp.aa_real_fun_nat_real tptp.comm_s7457072308508201937r_real A))) (= (tptp.aa_nat_real _let_1 (tptp.aa_nat_nat tptp.suc N)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real _let_1 N)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N)))))) (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.comm_s4663373288045622133er_nat A))) (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat tptp.suc N)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat _let_1 N)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat N)))))) (forall ((Z tptp.rat) (N tptp.nat)) (let ((_let_1 (tptp.comm_s4028243227959126397er_rat Z))) (= (tptp.aa_nat_rat _let_1 (tptp.aa_nat_nat tptp.suc N)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat Z) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat N))) (tptp.aa_nat_rat _let_1 N))))) (forall ((Z tptp.int) (N tptp.nat)) (let ((_let_1 (tptp.comm_s4660882817536571857er_int Z))) (= (tptp.aa_nat_int _let_1 (tptp.aa_nat_nat tptp.suc N)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int Z) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N))) (tptp.aa_nat_int _let_1 N))))) (forall ((Z tptp.real) (N tptp.nat)) (let ((_let_1 (tptp.aa_real_fun_nat_real tptp.comm_s7457072308508201937r_real Z))) (= (tptp.aa_nat_real _let_1 (tptp.aa_nat_nat tptp.suc N)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real Z) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N))) (tptp.aa_nat_real _let_1 N))))) (forall ((Z tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.comm_s4663373288045622133er_nat Z))) (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat tptp.suc N)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Z) (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat N))) (tptp.aa_nat_nat _let_1 N))))) (forall ((N tptp.nat) (K tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N) K)) (= (tptp.aa_nat_complex (tptp.comm_s2602460028002588243omplex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex N))) K) tptp.zero_zero_complex))) (forall ((N tptp.nat) (K tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N) K)) (= (tptp.aa_nat_Code_integer (tptp.comm_s8582702949713902594nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger N))) K) tptp.zero_z3403309356797280102nteger))) (forall ((N tptp.nat) (K tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N) K)) (= (tptp.aa_nat_rat (tptp.comm_s4028243227959126397er_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat N))) K) tptp.zero_zero_rat))) (forall ((N tptp.nat) (K tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N) K)) (= (tptp.aa_nat_int (tptp.comm_s4660882817536571857er_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N))) K) tptp.zero_zero_int))) (forall ((N tptp.nat) (K tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N) K)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.comm_s7457072308508201937r_real (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N))) K) tptp.zero_zero_real))) (forall ((N tptp.nat) (K tptp.nat)) (= (= (tptp.aa_nat_complex (tptp.comm_s2602460028002588243omplex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex N))) K) tptp.zero_zero_complex) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N) K)))) (forall ((N tptp.nat) (K tptp.nat)) (= (= (tptp.aa_nat_Code_integer (tptp.comm_s8582702949713902594nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger N))) K) tptp.zero_z3403309356797280102nteger) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N) K)))) (forall ((N tptp.nat) (K tptp.nat)) (= (= (tptp.aa_nat_rat (tptp.comm_s4028243227959126397er_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat N))) K) tptp.zero_zero_rat) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N) K)))) (forall ((N tptp.nat) (K tptp.nat)) (= (= (tptp.aa_nat_int (tptp.comm_s4660882817536571857er_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N))) K) tptp.zero_zero_int) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N) K)))) (forall ((N tptp.nat) (K tptp.nat)) (= (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.comm_s7457072308508201937r_real (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N))) K) tptp.zero_zero_real) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N) K)))) (forall ((A tptp.complex) (N tptp.nat)) (= (= (tptp.aa_nat_complex (tptp.comm_s2602460028002588243omplex A) N) tptp.zero_zero_complex) (exists ((K2 tptp.nat)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat K2) N)) (= A (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex K2))))))) (forall ((A tptp.rat) (N tptp.nat)) (= (= (tptp.aa_nat_rat (tptp.comm_s4028243227959126397er_rat A) N) tptp.zero_zero_rat) (exists ((K2 tptp.nat)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat K2) N)) (= A (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat K2))))))) (forall ((A tptp.real) (N tptp.nat)) (= (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.comm_s7457072308508201937r_real A) N) tptp.zero_zero_real) (exists ((K2 tptp.nat)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat K2) N)) (= A (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real K2))))))) (forall ((K tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) N)) (not (= (tptp.aa_nat_complex (tptp.comm_s2602460028002588243omplex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex N))) K) tptp.zero_zero_complex)))) (forall ((K tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) N)) (not (= (tptp.aa_nat_Code_integer (tptp.comm_s8582702949713902594nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger N))) K) tptp.zero_z3403309356797280102nteger)))) (forall ((K tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) N)) (not (= (tptp.aa_nat_rat (tptp.comm_s4028243227959126397er_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat N))) K) tptp.zero_zero_rat)))) (forall ((K tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) N)) (not (= (tptp.aa_nat_int (tptp.comm_s4660882817536571857er_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N))) K) tptp.zero_zero_int)))) (forall ((K tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) N)) (not (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.comm_s7457072308508201937r_real (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N))) K) tptp.zero_zero_real)))) (forall ((Z tptp.rat) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.comm_s4028243227959126397er_rat Z))) (= (tptp.aa_nat_rat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N) M)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat _let_1 N)) (tptp.aa_nat_rat (tptp.comm_s4028243227959126397er_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat Z) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat N))) M))))) (forall ((Z tptp.int) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.comm_s4660882817536571857er_int Z))) (= (tptp.aa_nat_int _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N) M)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int _let_1 N)) (tptp.aa_nat_int (tptp.comm_s4660882817536571857er_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int Z) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N))) M))))) (forall ((Z tptp.real) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.aa_real_fun_nat_real tptp.comm_s7457072308508201937r_real Z))) (= (tptp.aa_nat_real _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N) M)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real _let_1 N)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.comm_s7457072308508201937r_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real Z) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N))) M))))) (forall ((Z tptp.nat) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.comm_s4663373288045622133er_nat Z))) (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N) M)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat _let_1 N)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.comm_s4663373288045622133er_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Z) (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat N))) M))))) (forall ((K tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) N)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N)) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real K))) K)) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial N) K)))))) (forall ((K tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) N)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat N)) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat K))) K)) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial N) K)))))) (forall ((K tptp.nat) (K6 tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.binomial N))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) K6)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) K6)) N)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat _let_1 K)) (tptp.aa_nat_nat _let_1 K6))))))) (forall ((N tptp.nat) (K tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.binomial (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N)))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat _let_1 K)) (tptp.aa_nat_nat _let_1 N))))) (forall ((N tptp.nat) (K tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.binomial N))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat _let_1 K)) (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat N) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))))))) (forall ((K tptp.nat) (K6 tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.binomial N))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) K6)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat N) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) K)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K6) N)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat _let_1 K6)) (tptp.aa_nat_nat _let_1 K)))))))) (forall ((N tptp.nat) (K tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial N) K)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N)))) (forall ((X tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) Y)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) (tptp.aa_real_real tptp.sqrt Y))))) (forall ((N tptp.nat) (K tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.binomial (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) tptp.one_one_nat)))) (let ((_let_2 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat))) (=> (tptp.pp (tptp.aa_nat_bool _let_2 N)) (=> (tptp.pp (tptp.aa_nat_bool _let_2 K)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial N) K) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat K) tptp.one_one_nat))) (tptp.aa_nat_nat _let_1 K)))))))) (forall ((X tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.sqrt X)) Y)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Y) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))))) (forall ((X tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) Y)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) (tptp.aa_real_real tptp.sqrt Y))))) (forall ((K tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) K)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat K) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial N) K)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat N) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) tptp.one_one_nat)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat K) tptp.one_one_nat)))))) (= (tptp.aa_real_real tptp.tan_real _let_62) _let_60) (forall ((K tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) N)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial N) K) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat N)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat K)) (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) K))))))) (forall ((M tptp.nat) (N tptp.nat) (Z tptp.rat)) (let ((_let_1 (tptp.comm_s4028243227959126397er_rat Z))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)) (= (tptp.aa_nat_rat _let_1 N) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat _let_1 M)) (tptp.aa_nat_rat (tptp.comm_s4028243227959126397er_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat Z) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat M))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) M))))))) (forall ((M tptp.nat) (N tptp.nat) (Z tptp.int)) (let ((_let_1 (tptp.comm_s4660882817536571857er_int Z))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)) (= (tptp.aa_nat_int _let_1 N) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int _let_1 M)) (tptp.aa_nat_int (tptp.comm_s4660882817536571857er_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int Z) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int M))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) M))))))) (forall ((M tptp.nat) (N tptp.nat) (Z tptp.real)) (let ((_let_1 (tptp.aa_real_fun_nat_real tptp.comm_s7457072308508201937r_real Z))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)) (= (tptp.aa_nat_real _let_1 N) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real _let_1 M)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.comm_s7457072308508201937r_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real Z) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real M))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) M))))))) (forall ((M tptp.nat) (N tptp.nat) (Z tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.comm_s4663373288045622133er_nat Z))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)) (= (tptp.aa_nat_nat _let_1 N) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat _let_1 M)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.comm_s4663373288045622133er_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Z) (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat M))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) M))))))) (forall ((K tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.binomial N))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat K) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat N) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat _let_1 K)) (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat tptp.suc K))))))) (forall ((K tptp.nat) (K6 tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.binomial N))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat K) K6)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) K6)) N)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat _let_1 K)) (tptp.aa_nat_nat _let_1 K6))))))) (forall ((K tptp.nat) (K6 tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.binomial N))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat K) K6)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) K))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K6) N)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat _let_1 K6)) (tptp.aa_nat_nat _let_1 K)))))))) (forall ((N tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat N) _let_1))) (let ((_let_3 (tptp.aa_nat_fun_nat_nat tptp.binomial N))) (=> (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat _let_1) N))) (= (tptp.aa_nat_nat _let_3 (tptp.aa_nat_nat tptp.suc _let_2)) (tptp.aa_nat_nat _let_3 _let_2))))))) (forall ((N tptp.nat) (K tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.binomial (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) tptp.one_one_nat)))) (let ((_let_2 (tptp.aa_nat_nat tptp.suc K))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial N) _let_2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat _let_1 _let_2)) (tptp.aa_nat_nat _let_1 K))))))) (forall ((K tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) N)) (= (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial N) K)) (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex (tptp.aa_nat_complex tptp.semiri5044797733671781792omplex N)) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_nat_complex tptp.semiri5044797733671781792omplex K)) (tptp.aa_nat_complex tptp.semiri5044797733671781792omplex (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) K))))))) (forall ((K tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) N)) (= (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial N) K)) (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_nat_rat tptp.semiri773545260158071498ct_rat N)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat tptp.semiri773545260158071498ct_rat K)) (tptp.aa_nat_rat tptp.semiri773545260158071498ct_rat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) K))))))) (forall ((K tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) N)) (= (tptp.aa_nat_real tptp.semiri5074537144036343181t_real (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial N) K)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_nat_real tptp.semiri2265585572941072030t_real N)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real tptp.semiri2265585572941072030t_real K)) (tptp.aa_nat_real tptp.semiri2265585572941072030t_real (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) K))))))) (forall ((K tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) N)) (= (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_nat_complex tptp.semiri5044797733671781792omplex K)) (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial N) K))) (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex (tptp.aa_nat_complex tptp.semiri5044797733671781792omplex N)) (tptp.aa_nat_complex tptp.semiri5044797733671781792omplex (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) K)))))) (forall ((K tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) N)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat tptp.semiri773545260158071498ct_rat K)) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial N) K))) (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_nat_rat tptp.semiri773545260158071498ct_rat N)) (tptp.aa_nat_rat tptp.semiri773545260158071498ct_rat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) K)))))) (forall ((K tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) N)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real tptp.semiri2265585572941072030t_real K)) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial N) K))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_nat_real tptp.semiri2265585572941072030t_real N)) (tptp.aa_nat_real tptp.semiri2265585572941072030t_real (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) K)))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool _let_1 X)) (=> (tptp.pp (tptp.aa_real_bool _let_1 Y)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Y) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.sqrt X)) Y))))))) (forall ((Y tptp.real) (X tptp.real)) (=> (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Y) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) X) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) Y)) (= (tptp.aa_real_real tptp.sqrt X) Y)))) (forall ((U tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) U)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real U) (tptp.aa_real_real tptp.sqrt (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))))) U)))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (= (tptp.aa_real_real tptp.sqrt (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) _let_1)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Y) _let_1))) X) (= Y tptp.zero_zero_real)))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (= (tptp.aa_real_real tptp.sqrt (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) _let_1)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_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.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) (tptp.aa_real_real tptp.sqrt (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) _let_1)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Y) _let_1))))))) (forall ((Y tptp.real) (X tptp.real)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y) (tptp.aa_real_real tptp.sqrt (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) _let_1)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Y) _let_1))))))) (forall ((A tptp.real) (C tptp.real) (B2 tptp.real) (D tptp.real)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.sqrt (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) C)) _let_1)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real B2) D)) _let_1)))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real tptp.sqrt (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real A) _let_1)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real B2) _let_1)))) (tptp.aa_real_real tptp.sqrt (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real C) _let_1)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real D) _let_1)))))))) (forall ((X tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real X)) (tptp.aa_real_real tptp.sqrt Y))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) Y)))) (= (tptp.aa_real_real tptp.cos_real _let_67) _let_65) (= (tptp.aa_real_real tptp.sin_real _let_67) _let_65) (forall ((R tptp.complex) (K tptp.nat)) (let ((_let_1 (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex R))) (= (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_complex_complex (tptp.minus_minus_complex R) (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex K))) (tptp.aa_nat_complex (tptp.comm_s2602460028002588243omplex _let_1) K)) (tptp.aa_complex_complex (tptp.times_times_complex R) (tptp.aa_nat_complex (tptp.comm_s2602460028002588243omplex (tptp.aa_complex_complex (tptp.plus_plus_complex _let_1) tptp.one_one_complex)) K))))) (forall ((R tptp.code_integer) (K tptp.nat)) (let ((_let_1 (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger R))) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.minus_8373710615458151222nteger R (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger K))) (tptp.aa_nat_Code_integer (tptp.comm_s8582702949713902594nteger _let_1) K)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger R) (tptp.aa_nat_Code_integer (tptp.comm_s8582702949713902594nteger (tptp.plus_p5714425477246183910nteger _let_1 tptp.one_one_Code_integer)) K))))) (forall ((R tptp.rat) (K tptp.nat)) (let ((_let_1 (tptp.aa_rat_rat tptp.uminus_uminus_rat R))) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat (tptp.minus_minus_rat R) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat K))) (tptp.aa_nat_rat (tptp.comm_s4028243227959126397er_rat _let_1) K)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat R) (tptp.aa_nat_rat (tptp.comm_s4028243227959126397er_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat _let_1) tptp.one_one_rat)) K))))) (forall ((R tptp.int) (K tptp.nat)) (let ((_let_1 (tptp.aa_int_int tptp.uminus_uminus_int R))) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int R) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int K))) (tptp.aa_nat_int (tptp.comm_s4660882817536571857er_int _let_1) K)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int R) (tptp.aa_nat_int (tptp.comm_s4660882817536571857er_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int _let_1) tptp.one_one_int)) K))))) (forall ((R tptp.real) (K tptp.nat)) (let ((_let_1 (tptp.aa_real_real tptp.uminus_uminus_real R))) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real R) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real K))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.comm_s7457072308508201937r_real _let_1) K)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real R) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.comm_s7457072308508201937r_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real _let_1) tptp.one_one_real)) K))))) (forall ((N tptp.nat)) (= (tptp.aa_nat_complex (tptp.comm_s2602460028002588243omplex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex N))) N) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_nat_complex (tptp.power_power_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex tptp.one_one_complex)) N)) (tptp.aa_nat_complex tptp.semiri5044797733671781792omplex N)))) (forall ((N tptp.nat)) (= (tptp.aa_nat_Code_integer (tptp.comm_s8582702949713902594nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger N))) N) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) N)) (tptp.aa_nat_Code_integer tptp.semiri3624122377584611663nteger N)))) (forall ((N tptp.nat)) (= (tptp.aa_nat_rat (tptp.comm_s4028243227959126397er_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat N))) N) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat tptp.one_one_rat)) N)) (tptp.aa_nat_rat tptp.semiri773545260158071498ct_rat N)))) (forall ((N tptp.nat)) (= (tptp.aa_nat_int (tptp.comm_s4660882817536571857er_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N))) N) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int)) N)) (tptp.aa_nat_int tptp.semiri1406184849735516958ct_int N)))) (forall ((N tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.comm_s7457072308508201937r_real (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N))) N) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)) N)) (tptp.aa_nat_real tptp.semiri2265585572941072030t_real N)))) (forall ((N tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial N) _let_1) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat N) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) tptp.one_one_nat))) _let_1)))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool _let_1 X)) (=> (tptp.pp (tptp.aa_real_bool _let_1 Y)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Y) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.sqrt X)) Y))))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool _let_2 X)) (=> (tptp.pp (tptp.aa_real_bool _let_2 Y)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.sqrt (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) _let_1)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Y) _let_1)))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) Y)))))))) (= (tptp.aa_real_real tptp.tan_real _let_63) (tptp.aa_real_real _let_64 _let_60)) (forall ((N tptp.nat)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (let ((_let_2 (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1))) (let ((_let_3 (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_num_real tptp.numeral_numeral_real _let_1)))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat _let_2) N)) (= (tptp.aa_real_real tptp.sqrt (tptp.aa_nat_real _let_3 N)) (tptp.aa_nat_real _let_3 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat N) _let_2)))))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real X)) (tptp.aa_real_real tptp.sqrt (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) _let_1)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Y) _let_1))))))) (forall ((Y tptp.real) (X tptp.real)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real Y)) (tptp.aa_real_real tptp.sqrt (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) _let_1)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Y) _let_1))))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.sqrt (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) _let_1)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Y) _let_1)))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real tptp.abs_abs_real X)) (tptp.aa_real_real tptp.abs_abs_real Y)))))) (forall ((X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) X)) (= (tptp.aa_real_real tptp.ln_ln_real (tptp.aa_real_real tptp.sqrt X)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real tptp.ln_ln_real X)) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))))) (= (tptp.aa_real_real tptp.cos_real _let_63) _let_61) (= (tptp.aa_real_real tptp.sin_real _let_62) _let_61) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.aa_real_complex (tptp.aa_rea2649881322057434177omplex tptp.complex2 X) Y)) (tptp.aa_real_real tptp.sqrt (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) _let_1)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Y) _let_1)))))) (forall ((B2 tptp.complex) (K tptp.nat)) (= (tptp.aa_nat_complex (tptp.comm_s2602460028002588243omplex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex B2)) K) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_nat_complex (tptp.power_power_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex tptp.one_one_complex)) K)) (tptp.aa_nat_complex (tptp.comm_s2602460028002588243omplex (tptp.aa_complex_complex (tptp.plus_plus_complex (tptp.aa_complex_complex (tptp.minus_minus_complex B2) (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex K))) tptp.one_one_complex)) K)))) (forall ((B2 tptp.code_integer) (K tptp.nat)) (= (tptp.aa_nat_Code_integer (tptp.comm_s8582702949713902594nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger B2)) K) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) K)) (tptp.aa_nat_Code_integer (tptp.comm_s8582702949713902594nteger (tptp.plus_p5714425477246183910nteger (tptp.minus_8373710615458151222nteger B2 (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger K)) tptp.one_one_Code_integer)) K)))) (forall ((B2 tptp.rat) (K tptp.nat)) (= (tptp.aa_nat_rat (tptp.comm_s4028243227959126397er_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat B2)) K) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat tptp.one_one_rat)) K)) (tptp.aa_nat_rat (tptp.comm_s4028243227959126397er_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.minus_minus_rat B2) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat K))) tptp.one_one_rat)) K)))) (forall ((B2 tptp.int) (K tptp.nat)) (= (tptp.aa_nat_int (tptp.comm_s4660882817536571857er_int (tptp.aa_int_int tptp.uminus_uminus_int B2)) K) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int)) K)) (tptp.aa_nat_int (tptp.comm_s4660882817536571857er_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int B2) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int K))) tptp.one_one_int)) K)))) (forall ((B2 tptp.real) (K tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.comm_s7457072308508201937r_real (tptp.aa_real_real tptp.uminus_uminus_real B2)) K) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)) K)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.comm_s7457072308508201937r_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real B2) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real K))) tptp.one_one_real)) K)))) (forall ((B2 tptp.complex) (K tptp.nat)) (= (tptp.aa_nat_complex (tptp.comm_s2602460028002588243omplex (tptp.aa_complex_complex (tptp.plus_plus_complex (tptp.aa_complex_complex (tptp.minus_minus_complex B2) (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex K))) tptp.one_one_complex)) K) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_nat_complex (tptp.power_power_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex tptp.one_one_complex)) K)) (tptp.aa_nat_complex (tptp.comm_s2602460028002588243omplex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex B2)) K)))) (forall ((B2 tptp.code_integer) (K tptp.nat)) (= (tptp.aa_nat_Code_integer (tptp.comm_s8582702949713902594nteger (tptp.plus_p5714425477246183910nteger (tptp.minus_8373710615458151222nteger B2 (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger K)) tptp.one_one_Code_integer)) K) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) K)) (tptp.aa_nat_Code_integer (tptp.comm_s8582702949713902594nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger B2)) K)))) (forall ((B2 tptp.rat) (K tptp.nat)) (= (tptp.aa_nat_rat (tptp.comm_s4028243227959126397er_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.minus_minus_rat B2) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat K))) tptp.one_one_rat)) K) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat tptp.one_one_rat)) K)) (tptp.aa_nat_rat (tptp.comm_s4028243227959126397er_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat B2)) K)))) (forall ((B2 tptp.int) (K tptp.nat)) (= (tptp.aa_nat_int (tptp.comm_s4660882817536571857er_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int B2) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int K))) tptp.one_one_int)) K) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int)) K)) (tptp.aa_nat_int (tptp.comm_s4660882817536571857er_int (tptp.aa_int_int tptp.uminus_uminus_int B2)) K)))) (forall ((B2 tptp.real) (K tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.comm_s7457072308508201937r_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real B2) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real K))) tptp.one_one_real)) K) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)) K)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.comm_s7457072308508201937r_real (tptp.aa_real_real tptp.uminus_uminus_real B2)) K)))) (= tptp.finite_psubset_nat (tptp.collec6662362479098859352et_nat (tptp.produc6837115875915843293t_bool tptp.aTP_Lamm_nq))) (= tptp.finite_psubset_int (tptp.collec957716948307931664et_int (tptp.produc6614410065919771685t_bool tptp.aTP_Lamm_nr))) (= tptp.finite8643634255014194347omplex (tptp.collec5108298041176329748omplex (tptp.produc1847240705748860961x_bool tptp.aTP_Lamm_ns))) (forall ((X tptp.real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) (tptp.aa_real_real tptp.sqrt (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) tptp.one_one_real)))))) (forall ((X tptp.real) (Y tptp.real) (Xa2 tptp.real) (Ya tptp.real)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_real_real tptp.sqrt (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) _let_1)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Y) _let_1))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Xa2) _let_1)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Ya) _let_1)))))))) (forall ((N tptp.nat) (X tptp.real)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat _let_1) N)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) X)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real tptp.sqrt X)) N) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat N) _let_1))))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool _let_1 X)) (=> (tptp.pp (tptp.aa_real_bool _let_1 Y)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.sqrt (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real X) Y))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) Y)) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))))))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real X) (tptp.aa_real_real tptp.sqrt (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) _let_1)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Y) _let_1)))))) tptp.one_one_real)))) (forall ((X tptp.real) (U tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (let ((_let_2 (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1))) (let ((_let_3 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real U) (tptp.aa_real_real tptp.sqrt (tptp.aa_num_real tptp.numeral_numeral_real _let_1))))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.abs_abs_real X)) _let_3)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.abs_abs_real Y)) _let_3)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.sqrt (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) _let_2)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Y) _let_2)))) U)))))))) (forall ((X tptp.real)) (= (tptp.aa_real_real tptp.cos_real (tptp.aa_real_real tptp.arctan X)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.one_one_real) (tptp.aa_real_real tptp.sqrt (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real tptp.one_one_real) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))))))) (forall ((X tptp.real)) (= (tptp.aa_real_real tptp.sin_real (tptp.aa_real_real tptp.arctan X)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real X) (tptp.aa_real_real tptp.sqrt (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real tptp.one_one_real) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))))))) (forall ((N tptp.nat) (A tptp.complex)) (let ((_let_1 (tptp.aa_nat_complex (tptp.comm_s2602460028002588243omplex A) N))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_complex)) (=> (not _let_2) (= _let_1 (tptp.aa_complex_complex (tptp.set_fo1517530859248394432omplex (tptp.aTP_Lamm_nt A) tptp.zero_zero_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) tptp.one_one_nat)) tptp.one_one_complex))))))) (forall ((N tptp.nat) (A tptp.rat)) (let ((_let_1 (tptp.aa_nat_rat (tptp.comm_s4028243227959126397er_rat A) N))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_rat)) (=> (not _let_2) (= _let_1 (tptp.aa_rat_rat (tptp.set_fo1949268297981939178at_rat (tptp.aTP_Lamm_nu A) tptp.zero_zero_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) tptp.one_one_nat)) tptp.one_one_rat))))))) (forall ((N tptp.nat) (A tptp.int)) (let ((_let_1 (tptp.aa_nat_int (tptp.comm_s4660882817536571857er_int A) N))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_int)) (=> (not _let_2) (= _let_1 (tptp.aa_int_int (tptp.set_fo2581907887559384638at_int (tptp.aTP_Lamm_nv A) tptp.zero_zero_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) tptp.one_one_nat)) tptp.one_one_int))))))) (forall ((N tptp.nat) (A tptp.real)) (let ((_let_1 (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.comm_s7457072308508201937r_real A) N))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_real)) (=> (not _let_2) (= _let_1 (tptp.aa_real_real (tptp.aa_nat_fun_real_real (tptp.set_fo3111899725591712190t_real (tptp.aTP_Lamm_nw A) tptp.zero_zero_nat) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) tptp.one_one_nat)) tptp.one_one_real))))))) (forall ((N tptp.nat) (A tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.comm_s4663373288045622133er_nat A) N))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_nat)) (=> (not _let_2) (= _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.set_fo2584398358068434914at_nat (tptp.aTP_Lamm_nx A) tptp.zero_zero_nat) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) tptp.one_one_nat)) tptp.one_one_nat))))))) (forall ((X tptp.real) (U tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (let ((_let_2 (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1))) (let ((_let_3 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (let ((_let_4 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real U) (tptp.aa_num_real tptp.numeral_numeral_real _let_1)))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) _let_4)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y) _let_4)) (=> (tptp.pp (tptp.aa_real_bool _let_3 X)) (=> (tptp.pp (tptp.aa_real_bool _let_3 Y)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.sqrt (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) _let_2)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Y) _let_2)))) U))))))))))) (forall ((X tptp.real)) (let ((_let_1 (tptp.aa_real_real tptp.sin_real X))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) _let_1)) (= _let_1 (tptp.aa_real_real tptp.sqrt (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real tptp.one_one_real) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real tptp.cos_real X)) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))))))) (forall ((X tptp.real)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (let ((_let_2 (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real tptp.one_one_real))) (= (tptp.aa_real_real tptp.arctan X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_num_real tptp.numeral_numeral_real _let_1)) (tptp.aa_real_real tptp.arctan (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real X) (tptp.aa_real_real _let_2 (tptp.aa_real_real tptp.sqrt (tptp.aa_real_real _let_2 (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1)))))))))))) (forall ((N tptp.nat)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (let ((_let_2 (tptp.numera6690914467698888265omplex _let_1))) (let ((_let_3 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1)) N))) (= (tptp.aa_nat_complex tptp.semiri5044797733671781792omplex _let_3) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_nat_complex (tptp.power_power_complex _let_2) _let_3)) (tptp.aa_nat_complex (tptp.comm_s2602460028002588243omplex (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex tptp.one_one_complex) _let_2)) N))) (tptp.aa_nat_complex tptp.semiri5044797733671781792omplex N))))))) (forall ((N tptp.nat)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (let ((_let_2 (tptp.aa_num_rat tptp.numeral_numeral_rat _let_1))) (let ((_let_3 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1)) N))) (= (tptp.aa_nat_rat tptp.semiri773545260158071498ct_rat _let_3) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat (tptp.power_power_rat _let_2) _let_3)) (tptp.aa_nat_rat (tptp.comm_s4028243227959126397er_rat (tptp.aa_rat_rat (tptp.divide_divide_rat tptp.one_one_rat) _let_2)) N))) (tptp.aa_nat_rat tptp.semiri773545260158071498ct_rat N))))))) (forall ((N tptp.nat)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (let ((_let_2 (tptp.aa_num_real tptp.numeral_numeral_real _let_1))) (let ((_let_3 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1)) N))) (= (tptp.aa_nat_real tptp.semiri2265585572941072030t_real _let_3) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real _let_2) _let_3)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.comm_s7457072308508201937r_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.one_one_real) _let_2)) N))) (tptp.aa_nat_real tptp.semiri2265585572941072030t_real N))))))) (forall ((N tptp.nat)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 _let_1))) N)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_num_real tptp.numeral_numeral_real _let_1)) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N)))) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1)) N)) N))))))) (forall ((X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.one_one_real) X)) (= (tptp.aa_real_real tptp.arcosh_real X) (tptp.aa_real_real tptp.ln_ln_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) (tptp.aa_real_real tptp.sqrt (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) tptp.one_one_real))))))) (forall ((Z tptp.complex) (N tptp.nat)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (let ((_let_2 (tptp.aa_nat_nat tptp.suc N))) (= (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_nat_complex (tptp.comm_s2602460028002588243omplex Z) _let_2)) (tptp.aa_nat_complex (tptp.comm_s2602460028002588243omplex (tptp.aa_complex_complex (tptp.plus_plus_complex Z) (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex tptp.one_one_complex) (tptp.numera6690914467698888265omplex _let_1)))) _let_2)) (tptp.groups6464643781859351333omplex (tptp.aTP_Lamm_ny Z) (tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1)) N)) tptp.one_one_nat))))))) (forall ((Z tptp.rat) (N tptp.nat)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (let ((_let_2 (tptp.aa_nat_nat tptp.suc N))) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat (tptp.comm_s4028243227959126397er_rat Z) _let_2)) (tptp.aa_nat_rat (tptp.comm_s4028243227959126397er_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat Z) (tptp.aa_rat_rat (tptp.divide_divide_rat tptp.one_one_rat) (tptp.aa_num_rat tptp.numeral_numeral_rat _let_1)))) _let_2)) (tptp.groups73079841787564623at_rat (tptp.aTP_Lamm_nz Z) (tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1)) N)) tptp.one_one_nat))))))) (forall ((Z tptp.real) (N tptp.nat)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (let ((_let_2 (tptp.aa_nat_nat tptp.suc N))) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.comm_s7457072308508201937r_real Z) _let_2)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.comm_s7457072308508201937r_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real Z) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.one_one_real) (tptp.aa_num_real tptp.numeral_numeral_real _let_1)))) _let_2)) (tptp.groups129246275422532515t_real (tptp.aa_real_fun_nat_real tptp.aTP_Lamm_oa Z) (tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1)) N)) tptp.one_one_nat))))))) (forall ((X tptp.real)) (= (tptp.aa_real_real tptp.arsinh_real X) (tptp.aa_real_real tptp.ln_ln_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) (tptp.aa_real_real tptp.sqrt (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) tptp.one_one_real)))))) (forall ((N tptp.nat)) (let ((_let_1 (tptp.numera6690914467698888265omplex (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (= (tptp.aa_complex_complex (tptp.times_times_complex _let_1) (tptp.groups2073611262835488442omplex (tptp.aTP_Lamm_ob N) (tptp.set_ord_atMost_nat N))) (tptp.aa_nat_complex (tptp.power_power_complex _let_1) N))))) (forall ((N tptp.nat)) (let ((_let_1 (tptp.aa_num_rat tptp.numeral_numeral_rat (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat _let_1) (tptp.groups2906978787729119204at_rat (tptp.aTP_Lamm_oc N) (tptp.set_ord_atMost_nat N))) (tptp.aa_nat_rat (tptp.power_power_rat _let_1) N))))) (forall ((N tptp.nat)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int _let_1) (tptp.groups3539618377306564664at_int (tptp.aa_nat_fun_nat_int tptp.aTP_Lamm_od N) (tptp.set_ord_atMost_nat N))) (tptp.aa_nat_int (tptp.power_power_int _let_1) N))))) (forall ((N tptp.nat)) (let ((_let_1 (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real _let_1) (tptp.groups6591440286371151544t_real (tptp.aa_nat_fun_nat_real tptp.aTP_Lamm_oe N) (tptp.set_ord_atMost_nat N))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real _let_1) N))))) (forall ((N tptp.nat)) (let ((_let_1 (tptp.numera6690914467698888265omplex (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (= (tptp.aa_complex_complex (tptp.times_times_complex _let_1) (tptp.groups2073611262835488442omplex (tptp.aTP_Lamm_of N) (tptp.set_ord_atMost_nat N))) (tptp.aa_nat_complex (tptp.power_power_complex _let_1) N))))) (forall ((N tptp.nat)) (let ((_let_1 (tptp.aa_num_rat tptp.numeral_numeral_rat (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat _let_1) (tptp.groups2906978787729119204at_rat (tptp.aTP_Lamm_og N) (tptp.set_ord_atMost_nat N))) (tptp.aa_nat_rat (tptp.power_power_rat _let_1) N))))) (forall ((N tptp.nat)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int _let_1) (tptp.groups3539618377306564664at_int (tptp.aa_nat_fun_nat_int tptp.aTP_Lamm_oh N) (tptp.set_ord_atMost_nat N))) (tptp.aa_nat_int (tptp.power_power_int _let_1) N))))) (forall ((N tptp.nat)) (let ((_let_1 (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real _let_1) (tptp.groups6591440286371151544t_real (tptp.aa_nat_fun_nat_real tptp.aTP_Lamm_oi N) (tptp.set_ord_atMost_nat N))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real _let_1) N))))) (forall ((I tptp.real) (K tptp.real)) (= (tptp.member_real I (tptp.set_ord_atMost_real K)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real I) K)))) (forall ((I tptp.set_int) (K tptp.set_int)) (= (tptp.member_set_int I (tptp.set_or58775011639299419et_int K)) (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int I) K)))) (forall ((I tptp.rat) (K tptp.rat)) (= (tptp.member_rat I (tptp.set_ord_atMost_rat K)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat I) K)))) (forall ((I tptp.num) (K tptp.num)) (= (tptp.member_num I (tptp.set_ord_atMost_num K)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num I) K)))) (forall ((I tptp.nat) (K tptp.nat)) (= (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat I) (tptp.set_ord_atMost_nat K))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I) K)))) (forall ((I tptp.int) (K tptp.int)) (= (tptp.pp (tptp.aa_set_int_bool (tptp.member_int I) (tptp.set_ord_atMost_int K))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int I) K)))) (forall ((X tptp.set_int) (Y tptp.set_int)) (= (tptp.ord_le4403425263959731960et_int (tptp.set_or58775011639299419et_int X) (tptp.set_or58775011639299419et_int Y)) (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int X) Y)))) (forall ((X tptp.rat) (Y tptp.rat)) (= (tptp.ord_less_eq_set_rat (tptp.set_ord_atMost_rat X) (tptp.set_ord_atMost_rat Y)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) Y)))) (forall ((X tptp.num) (Y tptp.num)) (= (tptp.ord_less_eq_set_num (tptp.set_ord_atMost_num X) (tptp.set_ord_atMost_num Y)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X) Y)))) (forall ((X tptp.nat) (Y tptp.nat)) (= (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat (tptp.set_ord_atMost_nat X)) (tptp.set_ord_atMost_nat Y))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X) Y)))) (forall ((X tptp.int) (Y tptp.int)) (= (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int (tptp.set_ord_atMost_int X)) (tptp.set_ord_atMost_int Y))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X) Y)))) (forall ((L tptp.set_int) (H tptp.set_int) (H2 tptp.set_int)) (= (tptp.ord_le4403425263959731960et_int (tptp.set_or370866239135849197et_int L H) (tptp.set_or58775011639299419et_int H2)) (or (not (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int L) H))) (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int H) H2))))) (forall ((L tptp.rat) (H tptp.rat) (H2 tptp.rat)) (= (tptp.ord_less_eq_set_rat (tptp.set_or633870826150836451st_rat L H) (tptp.set_ord_atMost_rat H2)) (or (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat L) H))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat H) H2))))) (forall ((L tptp.num) (H tptp.num) (H2 tptp.num)) (= (tptp.ord_less_eq_set_num (tptp.set_or7049704709247886629st_num L H) (tptp.set_ord_atMost_num H2)) (or (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num L) H))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num H) H2))))) (forall ((L tptp.nat) (H tptp.nat) (H2 tptp.nat)) (= (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat (tptp.set_or1269000886237332187st_nat L H)) (tptp.set_ord_atMost_nat H2))) (or (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat L) H))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat H) H2))))) (forall ((L tptp.int) (H tptp.int) (H2 tptp.int)) (= (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int (tptp.aa_int_set_int (tptp.aa_int8639817059373041269et_int tptp.set_or1266510415728281911st_int L) H)) (tptp.set_ord_atMost_int H2))) (or (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int L) H))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int H) H2))))) (forall ((L tptp.real) (H tptp.real) (H2 tptp.real)) (= (tptp.ord_less_eq_set_real (tptp.set_or1222579329274155063t_real L H) (tptp.set_ord_atMost_real H2)) (or (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real L) H))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real H) H2))))) (forall ((G tptp.fun_nat_rat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N))) (= (tptp.groups2906978787729119204at_rat G (tptp.set_ord_atMost_nat _let_1)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.groups2906978787729119204at_rat G (tptp.set_ord_atMost_nat N))) (tptp.aa_nat_rat G _let_1))))) (forall ((G tptp.fun_nat_int) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N))) (= (tptp.groups3539618377306564664at_int G (tptp.set_ord_atMost_nat _let_1)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.groups3539618377306564664at_int G (tptp.set_ord_atMost_nat N))) (tptp.aa_nat_int G _let_1))))) (forall ((G tptp.fun_nat_nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N))) (let ((_let_2 (tptp.groups3542108847815614940at_nat G))) (= (tptp.aa_set_nat_nat _let_2 (tptp.set_ord_atMost_nat _let_1)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_set_nat_nat _let_2 (tptp.set_ord_atMost_nat N))) (tptp.aa_nat_nat G _let_1)))))) (forall ((G tptp.fun_nat_real) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N))) (= (tptp.groups6591440286371151544t_real G (tptp.set_ord_atMost_nat _let_1)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.groups6591440286371151544t_real G (tptp.set_ord_atMost_nat N))) (tptp.aa_nat_real G _let_1))))) (forall ((G tptp.fun_nat_real) (N tptp.nat)) (= (tptp.groups129246275422532515t_real G (tptp.set_ord_lessThan_nat (tptp.aa_nat_nat tptp.suc N))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.groups129246275422532515t_real G (tptp.set_ord_lessThan_nat N))) (tptp.aa_nat_real G N)))) (forall ((G tptp.fun_nat_rat) (N tptp.nat)) (= (tptp.groups73079841787564623at_rat G (tptp.set_ord_lessThan_nat (tptp.aa_nat_nat tptp.suc N))) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.groups73079841787564623at_rat G (tptp.set_ord_lessThan_nat N))) (tptp.aa_nat_rat G N)))) (forall ((G tptp.fun_nat_nat) (N tptp.nat)) (= (tptp.groups708209901874060359at_nat G (tptp.set_ord_lessThan_nat (tptp.aa_nat_nat tptp.suc N))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.groups708209901874060359at_nat G (tptp.set_ord_lessThan_nat N))) (tptp.aa_nat_nat G N)))) (forall ((G tptp.fun_nat_int) (N tptp.nat)) (= (tptp.groups705719431365010083at_int G (tptp.set_ord_lessThan_nat (tptp.aa_nat_nat tptp.suc N))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.groups705719431365010083at_int G (tptp.set_ord_lessThan_nat N))) (tptp.aa_nat_int G N)))) (forall ((G tptp.fun_nat_real) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N))) (= (tptp.groups129246275422532515t_real G (tptp.set_ord_atMost_nat _let_1)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.groups129246275422532515t_real G (tptp.set_ord_atMost_nat N))) (tptp.aa_nat_real G _let_1))))) (forall ((G tptp.fun_nat_rat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N))) (= (tptp.groups73079841787564623at_rat G (tptp.set_ord_atMost_nat _let_1)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.groups73079841787564623at_rat G (tptp.set_ord_atMost_nat N))) (tptp.aa_nat_rat G _let_1))))) (forall ((G tptp.fun_nat_nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N))) (= (tptp.groups708209901874060359at_nat G (tptp.set_ord_atMost_nat _let_1)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.groups708209901874060359at_nat G (tptp.set_ord_atMost_nat N))) (tptp.aa_nat_nat G _let_1))))) (forall ((G tptp.fun_nat_int) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N))) (= (tptp.groups705719431365010083at_int G (tptp.set_ord_atMost_nat _let_1)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.groups705719431365010083at_int G (tptp.set_ord_atMost_nat N))) (tptp.aa_nat_int G _let_1))))) (forall ((N tptp.nat) (M tptp.nat) (G tptp.fun_nat_complex)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N))) (let ((_let_2 (tptp.groups6464643781859351333omplex G (tptp.set_or1269000886237332187st_nat M _let_1)))) (let ((_let_3 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_1) M)))) (and (=> _let_3 (= _let_2 tptp.one_one_complex)) (=> (not _let_3) (= _let_2 (tptp.aa_complex_complex (tptp.times_times_complex (tptp.groups6464643781859351333omplex G (tptp.set_or1269000886237332187st_nat M N))) (tptp.aa_nat_complex G _let_1))))))))) (forall ((N tptp.nat) (M tptp.nat) (G tptp.fun_nat_real)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N))) (let ((_let_2 (tptp.groups129246275422532515t_real G (tptp.set_or1269000886237332187st_nat M _let_1)))) (let ((_let_3 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_1) M)))) (and (=> _let_3 (= _let_2 tptp.one_one_real)) (=> (not _let_3) (= _let_2 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.groups129246275422532515t_real G (tptp.set_or1269000886237332187st_nat M N))) (tptp.aa_nat_real G _let_1))))))))) (forall ((N tptp.nat) (M tptp.nat) (G tptp.fun_nat_rat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N))) (let ((_let_2 (tptp.groups73079841787564623at_rat G (tptp.set_or1269000886237332187st_nat M _let_1)))) (let ((_let_3 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_1) M)))) (and (=> _let_3 (= _let_2 tptp.one_one_rat)) (=> (not _let_3) (= _let_2 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.groups73079841787564623at_rat G (tptp.set_or1269000886237332187st_nat M N))) (tptp.aa_nat_rat G _let_1))))))))) (forall ((N tptp.nat) (M tptp.nat) (G tptp.fun_nat_nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N))) (let ((_let_2 (tptp.groups708209901874060359at_nat G (tptp.set_or1269000886237332187st_nat M _let_1)))) (let ((_let_3 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_1) M)))) (and (=> _let_3 (= _let_2 tptp.one_one_nat)) (=> (not _let_3) (= _let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.groups708209901874060359at_nat G (tptp.set_or1269000886237332187st_nat M N))) (tptp.aa_nat_nat G _let_1))))))))) (forall ((N tptp.nat) (M tptp.nat) (G tptp.fun_nat_int)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N))) (let ((_let_2 (tptp.groups705719431365010083at_int G (tptp.set_or1269000886237332187st_nat M _let_1)))) (let ((_let_3 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_1) M)))) (and (=> _let_3 (= _let_2 tptp.one_one_int)) (=> (not _let_3) (= _let_2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.groups705719431365010083at_int G (tptp.set_or1269000886237332187st_nat M N))) (tptp.aa_nat_int G _let_1))))))))) (forall ((G tptp.fun_nat_nat) (H tptp.fun_nat_nat) (A4 tptp.set_nat)) (= (tptp.groups708209901874060359at_nat (tptp.aa_fun5791449513213591928at_nat (tptp.aTP_Lamm_oj G) H) A4) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.groups708209901874060359at_nat G A4)) (tptp.groups708209901874060359at_nat H A4)))) (forall ((G tptp.fun_nat_int) (H tptp.fun_nat_int) (A4 tptp.set_nat)) (= (tptp.groups705719431365010083at_int (tptp.aa_fun5565043122120104496at_int (tptp.aTP_Lamm_ok G) H) A4) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.groups705719431365010083at_int G A4)) (tptp.groups705719431365010083at_int H A4)))) (forall ((G tptp.fun_int_int) (H tptp.fun_int_int) (A4 tptp.set_int)) (= (tptp.groups1705073143266064639nt_int (tptp.aa_fun6280345759651049192nt_int (tptp.aTP_Lamm_ol G) H) A4) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.groups1705073143266064639nt_int G A4)) (tptp.groups1705073143266064639nt_int H A4)))) (forall ((F tptp.fun_nat_nat) (A4 tptp.set_nat) (N tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.groups708209901874060359at_nat F A4)) N) (tptp.groups708209901874060359at_nat (tptp.aa_nat_fun_nat_nat (tptp.aTP_Lamm_om F) N) A4))) (forall ((F tptp.fun_nat_int) (A4 tptp.set_nat) (N tptp.nat)) (= (tptp.aa_nat_int (tptp.power_power_int (tptp.groups705719431365010083at_int F A4)) N) (tptp.groups705719431365010083at_int (tptp.aa_nat_fun_nat_int (tptp.aTP_Lamm_on F) N) A4))) (forall ((F tptp.fun_int_int) (A4 tptp.set_int) (N tptp.nat)) (= (tptp.aa_nat_int (tptp.power_power_int (tptp.groups1705073143266064639nt_int F A4)) N) (tptp.groups1705073143266064639nt_int (tptp.aa_nat_fun_int_int (tptp.aTP_Lamm_oo F) N) A4))) (forall ((F tptp.fun_nat_nat) (A tptp.nat) (A4 tptp.set_nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.groups708209901874060359at_nat (tptp.aa_nat_fun_nat_nat (tptp.aTP_Lamm_gn F) A) A4)) A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.groups708209901874060359at_nat F A4)) A))) (forall ((F tptp.fun_nat_int) (A tptp.int) (A4 tptp.set_nat)) (= (tptp.aa_int_int (tptp.modulo_modulo_int (tptp.groups705719431365010083at_int (tptp.aa_int_fun_nat_int (tptp.aTP_Lamm_op F) A) A4)) A) (tptp.aa_int_int (tptp.modulo_modulo_int (tptp.groups705719431365010083at_int F A4)) A))) (forall ((F tptp.fun_int_int) (A tptp.int) (A4 tptp.set_int)) (= (tptp.aa_int_int (tptp.modulo_modulo_int (tptp.groups1705073143266064639nt_int (tptp.aa_int_fun_int_int (tptp.aTP_Lamm_gm F) A) A4)) A) (tptp.aa_int_int (tptp.modulo_modulo_int (tptp.groups1705073143266064639nt_int F A4)) A))) (forall ((G tptp.fun_nat_real) (N tptp.nat)) (= (tptp.groups129246275422532515t_real G (tptp.set_ord_atMost_nat (tptp.aa_nat_nat tptp.suc N))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real G tptp.zero_zero_nat)) (tptp.groups129246275422532515t_real (tptp.aTP_Lamm_hw G) (tptp.set_ord_atMost_nat N))))) (forall ((G tptp.fun_nat_rat) (N tptp.nat)) (= (tptp.groups73079841787564623at_rat G (tptp.set_ord_atMost_nat (tptp.aa_nat_nat tptp.suc N))) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat G tptp.zero_zero_nat)) (tptp.groups73079841787564623at_rat (tptp.aTP_Lamm_ht G) (tptp.set_ord_atMost_nat N))))) (forall ((G tptp.fun_nat_nat) (N tptp.nat)) (= (tptp.groups708209901874060359at_nat G (tptp.set_ord_atMost_nat (tptp.aa_nat_nat tptp.suc N))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat G tptp.zero_zero_nat)) (tptp.groups708209901874060359at_nat (tptp.aTP_Lamm_hv G) (tptp.set_ord_atMost_nat N))))) (forall ((G tptp.fun_nat_int) (N tptp.nat)) (= (tptp.groups705719431365010083at_int G (tptp.set_ord_atMost_nat (tptp.aa_nat_nat tptp.suc N))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int G tptp.zero_zero_nat)) (tptp.groups705719431365010083at_int (tptp.aTP_Lamm_hu G) (tptp.set_ord_atMost_nat N))))) (forall ((U tptp.real)) (= (tptp.set_ord_atMost_real U) (tptp.collect_real (tptp.aa_rea7809428808904475482l_bool tptp.aTP_Lamm_oq U)))) (forall ((U tptp.set_int)) (= (tptp.set_or58775011639299419et_int U) (tptp.collect_set_int (tptp.aTP_Lamm_bu U)))) (forall ((U tptp.rat)) (= (tptp.set_ord_atMost_rat U) (tptp.collect_rat (tptp.aa_rat_fun_rat_bool tptp.aTP_Lamm_or U)))) (forall ((U tptp.num)) (= (tptp.set_ord_atMost_num U) (tptp.collect_num (tptp.aa_num_fun_num_bool tptp.aTP_Lamm_os U)))) (forall ((U tptp.nat)) (= (tptp.set_ord_atMost_nat U) (tptp.collect_nat (tptp.aa_nat_fun_nat_bool tptp.aTP_Lamm_bq U)))) (forall ((U tptp.int)) (= (tptp.set_ord_atMost_int U) (tptp.collect_int (tptp.aa_int_fun_int_bool tptp.aTP_Lamm_ot U)))) (forall ((A4 tptp.set_nat) (F tptp.fun_nat_real) (G tptp.fun_nat_real)) (=> (forall ((I3 tptp.nat)) (let ((_let_1 (tptp.aa_nat_real F I3))) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat I3) A4)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) _let_1)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real _let_1) (tptp.aa_nat_real G I3))))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.groups129246275422532515t_real F A4)) (tptp.groups129246275422532515t_real G A4))))) (forall ((A4 tptp.set_real) (F tptp.fun_real_real) (G tptp.fun_real_real)) (=> (forall ((I3 tptp.real)) (let ((_let_1 (tptp.aa_real_real F I3))) (=> (tptp.member_real I3 A4) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) _let_1)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real _let_1) (tptp.aa_real_real G I3))))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.groups1681761925125756287l_real F A4)) (tptp.groups1681761925125756287l_real G A4))))) (forall ((A4 tptp.set_int) (F tptp.fun_int_real) (G tptp.fun_int_real)) (=> (forall ((I3 tptp.int)) (let ((_let_1 (tptp.aa_int_real F I3))) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int I3) A4)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) _let_1)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real _let_1) (tptp.aa_int_real G I3))))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.groups2316167850115554303t_real F A4)) (tptp.groups2316167850115554303t_real G A4))))) (forall ((A4 tptp.set_complex) (F tptp.fun_complex_real) (G tptp.fun_complex_real)) (=> (forall ((I3 tptp.complex)) (let ((_let_1 (tptp.aa_complex_real F I3))) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex I3) A4)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) _let_1)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real _let_1) (tptp.aa_complex_real G I3))))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.groups766887009212190081x_real F A4)) (tptp.groups766887009212190081x_real G A4))))) (forall ((A4 tptp.set_nat) (F tptp.fun_nat_rat) (G tptp.fun_nat_rat)) (=> (forall ((I3 tptp.nat)) (let ((_let_1 (tptp.aa_nat_rat F I3))) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat I3) A4)) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat _let_1) (tptp.aa_nat_rat G I3))))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.groups73079841787564623at_rat F A4)) (tptp.groups73079841787564623at_rat G A4))))) (forall ((A4 tptp.set_real) (F tptp.fun_real_rat) (G tptp.fun_real_rat)) (=> (forall ((I3 tptp.real)) (let ((_let_1 (tptp.aa_real_rat F I3))) (=> (tptp.member_real I3 A4) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat _let_1) (tptp.aa_real_rat G I3))))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.groups4061424788464935467al_rat F A4)) (tptp.groups4061424788464935467al_rat G A4))))) (forall ((A4 tptp.set_int) (F tptp.fun_int_rat) (G tptp.fun_int_rat)) (=> (forall ((I3 tptp.int)) (let ((_let_1 (tptp.aa_int_rat F I3))) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int I3) A4)) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat _let_1) (tptp.aa_int_rat G I3))))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.groups1072433553688619179nt_rat F A4)) (tptp.groups1072433553688619179nt_rat G A4))))) (forall ((A4 tptp.set_complex) (F tptp.fun_complex_rat) (G tptp.fun_complex_rat)) (=> (forall ((I3 tptp.complex)) (let ((_let_1 (tptp.aa_complex_rat F I3))) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex I3) A4)) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat _let_1) (tptp.aa_complex_rat G I3))))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.groups225925009352817453ex_rat F A4)) (tptp.groups225925009352817453ex_rat G A4))))) (forall ((A4 tptp.set_real) (F tptp.fun_real_nat) (G tptp.fun_real_nat)) (=> (forall ((I3 tptp.real)) (let ((_let_1 (tptp.aa_real_nat F I3))) (=> (tptp.member_real I3 A4) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) _let_1)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat _let_1) (tptp.aa_real_nat G I3))))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.groups4696554848551431203al_nat F A4)) (tptp.groups4696554848551431203al_nat G A4))))) (forall ((A4 tptp.set_int) (F tptp.fun_int_nat) (G tptp.fun_int_nat)) (=> (forall ((I3 tptp.int)) (let ((_let_1 (tptp.aa_int_nat F I3))) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int I3) A4)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) _let_1)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat _let_1) (tptp.aa_int_nat G I3))))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.groups1707563613775114915nt_nat F A4)) (tptp.groups1707563613775114915nt_nat G A4))))) (forall ((A4 tptp.set_nat) (F tptp.fun_nat_nat)) (=> (forall ((X4 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X4) A4)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) (tptp.aa_nat_nat F X4))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) (tptp.groups708209901874060359at_nat F A4))))) (forall ((A4 tptp.set_nat) (F tptp.fun_nat_int)) (=> (forall ((X4 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X4) A4)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.aa_nat_int F X4))))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.groups705719431365010083at_int F A4))))) (forall ((A4 tptp.set_int) (F tptp.fun_int_int)) (=> (forall ((X4 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X4) A4)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.aa_int_int F X4))))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.groups1705073143266064639nt_int F A4))))) (forall ((A4 tptp.set_nat) (F tptp.fun_nat_nat)) (=> (forall ((X4 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X4) A4)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.aa_nat_nat F X4))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.groups708209901874060359at_nat F A4))))) (forall ((A4 tptp.set_nat) (F tptp.fun_nat_int)) (=> (forall ((X4 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X4) A4)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) (tptp.aa_nat_int F X4))))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) (tptp.groups705719431365010083at_int F A4))))) (forall ((A4 tptp.set_int) (F tptp.fun_int_int)) (=> (forall ((X4 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X4) A4)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) (tptp.aa_int_int F X4))))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) (tptp.groups1705073143266064639nt_int F A4))))) (forall ((A4 tptp.set_nat) (F tptp.fun_nat_real)) (=> (forall ((X4 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X4) A4)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.one_one_real) (tptp.aa_nat_real F X4))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.one_one_real) (tptp.groups129246275422532515t_real F A4))))) (forall ((A4 tptp.set_real) (F tptp.fun_real_real)) (=> (forall ((X4 tptp.real)) (=> (tptp.member_real X4 A4) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.one_one_real) (tptp.aa_real_real F X4))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.one_one_real) (tptp.groups1681761925125756287l_real F A4))))) (forall ((A4 tptp.set_int) (F tptp.fun_int_real)) (=> (forall ((X4 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X4) A4)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.one_one_real) (tptp.aa_int_real F X4))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.one_one_real) (tptp.groups2316167850115554303t_real F A4))))) (forall ((A4 tptp.set_complex) (F tptp.fun_complex_real)) (=> (forall ((X4 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex X4) A4)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.one_one_real) (tptp.aa_complex_real F X4))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.one_one_real) (tptp.groups766887009212190081x_real F A4))))) (forall ((A4 tptp.set_nat) (F tptp.fun_nat_rat)) (=> (forall ((X4 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X4) A4)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.one_one_rat) (tptp.aa_nat_rat F X4))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.one_one_rat) (tptp.groups73079841787564623at_rat F A4))))) (forall ((A4 tptp.set_real) (F tptp.fun_real_rat)) (=> (forall ((X4 tptp.real)) (=> (tptp.member_real X4 A4) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.one_one_rat) (tptp.aa_real_rat F X4))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.one_one_rat) (tptp.groups4061424788464935467al_rat F A4))))) (forall ((A4 tptp.set_int) (F tptp.fun_int_rat)) (=> (forall ((X4 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X4) A4)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.one_one_rat) (tptp.aa_int_rat F X4))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.one_one_rat) (tptp.groups1072433553688619179nt_rat F A4))))) (forall ((A4 tptp.set_complex) (F tptp.fun_complex_rat)) (=> (forall ((X4 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex X4) A4)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.one_one_rat) (tptp.aa_complex_rat F X4))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.one_one_rat) (tptp.groups225925009352817453ex_rat F A4))))) (forall ((A4 tptp.set_real) (F tptp.fun_real_nat)) (=> (forall ((X4 tptp.real)) (=> (tptp.member_real X4 A4) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.one_one_nat) (tptp.aa_real_nat F X4))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.one_one_nat) (tptp.groups4696554848551431203al_nat F A4))))) (forall ((A4 tptp.set_int) (F tptp.fun_int_nat)) (=> (forall ((X4 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X4) A4)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.one_one_nat) (tptp.aa_int_nat F X4))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.one_one_nat) (tptp.groups1707563613775114915nt_nat F A4))))) (forall ((G tptp.fun_nat_real) (N tptp.nat)) (= (tptp.groups129246275422532515t_real G (tptp.set_ord_atMost_nat N)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real G tptp.zero_zero_nat)) (tptp.groups129246275422532515t_real (tptp.aTP_Lamm_hw G) (tptp.set_ord_lessThan_nat N))))) (forall ((G tptp.fun_nat_rat) (N tptp.nat)) (= (tptp.groups73079841787564623at_rat G (tptp.set_ord_atMost_nat N)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat G tptp.zero_zero_nat)) (tptp.groups73079841787564623at_rat (tptp.aTP_Lamm_ht G) (tptp.set_ord_lessThan_nat N))))) (forall ((G tptp.fun_nat_nat) (N tptp.nat)) (= (tptp.groups708209901874060359at_nat G (tptp.set_ord_atMost_nat N)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat G tptp.zero_zero_nat)) (tptp.groups708209901874060359at_nat (tptp.aTP_Lamm_hv G) (tptp.set_ord_lessThan_nat N))))) (forall ((G tptp.fun_nat_int) (N tptp.nat)) (= (tptp.groups705719431365010083at_int G (tptp.set_ord_atMost_nat N)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int G tptp.zero_zero_nat)) (tptp.groups705719431365010083at_int (tptp.aTP_Lamm_hu G) (tptp.set_ord_lessThan_nat N))))) (forall ((H tptp.int) (L2 tptp.int) (H2 tptp.int)) (not (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int (tptp.set_ord_atMost_int H)) (tptp.aa_int_set_int (tptp.aa_int8639817059373041269et_int tptp.set_or1266510415728281911st_int L2) H2))))) (forall ((H tptp.real) (L2 tptp.real) (H2 tptp.real)) (not (tptp.ord_less_eq_set_real (tptp.set_ord_atMost_real H) (tptp.set_or1222579329274155063t_real L2 H2)))) (forall ((C tptp.real) (F tptp.fun_nat_nat) (A4 tptp.set_nat)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real C) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat F) A4)) (tptp.groups129246275422532515t_real (tptp.aa_fun1538629612289296340t_real (tptp.aTP_Lamm_ou C) F) A4))) (forall ((C tptp.complex) (F tptp.fun_nat_nat) (A4 tptp.set_nat)) (= (tptp.aa_nat_complex (tptp.power_power_complex C) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat F) A4)) (tptp.groups6464643781859351333omplex (tptp.aa_fun1958354139826840918omplex (tptp.aTP_Lamm_ov C) F) A4))) (forall ((C tptp.nat) (F tptp.fun_nat_nat) (A4 tptp.set_nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat C) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat F) A4)) (tptp.groups708209901874060359at_nat (tptp.aa_fun5791449513213591928at_nat (tptp.aTP_Lamm_ow C) F) A4))) (forall ((C tptp.int) (F tptp.fun_nat_nat) (A4 tptp.set_nat)) (= (tptp.aa_nat_int (tptp.power_power_int C) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat F) A4)) (tptp.groups705719431365010083at_int (tptp.aa_fun1613598493704395220at_int (tptp.aTP_Lamm_ox C) F) A4))) (forall ((C tptp.int) (F tptp.fun_int_nat) (A4 tptp.set_int)) (= (tptp.aa_nat_int (tptp.power_power_int C) (tptp.groups4541462559716669496nt_nat F A4)) (tptp.groups1705073143266064639nt_int (tptp.aa_fun2328901131235339916nt_int (tptp.aTP_Lamm_oy C) F) A4))) (forall ((G tptp.fun_nat_nat) (M tptp.nat) (K tptp.nat) (N tptp.nat)) (= (tptp.groups708209901874060359at_nat G (tptp.set_or1269000886237332187st_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) K) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N) K))) (tptp.groups708209901874060359at_nat (tptp.aa_nat_fun_nat_nat (tptp.aTP_Lamm_hl G) K) (tptp.set_or1269000886237332187st_nat M N)))) (forall ((G tptp.fun_nat_int) (M tptp.nat) (K tptp.nat) (N tptp.nat)) (= (tptp.groups705719431365010083at_int G (tptp.set_or1269000886237332187st_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) K) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N) K))) (tptp.groups705719431365010083at_int (tptp.aa_nat_fun_nat_int (tptp.aTP_Lamm_oz G) K) (tptp.set_or1269000886237332187st_nat M N)))) (forall ((S2 tptp.set_nat)) (= (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat S2)) (exists ((K2 tptp.nat)) (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat S2) (tptp.set_ord_atMost_nat K2)))))) (forall ((A4 tptp.set_nat) (F tptp.fun_nat_real)) (=> (forall ((X4 tptp.nat)) (let ((_let_1 (tptp.aa_nat_real F X4))) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X4) A4)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) _let_1)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real _let_1) tptp.one_one_real)))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.groups129246275422532515t_real F A4)) tptp.one_one_real)))) (forall ((A4 tptp.set_real) (F tptp.fun_real_real)) (=> (forall ((X4 tptp.real)) (let ((_let_1 (tptp.aa_real_real F X4))) (=> (tptp.member_real X4 A4) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) _let_1)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real _let_1) tptp.one_one_real)))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.groups1681761925125756287l_real F A4)) tptp.one_one_real)))) (forall ((A4 tptp.set_int) (F tptp.fun_int_real)) (=> (forall ((X4 tptp.int)) (let ((_let_1 (tptp.aa_int_real F X4))) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X4) A4)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) _let_1)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real _let_1) tptp.one_one_real)))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.groups2316167850115554303t_real F A4)) tptp.one_one_real)))) (forall ((A4 tptp.set_complex) (F tptp.fun_complex_real)) (=> (forall ((X4 tptp.complex)) (let ((_let_1 (tptp.aa_complex_real F X4))) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex X4) A4)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) _let_1)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real _let_1) tptp.one_one_real)))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.groups766887009212190081x_real F A4)) tptp.one_one_real)))) (forall ((A4 tptp.set_nat) (F tptp.fun_nat_rat)) (=> (forall ((X4 tptp.nat)) (let ((_let_1 (tptp.aa_nat_rat F X4))) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X4) A4)) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat _let_1) tptp.one_one_rat)))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.groups73079841787564623at_rat F A4)) tptp.one_one_rat)))) (forall ((A4 tptp.set_real) (F tptp.fun_real_rat)) (=> (forall ((X4 tptp.real)) (let ((_let_1 (tptp.aa_real_rat F X4))) (=> (tptp.member_real X4 A4) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat _let_1) tptp.one_one_rat)))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.groups4061424788464935467al_rat F A4)) tptp.one_one_rat)))) (forall ((A4 tptp.set_int) (F tptp.fun_int_rat)) (=> (forall ((X4 tptp.int)) (let ((_let_1 (tptp.aa_int_rat F X4))) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X4) A4)) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat _let_1) tptp.one_one_rat)))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.groups1072433553688619179nt_rat F A4)) tptp.one_one_rat)))) (forall ((A4 tptp.set_complex) (F tptp.fun_complex_rat)) (=> (forall ((X4 tptp.complex)) (let ((_let_1 (tptp.aa_complex_rat F X4))) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex X4) A4)) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat _let_1) tptp.one_one_rat)))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.groups225925009352817453ex_rat F A4)) tptp.one_one_rat)))) (forall ((A4 tptp.set_real) (F tptp.fun_real_nat)) (=> (forall ((X4 tptp.real)) (let ((_let_1 (tptp.aa_real_nat F X4))) (=> (tptp.member_real X4 A4) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) _let_1)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat _let_1) tptp.one_one_nat)))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.groups4696554848551431203al_nat F A4)) tptp.one_one_nat)))) (forall ((A4 tptp.set_int) (F tptp.fun_int_nat)) (=> (forall ((X4 tptp.int)) (let ((_let_1 (tptp.aa_int_nat F X4))) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X4) A4)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) _let_1)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat _let_1) tptp.one_one_nat)))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.groups1707563613775114915nt_nat F A4)) tptp.one_one_nat)))) (forall ((R2 tptp.fun_co1378794544173401837x_bool) (S2 tptp.set_nat) (H tptp.fun_nat_complex) (G tptp.fun_nat_complex)) (=> (tptp.pp (tptp.aa_complex_bool (tptp.aa_com1553036987509291606x_bool R2 tptp.one_one_complex) tptp.one_one_complex)) (=> (forall ((X15 tptp.complex) (Y15 tptp.complex) (X22 tptp.complex) (Y22 tptp.complex)) (=> (and (tptp.pp (tptp.aa_complex_bool (tptp.aa_com1553036987509291606x_bool R2 X15) X22)) (tptp.pp (tptp.aa_complex_bool (tptp.aa_com1553036987509291606x_bool R2 Y15) Y22))) (tptp.pp (tptp.aa_complex_bool (tptp.aa_com1553036987509291606x_bool R2 (tptp.aa_complex_complex (tptp.times_times_complex X15) Y15)) (tptp.aa_complex_complex (tptp.times_times_complex X22) Y22))))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat S2)) (=> (forall ((X4 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X4) S2)) (tptp.pp (tptp.aa_complex_bool (tptp.aa_com1553036987509291606x_bool R2 (tptp.aa_nat_complex H X4)) (tptp.aa_nat_complex G X4))))) (tptp.pp (tptp.aa_complex_bool (tptp.aa_com1553036987509291606x_bool R2 (tptp.groups6464643781859351333omplex H S2)) (tptp.groups6464643781859351333omplex G S2)))))))) (forall ((R2 tptp.fun_co1378794544173401837x_bool) (S2 tptp.set_int) (H tptp.fun_int_complex) (G tptp.fun_int_complex)) (=> (tptp.pp (tptp.aa_complex_bool (tptp.aa_com1553036987509291606x_bool R2 tptp.one_one_complex) tptp.one_one_complex)) (=> (forall ((X15 tptp.complex) (Y15 tptp.complex) (X22 tptp.complex) (Y22 tptp.complex)) (=> (and (tptp.pp (tptp.aa_complex_bool (tptp.aa_com1553036987509291606x_bool R2 X15) X22)) (tptp.pp (tptp.aa_complex_bool (tptp.aa_com1553036987509291606x_bool R2 Y15) Y22))) (tptp.pp (tptp.aa_complex_bool (tptp.aa_com1553036987509291606x_bool R2 (tptp.aa_complex_complex (tptp.times_times_complex X15) Y15)) (tptp.aa_complex_complex (tptp.times_times_complex X22) Y22))))) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int S2)) (=> (forall ((X4 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X4) S2)) (tptp.pp (tptp.aa_complex_bool (tptp.aa_com1553036987509291606x_bool R2 (tptp.aa_int_complex H X4)) (tptp.aa_int_complex G X4))))) (tptp.pp (tptp.aa_complex_bool (tptp.aa_com1553036987509291606x_bool R2 (tptp.groups7440179247065528705omplex H S2)) (tptp.groups7440179247065528705omplex G S2)))))))) (forall ((R2 tptp.fun_co1378794544173401837x_bool) (S2 tptp.set_complex) (H tptp.fun_complex_complex) (G tptp.fun_complex_complex)) (=> (tptp.pp (tptp.aa_complex_bool (tptp.aa_com1553036987509291606x_bool R2 tptp.one_one_complex) tptp.one_one_complex)) (=> (forall ((X15 tptp.complex) (Y15 tptp.complex) (X22 tptp.complex) (Y22 tptp.complex)) (=> (and (tptp.pp (tptp.aa_complex_bool (tptp.aa_com1553036987509291606x_bool R2 X15) X22)) (tptp.pp (tptp.aa_complex_bool (tptp.aa_com1553036987509291606x_bool R2 Y15) Y22))) (tptp.pp (tptp.aa_complex_bool (tptp.aa_com1553036987509291606x_bool R2 (tptp.aa_complex_complex (tptp.times_times_complex X15) Y15)) (tptp.aa_complex_complex (tptp.times_times_complex X22) Y22))))) (=> (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex S2)) (=> (forall ((X4 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex X4) S2)) (tptp.pp (tptp.aa_complex_bool (tptp.aa_com1553036987509291606x_bool R2 (tptp.aa_complex_complex H X4)) (tptp.aa_complex_complex G X4))))) (tptp.pp (tptp.aa_complex_bool (tptp.aa_com1553036987509291606x_bool R2 (tptp.groups3708469109370488835omplex H S2)) (tptp.groups3708469109370488835omplex G S2)))))))) (forall ((R2 tptp.fun_re1255401033344146673l_bool) (S2 tptp.set_nat) (H tptp.fun_nat_real) (G tptp.fun_nat_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool R2 tptp.one_one_real) tptp.one_one_real)) (=> (forall ((X15 tptp.real) (Y15 tptp.real) (X22 tptp.real) (Y22 tptp.real)) (=> (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool R2 X15) X22)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool R2 Y15) Y22))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool R2 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real X15) Y15)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real X22) Y22))))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat S2)) (=> (forall ((X4 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X4) S2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool R2 (tptp.aa_nat_real H X4)) (tptp.aa_nat_real G X4))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool R2 (tptp.groups129246275422532515t_real H S2)) (tptp.groups129246275422532515t_real G S2)))))))) (forall ((R2 tptp.fun_re1255401033344146673l_bool) (S2 tptp.set_int) (H tptp.fun_int_real) (G tptp.fun_int_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool R2 tptp.one_one_real) tptp.one_one_real)) (=> (forall ((X15 tptp.real) (Y15 tptp.real) (X22 tptp.real) (Y22 tptp.real)) (=> (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool R2 X15) X22)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool R2 Y15) Y22))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool R2 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real X15) Y15)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real X22) Y22))))) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int S2)) (=> (forall ((X4 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X4) S2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool R2 (tptp.aa_int_real H X4)) (tptp.aa_int_real G X4))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool R2 (tptp.groups2316167850115554303t_real H S2)) (tptp.groups2316167850115554303t_real G S2)))))))) (forall ((R2 tptp.fun_re1255401033344146673l_bool) (S2 tptp.set_complex) (H tptp.fun_complex_real) (G tptp.fun_complex_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool R2 tptp.one_one_real) tptp.one_one_real)) (=> (forall ((X15 tptp.real) (Y15 tptp.real) (X22 tptp.real) (Y22 tptp.real)) (=> (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool R2 X15) X22)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool R2 Y15) Y22))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool R2 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real X15) Y15)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real X22) Y22))))) (=> (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex S2)) (=> (forall ((X4 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex X4) S2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool R2 (tptp.aa_complex_real H X4)) (tptp.aa_complex_real G X4))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool R2 (tptp.groups766887009212190081x_real H S2)) (tptp.groups766887009212190081x_real G S2)))))))) (forall ((R2 tptp.fun_rat_fun_rat_bool) (S2 tptp.set_nat) (H tptp.fun_nat_rat) (G tptp.fun_nat_rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool R2 tptp.one_one_rat) tptp.one_one_rat)) (=> (forall ((X15 tptp.rat) (Y15 tptp.rat) (X22 tptp.rat) (Y22 tptp.rat)) (=> (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool R2 X15) X22)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool R2 Y15) Y22))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool R2 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat X15) Y15)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat X22) Y22))))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat S2)) (=> (forall ((X4 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X4) S2)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool R2 (tptp.aa_nat_rat H X4)) (tptp.aa_nat_rat G X4))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool R2 (tptp.groups73079841787564623at_rat H S2)) (tptp.groups73079841787564623at_rat G S2)))))))) (forall ((R2 tptp.fun_rat_fun_rat_bool) (S2 tptp.set_int) (H tptp.fun_int_rat) (G tptp.fun_int_rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool R2 tptp.one_one_rat) tptp.one_one_rat)) (=> (forall ((X15 tptp.rat) (Y15 tptp.rat) (X22 tptp.rat) (Y22 tptp.rat)) (=> (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool R2 X15) X22)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool R2 Y15) Y22))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool R2 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat X15) Y15)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat X22) Y22))))) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int S2)) (=> (forall ((X4 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X4) S2)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool R2 (tptp.aa_int_rat H X4)) (tptp.aa_int_rat G X4))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool R2 (tptp.groups1072433553688619179nt_rat H S2)) (tptp.groups1072433553688619179nt_rat G S2)))))))) (forall ((R2 tptp.fun_rat_fun_rat_bool) (S2 tptp.set_complex) (H tptp.fun_complex_rat) (G tptp.fun_complex_rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool R2 tptp.one_one_rat) tptp.one_one_rat)) (=> (forall ((X15 tptp.rat) (Y15 tptp.rat) (X22 tptp.rat) (Y22 tptp.rat)) (=> (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool R2 X15) X22)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool R2 Y15) Y22))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool R2 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat X15) Y15)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat X22) Y22))))) (=> (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex S2)) (=> (forall ((X4 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex X4) S2)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool R2 (tptp.aa_complex_rat H X4)) (tptp.aa_complex_rat G X4))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool R2 (tptp.groups225925009352817453ex_rat H S2)) (tptp.groups225925009352817453ex_rat G S2)))))))) (forall ((R2 tptp.fun_nat_fun_nat_bool) (S2 tptp.set_int) (H tptp.fun_int_nat) (G tptp.fun_int_nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool R2 tptp.one_one_nat) tptp.one_one_nat)) (=> (forall ((X15 tptp.nat) (Y15 tptp.nat) (X22 tptp.nat) (Y22 tptp.nat)) (=> (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool R2 X15) X22)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool R2 Y15) Y22))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool R2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat X15) Y15)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat X22) Y22))))) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int S2)) (=> (forall ((X4 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X4) S2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool R2 (tptp.aa_int_nat H X4)) (tptp.aa_int_nat G X4))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool R2 (tptp.groups1707563613775114915nt_nat H S2)) (tptp.groups1707563613775114915nt_nat G S2)))))))) (forall ((B4 tptp.set_complex) (A4 tptp.set_complex) (F tptp.fun_complex_nat)) (=> (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex B4)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.ord_le211207098394363844omplex A4) B4)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.groups861055069439313189ex_nat F A4)) (tptp.groups861055069439313189ex_nat F B4)))))) (forall ((B4 tptp.set_complex) (A4 tptp.set_complex) (F tptp.fun_complex_int)) (=> (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex B4)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.ord_le211207098394363844omplex A4) B4)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.groups858564598930262913ex_int F A4)) (tptp.groups858564598930262913ex_int F B4)))))) (forall ((B4 tptp.set_nat) (A4 tptp.set_nat) (F tptp.fun_nat_Code_integer)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat B4)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat A4) B4)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.groups3455450783089532116nteger F A4)) (tptp.groups3455450783089532116nteger F B4)))))) (forall ((B4 tptp.set_complex) (A4 tptp.set_complex) (F tptp.fun_co8153928105989009288nteger)) (=> (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex B4)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.ord_le211207098394363844omplex A4) B4)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.groups8682486955453173170nteger F A4)) (tptp.groups8682486955453173170nteger F B4)))))) (forall ((B4 tptp.set_int) (A4 tptp.set_int) (F tptp.fun_int_nat)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int B4)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int A4) B4)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.groups1707563613775114915nt_nat F A4)) (tptp.groups1707563613775114915nt_nat F B4)))))) (forall ((B4 tptp.set_int) (A4 tptp.set_int) (F tptp.fun_int_Code_integer)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int B4)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int A4) B4)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.groups3827104343326376752nteger F A4)) (tptp.groups3827104343326376752nteger F B4)))))) (forall ((B4 tptp.set_nat) (A4 tptp.set_nat) (F tptp.fun_nat_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat B4)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat A4) B4)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.groups708209901874060359at_nat F A4)) (tptp.groups708209901874060359at_nat F B4)))))) (forall ((B4 tptp.set_nat) (A4 tptp.set_nat) (F tptp.fun_nat_int)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat B4)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat A4) B4)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.groups705719431365010083at_int F A4)) (tptp.groups705719431365010083at_int F B4)))))) (forall ((B4 tptp.set_int) (A4 tptp.set_int) (F tptp.fun_int_int)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int B4)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int A4) B4)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.groups1705073143266064639nt_int F A4)) (tptp.groups1705073143266064639nt_int F B4)))))) (forall ((B4 tptp.set_real) (A4 tptp.set_real) (F tptp.fun_real_nat) (G tptp.fun_real_nat)) (=> (tptp.finite_finite_real B4) (=> (tptp.ord_less_eq_set_real A4 B4) (=> (forall ((A3 tptp.real)) (=> (tptp.member_real A3 A4) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_real_nat F A3)) (tptp.aa_real_nat G A3))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.groups4696554848551431203al_nat F A4)) (tptp.groups4696554848551431203al_nat G B4))))))) (forall ((B4 tptp.set_complex) (A4 tptp.set_complex) (F tptp.fun_complex_nat) (G tptp.fun_complex_nat)) (=> (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex B4)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.ord_le211207098394363844omplex A4) B4)) (=> (forall ((A3 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex A3) A4)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_complex_nat F A3)) (tptp.aa_complex_nat G A3))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.groups861055069439313189ex_nat F A4)) (tptp.groups861055069439313189ex_nat G B4))))))) (forall ((B4 tptp.set_real) (A4 tptp.set_real) (F tptp.fun_real_int) (G tptp.fun_real_int)) (=> (tptp.finite_finite_real B4) (=> (tptp.ord_less_eq_set_real A4 B4) (=> (forall ((A3 tptp.real)) (=> (tptp.member_real A3 A4) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_real_int F A3)) (tptp.aa_real_int G A3))))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.groups4694064378042380927al_int F A4)) (tptp.groups4694064378042380927al_int G B4))))))) (forall ((B4 tptp.set_complex) (A4 tptp.set_complex) (F tptp.fun_complex_int) (G tptp.fun_complex_int)) (=> (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex B4)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.ord_le211207098394363844omplex A4) B4)) (=> (forall ((A3 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex A3) A4)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_complex_int F A3)) (tptp.aa_complex_int G A3))))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.groups858564598930262913ex_int F A4)) (tptp.groups858564598930262913ex_int G B4))))))) (forall ((B4 tptp.set_real) (A4 tptp.set_real) (F tptp.fun_re6978948838062957830nteger) (G tptp.fun_re6978948838062957830nteger)) (=> (tptp.finite_finite_real B4) (=> (tptp.ord_less_eq_set_real A4 B4) (=> (forall ((A3 tptp.real)) (=> (tptp.member_real A3 A4) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.aa_real_Code_integer F A3)) (tptp.aa_real_Code_integer G A3))))) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.groups6225526099057966256nteger F A4)) (tptp.groups6225526099057966256nteger G B4))))))) (forall ((B4 tptp.set_nat) (A4 tptp.set_nat) (F tptp.fun_nat_Code_integer) (G tptp.fun_nat_Code_integer)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat B4)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat A4) B4)) (=> (forall ((A3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat A3) A4)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.aa_nat_Code_integer F A3)) (tptp.aa_nat_Code_integer G A3))))) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.groups3455450783089532116nteger F A4)) (tptp.groups3455450783089532116nteger G B4))))))) (forall ((B4 tptp.set_complex) (A4 tptp.set_complex) (F tptp.fun_co8153928105989009288nteger) (G tptp.fun_co8153928105989009288nteger)) (=> (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex B4)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.ord_le211207098394363844omplex A4) B4)) (=> (forall ((A3 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex A3) A4)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.aa_com4217951221296830281nteger F A3)) (tptp.aa_com4217951221296830281nteger G A3))))) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.groups8682486955453173170nteger F A4)) (tptp.groups8682486955453173170nteger G B4))))))) (forall ((B4 tptp.set_int) (A4 tptp.set_int) (F tptp.fun_int_nat) (G tptp.fun_int_nat)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int B4)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int A4) B4)) (=> (forall ((A3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int A3) A4)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_int_nat F A3)) (tptp.aa_int_nat G A3))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.groups1707563613775114915nt_nat F A4)) (tptp.groups1707563613775114915nt_nat G B4))))))) (forall ((B4 tptp.set_int) (A4 tptp.set_int) (F tptp.fun_int_Code_integer) (G tptp.fun_int_Code_integer)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int B4)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int A4) B4)) (=> (forall ((A3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int A3) A4)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.aa_int_Code_integer F A3)) (tptp.aa_int_Code_integer G A3))))) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.groups3827104343326376752nteger F A4)) (tptp.groups3827104343326376752nteger G B4))))))) (forall ((B4 tptp.set_nat) (A4 tptp.set_nat) (F tptp.fun_nat_nat) (G tptp.fun_nat_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat B4)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat A4) B4)) (=> (forall ((A3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat A3) A4)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_nat_nat F A3)) (tptp.aa_nat_nat G A3))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.groups708209901874060359at_nat F A4)) (tptp.groups708209901874060359at_nat G B4))))))) (forall ((G tptp.fun_nat_real) (N tptp.nat)) (= (tptp.groups129246275422532515t_real G (tptp.set_ord_atMost_nat (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N)))) (tptp.groups129246275422532515t_real (tptp.aTP_Lamm_pa G) (tptp.set_ord_atMost_nat N)))) (forall ((G tptp.fun_nat_rat) (N tptp.nat)) (= (tptp.groups73079841787564623at_rat G (tptp.set_ord_atMost_nat (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N)))) (tptp.groups73079841787564623at_rat (tptp.aTP_Lamm_pb G) (tptp.set_ord_atMost_nat N)))) (forall ((G tptp.fun_nat_nat) (N tptp.nat)) (= (tptp.groups708209901874060359at_nat G (tptp.set_ord_atMost_nat (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N)))) (tptp.groups708209901874060359at_nat (tptp.aTP_Lamm_pc G) (tptp.set_ord_atMost_nat N)))) (forall ((G tptp.fun_nat_int) (N tptp.nat)) (= (tptp.groups705719431365010083at_int G (tptp.set_ord_atMost_nat (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N)))) (tptp.groups705719431365010083at_int (tptp.aTP_Lamm_pd G) (tptp.set_ord_atMost_nat N)))) (forall ((G tptp.fun_nat_nat) (N tptp.nat)) (let ((_let_1 (tptp.set_ord_lessThan_nat N))) (= (tptp.groups708209901874060359at_nat (tptp.aa_nat_fun_nat_nat (tptp.aTP_Lamm_kv G) N) _let_1) (tptp.groups708209901874060359at_nat G _let_1)))) (forall ((G tptp.fun_nat_int) (N tptp.nat)) (let ((_let_1 (tptp.set_ord_lessThan_nat N))) (= (tptp.groups705719431365010083at_int (tptp.aa_nat_fun_nat_int (tptp.aTP_Lamm_pe G) N) _let_1) (tptp.groups705719431365010083at_int G _let_1)))) (forall ((A tptp.rat) (B2 tptp.rat)) (= (tptp.ord_less_eq_set_rat (tptp.set_ord_atMost_rat A) (tptp.set_ord_lessThan_rat B2)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B2)))) (forall ((A tptp.num) (B2 tptp.num)) (= (tptp.ord_less_eq_set_num (tptp.set_ord_atMost_num A) (tptp.set_ord_lessThan_num B2)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num A) B2)))) (forall ((A tptp.nat) (B2 tptp.nat)) (= (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat (tptp.set_ord_atMost_nat A)) (tptp.set_ord_lessThan_nat B2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) B2)))) (forall ((A tptp.int) (B2 tptp.int)) (= (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int (tptp.set_ord_atMost_int A)) (tptp.set_ord_lessThan_int B2))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B2)))) (forall ((A tptp.real) (B2 tptp.real)) (= (tptp.ord_less_eq_set_real (tptp.set_ord_atMost_real A) (tptp.set_or5984915006950818249n_real B2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B2)))) (forall ((G tptp.fun_nat_nat) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.set_or1269000886237332187st_nat N M))) (= (tptp.groups708209901874060359at_nat G _let_1) (tptp.groups708209901874060359at_nat (tptp.aa_nat_fun_nat_nat (tptp.aa_nat3783148529270815480at_nat (tptp.aTP_Lamm_hr G) N) M) _let_1)))) (forall ((G tptp.fun_nat_int) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.set_or1269000886237332187st_nat N M))) (= (tptp.groups705719431365010083at_int G _let_1) (tptp.groups705719431365010083at_int (tptp.aa_nat_fun_nat_int (tptp.aa_nat1293065384339088724at_int (tptp.aTP_Lamm_pf G) N) M) _let_1)))) (forall ((P2 tptp.nat) (K tptp.nat) (G tptp.fun_nat_complex) (H tptp.fun_nat_complex)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.one_one_nat) P2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) P2)) (= (tptp.groups6464643781859351333omplex (tptp.aa_fun2955221450537884980omplex (tptp.aa_fun7497765718855568684omplex (tptp.aTP_Lamm_pg K) G) H) (tptp.set_ord_atMost_nat P2)) (tptp.groups6464643781859351333omplex (tptp.aa_fun2955221450537884980omplex (tptp.aa_fun7497765718855568684omplex (tptp.aTP_Lamm_ph K) G) H) (tptp.set_ord_atMost_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat P2) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)))))))) (forall ((P2 tptp.nat) (K tptp.nat) (G tptp.fun_nat_real) (H tptp.fun_nat_real)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.one_one_nat) P2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) P2)) (= (tptp.groups129246275422532515t_real (tptp.aa_fun1839206346889086768t_real (tptp.aa_fun8674848580393814182t_real (tptp.aTP_Lamm_pi K) G) H) (tptp.set_ord_atMost_nat P2)) (tptp.groups129246275422532515t_real (tptp.aa_fun1839206346889086768t_real (tptp.aa_fun8674848580393814182t_real (tptp.aTP_Lamm_pj K) G) H) (tptp.set_ord_atMost_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat P2) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)))))))) (forall ((P2 tptp.nat) (K tptp.nat) (G tptp.fun_nat_rat) (H tptp.fun_nat_rat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.one_one_nat) P2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) P2)) (= (tptp.groups73079841787564623at_rat (tptp.aa_fun765758790203053448at_rat (tptp.aa_fun3638354034882855594at_rat (tptp.aTP_Lamm_pk K) G) H) (tptp.set_ord_atMost_nat P2)) (tptp.groups73079841787564623at_rat (tptp.aa_fun765758790203053448at_rat (tptp.aa_fun3638354034882855594at_rat (tptp.aTP_Lamm_pl K) G) H) (tptp.set_ord_atMost_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat P2) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)))))))) (forall ((P2 tptp.nat) (K tptp.nat) (G tptp.fun_nat_nat) (H tptp.fun_nat_nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.one_one_nat) P2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) P2)) (= (tptp.groups708209901874060359at_nat (tptp.aa_fun5791449513213591928at_nat (tptp.aa_fun6854695580826382482at_nat (tptp.aTP_Lamm_pm K) G) H) (tptp.set_ord_atMost_nat P2)) (tptp.groups708209901874060359at_nat (tptp.aa_fun5791449513213591928at_nat (tptp.aa_fun6854695580826382482at_nat (tptp.aTP_Lamm_pn K) G) H) (tptp.set_ord_atMost_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat P2) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)))))))) (forall ((P2 tptp.nat) (K tptp.nat) (G tptp.fun_nat_int) (H tptp.fun_nat_int)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.one_one_nat) P2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) P2)) (= (tptp.groups705719431365010083at_int (tptp.aa_fun5565043122120104496at_int (tptp.aa_fun5140708168904641446at_int (tptp.aTP_Lamm_po K) G) H) (tptp.set_ord_atMost_nat P2)) (tptp.groups705719431365010083at_int (tptp.aa_fun5565043122120104496at_int (tptp.aa_fun5140708168904641446at_int (tptp.aTP_Lamm_pp K) G) H) (tptp.set_ord_atMost_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat P2) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)))))))) (forall ((I5 tptp.set_real) (I tptp.real) (F tptp.fun_real_real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real))) (=> (tptp.finite_finite_real I5) (=> (tptp.member_real I I5) (=> (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real F I))) (=> (forall ((I3 tptp.real)) (=> (tptp.member_real I3 I5) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.one_one_real) (tptp.aa_real_real F I3))))) (tptp.pp (tptp.aa_real_bool _let_1 (tptp.groups1681761925125756287l_real F I5))))))))) (forall ((I5 tptp.set_nat) (I tptp.nat) (F tptp.fun_nat_real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat I5)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat I) I5)) (=> (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_nat_real F I))) (=> (forall ((I3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat I3) I5)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.one_one_real) (tptp.aa_nat_real F I3))))) (tptp.pp (tptp.aa_real_bool _let_1 (tptp.groups129246275422532515t_real F I5))))))))) (forall ((I5 tptp.set_int) (I tptp.int) (F tptp.fun_int_real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real))) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int I5)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int I) I5)) (=> (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_int_real F I))) (=> (forall ((I3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int I3) I5)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.one_one_real) (tptp.aa_int_real F I3))))) (tptp.pp (tptp.aa_real_bool _let_1 (tptp.groups2316167850115554303t_real F I5))))))))) (forall ((I5 tptp.set_complex) (I tptp.complex) (F tptp.fun_complex_real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real))) (=> (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex I5)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex I) I5)) (=> (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_complex_real F I))) (=> (forall ((I3 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex I3) I5)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.one_one_real) (tptp.aa_complex_real F I3))))) (tptp.pp (tptp.aa_real_bool _let_1 (tptp.groups766887009212190081x_real F I5))))))))) (forall ((I5 tptp.set_real) (I tptp.real) (F tptp.fun_real_rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.one_one_rat))) (=> (tptp.finite_finite_real I5) (=> (tptp.member_real I I5) (=> (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_real_rat F I))) (=> (forall ((I3 tptp.real)) (=> (tptp.member_real I3 I5) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.one_one_rat) (tptp.aa_real_rat F I3))))) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.groups4061424788464935467al_rat F I5))))))))) (forall ((I5 tptp.set_nat) (I tptp.nat) (F tptp.fun_nat_rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.one_one_rat))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat I5)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat I) I5)) (=> (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_nat_rat F I))) (=> (forall ((I3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat I3) I5)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.one_one_rat) (tptp.aa_nat_rat F I3))))) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.groups73079841787564623at_rat F I5))))))))) (forall ((I5 tptp.set_int) (I tptp.int) (F tptp.fun_int_rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.one_one_rat))) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int I5)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int I) I5)) (=> (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_int_rat F I))) (=> (forall ((I3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int I3) I5)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.one_one_rat) (tptp.aa_int_rat F I3))))) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.groups1072433553688619179nt_rat F I5))))))))) (forall ((I5 tptp.set_complex) (I tptp.complex) (F tptp.fun_complex_rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.one_one_rat))) (=> (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex I5)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex I) I5)) (=> (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_complex_rat F I))) (=> (forall ((I3 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex I3) I5)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.one_one_rat) (tptp.aa_complex_rat F I3))))) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.groups225925009352817453ex_rat F I5))))))))) (forall ((I5 tptp.set_real) (I tptp.real) (F tptp.fun_real_int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.one_one_int))) (=> (tptp.finite_finite_real I5) (=> (tptp.member_real I I5) (=> (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_real_int F I))) (=> (forall ((I3 tptp.real)) (=> (tptp.member_real I3 I5) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.one_one_int) (tptp.aa_real_int F I3))))) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.groups4694064378042380927al_int F I5))))))))) (forall ((I5 tptp.set_complex) (I tptp.complex) (F tptp.fun_complex_int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.one_one_int))) (=> (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex I5)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex I) I5)) (=> (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_complex_int F I))) (=> (forall ((I3 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex I3) I5)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.one_one_int) (tptp.aa_complex_int F I3))))) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.groups858564598930262913ex_int F I5))))))))) (forall ((I5 tptp.set_complex) (F tptp.fun_complex_real)) (=> (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex I5)) (=> (not (= I5 tptp.bot_bot_set_complex)) (=> (forall ((I3 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex I3) I5)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real) (tptp.aa_complex_real F I3))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real) (tptp.groups766887009212190081x_real F I5))))))) (forall ((I5 tptp.set_nat) (F tptp.fun_nat_real)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat I5)) (=> (not (= I5 tptp.bot_bot_set_nat)) (=> (forall ((I3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat I3) I5)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real) (tptp.aa_nat_real F I3))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real) (tptp.groups129246275422532515t_real F I5))))))) (forall ((I5 tptp.set_int) (F tptp.fun_int_real)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int I5)) (=> (not (= I5 tptp.bot_bot_set_int)) (=> (forall ((I3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int I3) I5)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real) (tptp.aa_int_real F I3))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real) (tptp.groups2316167850115554303t_real F I5))))))) (forall ((I5 tptp.set_real) (F tptp.fun_real_real)) (=> (tptp.finite_finite_real I5) (=> (not (= I5 tptp.bot_bot_set_real)) (=> (forall ((I3 tptp.real)) (=> (tptp.member_real I3 I5) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real) (tptp.aa_real_real F I3))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real) (tptp.groups1681761925125756287l_real F I5))))))) (forall ((I5 tptp.set_complex) (F tptp.fun_complex_rat)) (=> (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex I5)) (=> (not (= I5 tptp.bot_bot_set_complex)) (=> (forall ((I3 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex I3) I5)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.one_one_rat) (tptp.aa_complex_rat F I3))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.one_one_rat) (tptp.groups225925009352817453ex_rat F I5))))))) (forall ((I5 tptp.set_nat) (F tptp.fun_nat_rat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat I5)) (=> (not (= I5 tptp.bot_bot_set_nat)) (=> (forall ((I3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat I3) I5)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.one_one_rat) (tptp.aa_nat_rat F I3))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.one_one_rat) (tptp.groups73079841787564623at_rat F I5))))))) (forall ((I5 tptp.set_int) (F tptp.fun_int_rat)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int I5)) (=> (not (= I5 tptp.bot_bot_set_int)) (=> (forall ((I3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int I3) I5)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.one_one_rat) (tptp.aa_int_rat F I3))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.one_one_rat) (tptp.groups1072433553688619179nt_rat F I5))))))) (forall ((I5 tptp.set_real) (F tptp.fun_real_rat)) (=> (tptp.finite_finite_real I5) (=> (not (= I5 tptp.bot_bot_set_real)) (=> (forall ((I3 tptp.real)) (=> (tptp.member_real I3 I5) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.one_one_rat) (tptp.aa_real_rat F I3))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.one_one_rat) (tptp.groups4061424788464935467al_rat F I5))))))) (forall ((I5 tptp.set_complex) (F tptp.fun_complex_int)) (=> (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex I5)) (=> (not (= I5 tptp.bot_bot_set_complex)) (=> (forall ((I3 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex I3) I5)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.one_one_int) (tptp.aa_complex_int F I3))))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.one_one_int) (tptp.groups858564598930262913ex_int F I5))))))) (forall ((I5 tptp.set_real) (F tptp.fun_real_int)) (=> (tptp.finite_finite_real I5) (=> (not (= I5 tptp.bot_bot_set_real)) (=> (forall ((I3 tptp.real)) (=> (tptp.member_real I3 I5) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.one_one_int) (tptp.aa_real_int F I3))))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.one_one_int) (tptp.groups4694064378042380927al_int F I5))))))) (forall ((B4 tptp.set_nat) (A4 tptp.set_nat) (G tptp.fun_nat_real)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat B4) A4)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A4)) (= (tptp.groups129246275422532515t_real G A4) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.groups129246275422532515t_real G (tptp.minus_minus_set_nat A4 B4))) (tptp.groups129246275422532515t_real G B4)))))) (forall ((B4 tptp.set_complex) (A4 tptp.set_complex) (G tptp.fun_complex_real)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.ord_le211207098394363844omplex B4) A4)) (=> (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex A4)) (= (tptp.groups766887009212190081x_real G A4) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.groups766887009212190081x_real G (tptp.minus_811609699411566653omplex A4 B4))) (tptp.groups766887009212190081x_real G B4)))))) (forall ((B4 tptp.set_nat) (A4 tptp.set_nat) (G tptp.fun_nat_rat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat B4) A4)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A4)) (= (tptp.groups73079841787564623at_rat G A4) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.groups73079841787564623at_rat G (tptp.minus_minus_set_nat A4 B4))) (tptp.groups73079841787564623at_rat G B4)))))) (forall ((B4 tptp.set_complex) (A4 tptp.set_complex) (G tptp.fun_complex_rat)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.ord_le211207098394363844omplex B4) A4)) (=> (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex A4)) (= (tptp.groups225925009352817453ex_rat G A4) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.groups225925009352817453ex_rat G (tptp.minus_811609699411566653omplex A4 B4))) (tptp.groups225925009352817453ex_rat G B4)))))) (forall ((B4 tptp.set_complex) (A4 tptp.set_complex) (G tptp.fun_complex_nat)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.ord_le211207098394363844omplex B4) A4)) (=> (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex A4)) (= (tptp.groups861055069439313189ex_nat G A4) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.groups861055069439313189ex_nat G (tptp.minus_811609699411566653omplex A4 B4))) (tptp.groups861055069439313189ex_nat G B4)))))) (forall ((B4 tptp.set_complex) (A4 tptp.set_complex) (G tptp.fun_complex_int)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.ord_le211207098394363844omplex B4) A4)) (=> (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex A4)) (= (tptp.groups858564598930262913ex_int G A4) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.groups858564598930262913ex_int G (tptp.minus_811609699411566653omplex A4 B4))) (tptp.groups858564598930262913ex_int G B4)))))) (forall ((B4 tptp.set_int) (A4 tptp.set_int) (G tptp.fun_int_real)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int B4) A4)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A4)) (= (tptp.groups2316167850115554303t_real G A4) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.groups2316167850115554303t_real G (tptp.minus_minus_set_int A4 B4))) (tptp.groups2316167850115554303t_real G B4)))))) (forall ((B4 tptp.set_int) (A4 tptp.set_int) (G tptp.fun_int_rat)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int B4) A4)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A4)) (= (tptp.groups1072433553688619179nt_rat G A4) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.groups1072433553688619179nt_rat G (tptp.minus_minus_set_int A4 B4))) (tptp.groups1072433553688619179nt_rat G B4)))))) (forall ((B4 tptp.set_int) (A4 tptp.set_int) (G tptp.fun_int_nat)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int B4) A4)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A4)) (= (tptp.groups1707563613775114915nt_nat G A4) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.groups1707563613775114915nt_nat G (tptp.minus_minus_set_int A4 B4))) (tptp.groups1707563613775114915nt_nat G B4)))))) (forall ((B4 tptp.set_nat) (A4 tptp.set_nat) (G tptp.fun_nat_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat B4) A4)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A4)) (= (tptp.groups708209901874060359at_nat G A4) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.groups708209901874060359at_nat G (tptp.minus_minus_set_nat A4 B4))) (tptp.groups708209901874060359at_nat G B4)))))) (forall ((C4 tptp.set_real) (A4 tptp.set_real) (B4 tptp.set_real) (G tptp.fun_real_complex) (H tptp.fun_real_complex)) (=> (tptp.finite_finite_real C4) (=> (tptp.ord_less_eq_set_real A4 C4) (=> (tptp.ord_less_eq_set_real B4 C4) (=> (forall ((A3 tptp.real)) (=> (tptp.member_real A3 (tptp.minus_minus_set_real C4 A4)) (= (tptp.aa_real_complex G A3) tptp.one_one_complex))) (=> (forall ((B3 tptp.real)) (=> (tptp.member_real B3 (tptp.minus_minus_set_real C4 B4)) (= (tptp.aa_real_complex H B3) tptp.one_one_complex))) (= (= (tptp.groups713298508707869441omplex G A4) (tptp.groups713298508707869441omplex H B4)) (= (tptp.groups713298508707869441omplex G C4) (tptp.groups713298508707869441omplex H C4))))))))) (forall ((C4 tptp.set_nat) (A4 tptp.set_nat) (B4 tptp.set_nat) (G tptp.fun_nat_complex) (H tptp.fun_nat_complex)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat C4)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat A4) C4)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat B4) C4)) (=> (forall ((A3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat A3) (tptp.minus_minus_set_nat C4 A4))) (= (tptp.aa_nat_complex G A3) tptp.one_one_complex))) (=> (forall ((B3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat B3) (tptp.minus_minus_set_nat C4 B4))) (= (tptp.aa_nat_complex H B3) tptp.one_one_complex))) (= (= (tptp.groups6464643781859351333omplex G A4) (tptp.groups6464643781859351333omplex H B4)) (= (tptp.groups6464643781859351333omplex G C4) (tptp.groups6464643781859351333omplex H C4))))))))) (forall ((C4 tptp.set_complex) (A4 tptp.set_complex) (B4 tptp.set_complex) (G tptp.fun_complex_complex) (H tptp.fun_complex_complex)) (=> (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex C4)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.ord_le211207098394363844omplex A4) C4)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.ord_le211207098394363844omplex B4) C4)) (=> (forall ((A3 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex A3) (tptp.minus_811609699411566653omplex C4 A4))) (= (tptp.aa_complex_complex G A3) tptp.one_one_complex))) (=> (forall ((B3 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex B3) (tptp.minus_811609699411566653omplex C4 B4))) (= (tptp.aa_complex_complex H B3) tptp.one_one_complex))) (= (= (tptp.groups3708469109370488835omplex G A4) (tptp.groups3708469109370488835omplex H B4)) (= (tptp.groups3708469109370488835omplex G C4) (tptp.groups3708469109370488835omplex H C4))))))))) (forall ((C4 tptp.set_real) (A4 tptp.set_real) (B4 tptp.set_real) (G tptp.fun_real_real) (H tptp.fun_real_real)) (=> (tptp.finite_finite_real C4) (=> (tptp.ord_less_eq_set_real A4 C4) (=> (tptp.ord_less_eq_set_real B4 C4) (=> (forall ((A3 tptp.real)) (=> (tptp.member_real A3 (tptp.minus_minus_set_real C4 A4)) (= (tptp.aa_real_real G A3) tptp.one_one_real))) (=> (forall ((B3 tptp.real)) (=> (tptp.member_real B3 (tptp.minus_minus_set_real C4 B4)) (= (tptp.aa_real_real H B3) tptp.one_one_real))) (= (= (tptp.groups1681761925125756287l_real G A4) (tptp.groups1681761925125756287l_real H B4)) (= (tptp.groups1681761925125756287l_real G C4) (tptp.groups1681761925125756287l_real H C4))))))))) (forall ((C4 tptp.set_nat) (A4 tptp.set_nat) (B4 tptp.set_nat) (G tptp.fun_nat_real) (H tptp.fun_nat_real)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat C4)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat A4) C4)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat B4) C4)) (=> (forall ((A3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat A3) (tptp.minus_minus_set_nat C4 A4))) (= (tptp.aa_nat_real G A3) tptp.one_one_real))) (=> (forall ((B3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat B3) (tptp.minus_minus_set_nat C4 B4))) (= (tptp.aa_nat_real H B3) tptp.one_one_real))) (= (= (tptp.groups129246275422532515t_real G A4) (tptp.groups129246275422532515t_real H B4)) (= (tptp.groups129246275422532515t_real G C4) (tptp.groups129246275422532515t_real H C4))))))))) (forall ((C4 tptp.set_complex) (A4 tptp.set_complex) (B4 tptp.set_complex) (G tptp.fun_complex_real) (H tptp.fun_complex_real)) (=> (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex C4)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.ord_le211207098394363844omplex A4) C4)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.ord_le211207098394363844omplex B4) C4)) (=> (forall ((A3 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex A3) (tptp.minus_811609699411566653omplex C4 A4))) (= (tptp.aa_complex_real G A3) tptp.one_one_real))) (=> (forall ((B3 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex B3) (tptp.minus_811609699411566653omplex C4 B4))) (= (tptp.aa_complex_real H B3) tptp.one_one_real))) (= (= (tptp.groups766887009212190081x_real G A4) (tptp.groups766887009212190081x_real H B4)) (= (tptp.groups766887009212190081x_real G C4) (tptp.groups766887009212190081x_real H C4))))))))) (forall ((C4 tptp.set_real) (A4 tptp.set_real) (B4 tptp.set_real) (G tptp.fun_real_rat) (H tptp.fun_real_rat)) (=> (tptp.finite_finite_real C4) (=> (tptp.ord_less_eq_set_real A4 C4) (=> (tptp.ord_less_eq_set_real B4 C4) (=> (forall ((A3 tptp.real)) (=> (tptp.member_real A3 (tptp.minus_minus_set_real C4 A4)) (= (tptp.aa_real_rat G A3) tptp.one_one_rat))) (=> (forall ((B3 tptp.real)) (=> (tptp.member_real B3 (tptp.minus_minus_set_real C4 B4)) (= (tptp.aa_real_rat H B3) tptp.one_one_rat))) (= (= (tptp.groups4061424788464935467al_rat G A4) (tptp.groups4061424788464935467al_rat H B4)) (= (tptp.groups4061424788464935467al_rat G C4) (tptp.groups4061424788464935467al_rat H C4))))))))) (forall ((C4 tptp.set_nat) (A4 tptp.set_nat) (B4 tptp.set_nat) (G tptp.fun_nat_rat) (H tptp.fun_nat_rat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat C4)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat A4) C4)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat B4) C4)) (=> (forall ((A3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat A3) (tptp.minus_minus_set_nat C4 A4))) (= (tptp.aa_nat_rat G A3) tptp.one_one_rat))) (=> (forall ((B3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat B3) (tptp.minus_minus_set_nat C4 B4))) (= (tptp.aa_nat_rat H B3) tptp.one_one_rat))) (= (= (tptp.groups73079841787564623at_rat G A4) (tptp.groups73079841787564623at_rat H B4)) (= (tptp.groups73079841787564623at_rat G C4) (tptp.groups73079841787564623at_rat H C4))))))))) (forall ((C4 tptp.set_complex) (A4 tptp.set_complex) (B4 tptp.set_complex) (G tptp.fun_complex_rat) (H tptp.fun_complex_rat)) (=> (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex C4)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.ord_le211207098394363844omplex A4) C4)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.ord_le211207098394363844omplex B4) C4)) (=> (forall ((A3 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex A3) (tptp.minus_811609699411566653omplex C4 A4))) (= (tptp.aa_complex_rat G A3) tptp.one_one_rat))) (=> (forall ((B3 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex B3) (tptp.minus_811609699411566653omplex C4 B4))) (= (tptp.aa_complex_rat H B3) tptp.one_one_rat))) (= (= (tptp.groups225925009352817453ex_rat G A4) (tptp.groups225925009352817453ex_rat H B4)) (= (tptp.groups225925009352817453ex_rat G C4) (tptp.groups225925009352817453ex_rat H C4))))))))) (forall ((C4 tptp.set_real) (A4 tptp.set_real) (B4 tptp.set_real) (G tptp.fun_real_nat) (H tptp.fun_real_nat)) (=> (tptp.finite_finite_real C4) (=> (tptp.ord_less_eq_set_real A4 C4) (=> (tptp.ord_less_eq_set_real B4 C4) (=> (forall ((A3 tptp.real)) (=> (tptp.member_real A3 (tptp.minus_minus_set_real C4 A4)) (= (tptp.aa_real_nat G A3) tptp.one_one_nat))) (=> (forall ((B3 tptp.real)) (=> (tptp.member_real B3 (tptp.minus_minus_set_real C4 B4)) (= (tptp.aa_real_nat H B3) tptp.one_one_nat))) (= (= (tptp.groups4696554848551431203al_nat G A4) (tptp.groups4696554848551431203al_nat H B4)) (= (tptp.groups4696554848551431203al_nat G C4) (tptp.groups4696554848551431203al_nat H C4))))))))) (forall ((C4 tptp.set_real) (A4 tptp.set_real) (B4 tptp.set_real) (G tptp.fun_real_complex) (H tptp.fun_real_complex)) (=> (tptp.finite_finite_real C4) (=> (tptp.ord_less_eq_set_real A4 C4) (=> (tptp.ord_less_eq_set_real B4 C4) (=> (forall ((A3 tptp.real)) (=> (tptp.member_real A3 (tptp.minus_minus_set_real C4 A4)) (= (tptp.aa_real_complex G A3) tptp.one_one_complex))) (=> (forall ((B3 tptp.real)) (=> (tptp.member_real B3 (tptp.minus_minus_set_real C4 B4)) (= (tptp.aa_real_complex H B3) tptp.one_one_complex))) (=> (= (tptp.groups713298508707869441omplex G C4) (tptp.groups713298508707869441omplex H C4)) (= (tptp.groups713298508707869441omplex G A4) (tptp.groups713298508707869441omplex H B4))))))))) (forall ((C4 tptp.set_nat) (A4 tptp.set_nat) (B4 tptp.set_nat) (G tptp.fun_nat_complex) (H tptp.fun_nat_complex)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat C4)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat A4) C4)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat B4) C4)) (=> (forall ((A3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat A3) (tptp.minus_minus_set_nat C4 A4))) (= (tptp.aa_nat_complex G A3) tptp.one_one_complex))) (=> (forall ((B3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat B3) (tptp.minus_minus_set_nat C4 B4))) (= (tptp.aa_nat_complex H B3) tptp.one_one_complex))) (=> (= (tptp.groups6464643781859351333omplex G C4) (tptp.groups6464643781859351333omplex H C4)) (= (tptp.groups6464643781859351333omplex G A4) (tptp.groups6464643781859351333omplex H B4))))))))) (forall ((C4 tptp.set_complex) (A4 tptp.set_complex) (B4 tptp.set_complex) (G tptp.fun_complex_complex) (H tptp.fun_complex_complex)) (=> (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex C4)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.ord_le211207098394363844omplex A4) C4)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.ord_le211207098394363844omplex B4) C4)) (=> (forall ((A3 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex A3) (tptp.minus_811609699411566653omplex C4 A4))) (= (tptp.aa_complex_complex G A3) tptp.one_one_complex))) (=> (forall ((B3 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex B3) (tptp.minus_811609699411566653omplex C4 B4))) (= (tptp.aa_complex_complex H B3) tptp.one_one_complex))) (=> (= (tptp.groups3708469109370488835omplex G C4) (tptp.groups3708469109370488835omplex H C4)) (= (tptp.groups3708469109370488835omplex G A4) (tptp.groups3708469109370488835omplex H B4))))))))) (forall ((C4 tptp.set_real) (A4 tptp.set_real) (B4 tptp.set_real) (G tptp.fun_real_real) (H tptp.fun_real_real)) (=> (tptp.finite_finite_real C4) (=> (tptp.ord_less_eq_set_real A4 C4) (=> (tptp.ord_less_eq_set_real B4 C4) (=> (forall ((A3 tptp.real)) (=> (tptp.member_real A3 (tptp.minus_minus_set_real C4 A4)) (= (tptp.aa_real_real G A3) tptp.one_one_real))) (=> (forall ((B3 tptp.real)) (=> (tptp.member_real B3 (tptp.minus_minus_set_real C4 B4)) (= (tptp.aa_real_real H B3) tptp.one_one_real))) (=> (= (tptp.groups1681761925125756287l_real G C4) (tptp.groups1681761925125756287l_real H C4)) (= (tptp.groups1681761925125756287l_real G A4) (tptp.groups1681761925125756287l_real H B4))))))))) (forall ((C4 tptp.set_nat) (A4 tptp.set_nat) (B4 tptp.set_nat) (G tptp.fun_nat_real) (H tptp.fun_nat_real)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat C4)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat A4) C4)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat B4) C4)) (=> (forall ((A3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat A3) (tptp.minus_minus_set_nat C4 A4))) (= (tptp.aa_nat_real G A3) tptp.one_one_real))) (=> (forall ((B3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat B3) (tptp.minus_minus_set_nat C4 B4))) (= (tptp.aa_nat_real H B3) tptp.one_one_real))) (=> (= (tptp.groups129246275422532515t_real G C4) (tptp.groups129246275422532515t_real H C4)) (= (tptp.groups129246275422532515t_real G A4) (tptp.groups129246275422532515t_real H B4))))))))) (forall ((C4 tptp.set_complex) (A4 tptp.set_complex) (B4 tptp.set_complex) (G tptp.fun_complex_real) (H tptp.fun_complex_real)) (=> (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex C4)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.ord_le211207098394363844omplex A4) C4)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.ord_le211207098394363844omplex B4) C4)) (=> (forall ((A3 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex A3) (tptp.minus_811609699411566653omplex C4 A4))) (= (tptp.aa_complex_real G A3) tptp.one_one_real))) (=> (forall ((B3 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex B3) (tptp.minus_811609699411566653omplex C4 B4))) (= (tptp.aa_complex_real H B3) tptp.one_one_real))) (=> (= (tptp.groups766887009212190081x_real G C4) (tptp.groups766887009212190081x_real H C4)) (= (tptp.groups766887009212190081x_real G A4) (tptp.groups766887009212190081x_real H B4))))))))) (forall ((C4 tptp.set_real) (A4 tptp.set_real) (B4 tptp.set_real) (G tptp.fun_real_rat) (H tptp.fun_real_rat)) (=> (tptp.finite_finite_real C4) (=> (tptp.ord_less_eq_set_real A4 C4) (=> (tptp.ord_less_eq_set_real B4 C4) (=> (forall ((A3 tptp.real)) (=> (tptp.member_real A3 (tptp.minus_minus_set_real C4 A4)) (= (tptp.aa_real_rat G A3) tptp.one_one_rat))) (=> (forall ((B3 tptp.real)) (=> (tptp.member_real B3 (tptp.minus_minus_set_real C4 B4)) (= (tptp.aa_real_rat H B3) tptp.one_one_rat))) (=> (= (tptp.groups4061424788464935467al_rat G C4) (tptp.groups4061424788464935467al_rat H C4)) (= (tptp.groups4061424788464935467al_rat G A4) (tptp.groups4061424788464935467al_rat H B4))))))))) (forall ((C4 tptp.set_nat) (A4 tptp.set_nat) (B4 tptp.set_nat) (G tptp.fun_nat_rat) (H tptp.fun_nat_rat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat C4)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat A4) C4)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat B4) C4)) (=> (forall ((A3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat A3) (tptp.minus_minus_set_nat C4 A4))) (= (tptp.aa_nat_rat G A3) tptp.one_one_rat))) (=> (forall ((B3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat B3) (tptp.minus_minus_set_nat C4 B4))) (= (tptp.aa_nat_rat H B3) tptp.one_one_rat))) (=> (= (tptp.groups73079841787564623at_rat G C4) (tptp.groups73079841787564623at_rat H C4)) (= (tptp.groups73079841787564623at_rat G A4) (tptp.groups73079841787564623at_rat H B4))))))))) (forall ((C4 tptp.set_complex) (A4 tptp.set_complex) (B4 tptp.set_complex) (G tptp.fun_complex_rat) (H tptp.fun_complex_rat)) (=> (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex C4)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.ord_le211207098394363844omplex A4) C4)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.ord_le211207098394363844omplex B4) C4)) (=> (forall ((A3 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex A3) (tptp.minus_811609699411566653omplex C4 A4))) (= (tptp.aa_complex_rat G A3) tptp.one_one_rat))) (=> (forall ((B3 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex B3) (tptp.minus_811609699411566653omplex C4 B4))) (= (tptp.aa_complex_rat H B3) tptp.one_one_rat))) (=> (= (tptp.groups225925009352817453ex_rat G C4) (tptp.groups225925009352817453ex_rat H C4)) (= (tptp.groups225925009352817453ex_rat G A4) (tptp.groups225925009352817453ex_rat H B4))))))))) (forall ((C4 tptp.set_real) (A4 tptp.set_real) (B4 tptp.set_real) (G tptp.fun_real_nat) (H tptp.fun_real_nat)) (=> (tptp.finite_finite_real C4) (=> (tptp.ord_less_eq_set_real A4 C4) (=> (tptp.ord_less_eq_set_real B4 C4) (=> (forall ((A3 tptp.real)) (=> (tptp.member_real A3 (tptp.minus_minus_set_real C4 A4)) (= (tptp.aa_real_nat G A3) tptp.one_one_nat))) (=> (forall ((B3 tptp.real)) (=> (tptp.member_real B3 (tptp.minus_minus_set_real C4 B4)) (= (tptp.aa_real_nat H B3) tptp.one_one_nat))) (=> (= (tptp.groups4696554848551431203al_nat G C4) (tptp.groups4696554848551431203al_nat H C4)) (= (tptp.groups4696554848551431203al_nat G A4) (tptp.groups4696554848551431203al_nat H B4))))))))) (forall ((T3 tptp.set_nat) (S2 tptp.set_nat) (G tptp.fun_nat_complex)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat T3)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat S2) T3)) (=> (forall ((X4 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X4) (tptp.minus_minus_set_nat T3 S2))) (= (tptp.aa_nat_complex G X4) tptp.one_one_complex))) (= (tptp.groups6464643781859351333omplex G S2) (tptp.groups6464643781859351333omplex G T3)))))) (forall ((T3 tptp.set_complex) (S2 tptp.set_complex) (G tptp.fun_complex_complex)) (=> (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex T3)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.ord_le211207098394363844omplex S2) T3)) (=> (forall ((X4 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex X4) (tptp.minus_811609699411566653omplex T3 S2))) (= (tptp.aa_complex_complex G X4) tptp.one_one_complex))) (= (tptp.groups3708469109370488835omplex G S2) (tptp.groups3708469109370488835omplex G T3)))))) (forall ((T3 tptp.set_nat) (S2 tptp.set_nat) (G tptp.fun_nat_real)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat T3)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat S2) T3)) (=> (forall ((X4 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X4) (tptp.minus_minus_set_nat T3 S2))) (= (tptp.aa_nat_real G X4) tptp.one_one_real))) (= (tptp.groups129246275422532515t_real G S2) (tptp.groups129246275422532515t_real G T3)))))) (forall ((T3 tptp.set_complex) (S2 tptp.set_complex) (G tptp.fun_complex_real)) (=> (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex T3)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.ord_le211207098394363844omplex S2) T3)) (=> (forall ((X4 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex X4) (tptp.minus_811609699411566653omplex T3 S2))) (= (tptp.aa_complex_real G X4) tptp.one_one_real))) (= (tptp.groups766887009212190081x_real G S2) (tptp.groups766887009212190081x_real G T3)))))) (forall ((T3 tptp.set_nat) (S2 tptp.set_nat) (G tptp.fun_nat_rat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat T3)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat S2) T3)) (=> (forall ((X4 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X4) (tptp.minus_minus_set_nat T3 S2))) (= (tptp.aa_nat_rat G X4) tptp.one_one_rat))) (= (tptp.groups73079841787564623at_rat G S2) (tptp.groups73079841787564623at_rat G T3)))))) (forall ((T3 tptp.set_complex) (S2 tptp.set_complex) (G tptp.fun_complex_rat)) (=> (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex T3)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.ord_le211207098394363844omplex S2) T3)) (=> (forall ((X4 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex X4) (tptp.minus_811609699411566653omplex T3 S2))) (= (tptp.aa_complex_rat G X4) tptp.one_one_rat))) (= (tptp.groups225925009352817453ex_rat G S2) (tptp.groups225925009352817453ex_rat G T3)))))) (forall ((T3 tptp.set_complex) (S2 tptp.set_complex) (G tptp.fun_complex_nat)) (=> (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex T3)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.ord_le211207098394363844omplex S2) T3)) (=> (forall ((X4 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex X4) (tptp.minus_811609699411566653omplex T3 S2))) (= (tptp.aa_complex_nat G X4) tptp.one_one_nat))) (= (tptp.groups861055069439313189ex_nat G S2) (tptp.groups861055069439313189ex_nat G T3)))))) (forall ((T3 tptp.set_complex) (S2 tptp.set_complex) (G tptp.fun_complex_int)) (=> (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex T3)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.ord_le211207098394363844omplex S2) T3)) (=> (forall ((X4 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex X4) (tptp.minus_811609699411566653omplex T3 S2))) (= (tptp.aa_complex_int G X4) tptp.one_one_int))) (= (tptp.groups858564598930262913ex_int G S2) (tptp.groups858564598930262913ex_int G T3)))))) (forall ((T3 tptp.set_int) (S2 tptp.set_int) (G tptp.fun_int_complex)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int T3)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int S2) T3)) (=> (forall ((X4 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X4) (tptp.minus_minus_set_int T3 S2))) (= (tptp.aa_int_complex G X4) tptp.one_one_complex))) (= (tptp.groups7440179247065528705omplex G S2) (tptp.groups7440179247065528705omplex G T3)))))) (forall ((T3 tptp.set_int) (S2 tptp.set_int) (G tptp.fun_int_real)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int T3)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int S2) T3)) (=> (forall ((X4 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X4) (tptp.minus_minus_set_int T3 S2))) (= (tptp.aa_int_real G X4) tptp.one_one_real))) (= (tptp.groups2316167850115554303t_real G S2) (tptp.groups2316167850115554303t_real G T3)))))) (forall ((T3 tptp.set_nat) (S2 tptp.set_nat) (G tptp.fun_nat_complex)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat T3)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat S2) T3)) (=> (forall ((X4 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X4) (tptp.minus_minus_set_nat T3 S2))) (= (tptp.aa_nat_complex G X4) tptp.one_one_complex))) (= (tptp.groups6464643781859351333omplex G T3) (tptp.groups6464643781859351333omplex G S2)))))) (forall ((T3 tptp.set_complex) (S2 tptp.set_complex) (G tptp.fun_complex_complex)) (=> (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex T3)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.ord_le211207098394363844omplex S2) T3)) (=> (forall ((X4 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex X4) (tptp.minus_811609699411566653omplex T3 S2))) (= (tptp.aa_complex_complex G X4) tptp.one_one_complex))) (= (tptp.groups3708469109370488835omplex G T3) (tptp.groups3708469109370488835omplex G S2)))))) (forall ((T3 tptp.set_nat) (S2 tptp.set_nat) (G tptp.fun_nat_real)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat T3)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat S2) T3)) (=> (forall ((X4 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X4) (tptp.minus_minus_set_nat T3 S2))) (= (tptp.aa_nat_real G X4) tptp.one_one_real))) (= (tptp.groups129246275422532515t_real G T3) (tptp.groups129246275422532515t_real G S2)))))) (forall ((T3 tptp.set_complex) (S2 tptp.set_complex) (G tptp.fun_complex_real)) (=> (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex T3)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.ord_le211207098394363844omplex S2) T3)) (=> (forall ((X4 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex X4) (tptp.minus_811609699411566653omplex T3 S2))) (= (tptp.aa_complex_real G X4) tptp.one_one_real))) (= (tptp.groups766887009212190081x_real G T3) (tptp.groups766887009212190081x_real G S2)))))) (forall ((T3 tptp.set_nat) (S2 tptp.set_nat) (G tptp.fun_nat_rat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat T3)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat S2) T3)) (=> (forall ((X4 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X4) (tptp.minus_minus_set_nat T3 S2))) (= (tptp.aa_nat_rat G X4) tptp.one_one_rat))) (= (tptp.groups73079841787564623at_rat G T3) (tptp.groups73079841787564623at_rat G S2)))))) (forall ((T3 tptp.set_complex) (S2 tptp.set_complex) (G tptp.fun_complex_rat)) (=> (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex T3)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.ord_le211207098394363844omplex S2) T3)) (=> (forall ((X4 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex X4) (tptp.minus_811609699411566653omplex T3 S2))) (= (tptp.aa_complex_rat G X4) tptp.one_one_rat))) (= (tptp.groups225925009352817453ex_rat G T3) (tptp.groups225925009352817453ex_rat G S2)))))) (forall ((T3 tptp.set_complex) (S2 tptp.set_complex) (G tptp.fun_complex_nat)) (=> (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex T3)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.ord_le211207098394363844omplex S2) T3)) (=> (forall ((X4 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex X4) (tptp.minus_811609699411566653omplex T3 S2))) (= (tptp.aa_complex_nat G X4) tptp.one_one_nat))) (= (tptp.groups861055069439313189ex_nat G T3) (tptp.groups861055069439313189ex_nat G S2)))))) (forall ((T3 tptp.set_complex) (S2 tptp.set_complex) (G tptp.fun_complex_int)) (=> (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex T3)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.ord_le211207098394363844omplex S2) T3)) (=> (forall ((X4 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex X4) (tptp.minus_811609699411566653omplex T3 S2))) (= (tptp.aa_complex_int G X4) tptp.one_one_int))) (= (tptp.groups858564598930262913ex_int G T3) (tptp.groups858564598930262913ex_int G S2)))))) (forall ((T3 tptp.set_int) (S2 tptp.set_int) (G tptp.fun_int_complex)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int T3)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int S2) T3)) (=> (forall ((X4 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X4) (tptp.minus_minus_set_int T3 S2))) (= (tptp.aa_int_complex G X4) tptp.one_one_complex))) (= (tptp.groups7440179247065528705omplex G T3) (tptp.groups7440179247065528705omplex G S2)))))) (forall ((T3 tptp.set_int) (S2 tptp.set_int) (G tptp.fun_int_real)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int T3)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int S2) T3)) (=> (forall ((X4 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X4) (tptp.minus_minus_set_int T3 S2))) (= (tptp.aa_int_real G X4) tptp.one_one_real))) (= (tptp.groups2316167850115554303t_real G T3) (tptp.groups2316167850115554303t_real G S2)))))) (forall ((T3 tptp.set_real) (S2 tptp.set_real) (H tptp.fun_real_complex) (G tptp.fun_real_complex)) (=> (tptp.finite_finite_real T3) (=> (tptp.ord_less_eq_set_real S2 T3) (=> (forall ((X4 tptp.real)) (=> (tptp.member_real X4 (tptp.minus_minus_set_real T3 S2)) (= (tptp.aa_real_complex H X4) tptp.one_one_complex))) (=> (forall ((X4 tptp.real)) (=> (tptp.member_real X4 S2) (= (tptp.aa_real_complex G X4) (tptp.aa_real_complex H X4)))) (= (tptp.groups713298508707869441omplex G S2) (tptp.groups713298508707869441omplex H T3))))))) (forall ((T3 tptp.set_nat) (S2 tptp.set_nat) (H tptp.fun_nat_complex) (G tptp.fun_nat_complex)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat T3)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat S2) T3)) (=> (forall ((X4 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X4) (tptp.minus_minus_set_nat T3 S2))) (= (tptp.aa_nat_complex H X4) tptp.one_one_complex))) (=> (forall ((X4 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X4) S2)) (= (tptp.aa_nat_complex G X4) (tptp.aa_nat_complex H X4)))) (= (tptp.groups6464643781859351333omplex G S2) (tptp.groups6464643781859351333omplex H T3))))))) (forall ((T3 tptp.set_complex) (S2 tptp.set_complex) (H tptp.fun_complex_complex) (G tptp.fun_complex_complex)) (=> (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex T3)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.ord_le211207098394363844omplex S2) T3)) (=> (forall ((X4 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex X4) (tptp.minus_811609699411566653omplex T3 S2))) (= (tptp.aa_complex_complex H X4) tptp.one_one_complex))) (=> (forall ((X4 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex X4) S2)) (= (tptp.aa_complex_complex G X4) (tptp.aa_complex_complex H X4)))) (= (tptp.groups3708469109370488835omplex G S2) (tptp.groups3708469109370488835omplex H T3))))))) (forall ((T3 tptp.set_real) (S2 tptp.set_real) (H tptp.fun_real_real) (G tptp.fun_real_real)) (=> (tptp.finite_finite_real T3) (=> (tptp.ord_less_eq_set_real S2 T3) (=> (forall ((X4 tptp.real)) (=> (tptp.member_real X4 (tptp.minus_minus_set_real T3 S2)) (= (tptp.aa_real_real H X4) tptp.one_one_real))) (=> (forall ((X4 tptp.real)) (=> (tptp.member_real X4 S2) (= (tptp.aa_real_real G X4) (tptp.aa_real_real H X4)))) (= (tptp.groups1681761925125756287l_real G S2) (tptp.groups1681761925125756287l_real H T3))))))) (forall ((T3 tptp.set_nat) (S2 tptp.set_nat) (H tptp.fun_nat_real) (G tptp.fun_nat_real)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat T3)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat S2) T3)) (=> (forall ((X4 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X4) (tptp.minus_minus_set_nat T3 S2))) (= (tptp.aa_nat_real H X4) tptp.one_one_real))) (=> (forall ((X4 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X4) S2)) (= (tptp.aa_nat_real G X4) (tptp.aa_nat_real H X4)))) (= (tptp.groups129246275422532515t_real G S2) (tptp.groups129246275422532515t_real H T3))))))) (forall ((T3 tptp.set_complex) (S2 tptp.set_complex) (H tptp.fun_complex_real) (G tptp.fun_complex_real)) (=> (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex T3)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.ord_le211207098394363844omplex S2) T3)) (=> (forall ((X4 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex X4) (tptp.minus_811609699411566653omplex T3 S2))) (= (tptp.aa_complex_real H X4) tptp.one_one_real))) (=> (forall ((X4 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex X4) S2)) (= (tptp.aa_complex_real G X4) (tptp.aa_complex_real H X4)))) (= (tptp.groups766887009212190081x_real G S2) (tptp.groups766887009212190081x_real H T3))))))) (forall ((T3 tptp.set_real) (S2 tptp.set_real) (H tptp.fun_real_rat) (G tptp.fun_real_rat)) (=> (tptp.finite_finite_real T3) (=> (tptp.ord_less_eq_set_real S2 T3) (=> (forall ((X4 tptp.real)) (=> (tptp.member_real X4 (tptp.minus_minus_set_real T3 S2)) (= (tptp.aa_real_rat H X4) tptp.one_one_rat))) (=> (forall ((X4 tptp.real)) (=> (tptp.member_real X4 S2) (= (tptp.aa_real_rat G X4) (tptp.aa_real_rat H X4)))) (= (tptp.groups4061424788464935467al_rat G S2) (tptp.groups4061424788464935467al_rat H T3))))))) (forall ((T3 tptp.set_nat) (S2 tptp.set_nat) (H tptp.fun_nat_rat) (G tptp.fun_nat_rat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat T3)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat S2) T3)) (=> (forall ((X4 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X4) (tptp.minus_minus_set_nat T3 S2))) (= (tptp.aa_nat_rat H X4) tptp.one_one_rat))) (=> (forall ((X4 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X4) S2)) (= (tptp.aa_nat_rat G X4) (tptp.aa_nat_rat H X4)))) (= (tptp.groups73079841787564623at_rat G S2) (tptp.groups73079841787564623at_rat H T3))))))) (forall ((T3 tptp.set_complex) (S2 tptp.set_complex) (H tptp.fun_complex_rat) (G tptp.fun_complex_rat)) (=> (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex T3)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.ord_le211207098394363844omplex S2) T3)) (=> (forall ((X4 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex X4) (tptp.minus_811609699411566653omplex T3 S2))) (= (tptp.aa_complex_rat H X4) tptp.one_one_rat))) (=> (forall ((X4 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex X4) S2)) (= (tptp.aa_complex_rat G X4) (tptp.aa_complex_rat H X4)))) (= (tptp.groups225925009352817453ex_rat G S2) (tptp.groups225925009352817453ex_rat H T3))))))) (forall ((T3 tptp.set_real) (S2 tptp.set_real) (H tptp.fun_real_nat) (G tptp.fun_real_nat)) (=> (tptp.finite_finite_real T3) (=> (tptp.ord_less_eq_set_real S2 T3) (=> (forall ((X4 tptp.real)) (=> (tptp.member_real X4 (tptp.minus_minus_set_real T3 S2)) (= (tptp.aa_real_nat H X4) tptp.one_one_nat))) (=> (forall ((X4 tptp.real)) (=> (tptp.member_real X4 S2) (= (tptp.aa_real_nat G X4) (tptp.aa_real_nat H X4)))) (= (tptp.groups4696554848551431203al_nat G S2) (tptp.groups4696554848551431203al_nat H T3))))))) (forall ((T3 tptp.set_real) (S2 tptp.set_real) (G tptp.fun_real_complex) (H tptp.fun_real_complex)) (=> (tptp.finite_finite_real T3) (=> (tptp.ord_less_eq_set_real S2 T3) (=> (forall ((X4 tptp.real)) (=> (tptp.member_real X4 (tptp.minus_minus_set_real T3 S2)) (= (tptp.aa_real_complex G X4) tptp.one_one_complex))) (=> (forall ((X4 tptp.real)) (=> (tptp.member_real X4 S2) (= (tptp.aa_real_complex G X4) (tptp.aa_real_complex H X4)))) (= (tptp.groups713298508707869441omplex G T3) (tptp.groups713298508707869441omplex H S2))))))) (forall ((T3 tptp.set_nat) (S2 tptp.set_nat) (G tptp.fun_nat_complex) (H tptp.fun_nat_complex)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat T3)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat S2) T3)) (=> (forall ((X4 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X4) (tptp.minus_minus_set_nat T3 S2))) (= (tptp.aa_nat_complex G X4) tptp.one_one_complex))) (=> (forall ((X4 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X4) S2)) (= (tptp.aa_nat_complex G X4) (tptp.aa_nat_complex H X4)))) (= (tptp.groups6464643781859351333omplex G T3) (tptp.groups6464643781859351333omplex H S2))))))) (forall ((T3 tptp.set_complex) (S2 tptp.set_complex) (G tptp.fun_complex_complex) (H tptp.fun_complex_complex)) (=> (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex T3)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.ord_le211207098394363844omplex S2) T3)) (=> (forall ((X4 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex X4) (tptp.minus_811609699411566653omplex T3 S2))) (= (tptp.aa_complex_complex G X4) tptp.one_one_complex))) (=> (forall ((X4 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex X4) S2)) (= (tptp.aa_complex_complex G X4) (tptp.aa_complex_complex H X4)))) (= (tptp.groups3708469109370488835omplex G T3) (tptp.groups3708469109370488835omplex H S2))))))) (forall ((T3 tptp.set_real) (S2 tptp.set_real) (G tptp.fun_real_real) (H tptp.fun_real_real)) (=> (tptp.finite_finite_real T3) (=> (tptp.ord_less_eq_set_real S2 T3) (=> (forall ((X4 tptp.real)) (=> (tptp.member_real X4 (tptp.minus_minus_set_real T3 S2)) (= (tptp.aa_real_real G X4) tptp.one_one_real))) (=> (forall ((X4 tptp.real)) (=> (tptp.member_real X4 S2) (= (tptp.aa_real_real G X4) (tptp.aa_real_real H X4)))) (= (tptp.groups1681761925125756287l_real G T3) (tptp.groups1681761925125756287l_real H S2))))))) (forall ((T3 tptp.set_nat) (S2 tptp.set_nat) (G tptp.fun_nat_real) (H tptp.fun_nat_real)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat T3)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat S2) T3)) (=> (forall ((X4 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X4) (tptp.minus_minus_set_nat T3 S2))) (= (tptp.aa_nat_real G X4) tptp.one_one_real))) (=> (forall ((X4 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X4) S2)) (= (tptp.aa_nat_real G X4) (tptp.aa_nat_real H X4)))) (= (tptp.groups129246275422532515t_real G T3) (tptp.groups129246275422532515t_real H S2))))))) (forall ((T3 tptp.set_complex) (S2 tptp.set_complex) (G tptp.fun_complex_real) (H tptp.fun_complex_real)) (=> (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex T3)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.ord_le211207098394363844omplex S2) T3)) (=> (forall ((X4 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex X4) (tptp.minus_811609699411566653omplex T3 S2))) (= (tptp.aa_complex_real G X4) tptp.one_one_real))) (=> (forall ((X4 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex X4) S2)) (= (tptp.aa_complex_real G X4) (tptp.aa_complex_real H X4)))) (= (tptp.groups766887009212190081x_real G T3) (tptp.groups766887009212190081x_real H S2))))))) (forall ((T3 tptp.set_real) (S2 tptp.set_real) (G tptp.fun_real_rat) (H tptp.fun_real_rat)) (=> (tptp.finite_finite_real T3) (=> (tptp.ord_less_eq_set_real S2 T3) (=> (forall ((X4 tptp.real)) (=> (tptp.member_real X4 (tptp.minus_minus_set_real T3 S2)) (= (tptp.aa_real_rat G X4) tptp.one_one_rat))) (=> (forall ((X4 tptp.real)) (=> (tptp.member_real X4 S2) (= (tptp.aa_real_rat G X4) (tptp.aa_real_rat H X4)))) (= (tptp.groups4061424788464935467al_rat G T3) (tptp.groups4061424788464935467al_rat H S2))))))) (forall ((T3 tptp.set_nat) (S2 tptp.set_nat) (G tptp.fun_nat_rat) (H tptp.fun_nat_rat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat T3)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat S2) T3)) (=> (forall ((X4 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X4) (tptp.minus_minus_set_nat T3 S2))) (= (tptp.aa_nat_rat G X4) tptp.one_one_rat))) (=> (forall ((X4 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X4) S2)) (= (tptp.aa_nat_rat G X4) (tptp.aa_nat_rat H X4)))) (= (tptp.groups73079841787564623at_rat G T3) (tptp.groups73079841787564623at_rat H S2))))))) (forall ((T3 tptp.set_complex) (S2 tptp.set_complex) (G tptp.fun_complex_rat) (H tptp.fun_complex_rat)) (=> (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex T3)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.ord_le211207098394363844omplex S2) T3)) (=> (forall ((X4 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex X4) (tptp.minus_811609699411566653omplex T3 S2))) (= (tptp.aa_complex_rat G X4) tptp.one_one_rat))) (=> (forall ((X4 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex X4) S2)) (= (tptp.aa_complex_rat G X4) (tptp.aa_complex_rat H X4)))) (= (tptp.groups225925009352817453ex_rat G T3) (tptp.groups225925009352817453ex_rat H S2))))))) (forall ((T3 tptp.set_real) (S2 tptp.set_real) (G tptp.fun_real_nat) (H tptp.fun_real_nat)) (=> (tptp.finite_finite_real T3) (=> (tptp.ord_less_eq_set_real S2 T3) (=> (forall ((X4 tptp.real)) (=> (tptp.member_real X4 (tptp.minus_minus_set_real T3 S2)) (= (tptp.aa_real_nat G X4) tptp.one_one_nat))) (=> (forall ((X4 tptp.real)) (=> (tptp.member_real X4 S2) (= (tptp.aa_real_nat G X4) (tptp.aa_real_nat H X4)))) (= (tptp.groups4696554848551431203al_nat G T3) (tptp.groups4696554848551431203al_nat H S2))))))) (forall ((G tptp.fun_nat_real) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N))) (= (tptp.groups129246275422532515t_real G (tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat _let_1)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.groups129246275422532515t_real G (tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat N))) (tptp.aa_nat_real G _let_1))))) (forall ((G tptp.fun_nat_rat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N))) (= (tptp.groups73079841787564623at_rat G (tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat _let_1)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.groups73079841787564623at_rat G (tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat N))) (tptp.aa_nat_rat G _let_1))))) (forall ((G tptp.fun_nat_nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N))) (= (tptp.groups708209901874060359at_nat G (tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat _let_1)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.groups708209901874060359at_nat G (tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat N))) (tptp.aa_nat_nat G _let_1))))) (forall ((G tptp.fun_nat_int) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N))) (= (tptp.groups705719431365010083at_int G (tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat _let_1)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.groups705719431365010083at_int G (tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat N))) (tptp.aa_nat_int G _let_1))))) (forall ((M tptp.nat) (N tptp.nat) (G tptp.fun_nat_real)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)) (= (tptp.groups129246275422532515t_real G (tptp.set_or1269000886237332187st_nat M N)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real G M)) (tptp.groups129246275422532515t_real G (tptp.set_or1269000886237332187st_nat (tptp.aa_nat_nat tptp.suc M) N)))))) (forall ((M tptp.nat) (N tptp.nat) (G tptp.fun_nat_rat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)) (= (tptp.groups73079841787564623at_rat G (tptp.set_or1269000886237332187st_nat M N)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat G M)) (tptp.groups73079841787564623at_rat G (tptp.set_or1269000886237332187st_nat (tptp.aa_nat_nat tptp.suc M) N)))))) (forall ((M tptp.nat) (N tptp.nat) (G tptp.fun_nat_nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)) (= (tptp.groups708209901874060359at_nat G (tptp.set_or1269000886237332187st_nat M N)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat G M)) (tptp.groups708209901874060359at_nat G (tptp.set_or1269000886237332187st_nat (tptp.aa_nat_nat tptp.suc M) N)))))) (forall ((M tptp.nat) (N tptp.nat) (G tptp.fun_nat_int)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)) (= (tptp.groups705719431365010083at_int G (tptp.set_or1269000886237332187st_nat M N)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int G M)) (tptp.groups705719431365010083at_int G (tptp.set_or1269000886237332187st_nat (tptp.aa_nat_nat tptp.suc M) N)))))) (forall ((M tptp.nat) (N tptp.nat) (G tptp.fun_nat_real)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) _let_1)) (= (tptp.groups129246275422532515t_real G (tptp.set_or1269000886237332187st_nat M _let_1)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real G _let_1)) (tptp.groups129246275422532515t_real G (tptp.set_or1269000886237332187st_nat M N))))))) (forall ((M tptp.nat) (N tptp.nat) (G tptp.fun_nat_rat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) _let_1)) (= (tptp.groups73079841787564623at_rat G (tptp.set_or1269000886237332187st_nat M _let_1)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat G _let_1)) (tptp.groups73079841787564623at_rat G (tptp.set_or1269000886237332187st_nat M N))))))) (forall ((M tptp.nat) (N tptp.nat) (G tptp.fun_nat_nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) _let_1)) (= (tptp.groups708209901874060359at_nat G (tptp.set_or1269000886237332187st_nat M _let_1)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat G _let_1)) (tptp.groups708209901874060359at_nat G (tptp.set_or1269000886237332187st_nat M N))))))) (forall ((M tptp.nat) (N tptp.nat) (G tptp.fun_nat_int)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) _let_1)) (= (tptp.groups705719431365010083at_int G (tptp.set_or1269000886237332187st_nat M _let_1)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int G _let_1)) (tptp.groups705719431365010083at_int G (tptp.set_or1269000886237332187st_nat M N))))))) (forall ((G tptp.fun_nat_real) (N tptp.nat)) (= (tptp.groups129246275422532515t_real G (tptp.set_ord_lessThan_nat (tptp.aa_nat_nat tptp.suc N))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real G tptp.zero_zero_nat)) (tptp.groups129246275422532515t_real (tptp.aTP_Lamm_hw G) (tptp.set_ord_lessThan_nat N))))) (forall ((G tptp.fun_nat_rat) (N tptp.nat)) (= (tptp.groups73079841787564623at_rat G (tptp.set_ord_lessThan_nat (tptp.aa_nat_nat tptp.suc N))) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat G tptp.zero_zero_nat)) (tptp.groups73079841787564623at_rat (tptp.aTP_Lamm_ht G) (tptp.set_ord_lessThan_nat N))))) (forall ((G tptp.fun_nat_nat) (N tptp.nat)) (= (tptp.groups708209901874060359at_nat G (tptp.set_ord_lessThan_nat (tptp.aa_nat_nat tptp.suc N))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat G tptp.zero_zero_nat)) (tptp.groups708209901874060359at_nat (tptp.aTP_Lamm_hv G) (tptp.set_ord_lessThan_nat N))))) (forall ((G tptp.fun_nat_int) (N tptp.nat)) (= (tptp.groups705719431365010083at_int G (tptp.set_ord_lessThan_nat (tptp.aa_nat_nat tptp.suc N))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int G tptp.zero_zero_nat)) (tptp.groups705719431365010083at_int (tptp.aTP_Lamm_hu G) (tptp.set_ord_lessThan_nat N))))) (forall ((M tptp.nat) (N tptp.nat) (G tptp.fun_nat_real)) (let ((_let_1 (tptp.set_or1269000886237332187st_nat M N))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.groups129246275422532515t_real G _let_1)) (tptp.aa_nat_real G (tptp.aa_nat_nat tptp.suc N))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real G M)) (tptp.groups129246275422532515t_real (tptp.aTP_Lamm_hw G) _let_1)))))) (forall ((M tptp.nat) (N tptp.nat) (G tptp.fun_nat_rat)) (let ((_let_1 (tptp.set_or1269000886237332187st_nat M N))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.groups73079841787564623at_rat G _let_1)) (tptp.aa_nat_rat G (tptp.aa_nat_nat tptp.suc N))) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat G M)) (tptp.groups73079841787564623at_rat (tptp.aTP_Lamm_ht G) _let_1)))))) (forall ((M tptp.nat) (N tptp.nat) (G tptp.fun_nat_nat)) (let ((_let_1 (tptp.set_or1269000886237332187st_nat M N))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.groups708209901874060359at_nat G _let_1)) (tptp.aa_nat_nat G (tptp.aa_nat_nat tptp.suc N))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat G M)) (tptp.groups708209901874060359at_nat (tptp.aTP_Lamm_hv G) _let_1)))))) (forall ((M tptp.nat) (N tptp.nat) (G tptp.fun_nat_int)) (let ((_let_1 (tptp.set_or1269000886237332187st_nat M N))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.groups705719431365010083at_int G _let_1)) (tptp.aa_nat_int G (tptp.aa_nat_nat tptp.suc N))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int G M)) (tptp.groups705719431365010083at_int (tptp.aTP_Lamm_hu G) _let_1)))))) (forall ((G tptp.fun_nat_rat) (N tptp.nat)) (= (tptp.groups2906978787729119204at_rat G (tptp.set_ord_atMost_nat (tptp.aa_nat_nat tptp.suc N))) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_nat_rat G tptp.zero_zero_nat)) (tptp.groups2906978787729119204at_rat (tptp.aTP_Lamm_ht G) (tptp.set_ord_atMost_nat N))))) (forall ((G tptp.fun_nat_int) (N tptp.nat)) (= (tptp.groups3539618377306564664at_int G (tptp.set_ord_atMost_nat (tptp.aa_nat_nat tptp.suc N))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_nat_int G tptp.zero_zero_nat)) (tptp.groups3539618377306564664at_int (tptp.aTP_Lamm_hu G) (tptp.set_ord_atMost_nat N))))) (forall ((G tptp.fun_nat_nat) (N tptp.nat)) (= (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat G) (tptp.set_ord_atMost_nat (tptp.aa_nat_nat tptp.suc N))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat G tptp.zero_zero_nat)) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aTP_Lamm_hv G)) (tptp.set_ord_atMost_nat N))))) (forall ((G tptp.fun_nat_real) (N tptp.nat)) (= (tptp.groups6591440286371151544t_real G (tptp.set_ord_atMost_nat (tptp.aa_nat_nat tptp.suc N))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real G tptp.zero_zero_nat)) (tptp.groups6591440286371151544t_real (tptp.aTP_Lamm_hw G) (tptp.set_ord_atMost_nat N))))) (forall ((F tptp.fun_nat_complex) (I tptp.nat)) (= (tptp.groups2073611262835488442omplex (tptp.aTP_Lamm_lb F) (tptp.set_ord_atMost_nat I)) (tptp.aa_complex_complex (tptp.minus_minus_complex (tptp.aa_nat_complex F tptp.zero_zero_nat)) (tptp.aa_nat_complex F (tptp.aa_nat_nat tptp.suc I))))) (forall ((F tptp.fun_nat_rat) (I tptp.nat)) (= (tptp.groups2906978787729119204at_rat (tptp.aTP_Lamm_lc F) (tptp.set_ord_atMost_nat I)) (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_nat_rat F tptp.zero_zero_nat)) (tptp.aa_nat_rat F (tptp.aa_nat_nat tptp.suc I))))) (forall ((F tptp.fun_nat_int) (I tptp.nat)) (= (tptp.groups3539618377306564664at_int (tptp.aTP_Lamm_ld F) (tptp.set_ord_atMost_nat I)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_nat_int F tptp.zero_zero_nat)) (tptp.aa_nat_int F (tptp.aa_nat_nat tptp.suc I))))) (forall ((F tptp.fun_nat_real) (I tptp.nat)) (= (tptp.groups6591440286371151544t_real (tptp.aTP_Lamm_le F) (tptp.set_ord_atMost_nat I)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_nat_real F tptp.zero_zero_nat)) (tptp.aa_nat_real F (tptp.aa_nat_nat tptp.suc I))))) (forall ((C tptp.fun_nat_complex) (N tptp.nat) (D tptp.fun_nat_complex)) (= (forall ((X3 tptp.complex)) (let ((_let_1 (tptp.set_ord_atMost_nat N))) (= (tptp.groups2073611262835488442omplex (tptp.aa_com8181001469867462503omplex (tptp.aTP_Lamm_kn C) X3) _let_1) (tptp.groups2073611262835488442omplex (tptp.aa_com8181001469867462503omplex (tptp.aTP_Lamm_kn D) X3) _let_1)))) (forall ((I4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I4) N)) (= (tptp.aa_nat_complex C I4) (tptp.aa_nat_complex D I4)))))) (forall ((C tptp.fun_nat_real) (N tptp.nat) (D tptp.fun_nat_real)) (= (forall ((X3 tptp.real)) (let ((_let_1 (tptp.set_ord_atMost_nat N))) (= (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_kl C) X3) _let_1) (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_kl D) X3) _let_1)))) (forall ((I4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I4) N)) (= (tptp.aa_nat_real C I4) (tptp.aa_nat_real D I4)))))) (forall ((A tptp.fun_nat_int) (B4 tptp.int)) (=> (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.aa_nat_int A N2)))) (=> (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.groups3539618377306564664at_int A (tptp.set_ord_atMost_nat N2))) B4))) (tptp.summable_int A)))) (forall ((A tptp.fun_nat_nat) (B4 tptp.nat)) (=> (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) (tptp.aa_nat_nat A N2)))) (=> (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat A) (tptp.set_ord_atMost_nat N2))) B4))) (tptp.summable_nat A)))) (forall ((A tptp.fun_nat_real) (B4 tptp.real)) (=> (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_nat_real A N2)))) (=> (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.groups6591440286371151544t_real A (tptp.set_ord_atMost_nat N2))) B4))) (tptp.summable_real A)))) (forall ((F tptp.fun_nat_complex) (A tptp.nat) (B2 tptp.nat)) (= (tptp.groups6464643781859351333omplex F (tptp.set_or1269000886237332187st_nat A B2)) (tptp.aa_complex_complex (tptp.set_fo1517530859248394432omplex (tptp.aTP_Lamm_pq F) A B2) tptp.one_one_complex))) (forall ((F tptp.fun_nat_real) (A tptp.nat) (B2 tptp.nat)) (= (tptp.groups129246275422532515t_real F (tptp.set_or1269000886237332187st_nat A B2)) (tptp.aa_real_real (tptp.aa_nat_fun_real_real (tptp.set_fo3111899725591712190t_real (tptp.aTP_Lamm_pr F) A) B2) tptp.one_one_real))) (forall ((F tptp.fun_nat_rat) (A tptp.nat) (B2 tptp.nat)) (= (tptp.groups73079841787564623at_rat F (tptp.set_or1269000886237332187st_nat A B2)) (tptp.aa_rat_rat (tptp.set_fo1949268297981939178at_rat (tptp.aTP_Lamm_ps F) A B2) tptp.one_one_rat))) (forall ((F tptp.fun_nat_nat) (A tptp.nat) (B2 tptp.nat)) (= (tptp.groups708209901874060359at_nat F (tptp.set_or1269000886237332187st_nat A B2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.set_fo2584398358068434914at_nat (tptp.aTP_Lamm_pt F) A) B2) tptp.one_one_nat))) (forall ((F tptp.fun_nat_int) (A tptp.nat) (B2 tptp.nat)) (= (tptp.groups705719431365010083at_int F (tptp.set_or1269000886237332187st_nat A B2)) (tptp.aa_int_int (tptp.set_fo2581907887559384638at_int (tptp.aTP_Lamm_pu F) A B2) tptp.one_one_int))) (forall ((A4 tptp.set_complex) (F tptp.fun_complex_real) (G tptp.fun_complex_real)) (=> (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex A4)) (=> (forall ((I3 tptp.complex)) (let ((_let_1 (tptp.aa_complex_real F I3))) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex I3) A4)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) _let_1)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real _let_1) (tptp.aa_complex_real G I3))))))) (=> (not (= A4 tptp.bot_bot_set_complex)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.groups766887009212190081x_real F A4)) (tptp.groups766887009212190081x_real G A4))))))) (forall ((A4 tptp.set_nat) (F tptp.fun_nat_real) (G tptp.fun_nat_real)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A4)) (=> (forall ((I3 tptp.nat)) (let ((_let_1 (tptp.aa_nat_real F I3))) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat I3) A4)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) _let_1)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real _let_1) (tptp.aa_nat_real G I3))))))) (=> (not (= A4 tptp.bot_bot_set_nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.groups129246275422532515t_real F A4)) (tptp.groups129246275422532515t_real G A4))))))) (forall ((A4 tptp.set_int) (F tptp.fun_int_real) (G tptp.fun_int_real)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A4)) (=> (forall ((I3 tptp.int)) (let ((_let_1 (tptp.aa_int_real F I3))) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int I3) A4)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) _let_1)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real _let_1) (tptp.aa_int_real G I3))))))) (=> (not (= A4 tptp.bot_bot_set_int)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.groups2316167850115554303t_real F A4)) (tptp.groups2316167850115554303t_real G A4))))))) (forall ((A4 tptp.set_real) (F tptp.fun_real_real) (G tptp.fun_real_real)) (=> (tptp.finite_finite_real A4) (=> (forall ((I3 tptp.real)) (let ((_let_1 (tptp.aa_real_real F I3))) (=> (tptp.member_real I3 A4) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) _let_1)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real _let_1) (tptp.aa_real_real G I3))))))) (=> (not (= A4 tptp.bot_bot_set_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.groups1681761925125756287l_real F A4)) (tptp.groups1681761925125756287l_real G A4))))))) (forall ((A4 tptp.set_complex) (F tptp.fun_complex_rat) (G tptp.fun_complex_rat)) (=> (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex A4)) (=> (forall ((I3 tptp.complex)) (let ((_let_1 (tptp.aa_complex_rat F I3))) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex I3) A4)) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat _let_1) (tptp.aa_complex_rat G I3))))))) (=> (not (= A4 tptp.bot_bot_set_complex)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.groups225925009352817453ex_rat F A4)) (tptp.groups225925009352817453ex_rat G A4))))))) (forall ((A4 tptp.set_nat) (F tptp.fun_nat_rat) (G tptp.fun_nat_rat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A4)) (=> (forall ((I3 tptp.nat)) (let ((_let_1 (tptp.aa_nat_rat F I3))) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat I3) A4)) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat _let_1) (tptp.aa_nat_rat G I3))))))) (=> (not (= A4 tptp.bot_bot_set_nat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.groups73079841787564623at_rat F A4)) (tptp.groups73079841787564623at_rat G A4))))))) (forall ((A4 tptp.set_int) (F tptp.fun_int_rat) (G tptp.fun_int_rat)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A4)) (=> (forall ((I3 tptp.int)) (let ((_let_1 (tptp.aa_int_rat F I3))) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int I3) A4)) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat _let_1) (tptp.aa_int_rat G I3))))))) (=> (not (= A4 tptp.bot_bot_set_int)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.groups1072433553688619179nt_rat F A4)) (tptp.groups1072433553688619179nt_rat G A4))))))) (forall ((A4 tptp.set_real) (F tptp.fun_real_rat) (G tptp.fun_real_rat)) (=> (tptp.finite_finite_real A4) (=> (forall ((I3 tptp.real)) (let ((_let_1 (tptp.aa_real_rat F I3))) (=> (tptp.member_real I3 A4) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat _let_1) (tptp.aa_real_rat G I3))))))) (=> (not (= A4 tptp.bot_bot_set_real)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.groups4061424788464935467al_rat F A4)) (tptp.groups4061424788464935467al_rat G A4))))))) (forall ((A4 tptp.set_complex) (F tptp.fun_complex_nat) (G tptp.fun_complex_nat)) (=> (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex A4)) (=> (forall ((I3 tptp.complex)) (let ((_let_1 (tptp.aa_complex_nat F I3))) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex I3) A4)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) _let_1)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_1) (tptp.aa_complex_nat G I3))))))) (=> (not (= A4 tptp.bot_bot_set_complex)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.groups861055069439313189ex_nat F A4)) (tptp.groups861055069439313189ex_nat G A4))))))) (forall ((A4 tptp.set_int) (F tptp.fun_int_nat) (G tptp.fun_int_nat)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A4)) (=> (forall ((I3 tptp.int)) (let ((_let_1 (tptp.aa_int_nat F I3))) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int I3) A4)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) _let_1)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_1) (tptp.aa_int_nat G I3))))))) (=> (not (= A4 tptp.bot_bot_set_int)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.groups1707563613775114915nt_nat F A4)) (tptp.groups1707563613775114915nt_nat G A4))))))) (forall ((A4 tptp.set_nat) (F tptp.fun_nat_Code_integer)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A4)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.groups3455450783089532116nteger F A4))) (exists ((X3 tptp.nat)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) A4)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_nat_Code_integer F X3)))))))) (forall ((A4 tptp.set_int) (F tptp.fun_int_Code_integer)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A4)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.groups3827104343326376752nteger F A4))) (exists ((X3 tptp.int)) (and (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X3) A4)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_int_Code_integer F X3)))))))) (forall ((A4 tptp.set_complex) (F tptp.fun_co8153928105989009288nteger)) (=> (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex A4)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.groups8682486955453173170nteger F A4))) (exists ((X3 tptp.complex)) (and (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex X3) A4)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_com4217951221296830281nteger F X3)))))))) (forall ((A4 tptp.set_int) (F tptp.fun_int_nat)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A4)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.groups1707563613775114915nt_nat F A4))) (exists ((X3 tptp.int)) (and (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X3) A4)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_int_nat F X3)))))))) (forall ((A4 tptp.set_complex) (F tptp.fun_complex_nat)) (=> (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex A4)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.groups861055069439313189ex_nat F A4))) (exists ((X3 tptp.complex)) (and (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex X3) A4)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_complex_nat F X3)))))))) (forall ((A4 tptp.set_complex) (F tptp.fun_complex_int)) (=> (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex A4)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.groups858564598930262913ex_int F A4))) (exists ((X3 tptp.complex)) (and (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex X3) A4)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_complex_int F X3)))))))) (forall ((A4 tptp.set_nat) (F tptp.fun_nat_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A4)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.groups708209901874060359at_nat F A4))) (exists ((X3 tptp.nat)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) A4)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_nat_nat F X3)))))))) (forall ((A4 tptp.set_nat) (F tptp.fun_nat_int)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A4)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.groups705719431365010083at_int F A4))) (exists ((X3 tptp.nat)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) A4)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_nat_int F X3)))))))) (forall ((A4 tptp.set_int) (F tptp.fun_int_int)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A4)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.groups1705073143266064639nt_int F A4))) (exists ((X3 tptp.int)) (and (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X3) A4)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_int_int F X3)))))))) (forall ((R tptp.nat) (N tptp.nat)) (= (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_nat_fun_nat_nat tptp.aTP_Lamm_pv R)) (tptp.set_ord_atMost_nat N)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat R) N))) N))) (forall ((N tptp.nat) (M tptp.nat)) (= (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_nat_fun_nat_nat tptp.aTP_Lamm_pw N)) (tptp.set_ord_atMost_nat M)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N) M)) tptp.one_one_nat)) M))) (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N))) (= (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_nat_fun_nat_nat tptp.aTP_Lamm_pw N)) (tptp.set_ord_atMost_nat M)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat _let_1 M)) tptp.one_one_nat)) (tptp.aa_nat_nat _let_1 tptp.one_one_nat))))) (forall ((M tptp.nat) (N tptp.nat) (G tptp.fun_nat_real) (P2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N))) (let ((_let_2 (tptp.aa_nat_nat _let_1 P2))) (let ((_let_3 (tptp.aa_nat_nat _let_1 tptp.one_one_nat))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) _let_3)) (= (tptp.groups129246275422532515t_real G (tptp.set_or1269000886237332187st_nat M _let_2)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.groups129246275422532515t_real G (tptp.set_or1269000886237332187st_nat M N))) (tptp.groups129246275422532515t_real G (tptp.set_or1269000886237332187st_nat _let_3 _let_2))))))))) (forall ((M tptp.nat) (N tptp.nat) (G tptp.fun_nat_rat) (P2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N))) (let ((_let_2 (tptp.aa_nat_nat _let_1 P2))) (let ((_let_3 (tptp.aa_nat_nat _let_1 tptp.one_one_nat))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) _let_3)) (= (tptp.groups73079841787564623at_rat G (tptp.set_or1269000886237332187st_nat M _let_2)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.groups73079841787564623at_rat G (tptp.set_or1269000886237332187st_nat M N))) (tptp.groups73079841787564623at_rat G (tptp.set_or1269000886237332187st_nat _let_3 _let_2))))))))) (forall ((M tptp.nat) (N tptp.nat) (G tptp.fun_nat_nat) (P2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N))) (let ((_let_2 (tptp.aa_nat_nat _let_1 P2))) (let ((_let_3 (tptp.aa_nat_nat _let_1 tptp.one_one_nat))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) _let_3)) (= (tptp.groups708209901874060359at_nat G (tptp.set_or1269000886237332187st_nat M _let_2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.groups708209901874060359at_nat G (tptp.set_or1269000886237332187st_nat M N))) (tptp.groups708209901874060359at_nat G (tptp.set_or1269000886237332187st_nat _let_3 _let_2))))))))) (forall ((M tptp.nat) (N tptp.nat) (G tptp.fun_nat_int) (P2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N))) (let ((_let_2 (tptp.aa_nat_nat _let_1 P2))) (let ((_let_3 (tptp.aa_nat_nat _let_1 tptp.one_one_nat))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) _let_3)) (= (tptp.groups705719431365010083at_int G (tptp.set_or1269000886237332187st_nat M _let_2)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.groups705719431365010083at_int G (tptp.set_or1269000886237332187st_nat M N))) (tptp.groups705719431365010083at_int G (tptp.set_or1269000886237332187st_nat _let_3 _let_2))))))))) (forall ((I5 tptp.set_real) (Z tptp.fun_real_real) (W tptp.fun_real_real)) (=> (forall ((I3 tptp.real)) (=> (tptp.member_real I3 I5) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real (tptp.aa_real_real Z I3))) tptp.one_one_real)))) (=> (forall ((I3 tptp.real)) (=> (tptp.member_real I3 I5) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real (tptp.aa_real_real W I3))) tptp.one_one_real)))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.groups1681761925125756287l_real Z I5)) (tptp.groups1681761925125756287l_real W I5)))) (tptp.groups8097168146408367636l_real (tptp.aa_fun6946558556880649704l_real (tptp.aTP_Lamm_px Z) W) I5)))))) (forall ((I5 tptp.set_int) (Z tptp.fun_int_real) (W tptp.fun_int_real)) (=> (forall ((I3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int I3) I5)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real (tptp.aa_int_real Z I3))) tptp.one_one_real)))) (=> (forall ((I3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int I3) I5)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real (tptp.aa_int_real W I3))) tptp.one_one_real)))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.groups2316167850115554303t_real Z I5)) (tptp.groups2316167850115554303t_real W I5)))) (tptp.groups8778361861064173332t_real (tptp.aa_fun3252798400008884712t_real (tptp.aTP_Lamm_py Z) W) I5)))))) (forall ((I5 tptp.set_complex) (Z tptp.fun_complex_real) (W tptp.fun_complex_real)) (=> (forall ((I3 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex I3) I5)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real (tptp.aa_complex_real Z I3))) tptp.one_one_real)))) (=> (forall ((I3 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex I3) I5)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real (tptp.aa_complex_real W I3))) tptp.one_one_real)))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.groups766887009212190081x_real Z I5)) (tptp.groups766887009212190081x_real W I5)))) (tptp.groups5808333547571424918x_real (tptp.aa_fun8933909628229591020x_real (tptp.aTP_Lamm_pz Z) W) I5)))))) (forall ((I5 tptp.set_real) (Z tptp.fun_real_complex) (W tptp.fun_real_complex)) (=> (forall ((I3 tptp.real)) (=> (tptp.member_real I3 I5) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.aa_real_complex Z I3))) tptp.one_one_real)))) (=> (forall ((I3 tptp.real)) (=> (tptp.member_real I3 I5) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.aa_real_complex W I3))) tptp.one_one_real)))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.aa_complex_complex (tptp.minus_minus_complex (tptp.groups713298508707869441omplex Z I5)) (tptp.groups713298508707869441omplex W I5)))) (tptp.groups8097168146408367636l_real (tptp.aa_fun2786211375485122666l_real (tptp.aTP_Lamm_qa Z) W) I5)))))) (forall ((I5 tptp.set_int) (Z tptp.fun_int_complex) (W tptp.fun_int_complex)) (=> (forall ((I3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int I3) I5)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.aa_int_complex Z I3))) tptp.one_one_real)))) (=> (forall ((I3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int I3) I5)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.aa_int_complex W I3))) tptp.one_one_real)))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.aa_complex_complex (tptp.minus_minus_complex (tptp.groups7440179247065528705omplex Z I5)) (tptp.groups7440179247065528705omplex W I5)))) (tptp.groups8778361861064173332t_real (tptp.aa_fun1985759105522019690t_real (tptp.aTP_Lamm_qb Z) W) I5)))))) (forall ((I5 tptp.set_complex) (Z tptp.fun_complex_complex) (W tptp.fun_complex_complex)) (=> (forall ((I3 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex I3) I5)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.aa_complex_complex Z I3))) tptp.one_one_real)))) (=> (forall ((I3 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex I3) I5)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.aa_complex_complex W I3))) tptp.one_one_real)))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.aa_complex_complex (tptp.minus_minus_complex (tptp.groups3708469109370488835omplex Z I5)) (tptp.groups3708469109370488835omplex W I5)))) (tptp.groups5808333547571424918x_real (tptp.aa_fun1953249243402654830x_real (tptp.aTP_Lamm_qc Z) W) I5)))))) (forall ((I5 tptp.set_nat) (Z tptp.fun_nat_real) (W tptp.fun_nat_real)) (=> (forall ((I3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat I3) I5)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real (tptp.aa_nat_real Z I3))) tptp.one_one_real)))) (=> (forall ((I3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat I3) I5)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real (tptp.aa_nat_real W I3))) tptp.one_one_real)))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.groups129246275422532515t_real Z I5)) (tptp.groups129246275422532515t_real W I5)))) (tptp.groups6591440286371151544t_real (tptp.aa_fun1839206346889086768t_real (tptp.aTP_Lamm_qd Z) W) I5)))))) (forall ((I5 tptp.set_nat) (Z tptp.fun_nat_complex) (W tptp.fun_nat_complex)) (=> (forall ((I3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat I3) I5)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.aa_nat_complex Z I3))) tptp.one_one_real)))) (=> (forall ((I3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat I3) I5)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.aa_nat_complex W I3))) tptp.one_one_real)))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.aa_complex_complex (tptp.minus_minus_complex (tptp.groups6464643781859351333omplex Z I5)) (tptp.groups6464643781859351333omplex W I5)))) (tptp.groups6591440286371151544t_real (tptp.aa_fun7054779078796324018t_real (tptp.aTP_Lamm_qe Z) W) I5)))))) (forall ((C tptp.fun_nat_complex) (N tptp.nat)) (= (forall ((X3 tptp.complex)) (= (tptp.groups2073611262835488442omplex (tptp.aa_com8181001469867462503omplex (tptp.aTP_Lamm_kn C) X3) (tptp.set_ord_atMost_nat N)) tptp.zero_zero_complex)) (forall ((I4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I4) N)) (= (tptp.aa_nat_complex C I4) tptp.zero_zero_complex))))) (forall ((C tptp.fun_nat_real) (N tptp.nat)) (= (forall ((X3 tptp.real)) (= (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_kl C) X3) (tptp.set_ord_atMost_nat N)) tptp.zero_zero_real)) (forall ((I4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I4) N)) (= (tptp.aa_nat_real C I4) tptp.zero_zero_real))))) (forall ((C tptp.fun_nat_complex) (N tptp.nat) (K tptp.nat)) (=> (forall ((W2 tptp.complex)) (= (tptp.groups2073611262835488442omplex (tptp.aa_com8181001469867462503omplex (tptp.aTP_Lamm_kn C) W2) (tptp.set_ord_atMost_nat N)) tptp.zero_zero_complex)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) N)) (= (tptp.aa_nat_complex C K) tptp.zero_zero_complex)))) (forall ((C tptp.fun_nat_real) (N tptp.nat) (K tptp.nat)) (=> (forall ((W2 tptp.real)) (= (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_kl C) W2) (tptp.set_ord_atMost_nat N)) tptp.zero_zero_real)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) N)) (= (tptp.aa_nat_real C K) tptp.zero_zero_real)))) (forall ((G tptp.fun_nat_rat) (N tptp.nat)) (= (tptp.groups2906978787729119204at_rat G (tptp.set_ord_atMost_nat N)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_nat_rat G tptp.zero_zero_nat)) (tptp.groups2906978787729119204at_rat (tptp.aTP_Lamm_ht G) (tptp.set_ord_lessThan_nat N))))) (forall ((G tptp.fun_nat_int) (N tptp.nat)) (= (tptp.groups3539618377306564664at_int G (tptp.set_ord_atMost_nat N)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_nat_int G tptp.zero_zero_nat)) (tptp.groups3539618377306564664at_int (tptp.aTP_Lamm_hu G) (tptp.set_ord_lessThan_nat N))))) (forall ((G tptp.fun_nat_nat) (N tptp.nat)) (= (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat G) (tptp.set_ord_atMost_nat N)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat G tptp.zero_zero_nat)) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aTP_Lamm_hv G)) (tptp.set_ord_lessThan_nat N))))) (forall ((G tptp.fun_nat_real) (N tptp.nat)) (= (tptp.groups6591440286371151544t_real G (tptp.set_ord_atMost_nat N)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real G tptp.zero_zero_nat)) (tptp.groups6591440286371151544t_real (tptp.aTP_Lamm_hw G) (tptp.set_ord_lessThan_nat N))))) (forall ((F tptp.fun_nat_rat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) N))) (= (tptp.groups2906978787729119204at_rat F (tptp.set_ord_atMost_nat _let_1)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.groups2906978787729119204at_rat F (tptp.set_ord_atMost_nat M))) (tptp.groups2906978787729119204at_rat F (tptp.set_or1269000886237332187st_nat (tptp.aa_nat_nat tptp.suc M) _let_1)))))) (forall ((F tptp.fun_nat_int) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) N))) (= (tptp.groups3539618377306564664at_int F (tptp.set_ord_atMost_nat _let_1)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.groups3539618377306564664at_int F (tptp.set_ord_atMost_nat M))) (tptp.groups3539618377306564664at_int F (tptp.set_or1269000886237332187st_nat (tptp.aa_nat_nat tptp.suc M) _let_1)))))) (forall ((F tptp.fun_nat_nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) N))) (let ((_let_2 (tptp.groups3542108847815614940at_nat F))) (= (tptp.aa_set_nat_nat _let_2 (tptp.set_ord_atMost_nat _let_1)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_set_nat_nat _let_2 (tptp.set_ord_atMost_nat M))) (tptp.aa_set_nat_nat _let_2 (tptp.set_or1269000886237332187st_nat (tptp.aa_nat_nat tptp.suc M) _let_1))))))) (forall ((F tptp.fun_nat_real) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) N))) (= (tptp.groups6591440286371151544t_real F (tptp.set_ord_atMost_nat _let_1)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.groups6591440286371151544t_real F (tptp.set_ord_atMost_nat M))) (tptp.groups6591440286371151544t_real F (tptp.set_or1269000886237332187st_nat (tptp.aa_nat_nat tptp.suc M) _let_1)))))) (forall ((G tptp.fun_nat_fun_nat_nat) (N tptp.nat)) (= (tptp.groups977919841031483927at_nat (tptp.produc6842872674320459806at_nat G) (tptp.collec3392354462482085612at_nat (tptp.produc8955392012077580105t_bool (tptp.aTP_Lamm_qf N)))) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aTP_Lamm_qh G)) (tptp.set_ord_atMost_nat N)))) (forall ((G tptp.fun_nat_fun_nat_real) (N tptp.nat)) (= (tptp.groups4567486121110086003t_real (tptp.produc1703576794950452218t_real G) (tptp.collec3392354462482085612at_nat (tptp.produc8955392012077580105t_bool (tptp.aTP_Lamm_qf N)))) (tptp.groups6591440286371151544t_real (tptp.aTP_Lamm_qj G) (tptp.set_ord_atMost_nat N)))) (forall ((N tptp.nat) (M tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N) M)) (= (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat M) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat N)) (tptp.groups708209901874060359at_nat tptp.aTP_Lamm_al (tptp.set_or1269000886237332187st_nat (tptp.aa_nat_nat tptp.suc N) M)))))) (forall ((B4 tptp.set_real) (A4 tptp.set_real) (F tptp.fun_real_real)) (=> (tptp.finite_finite_real B4) (=> (tptp.ord_less_eq_set_real A4 B4) (=> (forall ((B3 tptp.real)) (=> (tptp.member_real B3 (tptp.minus_minus_set_real B4 A4)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.one_one_real) (tptp.aa_real_real F B3))))) (=> (forall ((A3 tptp.real)) (=> (tptp.member_real A3 A4) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_real_real F A3))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.groups1681761925125756287l_real F A4)) (tptp.groups1681761925125756287l_real F B4)))))))) (forall ((B4 tptp.set_nat) (A4 tptp.set_nat) (F tptp.fun_nat_real)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat B4)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat A4) B4)) (=> (forall ((B3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat B3) (tptp.minus_minus_set_nat B4 A4))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.one_one_real) (tptp.aa_nat_real F B3))))) (=> (forall ((A3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat A3) A4)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_nat_real F A3))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.groups129246275422532515t_real F A4)) (tptp.groups129246275422532515t_real F B4)))))))) (forall ((B4 tptp.set_complex) (A4 tptp.set_complex) (F tptp.fun_complex_real)) (=> (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex B4)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.ord_le211207098394363844omplex A4) B4)) (=> (forall ((B3 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex B3) (tptp.minus_811609699411566653omplex B4 A4))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.one_one_real) (tptp.aa_complex_real F B3))))) (=> (forall ((A3 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex A3) A4)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_complex_real F A3))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.groups766887009212190081x_real F A4)) (tptp.groups766887009212190081x_real F B4)))))))) (forall ((B4 tptp.set_real) (A4 tptp.set_real) (F tptp.fun_real_rat)) (=> (tptp.finite_finite_real B4) (=> (tptp.ord_less_eq_set_real A4 B4) (=> (forall ((B3 tptp.real)) (=> (tptp.member_real B3 (tptp.minus_minus_set_real B4 A4)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.one_one_rat) (tptp.aa_real_rat F B3))))) (=> (forall ((A3 tptp.real)) (=> (tptp.member_real A3 A4) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_real_rat F A3))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.groups4061424788464935467al_rat F A4)) (tptp.groups4061424788464935467al_rat F B4)))))))) (forall ((B4 tptp.set_nat) (A4 tptp.set_nat) (F tptp.fun_nat_rat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat B4)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat A4) B4)) (=> (forall ((B3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat B3) (tptp.minus_minus_set_nat B4 A4))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.one_one_rat) (tptp.aa_nat_rat F B3))))) (=> (forall ((A3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat A3) A4)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_nat_rat F A3))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.groups73079841787564623at_rat F A4)) (tptp.groups73079841787564623at_rat F B4)))))))) (forall ((B4 tptp.set_complex) (A4 tptp.set_complex) (F tptp.fun_complex_rat)) (=> (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex B4)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.ord_le211207098394363844omplex A4) B4)) (=> (forall ((B3 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex B3) (tptp.minus_811609699411566653omplex B4 A4))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.one_one_rat) (tptp.aa_complex_rat F B3))))) (=> (forall ((A3 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex A3) A4)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_complex_rat F A3))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.groups225925009352817453ex_rat F A4)) (tptp.groups225925009352817453ex_rat F B4)))))))) (forall ((B4 tptp.set_real) (A4 tptp.set_real) (F tptp.fun_real_int)) (=> (tptp.finite_finite_real B4) (=> (tptp.ord_less_eq_set_real A4 B4) (=> (forall ((B3 tptp.real)) (=> (tptp.member_real B3 (tptp.minus_minus_set_real B4 A4)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.one_one_int) (tptp.aa_real_int F B3))))) (=> (forall ((A3 tptp.real)) (=> (tptp.member_real A3 A4) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.aa_real_int F A3))))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.groups4694064378042380927al_int F A4)) (tptp.groups4694064378042380927al_int F B4)))))))) (forall ((B4 tptp.set_complex) (A4 tptp.set_complex) (F tptp.fun_complex_int)) (=> (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex B4)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.ord_le211207098394363844omplex A4) B4)) (=> (forall ((B3 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex B3) (tptp.minus_811609699411566653omplex B4 A4))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.one_one_int) (tptp.aa_complex_int F B3))))) (=> (forall ((A3 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex A3) A4)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.aa_complex_int F A3))))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.groups858564598930262913ex_int F A4)) (tptp.groups858564598930262913ex_int F B4)))))))) (forall ((B4 tptp.set_int) (A4 tptp.set_int) (F tptp.fun_int_real)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int B4)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int A4) B4)) (=> (forall ((B3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int B3) (tptp.minus_minus_set_int B4 A4))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.one_one_real) (tptp.aa_int_real F B3))))) (=> (forall ((A3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int A3) A4)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_int_real F A3))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.groups2316167850115554303t_real F A4)) (tptp.groups2316167850115554303t_real F B4)))))))) (forall ((B4 tptp.set_int) (A4 tptp.set_int) (F tptp.fun_int_rat)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int B4)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int A4) B4)) (=> (forall ((B3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int B3) (tptp.minus_minus_set_int B4 A4))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.one_one_rat) (tptp.aa_int_rat F B3))))) (=> (forall ((A3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int A3) A4)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_int_rat F A3))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.groups1072433553688619179nt_rat F A4)) (tptp.groups1072433553688619179nt_rat F B4)))))))) (forall ((M tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)) (= (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_nat_fun_nat_nat (tptp.aTP_Lamm_qk M) N)) (tptp.set_ord_atMost_nat M)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial (tptp.aa_nat_nat tptp.suc N)) M)))) (forall ((M tptp.nat) (N tptp.nat) (R tptp.nat)) (= (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_nat_fun_nat_nat (tptp.aa_nat3783148529270815480at_nat (tptp.aTP_Lamm_ql M) N) R)) (tptp.set_ord_atMost_nat R)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) N)) R))) (forall ((X tptp.complex) (N tptp.nat)) (let ((_let_1 (tptp.power_power_complex X))) (let ((_let_2 (tptp.minus_minus_complex tptp.one_one_complex))) (= (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_complex_complex _let_2 X)) (tptp.groups2073611262835488442omplex _let_1 (tptp.set_ord_atMost_nat N))) (tptp.aa_complex_complex _let_2 (tptp.aa_nat_complex _let_1 (tptp.aa_nat_nat tptp.suc N))))))) (forall ((X tptp.rat) (N tptp.nat)) (let ((_let_1 (tptp.power_power_rat X))) (let ((_let_2 (tptp.minus_minus_rat tptp.one_one_rat))) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat _let_2 X)) (tptp.groups2906978787729119204at_rat _let_1 (tptp.set_ord_atMost_nat N))) (tptp.aa_rat_rat _let_2 (tptp.aa_nat_rat _let_1 (tptp.aa_nat_nat tptp.suc N))))))) (forall ((X tptp.int) (N tptp.nat)) (let ((_let_1 (tptp.power_power_int X))) (let ((_let_2 (tptp.aa_int_fun_int_int tptp.minus_minus_int tptp.one_one_int))) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int _let_2 X)) (tptp.groups3539618377306564664at_int _let_1 (tptp.set_ord_atMost_nat N))) (tptp.aa_int_int _let_2 (tptp.aa_nat_int _let_1 (tptp.aa_nat_nat tptp.suc N))))))) (forall ((X tptp.real) (N tptp.nat)) (let ((_let_1 (tptp.aa_real_fun_nat_real tptp.power_power_real X))) (let ((_let_2 (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real tptp.one_one_real))) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real _let_2 X)) (tptp.groups6591440286371151544t_real _let_1 (tptp.set_ord_atMost_nat N))) (tptp.aa_real_real _let_2 (tptp.aa_nat_real _let_1 (tptp.aa_nat_nat tptp.suc N))))))) (forall ((C tptp.fun_nat_complex) (N tptp.nat)) (= (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex (tptp.collect_complex (tptp.aa_nat5545486172511849908x_bool (tptp.aTP_Lamm_qm C) N)))) (exists ((I4 tptp.nat)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I4) N)) (not (= (tptp.aa_nat_complex C I4) tptp.zero_zero_complex)))))) (forall ((C tptp.fun_nat_real) (N tptp.nat)) (= (tptp.finite_finite_real (tptp.collect_real (tptp.aa_nat_fun_real_bool (tptp.aTP_Lamm_qn C) N))) (exists ((I4 tptp.nat)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I4) N)) (not (= (tptp.aa_nat_real C I4) tptp.zero_zero_real)))))) (forall ((C tptp.fun_nat_complex) (K tptp.nat) (N tptp.nat)) (=> (not (= (tptp.aa_nat_complex C K) tptp.zero_zero_complex)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) N)) (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex (tptp.collect_complex (tptp.aa_nat5545486172511849908x_bool (tptp.aTP_Lamm_qm C) N))))))) (forall ((C tptp.fun_nat_real) (K tptp.nat) (N tptp.nat)) (=> (not (= (tptp.aa_nat_real C K) tptp.zero_zero_real)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) N)) (tptp.finite_finite_real (tptp.collect_real (tptp.aa_nat_fun_real_bool (tptp.aTP_Lamm_qn C) N)))))) (forall ((A tptp.rat) (N tptp.nat)) (= (tptp.aa_nat_rat (tptp.comm_s4028243227959126397er_rat A) (tptp.aa_nat_nat tptp.suc N)) (tptp.groups73079841787564623at_rat (tptp.aTP_Lamm_qo A) (tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat N)))) (forall ((A tptp.real) (N tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.comm_s7457072308508201937r_real A) (tptp.aa_nat_nat tptp.suc N)) (tptp.groups129246275422532515t_real (tptp.aa_real_fun_nat_real tptp.aTP_Lamm_qp A) (tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat N)))) (forall ((A tptp.nat) (N tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.comm_s4663373288045622133er_nat A) (tptp.aa_nat_nat tptp.suc N)) (tptp.groups708209901874060359at_nat (tptp.aa_nat_fun_nat_nat tptp.aTP_Lamm_qq A) (tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat N)))) (forall ((A tptp.int) (N tptp.nat)) (= (tptp.aa_nat_int (tptp.comm_s4660882817536571857er_int A) (tptp.aa_nat_nat tptp.suc N)) (tptp.groups705719431365010083at_int (tptp.aTP_Lamm_qr A) (tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat N)))) (forall ((C tptp.fun_nat_complex) (A tptp.complex) (N tptp.nat)) (=> (= (tptp.groups2073611262835488442omplex (tptp.aa_com8181001469867462503omplex (tptp.aTP_Lamm_kn C) A) (tptp.set_ord_atMost_nat N)) tptp.zero_zero_complex) (not (forall ((B3 tptp.fun_nat_complex)) (not (forall ((Z3 tptp.complex)) (= (tptp.groups2073611262835488442omplex (tptp.aa_com8181001469867462503omplex (tptp.aTP_Lamm_kn C) Z3) (tptp.set_ord_atMost_nat N)) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_complex_complex (tptp.minus_minus_complex Z3) A)) (tptp.groups2073611262835488442omplex (tptp.aa_com8181001469867462503omplex (tptp.aTP_Lamm_kn B3) Z3) (tptp.set_ord_lessThan_nat N)))))))))) (forall ((C tptp.fun_nat_rat) (A tptp.rat) (N tptp.nat)) (=> (= (tptp.groups2906978787729119204at_rat (tptp.aa_rat_fun_nat_rat (tptp.aTP_Lamm_qs C) A) (tptp.set_ord_atMost_nat N)) tptp.zero_zero_rat) (not (forall ((B3 tptp.fun_nat_rat)) (not (forall ((Z3 tptp.rat)) (= (tptp.groups2906978787729119204at_rat (tptp.aa_rat_fun_nat_rat (tptp.aTP_Lamm_qs C) Z3) (tptp.set_ord_atMost_nat N)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat (tptp.minus_minus_rat Z3) A)) (tptp.groups2906978787729119204at_rat (tptp.aa_rat_fun_nat_rat (tptp.aTP_Lamm_qs B3) Z3) (tptp.set_ord_lessThan_nat N)))))))))) (forall ((C tptp.fun_nat_int) (A tptp.int) (N tptp.nat)) (=> (= (tptp.groups3539618377306564664at_int (tptp.aa_int_fun_nat_int (tptp.aTP_Lamm_qt C) A) (tptp.set_ord_atMost_nat N)) tptp.zero_zero_int) (not (forall ((B3 tptp.fun_nat_int)) (not (forall ((Z3 tptp.int)) (= (tptp.groups3539618377306564664at_int (tptp.aa_int_fun_nat_int (tptp.aTP_Lamm_qt C) Z3) (tptp.set_ord_atMost_nat N)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int Z3) A)) (tptp.groups3539618377306564664at_int (tptp.aa_int_fun_nat_int (tptp.aTP_Lamm_qt B3) Z3) (tptp.set_ord_lessThan_nat N)))))))))) (forall ((C tptp.fun_nat_real) (A tptp.real) (N tptp.nat)) (=> (= (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_kl C) A) (tptp.set_ord_atMost_nat N)) tptp.zero_zero_real) (not (forall ((B3 tptp.fun_nat_real)) (not (forall ((Z3 tptp.real)) (= (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_kl C) Z3) (tptp.set_ord_atMost_nat N)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real Z3) A)) (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_kl B3) Z3) (tptp.set_ord_lessThan_nat N)))))))))) (forall ((C tptp.fun_nat_complex) (N tptp.nat) (A tptp.complex)) (exists ((B3 tptp.fun_nat_complex)) (forall ((Z3 tptp.complex)) (let ((_let_1 (tptp.set_ord_atMost_nat N))) (let ((_let_2 (tptp.aTP_Lamm_kn C))) (= (tptp.groups2073611262835488442omplex (tptp.aa_com8181001469867462503omplex _let_2 Z3) _let_1) (tptp.aa_complex_complex (tptp.plus_plus_complex (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_complex_complex (tptp.minus_minus_complex Z3) A)) (tptp.groups2073611262835488442omplex (tptp.aa_com8181001469867462503omplex (tptp.aTP_Lamm_kn B3) Z3) (tptp.set_ord_lessThan_nat N)))) (tptp.groups2073611262835488442omplex (tptp.aa_com8181001469867462503omplex _let_2 A) _let_1)))))))) (forall ((C tptp.fun_nat_rat) (N tptp.nat) (A tptp.rat)) (exists ((B3 tptp.fun_nat_rat)) (forall ((Z3 tptp.rat)) (let ((_let_1 (tptp.set_ord_atMost_nat N))) (let ((_let_2 (tptp.aTP_Lamm_qs C))) (= (tptp.groups2906978787729119204at_rat (tptp.aa_rat_fun_nat_rat _let_2 Z3) _let_1) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat (tptp.minus_minus_rat Z3) A)) (tptp.groups2906978787729119204at_rat (tptp.aa_rat_fun_nat_rat (tptp.aTP_Lamm_qs B3) Z3) (tptp.set_ord_lessThan_nat N)))) (tptp.groups2906978787729119204at_rat (tptp.aa_rat_fun_nat_rat _let_2 A) _let_1)))))))) (forall ((C tptp.fun_nat_int) (N tptp.nat) (A tptp.int)) (exists ((B3 tptp.fun_nat_int)) (forall ((Z3 tptp.int)) (let ((_let_1 (tptp.set_ord_atMost_nat N))) (let ((_let_2 (tptp.aTP_Lamm_qt C))) (= (tptp.groups3539618377306564664at_int (tptp.aa_int_fun_nat_int _let_2 Z3) _let_1) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int Z3) A)) (tptp.groups3539618377306564664at_int (tptp.aa_int_fun_nat_int (tptp.aTP_Lamm_qt B3) Z3) (tptp.set_ord_lessThan_nat N)))) (tptp.groups3539618377306564664at_int (tptp.aa_int_fun_nat_int _let_2 A) _let_1)))))))) (forall ((C tptp.fun_nat_real) (N tptp.nat) (A tptp.real)) (exists ((B3 tptp.fun_nat_real)) (forall ((Z3 tptp.real)) (let ((_let_1 (tptp.set_ord_atMost_nat N))) (let ((_let_2 (tptp.aTP_Lamm_kl C))) (= (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real _let_2 Z3) _let_1) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real Z3) A)) (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_kl B3) Z3) (tptp.set_ord_lessThan_nat N)))) (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real _let_2 A) _let_1)))))))) (forall ((A tptp.rat) (N tptp.nat)) (= (tptp.aa_nat_rat (tptp.comm_s4028243227959126397er_rat A) N) (tptp.groups73079841787564623at_rat (tptp.aa_nat_fun_nat_rat (tptp.aTP_Lamm_qu A) N) (tptp.set_or1269000886237332187st_nat tptp.one_one_nat N)))) (forall ((A tptp.real) (N tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.comm_s7457072308508201937r_real A) N) (tptp.groups129246275422532515t_real (tptp.aa_nat_fun_nat_real (tptp.aTP_Lamm_qv A) N) (tptp.set_or1269000886237332187st_nat tptp.one_one_nat N)))) (forall ((A tptp.nat) (N tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.comm_s4663373288045622133er_nat A) N) (tptp.groups708209901874060359at_nat (tptp.aa_nat_fun_nat_nat (tptp.aTP_Lamm_qw A) N) (tptp.set_or1269000886237332187st_nat tptp.one_one_nat N)))) (forall ((A tptp.int) (N tptp.nat)) (= (tptp.aa_nat_int (tptp.comm_s4660882817536571857er_int A) N) (tptp.groups705719431365010083at_int (tptp.aa_nat_fun_nat_int (tptp.aTP_Lamm_qx A) N) (tptp.set_or1269000886237332187st_nat tptp.one_one_nat N)))) (forall ((M tptp.nat) (N tptp.nat) (X tptp.complex)) (let ((_let_1 (tptp.power_power_complex X))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)) (= (tptp.groups2073611262835488442omplex _let_1 (tptp.set_or1269000886237332187st_nat M N)) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_nat_complex _let_1 M)) (tptp.groups2073611262835488442omplex _let_1 (tptp.set_ord_atMost_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) M)))))))) (forall ((M tptp.nat) (N tptp.nat) (X tptp.rat)) (let ((_let_1 (tptp.power_power_rat X))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)) (= (tptp.groups2906978787729119204at_rat _let_1 (tptp.set_or1269000886237332187st_nat M N)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat _let_1 M)) (tptp.groups2906978787729119204at_rat _let_1 (tptp.set_ord_atMost_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) M)))))))) (forall ((M tptp.nat) (N tptp.nat) (X tptp.int)) (let ((_let_1 (tptp.power_power_int X))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)) (= (tptp.groups3539618377306564664at_int _let_1 (tptp.set_or1269000886237332187st_nat M N)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int _let_1 M)) (tptp.groups3539618377306564664at_int _let_1 (tptp.set_ord_atMost_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) M)))))))) (forall ((M tptp.nat) (N tptp.nat) (X tptp.real)) (let ((_let_1 (tptp.aa_real_fun_nat_real tptp.power_power_real X))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)) (= (tptp.groups6591440286371151544t_real _let_1 (tptp.set_or1269000886237332187st_nat M N)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real _let_1 M)) (tptp.groups6591440286371151544t_real _let_1 (tptp.set_ord_atMost_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) M)))))))) (forall ((G tptp.fun_nat_fun_nat_nat) (N tptp.nat)) (= (tptp.groups977919841031483927at_nat (tptp.produc6842872674320459806at_nat G) (tptp.collec3392354462482085612at_nat (tptp.produc8955392012077580105t_bool (tptp.aTP_Lamm_qy N)))) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aTP_Lamm_qh G)) (tptp.set_ord_lessThan_nat N)))) (forall ((G tptp.fun_nat_fun_nat_real) (N tptp.nat)) (= (tptp.groups4567486121110086003t_real (tptp.produc1703576794950452218t_real G) (tptp.collec3392354462482085612at_nat (tptp.produc8955392012077580105t_bool (tptp.aTP_Lamm_qy N)))) (tptp.groups6591440286371151544t_real (tptp.aTP_Lamm_qj G) (tptp.set_ord_lessThan_nat N)))) (forall ((N tptp.nat) (M tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N) M)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat M)) (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat N)) (tptp.groups708209901874060359at_nat tptp.aTP_Lamm_al (tptp.set_or1269000886237332187st_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N) tptp.one_one_nat) M))))) (forall ((A tptp.fun_nat_complex) (B2 tptp.fun_nat_complex)) (=> (tptp.summable_real (tptp.aTP_Lamm_jm A)) (=> (tptp.summable_real (tptp.aTP_Lamm_jm B2)) (tptp.summable_complex (tptp.aa_fun2955221450537884980omplex (tptp.aTP_Lamm_ra A) B2))))) (forall ((A tptp.fun_nat_real) (B2 tptp.fun_nat_real)) (=> (tptp.summable_real (tptp.aTP_Lamm_jo A)) (=> (tptp.summable_real (tptp.aTP_Lamm_jo B2)) (tptp.summable_real (tptp.aa_fun1839206346889086768t_real (tptp.aTP_Lamm_rc A) B2))))) (forall ((N tptp.nat)) (= (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_nat_fun_nat_nat tptp.binomial N)) (tptp.set_ord_atMost_nat N)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N))) (forall ((A tptp.fun_nat_complex) (B2 tptp.fun_nat_complex)) (=> (tptp.summable_real (tptp.aTP_Lamm_jm A)) (=> (tptp.summable_real (tptp.aTP_Lamm_jm B2)) (= (tptp.aa_complex_complex (tptp.times_times_complex (tptp.suminf_complex A)) (tptp.suminf_complex B2)) (tptp.suminf_complex (tptp.aa_fun2955221450537884980omplex (tptp.aTP_Lamm_ra A) B2)))))) (forall ((A tptp.fun_nat_real) (B2 tptp.fun_nat_real)) (=> (tptp.summable_real (tptp.aTP_Lamm_jo A)) (=> (tptp.summable_real (tptp.aTP_Lamm_jo B2)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.suminf_real A)) (tptp.suminf_real B2)) (tptp.suminf_real (tptp.aa_fun1839206346889086768t_real (tptp.aTP_Lamm_rc A) B2)))))) (forall ((A tptp.nat) (B2 tptp.nat) (N tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) B2)) N) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_nat_fun_nat_nat (tptp.aa_nat3783148529270815480at_nat (tptp.aTP_Lamm_rd A) B2) N)) (tptp.set_ord_atMost_nat N)))) (forall ((G tptp.fun_nat_real) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.groups129246275422532515t_real G (tptp.set_or1269000886237332187st_nat (tptp.aa_nat_nat _let_1 M) (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat _let_1 N)))) (tptp.groups129246275422532515t_real (tptp.aTP_Lamm_pa G) (tptp.set_or1269000886237332187st_nat M N))))) (forall ((G tptp.fun_nat_rat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.groups73079841787564623at_rat G (tptp.set_or1269000886237332187st_nat (tptp.aa_nat_nat _let_1 M) (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat _let_1 N)))) (tptp.groups73079841787564623at_rat (tptp.aTP_Lamm_pb G) (tptp.set_or1269000886237332187st_nat M N))))) (forall ((G tptp.fun_nat_nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.groups708209901874060359at_nat G (tptp.set_or1269000886237332187st_nat (tptp.aa_nat_nat _let_1 M) (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat _let_1 N)))) (tptp.groups708209901874060359at_nat (tptp.aTP_Lamm_pc G) (tptp.set_or1269000886237332187st_nat M N))))) (forall ((G tptp.fun_nat_int) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.groups705719431365010083at_int G (tptp.set_or1269000886237332187st_nat (tptp.aa_nat_nat _let_1 M) (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat _let_1 N)))) (tptp.groups705719431365010083at_int (tptp.aTP_Lamm_pd G) (tptp.set_or1269000886237332187st_nat M N))))) (forall ((G tptp.fun_nat_rat) (N tptp.nat)) (= (tptp.groups2906978787729119204at_rat G (tptp.set_ord_atMost_nat (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N)))) (tptp.groups2906978787729119204at_rat (tptp.aTP_Lamm_it G) (tptp.set_ord_atMost_nat N)))) (forall ((G tptp.fun_nat_int) (N tptp.nat)) (= (tptp.groups3539618377306564664at_int G (tptp.set_ord_atMost_nat (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N)))) (tptp.groups3539618377306564664at_int (tptp.aTP_Lamm_iu G) (tptp.set_ord_atMost_nat N)))) (forall ((G tptp.fun_nat_nat) (N tptp.nat)) (= (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat G) (tptp.set_ord_atMost_nat (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N)))) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aTP_Lamm_iv G)) (tptp.set_ord_atMost_nat N)))) (forall ((G tptp.fun_nat_real) (N tptp.nat)) (= (tptp.groups6591440286371151544t_real G (tptp.set_ord_atMost_nat (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N)))) (tptp.groups6591440286371151544t_real (tptp.aTP_Lamm_iw G) (tptp.set_ord_atMost_nat N)))) (forall ((M tptp.nat) (A tptp.fun_nat_complex) (N tptp.nat) (B2 tptp.fun_nat_complex) (X tptp.complex)) (=> (forall ((I3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) I3)) (= (tptp.aa_nat_complex A I3) tptp.zero_zero_complex))) (=> (forall ((J2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N) J2)) (= (tptp.aa_nat_complex B2 J2) tptp.zero_zero_complex))) (= (tptp.aa_complex_complex (tptp.times_times_complex (tptp.groups2073611262835488442omplex (tptp.aa_com8181001469867462503omplex (tptp.aTP_Lamm_kn A) X) (tptp.set_ord_atMost_nat M))) (tptp.groups2073611262835488442omplex (tptp.aa_com8181001469867462503omplex (tptp.aTP_Lamm_kn B2) X) (tptp.set_ord_atMost_nat N))) (tptp.groups2073611262835488442omplex (tptp.aa_com8181001469867462503omplex (tptp.aa_fun3721018923249493343omplex (tptp.aTP_Lamm_re A) B2) X) (tptp.set_ord_atMost_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) N))))))) (forall ((M tptp.nat) (A tptp.fun_nat_rat) (N tptp.nat) (B2 tptp.fun_nat_rat) (X tptp.rat)) (=> (forall ((I3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) I3)) (= (tptp.aa_nat_rat A I3) tptp.zero_zero_rat))) (=> (forall ((J2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N) J2)) (= (tptp.aa_nat_rat B2 J2) tptp.zero_zero_rat))) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.groups2906978787729119204at_rat (tptp.aa_rat_fun_nat_rat (tptp.aTP_Lamm_qs A) X) (tptp.set_ord_atMost_nat M))) (tptp.groups2906978787729119204at_rat (tptp.aa_rat_fun_nat_rat (tptp.aTP_Lamm_qs B2) X) (tptp.set_ord_atMost_nat N))) (tptp.groups2906978787729119204at_rat (tptp.aa_rat_fun_nat_rat (tptp.aa_fun5559679822142647773at_rat (tptp.aTP_Lamm_rg A) B2) X) (tptp.set_ord_atMost_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) N))))))) (forall ((M tptp.nat) (A tptp.fun_nat_int) (N tptp.nat) (B2 tptp.fun_nat_int) (X tptp.int)) (=> (forall ((I3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) I3)) (= (tptp.aa_nat_int A I3) tptp.zero_zero_int))) (=> (forall ((J2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N) J2)) (= (tptp.aa_nat_int B2 J2) tptp.zero_zero_int))) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.groups3539618377306564664at_int (tptp.aa_int_fun_nat_int (tptp.aTP_Lamm_qt A) X) (tptp.set_ord_atMost_nat M))) (tptp.groups3539618377306564664at_int (tptp.aa_int_fun_nat_int (tptp.aTP_Lamm_qt B2) X) (tptp.set_ord_atMost_nat N))) (tptp.groups3539618377306564664at_int (tptp.aa_int_fun_nat_int (tptp.aa_fun2315716387381795033at_int (tptp.aTP_Lamm_ri A) B2) X) (tptp.set_ord_atMost_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) N))))))) (forall ((M tptp.nat) (A tptp.fun_nat_real) (N tptp.nat) (B2 tptp.fun_nat_real) (X tptp.real)) (=> (forall ((I3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) I3)) (= (tptp.aa_nat_real A I3) tptp.zero_zero_real))) (=> (forall ((J2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N) J2)) (= (tptp.aa_nat_real B2 J2) tptp.zero_zero_real))) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_kl A) X) (tptp.set_ord_atMost_nat M))) (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_kl B2) X) (tptp.set_ord_atMost_nat N))) (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real (tptp.aa_fun4732485501138722137t_real (tptp.aTP_Lamm_rj A) B2) X) (tptp.set_ord_atMost_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) N))))))) (forall ((A tptp.rat) (N tptp.nat)) (= (tptp.aa_nat_rat (tptp.comm_s4028243227959126397er_rat A) (tptp.aa_nat_nat tptp.suc N)) (tptp.groups73079841787564623at_rat (tptp.aa_nat_fun_nat_rat (tptp.aTP_Lamm_qu A) N) (tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat N)))) (forall ((A tptp.real) (N tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.comm_s7457072308508201937r_real A) (tptp.aa_nat_nat tptp.suc N)) (tptp.groups129246275422532515t_real (tptp.aa_nat_fun_nat_real (tptp.aTP_Lamm_qv A) N) (tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat N)))) (forall ((A tptp.nat) (N tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.comm_s4663373288045622133er_nat A) (tptp.aa_nat_nat tptp.suc N)) (tptp.groups708209901874060359at_nat (tptp.aa_nat_fun_nat_nat (tptp.aTP_Lamm_qw A) N) (tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat N)))) (forall ((A tptp.int) (N tptp.nat)) (= (tptp.aa_nat_int (tptp.comm_s4660882817536571857er_int A) (tptp.aa_nat_nat tptp.suc N)) (tptp.groups705719431365010083at_int (tptp.aa_nat_fun_nat_int (tptp.aTP_Lamm_qx A) N) (tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat N)))) (forall ((C tptp.fun_nat_complex) (N tptp.nat) (K tptp.complex)) (= (forall ((X3 tptp.complex)) (= (tptp.groups2073611262835488442omplex (tptp.aa_com8181001469867462503omplex (tptp.aTP_Lamm_kn C) X3) (tptp.set_ord_atMost_nat N)) K)) (and (= (tptp.aa_nat_complex C tptp.zero_zero_nat) K) (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) (tptp.set_or1269000886237332187st_nat tptp.one_one_nat N))) (= (tptp.aa_nat_complex C X3) tptp.zero_zero_complex)))))) (forall ((C tptp.fun_nat_real) (N tptp.nat) (K tptp.real)) (= (forall ((X3 tptp.real)) (= (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_kl C) X3) (tptp.set_ord_atMost_nat N)) K)) (and (= (tptp.aa_nat_real C tptp.zero_zero_nat) K) (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) (tptp.set_or1269000886237332187st_nat tptp.one_one_nat N))) (= (tptp.aa_nat_real C X3) tptp.zero_zero_real)))))) (forall ((A tptp.complex) (B2 tptp.complex) (N tptp.nat)) (= (tptp.aa_nat_complex (tptp.power_power_complex (tptp.aa_complex_complex (tptp.plus_plus_complex A) B2)) N) (tptp.groups2073611262835488442omplex (tptp.aa_nat6454746962644518025omplex (tptp.aa_com4347742694490471604omplex (tptp.aTP_Lamm_rk A) B2) N) (tptp.set_ord_atMost_nat N)))) (forall ((A tptp.rat) (B2 tptp.rat) (N tptp.nat)) (= (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) B2)) N) (tptp.groups2906978787729119204at_rat (tptp.aa_nat_fun_nat_rat (tptp.aa_rat250263598611652360at_rat (tptp.aTP_Lamm_rl A) B2) N) (tptp.set_ord_atMost_nat N)))) (forall ((A tptp.int) (B2 tptp.int) (N tptp.nat)) (= (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) B2)) N) (tptp.groups3539618377306564664at_int (tptp.aa_nat_fun_nat_int (tptp.aa_int431785320988601264at_int (tptp.aTP_Lamm_rm A) B2) N) (tptp.set_ord_atMost_nat N)))) (forall ((A tptp.nat) (B2 tptp.nat) (N tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) B2)) N) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_nat_fun_nat_nat (tptp.aa_nat3783148529270815480at_nat (tptp.aTP_Lamm_rd A) B2) N)) (tptp.set_ord_atMost_nat N)))) (forall ((A tptp.real) (B2 tptp.real) (N tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) B2)) N) (tptp.groups6591440286371151544t_real (tptp.aa_nat_fun_nat_real (tptp.aa_rea6853821027689443120t_real (tptp.aTP_Lamm_rn A) B2) N) (tptp.set_ord_atMost_nat N)))) (forall ((A tptp.rat) (B2 tptp.rat) (N tptp.nat)) (= (tptp.aa_nat_rat (tptp.comm_s4028243227959126397er_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) B2)) N) (tptp.groups2906978787729119204at_rat (tptp.aa_nat_fun_nat_rat (tptp.aa_rat250263598611652360at_rat (tptp.aTP_Lamm_ro A) B2) N) (tptp.set_ord_atMost_nat N)))) (forall ((A tptp.int) (B2 tptp.int) (N tptp.nat)) (= (tptp.aa_nat_int (tptp.comm_s4660882817536571857er_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) B2)) N) (tptp.groups3539618377306564664at_int (tptp.aa_nat_fun_nat_int (tptp.aa_int431785320988601264at_int (tptp.aTP_Lamm_rp A) B2) N) (tptp.set_ord_atMost_nat N)))) (forall ((A tptp.real) (B2 tptp.real) (N tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.comm_s7457072308508201937r_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) B2)) N) (tptp.groups6591440286371151544t_real (tptp.aa_nat_fun_nat_real (tptp.aa_rea6853821027689443120t_real (tptp.aTP_Lamm_rq A) B2) N) (tptp.set_ord_atMost_nat N)))) (forall ((M tptp.nat) (A tptp.fun_nat_nat) (N tptp.nat) (B2 tptp.fun_nat_nat) (X tptp.nat)) (=> (forall ((I3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) I3)) (= (tptp.aa_nat_nat A I3) tptp.zero_zero_nat))) (=> (forall ((J2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N) J2)) (= (tptp.aa_nat_nat B2 J2) tptp.zero_zero_nat))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_nat_fun_nat_nat (tptp.aTP_Lamm_rr A) X)) (tptp.set_ord_atMost_nat M))) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_nat_fun_nat_nat (tptp.aTP_Lamm_rr B2) X)) (tptp.set_ord_atMost_nat N))) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_nat_fun_nat_nat (tptp.aa_fun6650658898577385413at_nat (tptp.aTP_Lamm_rt A) B2) X)) (tptp.set_ord_atMost_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) N))))))) (forall ((N tptp.nat)) (= (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_nat_fun_nat_nat tptp.aTP_Lamm_ru N)) (tptp.set_ord_atMost_nat N)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N)) N))) (forall ((A tptp.fun_nat_complex) (B2 tptp.fun_nat_complex)) (=> (tptp.summable_real (tptp.aTP_Lamm_jm A)) (=> (tptp.summable_real (tptp.aTP_Lamm_jm B2)) (tptp.pp (tptp.aa_complex_bool (tptp.sums_complex (tptp.aa_fun2955221450537884980omplex (tptp.aTP_Lamm_ra A) B2)) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.suminf_complex A)) (tptp.suminf_complex B2))))))) (forall ((A tptp.fun_nat_real) (B2 tptp.fun_nat_real)) (=> (tptp.summable_real (tptp.aTP_Lamm_jo A)) (=> (tptp.summable_real (tptp.aTP_Lamm_jo B2)) (tptp.pp (tptp.aa_real_bool (tptp.sums_real (tptp.aa_fun1839206346889086768t_real (tptp.aTP_Lamm_rc A) B2)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.suminf_real A)) (tptp.suminf_real B2))))))) (forall ((P2 tptp.nat) (K tptp.nat) (G tptp.fun_nat_complex) (H tptp.fun_nat_complex)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.one_one_nat) P2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) P2)) (= (tptp.groups2073611262835488442omplex (tptp.aa_fun2955221450537884980omplex (tptp.aa_fun7497765718855568684omplex (tptp.aTP_Lamm_rv K) G) H) (tptp.set_ord_atMost_nat P2)) (tptp.groups2073611262835488442omplex (tptp.aa_fun2955221450537884980omplex (tptp.aa_fun7497765718855568684omplex (tptp.aTP_Lamm_ph K) G) H) (tptp.set_ord_atMost_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat P2) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)))))))) (forall ((P2 tptp.nat) (K tptp.nat) (G tptp.fun_nat_rat) (H tptp.fun_nat_rat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.one_one_nat) P2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) P2)) (= (tptp.groups2906978787729119204at_rat (tptp.aa_fun765758790203053448at_rat (tptp.aa_fun3638354034882855594at_rat (tptp.aTP_Lamm_rw K) G) H) (tptp.set_ord_atMost_nat P2)) (tptp.groups2906978787729119204at_rat (tptp.aa_fun765758790203053448at_rat (tptp.aa_fun3638354034882855594at_rat (tptp.aTP_Lamm_pl K) G) H) (tptp.set_ord_atMost_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat P2) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)))))))) (forall ((P2 tptp.nat) (K tptp.nat) (G tptp.fun_nat_int) (H tptp.fun_nat_int)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.one_one_nat) P2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) P2)) (= (tptp.groups3539618377306564664at_int (tptp.aa_fun5565043122120104496at_int (tptp.aa_fun5140708168904641446at_int (tptp.aTP_Lamm_rx K) G) H) (tptp.set_ord_atMost_nat P2)) (tptp.groups3539618377306564664at_int (tptp.aa_fun5565043122120104496at_int (tptp.aa_fun5140708168904641446at_int (tptp.aTP_Lamm_pp K) G) H) (tptp.set_ord_atMost_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat P2) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)))))))) (forall ((P2 tptp.nat) (K tptp.nat) (G tptp.fun_nat_nat) (H tptp.fun_nat_nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.one_one_nat) P2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) P2)) (= (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_fun5791449513213591928at_nat (tptp.aa_fun6854695580826382482at_nat (tptp.aTP_Lamm_ry K) G) H)) (tptp.set_ord_atMost_nat P2)) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_fun5791449513213591928at_nat (tptp.aa_fun6854695580826382482at_nat (tptp.aTP_Lamm_pn K) G) H)) (tptp.set_ord_atMost_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat P2) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)))))))) (forall ((P2 tptp.nat) (K tptp.nat) (G tptp.fun_nat_real) (H tptp.fun_nat_real)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.one_one_nat) P2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) P2)) (= (tptp.groups6591440286371151544t_real (tptp.aa_fun1839206346889086768t_real (tptp.aa_fun8674848580393814182t_real (tptp.aTP_Lamm_rz K) G) H) (tptp.set_ord_atMost_nat P2)) (tptp.groups6591440286371151544t_real (tptp.aa_fun1839206346889086768t_real (tptp.aa_fun8674848580393814182t_real (tptp.aTP_Lamm_pj K) G) H) (tptp.set_ord_atMost_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat P2) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)))))))) (forall ((N tptp.nat) (Z tptp.int) (A tptp.int)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.one_one_nat) N)) (= (= (tptp.aa_nat_int (tptp.power_power_int Z) N) A) (= (tptp.groups3539618377306564664at_int (tptp.aa_int_fun_nat_int (tptp.aa_int5842867502692063756at_int (tptp.aTP_Lamm_sa N) Z) A) (tptp.set_ord_atMost_nat N)) tptp.zero_zero_int)))) (forall ((N tptp.nat) (Z tptp.complex) (A tptp.complex)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.one_one_nat) N)) (= (= (tptp.aa_nat_complex (tptp.power_power_complex Z) N) A) (= (tptp.groups2073611262835488442omplex (tptp.aa_com8181001469867462503omplex (tptp.aa_com8177640530696437650omplex (tptp.aTP_Lamm_sb N) Z) A) (tptp.set_ord_atMost_nat N)) tptp.zero_zero_complex)))) (forall ((N tptp.nat) (Z tptp.code_integer) (A tptp.code_integer)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.one_one_nat) N)) (= (= (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger Z) N) A) (= (tptp.groups7501900531339628137nteger (tptp.aa_Cod1578151519121547077nteger (tptp.aa_Cod6397266357770349983nteger (tptp.aTP_Lamm_sc N) Z) A) (tptp.set_ord_atMost_nat N)) tptp.zero_z3403309356797280102nteger)))) (forall ((N tptp.nat) (Z tptp.rat) (A tptp.rat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.one_one_nat) N)) (= (= (tptp.aa_nat_rat (tptp.power_power_rat Z) N) A) (= (tptp.groups2906978787729119204at_rat (tptp.aa_rat_fun_nat_rat (tptp.aa_rat3146053865535587600at_rat (tptp.aTP_Lamm_sd N) Z) A) (tptp.set_ord_atMost_nat N)) tptp.zero_zero_rat)))) (forall ((N tptp.nat) (Z tptp.real) (A tptp.real)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.one_one_nat) N)) (= (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Z) N) A) (= (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real (tptp.aa_rea7841385751566875788t_real (tptp.aTP_Lamm_se N) Z) A) (tptp.set_ord_atMost_nat N)) tptp.zero_zero_real)))) (forall ((X tptp.complex) (N tptp.nat)) (let ((_let_1 (tptp.minus_minus_complex tptp.one_one_complex))) (let ((_let_2 (tptp.power_power_complex X))) (let ((_let_3 (tptp.groups2073611262835488442omplex _let_2 (tptp.set_ord_atMost_nat N)))) (let ((_let_4 (= X tptp.one_one_complex))) (and (=> _let_4 (= _let_3 (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N) tptp.one_one_nat)))) (=> (not _let_4) (= _let_3 (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex (tptp.aa_complex_complex _let_1 (tptp.aa_nat_complex _let_2 (tptp.aa_nat_nat tptp.suc N)))) (tptp.aa_complex_complex _let_1 X)))))))))) (forall ((X tptp.rat) (N tptp.nat)) (let ((_let_1 (tptp.minus_minus_rat tptp.one_one_rat))) (let ((_let_2 (tptp.power_power_rat X))) (let ((_let_3 (tptp.groups2906978787729119204at_rat _let_2 (tptp.set_ord_atMost_nat N)))) (let ((_let_4 (= X tptp.one_one_rat))) (and (=> _let_4 (= _let_3 (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N) tptp.one_one_nat)))) (=> (not _let_4) (= _let_3 (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_rat_rat _let_1 (tptp.aa_nat_rat _let_2 (tptp.aa_nat_nat tptp.suc N)))) (tptp.aa_rat_rat _let_1 X)))))))))) (forall ((X tptp.real) (N tptp.nat)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real tptp.one_one_real))) (let ((_let_2 (tptp.aa_real_fun_nat_real tptp.power_power_real X))) (let ((_let_3 (tptp.groups6591440286371151544t_real _let_2 (tptp.set_ord_atMost_nat N)))) (let ((_let_4 (= X tptp.one_one_real))) (and (=> _let_4 (= _let_3 (tptp.aa_nat_real tptp.semiri5074537144036343181t_real (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N) tptp.one_one_nat)))) (=> (not _let_4) (= _let_3 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real _let_1 (tptp.aa_nat_real _let_2 (tptp.aa_nat_nat tptp.suc N)))) (tptp.aa_real_real _let_1 X)))))))))) (forall ((N tptp.nat)) (=> (not (= N tptp.one_one_nat)) (= (tptp.groups2073611262835488442omplex (tptp.aTP_Lamm_sf N) (tptp.set_ord_atMost_nat N)) tptp.zero_zero_complex))) (forall ((N tptp.nat)) (=> (not (= N tptp.one_one_nat)) (= (tptp.groups7501900531339628137nteger (tptp.aTP_Lamm_sg N) (tptp.set_ord_atMost_nat N)) tptp.zero_z3403309356797280102nteger))) (forall ((N tptp.nat)) (=> (not (= N tptp.one_one_nat)) (= (tptp.groups2906978787729119204at_rat (tptp.aTP_Lamm_sh N) (tptp.set_ord_atMost_nat N)) tptp.zero_zero_rat))) (forall ((N tptp.nat)) (=> (not (= N tptp.one_one_nat)) (= (tptp.groups3539618377306564664at_int (tptp.aa_nat_fun_nat_int tptp.aTP_Lamm_si N) (tptp.set_ord_atMost_nat N)) tptp.zero_zero_int))) (forall ((N tptp.nat)) (=> (not (= N tptp.one_one_nat)) (= (tptp.groups6591440286371151544t_real (tptp.aa_nat_fun_nat_real tptp.aTP_Lamm_sj N) (tptp.set_ord_atMost_nat N)) tptp.zero_zero_real))) (forall ((N tptp.nat) (A tptp.fun_nat_complex) (X tptp.complex) (Y tptp.complex)) (let ((_let_1 (tptp.set_ord_atMost_nat N))) (let ((_let_2 (tptp.aTP_Lamm_kn A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.one_one_nat) N)) (= (tptp.aa_complex_complex (tptp.minus_minus_complex (tptp.groups2073611262835488442omplex (tptp.aa_com8181001469867462503omplex _let_2 X) _let_1)) (tptp.groups2073611262835488442omplex (tptp.aa_com8181001469867462503omplex _let_2 Y) _let_1)) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_complex_complex (tptp.minus_minus_complex X) Y)) (tptp.groups2073611262835488442omplex (tptp.aa_com8181001469867462503omplex (tptp.aa_com8177640530696437650omplex (tptp.aa_fun5031706661949900810omplex (tptp.aTP_Lamm_sl N) A) X) Y) (tptp.set_ord_lessThan_nat N)))))))) (forall ((N tptp.nat) (A tptp.fun_nat_rat) (X tptp.rat) (Y tptp.rat)) (let ((_let_1 (tptp.set_ord_atMost_nat N))) (let ((_let_2 (tptp.aTP_Lamm_qs A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.one_one_nat) N)) (= (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.groups2906978787729119204at_rat (tptp.aa_rat_fun_nat_rat _let_2 X) _let_1)) (tptp.groups2906978787729119204at_rat (tptp.aa_rat_fun_nat_rat _let_2 Y) _let_1)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat (tptp.minus_minus_rat X) Y)) (tptp.groups2906978787729119204at_rat (tptp.aa_rat_fun_nat_rat (tptp.aa_rat3146053865535587600at_rat (tptp.aa_fun8528462509625601970at_rat (tptp.aTP_Lamm_sn N) A) X) Y) (tptp.set_ord_lessThan_nat N)))))))) (forall ((N tptp.nat) (A tptp.fun_nat_int) (X tptp.int) (Y tptp.int)) (let ((_let_1 (tptp.set_ord_atMost_nat N))) (let ((_let_2 (tptp.aTP_Lamm_qt A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.one_one_nat) N)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.groups3539618377306564664at_int (tptp.aa_int_fun_nat_int _let_2 X) _let_1)) (tptp.groups3539618377306564664at_int (tptp.aa_int_fun_nat_int _let_2 Y) _let_1)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int X) Y)) (tptp.groups3539618377306564664at_int (tptp.aa_int_fun_nat_int (tptp.aa_int5842867502692063756at_int (tptp.aa_fun7421131748584218370at_int (tptp.aTP_Lamm_sp N) A) X) Y) (tptp.set_ord_lessThan_nat N)))))))) (forall ((N tptp.nat) (A tptp.fun_nat_real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.set_ord_atMost_nat N))) (let ((_let_2 (tptp.aTP_Lamm_kl A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.one_one_nat) N)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real _let_2 X) _let_1)) (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real _let_2 Y) _let_1)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real X) Y)) (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real (tptp.aa_rea7841385751566875788t_real (tptp.aa_fun2548873334967081986t_real (tptp.aTP_Lamm_sr N) A) X) Y) (tptp.set_ord_lessThan_nat N)))))))) (forall ((M tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat _let_1) M))) (= (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_nat_fun_nat_nat tptp.binomial (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat _let_2) tptp.one_one_nat))) (tptp.set_ord_atMost_nat M)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat _let_1) _let_2))))) (forall ((N tptp.nat)) (= (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_nat_fun_nat_nat tptp.aTP_Lamm_ss N)) (tptp.set_ord_atMost_nat N)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat N) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) tptp.one_one_nat))))) (forall ((N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (= (tptp.groups2073611262835488442omplex (tptp.aTP_Lamm_st N) (tptp.set_ord_atMost_nat N)) tptp.zero_zero_complex))) (forall ((N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (= (tptp.groups7501900531339628137nteger (tptp.aTP_Lamm_su N) (tptp.set_ord_atMost_nat N)) tptp.zero_z3403309356797280102nteger))) (forall ((N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (= (tptp.groups2906978787729119204at_rat (tptp.aTP_Lamm_sv N) (tptp.set_ord_atMost_nat N)) tptp.zero_zero_rat))) (forall ((N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (= (tptp.groups3539618377306564664at_int (tptp.aa_nat_fun_nat_int tptp.aTP_Lamm_sw N) (tptp.set_ord_atMost_nat N)) tptp.zero_zero_int))) (forall ((N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (= (tptp.groups6591440286371151544t_real (tptp.aa_nat_fun_nat_real tptp.aTP_Lamm_sx N) (tptp.set_ord_atMost_nat N)) tptp.zero_zero_real))) (forall ((E tptp.real) (C tptp.fun_nat_complex) (N tptp.nat)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) E)) (exists ((M8 tptp.real)) (forall ((Z3 tptp.complex)) (let ((_let_1 (tptp.aa_complex_real tptp.real_V1022390504157884413omplex Z3))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real M8) _let_1)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.groups2073611262835488442omplex (tptp.aa_com8181001469867462503omplex (tptp.aTP_Lamm_kn C) Z3) (tptp.set_ord_atMost_nat N)))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real E) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real _let_1) (tptp.aa_nat_nat tptp.suc N))))))))))) (forall ((E tptp.real) (C tptp.fun_nat_real) (N tptp.nat)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) E)) (exists ((M8 tptp.real)) (forall ((Z3 tptp.real)) (let ((_let_1 (tptp.aa_real_real tptp.real_V7735802525324610683m_real Z3))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real M8) _let_1)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_kl C) Z3) (tptp.set_ord_atMost_nat N)))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real E) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real _let_1) (tptp.aa_nat_nat tptp.suc N))))))))))) (forall ((N tptp.nat) (A tptp.fun_nat_complex) (X tptp.complex) (Y tptp.complex)) (let ((_let_1 (tptp.set_ord_atMost_nat N))) (let ((_let_2 (tptp.aTP_Lamm_kn A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.one_one_nat) N)) (= (tptp.aa_complex_complex (tptp.minus_minus_complex (tptp.groups2073611262835488442omplex (tptp.aa_com8181001469867462503omplex _let_2 X) _let_1)) (tptp.groups2073611262835488442omplex (tptp.aa_com8181001469867462503omplex _let_2 Y) _let_1)) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_complex_complex (tptp.minus_minus_complex X) Y)) (tptp.groups2073611262835488442omplex (tptp.aa_com8181001469867462503omplex (tptp.aa_com8177640530696437650omplex (tptp.aa_fun5031706661949900810omplex (tptp.aTP_Lamm_sz N) A) X) Y) (tptp.set_ord_lessThan_nat N)))))))) (forall ((N tptp.nat) (A tptp.fun_nat_rat) (X tptp.rat) (Y tptp.rat)) (let ((_let_1 (tptp.set_ord_atMost_nat N))) (let ((_let_2 (tptp.aTP_Lamm_qs A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.one_one_nat) N)) (= (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.groups2906978787729119204at_rat (tptp.aa_rat_fun_nat_rat _let_2 X) _let_1)) (tptp.groups2906978787729119204at_rat (tptp.aa_rat_fun_nat_rat _let_2 Y) _let_1)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat (tptp.minus_minus_rat X) Y)) (tptp.groups2906978787729119204at_rat (tptp.aa_rat_fun_nat_rat (tptp.aa_rat3146053865535587600at_rat (tptp.aa_fun8528462509625601970at_rat (tptp.aTP_Lamm_tb N) A) X) Y) (tptp.set_ord_lessThan_nat N)))))))) (forall ((N tptp.nat) (A tptp.fun_nat_int) (X tptp.int) (Y tptp.int)) (let ((_let_1 (tptp.set_ord_atMost_nat N))) (let ((_let_2 (tptp.aTP_Lamm_qt A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.one_one_nat) N)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.groups3539618377306564664at_int (tptp.aa_int_fun_nat_int _let_2 X) _let_1)) (tptp.groups3539618377306564664at_int (tptp.aa_int_fun_nat_int _let_2 Y) _let_1)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int X) Y)) (tptp.groups3539618377306564664at_int (tptp.aa_int_fun_nat_int (tptp.aa_int5842867502692063756at_int (tptp.aa_fun7421131748584218370at_int (tptp.aTP_Lamm_td N) A) X) Y) (tptp.set_ord_lessThan_nat N)))))))) (forall ((N tptp.nat) (A tptp.fun_nat_real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.set_ord_atMost_nat N))) (let ((_let_2 (tptp.aTP_Lamm_kl A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.one_one_nat) N)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real _let_2 X) _let_1)) (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real _let_2 Y) _let_1)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real X) Y)) (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real (tptp.aa_rea7841385751566875788t_real (tptp.aa_fun2548873334967081986t_real (tptp.aTP_Lamm_tf N) A) X) Y) (tptp.set_ord_lessThan_nat N)))))))) (forall ((A tptp.complex) (M tptp.nat)) (= (tptp.groups2073611262835488442omplex (tptp.aTP_Lamm_tg A) (tptp.set_ord_atMost_nat M)) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex (tptp.aa_complex_complex (tptp.plus_plus_complex (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex M)) tptp.one_one_complex)) (tptp.numera6690914467698888265omplex (tptp.aa_num_num tptp.bit0 tptp.one)))) (tptp.aa_nat_complex (tptp.gbinomial_complex A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) tptp.one_one_nat))))) (forall ((A tptp.rat) (M tptp.nat)) (= (tptp.groups2906978787729119204at_rat (tptp.aTP_Lamm_th A) (tptp.set_ord_atMost_nat M)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat M)) tptp.one_one_rat)) (tptp.aa_num_rat tptp.numeral_numeral_rat (tptp.aa_num_num tptp.bit0 tptp.one)))) (tptp.aa_nat_rat (tptp.gbinomial_rat A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) tptp.one_one_nat))))) (forall ((A tptp.real) (M tptp.nat)) (= (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real tptp.aTP_Lamm_ti A) (tptp.set_ord_atMost_nat M)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real M)) tptp.one_one_real)) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.gbinomial_real A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) tptp.one_one_nat))))) (forall ((M tptp.nat)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (let ((_let_2 (tptp.numera6690914467698888265omplex _let_1))) (= (tptp.groups2073611262835488442omplex (tptp.gbinomial_complex (tptp.aa_complex_complex (tptp.plus_plus_complex (tptp.aa_complex_complex (tptp.times_times_complex _let_2) (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex M))) tptp.one_one_complex)) (tptp.set_ord_atMost_nat M)) (tptp.aa_nat_complex (tptp.power_power_complex _let_2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1)) M)))))) (forall ((M tptp.nat)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (let ((_let_2 (tptp.aa_num_rat tptp.numeral_numeral_rat _let_1))) (= (tptp.groups2906978787729119204at_rat (tptp.gbinomial_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat _let_2) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat M))) tptp.one_one_rat)) (tptp.set_ord_atMost_nat M)) (tptp.aa_nat_rat (tptp.power_power_rat _let_2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1)) M)))))) (forall ((M tptp.nat)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (let ((_let_2 (tptp.aa_num_real tptp.numeral_numeral_real _let_1))) (= (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real tptp.gbinomial_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real _let_2) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real M))) tptp.one_one_real)) (tptp.set_ord_atMost_nat M)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real _let_2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1)) M)))))) (forall ((X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) tptp.one_one_real)) (= (tptp.aa_real_real tptp.cos_real (tptp.aa_real_real tptp.arcsin X)) (tptp.aa_real_real tptp.sqrt (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real tptp.one_one_real) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))))))) (forall ((Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real Y)) tptp.one_one_real)) (= (tptp.aa_real_real tptp.sin_real (tptp.aa_real_real tptp.arccos Y)) (tptp.aa_real_real tptp.sqrt (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real tptp.one_one_real) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Y) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))))))) (forall ((X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) tptp.one_one_real)) (= (tptp.aa_real_real tptp.sin_real (tptp.aa_real_real tptp.arccos X)) (tptp.aa_real_real tptp.sqrt (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real tptp.one_one_real) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))))))) (forall ((N tptp.nat)) (= (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat N) N)) (forall ((A4 tptp.set_int) (F tptp.fun_int_nat)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A4)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.groups1707563613775114915nt_nat F A4))) (forall ((X3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X3) A4)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.aa_int_nat F X3)))))))) (forall ((A4 tptp.set_complex) (F tptp.fun_complex_nat)) (=> (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex A4)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.groups861055069439313189ex_nat F A4))) (forall ((X3 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex X3) A4)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.aa_complex_nat F X3)))))))) (forall ((A4 tptp.set_nat) (F tptp.fun_nat_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A4)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.groups708209901874060359at_nat F A4))) (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) A4)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.aa_nat_nat F X3)))))))) (forall ((Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)) Y)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y) tptp.one_one_real)) (= (tptp.aa_real_real tptp.cos_real (tptp.aa_real_real tptp.arccos Y)) Y)))) (forall ((Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)) Y)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y) tptp.one_one_real)) (= (tptp.aa_real_real tptp.sin_real (tptp.aa_real_real tptp.arcsin Y)) Y)))) (= (tptp.aa_real_real tptp.arccos tptp.zero_zero_real) _let_30) (= (tptp.aa_real_real tptp.arcsin tptp.one_one_real) _let_30) (= (tptp.aa_real_real tptp.arcsin _let_57) _let_31) (forall ((A tptp.complex) (K tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc K))) (let ((_let_2 (tptp.gbinomial_complex A))) (= (tptp.aa_nat_complex (tptp.gbinomial_complex (tptp.aa_complex_complex (tptp.plus_plus_complex A) tptp.one_one_complex)) _let_1) (tptp.aa_complex_complex (tptp.plus_plus_complex (tptp.aa_nat_complex _let_2 K)) (tptp.aa_nat_complex _let_2 _let_1)))))) (forall ((A tptp.real) (K tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc K))) (let ((_let_2 (tptp.aa_real_fun_nat_real tptp.gbinomial_real A))) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.gbinomial_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) tptp.one_one_real)) _let_1) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real _let_2 K)) (tptp.aa_nat_real _let_2 _let_1)))))) (forall ((A tptp.rat) (K tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc K))) (let ((_let_2 (tptp.gbinomial_rat A))) (= (tptp.aa_nat_rat (tptp.gbinomial_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) tptp.one_one_rat)) _let_1) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_nat_rat _let_2 K)) (tptp.aa_nat_rat _let_2 _let_1)))))) (forall ((K tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_real_fun_nat_real tptp.gbinomial_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N)))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) N)) (= (tptp.aa_nat_real _let_1 K) (tptp.aa_nat_real _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) K)))))) (forall ((X tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) Y)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y) tptp.one_one_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.arccos Y)) (tptp.aa_real_real tptp.arccos X))))))) (forall ((X tptp.real) (Y tptp.real)) (=> (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real X)) tptp.one_one_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real Y)) tptp.one_one_real))) (= (= (tptp.aa_real_real tptp.arccos X) (tptp.aa_real_real tptp.arccos Y)) (= X Y)))) (forall ((X tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real X)) tptp.one_one_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real Y)) tptp.one_one_real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.arccos X)) (tptp.aa_real_real tptp.arccos Y))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y) X)))))) (forall ((X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) tptp.one_one_real)) (= (tptp.aa_real_real tptp.arcsin (tptp.aa_real_real tptp.uminus_uminus_real X)) (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_real_real tptp.arcsin X)))))) (forall ((X tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) Y)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y) tptp.one_one_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.arcsin X)) (tptp.aa_real_real tptp.arcsin Y))))))) (forall ((X tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real X)) tptp.one_one_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real Y)) tptp.one_one_real)) (= (= (tptp.aa_real_real tptp.arcsin X) (tptp.aa_real_real tptp.arcsin Y)) (= X Y))))) (forall ((X tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real X)) tptp.one_one_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real Y)) tptp.one_one_real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.arcsin X)) (tptp.aa_real_real tptp.arcsin Y))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) Y)))))) (forall ((A tptp.complex) (K tptp.nat)) (let ((_let_1 (tptp.gbinomial_complex (tptp.aa_complex_complex (tptp.minus_minus_complex A) tptp.one_one_complex)))) (let ((_let_2 (tptp.aa_nat_nat tptp.suc K))) (= (tptp.aa_nat_complex (tptp.gbinomial_complex A) _let_2) (tptp.aa_complex_complex (tptp.plus_plus_complex (tptp.aa_nat_complex _let_1 _let_2)) (tptp.aa_nat_complex _let_1 K)))))) (forall ((A tptp.real) (K tptp.nat)) (let ((_let_1 (tptp.aa_real_fun_nat_real tptp.gbinomial_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A) tptp.one_one_real)))) (let ((_let_2 (tptp.aa_nat_nat tptp.suc K))) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.gbinomial_real A) _let_2) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real _let_1 _let_2)) (tptp.aa_nat_real _let_1 K)))))) (forall ((A tptp.rat) (K tptp.nat)) (let ((_let_1 (tptp.gbinomial_rat (tptp.aa_rat_rat (tptp.minus_minus_rat A) tptp.one_one_rat)))) (let ((_let_2 (tptp.aa_nat_nat tptp.suc K))) (= (tptp.aa_nat_rat (tptp.gbinomial_rat A) _let_2) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_nat_rat _let_1 _let_2)) (tptp.aa_nat_rat _let_1 K)))))) (forall ((A tptp.complex) (K tptp.nat)) (let ((_let_1 (tptp.minus_minus_complex A))) (= (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_complex_complex _let_1 (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex K))) (tptp.aa_nat_complex (tptp.gbinomial_complex A) K)) (tptp.aa_complex_complex (tptp.times_times_complex A) (tptp.aa_nat_complex (tptp.gbinomial_complex (tptp.aa_complex_complex _let_1 tptp.one_one_complex)) K))))) (forall ((A tptp.rat) (K tptp.nat)) (let ((_let_1 (tptp.minus_minus_rat A))) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat _let_1 (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat K))) (tptp.aa_nat_rat (tptp.gbinomial_rat A) K)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) (tptp.aa_nat_rat (tptp.gbinomial_rat (tptp.aa_rat_rat _let_1 tptp.one_one_rat)) K))))) (forall ((A tptp.real) (K tptp.nat)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A))) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real _let_1 (tptp.aa_nat_real tptp.semiri5074537144036343181t_real K))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.gbinomial_real A) K)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.gbinomial_real (tptp.aa_real_real _let_1 tptp.one_one_real)) K))))) (forall ((K tptp.nat) (A tptp.real)) (let ((_let_1 (tptp.aa_nat_real tptp.semiri5074537144036343181t_real K))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real _let_1) A)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real A) _let_1)) K)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.gbinomial_real A) K)))))) (forall ((K tptp.nat) (A tptp.rat)) (let ((_let_1 (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat K))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat _let_1) A)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_rat_rat (tptp.divide_divide_rat A) _let_1)) K)) (tptp.aa_nat_rat (tptp.gbinomial_rat A) K)))))) (forall ((A tptp.rat) (K tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc K))) (let ((_let_2 (tptp.gbinomial_rat A))) (let ((_let_3 (tptp.aa_nat_rat _let_2 K))) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) _let_3) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat K)) _let_3)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat _let_1)) (tptp.aa_nat_rat _let_2 _let_1)))))))) (forall ((A tptp.real) (K tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc K))) (let ((_let_2 (tptp.aa_real_fun_nat_real tptp.gbinomial_real A))) (let ((_let_3 (tptp.aa_nat_real _let_2 K))) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) _let_3) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real K)) _let_3)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real _let_1)) (tptp.aa_nat_real _let_2 _let_1)))))))) (forall ((A tptp.rat) (K tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc K))) (let ((_let_2 (tptp.gbinomial_rat A))) (let ((_let_3 (tptp.aa_nat_rat _let_2 K))) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat _let_3) A) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat K)) _let_3)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat _let_1)) (tptp.aa_nat_rat _let_2 _let_1)))))))) (forall ((A tptp.real) (K tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc K))) (let ((_let_2 (tptp.aa_real_fun_nat_real tptp.gbinomial_real A))) (let ((_let_3 (tptp.aa_nat_real _let_2 K))) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real _let_3) A) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real K)) _let_3)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real _let_1)) (tptp.aa_nat_real _let_2 _let_1)))))))) (forall ((I tptp.nat) (J tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat I) J))) (= (tptp.groups705719431365010083at_int tptp.semiri1314217659103216013at_int (tptp.set_or1269000886237332187st_nat I _let_1)) (tptp.groups1705073143266064639nt_int tptp.aTP_Lamm_am (tptp.aa_int_set_int (tptp.aa_int8639817059373041269et_int tptp.set_or1266510415728281911st_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int I)) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int _let_1)))))) (forall ((Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)) Y)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y) tptp.one_one_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_real_real tptp.arccos Y)))))) (forall ((X tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Y)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y) tptp.one_one_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.arccos Y)) (tptp.aa_real_real tptp.arccos X))))))) (forall ((X tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real X)) tptp.one_one_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real Y)) tptp.one_one_real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.arccos X)) (tptp.aa_real_real tptp.arccos Y))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y) X)))))) (forall ((Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)) Y)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y) tptp.one_one_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.arccos Y)) tptp.pi))))) (forall ((X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) tptp.pi)) (= (tptp.aa_real_real tptp.arccos (tptp.aa_real_real tptp.cos_real X)) X)))) (forall ((X tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Y)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y) tptp.one_one_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.arcsin X)) (tptp.aa_real_real tptp.arcsin Y))))))) (forall ((X tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real X)) tptp.one_one_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real Y)) tptp.one_one_real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.arcsin X)) (tptp.aa_real_real tptp.arcsin Y))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Y)))))) (forall ((Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real Y)) tptp.one_one_real)) (= (tptp.aa_real_real tptp.cos_real (tptp.aa_real_real tptp.arccos Y)) Y))) (forall ((Theta tptp.real)) (let ((_let_1 (tptp.aa_real_real tptp.abs_abs_real Theta))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real _let_1) tptp.pi)) (= (tptp.aa_real_real tptp.arccos (tptp.aa_real_real tptp.cos_real Theta)) _let_1)))) (forall ((K tptp.nat) (A tptp.complex)) (let ((_let_1 (tptp.aa_complex_complex (tptp.plus_plus_complex A) tptp.one_one_complex))) (let ((_let_2 (tptp.aa_nat_nat tptp.suc K))) (= (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex _let_2)) (tptp.aa_nat_complex (tptp.gbinomial_complex _let_1) _let_2)) (tptp.aa_complex_complex (tptp.times_times_complex _let_1) (tptp.aa_nat_complex (tptp.gbinomial_complex A) K)))))) (forall ((K tptp.nat) (A tptp.rat)) (let ((_let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) tptp.one_one_rat))) (let ((_let_2 (tptp.aa_nat_nat tptp.suc K))) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat _let_2)) (tptp.aa_nat_rat (tptp.gbinomial_rat _let_1) _let_2)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat _let_1) (tptp.aa_nat_rat (tptp.gbinomial_rat A) K)))))) (forall ((K tptp.nat) (A tptp.real)) (let ((_let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) tptp.one_one_real))) (let ((_let_2 (tptp.aa_nat_nat tptp.suc K))) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real _let_2)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.gbinomial_real _let_1) _let_2)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real _let_1) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.gbinomial_real A) K)))))) (forall ((K tptp.nat) (A tptp.complex)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc K))) (= (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex _let_1)) (tptp.aa_nat_complex (tptp.gbinomial_complex A) _let_1)) (tptp.aa_complex_complex (tptp.times_times_complex A) (tptp.aa_nat_complex (tptp.gbinomial_complex (tptp.aa_complex_complex (tptp.minus_minus_complex A) tptp.one_one_complex)) K))))) (forall ((K tptp.nat) (A tptp.rat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc K))) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat _let_1)) (tptp.aa_nat_rat (tptp.gbinomial_rat A) _let_1)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) (tptp.aa_nat_rat (tptp.gbinomial_rat (tptp.aa_rat_rat (tptp.minus_minus_rat A) tptp.one_one_rat)) K))))) (forall ((K tptp.nat) (A tptp.real)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc K))) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real _let_1)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.gbinomial_real A) _let_1)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.gbinomial_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A) tptp.one_one_real)) K))))) (forall ((K tptp.nat) (M tptp.nat) (A tptp.complex)) (let ((_let_1 (tptp.gbinomial_complex A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) M)) (= (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_nat_complex _let_1 M)) (tptp.aa_nat_complex (tptp.gbinomial_complex (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex M)) K)) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_nat_complex _let_1 K)) (tptp.aa_nat_complex (tptp.gbinomial_complex (tptp.aa_complex_complex (tptp.minus_minus_complex A) (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex K))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) K))))))) (forall ((K tptp.nat) (M tptp.nat) (A tptp.rat)) (let ((_let_1 (tptp.gbinomial_rat A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) M)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat _let_1 M)) (tptp.aa_nat_rat (tptp.gbinomial_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat M)) K)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat _let_1 K)) (tptp.aa_nat_rat (tptp.gbinomial_rat (tptp.aa_rat_rat (tptp.minus_minus_rat A) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat K))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) K))))))) (forall ((K tptp.nat) (M tptp.nat) (A tptp.real)) (let ((_let_1 (tptp.aa_real_fun_nat_real tptp.gbinomial_real A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) M)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real _let_1 M)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.gbinomial_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real M)) K)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real _let_1 K)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.gbinomial_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real K))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) K))))))) (forall ((I5 tptp.set_real) (F tptp.fun_real_real)) (=> (tptp.finite_finite_real I5) (=> (forall ((I3 tptp.real)) (=> (tptp.member_real I3 I5) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) (tptp.aa_real_real F I3))))) (= (tptp.aa_real_real tptp.ln_ln_real (tptp.groups1681761925125756287l_real F I5)) (tptp.groups8097168146408367636l_real (tptp.aTP_Lamm_tj F) I5))))) (forall ((I5 tptp.set_int) (F tptp.fun_int_real)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int I5)) (=> (forall ((I3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int I3) I5)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) (tptp.aa_int_real F I3))))) (= (tptp.aa_real_real tptp.ln_ln_real (tptp.groups2316167850115554303t_real F I5)) (tptp.groups8778361861064173332t_real (tptp.aTP_Lamm_tk F) I5))))) (forall ((I5 tptp.set_complex) (F tptp.fun_complex_real)) (=> (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex I5)) (=> (forall ((I3 tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex I3) I5)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) (tptp.aa_complex_real F I3))))) (= (tptp.aa_real_real tptp.ln_ln_real (tptp.groups766887009212190081x_real F I5)) (tptp.groups5808333547571424918x_real (tptp.aTP_Lamm_tl F) I5))))) (forall ((I5 tptp.set_nat) (F tptp.fun_nat_real)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat I5)) (=> (forall ((I3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat I3) I5)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) (tptp.aa_nat_real F I3))))) (= (tptp.aa_real_real tptp.ln_ln_real (tptp.groups129246275422532515t_real F I5)) (tptp.groups6591440286371151544t_real (tptp.aTP_Lamm_tm F) I5))))) (forall ((A tptp.complex) (N tptp.nat)) (= (tptp.groups2073611262835488442omplex (tptp.aTP_Lamm_tn A) (tptp.set_ord_atMost_nat N)) (tptp.aa_nat_complex (tptp.gbinomial_complex (tptp.aa_complex_complex (tptp.plus_plus_complex (tptp.aa_complex_complex (tptp.plus_plus_complex A) (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex N))) tptp.one_one_complex)) N))) (forall ((A tptp.rat) (N tptp.nat)) (= (tptp.groups2906978787729119204at_rat (tptp.aTP_Lamm_to A) (tptp.set_ord_atMost_nat N)) (tptp.aa_nat_rat (tptp.gbinomial_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat N))) tptp.one_one_rat)) N))) (forall ((A tptp.real) (N tptp.nat)) (= (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real tptp.aTP_Lamm_tp A) (tptp.set_ord_atMost_nat N)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.gbinomial_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N))) tptp.one_one_real)) N))) (forall ((Y tptp.real)) (let ((_let_1 (tptp.aa_real_real tptp.arccos Y))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)) Y)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y) tptp.one_one_real)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) _let_1)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real _let_1) tptp.pi))))))) (forall ((Y tptp.real)) (let ((_let_1 (tptp.aa_real_real tptp.arccos Y))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)) Y)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y) tptp.one_one_real)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) _let_1)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real _let_1) tptp.pi))))))) (forall ((A tptp.complex) (K tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc K))) (let ((_let_2 (tptp.aa_complex_complex (tptp.plus_plus_complex A) tptp.one_one_complex))) (= (tptp.aa_nat_complex (tptp.gbinomial_complex _let_2) _let_1) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_nat_complex (tptp.gbinomial_complex A) K)) (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex _let_2) (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex _let_1))))))) (forall ((A tptp.rat) (K tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc K))) (let ((_let_2 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) tptp.one_one_rat))) (= (tptp.aa_nat_rat (tptp.gbinomial_rat _let_2) _let_1) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat (tptp.gbinomial_rat A) K)) (tptp.aa_rat_rat (tptp.divide_divide_rat _let_2) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat _let_1))))))) (forall ((A tptp.real) (K tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc K))) (let ((_let_2 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) tptp.one_one_real))) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.gbinomial_real _let_2) _let_1) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.gbinomial_real A) K)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real _let_2) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real _let_1))))))) (forall ((A tptp.complex) (K tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc K))) (let ((_let_2 (tptp.aa_complex_complex (tptp.plus_plus_complex A) tptp.one_one_complex))) (= (tptp.aa_nat_complex (tptp.gbinomial_complex _let_2) _let_1) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex _let_2) (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex _let_1))) (tptp.aa_nat_complex (tptp.gbinomial_complex A) K)))))) (forall ((A tptp.rat) (K tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc K))) (let ((_let_2 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) tptp.one_one_rat))) (= (tptp.aa_nat_rat (tptp.gbinomial_rat _let_2) _let_1) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat (tptp.divide_divide_rat _let_2) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat _let_1))) (tptp.aa_nat_rat (tptp.gbinomial_rat A) K)))))) (forall ((A tptp.real) (K tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc K))) (let ((_let_2 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) tptp.one_one_real))) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.gbinomial_real _let_2) _let_1) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real _let_2) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real _let_1))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.gbinomial_real A) K)))))) (forall ((K tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.power_power_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex tptp.one_one_complex)))) (= (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_nat_complex _let_1 K)) (tptp.aa_nat_complex (tptp.gbinomial_complex (tptp.aa_complex_complex (tptp.minus_minus_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex N))) tptp.one_one_complex)) K)) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_nat_complex _let_1 N)) (tptp.aa_nat_complex (tptp.gbinomial_complex (tptp.aa_complex_complex (tptp.minus_minus_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex K))) tptp.one_one_complex)) N))))) (forall ((K tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.power_power_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat tptp.one_one_rat)))) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat _let_1 K)) (tptp.aa_nat_rat (tptp.gbinomial_rat (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat N))) tptp.one_one_rat)) K)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat _let_1 N)) (tptp.aa_nat_rat (tptp.gbinomial_rat (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat K))) tptp.one_one_rat)) N))))) (forall ((K tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)))) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real _let_1 K)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.gbinomial_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N))) tptp.one_one_real)) K)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real _let_1 N)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.gbinomial_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real K))) tptp.one_one_real)) N))))) (forall ((A tptp.complex) (K tptp.nat)) (= (tptp.aa_nat_complex (tptp.gbinomial_complex A) K) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_nat_complex (tptp.power_power_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex tptp.one_one_complex)) K)) (tptp.aa_nat_complex (tptp.gbinomial_complex (tptp.aa_complex_complex (tptp.minus_minus_complex (tptp.aa_complex_complex (tptp.minus_minus_complex (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex K)) A)) tptp.one_one_complex)) K)))) (forall ((A tptp.rat) (K tptp.nat)) (= (tptp.aa_nat_rat (tptp.gbinomial_rat A) K) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat tptp.one_one_rat)) K)) (tptp.aa_nat_rat (tptp.gbinomial_rat (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat K)) A)) tptp.one_one_rat)) K)))) (forall ((A tptp.real) (K tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.gbinomial_real A) K) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)) K)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.gbinomial_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real K)) A)) tptp.one_one_real)) K)))) (forall ((X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) tptp.one_one_real)) (not (= (tptp.aa_real_real tptp.sin_real (tptp.aa_real_real tptp.arccos X)) tptp.zero_zero_real))))) (forall ((X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) tptp.zero_zero_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.pi)) X)) (= (tptp.aa_real_real tptp.arccos (tptp.aa_real_real tptp.cos_real X)) (tptp.aa_real_real tptp.uminus_uminus_real X))))) (forall ((X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) tptp.one_one_real)) (= (tptp.aa_real_real tptp.arccos (tptp.aa_real_real tptp.uminus_uminus_real X)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real tptp.pi) (tptp.aa_real_real tptp.arccos X)))))) (forall ((X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) tptp.one_one_real)) (not (= (tptp.aa_real_real tptp.cos_real (tptp.aa_real_real tptp.arcsin X)) tptp.zero_zero_real))))) (forall ((G tptp.fun_nat_fun_nat_nat) (N tptp.nat)) (= (tptp.groups4077766827762148844at_nat (tptp.produc6842872674320459806at_nat G) (tptp.collec3392354462482085612at_nat (tptp.produc8955392012077580105t_bool (tptp.aTP_Lamm_qf N)))) (tptp.groups708209901874060359at_nat (tptp.aTP_Lamm_tq G) (tptp.set_ord_atMost_nat N)))) (forall ((G tptp.fun_nat_fun_nat_int) (N tptp.nat)) (= (tptp.groups4075276357253098568at_int (tptp.produc6840382203811409530at_int G) (tptp.collec3392354462482085612at_nat (tptp.produc8955392012077580105t_bool (tptp.aTP_Lamm_qf N)))) (tptp.groups705719431365010083at_int (tptp.aTP_Lamm_ts G) (tptp.set_ord_atMost_nat N)))) (forall ((A tptp.complex) (K tptp.nat)) (= (tptp.aa_nat_complex (tptp.gbinomial_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex A)) K) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_nat_complex (tptp.power_power_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex tptp.one_one_complex)) K)) (tptp.aa_nat_complex (tptp.gbinomial_complex (tptp.aa_complex_complex (tptp.minus_minus_complex (tptp.aa_complex_complex (tptp.plus_plus_complex A) (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex K))) tptp.one_one_complex)) K)))) (forall ((A tptp.rat) (K tptp.nat)) (= (tptp.aa_nat_rat (tptp.gbinomial_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat A)) K) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat tptp.one_one_rat)) K)) (tptp.aa_nat_rat (tptp.gbinomial_rat (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat K))) tptp.one_one_rat)) K)))) (forall ((A tptp.real) (K tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.gbinomial_real (tptp.aa_real_real tptp.uminus_uminus_real A)) K) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)) K)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.gbinomial_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real K))) tptp.one_one_real)) K)))) (forall ((K tptp.nat) (A tptp.complex)) (let ((_let_1 (tptp.gbinomial_complex (tptp.aa_complex_complex (tptp.minus_minus_complex A) tptp.one_one_complex)))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) K)) (= (tptp.aa_nat_complex (tptp.gbinomial_complex A) K) (tptp.aa_complex_complex (tptp.plus_plus_complex (tptp.aa_nat_complex _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat K) tptp.one_one_nat))) (tptp.aa_nat_complex _let_1 K)))))) (forall ((K tptp.nat) (A tptp.real)) (let ((_let_1 (tptp.aa_real_fun_nat_real tptp.gbinomial_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A) tptp.one_one_real)))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) K)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.gbinomial_real A) K) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat K) tptp.one_one_nat))) (tptp.aa_nat_real _let_1 K)))))) (forall ((K tptp.nat) (A tptp.rat)) (let ((_let_1 (tptp.gbinomial_rat (tptp.aa_rat_rat (tptp.minus_minus_rat A) tptp.one_one_rat)))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) K)) (= (tptp.aa_nat_rat (tptp.gbinomial_rat A) K) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_nat_rat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat K) tptp.one_one_nat))) (tptp.aa_nat_rat _let_1 K)))))) (forall ((Y tptp.real)) (let ((_let_1 (tptp.aa_real_real tptp.arccos Y))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)) Y)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y) tptp.one_one_real)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) _let_1)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real _let_1) tptp.pi)) (= (tptp.aa_real_real tptp.cos_real _let_1) Y)))))) (forall ((G tptp.fun_nat_fun_nat_nat) (N tptp.nat)) (= (tptp.groups4077766827762148844at_nat (tptp.produc6842872674320459806at_nat G) (tptp.collec3392354462482085612at_nat (tptp.produc8955392012077580105t_bool (tptp.aTP_Lamm_qy N)))) (tptp.groups708209901874060359at_nat (tptp.aTP_Lamm_tq G) (tptp.set_ord_lessThan_nat N)))) (forall ((G tptp.fun_nat_fun_nat_int) (N tptp.nat)) (= (tptp.groups4075276357253098568at_int (tptp.produc6840382203811409530at_int G) (tptp.collec3392354462482085612at_nat (tptp.produc8955392012077580105t_bool (tptp.aTP_Lamm_qy N)))) (tptp.groups705719431365010083at_int (tptp.aTP_Lamm_ts G) (tptp.set_ord_lessThan_nat N)))) (forall ((A tptp.complex) (K tptp.nat)) (= (tptp.aa_nat_complex (tptp.gbinomial_complex A) K) (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_nat_complex (tptp.power_power_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex tptp.one_one_complex)) K)) (tptp.aa_nat_complex (tptp.comm_s2602460028002588243omplex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex A)) K))) (tptp.aa_nat_complex tptp.semiri5044797733671781792omplex K)))) (forall ((A tptp.rat) (K tptp.nat)) (= (tptp.aa_nat_rat (tptp.gbinomial_rat A) K) (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat tptp.one_one_rat)) K)) (tptp.aa_nat_rat (tptp.comm_s4028243227959126397er_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat A)) K))) (tptp.aa_nat_rat tptp.semiri773545260158071498ct_rat K)))) (forall ((A tptp.real) (K tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.gbinomial_real A) K) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)) K)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.comm_s7457072308508201937r_real (tptp.aa_real_real tptp.uminus_uminus_real A)) K))) (tptp.aa_nat_real tptp.semiri2265585572941072030t_real K)))) (forall ((A tptp.complex) (K tptp.nat)) (= (tptp.aa_nat_complex (tptp.gbinomial_complex A) K) (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex (tptp.aa_nat_complex (tptp.comm_s2602460028002588243omplex (tptp.aa_complex_complex (tptp.plus_plus_complex (tptp.aa_complex_complex (tptp.minus_minus_complex A) (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex K))) tptp.one_one_complex)) K)) (tptp.aa_nat_complex tptp.semiri5044797733671781792omplex K)))) (forall ((A tptp.rat) (K tptp.nat)) (= (tptp.aa_nat_rat (tptp.gbinomial_rat A) K) (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_nat_rat (tptp.comm_s4028243227959126397er_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.minus_minus_rat A) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat K))) tptp.one_one_rat)) K)) (tptp.aa_nat_rat tptp.semiri773545260158071498ct_rat K)))) (forall ((A tptp.real) (K tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.gbinomial_real A) K) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.comm_s7457072308508201937r_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real K))) tptp.one_one_real)) K)) (tptp.aa_nat_real tptp.semiri2265585572941072030t_real K)))) (forall ((X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real X)) tptp.one_one_real)) (= (tptp.aa_real_real tptp.arccos (tptp.aa_real_real tptp.uminus_uminus_real X)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real tptp.pi) (tptp.aa_real_real tptp.arccos X))))) (forall ((A tptp.complex) (M tptp.nat)) (= (tptp.groups2073611262835488442omplex (tptp.aTP_Lamm_tt A) (tptp.set_ord_atMost_nat M)) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_nat_complex (tptp.power_power_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex tptp.one_one_complex)) M)) (tptp.aa_nat_complex (tptp.gbinomial_complex (tptp.aa_complex_complex (tptp.minus_minus_complex A) tptp.one_one_complex)) M)))) (forall ((A tptp.rat) (M tptp.nat)) (= (tptp.groups2906978787729119204at_rat (tptp.aTP_Lamm_tu A) (tptp.set_ord_atMost_nat M)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat tptp.one_one_rat)) M)) (tptp.aa_nat_rat (tptp.gbinomial_rat (tptp.aa_rat_rat (tptp.minus_minus_rat A) tptp.one_one_rat)) M)))) (forall ((A tptp.real) (M tptp.nat)) (= (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real tptp.aTP_Lamm_tv A) (tptp.set_ord_atMost_nat M)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)) M)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.gbinomial_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A) tptp.one_one_real)) M)))) (forall ((M tptp.nat) (A tptp.complex) (X tptp.complex) (Y tptp.complex)) (let ((_let_1 (tptp.set_ord_atMost_nat M))) (= (tptp.groups2073611262835488442omplex (tptp.aa_com8181001469867462503omplex (tptp.aa_com8177640530696437650omplex (tptp.aa_com177695874307951165omplex (tptp.aTP_Lamm_tw M) A) X) Y) _let_1) (tptp.groups2073611262835488442omplex (tptp.aa_com8181001469867462503omplex (tptp.aa_com8177640530696437650omplex (tptp.aa_com177695874307951165omplex (tptp.aTP_Lamm_tx M) A) X) Y) _let_1)))) (forall ((M tptp.nat) (A tptp.rat) (X tptp.rat) (Y tptp.rat)) (let ((_let_1 (tptp.set_ord_atMost_nat M))) (= (tptp.groups2906978787729119204at_rat (tptp.aa_rat_fun_nat_rat (tptp.aa_rat3146053865535587600at_rat (tptp.aa_rat7467449789483521253at_rat (tptp.aTP_Lamm_ty M) A) X) Y) _let_1) (tptp.groups2906978787729119204at_rat (tptp.aa_rat_fun_nat_rat (tptp.aa_rat3146053865535587600at_rat (tptp.aa_rat7467449789483521253at_rat (tptp.aTP_Lamm_tz M) A) X) Y) _let_1)))) (forall ((M tptp.nat) (A tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.set_ord_atMost_nat M))) (= (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real (tptp.aa_rea7841385751566875788t_real (tptp.aa_rea1729780184207679413t_real (tptp.aTP_Lamm_ua M) A) X) Y) _let_1) (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real (tptp.aa_rea7841385751566875788t_real (tptp.aa_rea1729780184207679413t_real (tptp.aTP_Lamm_ub M) A) X) Y) _let_1)))) (forall ((K tptp.nat) (N tptp.nat)) (= (tptp.groups2073611262835488442omplex (tptp.aTP_Lamm_uc K) (tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat N)) (tptp.aa_nat_complex (tptp.gbinomial_complex (tptp.aa_complex_complex (tptp.plus_plus_complex (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex N)) tptp.one_one_complex)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat K) tptp.one_one_nat)))) (forall ((K tptp.nat) (N tptp.nat)) (= (tptp.groups2906978787729119204at_rat (tptp.aTP_Lamm_ud K) (tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat N)) (tptp.aa_nat_rat (tptp.gbinomial_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat N)) tptp.one_one_rat)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat K) tptp.one_one_nat)))) (forall ((K tptp.nat) (N tptp.nat)) (= (tptp.groups6591440286371151544t_real (tptp.aa_nat_fun_nat_real tptp.aTP_Lamm_ue K) (tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat N)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.gbinomial_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N)) tptp.one_one_real)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat K) tptp.one_one_nat)))) (forall ((A tptp.complex) (K tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc K))) (= (tptp.aa_nat_complex (tptp.gbinomial_complex A) _let_1) (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex (tptp.groups6464643781859351333omplex (tptp.aTP_Lamm_uf A) (tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat K))) (tptp.aa_nat_complex tptp.semiri5044797733671781792omplex _let_1))))) (forall ((A tptp.rat) (K tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc K))) (= (tptp.aa_nat_rat (tptp.gbinomial_rat A) _let_1) (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.groups73079841787564623at_rat (tptp.aTP_Lamm_ug A) (tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat K))) (tptp.aa_nat_rat tptp.semiri773545260158071498ct_rat _let_1))))) (forall ((A tptp.real) (K tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc K))) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.gbinomial_real A) _let_1) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.groups129246275422532515t_real (tptp.aa_real_fun_nat_real tptp.aTP_Lamm_uh A) (tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat K))) (tptp.aa_nat_real tptp.semiri2265585572941072030t_real _let_1))))) (forall ((A tptp.nat) (K tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc K))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.gbinomial_nat A) _let_1) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.groups708209901874060359at_nat (tptp.aa_nat_fun_nat_nat tptp.aTP_Lamm_ui A) (tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat K))) (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat _let_1))))) (forall ((A tptp.int) (K tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc K))) (= (tptp.aa_nat_int (tptp.gbinomial_int A) _let_1) (tptp.aa_int_int (tptp.divide_divide_int (tptp.groups705719431365010083at_int (tptp.aTP_Lamm_uj A) (tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat K))) (tptp.aa_nat_int tptp.semiri1406184849735516958ct_int _let_1))))) (forall ((K tptp.nat) (A tptp.complex)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) K)) (= (tptp.aa_nat_complex (tptp.gbinomial_complex A) K) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex A) (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex K))) (tptp.aa_nat_complex (tptp.gbinomial_complex (tptp.aa_complex_complex (tptp.minus_minus_complex A) tptp.one_one_complex)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat K) tptp.one_one_nat)))))) (forall ((K tptp.nat) (A tptp.rat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) K)) (= (tptp.aa_nat_rat (tptp.gbinomial_rat A) K) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat (tptp.divide_divide_rat A) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat K))) (tptp.aa_nat_rat (tptp.gbinomial_rat (tptp.aa_rat_rat (tptp.minus_minus_rat A) tptp.one_one_rat)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat K) tptp.one_one_nat)))))) (forall ((K tptp.nat) (A tptp.real)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) K)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.gbinomial_real A) K) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real A) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real K))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.gbinomial_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A) tptp.one_one_real)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat K) tptp.one_one_nat)))))) (forall ((Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) Y)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y) tptp.one_one_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.arccos Y)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))))))) (forall ((M tptp.nat)) (= (tptp.groups2073611262835488442omplex (tptp.aTP_Lamm_uk M) (tptp.set_ord_atMost_nat M)) (tptp.aa_nat_complex (tptp.power_power_complex (tptp.numera6690914467698888265omplex (tptp.aa_num_num tptp.bit0 tptp.one))) M))) (forall ((M tptp.nat)) (= (tptp.groups2906978787729119204at_rat (tptp.aTP_Lamm_ul M) (tptp.set_ord_atMost_nat M)) (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_num_rat tptp.numeral_numeral_rat (tptp.aa_num_num tptp.bit0 tptp.one))) M))) (forall ((M tptp.nat)) (= (tptp.groups6591440286371151544t_real (tptp.aa_nat_fun_nat_real tptp.aTP_Lamm_um M) (tptp.set_ord_atMost_nat M)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))) M))) (forall ((M tptp.nat) (A tptp.complex) (X tptp.complex) (Y tptp.complex)) (let ((_let_1 (tptp.set_ord_atMost_nat M))) (= (tptp.groups2073611262835488442omplex (tptp.aa_com8181001469867462503omplex (tptp.aa_com8177640530696437650omplex (tptp.aa_com177695874307951165omplex (tptp.aTP_Lamm_tw M) A) X) Y) _let_1) (tptp.groups2073611262835488442omplex (tptp.aa_com8181001469867462503omplex (tptp.aa_com8177640530696437650omplex (tptp.aa_com177695874307951165omplex (tptp.aTP_Lamm_un M) A) X) Y) _let_1)))) (forall ((M tptp.nat) (A tptp.rat) (X tptp.rat) (Y tptp.rat)) (let ((_let_1 (tptp.set_ord_atMost_nat M))) (= (tptp.groups2906978787729119204at_rat (tptp.aa_rat_fun_nat_rat (tptp.aa_rat3146053865535587600at_rat (tptp.aa_rat7467449789483521253at_rat (tptp.aTP_Lamm_ty M) A) X) Y) _let_1) (tptp.groups2906978787729119204at_rat (tptp.aa_rat_fun_nat_rat (tptp.aa_rat3146053865535587600at_rat (tptp.aa_rat7467449789483521253at_rat (tptp.aTP_Lamm_uo M) A) X) Y) _let_1)))) (forall ((M tptp.nat) (A tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.set_ord_atMost_nat M))) (= (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real (tptp.aa_rea7841385751566875788t_real (tptp.aa_rea1729780184207679413t_real (tptp.aTP_Lamm_ua M) A) X) Y) _let_1) (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real (tptp.aa_rea7841385751566875788t_real (tptp.aa_rea1729780184207679413t_real (tptp.aTP_Lamm_up M) A) X) Y) _let_1)))) (forall ((Y tptp.real)) (let ((_let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_2 (tptp.aa_real_real tptp.arcsin Y))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)) Y)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y) tptp.one_one_real)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.uminus_uminus_real _let_1)) _let_2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real _let_2) _let_1)))))))) (forall ((Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)) Y)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y) tptp.one_one_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))))) (tptp.aa_real_real tptp.arcsin Y)))))) (forall ((Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)) Y)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y) tptp.one_one_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.arcsin Y)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))))))) (forall ((Y tptp.real)) (let ((_let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_2 (tptp.aa_real_real tptp.arcsin Y))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)) Y)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y) tptp.one_one_real)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real _let_1)) _let_2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real _let_2) _let_1)))))))) (forall ((X tptp.real)) (let ((_let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real _let_1)) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) _let_1)) (= (tptp.aa_real_real tptp.arcsin (tptp.aa_real_real tptp.sin_real X)) X))))) (forall ((Y tptp.real)) (let ((_let_1 (tptp.aa_real_real tptp.arcsin Y))) (let ((_let_2 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)) Y)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y) tptp.one_one_real)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real _let_2)) _let_1)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real _let_1) _let_2)) (= (tptp.aa_real_real tptp.sin_real _let_1) Y))))))) (forall ((Y tptp.real)) (let ((_let_1 (tptp.aa_real_real tptp.arcsin Y))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)) Y)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y) tptp.one_one_real)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))))) _let_1)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real _let_1) tptp.pi)) (= (tptp.aa_real_real tptp.sin_real _let_1) Y)))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X))) (let ((_let_2 (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)) X)) (=> (tptp.pp (tptp.aa_real_bool _let_1 tptp.one_one_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.pi)) _let_2)) Y)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) _let_2))) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.arcsin X)) Y)) (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real tptp.sin_real Y))))))))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y))) (let ((_let_2 (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) tptp.one_one_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.pi)) _let_2)) Y)) (=> (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) _let_2))) (= (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real tptp.arcsin X))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.sin_real Y)) X)))))))))) (forall ((K tptp.nat) (A tptp.complex)) (let ((_let_1 (tptp.aa_nat_complex (tptp.gbinomial_complex A) K))) (let ((_let_2 (= K tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_complex)) (=> (not _let_2) (= _let_1 (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex (tptp.aa_complex_complex (tptp.set_fo1517530859248394432omplex (tptp.aTP_Lamm_uq A) tptp.zero_zero_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat K) tptp.one_one_nat)) tptp.one_one_complex)) (tptp.aa_nat_complex tptp.semiri5044797733671781792omplex K)))))))) (forall ((K tptp.nat) (A tptp.rat)) (let ((_let_1 (tptp.aa_nat_rat (tptp.gbinomial_rat A) K))) (let ((_let_2 (= K tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_rat)) (=> (not _let_2) (= _let_1 (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_rat_rat (tptp.set_fo1949268297981939178at_rat (tptp.aTP_Lamm_ur A) tptp.zero_zero_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat K) tptp.one_one_nat)) tptp.one_one_rat)) (tptp.aa_nat_rat tptp.semiri773545260158071498ct_rat K)))))))) (forall ((K tptp.nat) (A tptp.real)) (let ((_let_1 (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.gbinomial_real A) K))) (let ((_let_2 (= K tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_real)) (=> (not _let_2) (= _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_nat_fun_real_real (tptp.set_fo3111899725591712190t_real (tptp.aTP_Lamm_us A) tptp.zero_zero_nat) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat K) tptp.one_one_nat)) tptp.one_one_real)) (tptp.aa_nat_real tptp.semiri2265585572941072030t_real K)))))))) (forall ((R tptp.complex) (M tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc M))) (= (tptp.groups2073611262835488442omplex (tptp.aTP_Lamm_tg R) (tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat M)) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex _let_1)) (tptp.numera6690914467698888265omplex (tptp.aa_num_num tptp.bit0 tptp.one)))) (tptp.aa_nat_complex (tptp.gbinomial_complex R) _let_1))))) (forall ((R tptp.rat) (M tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc M))) (= (tptp.groups2906978787729119204at_rat (tptp.aTP_Lamm_th R) (tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat M)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat _let_1)) (tptp.aa_num_rat tptp.numeral_numeral_rat (tptp.aa_num_num tptp.bit0 tptp.one)))) (tptp.aa_nat_rat (tptp.gbinomial_rat R) _let_1))))) (forall ((R tptp.real) (M tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc M))) (= (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real tptp.aTP_Lamm_ti R) (tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat M)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real _let_1)) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.gbinomial_real R) _let_1))))) (forall ((N tptp.nat)) (= (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex N) (tptp.aa_complex_complex (tptp.semiri2816024913162550771omplex tptp.aTP_Lamm_ut N) tptp.zero_zero_complex))) (forall ((N tptp.nat)) (= (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat N) (tptp.aa_rat_rat (tptp.semiri7787848453975740701ux_rat tptp.aTP_Lamm_uu N) tptp.zero_zero_rat))) (forall ((N tptp.nat)) (= (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N) (tptp.aa_int_int (tptp.semiri8420488043553186161ux_int tptp.aTP_Lamm_uv N) tptp.zero_zero_int))) (forall ((N tptp.nat)) (= (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N) (tptp.aa_real_real (tptp.aa_nat_fun_real_real (tptp.semiri7260567687927622513x_real tptp.aTP_Lamm_uw) N) tptp.zero_zero_real))) (forall ((N tptp.nat)) (= (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat N) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.semiri8422978514062236437ux_nat tptp.aTP_Lamm_ux) N) tptp.zero_zero_nat))) (forall ((X tptp.vEBT_VEBT) (Y tptp.bool)) (let ((_let_1 (tptp.vEBT_Leaf tptp.fFalse tptp.fFalse))) (let ((_let_2 (tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel))) (let ((_let_3 (tptp.pp Y))) (=> (= (tptp.pp (tptp.aa_VEBT_VEBT_bool tptp.vEBT_VEBT_minNull X)) _let_3) (=> (tptp.pp (tptp.aa_VEBT_VEBT_bool _let_2 X)) (=> (=> (= X _let_1) (=> _let_3 (not (tptp.pp (tptp.aa_VEBT_VEBT_bool _let_2 _let_1))))) (=> (forall ((Uv2 tptp.bool)) (let ((_let_1 (tptp.vEBT_Leaf tptp.fTrue Uv2))) (=> (= X _let_1) (=> (not (tptp.pp Y)) (not (tptp.pp (tptp.aa_VEBT_VEBT_bool (tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel) _let_1))))))) (=> (forall ((Uu2 tptp.bool)) (let ((_let_1 (tptp.vEBT_Leaf Uu2 tptp.fTrue))) (=> (= X _let_1) (=> (not (tptp.pp Y)) (not (tptp.pp (tptp.aa_VEBT_VEBT_bool (tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel) _let_1))))))) (=> (forall ((Uw2 tptp.nat) (Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (let ((_let_1 (tptp.vEBT_Node tptp.none_P5556105721700978146at_nat Uw2 Ux2 Uy2))) (=> (= X _let_1) (=> (tptp.pp Y) (not (tptp.pp (tptp.aa_VEBT_VEBT_bool (tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel) _let_1))))))) (not (forall ((Uz2 tptp.product_prod_nat_nat) (Va3 tptp.nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (let ((_let_1 (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat Uz2) Va3 Vb2 Vc2))) (=> (= X _let_1) (=> (not (tptp.pp Y)) (not (tptp.pp (tptp.aa_VEBT_VEBT_bool (tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel) _let_1)))))))))))))))))) (forall ((X tptp.real) (Y tptp.real)) (tptp.pp (tptp.aa_real_bool (tptp.sums_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_uz X) Y)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real tptp.sin_real X)) (tptp.aa_real_real tptp.sin_real Y))))) (forall ((X tptp.complex) (Y tptp.complex)) (tptp.pp (tptp.aa_complex_bool (tptp.sums_complex (tptp.aa_com8181001469867462503omplex (tptp.aTP_Lamm_vb X) Y)) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_complex_complex tptp.sin_complex X)) (tptp.aa_complex_complex tptp.sin_complex Y))))) (forall ((X tptp.real) (N tptp.nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real tptp.sin_real X)) (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real tptp.aTP_Lamm_nd X) (tptp.set_ord_lessThan_nat N))))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real tptp.inverse_inverse_real (tptp.aa_nat_real tptp.semiri2265585572941072030t_real N))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real tptp.abs_abs_real X)) N))))) (forall ((X tptp.real) (Y tptp.real)) (tptp.pp (tptp.aa_real_bool (tptp.sums_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_vd X) Y)) (tptp.aa_real_real tptp.cos_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) Y))))) (forall ((X tptp.complex) (Y tptp.complex)) (tptp.pp (tptp.aa_complex_bool (tptp.sums_complex (tptp.aa_com8181001469867462503omplex (tptp.aTP_Lamm_vf X) Y)) (tptp.aa_complex_complex tptp.cos_complex (tptp.aa_complex_complex (tptp.plus_plus_complex X) Y))))) (forall ((A tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.real_V1485227260804924795R_real A))) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real _let_1 X)) Y) (tptp.aa_real_real _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real X) Y))))) (forall ((A tptp.real) (X tptp.complex) (Y tptp.complex)) (let ((_let_1 (tptp.real_V2046097035970521341omplex A))) (= (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_complex_complex _let_1 X)) Y) (tptp.aa_complex_complex _let_1 (tptp.aa_complex_complex (tptp.times_times_complex X) Y))))) (forall ((X tptp.real) (A tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.times_times_real X))) (let ((_let_2 (tptp.aa_rea7340605660300375871l_real tptp.real_V1485227260804924795R_real A))) (= (tptp.aa_real_real _let_1 (tptp.aa_real_real _let_2 Y)) (tptp.aa_real_real _let_2 (tptp.aa_real_real _let_1 Y)))))) (forall ((X tptp.complex) (A tptp.real) (Y tptp.complex)) (let ((_let_1 (tptp.times_times_complex X))) (let ((_let_2 (tptp.real_V2046097035970521341omplex A))) (= (tptp.aa_complex_complex _let_1 (tptp.aa_complex_complex _let_2 Y)) (tptp.aa_complex_complex _let_2 (tptp.aa_complex_complex _let_1 Y)))))) (forall ((A tptp.real) (B2 tptp.real)) (= (tptp.aa_real_real tptp.inverse_inverse_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) B2)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real tptp.inverse_inverse_real A)) (tptp.aa_real_real tptp.inverse_inverse_real B2)))) (forall ((A tptp.complex) (B2 tptp.complex)) (= (tptp.aa_complex_complex tptp.invers8013647133539491842omplex (tptp.aa_complex_complex (tptp.times_times_complex A) B2)) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_complex_complex tptp.invers8013647133539491842omplex A)) (tptp.aa_complex_complex tptp.invers8013647133539491842omplex B2)))) (forall ((A tptp.rat) (B2 tptp.rat)) (= (tptp.aa_rat_rat tptp.inverse_inverse_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) B2)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat tptp.inverse_inverse_rat A)) (tptp.aa_rat_rat tptp.inverse_inverse_rat B2)))) (forall ((A tptp.real) (B2 tptp.real)) (= (tptp.aa_real_real tptp.inverse_inverse_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real A) B2)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real B2) A))) (forall ((A tptp.complex) (B2 tptp.complex)) (= (tptp.aa_complex_complex tptp.invers8013647133539491842omplex (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex A) B2)) (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex B2) A))) (forall ((A tptp.rat) (B2 tptp.rat)) (= (tptp.aa_rat_rat tptp.inverse_inverse_rat (tptp.aa_rat_rat (tptp.divide_divide_rat A) B2)) (tptp.aa_rat_rat (tptp.divide_divide_rat B2) A))) (forall ((A tptp.real) (B2 tptp.real) (X tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.real_V1485227260804924795R_real A) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.real_V1485227260804924795R_real B2) X)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.real_V1485227260804924795R_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) B2)) X))) (forall ((A tptp.real) (B2 tptp.real) (X tptp.complex)) (= (tptp.aa_complex_complex (tptp.real_V2046097035970521341omplex A) (tptp.aa_complex_complex (tptp.real_V2046097035970521341omplex B2) X)) (tptp.aa_complex_complex (tptp.real_V2046097035970521341omplex (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) B2)) X))) (forall ((A tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.inverse_inverse_real A)) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) tptp.zero_zero_real)))) (forall ((A tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat tptp.inverse_inverse_rat A)) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) tptp.zero_zero_rat)))) (forall ((A tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (= (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real tptp.inverse_inverse_real A))) (tptp.pp (tptp.aa_real_bool _let_1 A))))) (forall ((A tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat))) (= (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat tptp.inverse_inverse_rat A))) (tptp.pp (tptp.aa_rat_bool _let_1 A))))) (forall ((A tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real))) (= (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real tptp.inverse_inverse_real A))) (tptp.pp (tptp.aa_real_bool _let_1 A))))) (forall ((A tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat))) (= (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat tptp.inverse_inverse_rat A))) (tptp.pp (tptp.aa_rat_bool _let_1 A))))) (forall ((A tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.inverse_inverse_real A)) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) tptp.zero_zero_real)))) (forall ((A tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat tptp.inverse_inverse_rat A)) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) tptp.zero_zero_rat)))) (forall ((A tptp.real) (B2 tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B2))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) tptp.zero_zero_real)) (=> (tptp.pp (tptp.aa_real_bool _let_1 tptp.zero_zero_real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.inverse_inverse_real A)) (tptp.aa_real_real tptp.inverse_inverse_real B2))) (tptp.pp (tptp.aa_real_bool _let_1 A))))))) (forall ((A tptp.rat) (B2 tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B2))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) tptp.zero_zero_rat)) (=> (tptp.pp (tptp.aa_rat_bool _let_1 tptp.zero_zero_rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat tptp.inverse_inverse_rat A)) (tptp.aa_rat_rat tptp.inverse_inverse_rat B2))) (tptp.pp (tptp.aa_rat_bool _let_1 A))))))) (forall ((A tptp.real) (B2 tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool _let_1 A)) (=> (tptp.pp (tptp.aa_real_bool _let_1 B2)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.inverse_inverse_real A)) (tptp.aa_real_real tptp.inverse_inverse_real B2))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B2) A))))))) (forall ((A tptp.rat) (B2 tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 A)) (=> (tptp.pp (tptp.aa_rat_bool _let_1 B2)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat tptp.inverse_inverse_rat A)) (tptp.aa_rat_rat tptp.inverse_inverse_rat B2))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B2) A))))))) (forall ((W tptp.int) (Z tptp.int)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_int_real tptp.ring_1_of_int_real W)) (tptp.aa_int_real tptp.ring_1_of_int_real Z))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int W) Z)))) (forall ((W tptp.int) (Z tptp.int)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_int_rat tptp.ring_1_of_int_rat W)) (tptp.aa_int_rat tptp.ring_1_of_int_rat Z))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int W) Z)))) (forall ((W tptp.int) (Z tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.ring_1_of_int_int W)) (tptp.aa_int_int tptp.ring_1_of_int_int Z))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int W) Z)))) (forall ((Z tptp.int) (N tptp.num)) (= (= (tptp.aa_int_complex tptp.ring_17405671764205052669omplex Z) (tptp.numera6690914467698888265omplex N)) (= Z (tptp.aa_num_int tptp.numeral_numeral_int N)))) (forall ((Z tptp.int) (N tptp.num)) (= (= (tptp.aa_int_real tptp.ring_1_of_int_real Z) (tptp.aa_num_real tptp.numeral_numeral_real N)) (= Z (tptp.aa_num_int tptp.numeral_numeral_int N)))) (forall ((Z tptp.int) (N tptp.num)) (= (= (tptp.aa_int_rat tptp.ring_1_of_int_rat Z) (tptp.aa_num_rat tptp.numeral_numeral_rat N)) (= Z (tptp.aa_num_int tptp.numeral_numeral_int N)))) (forall ((Z tptp.int) (N tptp.num)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int N))) (= (= (tptp.aa_int_int tptp.ring_1_of_int_int Z) _let_1) (= Z _let_1)))) (forall ((K tptp.num)) (= (tptp.aa_int_complex tptp.ring_17405671764205052669omplex (tptp.aa_num_int tptp.numeral_numeral_int K)) (tptp.numera6690914467698888265omplex K))) (forall ((K tptp.num)) (= (tptp.aa_int_real tptp.ring_1_of_int_real (tptp.aa_num_int tptp.numeral_numeral_int K)) (tptp.aa_num_real tptp.numeral_numeral_real K))) (forall ((K tptp.num)) (= (tptp.aa_int_rat tptp.ring_1_of_int_rat (tptp.aa_num_int tptp.numeral_numeral_int K)) (tptp.aa_num_rat tptp.numeral_numeral_rat K))) (forall ((K tptp.num)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int K))) (= (tptp.aa_int_int tptp.ring_1_of_int_int _let_1) _let_1))) (forall ((B2 tptp.complex) (U tptp.real) (A tptp.complex)) (let ((_let_1 (tptp.real_V2046097035970521341omplex U))) (= (= (tptp.aa_complex_complex (tptp.plus_plus_complex B2) (tptp.aa_complex_complex _let_1 A)) (tptp.aa_complex_complex (tptp.plus_plus_complex A) (tptp.aa_complex_complex _let_1 B2))) (or (= A B2) (= U tptp.one_one_real))))) (forall ((N tptp.int)) (= (tptp.aa_real_real tptp.sin_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real tptp.pi) (tptp.aa_int_real tptp.ring_1_of_int_real N))) tptp.zero_zero_real)) (forall ((X tptp.real) (I tptp.int)) (= (tptp.aa_real_real tptp.tan_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_int_real tptp.ring_1_of_int_real I)) tptp.pi))) (tptp.aa_real_real tptp.tan_real X))) (forall ((N tptp.int)) (= (tptp.aa_real_real tptp.sin_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))) tptp.pi)) (tptp.aa_int_real tptp.ring_1_of_int_real N))) tptp.zero_zero_real)) (forall ((N tptp.int)) (= (tptp.aa_real_real tptp.cos_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))) tptp.pi)) (tptp.aa_int_real tptp.ring_1_of_int_real N))) tptp.one_one_real)) (forall ((N tptp.int)) (let ((_let_1 (tptp.aa_real_real tptp.cos_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real tptp.pi) (tptp.aa_int_real tptp.ring_1_of_int_real N))))) (let ((_let_2 (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) N)))) (and (=> _let_2 (= _let_1 tptp.one_one_real)) (=> (not _let_2) (= _let_1 (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real))))))) (forall ((A tptp.real) (X tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.real_V1485227260804924795R_real A) X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) X))) (forall ((X tptp.real)) (= (tptp.aa_real_real tptp.sqrt (tptp.aa_real_real tptp.inverse_inverse_real X)) (tptp.aa_real_real tptp.inverse_inverse_real (tptp.aa_real_real tptp.sqrt X)))) (forall ((X tptp.real) (Y tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real X) Y) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real X) (tptp.aa_real_real tptp.inverse_inverse_real Y)))) (forall ((R tptp.real) (A tptp.real) (B2 tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.times_times_real R))) (= (tptp.aa_complex_complex (tptp.real_V2046097035970521341omplex R) (tptp.aa_real_complex (tptp.aa_rea2649881322057434177omplex tptp.complex2 A) B2)) (tptp.aa_real_complex (tptp.aa_rea2649881322057434177omplex tptp.complex2 (tptp.aa_real_real _let_1 A)) (tptp.aa_real_real _let_1 B2))))) (forall ((N tptp.int) (X tptp.int)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_int_real tptp.ring_1_of_int_real (tptp.aa_int_int (tptp.divide_divide_int N) X))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_int_real tptp.ring_1_of_int_real N)) (tptp.aa_int_real tptp.ring_1_of_int_real X))))) (forall ((D tptp.int) (N tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int D) N)) (= (tptp.aa_int_real tptp.ring_1_of_int_real (tptp.aa_int_int (tptp.divide_divide_int N) D)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_int_real tptp.ring_1_of_int_real N)) (tptp.aa_int_real tptp.ring_1_of_int_real D))))) (forall ((P tptp.fun_real_bool) (E tptp.real)) (=> (forall ((D2 tptp.real) (E2 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real D2) E2)) (=> (tptp.pp (tptp.aa_real_bool P D2)) (tptp.pp (tptp.aa_real_bool P E2))))) (=> (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_real_bool P (tptp.aa_real_real tptp.inverse_inverse_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real (tptp.aa_nat_nat tptp.suc N2)))))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) E)) (tptp.pp (tptp.aa_real_bool P E)))))) (forall ((P tptp.fun_real_bool) (E tptp.real)) (=> (forall ((D2 tptp.real) (E2 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real D2) E2)) (=> (tptp.pp (tptp.aa_real_bool P D2)) (tptp.pp (tptp.aa_real_bool P E2))))) (=> (forall ((N2 tptp.nat)) (=> (not (= N2 tptp.zero_zero_nat)) (tptp.pp (tptp.aa_real_bool P (tptp.aa_real_real tptp.inverse_inverse_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N2)))))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) E)) (tptp.pp (tptp.aa_real_bool P E)))))) (forall ((E tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) E)) (exists ((N5 tptp.nat)) (let ((_let_1 (tptp.aa_real_real tptp.inverse_inverse_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N5)))) (and (not (= N5 tptp.zero_zero_nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) _let_1)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real _let_1) E))))))) (forall ((N tptp.int) (M tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int N) M)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_int_real tptp.ring_1_of_int_real N)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_int_real tptp.ring_1_of_int_real M)) tptp.one_one_real))))) (forall ((X tptp.real)) (let ((_let_1 (tptp.aa_real_real tptp.sqrt X))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) X)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real _let_1) X) (tptp.aa_real_real tptp.inverse_inverse_real _let_1))))) (forall ((N tptp.int) (M tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int N) M)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_int_real tptp.ring_1_of_int_real N)) tptp.one_one_real)) (tptp.aa_int_real tptp.ring_1_of_int_real M))))) (forall ((X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) X)) (= (tptp.aa_real_real tptp.ln_ln_real (tptp.aa_real_real tptp.inverse_inverse_real X)) (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_real_real tptp.ln_ln_real X))))) (forall ((X tptp.real)) (= (= (tptp.aa_real_real tptp.sin_real X) tptp.zero_zero_real) (exists ((I4 tptp.int)) (= X (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_int_real tptp.ring_1_of_int_real I4)) tptp.pi))))) (forall ((X tptp.int) (D tptp.int)) (let ((_let_1 (tptp.aa_int_real tptp.ring_1_of_int_real D))) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_int_real tptp.ring_1_of_int_real X)) _let_1) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_int_real tptp.ring_1_of_int_real (tptp.aa_int_int (tptp.divide_divide_int X) D))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_int_real tptp.ring_1_of_int_real (tptp.aa_int_int (tptp.modulo_modulo_int X) D))) _let_1))))) (forall ((N tptp.int) (X tptp.int)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_int_real tptp.ring_1_of_int_real N)) (tptp.aa_int_real tptp.ring_1_of_int_real X))) (tptp.aa_int_real tptp.ring_1_of_int_real (tptp.aa_int_int (tptp.divide_divide_int N) X)))))) (forall ((N tptp.int) (X tptp.int)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_int_real tptp.ring_1_of_int_real N)) (tptp.aa_int_real tptp.ring_1_of_int_real X))) (tptp.aa_int_real tptp.ring_1_of_int_real (tptp.aa_int_int (tptp.divide_divide_int N) X)))) tptp.one_one_real))) (forall ((X tptp.real)) (let ((_let_1 (tptp.aa_real_real tptp.exp_real X))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real _let_1) (tptp.aa_real_real tptp.inverse_inverse_real _let_1)))))) (forall ((X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) X)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) (tptp.aa_real_real tptp.inverse_inverse_real X)))))) (forall ((X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) X)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real tptp.inverse_inverse_real (tptp.aa_real_real tptp.sqrt X))) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_real_real tptp.inverse_inverse_real X)))) (forall ((X tptp.real)) (= (= (tptp.aa_real_real tptp.cos_real X) tptp.one_one_real) (exists ((X3 tptp.int)) (= X (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_int_real tptp.ring_1_of_int_real X3)) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))) tptp.pi))))) (forall ((X tptp.real)) (= (tptp.aa_real_real tptp.tan_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))) X)) (tptp.aa_real_real tptp.inverse_inverse_real (tptp.aa_real_real tptp.tan_real X)))) (forall ((X tptp.real)) (let ((_let_1 (tptp.aa_real_real tptp.exp_real X))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) X)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real _let_1) (tptp.aa_real_real tptp.inverse_inverse_real _let_1))) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))))))) (forall ((X tptp.real)) (let ((_let_1 (tptp.aa_real_real tptp.exp_real X))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real X)) (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real _let_1) (tptp.aa_real_real tptp.inverse_inverse_real _let_1))) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))))))) (forall ((Theta tptp.real)) (not (forall ((K3 tptp.int)) (not (= (tptp.aa_real_real tptp.arccos (tptp.aa_real_real tptp.cos_real Theta)) (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real Theta) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_int_real tptp.ring_1_of_int_real K3)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))) tptp.pi))))))))) (forall ((X tptp.vEBT_VEBT)) (=> (not (tptp.pp (tptp.aa_VEBT_VEBT_bool tptp.vEBT_VEBT_minNull X))) (=> (tptp.pp (tptp.aa_VEBT_VEBT_bool (tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel) X)) (=> (forall ((Uv2 tptp.bool)) (let ((_let_1 (tptp.vEBT_Leaf tptp.fTrue Uv2))) (=> (= X _let_1) (not (tptp.pp (tptp.aa_VEBT_VEBT_bool (tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel) _let_1)))))) (=> (forall ((Uu2 tptp.bool)) (let ((_let_1 (tptp.vEBT_Leaf Uu2 tptp.fTrue))) (=> (= X _let_1) (not (tptp.pp (tptp.aa_VEBT_VEBT_bool (tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel) _let_1)))))) (not (forall ((Uz2 tptp.product_prod_nat_nat) (Va3 tptp.nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (let ((_let_1 (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat Uz2) Va3 Vb2 Vc2))) (=> (= X _let_1) (not (tptp.pp (tptp.aa_VEBT_VEBT_bool (tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel) _let_1)))))))))))) (forall ((X tptp.vEBT_VEBT)) (let ((_let_1 (tptp.vEBT_Leaf tptp.fFalse tptp.fFalse))) (let ((_let_2 (tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel))) (=> (tptp.pp (tptp.aa_VEBT_VEBT_bool tptp.vEBT_VEBT_minNull X)) (=> (tptp.pp (tptp.aa_VEBT_VEBT_bool _let_2 X)) (=> (=> (= X _let_1) (not (tptp.pp (tptp.aa_VEBT_VEBT_bool _let_2 _let_1)))) (not (forall ((Uw2 tptp.nat) (Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (let ((_let_1 (tptp.vEBT_Node tptp.none_P5556105721700978146at_nat Uw2 Ux2 Uy2))) (=> (= X _let_1) (not (tptp.pp (tptp.aa_VEBT_VEBT_bool (tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel) _let_1))))))))))))) (forall ((X tptp.real)) (= (= (tptp.aa_real_real tptp.cos_real X) tptp.zero_zero_real) (exists ((I4 tptp.int)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (and (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_num_int tptp.numeral_numeral_int _let_1)) I4))) (= X (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_int_real tptp.ring_1_of_int_real I4)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) (tptp.aa_num_real tptp.numeral_numeral_real _let_1))))))))) (forall ((X tptp.real)) (= (= (tptp.aa_real_real tptp.sin_real X) tptp.zero_zero_real) (exists ((I4 tptp.int)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_num_int tptp.numeral_numeral_int _let_1)) I4)) (= X (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_int_real tptp.ring_1_of_int_real I4)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) (tptp.aa_num_real tptp.numeral_numeral_real _let_1))))))))) (forall ((X tptp.real) (Y tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.sinh_real X)) (tptp.aa_real_real tptp.sinh_real Y))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Y)))) (forall ((X tptp.real) (Y tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.sinh_real X)) (tptp.aa_real_real tptp.sinh_real Y))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) Y)))) (forall ((X tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.sinh_real X)) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) tptp.zero_zero_real)))) (forall ((X tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real))) (= (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real tptp.sinh_real X))) (tptp.pp (tptp.aa_real_bool _let_1 X))))) (forall ((X tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (= (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real tptp.sinh_real X))) (tptp.pp (tptp.aa_real_bool _let_1 X))))) (forall ((X tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.sinh_real X)) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) tptp.zero_zero_real)))) (forall ((X tptp.complex) (Y tptp.complex)) (= (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex X) Y) (tptp.aa_complex_complex (tptp.times_times_complex X) (tptp.aa_complex_complex tptp.invers8013647133539491842omplex Y)))) (forall ((A tptp.real) (B2 tptp.real)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real A) _let_1)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real B2) _let_1)))) (= (tptp.aa_complex_complex tptp.invers8013647133539491842omplex (tptp.aa_real_complex (tptp.aa_rea2649881322057434177omplex tptp.complex2 A) B2)) (tptp.aa_real_complex (tptp.aa_rea2649881322057434177omplex tptp.complex2 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real A) _let_2)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real tptp.uminus_uminus_real B2)) _let_2)))))) (forall ((X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) X)) (= (tptp.aa_real_real tptp.sinh_real (tptp.aa_real_real tptp.ln_ln_real X)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real X) (tptp.aa_real_real tptp.inverse_inverse_real X))) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))))) (forall ((M tptp.num)) (= (tptp.unique5052692396658037445od_int (tptp.aa_num_num tptp.bitM M) (tptp.aa_num_num tptp.bit0 tptp.one)) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_num_int tptp.numeral_numeral_int M)) tptp.one_one_int)) tptp.one_one_int))) (forall ((X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.pi)) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.cot_real X)) tptp.zero_zero_real))))) (forall ((N tptp.nat)) (= (tptp.aa_nat_complex (tptp.power_power_complex tptp.imaginary_unit) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat N) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (tptp.aa_nat_complex (tptp.power_power_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex tptp.one_one_complex)) N))) (forall ((X tptp.complex)) (let ((_let_1 (tptp.times_times_complex tptp.imaginary_unit))) (= (tptp.aa_complex_complex _let_1 (tptp.aa_complex_complex _let_1 X)) (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex X)))) (forall ((K tptp.num)) (= (tptp.aa_num_nat tptp.pred_numeral (tptp.aa_num_num tptp.bit0 K)) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bitM K)))) (forall ((X tptp.complex)) (= (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex X) tptp.imaginary_unit) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex tptp.imaginary_unit)) X))) (= (tptp.aa_complex_complex _let_53 tptp.imaginary_unit) _let_54) (forall ((N tptp.nat)) (= (tptp.aa_real_real tptp.cot_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N)) tptp.pi)) tptp.zero_zero_real)) (forall ((Z tptp.complex) (N tptp.num)) (let ((_let_1 (tptp.numera6690914467698888265omplex N))) (= (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex Z) (tptp.aa_complex_complex (tptp.times_times_complex _let_1) tptp.imaginary_unit)) (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.aa_complex_complex (tptp.times_times_complex tptp.imaginary_unit) Z))) _let_1)))) (forall ((X tptp.real)) (= (tptp.aa_real_real tptp.cot_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))) tptp.pi))) (tptp.aa_real_real tptp.cot_real X))) (= (tptp.aa_nat_complex (tptp.power_power_complex tptp.imaginary_unit) _let_33) _let_54) (forall ((X tptp.real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.sinh_real X)) (tptp.aa_real_real tptp.cosh_real X)))) (forall ((X tptp.real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.sinh_real X)) (tptp.aa_real_real tptp.cosh_real X)))) (= (tptp.aa_num_num tptp.bitM tptp.one) tptp.one) (forall ((W tptp.num)) (not (= tptp.imaginary_unit (tptp.numera6690914467698888265omplex W)))) (forall ((X tptp.real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) (tptp.aa_real_real tptp.cosh_real X)))) (forall ((X tptp.real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_real_real tptp.cosh_real X)))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool _let_1 X)) (=> (tptp.pp (tptp.aa_real_bool _let_1 Y)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.cosh_real X)) (tptp.aa_real_real tptp.cosh_real Y))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) Y))))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) tptp.zero_zero_real)) (=> (tptp.pp (tptp.aa_real_bool _let_1 tptp.zero_zero_real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.cosh_real X)) (tptp.aa_real_real tptp.cosh_real Y))) (tptp.pp (tptp.aa_real_bool _let_1 X))))))) (forall ((X tptp.real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.one_one_real) (tptp.aa_real_real tptp.cosh_real X)))) (forall ((N tptp.num)) (= (tptp.aa_num_num tptp.bitM (tptp.aa_num_num tptp.bit0 N)) (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bitM N)))) (forall ((N tptp.num)) (= (tptp.aa_num_num tptp.bitM (tptp.aa_num_num tptp.bit1 N)) (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit0 N)))) (forall ((W tptp.complex) (Z tptp.complex)) (let ((_let_1 (tptp.times_times_complex tptp.imaginary_unit))) (= (= (tptp.aa_complex_complex _let_1 W) Z) (= W (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.aa_complex_complex _let_1 Z)))))) (forall ((W tptp.num)) (not (= tptp.imaginary_unit (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.numera6690914467698888265omplex W))))) (forall ((X tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Y)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.cosh_real X)) (tptp.aa_real_real tptp.cosh_real Y)))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool _let_1 X)) (=> (tptp.pp (tptp.aa_real_bool _let_1 Y)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.cosh_real X)) (tptp.aa_real_real tptp.cosh_real Y))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Y))))))) (forall ((X tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) tptp.zero_zero_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y) tptp.zero_zero_real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.cosh_real X)) (tptp.aa_real_real tptp.cosh_real Y))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y) X)))))) (forall ((X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) X)) (= (tptp.aa_real_real tptp.arcosh_real (tptp.aa_real_real tptp.cosh_real X)) X))) (forall ((N tptp.num)) (= (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 N)) (tptp.aa_nat_nat tptp.suc (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bitM N))))) (forall ((N tptp.num)) (= (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num tptp.one) (tptp.aa_num_num tptp.bitM N)) (tptp.aa_num_num tptp.bit0 N))) (forall ((N tptp.num)) (= (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num (tptp.aa_num_num tptp.bitM N)) tptp.one) (tptp.aa_num_num tptp.bit0 N))) (forall ((A tptp.real) (B2 tptp.real)) (= (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_real_complex (tptp.aa_rea2649881322057434177omplex tptp.complex2 A) B2)) tptp.imaginary_unit) (tptp.aa_real_complex (tptp.aa_rea2649881322057434177omplex tptp.complex2 (tptp.aa_real_real tptp.uminus_uminus_real B2)) A))) (forall ((A tptp.real) (B2 tptp.real)) (= (tptp.aa_complex_complex (tptp.times_times_complex tptp.imaginary_unit) (tptp.aa_real_complex (tptp.aa_rea2649881322057434177omplex tptp.complex2 A) B2)) (tptp.aa_real_complex (tptp.aa_rea2649881322057434177omplex tptp.complex2 (tptp.aa_real_real tptp.uminus_uminus_real B2)) A))) (forall ((X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) X)) (= (tptp.aa_real_real tptp.cosh_real (tptp.aa_real_real tptp.ln_ln_real X)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) (tptp.aa_real_real tptp.inverse_inverse_real X))) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))))) (forall ((X tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool _let_1 X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))))) (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real tptp.cot_real X))))))) (forall ((X tptp.real)) (= (tptp.aa_real_real tptp.tan_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))) X)) (tptp.aa_real_real tptp.cot_real X))) (= (tptp.aa_complex_real tptp.arg _let_56) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.pi)) _let_28)) (= (tptp.aa_complex_real tptp.arg tptp.imaginary_unit) _let_30) (= (tptp.aa_real_complex tptp.cis _let_31) _let_56) (forall ((X tptp.real)) (let ((_let_1 (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit0 tptp.one)))))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) X)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.log _let_1) X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real tptp.ln_ln_real (tptp.aa_real_real tptp.exp_real tptp.one_one_real))) (tptp.aa_real_real tptp.ln_ln_real _let_1))) (tptp.aa_real_real tptp.ln_ln_real X)))))) (forall ((A tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) A)) (=> (not (= A tptp.one_one_real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.log A) A) tptp.one_one_real)))) (forall ((A tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.log A))) (let ((_let_2 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real) A)) (=> (tptp.pp (tptp.aa_real_bool _let_2 X)) (=> (tptp.pp (tptp.aa_real_bool _let_2 Y)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real _let_1 X)) (tptp.aa_real_real _let_1 Y))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Y))))))))) (forall ((A tptp.real) (X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real) A)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) X)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.log A) X)) tptp.one_one_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) A)))))) (forall ((A tptp.real) (X tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real))) (=> (tptp.pp (tptp.aa_real_bool _let_1 A)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) X)) (= (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.log A) X))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) X))))))) (forall ((A tptp.real) (X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real) A)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) X)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.log A) X)) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) tptp.one_one_real)))))) (forall ((A tptp.real) (X tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real))) (let ((_let_2 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool _let_1 A)) (=> (tptp.pp (tptp.aa_real_bool _let_2 X)) (= (tptp.pp (tptp.aa_real_bool _let_2 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.log A) X))) (tptp.pp (tptp.aa_real_bool _let_1 X)))))))) (forall ((A tptp.real) (X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real) A)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) X)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.log A) X))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.one_one_real) X)))))) (forall ((A tptp.real) (X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real) A)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) X)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.log A) X)) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) tptp.one_one_real)))))) (forall ((A tptp.real) (X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real) A)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) X)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.one_one_real) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.log A) X))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) X)))))) (forall ((A tptp.real) (X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real) A)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) X)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.log A) X)) tptp.one_one_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) A)))))) (forall ((A tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.log A))) (let ((_let_2 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real) A)) (=> (tptp.pp (tptp.aa_real_bool _let_2 X)) (=> (tptp.pp (tptp.aa_real_bool _let_2 Y)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real _let_1 X)) (tptp.aa_real_real _let_1 Y))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) Y))))))))) (forall ((A tptp.real) (B2 tptp.nat)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) A)) (=> (not (= A tptp.one_one_real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.log A) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real A) B2)) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real B2))))) (= (tptp.aa_real_complex tptp.cis _let_30) tptp.imaginary_unit) (= (tptp.aa_real_complex tptp.cis _let_55) tptp.one_one_complex) (forall ((A tptp.real) (B2 tptp.real)) (= (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_real_complex tptp.cis A)) (tptp.aa_real_complex tptp.cis B2)) (tptp.aa_real_complex tptp.cis (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) B2)))) (forall ((A tptp.real) (B2 tptp.real) (X tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.log A))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) A)) (=> (not (= A tptp.one_one_real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.log B2) X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real _let_1 X)) (tptp.aa_real_real _let_1 B2))))))) (forall ((M tptp.nat) (B2 tptp.real) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_real tptp.semiri5074537144036343181t_real M))) (=> (= _let_1 (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real B2) N)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real) B2)) (= (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.log B2) _let_1)))))) (forall ((B2 tptp.real) (N tptp.nat) (M tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real B2) N)) M)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real) B2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.log B2) M)))))) (forall ((A tptp.real) (N tptp.nat)) (= (tptp.aa_nat_complex (tptp.power_power_complex (tptp.aa_real_complex tptp.cis A)) N) (tptp.aa_real_complex tptp.cis (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N)) A)))) (forall ((A tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.log A))) (let ((_let_2 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool _let_2 A)) (=> (not (= A tptp.one_one_real)) (=> (tptp.pp (tptp.aa_real_bool _let_2 X)) (=> (tptp.pp (tptp.aa_real_bool _let_2 Y)) (= (tptp.aa_real_real _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real X) Y)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real _let_1 X)) (tptp.aa_real_real _let_1 Y)))))))))) (forall ((A tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.log A))) (let ((_let_2 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool _let_2 A)) (=> (not (= A tptp.one_one_real)) (=> (tptp.pp (tptp.aa_real_bool _let_2 X)) (=> (tptp.pp (tptp.aa_real_bool _let_2 Y)) (= (tptp.aa_real_real _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real X) Y)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real _let_1 X)) (tptp.aa_real_real _let_1 Y)))))))))) (forall ((B2 tptp.real) (N tptp.nat) (M tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real B2) N)) M)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real) B2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.log B2) M)))))) (forall ((A tptp.real) (N tptp.nat) (X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) A)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.log (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real A) N)) X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.log A) X)) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N))))) (forall ((X tptp.real) (B2 tptp.real) (N tptp.nat)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.log B2))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) X)) (= (tptp.aa_real_real _let_1 (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) N)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N)) (tptp.aa_real_real _let_1 X)))))) (forall ((A tptp.real) (X tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.log A))) (let ((_let_2 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool _let_2 A)) (=> (not (= A tptp.one_one_real)) (=> (tptp.pp (tptp.aa_real_bool _let_2 X)) (= (tptp.aa_real_real _let_1 (tptp.aa_real_real tptp.inverse_inverse_real X)) (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_real_real _let_1 X))))))))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (=> (= M (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1)) N)) (= (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.log (tptp.aa_num_real tptp.numeral_numeral_real _let_1)) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real M)))))) (forall ((M tptp.nat) (B2 tptp.real) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_real tptp.semiri5074537144036343181t_real M))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real _let_1) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real B2) N))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real) B2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) M)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.log B2) _let_1)) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N)))))))) (forall ((A tptp.real) (B2 tptp.real) (X tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool _let_1 A)) (=> (not (= A tptp.one_one_real)) (=> (tptp.pp (tptp.aa_real_bool _let_1 B2)) (=> (not (= B2 tptp.one_one_real)) (=> (tptp.pp (tptp.aa_real_bool _let_1 X)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.log A) X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real tptp.ln_ln_real B2)) (tptp.aa_real_real tptp.ln_ln_real A))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.log B2) X)))))))))) (forall ((Z tptp.complex)) (let ((_let_1 (tptp.aa_complex_real tptp.arg Z))) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.pi)) _let_1)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real _let_1) tptp.pi))))) (forall ((M tptp.nat) (B2 tptp.real) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_real tptp.semiri5074537144036343181t_real M))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real _let_1) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real B2) N))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real) B2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) M)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.log B2) _let_1)) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N)))))))) (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1)) N)) M)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.log (tptp.aa_num_real tptp.numeral_numeral_real _let_1)) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real M))))))) (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1)) N)) M)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.log (tptp.aa_num_real tptp.numeral_numeral_real _let_1)) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real M))))))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1)) N))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) M)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.log (tptp.aa_num_real tptp.numeral_numeral_real _let_1)) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real M))) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N))))))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1)) N))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) M)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.log (tptp.aa_num_real tptp.numeral_numeral_real _let_1)) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real M))) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N))))))) (forall ((X tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.log (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit0 tptp.one))))))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) X)) (= (tptp.aa_real_real _let_1 X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real _let_1 (tptp.aa_real_real tptp.exp_real tptp.one_one_real))) (tptp.aa_real_real tptp.ln_ln_real X)))))) (forall ((B2 tptp.nat) (K tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat B2))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) B2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) K)) (= (= (tptp.aa_real_int tptp.archim7802044766580827645g_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.log (tptp.aa_nat_real tptp.semiri5074537144036343181t_real B2)) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real K))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N)) tptp.one_one_int)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat _let_1 N)) K)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N) tptp.one_one_nat)))))))))) (forall ((N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (tptp.pp (tptp.aa_set_complex_bool (tptp.bij_betw_nat_complex (tptp.aTP_Lamm_vg N) (tptp.set_ord_lessThan_nat N)) (tptp.collect_complex (tptp.aTP_Lamm_cq N)))))) (forall ((B2 tptp.nat) (N tptp.nat) (K tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat B2))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat _let_1 N)) K)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N) tptp.one_one_nat)))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) B2)) (= (tptp.aa_real_int tptp.archim7802044766580827645g_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.log (tptp.aa_nat_real tptp.semiri5074537144036343181t_real B2)) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real K))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N)) tptp.one_one_int))))))) (forall ((N tptp.nat)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (let ((_let_2 (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1))) (let ((_let_3 (tptp.aa_rea7340605660300375871l_real tptp.log (tptp.aa_num_real tptp.numeral_numeral_real _let_1)))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat _let_2) N)) (= (tptp.aa_real_int tptp.archim7802044766580827645g_real (tptp.aa_real_real _let_3 (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_real_int tptp.archim7802044766580827645g_real (tptp.aa_real_real _let_3 (tptp.aa_nat_real tptp.semiri5074537144036343181t_real (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) tptp.one_one_nat)) _let_2)) tptp.one_one_nat))))) tptp.one_one_int))))))) (forall ((A tptp.num) (B2 tptp.num)) (= (tptp.aa_real_int tptp.archim7802044766580827645g_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_num_real tptp.numeral_numeral_real A)) (tptp.aa_num_real tptp.numeral_numeral_real B2))) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_int_int (tptp.divide_divide_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int A))) (tptp.aa_num_int tptp.numeral_numeral_int B2))))) (forall ((A tptp.num) (B2 tptp.num)) (= (tptp.aa_real_int tptp.archim7802044766580827645g_real (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_num_real tptp.numeral_numeral_real A)) (tptp.aa_num_real tptp.numeral_numeral_real B2)))) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_int_int (tptp.divide_divide_int (tptp.aa_num_int tptp.numeral_numeral_int A)) (tptp.aa_num_int tptp.numeral_numeral_int B2))))) (forall ((X tptp.real) (B2 tptp.real) (K tptp.nat)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.powr_real B2))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real) B2)) (= (= (tptp.aa_real_int tptp.archim7802044766580827645g_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.log B2) X)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int K)) tptp.one_one_int)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real _let_1 (tptp.aa_nat_real tptp.semiri5074537144036343181t_real K))) X)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) (tptp.aa_real_real _let_1 (tptp.aa_nat_real tptp.semiri5074537144036343181t_real (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat K) tptp.one_one_nat))))))))))) (forall ((B2 tptp.nat) (K tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat B2))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) B2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) K)) (= (= (tptp.aa_real_int tptp.archim6058952711729229775r_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.log (tptp.aa_nat_real tptp.semiri5074537144036343181t_real B2)) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real K))) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat _let_1 N)) K)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat K) (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N) tptp.one_one_nat)))))))))) (forall ((D tptp.int)) (= (tptp.int_ge_less_than2 D) (tptp.collec213857154873943460nt_int (tptp.produc8560705615207772305t_bool (tptp.aTP_Lamm_vh D))))) (forall ((D tptp.int)) (= (tptp.int_ge_less_than D) (tptp.collec213857154873943460nt_int (tptp.produc8560705615207772305t_bool (tptp.aTP_Lamm_vi D))))) (forall ((X tptp.real) (A tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.powr_real X) A))) (not (= X tptp.zero_zero_real)))) (forall ((A tptp.real) (X tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.powr_real A) X)) tptp.zero_zero_real)) (= A tptp.zero_zero_real))) (forall ((X tptp.real) (A tptp.real) (B2 tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.powr_real X))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real) X)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real _let_1 A)) (tptp.aa_real_real _let_1 B2))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B2)))))) (forall ((A tptp.real) (X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real) A)) (= (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.powr_real A) X) tptp.one_one_real) (= X tptp.zero_zero_real)))) (forall ((X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) X)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.powr_real X) tptp.one_one_real) X))) (forall ((X tptp.real)) (= (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.powr_real X) tptp.one_one_real) X) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) X)))) (forall ((X tptp.real) (A tptp.real) (B2 tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.powr_real X))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real) X)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real _let_1 A)) (tptp.aa_real_real _let_1 B2))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) B2)))))) (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (tptp.aa_num_real tptp.numeral_numeral_real M))) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.powr_real _let_1) (tptp.aa_num_real tptp.numeral_numeral_real N)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real _let_1) (tptp.aa_num_nat tptp.numeral_numeral_nat N))))) (forall ((A tptp.real) (X tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool _let_1 A)) (=> (not (= A tptp.one_one_real)) (=> (tptp.pp (tptp.aa_real_bool _let_1 X)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.powr_real A) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.log A) X)) X)))))) (forall ((A tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) A)) (=> (not (= A tptp.one_one_real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.log A) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.powr_real A) Y)) Y)))) (forall ((A tptp.num) (B2 tptp.num)) (= (tptp.aa_real_int tptp.archim6058952711729229775r_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_num_real tptp.numeral_numeral_real A)) (tptp.aa_num_real tptp.numeral_numeral_real B2))) (tptp.aa_int_int (tptp.divide_divide_int (tptp.aa_num_int tptp.numeral_numeral_int A)) (tptp.aa_num_int tptp.numeral_numeral_int B2)))) (forall ((X tptp.real) (N tptp.num)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) X)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.powr_real X) (tptp.aa_num_real tptp.numeral_numeral_real N)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) (tptp.aa_num_nat tptp.numeral_numeral_nat N))))) (forall ((B2 tptp.num)) (= (tptp.aa_real_int tptp.archim6058952711729229775r_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.one_one_real) (tptp.aa_num_real tptp.numeral_numeral_real B2))) (tptp.aa_int_int (tptp.divide_divide_int tptp.one_one_int) (tptp.aa_num_int tptp.numeral_numeral_int B2)))) (forall ((A tptp.num) (B2 tptp.num)) (= (tptp.aa_real_int tptp.archim6058952711729229775r_real (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_num_real tptp.numeral_numeral_real A)) (tptp.aa_num_real tptp.numeral_numeral_real B2)))) (tptp.aa_int_int (tptp.divide_divide_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int A))) (tptp.aa_num_int tptp.numeral_numeral_int B2)))) (forall ((X tptp.real)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.powr_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.one_one_real) (tptp.aa_num_real tptp.numeral_numeral_real _let_1))) (tptp.aa_real_real tptp.abs_abs_real X)))) (forall ((B2 tptp.num)) (= (tptp.aa_real_int tptp.archim6058952711729229775r_real (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.one_one_real) (tptp.aa_num_real tptp.numeral_numeral_real B2)))) (tptp.aa_int_int (tptp.divide_divide_int (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int)) (tptp.aa_num_int tptp.numeral_numeral_int B2)))) (forall ((X tptp.real) (A tptp.real) (B2 tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.powr_real X))) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.powr_real (tptp.aa_real_real _let_1 A)) B2) (tptp.aa_real_real _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) B2))))) (forall ((A tptp.real) (X tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) tptp.zero_zero_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Y)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.powr_real Y) A)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.powr_real X) A))))))) (forall ((A tptp.real) (X tptp.real)) (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.powr_real A) X)) tptp.zero_zero_real)))) (forall ((X tptp.real) (Y tptp.real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.powr_real X) Y)))) (forall ((A tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool _let_1 A)) (=> (tptp.pp (tptp.aa_real_bool _let_1 X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) Y)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.powr_real X) A)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.powr_real Y) A)))))))) (forall ((X tptp.real) (A tptp.real) (B2 tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.powr_real X))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real _let_1 A)) (tptp.aa_real_real _let_1 B2))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real) X)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B2)))))) (forall ((A tptp.real) (B2 tptp.real) (X tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.powr_real X))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B2)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real) X)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real _let_1 A)) (tptp.aa_real_real _let_1 B2))))))) (forall ((A tptp.real) (B2 tptp.real) (X tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.powr_real X))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) B2)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.one_one_real) X)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real _let_1 A)) (tptp.aa_real_real _let_1 B2))))))) (forall ((A tptp.real) (X tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) A)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Y)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.powr_real X) A)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.powr_real Y) A))))))) (forall ((A tptp.real) (X tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) tptp.zero_zero_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) Y)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.powr_real Y) A)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.powr_real X) A))))))) (forall ((A tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.powr_real A))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) A)) (=> (not (= A tptp.one_one_real)) (= (= (tptp.aa_real_real _let_1 X) (tptp.aa_real_real _let_1 Y)) (= X Y)))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real))) (=> (tptp.pp (tptp.aa_real_bool _let_1 X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) Y)) (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.powr_real X) Y))))))) (forall ((A tptp.real) (X tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool _let_1 A)) (=> (tptp.pp (tptp.aa_real_bool _let_1 X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) tptp.one_one_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.powr_real X) A)) tptp.one_one_real))))))) (forall ((A tptp.real) (B2 tptp.real) (X tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) A)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) B2)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.one_one_real) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) Y)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.powr_real X) A)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.powr_real Y) B2)))))))) (forall ((X tptp.real) (A tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.one_one_real))) (=> (tptp.pp (tptp.aa_real_bool _let_1 X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) A)) (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.powr_real X) A))))))) (forall ((X tptp.real) (Y tptp.real) (A tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool _let_1 X)) (=> (tptp.pp (tptp.aa_real_bool _let_1 Y)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.powr_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real X) Y)) A) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.powr_real X) A)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.powr_real Y) A))))))) (forall ((X tptp.real) (Y tptp.real) (A tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool _let_1 X)) (=> (tptp.pp (tptp.aa_real_bool _let_1 Y)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.powr_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real X) Y)) A) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.powr_real X) A)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.powr_real Y) A))))))) (forall ((Y tptp.real) (A tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) Y)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.powr_real (tptp.aa_real_real tptp.inverse_inverse_real Y)) A) (tptp.aa_real_real tptp.inverse_inverse_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.powr_real Y) A))))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.powr_real B2))) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real A) (tptp.aa_real_real _let_1 C)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) (tptp.aa_real_real _let_1 (tptp.aa_real_real tptp.uminus_uminus_real C)))))) (forall ((X tptp.real) (Y tptp.real)) (=> (not (= X tptp.zero_zero_real)) (= (tptp.aa_real_real tptp.ln_ln_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.powr_real X) Y)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real Y) (tptp.aa_real_real tptp.ln_ln_real X))))) (forall ((X tptp.real) (B2 tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.log B2))) (=> (not (= X tptp.zero_zero_real)) (= (tptp.aa_real_real _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.powr_real X) Y)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real Y) (tptp.aa_real_real _let_1 X)))))) (forall ((X tptp.real) (B2 tptp.real) (K tptp.int)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.powr_real B2))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real) B2)) (= (= (tptp.aa_real_int tptp.archim6058952711729229775r_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.log B2) X)) K) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real _let_1 (tptp.aa_int_real tptp.ring_1_of_int_real K))) X)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) (tptp.aa_real_real _let_1 (tptp.aa_int_real tptp.ring_1_of_int_real (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int K) tptp.one_one_int))))))))))) (forall ((X tptp.real) (N tptp.nat)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) X)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.powr_real X) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) N)))) (forall ((B2 tptp.real) (X tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real) B2)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) X)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.powr_real B2) Y)) X)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.log B2) X))))))) (forall ((B2 tptp.real) (X tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real) B2)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) X)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.powr_real B2) Y))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.log B2) X)) Y)))))) (forall ((B2 tptp.real) (X tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real) B2)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) X)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.log B2) X)) Y)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.powr_real B2) Y))))))) (forall ((B2 tptp.real) (X tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real) B2)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) X)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.log B2) X))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.powr_real B2) Y)) X)))))) (forall ((N tptp.int) (X tptp.real)) (let ((_let_1 (tptp.aa_int_real tptp.ring_1_of_int_real N))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real _let_1) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real _let_1) tptp.one_one_real))) (= (tptp.aa_real_int tptp.archim6058952711729229775r_real X) N))))) (forall ((R tptp.real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real R) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_int_real tptp.ring_1_of_int_real (tptp.aa_real_int tptp.archim6058952711729229775r_real R))) tptp.one_one_real)))) (forall ((R tptp.real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real R) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_int_real tptp.ring_1_of_int_real (tptp.aa_real_int tptp.archim6058952711729229775r_real R))) tptp.one_one_real)))) (forall ((R tptp.real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real R) tptp.one_one_real)) (tptp.aa_int_real tptp.ring_1_of_int_real (tptp.aa_real_int tptp.archim6058952711729229775r_real R))))) (forall ((R tptp.real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real R) tptp.one_one_real)) (tptp.aa_int_real tptp.ring_1_of_int_real (tptp.aa_real_int tptp.archim6058952711729229775r_real R))))) (forall ((X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) X)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.powr_real X) (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.one_one_real) X)))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.powr_real X))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) X)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real X) (tptp.aa_real_real _let_1 Y)) (tptp.aa_real_real _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real tptp.one_one_real) Y)))))) (forall ((B2 tptp.real) (X tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real) B2)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) X)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.log B2) X))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.powr_real B2) Y)) X)))))) (forall ((B2 tptp.real) (X tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real) B2)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) X)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.log B2) X)) Y)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.powr_real B2) Y))))))) (forall ((B2 tptp.real) (X tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real) B2)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) X)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.powr_real B2) Y))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.log B2) X)) Y)))))) (forall ((B2 tptp.real) (X tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real) B2)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) X)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.powr_real B2) Y)) X)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.log B2) X))))))) (forall ((N tptp.int) (X tptp.real)) (let ((_let_1 (tptp.aa_int_real tptp.ring_1_of_int_real N))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real _let_1) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real _let_1) tptp.one_one_real))) (= (tptp.aa_real_int tptp.archim6058952711729229775r_real X) N))))) (forall ((B2 tptp.int) (A tptp.real)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) B2)) (= (tptp.aa_real_int tptp.archim6058952711729229775r_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real A) (tptp.aa_int_real tptp.ring_1_of_int_real B2))) (tptp.aa_int_int (tptp.divide_divide_int (tptp.aa_real_int tptp.archim6058952711729229775r_real A)) B2)))) (forall ((X tptp.real) (A tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.one_one_real) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) A)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.ln_ln_real X)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.powr_real X) A)) A)))))) (forall ((X tptp.real) (A tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) A)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.powr_real (tptp.aa_real_real tptp.ln_ln_real X)) A)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.powr_real A) A)) X)))))) (forall ((B2 tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.log B2))) (let ((_let_2 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool _let_2 B2)) (=> (not (= B2 tptp.one_one_real)) (=> (tptp.pp (tptp.aa_real_bool _let_2 X)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real _let_1 X)) Y) (tptp.aa_real_real _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.powr_real B2) Y)))))))))) (forall ((B2 tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.log B2))) (let ((_let_2 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool _let_2 B2)) (=> (not (= B2 tptp.one_one_real)) (=> (tptp.pp (tptp.aa_real_bool _let_2 X)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real Y) (tptp.aa_real_real _let_1 X)) (tptp.aa_real_real _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.powr_real B2) Y)) X))))))))) (forall ((B2 tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.log B2))) (let ((_let_2 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool _let_2 B2)) (=> (not (= B2 tptp.one_one_real)) (=> (tptp.pp (tptp.aa_real_bool _let_2 X)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real Y) (tptp.aa_real_real _let_1 X)) (tptp.aa_real_real _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.powr_real B2) Y)) X))))))))) (forall ((B2 tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.log B2))) (let ((_let_2 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool _let_2 B2)) (=> (not (= B2 tptp.one_one_real)) (=> (tptp.pp (tptp.aa_real_bool _let_2 X)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real _let_1 X)) Y) (tptp.aa_real_real _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.powr_real B2) (tptp.aa_real_real tptp.uminus_uminus_real Y))))))))))) (forall ((X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) X)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.powr_real X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.one_one_real) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))) (tptp.aa_real_real tptp.sqrt X)))) (forall ((X tptp.real) (N tptp.num)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) X)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.powr_real X) (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real N))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.one_one_real) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) (tptp.aa_num_nat tptp.numeral_numeral_nat N)))))) (forall ((N tptp.nat)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (let ((_let_2 (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1))) (let ((_let_3 (tptp.aa_rea7340605660300375871l_real tptp.log (tptp.aa_num_real tptp.numeral_numeral_real _let_1)))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat _let_2) N)) (= (tptp.aa_real_int tptp.archim6058952711729229775r_real (tptp.aa_real_real _let_3 (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_real_int tptp.archim6058952711729229775r_real (tptp.aa_real_real _let_3 (tptp.aa_nat_real tptp.semiri5074537144036343181t_real (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat N) _let_2))))) tptp.one_one_int))))))) (forall ((B2 tptp.nat) (N tptp.nat) (K tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat B2))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat _let_1 N)) K)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat K) (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N) tptp.one_one_nat)))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) B2)) (= (tptp.aa_real_int tptp.archim6058952711729229775r_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.log (tptp.aa_nat_real tptp.semiri5074537144036343181t_real B2)) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real K))) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N))))))) (forall ((A0 tptp.int) (A1 tptp.int) (P tptp.fun_int_fun_int_bool)) (=> (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.accp_P1096762738010456898nt_int tptp.upto_rel) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int A0) A1))) (=> (forall ((I3 tptp.int) (J2 tptp.int)) (=> (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.accp_P1096762738010456898nt_int tptp.upto_rel) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int I3) J2))) (=> (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int I3) J2)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool P (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int I3) tptp.one_one_int)) J2))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool P I3) J2))))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool P A0) A1))))) (= (tptp.aa_complex_complex tptp.exp_complex (tptp.aa_complex_complex _let_52 tptp.imaginary_unit)) _let_54) (= (tptp.aa_complex_complex tptp.exp_complex (tptp.aa_complex_complex _let_53 _let_51)) _let_54) (= (tptp.aa_complex_complex tptp.exp_complex (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_complex_complex (tptp.times_times_complex _let_50) _let_51)) tptp.imaginary_unit)) tptp.one_one_complex) (= (tptp.aa_complex_complex tptp.exp_complex (tptp.aa_complex_complex _let_53 (tptp.aa_complex_complex _let_52 _let_50))) tptp.one_one_complex) (forall ((Z tptp.complex)) (exists ((A3 tptp.complex) (R3 tptp.real)) (= Z (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_real_complex tptp.real_V4546457046886955230omplex R3)) (tptp.aa_complex_complex tptp.exp_complex A3))))) (forall ((R tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.times_times_real R))) (= (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_real_complex tptp.real_V4546457046886955230omplex R)) (tptp.aa_real_complex (tptp.aa_rea2649881322057434177omplex tptp.complex2 X) Y)) (tptp.aa_real_complex (tptp.aa_rea2649881322057434177omplex tptp.complex2 (tptp.aa_real_real _let_1 X)) (tptp.aa_real_real _let_1 Y))))) (forall ((X tptp.real) (Y tptp.real) (R tptp.real)) (= (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_real_complex (tptp.aa_rea2649881322057434177omplex tptp.complex2 X) Y)) (tptp.aa_real_complex tptp.real_V4546457046886955230omplex R)) (tptp.aa_real_complex (tptp.aa_rea2649881322057434177omplex tptp.complex2 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real X) R)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real Y) R)))) (forall ((B2 tptp.real)) (= (tptp.aa_real_complex tptp.cis B2) (tptp.aa_complex_complex tptp.exp_complex (tptp.aa_complex_complex (tptp.times_times_complex tptp.imaginary_unit) (tptp.aa_real_complex tptp.real_V4546457046886955230omplex B2))))) (forall ((R tptp.real)) (= (tptp.aa_complex_complex (tptp.times_times_complex tptp.imaginary_unit) (tptp.aa_real_complex tptp.real_V4546457046886955230omplex R)) (tptp.aa_real_complex (tptp.aa_rea2649881322057434177omplex tptp.complex2 tptp.zero_zero_real) R))) (forall ((R tptp.real)) (= (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_real_complex tptp.real_V4546457046886955230omplex R)) tptp.imaginary_unit) (tptp.aa_real_complex (tptp.aa_rea2649881322057434177omplex tptp.complex2 tptp.zero_zero_real) R))) (forall ((A tptp.real) (B2 tptp.real)) (= (tptp.aa_real_complex (tptp.aa_rea2649881322057434177omplex tptp.complex2 A) B2) (tptp.aa_complex_complex (tptp.plus_plus_complex (tptp.aa_real_complex tptp.real_V4546457046886955230omplex A)) (tptp.aa_complex_complex (tptp.times_times_complex tptp.imaginary_unit) (tptp.aa_real_complex tptp.real_V4546457046886955230omplex B2))))) (forall ((Z tptp.complex)) (exists ((R3 tptp.real) (A3 tptp.real)) (= Z (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_real_complex tptp.real_V4546457046886955230omplex R3)) (tptp.aa_complex_complex (tptp.plus_plus_complex (tptp.aa_real_complex tptp.real_V4546457046886955230omplex (tptp.aa_real_real tptp.cos_real A3))) (tptp.aa_complex_complex (tptp.times_times_complex tptp.imaginary_unit) (tptp.aa_real_complex tptp.real_V4546457046886955230omplex (tptp.aa_real_real tptp.sin_real A3)))))))) (forall ((A tptp.real)) (= (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.aa_complex_complex (tptp.plus_plus_complex (tptp.aa_real_complex tptp.real_V4546457046886955230omplex (tptp.aa_real_real tptp.cos_real A))) (tptp.aa_complex_complex (tptp.times_times_complex tptp.imaginary_unit) (tptp.aa_real_complex tptp.real_V4546457046886955230omplex (tptp.aa_real_real tptp.sin_real A))))) tptp.one_one_real)) (forall ((R tptp.real) (A tptp.real)) (= (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_real_complex tptp.real_V4546457046886955230omplex R)) (tptp.aa_complex_complex (tptp.plus_plus_complex (tptp.aa_real_complex tptp.real_V4546457046886955230omplex (tptp.aa_real_real tptp.cos_real A))) (tptp.aa_complex_complex (tptp.times_times_complex tptp.imaginary_unit) (tptp.aa_real_complex tptp.real_V4546457046886955230omplex (tptp.aa_real_real tptp.sin_real A)))))) (tptp.aa_real_real tptp.abs_abs_real R))) (= (tptp.aa_complex_complex tptp.csqrt tptp.imaginary_unit) (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex (tptp.aa_complex_complex _let_49 tptp.imaginary_unit)) (tptp.aa_real_complex tptp.real_V4546457046886955230omplex _let_48))) (forall ((Y tptp.real)) (= (tptp.aa_real_real tptp.arctan Y) (tptp.the_real (tptp.aa_rea7809428808904475482l_bool tptp.aTP_Lamm_vj Y)))) (forall ((Y tptp.real)) (= (tptp.aa_real_real tptp.arcsin Y) (tptp.the_real (tptp.aa_rea7809428808904475482l_bool tptp.aTP_Lamm_vk Y)))) (forall ((A4 tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A4)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_set_nat_nat tptp.nat_set_encode A4))) (not (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat tptp.zero_zero_nat) A4)))))) (forall ((Z tptp.complex)) (= (tptp.aa_nat_complex (tptp.power_power_complex (tptp.aa_complex_complex tptp.csqrt Z)) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) Z)) (forall ((X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) tptp.zero_zero_real)) (= (tptp.aa_real_real tptp.ln_ln_real X) (tptp.the_real tptp.aTP_Lamm_vl)))) (forall ((X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) X)) (= (tptp.aa_real_complex tptp.real_V4546457046886955230omplex (tptp.aa_real_real tptp.sqrt X)) (tptp.aa_complex_complex tptp.csqrt (tptp.aa_real_complex tptp.real_V4546457046886955230omplex X))))) (forall ((Y tptp.real)) (= (tptp.aa_real_real tptp.arccos Y) (tptp.the_real (tptp.aa_rea7809428808904475482l_bool tptp.aTP_Lamm_vm Y)))) (= tptp.nat_set_encode (tptp.groups3542108847815614940at_nat _let_47)) (= _let_30 _let_45) (= tptp.pi (tptp.aa_real_real _let_46 _let_45)) (forall ((L tptp.int) (K tptp.int) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat M) N)))) (let ((_let_2 (tptp.aa_int_int tptp.sgn_sgn_int L))) (let ((_let_3 (tptp.aa_int_fun_int_int tptp.times_times_int _let_2))) (let ((_let_4 (tptp.aa_int_int tptp.sgn_sgn_int K))) (let ((_let_5 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int _let_4) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int M)))) (let ((_let_6 (tptp.aa_int_int (tptp.modulo_modulo_int _let_5) (tptp.aa_int_int _let_3 (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N))))) (let ((_let_7 (= _let_4 _let_2))) (let ((_let_8 (or (= _let_2 tptp.zero_zero_int) (= _let_4 tptp.zero_zero_int) (= N tptp.zero_zero_nat)))) (and (=> _let_8 (= _let_6 _let_5)) (=> (not _let_8) (and (=> _let_7 (= _let_6 (tptp.aa_int_int _let_3 _let_1))) (=> (not _let_7) (= _let_6 (tptp.aa_int_int _let_3 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat N) (tptp.zero_n2687167440665602831ol_nat (tptp.aa_bool_bool tptp.fNot (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat N) M)))))) _let_1)))))))))))))))) (forall ((X32 tptp.num)) (= (tptp.aa_num_nat tptp.size_num (tptp.aa_num_num tptp.bit1 X32)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_num_nat tptp.size_num X32)) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)))) (forall ((X tptp.real) (I tptp.int)) (let ((_let_1 (tptp.aa_real_fun_nat_real tptp.power_power_real X))) (let ((_let_2 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.powr_real X) (tptp.aa_int_real tptp.ring_1_of_int_real I)))) (let ((_let_3 (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) I)))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) X)) (and (=> _let_3 (= _let_2 (tptp.aa_nat_real _let_1 (tptp.aa_int_nat tptp.nat2 I)))) (=> (not _let_3) (= _let_2 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.one_one_real) (tptp.aa_nat_real _let_1 (tptp.aa_int_nat tptp.nat2 (tptp.aa_int_int tptp.uminus_uminus_int I)))))))))))) (forall ((N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat))) (= (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat tptp.bit_se2002935070580805687sk_nat N))) (tptp.pp (tptp.aa_nat_bool _let_1 N))))) (forall ((K tptp.num)) (= (tptp.aa_int_nat tptp.nat2 (tptp.aa_num_int tptp.numeral_numeral_int K)) (tptp.aa_num_nat tptp.numeral_numeral_nat K))) (forall ((I tptp.int)) (= (= (tptp.aa_int_nat tptp.nat2 I) tptp.zero_zero_nat) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int I) tptp.zero_zero_int)))) (forall ((Z tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Z) tptp.zero_zero_int)) (= (tptp.aa_int_nat tptp.nat2 Z) tptp.zero_zero_nat))) (forall ((W tptp.int) (Z tptp.int)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_int_nat tptp.nat2 W)) (tptp.aa_int_nat tptp.nat2 Z))) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) Z)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int W) Z))))) (forall ((K tptp.num)) (= (tptp.aa_int_nat tptp.nat2 (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int K))) tptp.zero_zero_nat)) (forall ((Z tptp.int)) (let ((_let_1 (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_int_nat tptp.nat2 Z)))) (let ((_let_2 (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) Z)))) (and (=> _let_2 (= _let_1 Z)) (=> (not _let_2) (= _let_1 tptp.zero_zero_int)))))) (forall ((R tptp.int) (L tptp.int) (K tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int tptp.sgn_sgn_int R)) L)) K)) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int L) K)) (=> (= R tptp.zero_zero_int) (= K tptp.zero_zero_int))))) (forall ((L tptp.int) (R tptp.int) (K tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int L) (tptp.aa_int_int tptp.sgn_sgn_int R))) K)) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int L) K)) (=> (= R tptp.zero_zero_int) (= K tptp.zero_zero_int))))) (forall ((L tptp.int) (R tptp.int) (K tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int L))) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int tptp.sgn_sgn_int R)) K))) (or (tptp.pp (tptp.aa_int_bool _let_1 K)) (= R tptp.zero_zero_int))))) (forall ((L tptp.int) (K tptp.int) (R tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int L))) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int K) (tptp.aa_int_int tptp.sgn_sgn_int R)))) (or (tptp.pp (tptp.aa_int_bool _let_1 K)) (= R tptp.zero_zero_int))))) (forall ((Z tptp.int)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.aa_int_nat tptp.nat2 Z))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) Z)))) (forall ((V tptp.num) (V3 tptp.num)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_num_nat tptp.numeral_numeral_nat V)) (tptp.aa_num_nat tptp.numeral_numeral_nat V3)) (tptp.aa_int_nat tptp.nat2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_num_int tptp.numeral_numeral_int V)) (tptp.aa_num_int tptp.numeral_numeral_int V3))))) (forall ((Y tptp.int) (X tptp.num) (N tptp.nat)) (= (= (tptp.aa_int_nat tptp.nat2 Y) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat X)) N)) (= Y (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int X)) N)))) (forall ((X tptp.num) (N tptp.nat) (Y tptp.int)) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat X)) N) (tptp.aa_int_nat tptp.nat2 Y)) (= (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int X)) N) Y))) (forall ((X tptp.real) (A tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_int_nat tptp.nat2 (tptp.aa_real_int tptp.archim7802044766580827645g_real X))) A)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real A))))) (forall ((Z tptp.int)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)) (tptp.aa_int_nat tptp.nat2 Z))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.one_one_int) Z)))) (forall ((V tptp.num)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_num_nat tptp.numeral_numeral_nat V)) tptp.one_one_nat) (tptp.aa_int_nat tptp.nat2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_num_int tptp.numeral_numeral_int V)) tptp.one_one_int)))) (forall ((A tptp.int) (X tptp.num) (N tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_int_nat tptp.nat2 A)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat X)) N))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int X)) N))))) (forall ((X tptp.num) (N tptp.nat) (A tptp.int)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat X)) N)) (tptp.aa_int_nat tptp.nat2 A))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int X)) N)) A)))) (forall ((A tptp.int) (X tptp.num) (N tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_int_nat tptp.nat2 A)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat X)) N))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int X)) N))))) (forall ((X tptp.num) (N tptp.nat) (A tptp.int)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat X)) N)) (tptp.aa_int_nat tptp.nat2 A))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int X)) N)) A)))) (forall ((N tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N) (tptp.aa_nat_nat tptp.bit_se2002935070580805687sk_nat N)))) (forall ((N tptp.nat)) (= (tptp.aa_int_nat tptp.nat2 (tptp.aa_nat_int tptp.bit_se2000444600071755411sk_int N)) (tptp.aa_nat_nat tptp.bit_se2002935070580805687sk_nat N))) (= tptp.zero_zero_nat (tptp.aa_int_nat tptp.nat2 tptp.zero_zero_int)) (forall ((X5 tptp.num)) (= (tptp.aa_num_nat tptp.numeral_numeral_nat X5) (tptp.aa_int_nat tptp.nat2 (tptp.aa_num_int tptp.numeral_numeral_int X5)))) (forall ((X tptp.int) (Y tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X) Y)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_int_nat tptp.nat2 X)) (tptp.aa_int_nat tptp.nat2 Y))))) (forall ((K tptp.int)) (not (forall ((N2 tptp.nat) (L3 tptp.int)) (not (= K (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int tptp.sgn_sgn_int L3)) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N2))))))) (forall ((P tptp.fun_nat_bool)) (= (exists ((X_1 tptp.nat)) (tptp.pp (tptp.aa_nat_bool P X_1))) (exists ((X3 tptp.int)) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) X3)) (tptp.pp (tptp.aa_nat_bool P (tptp.aa_int_nat tptp.nat2 X3))))))) (forall ((P tptp.fun_nat_bool)) (= (forall ((X_1 tptp.nat)) (tptp.pp (tptp.aa_nat_bool P X_1))) (forall ((X3 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) X3)) (tptp.pp (tptp.aa_nat_bool P (tptp.aa_int_nat tptp.nat2 X3))))))) (forall ((Z tptp.int) (Z5 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.pp (tptp.aa_int_bool _let_1 Z)) (=> (tptp.pp (tptp.aa_int_bool _let_1 Z5)) (= (= (tptp.aa_int_nat tptp.nat2 Z) (tptp.aa_int_nat tptp.nat2 Z5)) (= Z Z5)))))) (= tptp.one_one_nat (tptp.aa_int_nat tptp.nat2 tptp.one_one_int)) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se4205575877204974255it_nat M) N) (tptp.aa_int_nat tptp.nat2 (tptp.aa_int_int (tptp.bit_se4203085406695923979it_int M) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N))))) (forall ((N tptp.nat)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.aa_nat_int tptp.bit_se2000444600071755411sk_int N)))) (forall ((N tptp.nat)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_nat_int tptp.bit_se2000444600071755411sk_int N)) tptp.zero_zero_int)))) (forall ((Z tptp.int) (W tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) Z)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_int_nat tptp.nat2 W)) (tptp.aa_int_nat tptp.nat2 Z))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int W) Z))))) (forall ((M tptp.nat) (Z tptp.int)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) (tptp.aa_int_nat tptp.nat2 Z))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int M)) Z)))) (forall ((X tptp.int) (N tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_int_nat tptp.nat2 X)) N)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N))))) (forall ((Z tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) Z)) (= (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_int_nat tptp.nat2 Z)) Z))) (forall ((M tptp.nat) (Z tptp.int)) (= (= (tptp.aa_nat_int tptp.semiri1314217659103216013at_int M) Z) (and (= M (tptp.aa_int_nat tptp.nat2 Z)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) Z))))) (forall ((A tptp.nat) (B2 tptp.nat)) (= (tptp.aa_int_nat tptp.nat2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int A)) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int B2))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) B2))) (forall ((L tptp.int) (K tptp.int)) (=> (not (= L tptp.zero_zero_int)) (=> (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int L) K))) (= (tptp.aa_int_int tptp.sgn_sgn_int (tptp.aa_int_int (tptp.modulo_modulo_int K) L)) (tptp.aa_int_int tptp.sgn_sgn_int L))))) (forall ((N tptp.nat) (M tptp.nat)) (= (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) M)) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_int_nat tptp.nat2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N)) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int M)))))) (forall ((W tptp.int) (Z tptp.int)) (= (tptp.aa_int_nat tptp.nat2 (tptp.aa_int_int tptp.abs_abs_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int W) Z))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_int_nat tptp.nat2 (tptp.aa_int_int tptp.abs_abs_int W))) (tptp.aa_int_nat tptp.nat2 (tptp.aa_int_int tptp.abs_abs_int Z))))) (forall ((X5 tptp.nat) (Xa tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat X5) Xa) (tptp.aa_int_nat tptp.nat2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int X5)) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int Xa))))) (forall ((X5 tptp.nat) (Xa tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat X5) Xa) (tptp.aa_int_nat tptp.nat2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int X5)) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int Xa))))) (forall ((X tptp.real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real (tptp.aa_int_nat tptp.nat2 (tptp.aa_real_int tptp.archim7802044766580827645g_real X)))))) (forall ((N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)) N)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N) (tptp.aa_nat_nat tptp.bit_se2002935070580805687sk_nat N))))) (forall ((X5 tptp.nat) (Xa tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat X5) Xa) (tptp.aa_int_nat tptp.nat2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int X5)) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int Xa))))) (forall ((X5 tptp.nat) (Xa tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat X5) Xa) (tptp.aa_int_nat tptp.nat2 (tptp.aa_int_int (tptp.divide_divide_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int X5)) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int Xa))))) (forall ((X5 tptp.nat) (Xa tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat X5) Xa) (tptp.aa_int_nat tptp.nat2 (tptp.aa_int_int (tptp.modulo_modulo_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int X5)) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int Xa))))) (forall ((I tptp.int)) (let ((_let_1 (tptp.aa_int_int tptp.sgn_sgn_int I))) (let ((_let_2 (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_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.aa_int_int tptp.uminus_uminus_int tptp.one_one_int)))))))))) (forall ((W tptp.int) (Z tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) W)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_int_nat tptp.nat2 W)) (tptp.aa_int_nat tptp.nat2 Z))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int W) Z))))) (forall ((W tptp.int) (Z tptp.int)) (=> (or (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) W)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) Z))) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_int_nat tptp.nat2 W)) (tptp.aa_int_nat tptp.nat2 Z))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int W) Z))))) (forall ((W tptp.int) (M tptp.nat)) (let ((_let_1 (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) W)))) (= (= (tptp.aa_int_nat tptp.nat2 W) M) (and (=> _let_1 (= W (tptp.aa_nat_int tptp.semiri1314217659103216013at_int M))) (=> (not _let_1) (= M tptp.zero_zero_nat)))))) (forall ((M tptp.nat) (W tptp.int)) (let ((_let_1 (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) W)))) (= (= M (tptp.aa_int_nat tptp.nat2 W)) (and (=> _let_1 (= W (tptp.aa_nat_int tptp.semiri1314217659103216013at_int M))) (=> (not _let_1) (= M tptp.zero_zero_nat)))))) (forall ((P tptp.fun_nat_bool) (I tptp.int)) (= (tptp.pp (tptp.aa_nat_bool P (tptp.aa_int_nat tptp.nat2 I))) (and (forall ((N5 tptp.nat)) (=> (= I (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N5)) (tptp.pp (tptp.aa_nat_bool P N5)))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int I) tptp.zero_zero_int)) (tptp.pp (tptp.aa_nat_bool P tptp.zero_zero_nat)))))) (forall ((K tptp.int) (N tptp.nat)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) K)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N) (tptp.aa_int_nat tptp.nat2 K))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N)) K))))) (forall ((Z tptp.int) (Z5 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.pp (tptp.aa_int_bool _let_1 Z)) (=> (tptp.pp (tptp.aa_int_bool _let_1 Z5)) (= (tptp.aa_int_nat tptp.nat2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int Z) Z5)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_int_nat tptp.nat2 Z)) (tptp.aa_int_nat tptp.nat2 Z5))))))) (forall ((V tptp.int) (K tptp.int) (L tptp.int)) (let ((_let_1 (tptp.aa_int_int tptp.abs_abs_int L))) (let ((_let_2 (tptp.aa_int_int tptp.abs_abs_int K))) (let ((_let_3 (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int tptp.sgn_sgn_int V)))) (=> (not (= V tptp.zero_zero_int)) (= (tptp.aa_int_int (tptp.divide_divide_int (tptp.aa_int_int _let_3 _let_2)) (tptp.aa_int_int _let_3 _let_1)) (tptp.aa_int_int (tptp.divide_divide_int _let_2) _let_1))))))) (forall ((Z tptp.int) (Z5 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) Z)) (= (tptp.aa_int_nat tptp.nat2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int Z) Z5)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_int_nat tptp.nat2 Z)) (tptp.aa_int_nat tptp.nat2 Z5))))) (forall ((X5 tptp.nat)) (= (tptp.aa_nat_nat tptp.suc X5) (tptp.aa_int_nat tptp.nat2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int X5)) tptp.one_one_int)))) (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.pp (tptp.aa_int_bool _let_1 X)) (=> (tptp.pp (tptp.aa_int_bool _let_1 Y)) (= (tptp.aa_int_nat tptp.nat2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int X) Y)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_int_nat tptp.nat2 X)) (tptp.aa_int_nat tptp.nat2 Y))))))) (forall ((Z5 tptp.int) (Z tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) Z5)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Z5) Z)) (= (tptp.aa_int_nat tptp.nat2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int Z) Z5)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_int_nat tptp.nat2 Z)) (tptp.aa_int_nat tptp.nat2 Z5)))))) (forall ((K tptp.int) (L tptp.int)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_int_nat tptp.nat2 (tptp.aa_int_int tptp.abs_abs_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int K) L)))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_int_nat tptp.nat2 (tptp.aa_int_int tptp.abs_abs_int K))) (tptp.aa_int_nat tptp.nat2 (tptp.aa_int_int tptp.abs_abs_int L)))))) (forall ((Y tptp.int) (X tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) Y)) (= (tptp.aa_int_nat tptp.nat2 (tptp.aa_int_int (tptp.divide_divide_int X) Y)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_int_nat tptp.nat2 X)) (tptp.aa_int_nat tptp.nat2 Y))))) (forall ((X tptp.int) (Y tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) X)) (= (tptp.aa_int_nat tptp.nat2 (tptp.aa_int_int (tptp.divide_divide_int X) Y)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_int_nat tptp.nat2 X)) (tptp.aa_int_nat tptp.nat2 Y))))) (forall ((L tptp.int) (K tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int L) K)) (= (tptp.aa_int_int (tptp.divide_divide_int K) L) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int tptp.sgn_sgn_int K)) (tptp.aa_int_int tptp.sgn_sgn_int L))) (tptp.aa_int_int (tptp.divide_divide_int (tptp.aa_int_int tptp.abs_abs_int K)) (tptp.aa_int_int tptp.abs_abs_int L)))))) (forall ((Z tptp.int) (N tptp.nat)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) Z)) (= (tptp.aa_int_nat tptp.nat2 (tptp.aa_nat_int (tptp.power_power_int Z) N)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_int_nat tptp.nat2 Z)) N)))) (forall ((X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) tptp.zero_zero_real)) (= (tptp.aa_int_nat tptp.nat2 (tptp.aa_real_int tptp.archim6058952711729229775r_real X)) tptp.zero_zero_nat))) (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.pp (tptp.aa_int_bool _let_1 X)) (=> (tptp.pp (tptp.aa_int_bool _let_1 Y)) (= (tptp.aa_int_nat tptp.nat2 (tptp.aa_int_int (tptp.modulo_modulo_int X) Y)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_int_nat tptp.nat2 X)) (tptp.aa_int_nat tptp.nat2 Y))))))) (forall ((K tptp.int) (L tptp.int)) (let ((_let_1 (tptp.aa_int_int tptp.abs_abs_int L))) (let ((_let_2 (tptp.aa_int_int tptp.abs_abs_int K))) (= (tptp.aa_int_int (tptp.divide_divide_int _let_2) _let_1) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_int_nat tptp.nat2 _let_2)) (tptp.aa_int_nat tptp.nat2 _let_1))))))) (forall ((N tptp.nat) (X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N)) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real (tptp.aa_nat_nat tptp.suc N)))) (= (tptp.aa_int_nat tptp.nat2 (tptp.aa_real_int tptp.archim6058952711729229775r_real X)) N)))) (forall ((X tptp.nat) (A tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real X)) A)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X) (tptp.aa_int_nat tptp.nat2 (tptp.aa_real_int tptp.archim6058952711729229775r_real A)))))) (forall ((L tptp.int) (K tptp.int)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_int_nat tptp.nat2 (tptp.aa_int_int tptp.abs_abs_int K))) (tptp.aa_int_nat tptp.nat2 (tptp.aa_int_int tptp.abs_abs_int L))))) (let ((_let_2 (tptp.aa_int_int (tptp.divide_divide_int K) L))) (let ((_let_3 (= (tptp.aa_int_int tptp.sgn_sgn_int K) (tptp.aa_int_int tptp.sgn_sgn_int L)))) (let ((_let_4 (= L tptp.zero_zero_int))) (and (=> _let_4 (= _let_2 tptp.zero_zero_int)) (=> (not _let_4) (and (=> _let_3 (= _let_2 (tptp.aa_nat_int tptp.semiri1314217659103216013at_int _let_1))) (=> (not _let_3) (= _let_2 (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat _let_1) (tptp.zero_n2687167440665602831ol_nat (tptp.aa_bool_bool tptp.fNot (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int L) K)))))))))))))))) (forall ((L tptp.int) (K tptp.int)) (let ((_let_1 (tptp.aa_int_int tptp.abs_abs_int L))) (let ((_let_2 (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_int_nat tptp.nat2 (tptp.aa_int_int tptp.abs_abs_int K))) (tptp.aa_int_nat tptp.nat2 _let_1))))) (let ((_let_3 (tptp.aa_int_int tptp.sgn_sgn_int L))) (let ((_let_4 (tptp.aa_int_fun_int_int tptp.times_times_int _let_3))) (let ((_let_5 (tptp.aa_int_int (tptp.modulo_modulo_int K) L))) (let ((_let_6 (= (tptp.aa_int_int tptp.sgn_sgn_int K) _let_3))) (let ((_let_7 (= L tptp.zero_zero_int))) (and (=> _let_7 (= _let_5 K)) (=> (not _let_7) (and (=> _let_6 (= _let_5 (tptp.aa_int_int _let_4 _let_2))) (=> (not _let_6) (= _let_5 (tptp.aa_int_int _let_4 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int _let_1) (tptp.aa_bool_int tptp.zero_n2684676970156552555ol_int (tptp.aa_bool_bool tptp.fNot (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int L) K))))) _let_2))))))))))))))) (= (tptp.aa_int_nat tptp.nat2 _let_44) _let_43) (forall ((Z tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) Z)) (= (tptp.aa_nat_nat tptp.suc (tptp.aa_int_nat tptp.nat2 Z)) (tptp.aa_int_nat tptp.nat2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int tptp.one_one_int) Z))))) (forall ((W tptp.int) (M tptp.nat)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) W)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_int_nat tptp.nat2 W)) M)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int W) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int M)))))) (forall ((Z tptp.int) (Z5 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Z) tptp.zero_zero_int)) (= (tptp.aa_int_nat tptp.nat2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int Z) Z5)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_int_nat tptp.nat2 (tptp.aa_int_int tptp.uminus_uminus_int Z))) (tptp.aa_int_nat tptp.nat2 (tptp.aa_int_int tptp.uminus_uminus_int Z5)))))) (forall ((A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (tptp.aa_int_nat tptp.nat2 (tptp.aa_int_int tptp.abs_abs_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int A)) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int B2)))))) (let ((_let_2 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B2)))) (and (=> _let_2 (= _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat B2) A))) (=> (not _let_2) (= _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat A) B2))))))) (forall ((N tptp.nat) (X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N)) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real (tptp.aa_nat_nat tptp.suc N)))) (= (tptp.aa_int_nat tptp.nat2 (tptp.aa_real_int tptp.archim6058952711729229775r_real X)) N)))) (= (tptp.aa_num_nat tptp.size_num tptp.one) tptp.zero_zero_nat) (forall ((Z5 tptp.int) (Z tptp.int)) (let ((_let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int Z) Z5))) (let ((_let_2 (tptp.aa_int_nat tptp.nat2 Z))) (let ((_let_3 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat _let_2) (tptp.aa_int_nat tptp.nat2 Z5)))) (let ((_let_4 (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Z5) tptp.zero_zero_int)))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.if_nat (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int _let_1) tptp.zero_zero_int)) tptp.zero_zero_nat) (tptp.aa_int_nat tptp.nat2 _let_1)))))))))) (forall ((N tptp.nat)) (= (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat tptp.bit_se2002935070580805687sk_nat N)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N))) (forall ((N tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat tptp.bit_se2002935070580805687sk_nat N)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N)))) (forall ((Z tptp.int) (M tptp.nat)) (let ((_let_1 (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) Z)))) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_int_nat tptp.nat2 Z)) M)) (and (=> _let_1 (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int Z) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int M)))) (=> (not _let_1) (= M tptp.zero_zero_nat)))))) (forall ((R tptp.int) (L tptp.int) (K tptp.int) (Q2 tptp.int)) (=> (= (tptp.aa_int_int tptp.sgn_sgn_int R) (tptp.aa_int_int tptp.sgn_sgn_int L)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int tptp.abs_abs_int R)) (tptp.aa_int_int tptp.abs_abs_int L))) (=> (= K (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int Q2) L)) R)) (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.eucl_rel_int K L) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int Q2) R))))))) (forall ((N tptp.nat)) (= (tptp.aa_nat_nat tptp.bit_se2002935070580805687sk_nat N) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N)) tptp.one_one_nat))) (forall ((N tptp.nat)) (= (tptp.aa_int_int (tptp.divide_divide_int (tptp.aa_nat_int tptp.bit_se2000444600071755411sk_int N)) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_nat_int tptp.bit_se2000444600071755411sk_int (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) tptp.one_one_nat)))) (forall ((N tptp.nat)) (= (tptp.aa_nat_int tptp.bit_se2000444600071755411sk_int N) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) N)) tptp.one_one_int))) (forall ((A1 tptp.int) (A22 tptp.int) (A32 tptp.product_prod_int_int)) (= (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.eucl_rel_int A1 A22) A32)) (or (exists ((K2 tptp.int)) (and (= A1 K2) (= A22 tptp.zero_zero_int) (= A32 (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int tptp.zero_zero_int) K2)))) (exists ((L4 tptp.int) (K2 tptp.int) (Q4 tptp.int)) (and (= A1 K2) (= A22 L4) (= A32 (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int Q4) tptp.zero_zero_int)) (not (= L4 tptp.zero_zero_int)) (= K2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int Q4) L4)))) (exists ((R5 tptp.int) (L4 tptp.int) (K2 tptp.int) (Q4 tptp.int)) (and (= A1 K2) (= A22 L4) (= A32 (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int Q4) R5)) (= (tptp.aa_int_int tptp.sgn_sgn_int R5) (tptp.aa_int_int tptp.sgn_sgn_int L4)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int tptp.abs_abs_int R5)) (tptp.aa_int_int tptp.abs_abs_int L4))) (= K2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int Q4) L4)) R5))))))) (forall ((A1 tptp.int) (A22 tptp.int) (A32 tptp.product_prod_int_int)) (=> (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.eucl_rel_int A1 A22) A32)) (=> (=> (= A22 tptp.zero_zero_int) (not (= A32 (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int tptp.zero_zero_int) A1)))) (=> (forall ((Q3 tptp.int)) (=> (= A32 (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int Q3) tptp.zero_zero_int)) (=> (not (= A22 tptp.zero_zero_int)) (not (= A1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int Q3) A22)))))) (not (forall ((R3 tptp.int) (Q3 tptp.int)) (=> (= A32 (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int Q3) R3)) (=> (= (tptp.aa_int_int tptp.sgn_sgn_int R3) (tptp.aa_int_int tptp.sgn_sgn_int A22)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int tptp.abs_abs_int R3)) (tptp.aa_int_int tptp.abs_abs_int A22))) (not (= A1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int Q3) A22)) R3)))))))))))) (forall ((K tptp.int)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) K)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1)) (tptp.aa_int_nat tptp.nat2 K))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_num_int tptp.numeral_numeral_int _let_1)) K)))))) (forall ((X tptp.real) (N tptp.int)) (let ((_let_1 (tptp.aa_real_fun_nat_real tptp.power_power_real X))) (let ((_let_2 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.powr_real X) (tptp.aa_int_real tptp.ring_1_of_int_real N)))) (let ((_let_3 (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) N)))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) X)) (and (=> _let_3 (= _let_2 (tptp.aa_nat_real _let_1 (tptp.aa_int_nat tptp.nat2 N)))) (=> (not _let_3) (= _let_2 (tptp.aa_real_real tptp.inverse_inverse_real (tptp.aa_nat_real _let_1 (tptp.aa_int_nat tptp.nat2 (tptp.aa_int_int tptp.uminus_uminus_int N)))))))))))) (forall ((X2 tptp.num)) (= (tptp.aa_num_nat tptp.size_num (tptp.aa_num_num tptp.bit0 X2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_num_nat tptp.size_num X2)) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)))) (forall ((L tptp.int) (K tptp.int) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat M) N))) (let ((_let_2 (tptp.aa_int_int tptp.sgn_sgn_int L))) (let ((_let_3 (tptp.aa_int_int tptp.sgn_sgn_int K))) (let ((_let_4 (tptp.aa_int_int (tptp.divide_divide_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int _let_3) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int M))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int _let_2) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N))))) (let ((_let_5 (= _let_3 _let_2))) (let ((_let_6 (or (= _let_2 tptp.zero_zero_int) (= _let_3 tptp.zero_zero_int) (= N tptp.zero_zero_nat)))) (and (=> _let_6 (= _let_4 tptp.zero_zero_int)) (=> (not _let_6) (and (=> _let_5 (= _let_4 (tptp.aa_nat_int tptp.semiri1314217659103216013at_int _let_1))) (=> (not _let_5) (= _let_4 (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat _let_1) (tptp.zero_n2687167440665602831ol_nat (tptp.aa_bool_bool tptp.fNot (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat N) M)))))))))))))))))) (forall ((K tptp.int) (L tptp.int)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_int_int (tptp.bit_se725231765392027082nd_int K) L))) (let ((_let_3 (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int))) (let ((_let_4 (= L _let_3))) (let ((_let_5 (= K _let_3))) (let ((_let_6 (or (= K tptp.zero_zero_int) (= L tptp.zero_zero_int)))) (and (=> _let_6 (= _let_2 tptp.zero_zero_int)) (=> (not _let_6) (and (=> _let_5 (= _let_2 L)) (=> (not _let_5) (and (=> _let_4 (= _let_2 K)) (=> (not _let_4) (= _let_2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.modulo_modulo_int K) _let_1)) (tptp.aa_int_int (tptp.modulo_modulo_int L) _let_1))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int _let_1) (tptp.aa_int_int (tptp.bit_se725231765392027082nd_int (tptp.aa_int_int (tptp.divide_divide_int K) _let_1)) (tptp.aa_int_int (tptp.divide_divide_int L) _let_1)))))))))))))))))) (forall ((X tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (= (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real tptp.sgn_sgn_real X))) (tptp.pp (tptp.aa_real_bool _let_1 X))))) (forall ((X tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.sgn_sgn_real X)) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) tptp.zero_zero_real)))) (forall ((N tptp.nat) (K tptp.int)) (= (tptp.aa_int_int (tptp.bit_concat_bit N K) tptp.zero_zero_int) (tptp.aa_int_int (tptp.bit_se2923211474154528505it_int N) K))) (forall ((K tptp.int) (L tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.bit_se725231765392027082nd_int K) L))) (or (tptp.pp (tptp.aa_int_bool _let_1 K)) (tptp.pp (tptp.aa_int_bool _let_1 L)))))) (forall ((K tptp.int) (L tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.bit_se725231765392027082nd_int K) L)) tptp.zero_zero_int)) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int K) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int L) tptp.zero_zero_int))))) (forall ((N tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se2925701944663578781it_nat N) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)) (tptp.zero_n2687167440665602831ol_nat (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)))) (forall ((N tptp.num)) (= (tptp.aa_int_int (tptp.bit_se725231765392027082nd_int tptp.one_one_int) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit1 N)))) tptp.one_one_int)) (forall ((N tptp.num)) (= (tptp.aa_int_int (tptp.bit_se725231765392027082nd_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit1 N)))) tptp.one_one_int) tptp.one_one_int)) (forall ((N tptp.num)) (= (tptp.aa_int_int (tptp.bit_se725231765392027082nd_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 N)))) tptp.one_one_int) tptp.zero_zero_int)) (forall ((N tptp.num)) (= (tptp.aa_int_int (tptp.bit_se725231765392027082nd_int tptp.one_one_int) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 N)))) tptp.zero_zero_int)) (forall ((K tptp.int) (N tptp.nat)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) K)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se2925701944663578781it_nat N) (tptp.aa_int_nat tptp.nat2 K)) (tptp.aa_int_nat tptp.nat2 (tptp.aa_int_int (tptp.bit_se2923211474154528505it_int N) K))))) (forall ((K tptp.int) (N tptp.nat)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) K)) (= (tptp.aa_int_nat tptp.nat2 (tptp.aa_int_int (tptp.bit_se2923211474154528505it_int N) K)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se2925701944663578781it_nat N) (tptp.aa_int_nat tptp.nat2 K))))) (forall ((N tptp.nat) (M tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se2925701944663578781it_nat N) M)) M))) (forall ((M tptp.nat) (N tptp.nat) (Q2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se2925701944663578781it_nat M) Q2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se2925701944663578781it_nat N) Q2))))) (forall ((N tptp.nat) (K tptp.int) (L tptp.int)) (let ((_let_1 (tptp.bit_se2923211474154528505it_int N))) (= (tptp.aa_int_int _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_int_int _let_1 K)) (tptp.aa_int_int _let_1 L))) (tptp.aa_int_int _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int K) L))))) (forall ((N tptp.nat) (K tptp.int) (L tptp.int)) (let ((_let_1 (tptp.bit_se2923211474154528505it_int N))) (= (tptp.aa_int_int _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int _let_1 K)) (tptp.aa_int_int _let_1 L))) (tptp.aa_int_int _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int K) L))))) (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (tptp.bit_se2923211474154528505it_int N))) (= (tptp.aa_int_int _let_1 (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_int_int _let_1 K))) (tptp.aa_int_int _let_1 (tptp.aa_int_int tptp.uminus_uminus_int K))))) (forall ((N tptp.nat) (B2 tptp.int)) (= (tptp.bit_concat_bit N (tptp.aa_int_int (tptp.bit_se2923211474154528505it_int N) B2)) (tptp.bit_concat_bit N B2))) (forall ((N tptp.nat) (K tptp.int) (L tptp.int) (R tptp.int) (S tptp.int)) (let ((_let_1 (tptp.bit_se2923211474154528505it_int N))) (= (= (tptp.aa_int_int (tptp.bit_concat_bit N K) L) (tptp.aa_int_int (tptp.bit_concat_bit N R) S)) (and (= (tptp.aa_int_int _let_1 K) (tptp.aa_int_int _let_1 R)) (= L S))))) (forall ((M tptp.nat) (N tptp.nat) (K tptp.int)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.bit_se2923211474154528505it_int M) K)) (tptp.aa_int_int (tptp.bit_se2923211474154528505it_int N) K))))) (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.pp (tptp.aa_int_bool _let_1 X)) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.bit_se725231765392027082nd_int X) Y)))))) (forall ((X tptp.int) (Y tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) X)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.bit_se725231765392027082nd_int X) Y)) X)))) (forall ((Y tptp.int) (X tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) Y)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.bit_se725231765392027082nd_int X) Y)) Y)))) (forall ((Y tptp.int) (Z tptp.int) (Ya tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) Y)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Y) Z)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.bit_se725231765392027082nd_int Y) Ya)) Z))))) (forall ((Y tptp.int) (Z tptp.int) (X tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) Y)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Y) Z)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.bit_se725231765392027082nd_int X) Y)) Z))))) (forall ((N tptp.nat) (K tptp.int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.aa_int_int (tptp.bit_se2923211474154528505it_int N) K)))) (forall ((N tptp.nat) (K tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.bit_se2923211474154528505it_int N) K)) K)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) K)))) (forall ((N tptp.nat) (K tptp.int)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.bit_se2923211474154528505it_int N) K)) tptp.zero_zero_int)))) (forall ((K tptp.int) (N tptp.nat)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_int K))) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.bit_se2923211474154528505it_int N) K))) (tptp.pp (tptp.aa_int_bool _let_1 tptp.zero_zero_int))))) (forall ((X tptp.num)) (= (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.pow X) tptp.one) X)) (forall ((Y tptp.int) (Z tptp.int) (X tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) Y)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Y) Z)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.bit_se725231765392027082nd_int X) Y)) Z))))) (forall ((Y tptp.int) (Z tptp.int) (Ya tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) Y)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Y) Z)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.bit_se725231765392027082nd_int Y) Ya)) Z))))) (forall ((L tptp.int) (K tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int L) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.bit_se725231765392027082nd_int K) L)) K)))) (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (tptp.bit_se2923211474154528505it_int N))) (= (= (tptp.aa_int_int _let_1 K) (tptp.aa_nat_int tptp.bit_se2000444600071755411sk_int N)) (= (tptp.aa_int_int _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int K) tptp.one_one_int)) tptp.zero_zero_int)))) (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (tptp.bit_se2923211474154528505it_int N))) (let ((_let_2 (tptp.aa_int_int _let_1 K))) (=> (not (= _let_2 tptp.zero_zero_int)) (= (tptp.aa_int_int _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int K) tptp.one_one_int)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int _let_2) tptp.one_one_int)))))) (forall ((A tptp.real)) (let ((_let_1 (tptp.aa_real_real tptp.sgn_sgn_real A))) (let ((_let_2 (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) A)))) (let ((_let_3 (= A 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.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)))))))))) (forall ((K tptp.int) (L tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.bit_se725231765392027082nd_int K) L))) (or (tptp.pp (tptp.aa_int_bool _let_1 K)) (tptp.pp (tptp.aa_int_bool _let_1 L)))))) (forall ((M tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se2925701944663578781it_nat N) M) M))) (forall ((N tptp.nat) (M tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se2925701944663578781it_nat N) M)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N)))) (forall ((N tptp.nat) (M tptp.nat)) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se2925701944663578781it_nat N) M) M) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N))))) (forall ((N tptp.nat) (M tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se2925701944663578781it_nat N) M) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat M) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N)))) (forall ((A tptp.real) (N tptp.nat) (X tptp.real) (B2 tptp.real)) (=> (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real tptp.sgn_sgn_real A)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real tptp.abs_abs_real A)) N)) X) (=> (= X (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real tptp.sgn_sgn_real B2)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real tptp.abs_abs_real B2)) N))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (= A B2))))) (forall ((N tptp.nat) (K tptp.int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.bit_se2923211474154528505it_int N) K)) (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) N)))) (forall ((N tptp.nat) (K tptp.int)) (= (tptp.aa_int_int (tptp.bit_se2923211474154528505it_int N) K) (tptp.aa_int_int (tptp.modulo_modulo_int K) (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) N)))) (forall ((N tptp.nat) (M tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se2925701944663578781it_nat N) M)) M)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N)) M)))) (forall ((N tptp.nat) (K tptp.num)) (= (tptp.aa_int_int (tptp.bit_se2923211474154528505it_int (tptp.aa_nat_nat tptp.suc N)) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 K)))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.bit_se2923211474154528505it_int N) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int K)))) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))))) (forall ((N tptp.nat) (K tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.bit_se2923211474154528505it_int N) K)) K)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) N)) K)))) (forall ((K tptp.int) (N tptp.nat)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int K) (tptp.aa_int_int (tptp.bit_se2923211474154528505it_int N) K))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int K) (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) N))))) (forall ((Z tptp.complex) (X tptp.real)) (=> (= (tptp.aa_complex_complex tptp.sgn_sgn_complex Z) (tptp.aa_real_complex tptp.cis X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.pi)) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) tptp.pi)) (= (tptp.aa_complex_real tptp.arg Z) X))))) (forall ((K tptp.int) (N tptp.nat)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) K)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int K) (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) N))) (= (tptp.aa_int_int (tptp.bit_se2923211474154528505it_int N) K) K)))) (forall ((N tptp.nat) (K tptp.int)) (= (= (tptp.aa_int_int (tptp.bit_se2923211474154528505it_int N) K) K) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) K)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int K) (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) N)))))) (forall ((L tptp.num) (K tptp.num)) (= (tptp.aa_int_int (tptp.bit_se2923211474154528505it_int (tptp.aa_num_nat tptp.numeral_numeral_nat L)) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 K)))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.bit_se2923211474154528505it_int (tptp.aa_num_nat tptp.pred_numeral L)) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int K)))) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))))) (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (tptp.bit_se2923211474154528505it_int N))) (let ((_let_2 (tptp.aa_int_int _let_1 K))) (=> (not (= _let_2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) N)) tptp.one_one_int))) (= (tptp.aa_int_int _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int K) tptp.one_one_int)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int tptp.one_one_int) _let_2)))))) (forall ((N tptp.nat) (K tptp.int)) (= (= (tptp.aa_int_int (tptp.bit_se2923211474154528505it_int N) K) (tptp.aa_nat_int tptp.bit_se2000444600071755411sk_int N)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) N)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int K) tptp.one_one_int))))) (forall ((Z tptp.complex)) (let ((_let_1 (tptp.aa_complex_real tptp.arg Z))) (=> (not (= Z tptp.zero_zero_complex)) (and (= (tptp.aa_complex_complex tptp.sgn_sgn_complex Z) (tptp.aa_real_complex tptp.cis _let_1)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.pi)) _let_1)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real _let_1) tptp.pi)))))) (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) N))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int _let_1) K)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.bit_se2923211474154528505it_int N) K)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int K) _let_1))))))) (forall ((K tptp.int) (N tptp.nat)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int K) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int K) (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) N))) (tptp.aa_int_int (tptp.bit_se2923211474154528505it_int N) K))))) (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) N))) (= (tptp.aa_int_int (tptp.bit_ri631733984087533419it_int N) K) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_int_int (tptp.bit_se2923211474154528505it_int (tptp.aa_nat_nat tptp.suc N)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int K) _let_1))) _let_1)))) (forall ((K tptp.int) (L tptp.int)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int _let_1))) (= (tptp.aa_int_int (tptp.bit_se725231765392027082nd_int K) L) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_bool_int tptp.zero_n2684676970156552555ol_int (tptp.aa_bool_bool (tptp.fconj (tptp.aa_bool_bool tptp.fNot (tptp.aa_int_bool _let_2 K))) (tptp.aa_bool_bool tptp.fNot (tptp.aa_int_bool _let_2 L))))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int _let_1) (tptp.aa_int_int (tptp.bit_se725231765392027082nd_int (tptp.aa_int_int (tptp.divide_divide_int K) _let_1)) (tptp.aa_int_int (tptp.divide_divide_int L) _let_1)))))))) (forall ((K tptp.int) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) N))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) K)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int K) _let_1)) (= (tptp.aa_int_int (tptp.bit_se2923211474154528505it_int N) (tptp.aa_int_int tptp.uminus_uminus_int K)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int _let_1) K)))))) (forall ((X tptp.real)) (=> (not (= X tptp.zero_zero_real)) (= (tptp.aa_real_real tptp.arctan (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.one_one_real) X)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real tptp.sgn_sgn_real X)) tptp.pi)) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))) (tptp.aa_real_real tptp.arctan X))))) (forall ((L tptp.num) (K tptp.num)) (= (tptp.aa_int_int (tptp.bit_se2923211474154528505it_int (tptp.aa_num_nat tptp.numeral_numeral_nat L)) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit1 K)))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.bit_se2923211474154528505it_int (tptp.aa_num_nat tptp.pred_numeral L)) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.inc K))))) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one)))) tptp.one_one_int))) (forall ((K tptp.int) (L tptp.int)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int _let_1))) (let ((_let_3 (tptp.aa_bool_int tptp.zero_n2684676970156552555ol_int (tptp.aa_bool_bool (tptp.fconj (tptp.aa_bool_bool tptp.fNot (tptp.aa_int_bool _let_2 K))) (tptp.aa_bool_bool tptp.fNot (tptp.aa_int_bool _let_2 L)))))) (let ((_let_4 (tptp.aa_int_int (tptp.bit_se725231765392027082nd_int K) L))) (let ((_let_5 (tptp.insert_int tptp.zero_zero_int (tptp.insert_int (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int) tptp.bot_bot_set_int)))) (let ((_let_6 (and (tptp.pp (tptp.aa_set_int_bool (tptp.member_int K) _let_5)) (tptp.pp (tptp.aa_set_int_bool (tptp.member_int L) _let_5))))) (and (=> _let_6 (= _let_4 (tptp.aa_int_int tptp.uminus_uminus_int _let_3))) (=> (not _let_6) (= _let_4 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int _let_3) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int _let_1) (tptp.aa_int_int (tptp.bit_se725231765392027082nd_int (tptp.aa_int_int (tptp.divide_divide_int K) _let_1)) (tptp.aa_int_int (tptp.divide_divide_int L) _let_1)))))))))))))) (forall ((X tptp.int) (Xa2 tptp.int) (Y tptp.int)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int _let_1))) (let ((_let_3 (tptp.aa_bool_int tptp.zero_n2684676970156552555ol_int (tptp.aa_bool_bool (tptp.fconj (tptp.aa_bool_bool tptp.fNot (tptp.aa_int_bool _let_2 X))) (tptp.aa_bool_bool tptp.fNot (tptp.aa_int_bool _let_2 Xa2)))))) (let ((_let_4 (tptp.insert_int tptp.zero_zero_int (tptp.insert_int (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int) tptp.bot_bot_set_int)))) (let ((_let_5 (and (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X) _let_4)) (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Xa2) _let_4))))) (=> (= (tptp.aa_int_int (tptp.bit_se725231765392027082nd_int X) Xa2) Y) (and (=> _let_5 (= Y (tptp.aa_int_int tptp.uminus_uminus_int _let_3))) (=> (not _let_5) (= Y (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int _let_3) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int _let_1) (tptp.aa_int_int (tptp.bit_se725231765392027082nd_int (tptp.aa_int_int (tptp.divide_divide_int X) _let_1)) (tptp.aa_int_int (tptp.divide_divide_int Xa2) _let_1)))))))))))))) (forall ((N tptp.nat) (K tptp.num)) (= (tptp.aa_int_int (tptp.bit_se2923211474154528505it_int (tptp.aa_nat_nat tptp.suc N)) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit1 K)))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.bit_se2923211474154528505it_int N) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.inc K))))) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one)))) tptp.one_one_int))) (forall ((K tptp.num)) (= (tptp.aa_num_nat tptp.pred_numeral (tptp.aa_num_num tptp.inc K)) (tptp.aa_num_nat tptp.numeral_numeral_nat K))) (forall ((Y tptp.num)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se727722235901077358nd_nat (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 Y))) tptp.zero_zero_nat)) (forall ((X tptp.num)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se727722235901077358nd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 X))) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)) tptp.zero_zero_nat)) (forall ((X tptp.num)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se727722235901077358nd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 X))) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)) tptp.one_one_nat)) (forall ((Y tptp.num)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se727722235901077358nd_nat (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 Y))) tptp.one_one_nat)) (forall ((N tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se727722235901077358nd_nat N) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat N) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (forall ((N tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se727722235901077358nd_nat (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)) N) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat N) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (forall ((P tptp.fun_num_bool) (X tptp.num)) (=> (tptp.pp (tptp.aa_num_bool P tptp.one)) (=> (forall ((X4 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool P X4)) (tptp.pp (tptp.aa_num_bool P (tptp.aa_num_num tptp.inc X4))))) (tptp.pp (tptp.aa_num_bool P X))))) (forall ((X tptp.num) (Y tptp.num)) (let ((_let_1 (tptp.aa_num_fun_num_num tptp.plus_plus_num X))) (= (tptp.aa_num_num _let_1 (tptp.aa_num_num tptp.inc Y)) (tptp.aa_num_num tptp.inc (tptp.aa_num_num _let_1 Y))))) (= (tptp.aa_num_num tptp.inc tptp.one) _let_24) (forall ((X tptp.num)) (= (tptp.aa_num_num tptp.inc (tptp.aa_num_num tptp.bit0 X)) (tptp.aa_num_num tptp.bit1 X))) (forall ((X tptp.num)) (= (tptp.aa_num_num tptp.inc (tptp.aa_num_num tptp.bit1 X)) (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.inc X)))) (forall ((X tptp.num)) (= (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num X) tptp.one) (tptp.aa_num_num tptp.inc X))) (forall ((N tptp.num)) (= (tptp.aa_num_num tptp.inc (tptp.aa_num_num tptp.bitM N)) (tptp.aa_num_num tptp.bit0 N))) (forall ((N tptp.num)) (= (tptp.aa_num_num tptp.bitM (tptp.aa_num_num tptp.inc N)) (tptp.aa_num_num tptp.bit1 N))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se727722235901077358nd_nat M) N) (tptp.aa_int_nat tptp.nat2 (tptp.aa_int_int (tptp.bit_se725231765392027082nd_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int M)) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N))))) (forall ((X tptp.num) (Y tptp.num)) (let ((_let_1 (tptp.aa_num_fun_num_num tptp.times_times_num X))) (= (tptp.aa_num_num _let_1 (tptp.aa_num_num tptp.inc Y)) (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num (tptp.aa_num_num _let_1 Y)) X)))) (forall ((M tptp.int) (N tptp.int)) (let ((_let_1 (tptp.aa_int8639817059373041269et_int tptp.set_or1266510415728281911st_int M))) (let ((_let_2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int tptp.one_one_int) N))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int M) _let_2)) (= (tptp.aa_int_set_int _let_1 _let_2) (tptp.insert_int _let_2 (tptp.aa_int_set_int _let_1 N))))))) (forall ((J tptp.int) (I tptp.int)) (let ((_let_1 (tptp.aa_int_set_int (tptp.aa_int8639817059373041269et_int tptp.set_or1266510415728281911st_int I) J))) (let ((_let_2 (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int J) I)))) (and (=> _let_2 (= _let_1 tptp.bot_bot_set_int)) (=> (not _let_2) (= _let_1 (tptp.insert_int I (tptp.aa_int_set_int (tptp.aa_int8639817059373041269et_int tptp.set_or1266510415728281911st_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int I) tptp.one_one_int)) J)))))))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se727722235901077358nd_nat M) N))) (let ((_let_3 (or (= M tptp.zero_zero_nat) (= N tptp.zero_zero_nat)))) (and (=> _let_3 (= _let_2 tptp.zero_zero_nat)) (=> (not _let_3) (= _let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat M) _let_1)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat N) _let_1))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat _let_1) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se727722235901077358nd_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat M) _let_1)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat N) _let_1))))))))))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat _let_1))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se727722235901077358nd_nat M) N) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.zero_n2687167440665602831ol_nat (tptp.aa_bool_bool (tptp.fconj (tptp.aa_bool_bool tptp.fNot (tptp.aa_nat_bool _let_2 M))) (tptp.aa_bool_bool tptp.fNot (tptp.aa_nat_bool _let_2 N))))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat _let_1) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se727722235901077358nd_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat M) _let_1)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat N) _let_1)))))))) (forall ((K tptp.int) (L tptp.int)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int _let_1))) (let ((_let_3 (tptp.aa_bool_int tptp.zero_n2684676970156552555ol_int (tptp.aa_bool_bool (tptp.fconj (tptp.aa_bool_bool tptp.fNot (tptp.aa_int_bool _let_2 K))) (tptp.aa_bool_bool tptp.fNot (tptp.aa_int_bool _let_2 L)))))) (let ((_let_4 (tptp.aa_int_int (tptp.bit_se725231765392027082nd_int K) L))) (let ((_let_5 (tptp.insert_int tptp.zero_zero_int (tptp.insert_int (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int) tptp.bot_bot_set_int)))) (let ((_let_6 (and (tptp.pp (tptp.aa_set_int_bool (tptp.member_int K) _let_5)) (tptp.pp (tptp.aa_set_int_bool (tptp.member_int L) _let_5))))) (=> (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.accp_P1096762738010456898nt_int tptp.bit_and_int_rel) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int K) L))) (and (=> _let_6 (= _let_4 (tptp.aa_int_int tptp.uminus_uminus_int _let_3))) (=> (not _let_6) (= _let_4 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int _let_3) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int _let_1) (tptp.aa_int_int (tptp.bit_se725231765392027082nd_int (tptp.aa_int_int (tptp.divide_divide_int K) _let_1)) (tptp.aa_int_int (tptp.divide_divide_int L) _let_1))))))))))))))) (forall ((X tptp.int) (Xa2 tptp.int) (Y tptp.int)) (let ((_let_1 (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.accp_P1096762738010456898nt_int tptp.bit_and_int_rel) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int X) Xa2))))) (let ((_let_2 (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_3 (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int _let_2))) (let ((_let_4 (tptp.aa_bool_int tptp.zero_n2684676970156552555ol_int (tptp.aa_bool_bool (tptp.fconj (tptp.aa_bool_bool tptp.fNot (tptp.aa_int_bool _let_3 X))) (tptp.aa_bool_bool tptp.fNot (tptp.aa_int_bool _let_3 Xa2)))))) (let ((_let_5 (tptp.insert_int tptp.zero_zero_int (tptp.insert_int (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int) tptp.bot_bot_set_int)))) (let ((_let_6 (and (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X) _let_5)) (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Xa2) _let_5))))) (=> (= (tptp.aa_int_int (tptp.bit_se725231765392027082nd_int X) Xa2) Y) (=> _let_1 (not (=> (and (=> _let_6 (= Y (tptp.aa_int_int tptp.uminus_uminus_int _let_4))) (=> (not _let_6) (= Y (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int _let_4) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int _let_2) (tptp.aa_int_int (tptp.bit_se725231765392027082nd_int (tptp.aa_int_int (tptp.divide_divide_int X) _let_2)) (tptp.aa_int_int (tptp.divide_divide_int Xa2) _let_2))))))) (not _let_1)))))))))))) (forall ((A0 tptp.int) (A1 tptp.int) (P tptp.fun_int_fun_int_bool)) (=> (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.accp_P1096762738010456898nt_int tptp.bit_and_int_rel) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int A0) A1))) (=> (forall ((K3 tptp.int) (L3 tptp.int)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.insert_int tptp.zero_zero_int (tptp.insert_int (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int) tptp.bot_bot_set_int)))) (=> (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.accp_P1096762738010456898nt_int tptp.bit_and_int_rel) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int K3) L3))) (=> (=> (not (and (tptp.pp (tptp.aa_set_int_bool (tptp.member_int K3) _let_2)) (tptp.pp (tptp.aa_set_int_bool (tptp.member_int L3) _let_2)))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool P (tptp.aa_int_int (tptp.divide_divide_int K3) _let_1)) (tptp.aa_int_int (tptp.divide_divide_int L3) _let_1)))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool P K3) L3))))))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool P A0) A1))))) (forall ((Z tptp.complex)) (let ((_let_1 (tptp.aa_complex_real tptp.arg Z))) (let ((_let_2 (= Z tptp.zero_zero_complex))) (and (=> _let_2 (= _let_1 tptp.zero_zero_real)) (=> (not _let_2) (= _let_1 (tptp.fChoice_real (tptp.aa_com8943241093633526360l_bool tptp.aTP_Lamm_vo Z)))))))) (forall ((A4 tptp.set_nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A4)) (=> (not (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat N) A4))) (= (tptp.aa_set_nat_nat tptp.nat_set_encode (tptp.insert_nat N A4)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N)) (tptp.aa_set_nat_nat tptp.nat_set_encode A4)))))) (forall ((M tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)) (= (tptp.insert_nat M (tptp.set_or1269000886237332187st_nat (tptp.aa_nat_nat tptp.suc M) N)) (tptp.set_or1269000886237332187st_nat M N)))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) _let_1)) (= (tptp.set_or1269000886237332187st_nat M _let_1) (tptp.insert_nat _let_1 (tptp.set_or1269000886237332187st_nat M N)))))) (forall ((M tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)) (= (tptp.set_or1269000886237332187st_nat M N) (tptp.insert_nat M (tptp.set_or1269000886237332187st_nat (tptp.aa_nat_nat tptp.suc M) N))))) (forall ((K tptp.num)) (let ((_let_1 (tptp.aa_num_nat tptp.pred_numeral K))) (= (tptp.set_ord_lessThan_nat (tptp.aa_num_nat tptp.numeral_numeral_nat K)) (tptp.insert_nat _let_1 (tptp.set_ord_lessThan_nat _let_1))))) (forall ((K tptp.num)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat K))) (= (tptp.set_ord_atMost_nat _let_1) (tptp.insert_nat _let_1 (tptp.set_ord_atMost_nat (tptp.aa_num_nat tptp.pred_numeral K)))))) (forall ((N tptp.nat) (Z tptp.nat)) (let ((_let_1 (tptp.nat_set_decode Z))) (=> (not (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat N) _let_1))) (= (tptp.nat_set_decode (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N)) Z)) (tptp.insert_nat N _let_1))))) (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N))) (= (tptp.aa_int_int (tptp.bit_ri631733984087533419it_int N) K) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_int_int (tptp.bit_se2923211474154528505it_int _let_1) K)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) _let_1)) (tptp.aa_bool_int tptp.zero_n2684676970156552555ol_int (tptp.aa_nat_bool (tptp.aa_int_fun_nat_bool tptp.bit_se1146084159140164899it_int K) N))))))) (forall ((K tptp.int) (L tptp.int)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_int_int (tptp.bit_se1409905431419307370or_int K) L))) (let ((_let_3 (= L tptp.zero_zero_int))) (let ((_let_4 (= K tptp.zero_zero_int))) (let ((_let_5 (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int))) (let ((_let_6 (or (= K _let_5) (= L _let_5)))) (and (=> _let_6 (= _let_2 _let_5)) (=> (not _let_6) (and (=> _let_4 (= _let_2 L)) (=> (not _let_4) (and (=> _let_3 (= _let_2 K)) (=> (not _let_3) (= _let_2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.ord_max_int (tptp.aa_int_int (tptp.modulo_modulo_int K) _let_1)) (tptp.aa_int_int (tptp.modulo_modulo_int L) _let_1))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int _let_1) (tptp.aa_int_int (tptp.bit_se1409905431419307370or_int (tptp.aa_int_int (tptp.divide_divide_int K) _let_1)) (tptp.aa_int_int (tptp.divide_divide_int L) _let_1)))))))))))))))))) (forall ((N tptp.real)) (=> (tptp.member_real N tptp.ring_1_Ints_real) (= (tptp.aa_real_complex tptp.cis (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))) tptp.pi)) N)) tptp.one_one_complex))) (forall ((N tptp.nat) (K tptp.int)) (= (tptp.aa_int_int (tptp.bit_se2923211474154528505it_int (tptp.aa_nat_nat tptp.suc N)) K) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) N)) (tptp.aa_bool_int tptp.zero_n2684676970156552555ol_int (tptp.aa_nat_bool (tptp.aa_int_fun_nat_bool tptp.bit_se1146084159140164899it_int K) N)))) (tptp.aa_int_int (tptp.bit_se2923211474154528505it_int N) K)))) (forall ((K tptp.int) (L tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.bit_se1409905431419307370or_int K) L))) (and (tptp.pp (tptp.aa_int_bool _let_1 K)) (tptp.pp (tptp.aa_int_bool _let_1 L)))))) (forall ((K tptp.int) (L tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.bit_se1409905431419307370or_int K) L)) tptp.zero_zero_int)) (or (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int K) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int L) tptp.zero_zero_int))))) (forall ((N tptp.nat) (K tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.aa_int_int (tptp.bit_ri631733984087533419it_int N) K))) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_int_fun_nat_bool tptp.bit_se1146084159140164899it_int K) N))))) (forall ((N tptp.nat) (K tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.bit_ri631733984087533419it_int N) K)) tptp.zero_zero_int)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_int_fun_nat_bool tptp.bit_se1146084159140164899it_int K) N)))) (forall ((W tptp.num) (N tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_int_fun_nat_bool tptp.bit_se1146084159140164899it_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 W)))) (tptp.aa_nat_nat tptp.suc N))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_int_fun_nat_bool tptp.bit_se1146084159140164899it_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int W))) N)))) (forall ((W tptp.num) (N tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_int_fun_nat_bool tptp.bit_se1146084159140164899it_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit1 W)))) (tptp.aa_nat_nat tptp.suc N))) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_int_fun_nat_bool tptp.bit_se1146084159140164899it_int (tptp.aa_num_int tptp.numeral_numeral_int W)) N))))) (forall ((N tptp.num)) (let ((_let_1 (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit1 N))))) (= (tptp.aa_int_int (tptp.bit_se1409905431419307370or_int _let_1) tptp.one_one_int) _let_1))) (forall ((N tptp.num)) (let ((_let_1 (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit1 N))))) (= (tptp.aa_int_int (tptp.bit_se1409905431419307370or_int tptp.one_one_int) _let_1) _let_1))) (forall ((W tptp.num) (N tptp.num)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_int_fun_nat_bool tptp.bit_se1146084159140164899it_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 W)))) (tptp.aa_num_nat tptp.numeral_numeral_nat N))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_int_fun_nat_bool tptp.bit_se1146084159140164899it_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int W))) (tptp.aa_num_nat tptp.pred_numeral N))))) (forall ((W tptp.num) (N tptp.num)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_int_fun_nat_bool tptp.bit_se1146084159140164899it_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit1 W)))) (tptp.aa_num_nat tptp.numeral_numeral_nat N))) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_int_fun_nat_bool tptp.bit_se1146084159140164899it_int (tptp.aa_num_int tptp.numeral_numeral_int W)) (tptp.aa_num_nat tptp.pred_numeral N)))))) (forall ((K tptp.int) (L tptp.int) (N tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_int_fun_nat_bool tptp.bit_se1146084159140164899it_int (tptp.aa_int_int (tptp.bit_se1409905431419307370or_int K) L)) N)) (or (tptp.pp (tptp.aa_nat_bool (tptp.aa_int_fun_nat_bool tptp.bit_se1146084159140164899it_int K) N)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_int_fun_nat_bool tptp.bit_se1146084159140164899it_int L) N))))) (forall ((K tptp.int) (L tptp.int) (N tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_int_fun_nat_bool tptp.bit_se1146084159140164899it_int (tptp.aa_int_int (tptp.bit_se725231765392027082nd_int K) L)) N)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_int_fun_nat_bool tptp.bit_se1146084159140164899it_int K) N)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_int_fun_nat_bool tptp.bit_se1146084159140164899it_int L) N))))) (forall ((L tptp.int) (K tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) L)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int K) (tptp.aa_int_int (tptp.bit_se1409905431419307370or_int K) L))))) (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.pp (tptp.aa_int_bool _let_1 X)) (=> (tptp.pp (tptp.aa_int_bool _let_1 Y)) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.bit_se1409905431419307370or_int X) Y))))))) (forall ((X tptp.int) (Y tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.bit_se725231765392027082nd_int X) Y)) (tptp.aa_int_int (tptp.bit_se1409905431419307370or_int X) Y)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int X) Y))) (forall ((K tptp.int) (N tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_int_fun_nat_bool tptp.bit_se1146084159140164899it_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_int_int tptp.uminus_uminus_int K)) tptp.one_one_int)) N)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_int_fun_nat_bool tptp.bit_se1146084159140164899it_int K) N))))) (forall ((N tptp.nat) (M tptp.nat) (K tptp.int)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N) M)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_int_fun_nat_bool tptp.bit_se1146084159140164899it_int K) N)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) (tptp.aa_int_int (tptp.bit_se2923211474154528505it_int M) K)))))) (forall ((M tptp.nat) (K tptp.int) (L tptp.int) (N tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_int_fun_nat_bool tptp.bit_se1146084159140164899it_int (tptp.aa_int_int (tptp.bit_concat_bit M K) L)) N)) (or (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N) M)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_int_fun_nat_bool tptp.bit_se1146084159140164899it_int K) N))) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_int_fun_nat_bool tptp.bit_se1146084159140164899it_int L) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) M))))))) (forall ((X tptp.real)) (= (= (tptp.aa_real_real tptp.sin_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real X) tptp.pi)) tptp.zero_zero_real) (tptp.member_real X tptp.ring_1_Ints_real))) (forall ((N tptp.nat) (K tptp.int)) (= (tptp.aa_int_int (tptp.bit_ri631733984087533419it_int N) K) (tptp.aa_int_int (tptp.bit_concat_bit N K) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_bool_int tptp.zero_n2684676970156552555ol_int (tptp.aa_nat_bool (tptp.aa_int_fun_nat_bool tptp.bit_se1146084159140164899it_int K) N)))))) (forall ((K tptp.int)) (not (forall ((N2 tptp.nat)) (let ((_let_1 (tptp.aa_int_fun_nat_bool tptp.bit_se1146084159140164899it_int K))) (=> (forall ((M2 tptp.nat)) (let ((_let_1 (tptp.aa_int_fun_nat_bool tptp.bit_se1146084159140164899it_int K))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) M2)) (= (tptp.pp (tptp.aa_nat_bool _let_1 M2)) (tptp.pp (tptp.aa_nat_bool _let_1 N2)))))) (not (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)) (= (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2) tptp.one_one_nat))) (not (tptp.pp (tptp.aa_nat_bool _let_1 N2))))))))))) (forall ((K tptp.int) (N tptp.nat)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_int_fun_nat_bool tptp.bit_se1146084159140164899it_int K) N)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int _let_1) (tptp.aa_int_int (tptp.divide_divide_int K) (tptp.aa_nat_int (tptp.power_power_int _let_1) N)))))))) (forall ((X tptp.int) (N tptp.nat) (Y tptp.int)) (let ((_let_1 (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) N))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) X)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) _let_1)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Y) _let_1)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.bit_se1409905431419307370or_int X) Y)) _let_1))))))) (forall ((N tptp.real)) (=> (tptp.member_real N tptp.ring_1_Ints_real) (= (tptp.aa_real_real tptp.sin_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))) tptp.pi)) N)) tptp.zero_zero_real))) (forall ((N tptp.real)) (=> (tptp.member_real N tptp.ring_1_Ints_real) (= (tptp.aa_real_real tptp.cos_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))) tptp.pi)) N)) tptp.one_one_real))) (forall ((K tptp.int) (L tptp.int)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int _let_1))) (= (tptp.aa_int_int (tptp.bit_se1409905431419307370or_int K) L) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_bool_int tptp.zero_n2684676970156552555ol_int (tptp.aa_bool_bool (tptp.fdisj (tptp.aa_bool_bool tptp.fNot (tptp.aa_int_bool _let_2 K))) (tptp.aa_bool_bool tptp.fNot (tptp.aa_int_bool _let_2 L))))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int _let_1) (tptp.aa_int_int (tptp.bit_se1409905431419307370or_int (tptp.aa_int_int (tptp.divide_divide_int K) _let_1)) (tptp.aa_int_int (tptp.divide_divide_int L) _let_1)))))))) (forall ((N tptp.nat) (K tptp.int)) (= (tptp.aa_int_int (tptp.bit_se7879613467334960850it_int N) K) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int K) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_bool_int tptp.zero_n2684676970156552555ol_int (tptp.aa_bool_bool tptp.fNot (tptp.aa_nat_bool (tptp.aa_int_fun_nat_bool tptp.bit_se1146084159140164899it_int K) N)))) (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) N))))) (forall ((N tptp.nat) (K tptp.int)) (= (tptp.aa_int_int (tptp.bit_se4203085406695923979it_int N) K) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int K) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_bool_int tptp.zero_n2684676970156552555ol_int (tptp.aa_nat_bool (tptp.aa_int_fun_nat_bool tptp.bit_se1146084159140164899it_int K) N))) (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) N))))) (forall ((N tptp.num)) (= (tptp.aa_int_int (tptp.bit_se1409905431419307370or_int tptp.one_one_int) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 N)))) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.bit_or_not_num_neg tptp.one) (tptp.aa_num_num tptp.bitM N)))))) (forall ((N tptp.num)) (= (tptp.aa_int_int (tptp.bit_se1409905431419307370or_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 N)))) tptp.one_one_int) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.bit_or_not_num_neg tptp.one) (tptp.aa_num_num tptp.bitM N)))))) (forall ((N tptp.nat)) (let ((_let_1 (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se6528837805403552850or_nat N) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N) (tptp.zero_n2687167440665602831ol_nat _let_1))) (tptp.zero_n2687167440665602831ol_nat (tptp.aa_bool_bool tptp.fNot _let_1)))))) (forall ((Y tptp.num)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 Y)))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se1412395901928357646or_nat (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)) _let_1) _let_1))) (forall ((X tptp.num)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 X)))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se1412395901928357646or_nat _let_1) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)) _let_1))) (forall ((X tptp.num)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se1412395901928357646or_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 X))) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 X)))) (forall ((Y tptp.num)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se1412395901928357646or_nat (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 Y))) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 Y)))) (forall ((X tptp.num)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se6528837805403552850or_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 X))) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 X)))) (forall ((X tptp.num)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se6528837805403552850or_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 X))) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 X)))) (forall ((Y tptp.num)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se6528837805403552850or_nat (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 Y))) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 Y)))) (forall ((Y tptp.num)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se6528837805403552850or_nat (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 Y))) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 Y)))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.aa_int_int (tptp.bit_se1409905431419307370or_int (tptp.aa_num_int tptp.numeral_numeral_int M)) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit1 N)))) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.bit_or_not_num_neg M) (tptp.aa_num_num tptp.bit0 N)))))) (forall ((N tptp.num) (M tptp.num)) (= (tptp.aa_int_int (tptp.bit_se1409905431419307370or_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit1 N)))) (tptp.aa_num_int tptp.numeral_numeral_int M)) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.bit_or_not_num_neg M) (tptp.aa_num_num tptp.bit0 N)))))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.aa_int_int (tptp.bit_se1409905431419307370or_int (tptp.aa_num_int tptp.numeral_numeral_int M)) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 N)))) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.bit_or_not_num_neg M) (tptp.aa_num_num tptp.bitM N)))))) (forall ((N tptp.num) (M tptp.num)) (= (tptp.aa_int_int (tptp.bit_se1409905431419307370or_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 N)))) (tptp.aa_num_int tptp.numeral_numeral_int M)) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.bit_or_not_num_neg M) (tptp.aa_num_num tptp.bitM N)))))) (= (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.bit_or_not_num_neg tptp.one) tptp.one) tptp.one) (forall ((N tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.bit_se1148574629649215175it_nat (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)) N)) (= N tptp.zero_zero_nat))) (forall ((N tptp.nat)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.bit_se1148574629649215175it_nat (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)) (tptp.aa_nat_nat tptp.suc N))))) (forall ((N tptp.num)) (= (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.bit_or_not_num_neg (tptp.aa_num_num tptp.bit0 N)) tptp.one) (tptp.aa_num_num tptp.bit0 tptp.one))) (forall ((N tptp.num) (M tptp.num)) (= (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.bit_or_not_num_neg (tptp.aa_num_num tptp.bit0 N)) (tptp.aa_num_num tptp.bit1 M)) (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.bit_or_not_num_neg N) M)))) (forall ((N tptp.num)) (= (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.bit_or_not_num_neg (tptp.aa_num_num tptp.bit1 N)) tptp.one) tptp.one)) (forall ((M tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit1 M))) (= (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.bit_or_not_num_neg tptp.one) _let_1) _let_1))) (forall ((N tptp.num) (M tptp.num)) (= (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.bit_or_not_num_neg (tptp.aa_num_num tptp.bit0 N)) (tptp.aa_num_num tptp.bit0 M)) (tptp.aa_num_num tptp.bitM (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.bit_or_not_num_neg N) M)))) (forall ((N tptp.num)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.bit_se1148574629649215175it_nat (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)) (tptp.aa_num_nat tptp.numeral_numeral_nat N))))) (forall ((N tptp.num) (M tptp.num)) (= (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.bit_or_not_num_neg (tptp.aa_num_num tptp.bit1 N)) (tptp.aa_num_num tptp.bit1 M)) (tptp.aa_num_num tptp.bitM (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.bit_or_not_num_neg N) M)))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se1412395901928357646or_nat M) N) (tptp.aa_int_nat tptp.nat2 (tptp.aa_int_int (tptp.bit_se1409905431419307370or_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int M)) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N))))) (forall ((M tptp.num)) (= (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.bit_or_not_num_neg tptp.one) (tptp.aa_num_num tptp.bit0 M)) (tptp.aa_num_num tptp.bit1 M))) (forall ((N tptp.num) (M tptp.num)) (= (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.bit_or_not_num_neg (tptp.aa_num_num tptp.bit1 N)) (tptp.aa_num_num tptp.bit0 M)) (tptp.aa_num_num tptp.bitM (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.bit_or_not_num_neg N) M)))) (forall ((K tptp.int) (N tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.bit_se1148574629649215175it_nat (tptp.aa_int_nat tptp.nat2 K)) N)) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) K)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_int_fun_nat_bool tptp.bit_se1146084159140164899it_int K) N))))) (forall ((X tptp.num) (Xa2 tptp.num) (Y tptp.num)) (let ((_let_1 (= Xa2 tptp.one))) (let ((_let_2 (=> _let_1 (not (= Y tptp.one))))) (let ((_let_3 (= X tptp.one))) (=> (= (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.bit_or_not_num_neg X) Xa2) Y) (=> (=> _let_3 _let_2) (=> (=> _let_3 (forall ((M3 tptp.num)) (=> (= Xa2 (tptp.aa_num_num tptp.bit0 M3)) (not (= Y (tptp.aa_num_num tptp.bit1 M3)))))) (=> (=> _let_3 (forall ((M3 tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit1 M3))) (=> (= Xa2 _let_1) (not (= Y _let_1)))))) (=> (=> (exists ((N2 tptp.num)) (= X (tptp.aa_num_num tptp.bit0 N2))) (=> _let_1 (not (= Y (tptp.aa_num_num tptp.bit0 tptp.one))))) (=> (forall ((N2 tptp.num)) (=> (= X (tptp.aa_num_num tptp.bit0 N2)) (forall ((M3 tptp.num)) (=> (= Xa2 (tptp.aa_num_num tptp.bit0 M3)) (not (= Y (tptp.aa_num_num tptp.bitM (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.bit_or_not_num_neg N2) M3)))))))) (=> (forall ((N2 tptp.num)) (=> (= X (tptp.aa_num_num tptp.bit0 N2)) (forall ((M3 tptp.num)) (=> (= Xa2 (tptp.aa_num_num tptp.bit1 M3)) (not (= Y (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.bit_or_not_num_neg N2) M3)))))))) (=> (=> (exists ((N2 tptp.num)) (= X (tptp.aa_num_num tptp.bit1 N2))) _let_2) (=> (forall ((N2 tptp.num)) (=> (= X (tptp.aa_num_num tptp.bit1 N2)) (forall ((M3 tptp.num)) (=> (= Xa2 (tptp.aa_num_num tptp.bit0 M3)) (not (= Y (tptp.aa_num_num tptp.bitM (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.bit_or_not_num_neg N2) M3)))))))) (not (forall ((N2 tptp.num)) (=> (= X (tptp.aa_num_num tptp.bit1 N2)) (forall ((M3 tptp.num)) (=> (= Xa2 (tptp.aa_num_num tptp.bit1 M3)) (not (= Y (tptp.aa_num_num tptp.bitM (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.bit_or_not_num_neg N2) M3)))))))))))))))))))))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.bit_se1148574629649215175it_nat M) N)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat _let_1) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat M) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat _let_1) N)))))))) (forall ((N tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se1412395901928357646or_nat (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)) N) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N) (tptp.zero_n2687167440665602831ol_nat (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N))))) (forall ((N tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se1412395901928357646or_nat N) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N) (tptp.zero_n2687167440665602831ol_nat (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N))))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat _let_1))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se1412395901928357646or_nat M) N) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.zero_n2687167440665602831ol_nat (tptp.aa_bool_bool (tptp.fdisj (tptp.aa_bool_bool tptp.fNot (tptp.aa_nat_bool _let_2 M))) (tptp.aa_bool_bool tptp.fNot (tptp.aa_nat_bool _let_2 N))))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat _let_1) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se1412395901928357646or_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat M) _let_1)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat N) _let_1)))))))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se6528837805403552850or_nat M) N))) (let ((_let_3 (= N tptp.zero_zero_nat))) (let ((_let_4 (= M tptp.zero_zero_nat))) (and (=> _let_4 (= _let_2 N)) (=> (not _let_4) (and (=> _let_3 (= _let_2 M)) (=> (not _let_3) (= _let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat M) _let_1)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat N) _let_1))) _let_1)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat _let_1) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se6528837805403552850or_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat M) _let_1)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat N) _let_1)))))))))))))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat _let_1))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se6528837805403552850or_nat M) N) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.zero_n2687167440665602831ol_nat (tptp.aa_bool_bool tptp.fNot (tptp.aa_bool_bool (tptp.aa_boo8970175072276269406l_bool tptp.fequal_bool (tptp.aa_bool_bool tptp.fNot (tptp.aa_nat_bool _let_2 M))) (tptp.aa_bool_bool tptp.fNot (tptp.aa_nat_bool _let_2 N)))))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat _let_1) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se6528837805403552850or_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat M) _let_1)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat N) _let_1)))))))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se1412395901928357646or_nat M) N))) (let ((_let_3 (= N tptp.zero_zero_nat))) (let ((_let_4 (= M tptp.zero_zero_nat))) (and (=> _let_4 (= _let_2 N)) (=> (not _let_4) (and (=> _let_3 (= _let_2 M)) (=> (not _let_3) (= _let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat M) _let_1)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat N) _let_1))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat _let_1) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se1412395901928357646or_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat M) _let_1)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat N) _let_1)))))))))))))) (forall ((N tptp.nat)) (let ((_let_1 (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se6528837805403552850or_nat (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)) N) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N) (tptp.zero_n2687167440665602831ol_nat _let_1))) (tptp.zero_n2687167440665602831ol_nat (tptp.aa_bool_bool tptp.fNot _let_1)))))) (forall ((X tptp.num) (Xa2 tptp.num) (Y tptp.num)) (let ((_let_1 (= X tptp.one))) (let ((_let_2 (tptp.accp_P3113834385874906142um_num tptp.bit_or3848514188828904588eg_rel))) (=> (= (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.bit_or_not_num_neg X) Xa2) Y) (=> (tptp.pp (tptp.aa_Pro762926636801165566m_bool _let_2 (tptp.product_Pair_num_num X Xa2))) (=> (=> _let_1 (=> (= Xa2 tptp.one) (=> (= Y tptp.one) (not (tptp.pp (tptp.aa_Pro762926636801165566m_bool _let_2 (tptp.product_Pair_num_num tptp.one tptp.one))))))) (=> (=> _let_1 (forall ((M3 tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 M3))) (=> (= Xa2 _let_1) (=> (= Y (tptp.aa_num_num tptp.bit1 M3)) (not (tptp.pp (tptp.aa_Pro762926636801165566m_bool (tptp.accp_P3113834385874906142um_num tptp.bit_or3848514188828904588eg_rel) (tptp.product_Pair_num_num tptp.one _let_1))))))))) (=> (=> _let_1 (forall ((M3 tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit1 M3))) (=> (= Xa2 _let_1) (=> (= Y _let_1) (not (tptp.pp (tptp.aa_Pro762926636801165566m_bool (tptp.accp_P3113834385874906142um_num tptp.bit_or3848514188828904588eg_rel) (tptp.product_Pair_num_num tptp.one _let_1))))))))) (=> (forall ((N2 tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 N2))) (=> (= X _let_1) (=> (= Xa2 tptp.one) (=> (= Y (tptp.aa_num_num tptp.bit0 tptp.one)) (not (tptp.pp (tptp.aa_Pro762926636801165566m_bool (tptp.accp_P3113834385874906142um_num tptp.bit_or3848514188828904588eg_rel) (tptp.product_Pair_num_num _let_1 tptp.one))))))))) (=> (forall ((N2 tptp.num)) (=> (= X (tptp.aa_num_num tptp.bit0 N2)) (forall ((M3 tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 M3))) (=> (= Xa2 _let_1) (=> (= Y (tptp.aa_num_num tptp.bitM (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.bit_or_not_num_neg N2) M3))) (not (tptp.pp (tptp.aa_Pro762926636801165566m_bool (tptp.accp_P3113834385874906142um_num tptp.bit_or3848514188828904588eg_rel) (tptp.product_Pair_num_num (tptp.aa_num_num tptp.bit0 N2) _let_1)))))))))) (=> (forall ((N2 tptp.num)) (=> (= X (tptp.aa_num_num tptp.bit0 N2)) (forall ((M3 tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit1 M3))) (=> (= Xa2 _let_1) (=> (= Y (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.bit_or_not_num_neg N2) M3))) (not (tptp.pp (tptp.aa_Pro762926636801165566m_bool (tptp.accp_P3113834385874906142um_num tptp.bit_or3848514188828904588eg_rel) (tptp.product_Pair_num_num (tptp.aa_num_num tptp.bit0 N2) _let_1)))))))))) (=> (forall ((N2 tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit1 N2))) (=> (= X _let_1) (=> (= Xa2 tptp.one) (=> (= Y tptp.one) (not (tptp.pp (tptp.aa_Pro762926636801165566m_bool (tptp.accp_P3113834385874906142um_num tptp.bit_or3848514188828904588eg_rel) (tptp.product_Pair_num_num _let_1 tptp.one))))))))) (=> (forall ((N2 tptp.num)) (=> (= X (tptp.aa_num_num tptp.bit1 N2)) (forall ((M3 tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 M3))) (=> (= Xa2 _let_1) (=> (= Y (tptp.aa_num_num tptp.bitM (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.bit_or_not_num_neg N2) M3))) (not (tptp.pp (tptp.aa_Pro762926636801165566m_bool (tptp.accp_P3113834385874906142um_num tptp.bit_or3848514188828904588eg_rel) (tptp.product_Pair_num_num (tptp.aa_num_num tptp.bit1 N2) _let_1)))))))))) (not (forall ((N2 tptp.num)) (=> (= X (tptp.aa_num_num tptp.bit1 N2)) (forall ((M3 tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit1 M3))) (=> (= Xa2 _let_1) (=> (= Y (tptp.aa_num_num tptp.bitM (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.bit_or_not_num_neg N2) M3))) (not (tptp.pp (tptp.aa_Pro762926636801165566m_bool (tptp.accp_P3113834385874906142um_num tptp.bit_or3848514188828904588eg_rel) (tptp.product_Pair_num_num (tptp.aa_num_num tptp.bit1 N2) _let_1)))))))))))))))))))))))) (forall ((Bs tptp.list_bool)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one)))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.groups4048646594741130792ol_int tptp.zero_n2684676970156552555ol_int _let_1 Bs)) (tptp.aa_nat_int (tptp.power_power_int _let_1) (tptp.size_size_list_bool Bs)))))) (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.bit_se545348938243370406it_int N) K))) (tptp.pp (tptp.aa_int_bool _let_1 K))))) (forall ((N tptp.nat) (K tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.bit_se545348938243370406it_int N) K)) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int K) tptp.zero_zero_int)))) (forall ((N tptp.nat) (L tptp.int)) (= (tptp.aa_int_int (tptp.bit_concat_bit N tptp.zero_zero_int) L) (tptp.aa_int_int (tptp.bit_se545348938243370406it_int N) L))) (forall ((K tptp.int) (L tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.bit_se6526347334894502574or_int K) L))) (= (tptp.pp (tptp.aa_int_bool _let_1 K)) (tptp.pp (tptp.aa_int_bool _let_1 L)))))) (forall ((K tptp.int) (L tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.bit_se6526347334894502574or_int K) L)) tptp.zero_zero_int)) (not (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int K) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int L) tptp.zero_zero_int)))))) (forall ((N tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se547839408752420682it_nat N) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N))) (forall ((K tptp.int) (L tptp.int) (N tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_int_fun_nat_bool tptp.bit_se1146084159140164899it_int (tptp.aa_int_int (tptp.bit_se6526347334894502574or_int K) L)) N)) (not (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_int_fun_nat_bool tptp.bit_se1146084159140164899it_int K) N)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_int_fun_nat_bool tptp.bit_se1146084159140164899it_int L) N)))))) (forall ((N tptp.nat) (K tptp.int)) (= (tptp.aa_int_int (tptp.bit_se2159334234014336723it_int N) K) (tptp.aa_int_int (tptp.bit_se6526347334894502574or_int K) (tptp.aa_int_int (tptp.bit_se545348938243370406it_int N) tptp.one_one_int)))) (forall ((N tptp.nat) (K tptp.int)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se547839408752420682it_nat N) (tptp.aa_int_nat tptp.nat2 K)) (tptp.aa_int_nat tptp.nat2 (tptp.aa_int_int (tptp.bit_se545348938243370406it_int N) K)))) (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.pp (tptp.aa_int_bool _let_1 X)) (=> (tptp.pp (tptp.aa_int_bool _let_1 Y)) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.bit_se6526347334894502574or_int X) Y))))))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se2161824704523386999it_nat M) N) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se6528837805403552850or_nat N) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se547839408752420682it_nat M) tptp.one_one_nat)))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se7882103937844011126it_nat M) N) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se1412395901928357646or_nat N) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se547839408752420682it_nat M) tptp.one_one_nat)))) (forall ((M tptp.nat) (K tptp.int) (N tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_int_fun_nat_bool tptp.bit_se1146084159140164899it_int (tptp.aa_int_int (tptp.bit_se545348938243370406it_int M) K)) N)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_int_fun_nat_bool tptp.bit_se1146084159140164899it_int K) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) M)))))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se6528837805403552850or_nat M) N) (tptp.aa_int_nat tptp.nat2 (tptp.aa_int_int (tptp.bit_se6526347334894502574or_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int M)) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N))))) (forall ((M tptp.nat) (Q2 tptp.nat) (N tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.bit_se1148574629649215175it_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se547839408752420682it_nat M) Q2)) N)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.bit_se1148574629649215175it_nat Q2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) M)))))) (forall ((N tptp.nat) (K tptp.int) (L tptp.int)) (= (tptp.aa_int_int (tptp.bit_concat_bit N K) L) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.bit_se2923211474154528505it_int N) K)) (tptp.aa_int_int (tptp.bit_se545348938243370406it_int N) L)))) (forall ((N tptp.nat) (K tptp.int) (L tptp.int)) (= (tptp.aa_int_int (tptp.bit_concat_bit N K) L) (tptp.aa_int_int (tptp.bit_se1409905431419307370or_int (tptp.aa_int_int (tptp.bit_se2923211474154528505it_int N) K)) (tptp.aa_int_int (tptp.bit_se545348938243370406it_int N) L)))) (forall ((N tptp.nat) (K tptp.int)) (= (tptp.aa_int_int (tptp.bit_se7879613467334960850it_int N) K) (tptp.aa_int_int (tptp.bit_se1409905431419307370or_int K) (tptp.aa_int_int (tptp.bit_se545348938243370406it_int N) tptp.one_one_int)))) (forall ((N tptp.nat) (K tptp.int)) (= (tptp.aa_int_int (tptp.bit_se545348938243370406it_int N) K) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int K) (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) N)))) (forall ((N tptp.nat) (M tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se547839408752420682it_nat N) M) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat M) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N)))) (forall ((N tptp.nat)) (= (tptp.aa_int_int (tptp.bit_se545348938243370406it_int N) (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int)) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) N)))) (forall ((X tptp.int) (N tptp.nat) (Y tptp.int)) (let ((_let_1 (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) N))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) X)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) _let_1)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Y) _let_1)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.bit_se6526347334894502574or_int X) Y)) _let_1))))))) (forall ((K tptp.int) (L tptp.int)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int _let_1))) (= (tptp.aa_int_int (tptp.bit_se6526347334894502574or_int K) L) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_bool_int tptp.zero_n2684676970156552555ol_int (tptp.aa_bool_bool tptp.fNot (tptp.aa_bool_bool (tptp.aa_boo8970175072276269406l_bool tptp.fequal_bool (tptp.aa_bool_bool tptp.fNot (tptp.aa_int_bool _let_2 K))) (tptp.aa_bool_bool tptp.fNot (tptp.aa_int_bool _let_2 L)))))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int _let_1) (tptp.aa_int_int (tptp.bit_se6526347334894502574or_int (tptp.aa_int_int (tptp.divide_divide_int K) _let_1)) (tptp.aa_int_int (tptp.divide_divide_int L) _let_1)))))))) (forall ((K tptp.int) (L tptp.int)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_int_int (tptp.bit_se6526347334894502574or_int K) L))) (let ((_let_3 (= L tptp.zero_zero_int))) (let ((_let_4 (= K tptp.zero_zero_int))) (let ((_let_5 (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int))) (let ((_let_6 (= L _let_5))) (let ((_let_7 (= K _let_5))) (and (=> _let_7 (= _let_2 (tptp.aa_int_int tptp.bit_ri7919022796975470100ot_int L))) (=> (not _let_7) (and (=> _let_6 (= _let_2 (tptp.aa_int_int tptp.bit_ri7919022796975470100ot_int K))) (=> (not _let_6) (and (=> _let_4 (= _let_2 L)) (=> (not _let_4) (and (=> _let_3 (= _let_2 K)) (=> (not _let_3) (= _let_2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int tptp.abs_abs_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_int_int (tptp.modulo_modulo_int K) _let_1)) (tptp.aa_int_int (tptp.modulo_modulo_int L) _let_1)))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int _let_1) (tptp.aa_int_int (tptp.bit_se6526347334894502574or_int (tptp.aa_int_int (tptp.divide_divide_int K) _let_1)) (tptp.aa_int_int (tptp.divide_divide_int L) _let_1))))))))))))))))))))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat tptp.aTP_Lamm_al) (tptp.set_or4665077453230672383an_nat M N)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat N) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) tptp.one_one_nat))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat M) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) tptp.one_one_nat)))) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (forall ((X7 tptp.fun_nat_real)) (= (tptp.topolo4055970368930404560y_real X7) (forall ((J3 tptp.nat)) (exists ((M9 tptp.nat)) (forall ((M6 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M9) M6)) (forall ((N5 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M9) N5)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_nat_real X7 M6)) (tptp.aa_nat_real X7 N5)))) (tptp.aa_real_real tptp.inverse_inverse_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real (tptp.aa_nat_nat tptp.suc J3))))))))))))) (forall ((K tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.aa_int_int tptp.bit_ri7919022796975470100ot_int K))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int K) tptp.zero_zero_int)))) (forall ((K tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int tptp.bit_ri7919022796975470100ot_int K)) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) K)))) (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int N))) (let ((_let_2 (tptp.aa_num_int tptp.numeral_numeral_int M))) (= (tptp.aa_int_int (tptp.bit_se725231765392027082nd_int (tptp.aa_int_int tptp.uminus_uminus_int _let_2)) (tptp.aa_int_int tptp.uminus_uminus_int _let_1)) (tptp.aa_int_int tptp.bit_ri7919022796975470100ot_int (tptp.aa_int_int (tptp.bit_se1409905431419307370or_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int _let_2) tptp.one_one_int)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int _let_1) tptp.one_one_int))))))) (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int N))) (let ((_let_2 (tptp.aa_num_int tptp.numeral_numeral_int M))) (= (tptp.aa_int_int (tptp.bit_se1409905431419307370or_int (tptp.aa_int_int tptp.uminus_uminus_int _let_2)) (tptp.aa_int_int tptp.uminus_uminus_int _let_1)) (tptp.aa_int_int tptp.bit_ri7919022796975470100ot_int (tptp.aa_int_int (tptp.bit_se725231765392027082nd_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int _let_2) tptp.one_one_int)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int _let_1) tptp.one_one_int))))))) (forall ((K tptp.int) (N tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_int_fun_nat_bool tptp.bit_se1146084159140164899it_int (tptp.aa_int_int tptp.bit_ri7919022796975470100ot_int K)) N)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_int_fun_nat_bool tptp.bit_se1146084159140164899it_int K) N))))) (forall ((N tptp.nat) (P tptp.fun_nat_bool)) (= (exists ((M6 tptp.nat)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M6) N)) (tptp.pp (tptp.aa_nat_bool P M6)))) (exists ((X3 tptp.nat)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) (tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat N))) (tptp.pp (tptp.aa_nat_bool P X3)))))) (forall ((N tptp.nat) (P tptp.fun_nat_bool)) (= (forall ((M6 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M6) N)) (tptp.pp (tptp.aa_nat_bool P M6)))) (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) (tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat N))) (tptp.pp (tptp.aa_nat_bool P X3)))))) (forall ((K tptp.int) (L tptp.int)) (= (tptp.aa_int_int (tptp.bit_se1409905431419307370or_int K) L) (tptp.aa_int_int tptp.bit_ri7919022796975470100ot_int (tptp.aa_int_int (tptp.bit_se725231765392027082nd_int (tptp.aa_int_int tptp.bit_ri7919022796975470100ot_int K)) (tptp.aa_int_int tptp.bit_ri7919022796975470100ot_int L))))) (forall ((K tptp.int)) (= (tptp.aa_int_int tptp.bit_ri7919022796975470100ot_int K) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_int_int tptp.uminus_uminus_int K)) tptp.one_one_int))) (= (tptp.aa_int_int (tptp.bit_se725231765392027082nd_int tptp.one_one_int) _let_41) tptp.zero_zero_int) (= (tptp.aa_int_int (tptp.bit_se1409905431419307370or_int tptp.one_one_int) _let_41) (tptp.aa_int_int tptp.bit_ri7919022796975470100ot_int tptp.zero_zero_int)) (forall ((N tptp.nat) (K tptp.int)) (= (tptp.aa_int_int (tptp.bit_se4203085406695923979it_int N) K) (tptp.aa_int_int (tptp.bit_se725231765392027082nd_int K) (tptp.aa_int_int tptp.bit_ri7919022796975470100ot_int (tptp.aa_int_int (tptp.bit_se545348938243370406it_int N) tptp.one_one_int))))) (forall ((K tptp.int) (L tptp.int)) (= (tptp.aa_int_int (tptp.bit_se6526347334894502574or_int K) L) (tptp.aa_int_int (tptp.bit_se1409905431419307370or_int (tptp.aa_int_int (tptp.bit_se725231765392027082nd_int K) (tptp.aa_int_int tptp.bit_ri7919022796975470100ot_int L))) (tptp.aa_int_int (tptp.bit_se725231765392027082nd_int (tptp.aa_int_int tptp.bit_ri7919022796975470100ot_int K)) L)))) (forall ((N3 tptp.set_nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat N3) (tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat N))) (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat N3)))) (forall ((K tptp.int)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.aa_int_int (tptp.divide_divide_int (tptp.aa_int_int tptp.bit_ri7919022796975470100ot_int K)) _let_1) (tptp.aa_int_int tptp.bit_ri7919022796975470100ot_int (tptp.aa_int_int (tptp.divide_divide_int K) _let_1))))) (forall ((K tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int tptp.bit_ri7919022796975470100ot_int K))) (not (tptp.pp (tptp.aa_int_bool _let_1 K)))))) (forall ((N tptp.num)) (= (tptp.aa_int_int (tptp.bit_se725231765392027082nd_int tptp.one_one_int) (tptp.aa_int_int tptp.bit_ri7919022796975470100ot_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 N)))) tptp.one_one_int)) (forall ((M tptp.num)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 M)))) (= (tptp.aa_int_int (tptp.bit_se725231765392027082nd_int _let_1) (tptp.aa_int_int tptp.bit_ri7919022796975470100ot_int tptp.one_one_int)) _let_1))) (forall ((N tptp.num)) (let ((_let_1 (tptp.aa_int_int tptp.bit_ri7919022796975470100ot_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 N))))) (= (tptp.aa_int_int (tptp.bit_se1409905431419307370or_int tptp.one_one_int) _let_1) _let_1))) (forall ((M tptp.num)) (let ((_let_1 (tptp.aa_int_int tptp.bit_ri7919022796975470100ot_int tptp.one_one_int))) (= (tptp.aa_int_int (tptp.bit_se1409905431419307370or_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 M))) _let_1) _let_1))) (forall ((K tptp.int) (N tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_int_fun_nat_bool tptp.bit_se1146084159140164899it_int (tptp.aa_int_int tptp.uminus_uminus_int K)) N)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_int_fun_nat_bool tptp.bit_se1146084159140164899it_int (tptp.aa_int_int tptp.bit_ri7919022796975470100ot_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int K) tptp.one_one_int))) N)))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.bit_or_not_num_neg M) N)) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_int_int (tptp.bit_se1409905431419307370or_int (tptp.aa_num_int tptp.numeral_numeral_int M)) (tptp.aa_int_int tptp.bit_ri7919022796975470100ot_int (tptp.aa_num_int tptp.numeral_numeral_int N)))))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.aa_int_int (tptp.bit_se1409905431419307370or_int (tptp.aa_int_int tptp.bit_ri7919022796975470100ot_int (tptp.aa_num_int tptp.numeral_numeral_int M))) (tptp.aa_num_int tptp.numeral_numeral_int N)) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.bit_or_not_num_neg N) M))))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.aa_int_int (tptp.bit_se1409905431419307370or_int (tptp.aa_num_int tptp.numeral_numeral_int M)) (tptp.aa_int_int tptp.bit_ri7919022796975470100ot_int (tptp.aa_num_int tptp.numeral_numeral_int N))) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.bit_or_not_num_neg M) N))))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.set_or4665077453230672383an_nat M (tptp.aa_nat_nat tptp.suc N)))) (let ((_let_2 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)))) (and (=> _let_2 (= _let_1 (tptp.insert_nat N (tptp.set_or4665077453230672383an_nat M N)))) (=> (not _let_2) (= _let_1 tptp.bot_bot_set_nat)))))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.aa_int_int (tptp.bit_se725231765392027082nd_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 M))) (tptp.aa_int_int tptp.bit_ri7919022796975470100ot_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 N)))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_int_int (tptp.bit_se725231765392027082nd_int (tptp.aa_num_int tptp.numeral_numeral_int M)) (tptp.aa_int_int tptp.bit_ri7919022796975470100ot_int (tptp.aa_num_int tptp.numeral_numeral_int N)))))) (forall ((M tptp.num)) (= (tptp.aa_int_int (tptp.bit_se725231765392027082nd_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit1 M))) (tptp.aa_int_int tptp.bit_ri7919022796975470100ot_int tptp.one_one_int)) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 M)))) (forall ((N tptp.num)) (= (tptp.aa_int_int (tptp.bit_se1409905431419307370or_int tptp.one_one_int) (tptp.aa_int_int tptp.bit_ri7919022796975470100ot_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit1 N)))) (tptp.aa_int_int tptp.bit_ri7919022796975470100ot_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 N))))) (forall ((N tptp.num)) (= (tptp.aa_int_int (tptp.bit_se725231765392027082nd_int tptp.one_one_int) (tptp.aa_int_int tptp.bit_ri7919022796975470100ot_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit1 N)))) tptp.zero_zero_int)) (forall ((M tptp.num)) (= (tptp.aa_int_int (tptp.bit_se1409905431419307370or_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit1 M))) (tptp.aa_int_int tptp.bit_ri7919022796975470100ot_int tptp.one_one_int)) (tptp.aa_int_int tptp.bit_ri7919022796975470100ot_int tptp.zero_zero_int))) (forall ((M tptp.nat) (K tptp.num)) (let ((_let_1 (tptp.set_or4665077453230672383an_nat M (tptp.aa_num_nat tptp.numeral_numeral_nat K)))) (let ((_let_2 (tptp.aa_num_nat tptp.pred_numeral K))) (let ((_let_3 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) _let_2)))) (and (=> _let_3 (= _let_1 (tptp.insert_nat _let_2 (tptp.set_or4665077453230672383an_nat M _let_2)))) (=> (not _let_3) (= _let_1 tptp.bot_bot_set_nat))))))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.aa_int_int (tptp.bit_se725231765392027082nd_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit1 M))) (tptp.aa_int_int tptp.bit_ri7919022796975470100ot_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit1 N)))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_int_int (tptp.bit_se725231765392027082nd_int (tptp.aa_num_int tptp.numeral_numeral_int M)) (tptp.aa_int_int tptp.bit_ri7919022796975470100ot_int (tptp.aa_num_int tptp.numeral_numeral_int N)))))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.aa_int_int (tptp.bit_se725231765392027082nd_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 M))) (tptp.aa_int_int tptp.bit_ri7919022796975470100ot_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit1 N)))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_int_int (tptp.bit_se725231765392027082nd_int (tptp.aa_num_int tptp.numeral_numeral_int M)) (tptp.aa_int_int tptp.bit_ri7919022796975470100ot_int (tptp.aa_num_int tptp.numeral_numeral_int N)))))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.aa_int_int (tptp.bit_se1409905431419307370or_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 M))) (tptp.aa_int_int tptp.bit_ri7919022796975470100ot_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit1 N)))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_int_int (tptp.bit_se1409905431419307370or_int (tptp.aa_num_int tptp.numeral_numeral_int M)) (tptp.aa_int_int tptp.bit_ri7919022796975470100ot_int (tptp.aa_num_int tptp.numeral_numeral_int N)))))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.aa_int_int (tptp.bit_se1409905431419307370or_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 M))) (tptp.aa_int_int tptp.bit_ri7919022796975470100ot_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 N)))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int tptp.one_one_int) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_int_int (tptp.bit_se1409905431419307370or_int (tptp.aa_num_int tptp.numeral_numeral_int M)) (tptp.aa_int_int tptp.bit_ri7919022796975470100ot_int (tptp.aa_num_int tptp.numeral_numeral_int N))))))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.aa_int_int (tptp.bit_se725231765392027082nd_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit1 M))) (tptp.aa_int_int tptp.bit_ri7919022796975470100ot_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 N)))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int tptp.one_one_int) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_int_int (tptp.bit_se725231765392027082nd_int (tptp.aa_num_int tptp.numeral_numeral_int M)) (tptp.aa_int_int tptp.bit_ri7919022796975470100ot_int (tptp.aa_num_int tptp.numeral_numeral_int N))))))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.aa_int_int (tptp.bit_se1409905431419307370or_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit1 M))) (tptp.aa_int_int tptp.bit_ri7919022796975470100ot_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 N)))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int tptp.one_one_int) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_int_int (tptp.bit_se1409905431419307370or_int (tptp.aa_num_int tptp.numeral_numeral_int M)) (tptp.aa_int_int tptp.bit_ri7919022796975470100ot_int (tptp.aa_num_int tptp.numeral_numeral_int N))))))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.aa_int_int (tptp.bit_se1409905431419307370or_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit1 M))) (tptp.aa_int_int tptp.bit_ri7919022796975470100ot_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit1 N)))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int tptp.one_one_int) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_int_int (tptp.bit_se1409905431419307370or_int (tptp.aa_num_int tptp.numeral_numeral_int M)) (tptp.aa_int_int tptp.bit_ri7919022796975470100ot_int (tptp.aa_num_int tptp.numeral_numeral_int N))))))) (forall ((K tptp.int)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.aa_int_int tptp.bit_ri7919022796975470100ot_int K) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_bool_int tptp.zero_n2684676970156552555ol_int (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int _let_1) K))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int _let_1) (tptp.aa_int_int tptp.bit_ri7919022796975470100ot_int (tptp.aa_int_int (tptp.divide_divide_int K) _let_1))))))) (forall ((K tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat _let_1) (tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat K)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat _let_1 K)) tptp.one_one_nat)))) (forall ((N tptp.nat) (A tptp.fun_nat_nat) (B2 tptp.fun_nat_nat)) (let ((_let_1 (tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat N))) (=> (forall ((I3 tptp.nat) (J2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I3) J2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat J2) N)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat A I3)) (tptp.aa_nat_nat A J2)))))) (=> (forall ((I3 tptp.nat) (J2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I3) J2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat J2) N)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat B2 J2)) (tptp.aa_nat_nat B2 I3)))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat N) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_fun5791449513213591928at_nat (tptp.aTP_Lamm_oj A) B2)) _let_1))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat A) _let_1)) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat B2) _let_1)))))))) (forall ((T tptp.vEBT_VEBT) (D tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_VEBT_valid T) D)) (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt T) D)))) (forall ((T tptp.vEBT_VEBT) (D tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt T) D)) (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_VEBT_valid T) D)))) (forall ((T tptp.vEBT_VEBT) (D tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_VEBT_valid T) D)) (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt T) D)))) (= tptp.code_Target_positive tptp.numeral_numeral_int) (forall ((L tptp.num) (Qr tptp.produc8923325533196201883nteger)) (= (tptp.unique4921790084139445826nteger L Qr) (tptp.produc6916734918728496179nteger (tptp.aTP_Lamm_fm L) Qr))) (forall ((L tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger tptp.zero_z3403309356797280102nteger) L) tptp.zero_z3403309356797280102nteger)) (forall ((K tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger K) tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger)) (forall ((X tptp.produc5207004643709237345nteger)) (not (forall ((F2 tptp.fun_Co6545587727236015215e_term) (D2 tptp.code_integer) (I3 tptp.code_integer)) (not (= X (tptp.produc4282985567423050387nteger F2 (tptp.produc1086072967326762835nteger D2 I3))))))) (forall ((X tptp.produc1616345218596728535nteger)) (not (forall ((F2 tptp.fun_Pr272337284026993017e_term) (D2 tptp.code_integer) (I3 tptp.code_integer)) (not (= X (tptp.produc7384524951051686153nteger F2 (tptp.produc1086072967326762835nteger D2 I3))))))) (tptp.pp (tptp.aa_Code_integer_bool _let_40 tptp.zero_z3403309356797280102nteger)) (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger N))) (let ((_let_2 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger M))) (= (tptp.unique3479559517661332726nteger M N) (tptp.produc1086072967326762835nteger (tptp.divide6298287555418463151nteger _let_2 _let_1) (tptp.modulo364778990260209775nteger _let_2 _let_1)))))) (forall ((K tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod1783974652533396728nteger tptp.sgn_sgn_Code_integer K))) (let ((_let_2 (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger K) tptp.zero_z3403309356797280102nteger)))) (let ((_let_3 (= K tptp.zero_z3403309356797280102nteger))) (and (=> _let_3 (= _let_1 tptp.zero_z3403309356797280102nteger)) (=> (not _let_3) (and (=> _let_2 (= _let_1 (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (=> (not _let_2) (= _let_1 tptp.one_one_Code_integer))))))))) (forall ((K tptp.int)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (let ((_let_2 (tptp.aa_num_int tptp.numeral_numeral_int _let_1))) (let ((_let_3 (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger _let_1)) (tptp.aa_int_Code_integer tptp.code_integer_of_int (tptp.aa_int_int (tptp.divide_divide_int K) _let_2))))) (let ((_let_4 (tptp.aa_int_Code_integer tptp.code_integer_of_int K))) (let ((_let_5 (= K tptp.zero_zero_int))) (let ((_let_6 (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int K) tptp.zero_zero_int)))) (and (=> _let_6 (= _let_4 (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_int_Code_integer tptp.code_integer_of_int (tptp.aa_int_int tptp.uminus_uminus_int K))))) (=> (not _let_6) (and (=> _let_5 (= _let_4 tptp.zero_z3403309356797280102nteger)) (=> (not _let_5) (= _let_4 (tptp.if_Code_integer (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.fequal_int (tptp.aa_int_int (tptp.modulo_modulo_int K) _let_2)) tptp.zero_zero_int) _let_3 (tptp.plus_p5714425477246183910nteger _let_3 tptp.one_one_Code_integer)))))))))))))) (= tptp.code_positive tptp.numera6620942414471956472nteger) (forall ((K tptp.code_integer)) (let ((_let_1 (tptp.abs_abs_Code_integer K))) (let ((_let_2 (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger K) tptp.zero_z3403309356797280102nteger)))) (and (=> _let_2 (= _let_1 (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger K))) (=> (not _let_2) (= _let_1 K)))))) (forall ((Xa2 tptp.int) (X tptp.int)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_int_Code_integer tptp.code_integer_of_int Xa2)) (tptp.aa_int_Code_integer tptp.code_integer_of_int X))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Xa2) X)))) (not (tptp.pp (tptp.aa_Code_integer_bool _let_39 tptp.zero_z3403309356797280102nteger))) (forall ((Xa2 tptp.int) (X tptp.int)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_int_Code_integer tptp.code_integer_of_int Xa2)) (tptp.aa_int_Code_integer tptp.code_integer_of_int X)) (tptp.aa_int_Code_integer tptp.code_integer_of_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int Xa2) X)))) (forall ((Xa2 tptp.int) (X tptp.int)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_int_Code_integer tptp.code_integer_of_int Xa2)) (tptp.aa_int_Code_integer tptp.code_integer_of_int X))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Xa2) X)))) (forall ((K tptp.code_integer)) (let ((_let_1 (tptp.code_int_of_integer K))) (let ((_let_2 (= K tptp.zero_z3403309356797280102nteger))) (let ((_let_3 (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger K) tptp.zero_z3403309356797280102nteger)))) (and (=> _let_3 (= _let_1 (tptp.aa_int_int tptp.uminus_uminus_int (tptp.code_int_of_integer (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger K))))) (=> (not _let_3) (and (=> _let_2 (= _let_1 tptp.zero_zero_int)) (=> (not _let_2) (= _let_1 (tptp.produc1553301316500091796er_int tptp.aTP_Lamm_vp (tptp.code_divmod_integer K (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))))))))))))) (forall ((K tptp.code_integer)) (let ((_let_1 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.code_bit_cut_integer K) (tptp.produc5135875973608410785r_bool (tptp.divide6298287555418463151nteger K _let_1) (tptp.aa_bool_bool tptp.fNot (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer _let_1) K)))))) (forall ((K tptp.num)) (= (tptp.code_int_of_integer (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger K)) (tptp.aa_num_int tptp.numeral_numeral_int K))) (forall ((X tptp.code_integer) (Xa2 tptp.code_integer)) (= (tptp.code_int_of_integer (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger X) Xa2)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.code_int_of_integer X)) (tptp.code_int_of_integer Xa2)))) (forall ((X tptp.code_integer) (Xa2 tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger X) Xa2)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.code_int_of_integer X)) (tptp.code_int_of_integer Xa2))))) (forall ((K tptp.code_integer) (L tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger K) L)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.code_int_of_integer K)) (tptp.code_int_of_integer L))))) (forall ((K tptp.code_integer) (L tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger K) L)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.code_int_of_integer K)) (tptp.code_int_of_integer L))))) (forall ((X tptp.code_integer) (Xa2 tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger X) Xa2)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.code_int_of_integer X)) (tptp.code_int_of_integer Xa2))))) (forall ((K tptp.code_integer) (L tptp.code_integer)) (= (tptp.code_divmod_integer K L) (tptp.produc1086072967326762835nteger (tptp.divide6298287555418463151nteger K L) (tptp.modulo364778990260209775nteger K L)))) (forall ((K tptp.code_integer)) (let ((_let_1 (tptp.code_num_of_integer K))) (let ((_let_2 (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger K) tptp.one_one_Code_integer)))) (and (=> _let_2 (= _let_1 tptp.one)) (=> (not _let_2) (= _let_1 (tptp.produc7336495610019696514er_num tptp.aTP_Lamm_vq (tptp.code_divmod_integer K (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one)))))))))) (forall ((K tptp.code_integer)) (let ((_let_1 (tptp.code_bit_cut_integer K))) (let ((_let_2 (= K tptp.zero_z3403309356797280102nteger))) (and (=> _let_2 (= _let_1 (tptp.produc5135875973608410785r_bool tptp.zero_z3403309356797280102nteger tptp.fFalse))) (=> (not _let_2) (= _let_1 (tptp.produc6117575242473779287r_bool (tptp.aTP_Lamm_vr K) (tptp.code_divmod_abs K (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one)))))))))) (forall ((K tptp.code_integer)) (let ((_let_1 (tptp.code_nat_of_integer K))) (let ((_let_2 (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger K) tptp.zero_z3403309356797280102nteger)))) (and (=> _let_2 (= _let_1 tptp.zero_zero_nat)) (=> (not _let_2) (= _let_1 (tptp.produc1555791787009142072er_nat tptp.aTP_Lamm_vs (tptp.code_divmod_integer K (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one)))))))))) (forall ((K tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger K) tptp.zero_z3403309356797280102nteger)) (= (tptp.code_nat_of_integer K) tptp.zero_zero_nat))) (forall ((K tptp.num)) (= (tptp.code_nat_of_integer (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger K)) (tptp.aa_num_nat tptp.numeral_numeral_nat K))) (forall ((J tptp.code_integer)) (= (tptp.code_divmod_abs tptp.zero_z3403309356797280102nteger J) (tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger tptp.zero_z3403309356797280102nteger))) (forall ((J tptp.code_integer)) (= (tptp.code_divmod_abs J tptp.zero_z3403309356797280102nteger) (tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger (tptp.abs_abs_Code_integer J)))) (forall ((K tptp.code_integer) (L tptp.code_integer)) (let ((_let_1 (tptp.abs_abs_Code_integer L))) (let ((_let_2 (tptp.abs_abs_Code_integer K))) (= (tptp.code_divmod_abs K L) (tptp.produc1086072967326762835nteger (tptp.divide6298287555418463151nteger _let_2 _let_1) (tptp.modulo364778990260209775nteger _let_2 _let_1)))))) (forall ((K tptp.code_integer) (L tptp.code_integer)) (let ((_let_1 (tptp.code_divmod_abs K L))) (let ((_let_2 (tptp.code_divmod_integer K L))) (let ((_let_3 (= L tptp.zero_z3403309356797280102nteger))) (let ((_let_4 (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger))) (let ((_let_5 (tptp.pp (tptp.aa_Code_integer_bool _let_4 L)))) (let ((_let_6 (tptp.pp (tptp.aa_Code_integer_bool _let_4 K)))) (let ((_let_7 (= K tptp.zero_z3403309356797280102nteger))) (and (=> _let_7 (= _let_2 (tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger tptp.zero_z3403309356797280102nteger))) (=> (not _let_7) (and (=> _let_5 (and (=> _let_6 (= _let_2 _let_1)) (=> (not _let_6) (= _let_2 (tptp.produc6916734918728496179nteger (tptp.aTP_Lamm_vt L) _let_1))))) (=> (not _let_5) (and (=> _let_3 (= _let_2 (tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger K))) (=> (not _let_3) (= _let_2 (tptp.aa_Pro4693618923521437820nteger (tptp.aa_fun2509385170507305080nteger tptp.produc6499014454317279255nteger tptp.uminus1351360451143612070nteger) (tptp.if_Pro6119634080678213985nteger (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger K) tptp.zero_z3403309356797280102nteger) _let_1 (tptp.produc6916734918728496179nteger (tptp.aTP_Lamm_vu L) _let_1)))))))))))))))))) (forall ((Z tptp.complex)) (= (tptp.aa_complex_real tptp.re (tptp.aa_complex_complex tptp.csqrt Z)) (tptp.aa_real_real tptp.sqrt (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex Z)) (tptp.aa_complex_real tptp.re Z))) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))))) (forall ((N tptp.nat)) (= (tptp.finite_card_nat (tptp.collect_nat (tptp.aa_nat_fun_nat_bool tptp.aTP_Lamm_br N))) N)) (forall ((L tptp.nat) (U tptp.nat)) (= (tptp.finite_card_nat (tptp.set_or4665077453230672383an_nat L U)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat U) L))) (forall ((N tptp.nat)) (= (tptp.finite_card_nat (tptp.collect_nat (tptp.aa_nat_fun_nat_bool tptp.aTP_Lamm_bq N))) (tptp.aa_nat_nat tptp.suc N))) (forall ((L tptp.nat) (U tptp.nat)) (= (tptp.finite_card_nat (tptp.set_or1269000886237332187st_nat L U)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat tptp.suc U)) L))) (forall ((V tptp.num)) (= (tptp.aa_complex_real tptp.re (tptp.numera6690914467698888265omplex V)) (tptp.aa_num_real tptp.numeral_numeral_real V))) (forall ((Z tptp.complex) (W tptp.num)) (= (tptp.aa_complex_real tptp.re (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex Z) (tptp.numera6690914467698888265omplex W))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_complex_real tptp.re Z)) (tptp.aa_num_real tptp.numeral_numeral_real W)))) (forall ((X tptp.complex)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_complex_real tptp.re X)) (tptp.aa_complex_real tptp.real_V1022390504157884413omplex X)))) (forall ((R tptp.real) (X tptp.complex)) (= (tptp.aa_complex_real tptp.re (tptp.aa_complex_complex (tptp.real_V2046097035970521341omplex R) X)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real R) (tptp.aa_complex_real tptp.re X)))) (forall ((X tptp.complex)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_complex_real tptp.re X))) (tptp.aa_complex_real tptp.real_V1022390504157884413omplex X)))) (forall ((Z tptp.complex)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_complex_real tptp.re (tptp.aa_complex_complex tptp.csqrt Z))))) (forall ((M7 tptp.set_nat) (I tptp.nat)) (=> (not (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat tptp.zero_zero_nat) M7))) (= (tptp.finite_card_nat (tptp.collect_nat (tptp.aa_nat_fun_nat_bool (tptp.aTP_Lamm_vv M7) I))) (tptp.finite_card_nat (tptp.collect_nat (tptp.aa_nat_fun_nat_bool (tptp.aTP_Lamm_vw M7) I)))))) (forall ((M7 tptp.set_nat) (I tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat tptp.zero_zero_nat) M7)) (= (tptp.aa_nat_nat tptp.suc (tptp.finite_card_nat (tptp.collect_nat (tptp.aa_nat_fun_nat_bool (tptp.aTP_Lamm_vv M7) I)))) (tptp.finite_card_nat (tptp.collect_nat (tptp.aa_nat_fun_nat_bool (tptp.aTP_Lamm_vw M7) I)))))) (forall ((M7 tptp.set_nat) (I tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat tptp.zero_zero_nat) M7)) (not (= (tptp.finite_card_nat (tptp.collect_nat (tptp.aa_nat_fun_nat_bool (tptp.aTP_Lamm_vw M7) I))) tptp.zero_zero_nat)))) (forall ((A4 tptp.set_nat) (K tptp.nat)) (let ((_let_1 (tptp.set_or4665077453230672383an_nat K (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat K) (tptp.finite_card_nat A4))))) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat A4) _let_1)) (= A4 _let_1)))) (forall ((N3 tptp.set_nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat N3) (tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat N))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.finite_card_nat N3)) N)))) (forall ((S2 tptp.set_nat)) (let ((_let_1 (tptp.groups3542108847815614940at_nat tptp.aTP_Lamm_al))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_set_nat_nat _let_1 (tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat (tptp.finite_card_nat S2)))) (tptp.aa_set_nat_nat _let_1 S2))))) (forall ((C tptp.complex) (N tptp.nat)) (=> (not (= C tptp.zero_zero_complex)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (= (tptp.finite_card_complex (tptp.collect_complex (tptp.aa_nat5545486172511849908x_bool (tptp.aTP_Lamm_vx C) N))) N)))) (forall ((N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (= (tptp.finite_card_complex (tptp.collect_complex (tptp.aTP_Lamm_cq N))) N))) (forall ((Z tptp.complex)) (let ((_let_1 (tptp.aa_complex_real tptp.real_V1022390504157884413omplex Z))) (let ((_let_2 (tptp.aa_complex_real tptp.re Z))) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real _let_1) _let_2)) tptp.zero_zero_real)) (= _let_2 (tptp.aa_real_real tptp.uminus_uminus_real _let_1)))))) (forall ((N tptp.nat) (A tptp.real)) (= (tptp.aa_real_real tptp.cos_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N)) A)) (tptp.aa_complex_real tptp.re (tptp.aa_nat_complex (tptp.power_power_complex (tptp.aa_real_complex tptp.cis A)) N)))) (forall ((Z tptp.complex)) (let ((_let_1 (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_complex_real tptp.re Z))) (let ((_let_3 (tptp.aa_complex_real tptp.real_V1022390504157884413omplex Z))) (let ((_let_4 (tptp.aa_complex_real tptp.im Z))) (= (tptp.aa_complex_complex tptp.csqrt Z) (tptp.aa_real_complex (tptp.aa_rea2649881322057434177omplex tptp.complex2 (tptp.aa_real_real tptp.sqrt (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real _let_3) _let_2)) _let_1))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real (tptp.if_real (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.fequal_real _let_4) tptp.zero_zero_real)) tptp.one_one_real) (tptp.aa_real_real tptp.sgn_sgn_real _let_4))) (tptp.aa_real_real tptp.sqrt (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real _let_3) _let_2)) _let_1)))))))))) (forall ((Z tptp.complex)) (let ((_let_1 (tptp.aa_complex_real tptp.im Z))) (= (tptp.aa_complex_real tptp.im (tptp.aa_complex_complex tptp.csqrt Z)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real (tptp.if_real (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.fequal_real _let_1) tptp.zero_zero_real)) tptp.one_one_real) (tptp.aa_real_real tptp.sgn_sgn_real _let_1))) (tptp.aa_real_real tptp.sqrt (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex Z)) (tptp.aa_complex_real tptp.re Z))) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))))))) (forall ((X tptp.complex)) (let ((_let_1 (tptp.aa_complex_real tptp.re X))) (=> (= (tptp.aa_complex_real tptp.im X) tptp.zero_zero_real) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real _let_1) tptp.zero_zero_real)) (= (tptp.aa_complex_complex tptp.csqrt X) (tptp.aa_complex_complex (tptp.times_times_complex tptp.imaginary_unit) (tptp.aa_real_complex tptp.real_V4546457046886955230omplex (tptp.aa_real_real tptp.sqrt (tptp.aa_real_real tptp.abs_abs_real _let_1))))))))) (forall ((V tptp.num)) (= (tptp.aa_complex_real tptp.im (tptp.numera6690914467698888265omplex V)) tptp.zero_zero_real)) (forall ((Z tptp.complex)) (= (tptp.aa_complex_real tptp.im (tptp.aa_complex_complex (tptp.times_times_complex tptp.imaginary_unit) Z)) (tptp.aa_complex_real tptp.re Z))) (forall ((Z tptp.complex)) (= (tptp.aa_complex_real tptp.re (tptp.aa_complex_complex (tptp.times_times_complex tptp.imaginary_unit) Z)) (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_complex_real tptp.im Z)))) (forall ((Z tptp.complex) (W tptp.num)) (= (tptp.aa_complex_real tptp.im (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex Z) (tptp.numera6690914467698888265omplex W))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_complex_real tptp.im Z)) (tptp.aa_num_real tptp.numeral_numeral_real W)))) (forall ((X tptp.complex)) (let ((_let_1 (tptp.aa_complex_real tptp.re X))) (=> (= (tptp.aa_complex_real tptp.im X) tptp.zero_zero_real) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) _let_1)) (= (tptp.aa_complex_complex tptp.csqrt X) (tptp.aa_real_complex tptp.real_V4546457046886955230omplex (tptp.aa_real_real tptp.sqrt _let_1))))))) (forall ((X tptp.complex)) (let ((_let_1 (tptp.aa_complex_real tptp.im X))) (=> (or (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real _let_1) tptp.zero_zero_real)) (and (= _let_1 tptp.zero_zero_real) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_complex_real tptp.re X))))) (= (tptp.aa_complex_complex tptp.csqrt (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex X)) (tptp.aa_complex_complex (tptp.times_times_complex tptp.imaginary_unit) (tptp.aa_complex_complex tptp.csqrt X)))))) (forall ((R tptp.real) (X tptp.complex)) (= (tptp.aa_complex_real tptp.im (tptp.aa_complex_complex (tptp.real_V2046097035970521341omplex R) X)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real R) (tptp.aa_complex_real tptp.im X)))) (forall ((X tptp.complex)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_complex_real tptp.im X))) (tptp.aa_complex_real tptp.real_V1022390504157884413omplex X)))) (forall ((X tptp.complex) (Y tptp.complex)) (= (tptp.aa_complex_real tptp.im (tptp.aa_complex_complex (tptp.times_times_complex X) Y)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_complex_real tptp.re X)) (tptp.aa_complex_real tptp.im Y))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_complex_real tptp.im X)) (tptp.aa_complex_real tptp.re Y))))) (forall ((X tptp.complex) (Y tptp.complex)) (=> (= (tptp.aa_complex_real tptp.re X) (tptp.aa_complex_real tptp.re Y)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex X)) (tptp.aa_complex_real tptp.real_V1022390504157884413omplex Y))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_complex_real tptp.im X))) (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_complex_real tptp.im Y))))))) (forall ((X tptp.complex) (Y tptp.complex)) (=> (= (tptp.aa_complex_real tptp.im X) (tptp.aa_complex_real tptp.im Y)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex X)) (tptp.aa_complex_real tptp.real_V1022390504157884413omplex Y))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_complex_real tptp.re X))) (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_complex_real tptp.re Y))))))) (forall ((X tptp.complex) (Y tptp.complex)) (= (tptp.aa_complex_real tptp.re (tptp.aa_complex_complex (tptp.times_times_complex X) Y)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_complex_real tptp.re X)) (tptp.aa_complex_real tptp.re Y))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_complex_real tptp.im X)) (tptp.aa_complex_real tptp.im Y))))) (forall ((R tptp.real) (X tptp.complex)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.times_times_real R))) (= (tptp.aa_complex_complex (tptp.real_V2046097035970521341omplex R) X) (tptp.aa_real_complex (tptp.aa_rea2649881322057434177omplex tptp.complex2 (tptp.aa_real_real _let_1 (tptp.aa_complex_real tptp.re X))) (tptp.aa_real_real _let_1 (tptp.aa_complex_real tptp.im X)))))) (forall ((Z tptp.complex)) (let ((_let_1 (tptp.aa_complex_complex tptp.csqrt Z))) (let ((_let_2 (tptp.aa_complex_real tptp.re _let_1))) (or (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) _let_2)) (and (= _let_2 tptp.zero_zero_real) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_complex_real tptp.im _let_1)))))))) (forall ((Z tptp.complex)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex Z)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_complex_real tptp.re Z))) (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_complex_real tptp.im Z)))))) (forall ((N tptp.nat) (A tptp.real)) (= (tptp.aa_real_real tptp.sin_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N)) A)) (tptp.aa_complex_real tptp.im (tptp.aa_nat_complex (tptp.power_power_complex (tptp.aa_real_complex tptp.cis A)) N)))) (forall ((Z tptp.complex)) (= (tptp.aa_complex_real tptp.re (tptp.aa_complex_complex tptp.exp_complex Z)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real tptp.exp_real (tptp.aa_complex_real tptp.re Z))) (tptp.aa_real_real tptp.cos_real (tptp.aa_complex_real tptp.im Z))))) (forall ((Z tptp.complex)) (= (tptp.aa_complex_real tptp.im (tptp.aa_complex_complex tptp.exp_complex Z)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real tptp.exp_real (tptp.aa_complex_real tptp.re Z))) (tptp.aa_real_real tptp.sin_real (tptp.aa_complex_real tptp.im Z))))) (forall ((A tptp.complex)) (= A (tptp.aa_complex_complex (tptp.plus_plus_complex (tptp.aa_real_complex tptp.real_V4546457046886955230omplex (tptp.aa_complex_real tptp.re A))) (tptp.aa_complex_complex (tptp.times_times_complex tptp.imaginary_unit) (tptp.aa_real_complex tptp.real_V4546457046886955230omplex (tptp.aa_complex_real tptp.im A)))))) (forall ((X tptp.complex) (Y tptp.complex)) (let ((_let_1 (tptp.aa_complex_real tptp.re Y))) (let ((_let_2 (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_complex_real tptp.im X)))) (let ((_let_3 (tptp.aa_complex_real tptp.im Y))) (let ((_let_4 (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_complex_real tptp.re X)))) (= (tptp.aa_complex_complex (tptp.times_times_complex X) Y) (tptp.aa_real_complex (tptp.aa_rea2649881322057434177omplex tptp.complex2 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real _let_4 _let_1)) (tptp.aa_real_real _let_2 _let_3))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real _let_4 _let_3)) (tptp.aa_real_real _let_2 _let_1))))))))) (forall ((Z tptp.complex)) (= (tptp.aa_complex_complex tptp.exp_complex Z) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_real_complex tptp.real_V4546457046886955230omplex (tptp.aa_real_real tptp.exp_real (tptp.aa_complex_real tptp.re Z)))) (tptp.aa_real_complex tptp.cis (tptp.aa_complex_real tptp.im Z))))) (forall ((Z tptp.complex)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex Z)) _let_1) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_complex_real tptp.re Z)) _let_1)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_complex_real tptp.im Z)) _let_1))))) (forall ((X tptp.complex)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (= (tptp.aa_complex_real tptp.im (tptp.aa_nat_complex (tptp.power_power_complex X) (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_num_real tptp.numeral_numeral_real _let_1)) (tptp.aa_complex_real tptp.re X))) (tptp.aa_complex_real tptp.im X))))) (forall ((X tptp.complex)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.aa_complex_real tptp.re (tptp.aa_nat_complex (tptp.power_power_complex X) _let_1)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_complex_real tptp.re X)) _let_1)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_complex_real tptp.im X)) _let_1))))) (forall ((Z tptp.complex)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (= Z tptp.zero_zero_complex) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_complex_real tptp.re Z)) _let_1)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_complex_real tptp.im Z)) _let_1)) tptp.zero_zero_real)))) (forall ((Z tptp.complex)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.aa_complex_real tptp.real_V1022390504157884413omplex Z) (tptp.aa_real_real tptp.sqrt (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_complex_real tptp.re Z)) _let_1)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_complex_real tptp.im Z)) _let_1)))))) (forall ((X tptp.complex)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_complex_real tptp.re X))) (= (tptp.aa_complex_real tptp.re (tptp.aa_complex_complex tptp.invers8013647133539491842omplex X)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real _let_2) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real _let_2) _let_1)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_complex_real tptp.im X)) _let_1))))))) (forall ((Z tptp.complex)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (not (= Z tptp.zero_zero_complex)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_complex_real tptp.re Z)) _let_1)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_complex_real tptp.im Z)) _let_1))))))) (forall ((X tptp.complex) (Y tptp.complex)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_complex_real tptp.im Y))) (let ((_let_3 (tptp.aa_complex_real tptp.re Y))) (= (tptp.aa_complex_real tptp.re (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex X) Y)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_complex_real tptp.re X)) _let_3)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_complex_real tptp.im X)) _let_2))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real _let_3) _let_1)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real _let_2) _let_1)))))))) (forall ((W tptp.complex) (Z tptp.complex)) (let ((_let_1 (tptp.aa_complex_real tptp.re W))) (=> (= (tptp.aa_nat_complex (tptp.power_power_complex W) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) Z) (=> (or (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) _let_1)) (and (= _let_1 tptp.zero_zero_real) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_complex_real tptp.im W))))) (= (tptp.aa_complex_complex tptp.csqrt Z) W))))) (forall ((B2 tptp.complex)) (let ((_let_1 (tptp.aa_complex_real tptp.re B2))) (=> (or (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) _let_1)) (and (= _let_1 tptp.zero_zero_real) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_complex_real tptp.im B2))))) (= (tptp.aa_complex_complex tptp.csqrt (tptp.aa_nat_complex (tptp.power_power_complex B2) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) B2)))) (forall ((X tptp.complex)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_complex_real tptp.im X))) (= (tptp.aa_complex_real tptp.im (tptp.aa_complex_complex tptp.invers8013647133539491842omplex X)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real tptp.uminus_uminus_real _let_2)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_complex_real tptp.re X)) _let_1)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real _let_2) _let_1))))))) (forall ((X tptp.complex) (Y tptp.complex)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_complex_real tptp.im Y))) (let ((_let_3 (tptp.aa_complex_real tptp.re Y))) (= (tptp.aa_complex_real tptp.im (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex X) Y)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_complex_real tptp.im X)) _let_3)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_complex_real tptp.re X)) _let_2))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real _let_3) _let_1)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real _let_2) _let_1)))))))) (forall ((Z tptp.complex)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_complex_real tptp.re Z))) (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_complex_real tptp.im Z)))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real tptp.sqrt (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))) (tptp.aa_complex_real tptp.real_V1022390504157884413omplex Z))))) (forall ((Z tptp.complex)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_complex_real tptp.real_V1022390504157884413omplex Z))) (=> (not (= Z tptp.zero_zero_complex)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_complex_real tptp.re Z)) _let_2)) _let_1)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_complex_real tptp.im Z)) _let_2)) _let_1)) tptp.one_one_real))))) (forall ((X tptp.complex)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_complex_real tptp.im X))) (let ((_let_3 (tptp.aa_complex_real tptp.re X))) (let ((_let_4 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real _let_3) _let_1)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real _let_2) _let_1)))) (= (tptp.aa_complex_complex tptp.invers8013647133539491842omplex X) (tptp.aa_real_complex (tptp.aa_rea2649881322057434177omplex tptp.complex2 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real _let_3) _let_4)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real tptp.uminus_uminus_real _let_2)) _let_4)))))))) (forall ((X tptp.complex) (Y tptp.complex)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_complex_real tptp.im Y))) (let ((_let_3 (tptp.aa_complex_real tptp.re Y))) (let ((_let_4 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real _let_3) _let_1)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real _let_2) _let_1)))) (let ((_let_5 (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_complex_real tptp.re X)))) (let ((_let_6 (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_complex_real tptp.im X)))) (= (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex X) Y) (tptp.aa_real_complex (tptp.aa_rea2649881322057434177omplex tptp.complex2 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real _let_5 _let_3)) (tptp.aa_real_real _let_6 _let_2))) _let_4)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real _let_6 _let_3)) (tptp.aa_real_real _let_5 _let_2))) _let_4)))))))))) (forall ((R tptp.complex) (Z tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex R) tptp.real_V2521375963428798218omplex)) (= (tptp.aa_complex_real tptp.im (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex R) Z)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_complex_real tptp.re R))) (tptp.aa_complex_real tptp.im Z))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex Z)) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))))) (forall ((Y tptp.complex) (X tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex Y) tptp.real_V2521375963428798218omplex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex X) tptp.real_V2521375963428798218omplex)) (= (= (tptp.aa_complex_complex (tptp.times_times_complex tptp.imaginary_unit) Y) X) (and (= X tptp.zero_zero_complex) (= Y tptp.zero_zero_complex)))))) (forall ((Y tptp.complex) (X tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex Y) tptp.real_V2521375963428798218omplex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex X) tptp.real_V2521375963428798218omplex)) (= (= X (tptp.aa_complex_complex (tptp.times_times_complex tptp.imaginary_unit) Y)) (and (= X tptp.zero_zero_complex) (= Y tptp.zero_zero_complex)))))) (forall ((R tptp.complex) (Z tptp.complex)) (=> (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex R) tptp.real_V2521375963428798218omplex)) (= (tptp.aa_complex_real tptp.re (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex R) Z)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_complex_real tptp.re R)) (tptp.aa_complex_real tptp.re Z))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex Z)) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))))) (forall ((Z tptp.complex)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.aa_complex_complex (tptp.times_times_complex Z) (tptp.aa_complex_complex tptp.cnj Z)) (tptp.aa_real_complex tptp.real_V4546457046886955230omplex (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_complex_real tptp.re Z)) _let_1)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_complex_real tptp.im Z)) _let_1)))))) (forall ((Z tptp.complex) (W tptp.complex)) (let ((_let_1 (tptp.aa_complex_complex (tptp.times_times_complex Z) (tptp.aa_complex_complex tptp.cnj W)))) (= (tptp.aa_complex_complex (tptp.plus_plus_complex _let_1) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_complex_complex tptp.cnj Z)) W)) (tptp.aa_real_complex tptp.real_V4546457046886955230omplex (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_complex_real tptp.re _let_1)))))) (forall ((A tptp.complex) (B2 tptp.complex)) (= (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex A) B2) (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex (tptp.aa_complex_complex (tptp.times_times_complex A) (tptp.aa_complex_complex tptp.cnj B2))) (tptp.aa_real_complex tptp.real_V4546457046886955230omplex (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex B2)) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))))) (forall ((X tptp.complex) (Y tptp.complex)) (= (tptp.aa_complex_complex tptp.cnj (tptp.aa_complex_complex (tptp.times_times_complex X) Y)) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_complex_complex tptp.cnj X)) (tptp.aa_complex_complex tptp.cnj Y)))) (forall ((W tptp.num)) (let ((_let_1 (tptp.numera6690914467698888265omplex W))) (= (tptp.aa_complex_complex tptp.cnj _let_1) _let_1))) (forall ((W tptp.num)) (let ((_let_1 (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.numera6690914467698888265omplex W)))) (= (tptp.aa_complex_complex tptp.cnj _let_1) _let_1))) (forall ((Z tptp.complex)) (= (tptp.aa_complex_real tptp.im (tptp.aa_complex_complex (tptp.times_times_complex Z) (tptp.aa_complex_complex tptp.cnj Z))) tptp.zero_zero_real)) (forall ((A tptp.complex) (B2 tptp.complex)) (= (= (tptp.aa_complex_real tptp.re (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex A) B2)) tptp.zero_zero_real) (= (tptp.aa_complex_real tptp.re (tptp.aa_complex_complex (tptp.times_times_complex A) (tptp.aa_complex_complex tptp.cnj B2))) tptp.zero_zero_real))) (forall ((A tptp.complex) (B2 tptp.complex)) (= (= (tptp.aa_complex_real tptp.im (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex A) B2)) tptp.zero_zero_real) (= (tptp.aa_complex_real tptp.im (tptp.aa_complex_complex (tptp.times_times_complex A) (tptp.aa_complex_complex tptp.cnj B2))) tptp.zero_zero_real))) (forall ((Z tptp.complex)) (= (tptp.aa_complex_real tptp.real_V1022390504157884413omplex Z) (tptp.aa_real_real tptp.sqrt (tptp.aa_complex_real tptp.re (tptp.aa_complex_complex (tptp.times_times_complex Z) (tptp.aa_complex_complex tptp.cnj Z)))))) (forall ((A tptp.complex) (B2 tptp.complex)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_complex_real tptp.re (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex A) B2))) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_complex_real tptp.re (tptp.aa_complex_complex (tptp.times_times_complex A) (tptp.aa_complex_complex tptp.cnj B2)))) tptp.zero_zero_real)))) (forall ((A tptp.complex) (B2 tptp.complex)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real))) (= (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_complex_real tptp.re (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex A) B2)))) (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_complex_real tptp.re (tptp.aa_complex_complex (tptp.times_times_complex A) (tptp.aa_complex_complex tptp.cnj B2)))))))) (forall ((A tptp.complex) (B2 tptp.complex)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_complex_real tptp.re (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex A) B2))) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_complex_real tptp.re (tptp.aa_complex_complex (tptp.times_times_complex A) (tptp.aa_complex_complex tptp.cnj B2)))) tptp.zero_zero_real)))) (forall ((A tptp.complex) (B2 tptp.complex)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (= (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_complex_real tptp.re (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex A) B2)))) (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_complex_real tptp.re (tptp.aa_complex_complex (tptp.times_times_complex A) (tptp.aa_complex_complex tptp.cnj B2)))))))) (forall ((A tptp.complex) (B2 tptp.complex)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_complex_real tptp.im (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex A) B2))) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_complex_real tptp.im (tptp.aa_complex_complex (tptp.times_times_complex A) (tptp.aa_complex_complex tptp.cnj B2)))) tptp.zero_zero_real)))) (forall ((A tptp.complex) (B2 tptp.complex)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real))) (= (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_complex_real tptp.im (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex A) B2)))) (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_complex_real tptp.im (tptp.aa_complex_complex (tptp.times_times_complex A) (tptp.aa_complex_complex tptp.cnj B2)))))))) (forall ((A tptp.complex) (B2 tptp.complex)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_complex_real tptp.im (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex A) B2))) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_complex_real tptp.im (tptp.aa_complex_complex (tptp.times_times_complex A) (tptp.aa_complex_complex tptp.cnj B2)))) tptp.zero_zero_real)))) (forall ((A tptp.complex) (B2 tptp.complex)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (= (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_complex_real tptp.im (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex A) B2)))) (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_complex_real tptp.im (tptp.aa_complex_complex (tptp.times_times_complex A) (tptp.aa_complex_complex tptp.cnj B2)))))))) (forall ((Z tptp.complex)) (= (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.aa_complex_complex (tptp.times_times_complex Z) (tptp.aa_complex_complex tptp.cnj Z))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex Z)) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (forall ((A tptp.complex) (B2 tptp.complex)) (let ((_let_1 (tptp.aa_complex_complex (tptp.times_times_complex A) (tptp.aa_complex_complex tptp.cnj B2)))) (let ((_let_2 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real))) (let ((_let_3 (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex A) B2))) (and (= (tptp.pp (tptp.aa_real_bool _let_2 (tptp.aa_complex_real tptp.re _let_3))) (tptp.pp (tptp.aa_real_bool _let_2 (tptp.aa_complex_real tptp.re _let_1)))) (= (tptp.pp (tptp.aa_real_bool _let_2 (tptp.aa_complex_real tptp.im _let_3))) (tptp.pp (tptp.aa_real_bool _let_2 (tptp.aa_complex_real tptp.im _let_1))))))))) (forall ((Z tptp.complex)) (= (tptp.aa_real_complex tptp.real_V4546457046886955230omplex (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex Z)) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (tptp.aa_complex_complex (tptp.times_times_complex Z) (tptp.aa_complex_complex tptp.cnj Z)))) (forall ((Z tptp.complex)) (= (tptp.aa_complex_complex (tptp.plus_plus_complex Z) (tptp.aa_complex_complex tptp.cnj Z)) (tptp.aa_real_complex tptp.real_V4546457046886955230omplex (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_complex_real tptp.re Z))))) (forall ((Z tptp.complex)) (= (tptp.aa_complex_complex (tptp.minus_minus_complex Z) (tptp.aa_complex_complex tptp.cnj Z)) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_real_complex tptp.real_V4546457046886955230omplex (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_complex_real tptp.im Z)))) tptp.imaginary_unit))) (forall ((Nat tptp.nat)) (= (not (= Nat tptp.zero_zero_nat)) (tptp.pp (tptp.aa_nat_bool (tptp.case_nat_bool tptp.fFalse tptp.aTP_Lamm_vy) Nat)))) (forall ((Nat tptp.nat)) (= (= Nat tptp.zero_zero_nat) (tptp.pp (tptp.aa_nat_bool (tptp.case_nat_bool tptp.fTrue tptp.aTP_Lamm_vz) Nat)))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat tptp.suc M)) N)) (tptp.pp (tptp.aa_nat_bool (tptp.case_nat_bool tptp.fFalse (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M)) N)))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat M) _let_1) (tptp.aa_nat_nat (tptp.case_nat_nat _let_1 (tptp.aa_nat_fun_nat_nat tptp.aTP_Lamm_wa N)) M)))) (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat _let_1) M) (tptp.aa_nat_nat (tptp.case_nat_nat _let_1 (tptp.aa_nat_fun_nat_nat tptp.aTP_Lamm_wb N)) M)))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M))) (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat tptp.suc N)) (tptp.aa_nat_nat (tptp.case_nat_nat tptp.zero_zero_nat tptp.aTP_Lamm_al) (tptp.aa_nat_nat _let_1 N))))) (forall ((Nat tptp.nat)) (= (tptp.aa_nat_nat tptp.pred Nat) (tptp.aa_nat_nat (tptp.case_nat_nat tptp.zero_zero_nat tptp.aTP_Lamm_al) Nat))) (forall ((X tptp.real)) (= (tptp.aa_real_int tptp.archim6058952711729229775r_real X) (tptp.the_int (tptp.aa_real_fun_int_bool tptp.aTP_Lamm_wc X)))) (forall ((X tptp.rat)) (= (tptp.aa_rat_int tptp.archim3151403230148437115or_rat X) (tptp.the_int (tptp.aTP_Lamm_wd X)))) (forall ((X tptp.nat)) (= (tptp.bezw X tptp.zero_zero_nat) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int tptp.one_one_int) tptp.zero_zero_int))) (forall ((X tptp.nat) (Xa2 tptp.nat) (Y tptp.product_prod_nat_nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc X))) (let ((_let_2 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Xa2) X)))) (=> (= (tptp.nat_prod_decode_aux X Xa2) Y) (and (=> _let_2 (= Y (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Xa2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat X) Xa2)))) (=> (not _let_2) (= Y (tptp.nat_prod_decode_aux _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Xa2) _let_1))))))))) (forall ((X tptp.rat) (Y tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) Y)) (or (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) Y)) (= X Y)))) (forall ((R tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) R)) (not (forall ((S3 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) S3)) (forall ((T4 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) T4)) (not (= R (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat S3) T4)))))))))) (forall ((A tptp.rat)) (let ((_let_1 (tptp.aa_rat_rat tptp.sgn_sgn_rat A))) (let ((_let_2 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) A)))) (let ((_let_3 (= A 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.aa_rat_rat tptp.uminus_uminus_rat tptp.one_one_rat)))))))))) (forall ((A tptp.rat)) (let ((_let_1 (tptp.aa_rat_rat tptp.abs_abs_rat A))) (let ((_let_2 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) tptp.zero_zero_rat)))) (and (=> _let_2 (= _let_1 (tptp.aa_rat_rat tptp.uminus_uminus_rat A))) (=> (not _let_2) (= _let_1 A)))))) (forall ((M tptp.nat) (K tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc K))) (let ((_let_2 (tptp.nat_prod_decode_aux K M))) (let ((_let_3 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) K)))) (and (=> _let_3 (= _let_2 (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat M) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat K) M)))) (=> (not _let_3) (= _let_2 (tptp.nat_prod_decode_aux _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) _let_1))))))))) (forall ((X tptp.nat) (Xa2 tptp.nat) (Y tptp.product_prod_nat_nat)) (let ((_let_1 (tptp.pp (tptp.aa_Pro2232559814647311250t_bool (tptp.accp_P4275260045618599050at_nat tptp.nat_pr5047031295181774490ux_rel) (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat X) Xa2))))) (let ((_let_2 (tptp.aa_nat_nat tptp.suc X))) (let ((_let_3 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Xa2) X)))) (=> (= (tptp.nat_prod_decode_aux X Xa2) Y) (=> _let_1 (not (=> (and (=> _let_3 (= Y (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Xa2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat X) Xa2)))) (=> (not _let_3) (= Y (tptp.nat_prod_decode_aux _let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Xa2) _let_2))))) (not _let_1))))))))) (forall ((P2 tptp.rat)) (= (tptp.quotient_of (tptp.aa_rat_rat tptp.inverse_inverse_rat P2)) (tptp.aa_Pro6970504127699319548nt_int (tptp.produc4245557441103728435nt_int tptp.aTP_Lamm_we) (tptp.quotient_of P2)))) (forall ((Q2 tptp.int) (P2 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Q2) tptp.zero_zero_int)) (= (tptp.aa_Pro6970504127699319548nt_int tptp.normalize (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int P2) Q2)) (tptp.aa_Pro6970504127699319548nt_int tptp.normalize (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int (tptp.aa_int_int tptp.uminus_uminus_int P2)) (tptp.aa_int_int tptp.uminus_uminus_int Q2)))))) (forall ((K tptp.num)) (= (tptp.quotient_of (tptp.aa_num_rat tptp.numeral_numeral_rat K)) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int (tptp.aa_num_int tptp.numeral_numeral_int K)) tptp.one_one_int))) (forall ((P2 tptp.int)) (= (tptp.aa_Pro6970504127699319548nt_int tptp.normalize (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int P2) tptp.zero_zero_int)) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int))) (= (tptp.quotient_of tptp.one_one_rat) _let_18) (= (tptp.quotient_of tptp.zero_zero_rat) _let_17) (forall ((K tptp.num)) (= (tptp.quotient_of (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat K))) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int K))) tptp.one_one_int))) (= (tptp.quotient_of _let_38) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int _let_37) tptp.one_one_int)) (forall ((Q2 tptp.rat) (R tptp.rat)) (= (tptp.aa_rat_rat (tptp.divide_divide_rat Q2) R) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat Q2) (tptp.aa_rat_rat tptp.inverse_inverse_rat R)))) (forall ((P2 tptp.rat) (Q2 tptp.rat)) (= (tptp.quotient_of (tptp.aa_rat_rat (tptp.divide_divide_rat P2) Q2)) (tptp.aa_Pro6970504127699319548nt_int (tptp.produc4245557441103728435nt_int (tptp.aTP_Lamm_wg Q2)) (tptp.quotient_of P2)))) (forall ((P2 tptp.rat) (Q2 tptp.rat)) (= (tptp.quotient_of (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat P2) Q2)) (tptp.aa_Pro6970504127699319548nt_int (tptp.produc4245557441103728435nt_int (tptp.aTP_Lamm_wi Q2)) (tptp.quotient_of P2)))) (forall ((R tptp.rat) (N tptp.int) (D tptp.int)) (=> (= (tptp.quotient_of R) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int N) D)) (= R (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_int_rat tptp.ring_1_of_int_rat N)) (tptp.aa_int_rat tptp.ring_1_of_int_rat D))))) (forall ((P2 tptp.rat) (Q2 tptp.rat)) (= (tptp.quotient_of (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat P2) Q2)) (tptp.aa_Pro6970504127699319548nt_int (tptp.produc4245557441103728435nt_int (tptp.aTP_Lamm_wk Q2)) (tptp.quotient_of P2)))) (forall ((P2 tptp.rat) (Q2 tptp.rat)) (= (tptp.quotient_of (tptp.aa_rat_rat (tptp.minus_minus_rat P2) Q2)) (tptp.aa_Pro6970504127699319548nt_int (tptp.produc4245557441103728435nt_int (tptp.aTP_Lamm_wm Q2)) (tptp.quotient_of P2)))) (forall ((R tptp.rat) (P2 tptp.int) (Q2 tptp.int)) (=> (= (tptp.quotient_of R) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int P2) Q2)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) Q2)))) (forall ((P2 tptp.rat)) (= (tptp.quotient_of (tptp.aa_rat_rat tptp.uminus_uminus_rat P2)) (tptp.aa_Pro6970504127699319548nt_int (tptp.produc4245557441103728435nt_int tptp.aTP_Lamm_wn) (tptp.quotient_of P2)))) (forall ((P2 tptp.rat)) (= (tptp.quotient_of (tptp.aa_rat_rat tptp.abs_abs_rat P2)) (tptp.aa_Pro6970504127699319548nt_int (tptp.produc4245557441103728435nt_int tptp.aTP_Lamm_wo) (tptp.quotient_of P2)))) (forall ((R tptp.product_prod_int_int) (P2 tptp.int) (Q2 tptp.int)) (=> (= (tptp.aa_Pro6970504127699319548nt_int tptp.normalize R) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int P2) Q2)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) Q2)))) (forall ((Q2 tptp.int) (S tptp.int) (P2 tptp.int) (R tptp.int)) (=> (not (= Q2 tptp.zero_zero_int)) (=> (not (= S tptp.zero_zero_int)) (=> (= (tptp.aa_Pro6970504127699319548nt_int tptp.normalize (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int P2) Q2)) (tptp.aa_Pro6970504127699319548nt_int tptp.normalize (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int R) S))) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int P2) S) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int R) Q2)))))) (forall ((P2 tptp.rat) (Q2 tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat P2) Q2)) (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.produc8560705615207772305t_bool (tptp.aTP_Lamm_wq Q2)) (tptp.quotient_of P2))))) (forall ((P2 tptp.rat) (Q2 tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat P2) Q2)) (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.produc8560705615207772305t_bool (tptp.aTP_Lamm_ws Q2)) (tptp.quotient_of P2))))) (forall ((A tptp.int)) (= (tptp.quotient_of (tptp.aa_int_rat tptp.of_int A)) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int A) tptp.one_one_int))) (forall ((L tptp.num) (K tptp.num)) (= (tptp.aa_int_int (tptp.bit_se8568078237143864401it_int (tptp.aa_num_nat tptp.numeral_numeral_nat L)) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit1 K)))) (tptp.aa_int_int (tptp.bit_se8568078237143864401it_int (tptp.aa_num_nat tptp.pred_numeral L)) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.inc K)))))) (forall ((K tptp.num)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)) (tptp.aa_num_nat tptp.numeral_numeral_nat K)) (tptp.aa_Pro4243173770044397973at_nat tptp.product_fst_nat_nat (tptp.unique5055182867167087721od_nat tptp.one K)))) (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.bit_se8568078237143864401it_int N) K))) (tptp.pp (tptp.aa_int_bool _let_1 K))))) (forall ((N tptp.nat) (K tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.bit_se8568078237143864401it_int N) K)) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int K) tptp.zero_zero_int)))) (forall ((N tptp.nat)) (let ((_let_1 (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int))) (= (tptp.aa_int_int (tptp.bit_se8568078237143864401it_int N) _let_1) _let_1))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.aa_Pro4243173770044397973at_nat tptp.product_fst_nat_nat (tptp.divmod_nat M N)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat M) N))) (forall ((N tptp.nat) (K tptp.num)) (= (tptp.aa_int_int (tptp.bit_se8568078237143864401it_int (tptp.aa_nat_nat tptp.suc N)) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 K)))) (tptp.aa_int_int (tptp.bit_se8568078237143864401it_int N) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int K))))) (forall ((L tptp.num) (K tptp.num)) (= (tptp.aa_int_int (tptp.bit_se8568078237143864401it_int (tptp.aa_num_nat tptp.numeral_numeral_nat L)) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 K)))) (tptp.aa_int_int (tptp.bit_se8568078237143864401it_int (tptp.aa_num_nat tptp.pred_numeral L)) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int K))))) (forall ((N tptp.nat) (K tptp.num)) (= (tptp.aa_int_int (tptp.bit_se8568078237143864401it_int (tptp.aa_nat_nat tptp.suc N)) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit1 K)))) (tptp.aa_int_int (tptp.bit_se8568078237143864401it_int N) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.inc K)))))) (forall ((M tptp.nat) (N tptp.nat) (K tptp.int)) (= (tptp.aa_int_int (tptp.bit_se8568078237143864401it_int M) (tptp.aa_int_int (tptp.bit_se545348938243370406it_int N) K)) (tptp.aa_int_int (tptp.bit_se8568078237143864401it_int (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) N)) (tptp.aa_int_int (tptp.bit_se545348938243370406it_int (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) M)) K)))) (forall ((N tptp.nat) (K tptp.int)) (= (tptp.aa_int_int (tptp.bit_se8568078237143864401it_int N) K) (tptp.aa_int_int (tptp.divide_divide_int K) (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) N)))) (forall ((K tptp.num)) (= (tptp.frct (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int tptp.one_one_int) (tptp.aa_num_int tptp.numeral_numeral_int K))) (tptp.aa_rat_rat (tptp.divide_divide_rat tptp.one_one_rat) (tptp.aa_num_rat tptp.numeral_numeral_rat K)))) (forall ((K tptp.num) (L tptp.num)) (= (tptp.frct (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int (tptp.aa_num_int tptp.numeral_numeral_int K)) (tptp.aa_num_int tptp.numeral_numeral_int L))) (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_num_rat tptp.numeral_numeral_rat K)) (tptp.aa_num_rat tptp.numeral_numeral_rat L)))) (forall ((K tptp.num)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)) (tptp.aa_num_nat tptp.numeral_numeral_nat K)) (tptp.aa_Pro4243173770044397973at_nat tptp.product_snd_nat_nat (tptp.unique5055182867167087721od_nat tptp.one K)))) (forall ((N tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se8570568707652914677it_nat N) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)) (tptp.zero_n2687167440665602831ol_nat (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.fequal_nat N) tptp.zero_zero_nat)))) (forall ((N tptp.nat) (K tptp.int)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se8570568707652914677it_nat N) (tptp.aa_int_nat tptp.nat2 K)) (tptp.aa_int_nat tptp.nat2 (tptp.aa_int_int (tptp.bit_se8568078237143864401it_int N) K)))) (forall ((N tptp.nat) (M tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se8570568707652914677it_nat N) M) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat M) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N)))) (forall ((A tptp.int)) (= (tptp.frct (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int tptp.zero_zero_int) A)) tptp.zero_zero_rat)) (forall ((A tptp.int)) (= (tptp.frct (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int A) tptp.zero_zero_int)) tptp.zero_zero_rat)) (forall ((A tptp.int) (B2 tptp.int)) (let ((_let_1 (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int A))) (= (tptp.frct (tptp.aa_int7462565939943104719nt_int _let_1 (tptp.aa_int_int tptp.uminus_uminus_int B2))) (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.frct (tptp.aa_int7462565939943104719nt_int _let_1 B2)))))) (forall ((A tptp.int) (B2 tptp.int)) (= (tptp.frct (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int (tptp.aa_int_int tptp.uminus_uminus_int A)) B2)) (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.frct (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int A) B2))))) (= (tptp.frct _let_18) tptp.one_one_rat) (forall ((P2 tptp.rat)) (= (tptp.quotient_of (tptp.aa_rat_rat tptp.sgn_sgn_rat P2)) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int (tptp.aa_int_int tptp.sgn_sgn_int (tptp.product_fst_int_int (tptp.quotient_of P2)))) tptp.one_one_int))) (forall ((K tptp.num)) (= (tptp.frct (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int (tptp.aa_num_int tptp.numeral_numeral_int K)) tptp.one_one_int)) (tptp.aa_num_rat tptp.numeral_numeral_rat K))) (forall ((R tptp.rat)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) (tptp.product_snd_int_int (tptp.quotient_of R))))) (forall ((Y tptp.nat) (X tptp.nat)) (let ((_let_1 (tptp.bezw Y (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat X) Y)))) (let ((_let_2 (tptp.product_snd_int_int _let_1))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) Y)) (= (tptp.bezw X Y) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int _let_2) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.product_fst_int_int _let_1)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int _let_2) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat X) Y)))))))))) (forall ((Y tptp.nat) (X tptp.nat)) (let ((_let_1 (tptp.bezw Y (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat X) Y)))) (let ((_let_2 (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.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int tptp.one_one_int) tptp.zero_zero_int))) (=> (not _let_4) (= _let_3 (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int _let_2) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.product_fst_int_int _let_1)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int _let_2) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat X) Y))))))))))))) (forall ((X tptp.nat) (Xa2 tptp.nat) (Y tptp.product_prod_int_int)) (let ((_let_1 (tptp.bezw Xa2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat X) Xa2)))) (let ((_let_2 (tptp.product_snd_int_int _let_1))) (let ((_let_3 (= Xa2 tptp.zero_zero_nat))) (=> (= (tptp.bezw X Xa2) Y) (and (=> _let_3 (= Y (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int tptp.one_one_int) tptp.zero_zero_int))) (=> (not _let_3) (= Y (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int _let_2) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.product_fst_int_int _let_1)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int _let_2) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat X) Xa2))))))))))))) (forall ((X tptp.nat) (Xa2 tptp.nat) (Y tptp.product_prod_int_int)) (let ((_let_1 (tptp.pp (tptp.aa_Pro2232559814647311250t_bool (tptp.accp_P4275260045618599050at_nat tptp.bezw_rel) (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat X) Xa2))))) (let ((_let_2 (tptp.bezw Xa2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat X) Xa2)))) (let ((_let_3 (tptp.product_snd_int_int _let_2))) (let ((_let_4 (= Xa2 tptp.zero_zero_nat))) (=> (= (tptp.bezw X Xa2) Y) (=> _let_1 (not (=> (and (=> _let_4 (= Y (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int tptp.one_one_int) tptp.zero_zero_int))) (=> (not _let_4) (= Y (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int _let_3) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.product_fst_int_int _let_2)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int _let_3) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat X) Xa2)))))))) (not _let_1)))))))))) (forall ((N tptp.num)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int N))) (= (tptp.aa_int_int (tptp.modulo_modulo_int (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int)) _let_1) (tptp.aa_int_int (tptp.adjust_mod _let_1) (tptp.product_snd_int_int (tptp.unique5052692396658037445od_int tptp.one N)))))) (forall ((N tptp.num)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int N))) (= (tptp.aa_int_int (tptp.modulo_modulo_int tptp.one_one_int) (tptp.aa_int_int tptp.uminus_uminus_int _let_1)) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_int_int (tptp.adjust_mod _let_1) (tptp.product_snd_int_int (tptp.unique5052692396658037445od_int tptp.one N))))))) (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int N))) (= (tptp.aa_int_int (tptp.modulo_modulo_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int M))) _let_1) (tptp.aa_int_int (tptp.adjust_mod _let_1) (tptp.product_snd_int_int (tptp.unique5052692396658037445od_int M N)))))) (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int N))) (= (tptp.aa_int_int (tptp.modulo_modulo_int (tptp.aa_num_int tptp.numeral_numeral_int M)) (tptp.aa_int_int tptp.uminus_uminus_int _let_1)) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_int_int (tptp.adjust_mod _let_1) (tptp.product_snd_int_int (tptp.unique5052692396658037445od_int M N))))))) (forall ((P2 tptp.product_prod_int_int)) (let ((_let_1 (tptp.product_snd_int_int P2))) (let ((_let_2 (tptp.product_fst_int_int P2))) (let ((_let_3 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.gcd_gcd_int _let_2) _let_1))) (let ((_let_4 (tptp.aa_int_int tptp.uminus_uminus_int _let_3))) (let ((_let_5 (tptp.divide_divide_int _let_1))) (let ((_let_6 (tptp.divide_divide_int _let_2))) (let ((_let_7 (tptp.aa_Pro6970504127699319548nt_int tptp.normalize P2))) (let ((_let_8 (= _let_1 tptp.zero_zero_int))) (let ((_let_9 (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) _let_1)))) (and (=> _let_9 (= _let_7 (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int (tptp.aa_int_int _let_6 _let_3)) (tptp.aa_int_int _let_5 _let_3)))) (=> (not _let_9) (and (=> _let_8 (= _let_7 (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int))) (=> (not _let_8) (= _let_7 (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int (tptp.aa_int_int _let_6 _let_4)) (tptp.aa_int_int _let_5 _let_4))))))))))))))))) (forall ((M tptp.int) (N tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.gcd_gcd_int M) N))) (or (not (= M tptp.zero_zero_int)) (not (= N tptp.zero_zero_int))))) (forall ((X tptp.int) (N tptp.num)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int N))) (let ((_let_2 (tptp.aa_int_fun_int_int tptp.gcd_gcd_int X))) (= (tptp.aa_int_int _let_2 (tptp.aa_int_int tptp.uminus_uminus_int _let_1)) (tptp.aa_int_int _let_2 _let_1))))) (forall ((N tptp.num) (X tptp.int)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int N))) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.gcd_gcd_int (tptp.aa_int_int tptp.uminus_uminus_int _let_1)) X) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.gcd_gcd_int _let_1) X)))) (forall ((X tptp.int) (Y tptp.int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.gcd_gcd_int X) Y)))) (forall ((X tptp.int) (Y tptp.int)) (exists ((U2 tptp.int) (V2 tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int U2) X)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int V2) Y)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.gcd_gcd_int X) Y)))) (forall ((K tptp.int) (M tptp.int) (N tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.times_times_int K))) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int tptp.abs_abs_int K)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.gcd_gcd_int M) N)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.gcd_gcd_int (tptp.aa_int_int _let_1 M)) (tptp.aa_int_int _let_1 N))))) (forall ((B2 tptp.int) (A tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) B2)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.gcd_gcd_int A) B2)) B2)))) (forall ((A tptp.int) (B2 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) A)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.gcd_gcd_int A) B2)) A)))) (forall ((X tptp.int) (Y tptp.int) (P tptp.fun_int_bool)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.gcd_gcd_int X))) (let ((_let_2 (tptp.pp (tptp.aa_int_bool P (tptp.aa_int_int _let_1 Y))))) (let ((_let_3 (tptp.aa_int_int tptp.uminus_uminus_int Y))) (let ((_let_4 (tptp.aa_int_fun_int_int tptp.gcd_gcd_int (tptp.aa_int_int tptp.uminus_uminus_int X)))) (let ((_let_5 (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Y) tptp.zero_zero_int)))) (let ((_let_6 (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X) tptp.zero_zero_int)))) (let ((_let_7 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_8 (tptp.pp (tptp.aa_int_bool _let_7 Y)))) (let ((_let_9 (tptp.pp (tptp.aa_int_bool _let_7 X)))) (=> (=> _let_9 (=> _let_8 _let_2)) (=> (=> _let_9 (=> _let_5 (tptp.pp (tptp.aa_int_bool P (tptp.aa_int_int _let_1 _let_3))))) (=> (=> _let_6 (=> _let_8 (tptp.pp (tptp.aa_int_bool P (tptp.aa_int_int _let_4 Y))))) (=> (=> _let_6 (=> _let_5 (tptp.pp (tptp.aa_int_bool P (tptp.aa_int_int _let_4 _let_3))))) _let_2)))))))))))))) (forall ((D tptp.int) (A tptp.int) (B2 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int D))) (= (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) D)) (tptp.pp (tptp.aa_int_bool _let_1 A)) (tptp.pp (tptp.aa_int_bool _let_1 B2)) (forall ((E3 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int E3))) (=> (and (tptp.pp (tptp.aa_int_bool _let_1 A)) (tptp.pp (tptp.aa_int_bool _let_1 B2))) (tptp.pp (tptp.aa_int_bool _let_1 D)))))) (= D (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.gcd_gcd_int A) B2))))) (forall ((Y tptp.int) (X tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) Y)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.gcd_gcd_int X) Y) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.gcd_gcd_int Y) (tptp.aa_int_int (tptp.modulo_modulo_int X) Y))))) (forall ((N tptp.nat) (P tptp.fun_nat_bool) (M tptp.nat)) (=> (forall ((K3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N) K3)) (tptp.pp (tptp.aa_nat_bool P K3)))) (=> (forall ((K3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K3) N)) (=> (forall ((I2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat K3) I2)) (tptp.pp (tptp.aa_nat_bool P I2)))) (tptp.pp (tptp.aa_nat_bool P K3))))) (tptp.pp (tptp.aa_nat_bool P M))))) (forall ((S2 tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat S2)) (exists ((R3 tptp.fun_nat_nat)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.strict1292158309912662752at_nat R3) (tptp.set_ord_lessThan_nat (tptp.finite_card_nat S2)))) (forall ((N8 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N8) (tptp.finite_card_nat S2))) (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat (tptp.aa_nat_nat R3 N8)) S2)))))))) (forall ((K tptp.code_integer) (L tptp.code_integer)) (let ((_let_1 (tptp.code_divmod_abs K L))) (let ((_let_2 (tptp.code_divmod_integer K L))) (let ((_let_3 (= L tptp.zero_z3403309356797280102nteger))) (let ((_let_4 (= K tptp.zero_z3403309356797280102nteger))) (and (=> _let_4 (= _let_2 (tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger tptp.zero_z3403309356797280102nteger))) (=> (not _let_4) (and (=> _let_3 (= _let_2 (tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger K))) (=> (not _let_3) (= _let_2 (tptp.aa_Pro4693618923521437820nteger (tptp.comp_C7848664941760151970nteger (tptp.comp_f6739083541385432444nteger tptp.produc6499014454317279255nteger tptp.times_3573771949741848930nteger) tptp.sgn_sgn_Code_integer L) (tptp.if_Pro6119634080678213985nteger (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.fequal_Code_integer (tptp.aa_Cod1783974652533396728nteger tptp.sgn_sgn_Code_integer K)) (tptp.aa_Cod1783974652533396728nteger tptp.sgn_sgn_Code_integer L)) _let_1 (tptp.produc6916734918728496179nteger (tptp.aTP_Lamm_wt L) _let_1))))))))))))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.gcd_gcd_nat M) N))) (or (not (= M tptp.zero_zero_nat)) (not (= N tptp.zero_zero_nat))))) (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat K))) (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.gcd_gcd_nat M) N)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.gcd_gcd_nat (tptp.aa_nat_nat _let_1 M)) (tptp.aa_nat_nat _let_1 N))))) (forall ((B2 tptp.nat) (A tptp.nat)) (=> (not (= B2 tptp.zero_zero_nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.gcd_gcd_nat A) B2)) B2)))) (forall ((A tptp.nat) (B2 tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.gcd_gcd_nat A) B2)) A)))) (forall ((N tptp.nat) (M tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N) M)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.gcd_gcd_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) N)) N) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.gcd_gcd_nat M) N)))) (forall ((M tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.gcd_gcd_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) M)) N) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.gcd_gcd_nat M) N)))) (forall ((A tptp.nat) (B2 tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (exists ((X4 tptp.nat) (Y4 tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) X4) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B2) Y4)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.gcd_gcd_nat A) B2)))))) (forall ((B2 tptp.nat) (A tptp.nat)) (exists ((X4 tptp.nat) (Y4 tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.gcd_gcd_nat A) B2))) (let ((_let_2 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A))) (let ((_let_3 (tptp.aa_nat_nat _let_2 Y4))) (let ((_let_4 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B2))) (let ((_let_5 (tptp.aa_nat_nat _let_4 X4))) (let ((_let_6 (tptp.aa_nat_nat _let_4 Y4))) (let ((_let_7 (tptp.aa_nat_nat _let_2 X4))) (or (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat _let_6) _let_7)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat _let_7) _let_6) _let_1)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat _let_3) _let_5)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat _let_5) _let_3) _let_1)))))))))))) (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (tptp.bezw X Y))) (= (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.gcd_gcd_nat X) Y)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.product_fst_int_int _let_1)) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int X))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.product_snd_int_int _let_1)) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int Y)))))) (forall ((X tptp.nat) (Xa2 tptp.nat) (Y tptp.nat)) (let ((_let_1 (tptp.pp (tptp.aa_Pro2232559814647311250t_bool (tptp.accp_P4275260045618599050at_nat tptp.gcd_nat_rel) (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat X) Xa2))))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (=> (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.gcd_gcd_nat X) Xa2) Y) (=> _let_1 (not (=> (and (=> _let_2 (= Y X)) (=> (not _let_2) (= Y (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.gcd_gcd_nat Xa2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat X) Xa2))))) (not _let_1)))))))) (= tptp.code_negative (tptp.comp_C3531382070062128313er_num tptp.uminus1351360451143612070nteger tptp.numera6620942414471956472nteger)) (= tptp.code_Target_negative (tptp.comp_int_int_num tptp.uminus_uminus_int tptp.numeral_numeral_int)) (forall ((N tptp.nat) (X tptp.real)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) X)) (= (tptp.aa_real_real (tptp.aa_nat_fun_real_real tptp.root N) X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.powr_real X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.one_one_real) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N))))))) (forall ((N tptp.nat)) (= (tptp.aa_real_real (tptp.aa_nat_fun_real_real tptp.root N) tptp.zero_zero_real) tptp.zero_zero_real)) (forall ((X tptp.real)) (= (tptp.aa_real_real (tptp.aa_nat_fun_real_real tptp.root (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)) X) X)) (forall ((X tptp.real)) (= (tptp.aa_real_real (tptp.aa_nat_fun_real_real tptp.root tptp.zero_zero_nat) X) tptp.zero_zero_real)) (forall ((N tptp.nat) (X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_nat_fun_real_real tptp.root N))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (= (= (tptp.aa_real_real _let_1 X) (tptp.aa_real_real _let_1 Y)) (= X Y))))) (forall ((N tptp.nat) (X tptp.real)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (= (= (tptp.aa_real_real (tptp.aa_nat_fun_real_real tptp.root N) X) tptp.zero_zero_real) (= X tptp.zero_zero_real)))) (forall ((N tptp.nat) (X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_nat_fun_real_real tptp.root N))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real _let_1 X)) (tptp.aa_real_real _let_1 Y))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Y)))))) (forall ((N tptp.nat) (X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_nat_fun_real_real tptp.root N))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real _let_1 X)) (tptp.aa_real_real _let_1 Y))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) Y)))))) (forall ((N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (= (tptp.aa_real_real (tptp.aa_nat_fun_real_real tptp.root N) tptp.one_one_real) tptp.one_one_real))) (forall ((N tptp.nat) (X tptp.real)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (= (= (tptp.aa_real_real (tptp.aa_nat_fun_real_real tptp.root N) X) tptp.one_one_real) (= X tptp.one_one_real)))) (forall ((N tptp.nat) (X tptp.real)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_nat_fun_real_real tptp.root N) X)) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) tptp.zero_zero_real))))) (forall ((N tptp.nat) (Y tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (= (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real (tptp.aa_nat_fun_real_real tptp.root N) Y))) (tptp.pp (tptp.aa_real_bool _let_1 Y)))))) (forall ((N tptp.nat) (X tptp.real)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_nat_fun_real_real tptp.root N) X)) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) tptp.zero_zero_real))))) (forall ((N tptp.nat) (Y tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (= (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real (tptp.aa_nat_fun_real_real tptp.root N) Y))) (tptp.pp (tptp.aa_real_bool _let_1 Y)))))) (forall ((N tptp.nat) (Y tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (= (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real (tptp.aa_nat_fun_real_real tptp.root N) Y))) (tptp.pp (tptp.aa_real_bool _let_1 Y)))))) (forall ((N tptp.nat) (X tptp.real)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_nat_fun_real_real tptp.root N) X)) tptp.one_one_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) tptp.one_one_real))))) (forall ((N tptp.nat) (X tptp.real)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_nat_fun_real_real tptp.root N) X)) tptp.one_one_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) tptp.one_one_real))))) (forall ((N tptp.nat) (Y tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.one_one_real))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (= (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real (tptp.aa_nat_fun_real_real tptp.root N) Y))) (tptp.pp (tptp.aa_real_bool _let_1 Y)))))) (forall ((N tptp.nat) (X tptp.real)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) X)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real (tptp.aa_nat_fun_real_real tptp.root N) X)) N) X)))) (forall ((N tptp.nat) (X tptp.real)) (let ((_let_1 (tptp.aa_nat_fun_real_real tptp.root N))) (= (tptp.aa_real_real _let_1 (tptp.aa_real_real tptp.inverse_inverse_real X)) (tptp.aa_real_real tptp.inverse_inverse_real (tptp.aa_real_real _let_1 X))))) (forall ((N tptp.nat) (X tptp.real)) (let ((_let_1 (tptp.aa_nat_fun_real_real tptp.root N))) (= (tptp.aa_real_real _let_1 (tptp.aa_real_real tptp.uminus_uminus_real X)) (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_real_real _let_1 X))))) (forall ((M tptp.nat) (N tptp.nat) (X tptp.real)) (let ((_let_1 (tptp.aa_nat_fun_real_real tptp.root M))) (let ((_let_2 (tptp.aa_nat_fun_real_real tptp.root N))) (= (tptp.aa_real_real _let_1 (tptp.aa_real_real _let_2 X)) (tptp.aa_real_real _let_2 (tptp.aa_real_real _let_1 X)))))) (forall ((N tptp.nat) (X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_nat_fun_real_real tptp.root N))) (= (tptp.aa_real_real _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real X) Y)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real _let_1 X)) (tptp.aa_real_real _let_1 Y))))) (forall ((M tptp.nat) (N tptp.nat) (X tptp.real)) (= (tptp.aa_real_real (tptp.aa_nat_fun_real_real tptp.root (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat M) N)) X) (tptp.aa_real_real (tptp.aa_nat_fun_real_real tptp.root M) (tptp.aa_real_real (tptp.aa_nat_fun_real_real tptp.root N) X)))) (forall ((N tptp.nat) (X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_nat_fun_real_real tptp.root N))) (= (tptp.aa_real_real _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real X) Y)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real _let_1 X)) (tptp.aa_real_real _let_1 Y))))) (forall ((X tptp.real) (N tptp.nat)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool _let_1 X)) (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real (tptp.aa_nat_fun_real_real tptp.root N) X)))))) (forall ((N tptp.nat) (X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_nat_fun_real_real tptp.root N))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Y)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real _let_1 X)) (tptp.aa_real_real _let_1 Y))))))) (forall ((N tptp.nat) (X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_nat_fun_real_real tptp.root N))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) Y)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real _let_1 X)) (tptp.aa_real_real _let_1 Y))))))) (forall ((N tptp.nat) (X tptp.real) (K tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_real_real tptp.root N))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (= (tptp.aa_real_real _let_1 (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) K)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real _let_1 X)) K))))) (forall ((N tptp.nat) (X tptp.real)) (let ((_let_1 (tptp.aa_nat_fun_real_real tptp.root N))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (= (tptp.aa_real_real _let_1 (tptp.aa_real_real tptp.abs_abs_real X)) (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_real_real _let_1 X)))))) (forall ((N tptp.nat) (X tptp.real)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (= (tptp.aa_real_real tptp.sgn_sgn_real (tptp.aa_real_real (tptp.aa_nat_fun_real_real tptp.root N) X)) (tptp.aa_real_real tptp.sgn_sgn_real X)))) (forall ((N tptp.nat) (X tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (=> (tptp.pp (tptp.aa_real_bool _let_1 X)) (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real (tptp.aa_nat_fun_real_real tptp.root N) X))))))) (forall ((N tptp.nat) (N3 tptp.nat) (X tptp.real)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N) N3)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real) X)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_nat_fun_real_real tptp.root N3) X)) (tptp.aa_real_real (tptp.aa_nat_fun_real_real tptp.root N) X))))))) (= tptp.sqrt (tptp.aa_nat_fun_real_real tptp.root _let_33)) (forall ((N tptp.nat) (Y tptp.real)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (= (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_real_real (tptp.aa_nat_fun_real_real tptp.root N) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Y) N))) (tptp.aa_real_real tptp.abs_abs_real Y)))) (forall ((N tptp.nat) (X tptp.real)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) X)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_real_real (tptp.aa_nat_fun_real_real tptp.root N) X)))))) (forall ((N tptp.nat) (N3 tptp.nat) (X tptp.real)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N) N3)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) tptp.one_one_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_nat_fun_real_real tptp.root N) X)) (tptp.aa_real_real (tptp.aa_nat_fun_real_real tptp.root N3) X)))))))) (forall ((N tptp.nat) (N3 tptp.nat) (X tptp.real)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N) N3)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.one_one_real) X)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_nat_fun_real_real tptp.root N3) X)) (tptp.aa_real_real (tptp.aa_nat_fun_real_real tptp.root N) X))))))) (forall ((N tptp.nat) (X tptp.real)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) X)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real (tptp.aa_nat_fun_real_real tptp.root N) X)) N) X)))) (forall ((N tptp.nat) (Y tptp.real) (X tptp.real)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) Y)) (=> (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Y) N) X) (= (tptp.aa_real_real (tptp.aa_nat_fun_real_real tptp.root N) X) Y))))) (forall ((N tptp.nat) (X tptp.real)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) X)) (= (tptp.aa_real_real (tptp.aa_nat_fun_real_real tptp.root N) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) N)) X)))) (forall ((N tptp.nat) (X tptp.real)) (=> (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N))) (= (tptp.aa_real_real (tptp.aa_nat_fun_real_real tptp.root N) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) N)) X))) (forall ((N tptp.nat) (Y tptp.real) (X tptp.real)) (=> (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N))) (=> (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Y) N) X) (= (tptp.aa_real_real (tptp.aa_nat_fun_real_real tptp.root N) X) Y)))) (forall ((N tptp.nat) (X tptp.real)) (=> (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N))) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real (tptp.aa_nat_fun_real_real tptp.root N) X)) N) X))) (forall ((N tptp.nat) (N3 tptp.nat) (X tptp.real)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N) N3)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) tptp.one_one_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_nat_fun_real_real tptp.root N) X)) (tptp.aa_real_real (tptp.aa_nat_fun_real_real tptp.root N3) X)))))))) (forall ((N tptp.nat) (X tptp.real)) (let ((_let_1 (tptp.aa_real_real (tptp.aa_nat_fun_real_real tptp.root N) X))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real tptp.sgn_sgn_real _let_1)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real tptp.abs_abs_real _let_1)) N)) X)))) (forall ((N tptp.nat) (Y tptp.real)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (= (tptp.aa_real_real (tptp.aa_nat_fun_real_real tptp.root N) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real tptp.sgn_sgn_real Y)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real tptp.abs_abs_real Y)) N))) Y))) (forall ((N tptp.nat) (B2 tptp.real)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) B2)) (= (tptp.aa_real_real tptp.ln_ln_real (tptp.aa_real_real (tptp.aa_nat_fun_real_real tptp.root N) B2)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real tptp.ln_ln_real B2)) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N)))))) (forall ((N tptp.nat) (A tptp.real) (B2 tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.log B2))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) A)) (= (tptp.aa_real_real _let_1 (tptp.aa_real_real (tptp.aa_nat_fun_real_real tptp.root N) A)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real _let_1 A)) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N))))))) (forall ((N tptp.nat) (B2 tptp.real) (X tptp.real)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) B2)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.log (tptp.aa_real_real (tptp.aa_nat_fun_real_real tptp.root N) B2)) X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.log B2) X)))))) (forall ((P tptp.fun_real_bool) (N tptp.nat) (X tptp.real)) (= (tptp.pp (tptp.aa_real_bool P (tptp.aa_real_real (tptp.aa_nat_fun_real_real tptp.root N) X))) (and (=> (= N tptp.zero_zero_nat) (tptp.pp (tptp.aa_real_bool P tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (forall ((Y3 tptp.real)) (=> (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real tptp.sgn_sgn_real Y3)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real tptp.abs_abs_real Y3)) N)) X) (tptp.pp (tptp.aa_real_bool P Y3)))))))) (forall ((C tptp.complex) (N tptp.nat)) (=> (not (= C tptp.zero_zero_complex)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (tptp.pp (tptp.aa_set_complex_bool (tptp.bij_be1856998921033663316omplex (tptp.times_times_complex (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_real_complex tptp.real_V4546457046886955230omplex (tptp.aa_real_real (tptp.aa_nat_fun_real_real tptp.root N) (tptp.aa_complex_real tptp.real_V1022390504157884413omplex C)))) (tptp.aa_real_complex tptp.cis (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_complex_real tptp.arg C)) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N))))) (tptp.collect_complex (tptp.aTP_Lamm_cq N))) (tptp.collect_complex (tptp.aa_nat5545486172511849908x_bool (tptp.aTP_Lamm_vx C) N))))))) (forall ((K tptp.int) (N tptp.num)) (let ((_let_1 (tptp.bit_se6526347334894502574or_int K))) (= (tptp.aa_int_int _let_1 (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int N))) (tptp.aa_int_int tptp.bit_ri7919022796975470100ot_int (tptp.aa_int_int _let_1 (tptp.aa_num_int (tptp.neg_numeral_sub_int N) tptp.one)))))) (forall ((N tptp.num) (K tptp.int)) (= (tptp.aa_int_int (tptp.bit_se6526347334894502574or_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int N))) K) (tptp.aa_int_int tptp.bit_ri7919022796975470100ot_int (tptp.aa_int_int (tptp.bit_se6526347334894502574or_int (tptp.aa_num_int (tptp.neg_numeral_sub_int N) tptp.one)) K)))) (forall ((N tptp.num)) (= (tptp.aa_num_int (tptp.neg_numeral_sub_int (tptp.aa_num_num tptp.bitM N)) tptp.one) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_num_int (tptp.neg_numeral_sub_int N) tptp.one)))) (forall ((N tptp.nat)) (= (tptp.compow_fun_nat_nat N tptp.suc) (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N))) (tptp.semila1623282765462674594er_nat tptp.ord_max_nat tptp.zero_zero_nat tptp.aTP_Lamm_bq tptp.aTP_Lamm_br) (forall ((Xa2 tptp.product_prod_nat_nat) (X tptp.product_prod_nat_nat)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_Pro4240683299535347697at_int tptp.abs_Integ Xa2)) (tptp.aa_Pro4240683299535347697at_int tptp.abs_Integ X)) (tptp.aa_Pro4240683299535347697at_int tptp.abs_Integ (tptp.aa_Pro262675715343573244at_nat (tptp.aa_Pro8023792847356852296at_nat (tptp.produc4528391901023682385at_nat tptp.aTP_Lamm_wv) Xa2) X)))) (forall ((Z tptp.int)) (not (forall ((X4 tptp.nat) (Y4 tptp.nat)) (not (= Z (tptp.aa_Pro4240683299535347697at_int tptp.abs_Integ (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat X4) Y4))))))) (forall ((X tptp.product_prod_nat_nat)) (= (tptp.aa_int_nat tptp.nat2 (tptp.aa_Pro4240683299535347697at_int tptp.abs_Integ X)) (tptp.aa_Pro4243173770044397973at_nat (tptp.produc6842872674320459806at_nat tptp.minus_minus_nat) X))) (= tptp.zero_zero_int (tptp.aa_Pro4240683299535347697at_int tptp.abs_Integ _let_9)) (forall ((N tptp.nat)) (= (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N) (tptp.aa_Pro4240683299535347697at_int tptp.abs_Integ (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat N) tptp.zero_zero_nat)))) (forall ((X tptp.product_prod_nat_nat)) (= (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_Pro4240683299535347697at_int tptp.abs_Integ X)) (tptp.aa_Pro4240683299535347697at_int tptp.abs_Integ (tptp.aa_Pro262675715343573244at_nat (tptp.produc2626176000494625587at_nat tptp.aTP_Lamm_ww) X)))) (= tptp.one_one_int (tptp.aa_Pro4240683299535347697at_int tptp.abs_Integ _let_10)) (forall ((Xa2 tptp.product_prod_nat_nat) (X tptp.product_prod_nat_nat)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_Pro4240683299535347697at_int tptp.abs_Integ Xa2)) (tptp.aa_Pro4240683299535347697at_int tptp.abs_Integ X))) (tptp.pp (tptp.aa_Pro2232559814647311250t_bool (tptp.aa_Pro595088089689268830t_bool (tptp.produc5023667602222594023t_bool tptp.aTP_Lamm_wy) Xa2) X)))) (forall ((Xa2 tptp.product_prod_nat_nat) (X tptp.product_prod_nat_nat)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_Pro4240683299535347697at_int tptp.abs_Integ Xa2)) (tptp.aa_Pro4240683299535347697at_int tptp.abs_Integ X))) (tptp.pp (tptp.aa_Pro2232559814647311250t_bool (tptp.aa_Pro595088089689268830t_bool (tptp.produc5023667602222594023t_bool tptp.aTP_Lamm_xa) Xa2) X)))) (forall ((Xa2 tptp.product_prod_nat_nat) (X tptp.product_prod_nat_nat)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_Pro4240683299535347697at_int tptp.abs_Integ Xa2)) (tptp.aa_Pro4240683299535347697at_int tptp.abs_Integ X)) (tptp.aa_Pro4240683299535347697at_int tptp.abs_Integ (tptp.aa_Pro262675715343573244at_nat (tptp.aa_Pro8023792847356852296at_nat (tptp.produc4528391901023682385at_nat tptp.aTP_Lamm_xc) Xa2) X)))) (forall ((Xa2 tptp.product_prod_nat_nat) (X tptp.product_prod_nat_nat)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_Pro4240683299535347697at_int tptp.abs_Integ Xa2)) (tptp.aa_Pro4240683299535347697at_int tptp.abs_Integ X)) (tptp.aa_Pro4240683299535347697at_int tptp.abs_Integ (tptp.aa_Pro262675715343573244at_nat (tptp.aa_Pro8023792847356852296at_nat (tptp.produc4528391901023682385at_nat tptp.aTP_Lamm_xe) Xa2) X)))) (forall ((X tptp.int) (Xa2 tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X) Xa2)) (tptp.pp (tptp.aa_Pro2232559814647311250t_bool (tptp.aa_Pro595088089689268830t_bool (tptp.produc5023667602222594023t_bool tptp.aTP_Lamm_xa) (tptp.aa_int1417691210696471063at_nat tptp.rep_Integ X)) (tptp.aa_int1417691210696471063at_nat tptp.rep_Integ Xa2))))) (forall ((X tptp.int) (Xa2 tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) Xa2)) (tptp.pp (tptp.aa_Pro2232559814647311250t_bool (tptp.aa_Pro595088089689268830t_bool (tptp.produc5023667602222594023t_bool tptp.aTP_Lamm_wy) (tptp.aa_int1417691210696471063at_nat tptp.rep_Integ X)) (tptp.aa_int1417691210696471063at_nat tptp.rep_Integ Xa2))))) (forall ((X tptp.int)) (= (tptp.aa_int_nat tptp.nat2 X) (tptp.aa_Pro4243173770044397973at_nat (tptp.produc6842872674320459806at_nat tptp.minus_minus_nat) (tptp.aa_int1417691210696471063at_nat tptp.rep_Integ X)))) (= tptp.nat_prod_encode (tptp.produc6842872674320459806at_nat tptp.aTP_Lamm_xf)) (= tptp.uminus_uminus_int (tptp.aa_fun8399641135911395862nt_int _let_36 _let_11)) (forall ((A tptp.nat) (B2 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) (tptp.aa_Pro4243173770044397973at_nat tptp.nat_prod_encode (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat A) B2))))) (forall ((B2 tptp.nat) (A tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B2) (tptp.aa_Pro4243173770044397973at_nat tptp.nat_prod_encode (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat A) B2))))) (forall ((K tptp.nat) (M tptp.nat)) (= (tptp.aa_Pro4243173770044397973at_nat tptp.nat_prod_encode (tptp.nat_prod_decode_aux K M)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat tptp.nat_triangle K)) M))) (= tptp.times_times_int (tptp.map_fu8294830438409148311nt_int tptp.rep_Integ _let_36 _let_13)) (= tptp.minus_minus_int (tptp.map_fu8294830438409148311nt_int tptp.rep_Integ _let_36 _let_5)) (= tptp.plus_plus_int (tptp.map_fu8294830438409148311nt_int tptp.rep_Integ _let_36 _let_3)) (forall ((N tptp.nat)) (let ((_let_1 (tptp.aa_nat_num tptp.num_of_nat (tptp.aa_nat_nat tptp.suc N)))) (let ((_let_2 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)))) (and (=> _let_2 (= _let_1 (tptp.aa_num_num tptp.inc (tptp.aa_nat_num tptp.num_of_nat N)))) (=> (not _let_2) (= _let_1 tptp.one)))))) (forall ((X tptp.num) (Y tptp.num)) (let ((_let_1 (tptp.aa_num_fun_num_num tptp.pow X))) (= (tptp.aa_num_num _let_1 (tptp.aa_num_num tptp.bit1 Y)) (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.times_times_num (tptp.aa_num_num tptp.sqr (tptp.aa_num_num _let_1 Y))) X)))) (forall ((Q2 tptp.num)) (= (tptp.aa_nat_num tptp.num_of_nat (tptp.aa_num_nat tptp.numeral_numeral_nat Q2)) Q2)) (forall ((N tptp.num)) (= (tptp.aa_num_num tptp.sqr (tptp.aa_num_num tptp.bit0 N)) (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.sqr N))))) (= (tptp.aa_num_num tptp.sqr tptp.one) tptp.one) (forall ((X tptp.num)) (= (tptp.aa_num_num tptp.sqr X) (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.times_times_num X) X))) (= (tptp.aa_nat_num tptp.num_of_nat tptp.zero_zero_nat) tptp.one) (forall ((N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (= (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_nat_num tptp.num_of_nat N)) N))) (forall ((N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N) tptp.one_one_nat)) (= (tptp.aa_nat_num tptp.num_of_nat N) tptp.one))) (forall ((X tptp.num) (Y tptp.num)) (let ((_let_1 (tptp.aa_num_fun_num_num tptp.pow X))) (= (tptp.aa_num_num _let_1 (tptp.aa_num_num tptp.bit0 Y)) (tptp.aa_num_num tptp.sqr (tptp.aa_num_num _let_1 Y))))) (forall ((N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (= (tptp.aa_nat_num tptp.num_of_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N) N)) (tptp.aa_num_num tptp.bit0 (tptp.aa_nat_num tptp.num_of_nat N))))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 M)) (=> (tptp.pp (tptp.aa_nat_bool _let_1 N)) (= (tptp.aa_nat_num tptp.num_of_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) N)) (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num (tptp.aa_nat_num tptp.num_of_nat M)) (tptp.aa_nat_num tptp.num_of_nat N))))))) (forall ((N tptp.num)) (= (tptp.aa_num_num tptp.sqr (tptp.aa_num_num tptp.bit1 N)) (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num (tptp.aa_num_num tptp.sqr N)) N))))) (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_VEBT_valid X) Xa2))) (=> (=> (exists ((Uu2 tptp.bool) (Uv2 tptp.bool)) (= X (tptp.vEBT_Leaf Uu2 Uv2))) (= Xa2 tptp.one_one_nat)) (not (forall ((Mima tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Deg2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat Deg2) _let_1)))) (=> (= X (tptp.vEBT_Node Mima Deg2 TreeList2 Summary2)) (and (= Deg2 Xa2) (forall ((X4 tptp.vEBT_VEBT)) (=> (tptp.pp (tptp.aa_set8260762808118238015T_bool (tptp.aa_VEB289770264548726718T_bool tptp.member_VEBT_VEBT X4) (tptp.set_VEBT_VEBT2 TreeList2))) (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_VEBT_valid X4) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat Deg2) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))))) (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_VEBT_valid Summary2) _let_2)) (= (tptp.size_s6755466524823107622T_VEBT TreeList2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat _let_1) _let_2)) (tptp.pp (tptp.aa_opt6800557945374683724t_bool (tptp.case_o7912701867834613557at_nat (tptp.aa_bool_bool (tptp.fconj (tptp.aa_bool_bool tptp.fNot (tptp.aa_fun_nat_bool_bool tptp.fEx_nat (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions Summary2)))) (tptp.fAll_VEBT_VEBT (tptp.cOMBS_6222329278419335549l_bool (tptp.cOMBB_3438363824644082366T_VEBT tptp.fimplies (tptp.cOMBC_771164880915498576T_bool tptp.member_VEBT_VEBT (tptp.set_VEBT_VEBT2 TreeList2))) (tptp.cOMBB_3745307990312268622T_VEBT tptp.fNot (tptp.cOMBB_2885587777813823575T_VEBT tptp.fEx_nat tptp.vEBT_V8194947554948674370ptions))))) (tptp.produc8955392012077580105t_bool (tptp.aa_VEB1917483692448707121t_bool (tptp.aa_lis1179741779018426550t_bool (tptp.aTP_Lamm_xg Deg2) TreeList2) Summary2))) Mima))))))))))) (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_VEBT_valid X) Xa2)) (=> (=> (exists ((Uu2 tptp.bool) (Uv2 tptp.bool)) (= X (tptp.vEBT_Leaf Uu2 Uv2))) (not (= Xa2 tptp.one_one_nat))) (not (forall ((Mima tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Deg2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat Deg2) _let_1)))) (=> (= X (tptp.vEBT_Node Mima Deg2 TreeList2 Summary2)) (not (and (= Deg2 Xa2) (forall ((X5 tptp.vEBT_VEBT)) (=> (tptp.pp (tptp.aa_set8260762808118238015T_bool (tptp.aa_VEB289770264548726718T_bool tptp.member_VEBT_VEBT X5) (tptp.set_VEBT_VEBT2 TreeList2))) (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_VEBT_valid X5) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat Deg2) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))))) (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_VEBT_valid Summary2) _let_2)) (= (tptp.size_s6755466524823107622T_VEBT TreeList2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat _let_1) _let_2)) (tptp.pp (tptp.aa_opt6800557945374683724t_bool (tptp.case_o7912701867834613557at_nat (tptp.aa_bool_bool (tptp.fconj (tptp.aa_bool_bool tptp.fNot (tptp.aa_fun_nat_bool_bool tptp.fEx_nat (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions Summary2)))) (tptp.fAll_VEBT_VEBT (tptp.cOMBS_6222329278419335549l_bool (tptp.cOMBB_3438363824644082366T_VEBT tptp.fimplies (tptp.cOMBC_771164880915498576T_bool tptp.member_VEBT_VEBT (tptp.set_VEBT_VEBT2 TreeList2))) (tptp.cOMBB_3745307990312268622T_VEBT tptp.fNot (tptp.cOMBB_2885587777813823575T_VEBT tptp.fEx_nat tptp.vEBT_V8194947554948674370ptions))))) (tptp.produc8955392012077580105t_bool (tptp.aa_VEB1917483692448707121t_bool (tptp.aa_lis1179741779018426550t_bool (tptp.aTP_Lamm_xg Deg2) TreeList2) Summary2))) Mima)))))))))))) (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y tptp.bool)) (let ((_let_1 (tptp.pp Y))) (=> (= (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_VEBT_valid X) Xa2)) _let_1) (=> (=> (exists ((Uu2 tptp.bool) (Uv2 tptp.bool)) (= X (tptp.vEBT_Leaf Uu2 Uv2))) (= _let_1 (not (= Xa2 tptp.one_one_nat)))) (not (forall ((Mima tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Deg2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat Deg2) _let_1)))) (=> (= X (tptp.vEBT_Node Mima Deg2 TreeList2 Summary2)) (= (tptp.pp Y) (not (and (= Deg2 Xa2) (forall ((X3 tptp.vEBT_VEBT)) (=> (tptp.pp (tptp.aa_set8260762808118238015T_bool (tptp.aa_VEB289770264548726718T_bool tptp.member_VEBT_VEBT X3) (tptp.set_VEBT_VEBT2 TreeList2))) (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_VEBT_valid X3) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat Deg2) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))))) (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_VEBT_valid Summary2) _let_2)) (= (tptp.size_s6755466524823107622T_VEBT TreeList2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat _let_1) _let_2)) (tptp.pp (tptp.aa_opt6800557945374683724t_bool (tptp.case_o7912701867834613557at_nat (tptp.aa_bool_bool (tptp.fconj (tptp.aa_bool_bool tptp.fNot (tptp.aa_fun_nat_bool_bool tptp.fEx_nat (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions Summary2)))) (tptp.fAll_VEBT_VEBT (tptp.cOMBS_6222329278419335549l_bool (tptp.cOMBB_3438363824644082366T_VEBT tptp.fimplies (tptp.cOMBC_771164880915498576T_bool tptp.member_VEBT_VEBT (tptp.set_VEBT_VEBT2 TreeList2))) (tptp.cOMBB_3745307990312268622T_VEBT tptp.fNot (tptp.cOMBB_2885587777813823575T_VEBT tptp.fEx_nat tptp.vEBT_V8194947554948674370ptions))))) (tptp.produc8955392012077580105t_bool (tptp.aa_VEB1917483692448707121t_bool (tptp.aa_lis1179741779018426550t_bool (tptp.aTP_Lamm_xg Deg2) TreeList2) Summary2))) Mima)))))))))))))) (forall ((Mima2 tptp.option4927543243414619207at_nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (Deg4 tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Deg) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat Deg) _let_1)))) (= (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_VEBT_valid (tptp.vEBT_Node Mima2 Deg TreeList Summary)) Deg4)) (and (= Deg Deg4) (forall ((X3 tptp.vEBT_VEBT)) (=> (tptp.pp (tptp.aa_set8260762808118238015T_bool (tptp.aa_VEB289770264548726718T_bool tptp.member_VEBT_VEBT X3) (tptp.set_VEBT_VEBT2 TreeList))) (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_VEBT_valid X3) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat Deg) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))))) (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_VEBT_valid Summary) _let_2)) (= (tptp.size_s6755466524823107622T_VEBT TreeList) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat _let_1) _let_2)) (tptp.pp (tptp.aa_opt6800557945374683724t_bool (tptp.case_o7912701867834613557at_nat (tptp.aa_bool_bool (tptp.fconj (tptp.aa_bool_bool tptp.fNot (tptp.aa_fun_nat_bool_bool tptp.fEx_nat (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions Summary)))) (tptp.fAll_VEBT_VEBT (tptp.cOMBS_6222329278419335549l_bool (tptp.cOMBB_3438363824644082366T_VEBT tptp.fimplies (tptp.cOMBC_771164880915498576T_bool tptp.member_VEBT_VEBT (tptp.set_VEBT_VEBT2 TreeList))) (tptp.cOMBB_3745307990312268622T_VEBT tptp.fNot (tptp.cOMBB_2885587777813823575T_VEBT tptp.fEx_nat tptp.vEBT_V8194947554948674370ptions))))) (tptp.produc8955392012077580105t_bool (tptp.aa_VEB1917483692448707121t_bool (tptp.aa_lis1179741779018426550t_bool (tptp.aTP_Lamm_xg Deg) TreeList) Summary))) Mima2))))))) (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_VEBT_valid X) Xa2))) (=> (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel (tptp.produc738532404422230701BT_nat X Xa2)) (=> (forall ((Uu2 tptp.bool) (Uv2 tptp.bool)) (let ((_let_1 (tptp.vEBT_Leaf Uu2 Uv2))) (=> (= X _let_1) (=> (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel (tptp.produc738532404422230701BT_nat _let_1 Xa2)) (= Xa2 tptp.one_one_nat))))) (not (forall ((Mima tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Deg2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat Deg2) _let_1)))) (let ((_let_3 (tptp.vEBT_Node Mima Deg2 TreeList2 Summary2))) (=> (= X _let_3) (=> (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel (tptp.produc738532404422230701BT_nat _let_3 Xa2)) (and (= Deg2 Xa2) (forall ((X4 tptp.vEBT_VEBT)) (=> (tptp.pp (tptp.aa_set8260762808118238015T_bool (tptp.aa_VEB289770264548726718T_bool tptp.member_VEBT_VEBT X4) (tptp.set_VEBT_VEBT2 TreeList2))) (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_VEBT_valid X4) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat Deg2) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))))) (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_VEBT_valid Summary2) _let_2)) (= (tptp.size_s6755466524823107622T_VEBT TreeList2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat _let_1) _let_2)) (tptp.pp (tptp.aa_opt6800557945374683724t_bool (tptp.case_o7912701867834613557at_nat (tptp.aa_bool_bool (tptp.fconj (tptp.aa_bool_bool tptp.fNot (tptp.aa_fun_nat_bool_bool tptp.fEx_nat (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions Summary2)))) (tptp.fAll_VEBT_VEBT (tptp.cOMBS_6222329278419335549l_bool (tptp.cOMBB_3438363824644082366T_VEBT tptp.fimplies (tptp.cOMBC_771164880915498576T_bool tptp.member_VEBT_VEBT (tptp.set_VEBT_VEBT2 TreeList2))) (tptp.cOMBB_3745307990312268622T_VEBT tptp.fNot (tptp.cOMBB_2885587777813823575T_VEBT tptp.fEx_nat tptp.vEBT_V8194947554948674370ptions))))) (tptp.produc8955392012077580105t_bool (tptp.aa_VEB1917483692448707121t_bool (tptp.aa_lis1179741779018426550t_bool (tptp.aTP_Lamm_xg Deg2) TreeList2) Summary2))) Mima)))))))))))))) (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_VEBT_valid X) Xa2)) (=> (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel (tptp.produc738532404422230701BT_nat X Xa2)) (=> (forall ((Uu2 tptp.bool) (Uv2 tptp.bool)) (let ((_let_1 (tptp.vEBT_Leaf Uu2 Uv2))) (=> (= X _let_1) (=> (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel (tptp.produc738532404422230701BT_nat _let_1 Xa2)) (not (= Xa2 tptp.one_one_nat)))))) (not (forall ((Mima tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Deg2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat Deg2) _let_1)))) (let ((_let_3 (tptp.vEBT_Node Mima Deg2 TreeList2 Summary2))) (=> (= X _let_3) (=> (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel (tptp.produc738532404422230701BT_nat _let_3 Xa2)) (not (and (= Deg2 Xa2) (forall ((X5 tptp.vEBT_VEBT)) (=> (tptp.pp (tptp.aa_set8260762808118238015T_bool (tptp.aa_VEB289770264548726718T_bool tptp.member_VEBT_VEBT X5) (tptp.set_VEBT_VEBT2 TreeList2))) (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_VEBT_valid X5) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat Deg2) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))))) (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_VEBT_valid Summary2) _let_2)) (= (tptp.size_s6755466524823107622T_VEBT TreeList2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat _let_1) _let_2)) (tptp.pp (tptp.aa_opt6800557945374683724t_bool (tptp.case_o7912701867834613557at_nat (tptp.aa_bool_bool (tptp.fconj (tptp.aa_bool_bool tptp.fNot (tptp.aa_fun_nat_bool_bool tptp.fEx_nat (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions Summary2)))) (tptp.fAll_VEBT_VEBT (tptp.cOMBS_6222329278419335549l_bool (tptp.cOMBB_3438363824644082366T_VEBT tptp.fimplies (tptp.cOMBC_771164880915498576T_bool tptp.member_VEBT_VEBT (tptp.set_VEBT_VEBT2 TreeList2))) (tptp.cOMBB_3745307990312268622T_VEBT tptp.fNot (tptp.cOMBB_2885587777813823575T_VEBT tptp.fEx_nat tptp.vEBT_V8194947554948674370ptions))))) (tptp.produc8955392012077580105t_bool (tptp.aa_VEB1917483692448707121t_bool (tptp.aa_lis1179741779018426550t_bool (tptp.aTP_Lamm_xg Deg2) TreeList2) Summary2))) Mima))))))))))))))) (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y tptp.bool)) (=> (= (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_VEBT_valid X) Xa2)) (tptp.pp Y)) (=> (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel (tptp.produc738532404422230701BT_nat X Xa2)) (=> (forall ((Uu2 tptp.bool) (Uv2 tptp.bool)) (let ((_let_1 (tptp.vEBT_Leaf Uu2 Uv2))) (=> (= X _let_1) (=> (= (tptp.pp Y) (= Xa2 tptp.one_one_nat)) (not (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel (tptp.produc738532404422230701BT_nat _let_1 Xa2))))))) (not (forall ((Mima tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (tptp.vEBT_Node Mima Deg2 TreeList2 Summary2))) (let ((_let_2 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_3 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Deg2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat Deg2) _let_2)))) (=> (= X _let_1) (=> (= (tptp.pp Y) (and (= Deg2 Xa2) (forall ((X3 tptp.vEBT_VEBT)) (=> (tptp.pp (tptp.aa_set8260762808118238015T_bool (tptp.aa_VEB289770264548726718T_bool tptp.member_VEBT_VEBT X3) (tptp.set_VEBT_VEBT2 TreeList2))) (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_VEBT_valid X3) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat Deg2) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))))) (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_VEBT_valid Summary2) _let_3)) (= (tptp.size_s6755466524823107622T_VEBT TreeList2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat _let_2) _let_3)) (tptp.pp (tptp.aa_opt6800557945374683724t_bool (tptp.case_o7912701867834613557at_nat (tptp.aa_bool_bool (tptp.fconj (tptp.aa_bool_bool tptp.fNot (tptp.aa_fun_nat_bool_bool tptp.fEx_nat (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions Summary2)))) (tptp.fAll_VEBT_VEBT (tptp.cOMBS_6222329278419335549l_bool (tptp.cOMBB_3438363824644082366T_VEBT tptp.fimplies (tptp.cOMBC_771164880915498576T_bool tptp.member_VEBT_VEBT (tptp.set_VEBT_VEBT2 TreeList2))) (tptp.cOMBB_3745307990312268622T_VEBT tptp.fNot (tptp.cOMBB_2885587777813823575T_VEBT tptp.fEx_nat tptp.vEBT_V8194947554948674370ptions))))) (tptp.produc8955392012077580105t_bool (tptp.aa_VEB1917483692448707121t_bool (tptp.aa_lis1179741779018426550t_bool (tptp.aTP_Lamm_xg Deg2) TreeList2) Summary2))) Mima)))) (not (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel (tptp.produc738532404422230701BT_nat _let_1 Xa2)))))))))))))) (forall ((X7 tptp.set_int)) (= (tptp.complete_Sup_Sup_int X7) (tptp.the_int (tptp.aTP_Lamm_xh X7)))) (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat M))) (= (tptp.aa_int_int (tptp.bit_se2923211474154528505it_int _let_1) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int N))) (tptp.case_option_int_num tptp.zero_zero_int (tptp.aTP_Lamm_xi M) (tptp.bit_take_bit_num _let_1 N))))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.aa_int_int (tptp.bit_se725231765392027082nd_int (tptp.aa_num_int tptp.numeral_numeral_int M)) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 N)))) (tptp.case_option_int_num tptp.zero_zero_int tptp.numeral_numeral_int (tptp.bit_and_not_num M (tptp.aa_num_num tptp.bitM N))))) (forall ((M tptp.num)) (= (tptp.bit_take_bit_num tptp.zero_zero_nat M) tptp.none_num)) (forall ((N tptp.nat)) (= (tptp.bit_take_bit_num (tptp.aa_nat_nat tptp.suc N) tptp.one) (tptp.some_num tptp.one))) (forall ((R tptp.num)) (= (tptp.bit_take_bit_num (tptp.aa_num_nat tptp.numeral_numeral_nat R) tptp.one) (tptp.some_num tptp.one))) (forall ((N tptp.nat) (M tptp.num)) (= (tptp.bit_take_bit_num (tptp.aa_nat_nat tptp.suc N) (tptp.aa_num_num tptp.bit0 M)) (tptp.case_o6005452278849405969um_num tptp.none_num tptp.aTP_Lamm_xj (tptp.bit_take_bit_num N M)))) (forall ((N tptp.nat) (M tptp.num)) (= (tptp.bit_take_bit_num (tptp.aa_nat_nat tptp.suc N) (tptp.aa_num_num tptp.bit1 M)) (tptp.some_num (tptp.case_option_num_num tptp.one tptp.bit1 (tptp.bit_take_bit_num N M))))) (forall ((R tptp.num) (M tptp.num)) (= (tptp.bit_take_bit_num (tptp.aa_num_nat tptp.numeral_numeral_nat R) (tptp.aa_num_num tptp.bit0 M)) (tptp.case_o6005452278849405969um_num tptp.none_num tptp.aTP_Lamm_xj (tptp.bit_take_bit_num (tptp.aa_num_nat tptp.pred_numeral R) M)))) (forall ((R tptp.num) (M tptp.num)) (= (tptp.bit_take_bit_num (tptp.aa_num_nat tptp.numeral_numeral_nat R) (tptp.aa_num_num tptp.bit1 M)) (tptp.some_num (tptp.case_option_num_num tptp.one tptp.bit1 (tptp.bit_take_bit_num (tptp.aa_num_nat tptp.pred_numeral R) M))))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.aa_int_int (tptp.bit_se725231765392027082nd_int (tptp.aa_num_int tptp.numeral_numeral_int M)) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit1 N)))) (tptp.case_option_int_num tptp.zero_zero_int tptp.numeral_numeral_int (tptp.bit_and_not_num M (tptp.aa_num_num tptp.bit0 N))))) (forall ((N tptp.num) (M tptp.num)) (= (tptp.aa_int_int (tptp.bit_se725231765392027082nd_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit1 N)))) (tptp.aa_num_int tptp.numeral_numeral_int M)) (tptp.case_option_int_num tptp.zero_zero_int tptp.numeral_numeral_int (tptp.bit_and_not_num M (tptp.aa_num_num tptp.bit0 N))))) (forall ((N tptp.num) (M tptp.num)) (= (tptp.aa_int_int (tptp.bit_se725231765392027082nd_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 N)))) (tptp.aa_num_int tptp.numeral_numeral_int M)) (tptp.case_option_int_num tptp.zero_zero_int tptp.numeral_numeral_int (tptp.bit_and_not_num M (tptp.aa_num_num tptp.bitM N))))) (forall ((N tptp.nat) (M tptp.num)) (= (tptp.bit_take_bit_num N (tptp.aa_num_num tptp.bit0 M)) (tptp.case_nat_option_num tptp.none_num (tptp.aTP_Lamm_xk M) N))) (= (tptp.bit_and_not_num tptp.one tptp.one) tptp.none_num) (forall ((N tptp.nat)) (= (tptp.bit_take_bit_num N tptp.one) (tptp.case_nat_option_num tptp.none_num tptp.aTP_Lamm_xl N))) (forall ((M tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 M))) (= (tptp.bit_and_not_num _let_1 tptp.one) (tptp.some_num _let_1)))) (forall ((N tptp.num)) (= (tptp.bit_and_not_num tptp.one (tptp.aa_num_num tptp.bit0 N)) (tptp.some_num tptp.one))) (forall ((P tptp.fun_nat_bool) (B2 tptp.nat)) (=> (exists ((X_13 tptp.nat)) (tptp.pp (tptp.aa_nat_bool P X_13))) (=> (forall ((Y4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool P Y4)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Y4) B2)))) (tptp.pp (tptp.aa_nat_bool P (tptp.order_Greatest_nat P)))))) (forall ((P tptp.fun_nat_bool) (K tptp.nat) (B2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool P K)) (=> (forall ((Y4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool P Y4)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Y4) B2)))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) (tptp.order_Greatest_nat P)))))) (forall ((P tptp.fun_nat_bool) (K tptp.nat) (B2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool P K)) (=> (forall ((Y4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool P Y4)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Y4) B2)))) (tptp.pp (tptp.aa_nat_bool P (tptp.order_Greatest_nat P)))))) (forall ((N tptp.num)) (= (tptp.bit_and_not_num tptp.one (tptp.aa_num_num tptp.bit1 N)) tptp.none_num)) (forall ((N tptp.nat) (M tptp.num)) (= (tptp.bit_take_bit_num N (tptp.aa_num_num tptp.bit1 M)) (tptp.case_nat_option_num tptp.none_num (tptp.aTP_Lamm_xm M) N))) (forall ((M tptp.num)) (= (tptp.bit_and_not_num (tptp.aa_num_num tptp.bit1 M) tptp.one) (tptp.some_num (tptp.aa_num_num tptp.bit0 M)))) (forall ((M tptp.num) (N tptp.num) (Q2 tptp.num)) (= (= (tptp.bit_and_not_num M N) (tptp.some_num Q2)) (= (tptp.aa_int_int (tptp.bit_se725231765392027082nd_int (tptp.aa_num_int tptp.numeral_numeral_int M)) (tptp.aa_int_int tptp.bit_ri7919022796975470100ot_int (tptp.aa_num_int tptp.numeral_numeral_int N))) (tptp.aa_num_int tptp.numeral_numeral_int Q2)))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.bit_and_not_num (tptp.aa_num_num tptp.bit1 M) (tptp.aa_num_num tptp.bit0 N)) (tptp.case_o6005452278849405969um_num (tptp.some_num tptp.one) tptp.aTP_Lamm_xn (tptp.bit_and_not_num M N)))) (forall ((M tptp.num) (N tptp.num)) (= (= (tptp.bit_and_not_num M N) tptp.none_num) (= (tptp.aa_int_int (tptp.bit_se725231765392027082nd_int (tptp.aa_num_int tptp.numeral_numeral_int M)) (tptp.aa_int_int tptp.bit_ri7919022796975470100ot_int (tptp.aa_num_int tptp.numeral_numeral_int N))) tptp.zero_zero_int))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.aa_int_int (tptp.bit_se725231765392027082nd_int (tptp.aa_int_int tptp.bit_ri7919022796975470100ot_int (tptp.aa_num_int tptp.numeral_numeral_int M))) (tptp.aa_num_int tptp.numeral_numeral_int N)) (tptp.case_option_int_num tptp.zero_zero_int tptp.numeral_numeral_int (tptp.bit_and_not_num N M)))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.aa_int_int (tptp.bit_se725231765392027082nd_int (tptp.aa_num_int tptp.numeral_numeral_int M)) (tptp.aa_int_int tptp.bit_ri7919022796975470100ot_int (tptp.aa_num_int tptp.numeral_numeral_int N))) (tptp.case_option_int_num tptp.zero_zero_int tptp.numeral_numeral_int (tptp.bit_and_not_num M N)))) (forall ((N tptp.nat) (M tptp.num)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se2925701944663578781it_nat N) (tptp.aa_num_nat tptp.numeral_numeral_nat M)))) (let ((_let_2 (tptp.bit_take_bit_num N M))) (let ((_let_3 (= _let_1 tptp.zero_zero_nat))) (and (=> _let_3 (= _let_2 tptp.none_num)) (=> (not _let_3) (= _let_2 (tptp.some_num (tptp.aa_nat_num tptp.num_of_nat _let_1))))))))) (forall ((N tptp.nat) (M tptp.num)) (= (tptp.bit_take_bit_num N M) (tptp.produc478579273971653890on_num tptp.aTP_Lamm_xr (tptp.product_Pair_nat_num N M)))) (= (tptp.aa_num_Code_integer tptp.code_integer_of_num _let_24) _let_35) (= tptp.code_integer_of_num tptp.numera6620942414471956472nteger) (= (tptp.aa_num_Code_integer tptp.code_integer_of_num tptp.one) tptp.one_one_Code_integer) (forall ((N tptp.num)) (let ((_let_1 (tptp.aa_num_Code_integer tptp.code_integer_of_num N))) (= (tptp.aa_num_Code_integer tptp.code_integer_of_num (tptp.aa_num_num tptp.bit0 N)) (tptp.plus_p5714425477246183910nteger _let_1 _let_1)))) (forall ((X tptp.num) (Xa2 tptp.num) (Y tptp.option_num)) (let ((_let_1 (not (= Y tptp.none_num)))) (let ((_let_2 (= X tptp.one))) (=> (= (tptp.bit_and_not_num X Xa2) Y) (=> (=> _let_2 (=> (= Xa2 tptp.one) _let_1)) (=> (=> _let_2 (=> (exists ((N2 tptp.num)) (= Xa2 (tptp.aa_num_num tptp.bit0 N2))) (not (= Y (tptp.some_num tptp.one))))) (=> (=> _let_2 (=> (exists ((N2 tptp.num)) (= Xa2 (tptp.aa_num_num tptp.bit1 N2))) _let_1)) (=> (forall ((M3 tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 M3))) (=> (= X _let_1) (=> (= Xa2 tptp.one) (not (= Y (tptp.some_num _let_1))))))) (=> (forall ((M3 tptp.num)) (=> (= X (tptp.aa_num_num tptp.bit0 M3)) (forall ((N2 tptp.num)) (=> (= Xa2 (tptp.aa_num_num tptp.bit0 N2)) (not (= Y (tptp.map_option_num_num tptp.bit0 (tptp.bit_and_not_num M3 N2)))))))) (=> (forall ((M3 tptp.num)) (=> (= X (tptp.aa_num_num tptp.bit0 M3)) (forall ((N2 tptp.num)) (=> (= Xa2 (tptp.aa_num_num tptp.bit1 N2)) (not (= Y (tptp.map_option_num_num tptp.bit0 (tptp.bit_and_not_num M3 N2)))))))) (=> (forall ((M3 tptp.num)) (=> (= X (tptp.aa_num_num tptp.bit1 M3)) (=> (= Xa2 tptp.one) (not (= Y (tptp.some_num (tptp.aa_num_num tptp.bit0 M3))))))) (=> (forall ((M3 tptp.num)) (=> (= X (tptp.aa_num_num tptp.bit1 M3)) (forall ((N2 tptp.num)) (=> (= Xa2 (tptp.aa_num_num tptp.bit0 N2)) (not (= Y (tptp.case_o6005452278849405969um_num (tptp.some_num tptp.one) tptp.aTP_Lamm_xn (tptp.bit_and_not_num M3 N2)))))))) (not (forall ((M3 tptp.num)) (=> (= X (tptp.aa_num_num tptp.bit1 M3)) (forall ((N2 tptp.num)) (=> (= Xa2 (tptp.aa_num_num tptp.bit1 N2)) (not (= Y (tptp.map_option_num_num tptp.bit0 (tptp.bit_and_not_num M3 N2))))))))))))))))))))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.aa_num_option_num (tptp.aa_num6390622462783740633on_num tptp.bit_un2480387367778600638or_num (tptp.aa_num_num tptp.bit0 M)) (tptp.aa_num_num tptp.bit1 N)) (tptp.some_num (tptp.case_option_num_num tptp.one tptp.bit1 (tptp.aa_num_option_num (tptp.aa_num6390622462783740633on_num tptp.bit_un2480387367778600638or_num M) N))))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.aa_num_option_num (tptp.aa_num6390622462783740633on_num tptp.bit_un2480387367778600638or_num (tptp.aa_num_num tptp.bit1 M)) (tptp.aa_num_num tptp.bit0 N)) (tptp.some_num (tptp.case_option_num_num tptp.one tptp.bit1 (tptp.aa_num_option_num (tptp.aa_num6390622462783740633on_num tptp.bit_un2480387367778600638or_num M) N))))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.aa_num_option_num (tptp.aa_num6390622462783740633on_num tptp.bit_un2480387367778600638or_num (tptp.aa_num_num tptp.bit0 M)) (tptp.aa_num_num tptp.bit0 N)) (tptp.map_option_num_num tptp.bit0 (tptp.aa_num_option_num (tptp.aa_num6390622462783740633on_num tptp.bit_un2480387367778600638or_num M) N)))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.aa_num_option_num (tptp.aa_num6390622462783740633on_num tptp.bit_un2480387367778600638or_num (tptp.aa_num_num tptp.bit1 M)) (tptp.aa_num_num tptp.bit1 N)) (tptp.map_option_num_num tptp.bit0 (tptp.aa_num_option_num (tptp.aa_num6390622462783740633on_num tptp.bit_un2480387367778600638or_num M) N)))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.bit_and_not_num (tptp.aa_num_num tptp.bit0 M) (tptp.aa_num_num tptp.bit0 N)) (tptp.map_option_num_num tptp.bit0 (tptp.bit_and_not_num M N)))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.bit_and_not_num (tptp.aa_num_num tptp.bit0 M) (tptp.aa_num_num tptp.bit1 N)) (tptp.map_option_num_num tptp.bit0 (tptp.bit_and_not_num M N)))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.bit_and_not_num (tptp.aa_num_num tptp.bit1 M) (tptp.aa_num_num tptp.bit1 N)) (tptp.map_option_num_num tptp.bit0 (tptp.bit_and_not_num M N)))) (= (tptp.aa_num_option_num (tptp.aa_num6390622462783740633on_num tptp.bit_un2480387367778600638or_num tptp.one) tptp.one) tptp.none_num) (forall ((X tptp.num) (Xa2 tptp.num) (Y tptp.option_num)) (let ((_let_1 (= X tptp.one))) (=> (= (tptp.aa_num_option_num (tptp.aa_num6390622462783740633on_num tptp.bit_un2480387367778600638or_num X) Xa2) Y) (=> (=> _let_1 (=> (= Xa2 tptp.one) (not (= Y tptp.none_num)))) (=> (=> _let_1 (forall ((N2 tptp.num)) (=> (= Xa2 (tptp.aa_num_num tptp.bit0 N2)) (not (= Y (tptp.some_num (tptp.aa_num_num tptp.bit1 N2))))))) (=> (=> _let_1 (forall ((N2 tptp.num)) (=> (= Xa2 (tptp.aa_num_num tptp.bit1 N2)) (not (= Y (tptp.some_num (tptp.aa_num_num tptp.bit0 N2))))))) (=> (forall ((M3 tptp.num)) (=> (= X (tptp.aa_num_num tptp.bit0 M3)) (=> (= Xa2 tptp.one) (not (= Y (tptp.some_num (tptp.aa_num_num tptp.bit1 M3))))))) (=> (forall ((M3 tptp.num)) (=> (= X (tptp.aa_num_num tptp.bit0 M3)) (forall ((N2 tptp.num)) (=> (= Xa2 (tptp.aa_num_num tptp.bit0 N2)) (not (= Y (tptp.map_option_num_num tptp.bit0 (tptp.aa_num_option_num (tptp.aa_num6390622462783740633on_num tptp.bit_un2480387367778600638or_num M3) N2)))))))) (=> (forall ((M3 tptp.num)) (=> (= X (tptp.aa_num_num tptp.bit0 M3)) (forall ((N2 tptp.num)) (=> (= Xa2 (tptp.aa_num_num tptp.bit1 N2)) (not (= Y (tptp.some_num (tptp.case_option_num_num tptp.one tptp.bit1 (tptp.aa_num_option_num (tptp.aa_num6390622462783740633on_num tptp.bit_un2480387367778600638or_num M3) N2))))))))) (=> (forall ((M3 tptp.num)) (=> (= X (tptp.aa_num_num tptp.bit1 M3)) (=> (= Xa2 tptp.one) (not (= Y (tptp.some_num (tptp.aa_num_num tptp.bit0 M3))))))) (=> (forall ((M3 tptp.num)) (=> (= X (tptp.aa_num_num tptp.bit1 M3)) (forall ((N2 tptp.num)) (=> (= Xa2 (tptp.aa_num_num tptp.bit0 N2)) (not (= Y (tptp.some_num (tptp.case_option_num_num tptp.one tptp.bit1 (tptp.aa_num_option_num (tptp.aa_num6390622462783740633on_num tptp.bit_un2480387367778600638or_num M3) N2))))))))) (not (forall ((M3 tptp.num)) (=> (= X (tptp.aa_num_num tptp.bit1 M3)) (forall ((N2 tptp.num)) (=> (= Xa2 (tptp.aa_num_num tptp.bit1 N2)) (not (= Y (tptp.map_option_num_num tptp.bit0 (tptp.aa_num_option_num (tptp.aa_num6390622462783740633on_num tptp.bit_un2480387367778600638or_num M3) N2)))))))))))))))))))) (forall ((M tptp.num)) (= (tptp.aa_num_option_num (tptp.aa_num6390622462783740633on_num tptp.bit_un2480387367778600638or_num (tptp.aa_num_num tptp.bit1 M)) tptp.one) (tptp.some_num (tptp.aa_num_num tptp.bit0 M)))) (forall ((M tptp.num)) (= (tptp.aa_num_option_num (tptp.aa_num6390622462783740633on_num tptp.bit_un2480387367778600638or_num (tptp.aa_num_num tptp.bit0 M)) tptp.one) (tptp.some_num (tptp.aa_num_num tptp.bit1 M)))) (forall ((N tptp.num)) (= (tptp.aa_num_option_num (tptp.aa_num6390622462783740633on_num tptp.bit_un2480387367778600638or_num tptp.one) (tptp.aa_num_num tptp.bit1 N)) (tptp.some_num (tptp.aa_num_num tptp.bit0 N)))) (forall ((N tptp.num)) (= (tptp.aa_num_option_num (tptp.aa_num6390622462783740633on_num tptp.bit_un2480387367778600638or_num tptp.one) (tptp.aa_num_num tptp.bit0 N)) (tptp.some_num (tptp.aa_num_num tptp.bit1 N)))) (forall ((X tptp.num) (Xa2 tptp.num) (Y tptp.option_num)) (let ((_let_1 (= X tptp.one))) (let ((_let_2 (tptp.accp_P3113834385874906142um_num tptp.bit_and_not_num_rel))) (=> (= (tptp.bit_and_not_num X Xa2) Y) (=> (tptp.pp (tptp.aa_Pro762926636801165566m_bool _let_2 (tptp.product_Pair_num_num X Xa2))) (=> (=> _let_1 (=> (= Xa2 tptp.one) (=> (= Y tptp.none_num) (not (tptp.pp (tptp.aa_Pro762926636801165566m_bool _let_2 (tptp.product_Pair_num_num tptp.one tptp.one))))))) (=> (=> _let_1 (forall ((N2 tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 N2))) (=> (= Xa2 _let_1) (=> (= Y (tptp.some_num tptp.one)) (not (tptp.pp (tptp.aa_Pro762926636801165566m_bool (tptp.accp_P3113834385874906142um_num tptp.bit_and_not_num_rel) (tptp.product_Pair_num_num tptp.one _let_1))))))))) (=> (=> _let_1 (forall ((N2 tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit1 N2))) (=> (= Xa2 _let_1) (=> (= Y tptp.none_num) (not (tptp.pp (tptp.aa_Pro762926636801165566m_bool (tptp.accp_P3113834385874906142um_num tptp.bit_and_not_num_rel) (tptp.product_Pair_num_num tptp.one _let_1))))))))) (=> (forall ((M3 tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 M3))) (=> (= X _let_1) (=> (= Xa2 tptp.one) (=> (= Y (tptp.some_num _let_1)) (not (tptp.pp (tptp.aa_Pro762926636801165566m_bool (tptp.accp_P3113834385874906142um_num tptp.bit_and_not_num_rel) (tptp.product_Pair_num_num _let_1 tptp.one))))))))) (=> (forall ((M3 tptp.num)) (=> (= X (tptp.aa_num_num tptp.bit0 M3)) (forall ((N2 tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 N2))) (=> (= Xa2 _let_1) (=> (= Y (tptp.map_option_num_num tptp.bit0 (tptp.bit_and_not_num M3 N2))) (not (tptp.pp (tptp.aa_Pro762926636801165566m_bool (tptp.accp_P3113834385874906142um_num tptp.bit_and_not_num_rel) (tptp.product_Pair_num_num (tptp.aa_num_num tptp.bit0 M3) _let_1)))))))))) (=> (forall ((M3 tptp.num)) (=> (= X (tptp.aa_num_num tptp.bit0 M3)) (forall ((N2 tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit1 N2))) (=> (= Xa2 _let_1) (=> (= Y (tptp.map_option_num_num tptp.bit0 (tptp.bit_and_not_num M3 N2))) (not (tptp.pp (tptp.aa_Pro762926636801165566m_bool (tptp.accp_P3113834385874906142um_num tptp.bit_and_not_num_rel) (tptp.product_Pair_num_num (tptp.aa_num_num tptp.bit0 M3) _let_1)))))))))) (=> (forall ((M3 tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit1 M3))) (=> (= X _let_1) (=> (= Xa2 tptp.one) (=> (= Y (tptp.some_num (tptp.aa_num_num tptp.bit0 M3))) (not (tptp.pp (tptp.aa_Pro762926636801165566m_bool (tptp.accp_P3113834385874906142um_num tptp.bit_and_not_num_rel) (tptp.product_Pair_num_num _let_1 tptp.one))))))))) (=> (forall ((M3 tptp.num)) (=> (= X (tptp.aa_num_num tptp.bit1 M3)) (forall ((N2 tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 N2))) (=> (= Xa2 _let_1) (=> (= Y (tptp.case_o6005452278849405969um_num (tptp.some_num tptp.one) tptp.aTP_Lamm_xn (tptp.bit_and_not_num M3 N2))) (not (tptp.pp (tptp.aa_Pro762926636801165566m_bool (tptp.accp_P3113834385874906142um_num tptp.bit_and_not_num_rel) (tptp.product_Pair_num_num (tptp.aa_num_num tptp.bit1 M3) _let_1)))))))))) (not (forall ((M3 tptp.num)) (=> (= X (tptp.aa_num_num tptp.bit1 M3)) (forall ((N2 tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit1 N2))) (=> (= Xa2 _let_1) (=> (= Y (tptp.map_option_num_num tptp.bit0 (tptp.bit_and_not_num M3 N2))) (not (tptp.pp (tptp.aa_Pro762926636801165566m_bool (tptp.accp_P3113834385874906142um_num tptp.bit_and_not_num_rel) (tptp.product_Pair_num_num (tptp.aa_num_num tptp.bit1 M3) _let_1)))))))))))))))))))))))) (forall ((X tptp.num) (Xa2 tptp.num) (Y tptp.option_num)) (let ((_let_1 (= X tptp.one))) (let ((_let_2 (tptp.accp_P3113834385874906142um_num tptp.bit_un2901131394128224187um_rel))) (=> (= (tptp.aa_num_option_num (tptp.aa_num6390622462783740633on_num tptp.bit_un2480387367778600638or_num X) Xa2) Y) (=> (tptp.pp (tptp.aa_Pro762926636801165566m_bool _let_2 (tptp.product_Pair_num_num X Xa2))) (=> (=> _let_1 (=> (= Xa2 tptp.one) (=> (= Y tptp.none_num) (not (tptp.pp (tptp.aa_Pro762926636801165566m_bool _let_2 (tptp.product_Pair_num_num tptp.one tptp.one))))))) (=> (=> _let_1 (forall ((N2 tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 N2))) (=> (= Xa2 _let_1) (=> (= Y (tptp.some_num (tptp.aa_num_num tptp.bit1 N2))) (not (tptp.pp (tptp.aa_Pro762926636801165566m_bool (tptp.accp_P3113834385874906142um_num tptp.bit_un2901131394128224187um_rel) (tptp.product_Pair_num_num tptp.one _let_1))))))))) (=> (=> _let_1 (forall ((N2 tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit1 N2))) (=> (= Xa2 _let_1) (=> (= Y (tptp.some_num (tptp.aa_num_num tptp.bit0 N2))) (not (tptp.pp (tptp.aa_Pro762926636801165566m_bool (tptp.accp_P3113834385874906142um_num tptp.bit_un2901131394128224187um_rel) (tptp.product_Pair_num_num tptp.one _let_1))))))))) (=> (forall ((M3 tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 M3))) (=> (= X _let_1) (=> (= Xa2 tptp.one) (=> (= Y (tptp.some_num (tptp.aa_num_num tptp.bit1 M3))) (not (tptp.pp (tptp.aa_Pro762926636801165566m_bool (tptp.accp_P3113834385874906142um_num tptp.bit_un2901131394128224187um_rel) (tptp.product_Pair_num_num _let_1 tptp.one))))))))) (=> (forall ((M3 tptp.num)) (=> (= X (tptp.aa_num_num tptp.bit0 M3)) (forall ((N2 tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 N2))) (=> (= Xa2 _let_1) (=> (= Y (tptp.map_option_num_num tptp.bit0 (tptp.aa_num_option_num (tptp.aa_num6390622462783740633on_num tptp.bit_un2480387367778600638or_num M3) N2))) (not (tptp.pp (tptp.aa_Pro762926636801165566m_bool (tptp.accp_P3113834385874906142um_num tptp.bit_un2901131394128224187um_rel) (tptp.product_Pair_num_num (tptp.aa_num_num tptp.bit0 M3) _let_1)))))))))) (=> (forall ((M3 tptp.num)) (=> (= X (tptp.aa_num_num tptp.bit0 M3)) (forall ((N2 tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit1 N2))) (=> (= Xa2 _let_1) (=> (= Y (tptp.some_num (tptp.case_option_num_num tptp.one tptp.bit1 (tptp.aa_num_option_num (tptp.aa_num6390622462783740633on_num tptp.bit_un2480387367778600638or_num M3) N2)))) (not (tptp.pp (tptp.aa_Pro762926636801165566m_bool (tptp.accp_P3113834385874906142um_num tptp.bit_un2901131394128224187um_rel) (tptp.product_Pair_num_num (tptp.aa_num_num tptp.bit0 M3) _let_1)))))))))) (=> (forall ((M3 tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit1 M3))) (=> (= X _let_1) (=> (= Xa2 tptp.one) (=> (= Y (tptp.some_num (tptp.aa_num_num tptp.bit0 M3))) (not (tptp.pp (tptp.aa_Pro762926636801165566m_bool (tptp.accp_P3113834385874906142um_num tptp.bit_un2901131394128224187um_rel) (tptp.product_Pair_num_num _let_1 tptp.one))))))))) (=> (forall ((M3 tptp.num)) (=> (= X (tptp.aa_num_num tptp.bit1 M3)) (forall ((N2 tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 N2))) (=> (= Xa2 _let_1) (=> (= Y (tptp.some_num (tptp.case_option_num_num tptp.one tptp.bit1 (tptp.aa_num_option_num (tptp.aa_num6390622462783740633on_num tptp.bit_un2480387367778600638or_num M3) N2)))) (not (tptp.pp (tptp.aa_Pro762926636801165566m_bool (tptp.accp_P3113834385874906142um_num tptp.bit_un2901131394128224187um_rel) (tptp.product_Pair_num_num (tptp.aa_num_num tptp.bit1 M3) _let_1)))))))))) (not (forall ((M3 tptp.num)) (=> (= X (tptp.aa_num_num tptp.bit1 M3)) (forall ((N2 tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit1 N2))) (=> (= Xa2 _let_1) (=> (= Y (tptp.map_option_num_num tptp.bit0 (tptp.aa_num_option_num (tptp.aa_num6390622462783740633on_num tptp.bit_un2480387367778600638or_num M3) N2))) (not (tptp.pp (tptp.aa_Pro762926636801165566m_bool (tptp.accp_P3113834385874906142um_num tptp.bit_un2901131394128224187um_rel) (tptp.product_Pair_num_num (tptp.aa_num_num tptp.bit1 M3) _let_1)))))))))))))))))))))))) (forall ((X tptp.num) (Xa2 tptp.num) (Y tptp.option_num)) (let ((_let_1 (not (= Y (tptp.some_num tptp.one))))) (let ((_let_2 (= Xa2 tptp.one))) (let ((_let_3 (=> _let_2 _let_1))) (let ((_let_4 (not (= Y tptp.none_num)))) (let ((_let_5 (= X tptp.one))) (=> (= (tptp.aa_num_option_num (tptp.aa_num6390622462783740633on_num tptp.bit_un7362597486090784418nd_num X) Xa2) Y) (=> (=> _let_5 _let_3) (=> (=> _let_5 (=> (exists ((N2 tptp.num)) (= Xa2 (tptp.aa_num_num tptp.bit0 N2))) _let_4)) (=> (=> _let_5 (=> (exists ((N2 tptp.num)) (= Xa2 (tptp.aa_num_num tptp.bit1 N2))) _let_1)) (=> (=> (exists ((M3 tptp.num)) (= X (tptp.aa_num_num tptp.bit0 M3))) (=> _let_2 _let_4)) (=> (forall ((M3 tptp.num)) (=> (= X (tptp.aa_num_num tptp.bit0 M3)) (forall ((N2 tptp.num)) (=> (= Xa2 (tptp.aa_num_num tptp.bit0 N2)) (not (= Y (tptp.map_option_num_num tptp.bit0 (tptp.aa_num_option_num (tptp.aa_num6390622462783740633on_num tptp.bit_un7362597486090784418nd_num M3) N2)))))))) (=> (forall ((M3 tptp.num)) (=> (= X (tptp.aa_num_num tptp.bit0 M3)) (forall ((N2 tptp.num)) (=> (= Xa2 (tptp.aa_num_num tptp.bit1 N2)) (not (= Y (tptp.map_option_num_num tptp.bit0 (tptp.aa_num_option_num (tptp.aa_num6390622462783740633on_num tptp.bit_un7362597486090784418nd_num M3) N2)))))))) (=> (=> (exists ((M3 tptp.num)) (= X (tptp.aa_num_num tptp.bit1 M3))) _let_3) (=> (forall ((M3 tptp.num)) (=> (= X (tptp.aa_num_num tptp.bit1 M3)) (forall ((N2 tptp.num)) (=> (= Xa2 (tptp.aa_num_num tptp.bit0 N2)) (not (= Y (tptp.map_option_num_num tptp.bit0 (tptp.aa_num_option_num (tptp.aa_num6390622462783740633on_num tptp.bit_un7362597486090784418nd_num M3) N2)))))))) (not (forall ((M3 tptp.num)) (=> (= X (tptp.aa_num_num tptp.bit1 M3)) (forall ((N2 tptp.num)) (=> (= Xa2 (tptp.aa_num_num tptp.bit1 N2)) (not (= Y (tptp.case_o6005452278849405969um_num (tptp.some_num tptp.one) tptp.aTP_Lamm_xn (tptp.aa_num_option_num (tptp.aa_num6390622462783740633on_num tptp.bit_un7362597486090784418nd_num M3) N2)))))))))))))))))))))))) (= tptp.bit_un2901131394128224187um_rel tptp.bit_un3595099601533988841um_rel) (= tptp.bit_un2480387367778600638or_num tptp.bit_un6178654185764691216or_num) (= (tptp.aa_num_option_num (tptp.aa_num6390622462783740633on_num tptp.bit_un7362597486090784418nd_num tptp.one) tptp.one) (tptp.some_num tptp.one)) (forall ((M tptp.num) (N tptp.num)) (= (tptp.aa_num_option_num (tptp.aa_num6390622462783740633on_num tptp.bit_un7362597486090784418nd_num (tptp.aa_num_num tptp.bit0 M)) (tptp.aa_num_num tptp.bit0 N)) (tptp.map_option_num_num tptp.bit0 (tptp.aa_num_option_num (tptp.aa_num6390622462783740633on_num tptp.bit_un7362597486090784418nd_num M) N)))) (forall ((N tptp.num)) (= (tptp.aa_num_option_num (tptp.aa_num6390622462783740633on_num tptp.bit_un7362597486090784418nd_num tptp.one) (tptp.aa_num_num tptp.bit1 N)) (tptp.some_num tptp.one))) (forall ((M tptp.num)) (= (tptp.aa_num_option_num (tptp.aa_num6390622462783740633on_num tptp.bit_un7362597486090784418nd_num (tptp.aa_num_num tptp.bit1 M)) tptp.one) (tptp.some_num tptp.one))) (forall ((M tptp.num)) (= (tptp.aa_num_option_num (tptp.aa_num6390622462783740633on_num tptp.bit_un7362597486090784418nd_num (tptp.aa_num_num tptp.bit0 M)) tptp.one) tptp.none_num)) (forall ((N tptp.num)) (= (tptp.aa_num_option_num (tptp.aa_num6390622462783740633on_num tptp.bit_un7362597486090784418nd_num tptp.one) (tptp.aa_num_num tptp.bit0 N)) tptp.none_num)) (forall ((M tptp.num) (N tptp.num)) (= (tptp.aa_num_option_num (tptp.aa_num6390622462783740633on_num tptp.bit_un7362597486090784418nd_num (tptp.aa_num_num tptp.bit0 M)) (tptp.aa_num_num tptp.bit1 N)) (tptp.map_option_num_num tptp.bit0 (tptp.aa_num_option_num (tptp.aa_num6390622462783740633on_num tptp.bit_un7362597486090784418nd_num M) N)))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.aa_num_option_num (tptp.aa_num6390622462783740633on_num tptp.bit_un7362597486090784418nd_num (tptp.aa_num_num tptp.bit1 M)) (tptp.aa_num_num tptp.bit0 N)) (tptp.map_option_num_num tptp.bit0 (tptp.aa_num_option_num (tptp.aa_num6390622462783740633on_num tptp.bit_un7362597486090784418nd_num M) N)))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.aa_num_option_num (tptp.aa_num6390622462783740633on_num tptp.bit_un7362597486090784418nd_num (tptp.aa_num_num tptp.bit1 M)) (tptp.aa_num_num tptp.bit1 N)) (tptp.case_o6005452278849405969um_num (tptp.some_num tptp.one) tptp.aTP_Lamm_xn (tptp.aa_num_option_num (tptp.aa_num6390622462783740633on_num tptp.bit_un7362597486090784418nd_num M) N)))) (forall ((X tptp.num) (Xa2 tptp.num) (Y tptp.option_num)) (let ((_let_1 (= X tptp.one))) (let ((_let_2 (tptp.accp_P3113834385874906142um_num tptp.bit_un4731106466462545111um_rel))) (=> (= (tptp.aa_num_option_num (tptp.aa_num6390622462783740633on_num tptp.bit_un7362597486090784418nd_num X) Xa2) Y) (=> (tptp.pp (tptp.aa_Pro762926636801165566m_bool _let_2 (tptp.product_Pair_num_num X Xa2))) (=> (=> _let_1 (=> (= Xa2 tptp.one) (=> (= Y (tptp.some_num tptp.one)) (not (tptp.pp (tptp.aa_Pro762926636801165566m_bool _let_2 (tptp.product_Pair_num_num tptp.one tptp.one))))))) (=> (=> _let_1 (forall ((N2 tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 N2))) (=> (= Xa2 _let_1) (=> (= Y tptp.none_num) (not (tptp.pp (tptp.aa_Pro762926636801165566m_bool (tptp.accp_P3113834385874906142um_num tptp.bit_un4731106466462545111um_rel) (tptp.product_Pair_num_num tptp.one _let_1))))))))) (=> (=> _let_1 (forall ((N2 tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit1 N2))) (=> (= Xa2 _let_1) (=> (= Y (tptp.some_num tptp.one)) (not (tptp.pp (tptp.aa_Pro762926636801165566m_bool (tptp.accp_P3113834385874906142um_num tptp.bit_un4731106466462545111um_rel) (tptp.product_Pair_num_num tptp.one _let_1))))))))) (=> (forall ((M3 tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 M3))) (=> (= X _let_1) (=> (= Xa2 tptp.one) (=> (= Y tptp.none_num) (not (tptp.pp (tptp.aa_Pro762926636801165566m_bool (tptp.accp_P3113834385874906142um_num tptp.bit_un4731106466462545111um_rel) (tptp.product_Pair_num_num _let_1 tptp.one))))))))) (=> (forall ((M3 tptp.num)) (=> (= X (tptp.aa_num_num tptp.bit0 M3)) (forall ((N2 tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 N2))) (=> (= Xa2 _let_1) (=> (= Y (tptp.map_option_num_num tptp.bit0 (tptp.aa_num_option_num (tptp.aa_num6390622462783740633on_num tptp.bit_un7362597486090784418nd_num M3) N2))) (not (tptp.pp (tptp.aa_Pro762926636801165566m_bool (tptp.accp_P3113834385874906142um_num tptp.bit_un4731106466462545111um_rel) (tptp.product_Pair_num_num (tptp.aa_num_num tptp.bit0 M3) _let_1)))))))))) (=> (forall ((M3 tptp.num)) (=> (= X (tptp.aa_num_num tptp.bit0 M3)) (forall ((N2 tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit1 N2))) (=> (= Xa2 _let_1) (=> (= Y (tptp.map_option_num_num tptp.bit0 (tptp.aa_num_option_num (tptp.aa_num6390622462783740633on_num tptp.bit_un7362597486090784418nd_num M3) N2))) (not (tptp.pp (tptp.aa_Pro762926636801165566m_bool (tptp.accp_P3113834385874906142um_num tptp.bit_un4731106466462545111um_rel) (tptp.product_Pair_num_num (tptp.aa_num_num tptp.bit0 M3) _let_1)))))))))) (=> (forall ((M3 tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit1 M3))) (=> (= X _let_1) (=> (= Xa2 tptp.one) (=> (= Y (tptp.some_num tptp.one)) (not (tptp.pp (tptp.aa_Pro762926636801165566m_bool (tptp.accp_P3113834385874906142um_num tptp.bit_un4731106466462545111um_rel) (tptp.product_Pair_num_num _let_1 tptp.one))))))))) (=> (forall ((M3 tptp.num)) (=> (= X (tptp.aa_num_num tptp.bit1 M3)) (forall ((N2 tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 N2))) (=> (= Xa2 _let_1) (=> (= Y (tptp.map_option_num_num tptp.bit0 (tptp.aa_num_option_num (tptp.aa_num6390622462783740633on_num tptp.bit_un7362597486090784418nd_num M3) N2))) (not (tptp.pp (tptp.aa_Pro762926636801165566m_bool (tptp.accp_P3113834385874906142um_num tptp.bit_un4731106466462545111um_rel) (tptp.product_Pair_num_num (tptp.aa_num_num tptp.bit1 M3) _let_1)))))))))) (not (forall ((M3 tptp.num)) (=> (= X (tptp.aa_num_num tptp.bit1 M3)) (forall ((N2 tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit1 N2))) (=> (= Xa2 _let_1) (=> (= Y (tptp.case_o6005452278849405969um_num (tptp.some_num tptp.one) tptp.aTP_Lamm_xn (tptp.aa_num_option_num (tptp.aa_num6390622462783740633on_num tptp.bit_un7362597486090784418nd_num M3) N2))) (not (tptp.pp (tptp.aa_Pro762926636801165566m_bool (tptp.accp_P3113834385874906142um_num tptp.bit_un4731106466462545111um_rel) (tptp.product_Pair_num_num (tptp.aa_num_num tptp.bit1 M3) _let_1)))))))))))))))))))))))) (= tptp.bit_un7362597486090784418nd_num tptp.bit_un1837492267222099188nd_num) (= tptp.bit_un4731106466462545111um_rel tptp.bit_un5425074673868309765um_rel) (= tptp.field_5140801741446780682s_real (tptp.collect_real tptp.aTP_Lamm_xs)) (forall ((A tptp.int) (B2 tptp.int)) (let ((_let_1 (tptp.aa_int_int (tptp.divide_divide_int A) B2))) (let ((_let_2 (tptp.aa_int_rat (tptp.aa_int_fun_int_rat tptp.fract A) B2))) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_int_rat tptp.ring_1_of_int_rat _let_1)) _let_2)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat _let_2) (tptp.aa_int_rat tptp.ring_1_of_int_rat (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int _let_1) tptp.one_one_int)))))))) (forall ((X tptp.real)) (= (tptp.member_real (tptp.aa_real_real tptp.abs_abs_real X) tptp.field_5140801741446780682s_real) (tptp.member_real X tptp.field_5140801741446780682s_real))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int) (D tptp.int)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_int_rat (tptp.aa_int_fun_int_rat tptp.fract A) B2)) (tptp.aa_int_rat (tptp.aa_int_fun_int_rat tptp.fract C) D)) (tptp.aa_int_rat (tptp.aa_int_fun_int_rat tptp.fract (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B2) D)))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int) (D tptp.int)) (= (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_int_rat (tptp.aa_int_fun_int_rat tptp.fract A) B2)) (tptp.aa_int_rat (tptp.aa_int_fun_int_rat tptp.fract C) D)) (tptp.aa_int_rat (tptp.aa_int_fun_int_rat tptp.fract (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) D)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B2) C)))) (forall ((B2 tptp.int) (D tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B2) D))) (=> (not (= B2 tptp.zero_zero_int)) (=> (not (= D tptp.zero_zero_int)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_int_rat (tptp.aa_int_fun_int_rat tptp.fract A) B2)) (tptp.aa_int_rat (tptp.aa_int_fun_int_rat tptp.fract C) D))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) D)) _let_1)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int C) B2)) _let_1)))))))) (forall ((B2 tptp.int) (D tptp.int) (A tptp.int) (C tptp.int)) (=> (not (= B2 tptp.zero_zero_int)) (=> (not (= D tptp.zero_zero_int)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_int_rat (tptp.aa_int_fun_int_rat tptp.fract A) B2)) (tptp.aa_int_rat (tptp.aa_int_fun_int_rat tptp.fract C) D)) (tptp.aa_int_rat (tptp.aa_int_fun_int_rat tptp.fract (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) D)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int C) B2))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B2) D)))))) (forall ((B2 tptp.int) (D tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B2) D))) (=> (not (= B2 tptp.zero_zero_int)) (=> (not (= D tptp.zero_zero_int)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_int_rat (tptp.aa_int_fun_int_rat tptp.fract A) B2)) (tptp.aa_int_rat (tptp.aa_int_fun_int_rat tptp.fract C) D))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) D)) _let_1)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int C) B2)) _let_1)))))))) (forall ((B2 tptp.int) (D tptp.int) (A tptp.int) (C tptp.int)) (=> (not (= B2 tptp.zero_zero_int)) (=> (not (= D tptp.zero_zero_int)) (= (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_int_rat (tptp.aa_int_fun_int_rat tptp.fract A) B2)) (tptp.aa_int_rat (tptp.aa_int_fun_int_rat tptp.fract C) D)) (tptp.aa_int_rat (tptp.aa_int_fun_int_rat tptp.fract (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) D)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int C) B2))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B2) D)))))) (forall ((A tptp.int) (B2 tptp.int)) (= (tptp.aa_rat_rat tptp.sgn_sgn_rat (tptp.aa_int_rat (tptp.aa_int_fun_int_rat tptp.fract A) B2)) (tptp.aa_int_rat tptp.ring_1_of_int_rat (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int tptp.sgn_sgn_int A)) (tptp.aa_int_int tptp.sgn_sgn_int B2))))) (forall ((X tptp.real)) (exists ((X4 tptp.real)) (and (tptp.member_real X4 tptp.field_5140801741446780682s_real) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) X4))))) (forall ((X tptp.real)) (exists ((X4 tptp.real)) (and (tptp.member_real X4 tptp.field_5140801741446780682s_real) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X4) X))))) (forall ((X tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Y)) (exists ((X4 tptp.real)) (and (tptp.member_real X4 tptp.field_5140801741446780682s_real) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) X4)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X4) Y)))))) (forall ((P tptp.fun_rat_bool) (Q2 tptp.rat)) (=> (forall ((A3 tptp.int) (B3 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) B3)) (tptp.pp (tptp.aa_rat_bool P (tptp.aa_int_rat (tptp.aa_int_fun_int_rat tptp.fract A3) B3))))) (tptp.pp (tptp.aa_rat_bool P Q2)))) (forall ((B2 tptp.int) (D tptp.int) (A tptp.int) (C tptp.int)) (=> (not (= B2 tptp.zero_zero_int)) (=> (not (= D tptp.zero_zero_int)) (= (= (tptp.aa_int_rat (tptp.aa_int_fun_int_rat tptp.fract A) B2) (tptp.aa_int_rat (tptp.aa_int_fun_int_rat tptp.fract C) D)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) D) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int C) B2)))))) (forall ((C tptp.int) (A tptp.int) (B2 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.times_times_int C))) (=> (not (= C tptp.zero_zero_int)) (= (tptp.aa_int_rat (tptp.aa_int_fun_int_rat tptp.fract (tptp.aa_int_int _let_1 A)) (tptp.aa_int_int _let_1 B2)) (tptp.aa_int_rat (tptp.aa_int_fun_int_rat tptp.fract A) B2))))) (forall ((A tptp.int) (B2 tptp.int) (P2 tptp.int) (Q2 tptp.int)) (let ((_let_1 (tptp.aa_int_rat (tptp.aa_int_fun_int_rat tptp.fract A) B2))) (=> (= (tptp.quotient_of _let_1) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int P2) Q2)) (= (tptp.aa_int_rat (tptp.aa_int_fun_int_rat tptp.fract P2) Q2) _let_1)))) (forall ((A tptp.int) (B2 tptp.int) (P2 tptp.int) (Q2 tptp.int)) (=> (= (tptp.aa_Pro6970504127699319548nt_int tptp.normalize (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int A) B2)) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int P2) Q2)) (= (tptp.aa_int_rat (tptp.aa_int_fun_int_rat tptp.fract P2) Q2) (tptp.aa_int_rat (tptp.aa_int_fun_int_rat tptp.fract A) B2)))) (forall ((K tptp.num)) (= (tptp.aa_num_rat tptp.numeral_numeral_rat K) (tptp.aa_int_rat (tptp.aa_int_fun_int_rat tptp.fract (tptp.aa_num_int tptp.numeral_numeral_int K)) tptp.one_one_int))) (forall ((W tptp.num)) (= (tptp.aa_int_rat (tptp.aa_int_fun_int_rat tptp.fract (tptp.aa_num_int tptp.numeral_numeral_int W)) tptp.one_one_int) (tptp.aa_num_rat tptp.numeral_numeral_rat W))) (forall ((A tptp.int) (B2 tptp.int)) (= (tptp.quotient_of (tptp.aa_int_rat (tptp.aa_int_fun_int_rat tptp.fract A) B2)) (tptp.aa_Pro6970504127699319548nt_int tptp.normalize (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int A) B2)))) (forall ((B2 tptp.int) (A tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int))) (=> (tptp.pp (tptp.aa_int_bool _let_1 B2)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) (tptp.aa_int_rat (tptp.aa_int_fun_int_rat tptp.fract A) B2))) (tptp.pp (tptp.aa_int_bool _let_1 A)))))) (forall ((B2 tptp.int) (A tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) B2)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_int_rat (tptp.aa_int_fun_int_rat tptp.fract A) B2)) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) tptp.zero_zero_int))))) (forall ((B2 tptp.int) (A tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) B2)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.one_one_rat) (tptp.aa_int_rat (tptp.aa_int_fun_int_rat tptp.fract A) B2))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B2) A))))) (forall ((B2 tptp.int) (A tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) B2)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_int_rat (tptp.aa_int_fun_int_rat tptp.fract A) B2)) tptp.one_one_rat)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B2))))) (= tptp.field_5140801741446780682s_real (tptp.collect_real tptp.aTP_Lamm_xt)) (forall ((B2 tptp.int) (A tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) B2)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_int_rat (tptp.aa_int_fun_int_rat tptp.fract A) B2)) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) tptp.zero_zero_int))))) (forall ((B2 tptp.int) (A tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) B2)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_int_rat (tptp.aa_int_fun_int_rat tptp.fract A) B2))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) A))))) (forall ((B2 tptp.int) (A tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) B2)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_int_rat (tptp.aa_int_fun_int_rat tptp.fract A) B2)) tptp.one_one_rat)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B2))))) (forall ((B2 tptp.int) (A tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) B2)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.one_one_rat) (tptp.aa_int_rat (tptp.aa_int_fun_int_rat tptp.fract A) B2))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B2) A))))) (forall ((K tptp.num)) (= (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat K)) (tptp.aa_int_rat (tptp.aa_int_fun_int_rat tptp.fract (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int K))) tptp.one_one_int))) (forall ((W tptp.num)) (= (tptp.aa_int_rat (tptp.aa_int_fun_int_rat tptp.fract (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int W))) tptp.one_one_int) (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat W)))) (forall ((C tptp.nat) (Y tptp.nat) (X tptp.nat)) (let ((_let_1 (tptp.image_nat_nat (tptp.aa_nat_fun_nat_nat tptp.aTP_Lamm_xu C) (tptp.set_or4665077453230672383an_nat X Y)))) (let ((_let_2 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Y)))) (let ((_let_3 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat C) Y)))) (and (=> _let_3 (= _let_1 (tptp.set_or4665077453230672383an_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat X) C) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Y) C)))) (=> (not _let_3) (and (=> _let_2 (= _let_1 (tptp.insert_nat tptp.zero_zero_nat tptp.bot_bot_set_nat))) (=> (not _let_2) (= _let_1 tptp.bot_bot_set_nat))))))))) (= tptp.semiri1316708129612266289at_nat tptp.id_nat) (forall ((M7 tptp.set_nat) (N3 tptp.set_nat)) (= (tptp.pp (tptp.aa_set_nat_bool (tptp.bij_betw_nat_nat tptp.suc M7) N3)) (= (tptp.image_nat_nat tptp.suc M7) N3))) (= tptp.ord_less_int (tptp.map_fu2743658913401090412t_bool tptp.rep_Integ _let_34 _let_8)) (= tptp.ord_less_eq_int (tptp.map_fu2743658913401090412t_bool tptp.rep_Integ _let_34 _let_6)) (= tptp.nat2 (tptp.map_fu2345160673673942751at_nat tptp.rep_Integ tptp.id_nat _let_12)) (forall ((A tptp.int) (B2 tptp.int)) (= (tptp.pp (tptp.aa_rat_bool tptp.positive (tptp.aa_int_rat (tptp.aa_int_fun_int_rat tptp.fract A) B2))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) B2))))) (forall ((X7 tptp.set_real)) (= (tptp.comple4887499456419720421f_real X7) (tptp.aa_real_real tptp.uminus_uminus_real (tptp.comple1385675409528146559p_real (tptp.image_real_real tptp.uminus_uminus_real X7))))) (forall ((X tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool tptp.positive X)) (=> (tptp.pp (tptp.aa_rat_bool tptp.positive Y)) (tptp.pp (tptp.aa_rat_bool tptp.positive (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat X) Y)))))) (forall ((S2 tptp.set_int)) (= (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int S2)) (exists ((K2 tptp.int)) (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int (tptp.image_int_int tptp.abs_abs_int S2)) (tptp.set_ord_atMost_int K2)))))) (forall ((S2 tptp.set_int)) (= (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int S2)) (exists ((K2 tptp.int)) (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int (tptp.image_int_int tptp.abs_abs_int S2)) (tptp.set_ord_lessThan_int K2)))))) (forall ((X7 tptp.fun_nat_real)) (=> (tptp.summable_real X7) (=> (forall ((I3 tptp.nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_nat_real X7 I3)))) (= (tptp.suminf_real X7) (tptp.comple1385675409528146559p_real (tptp.image_nat_real (tptp.aTP_Lamm_xv X7) tptp.top_top_set_nat)))))) (forall ((X tptp.rat) (Y tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) Y)) (tptp.pp (tptp.aa_rat_bool tptp.positive (tptp.aa_rat_rat (tptp.minus_minus_rat Y) X))))) (forall ((U tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) U)) (= (tptp.aa_int_set_int (tptp.aa_int8639817059373041269et_int tptp.set_or4662586982721622107an_int tptp.zero_zero_int) U) (tptp.image_nat_int tptp.semiri1314217659103216013at_int (tptp.set_ord_lessThan_nat (tptp.aa_int_nat tptp.nat2 U)))))) (forall ((N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (= (tptp.image_nat_nat (tptp.aa_nat_fun_nat_nat tptp.aTP_Lamm_xw N) tptp.top_top_set_nat) (tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat N)))) (forall ((X tptp.rat)) (let ((_let_1 (tptp.aa_rat7754553326175492643nt_int tptp.rep_Rat X))) (= (tptp.pp (tptp.aa_rat_bool tptp.positive X)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.product_fst_int_int _let_1)) (tptp.product_snd_int_int _let_1))))))) (= (tptp.finite_card_bool tptp.top_top_set_bool) _let_33) (forall ((A tptp.real)) (let ((_let_1 (tptp.image_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) tptp.top_top_set_real))) (let ((_let_2 (= A tptp.zero_zero_real))) (and (=> _let_2 (= _let_1 (tptp.insert_real tptp.zero_zero_real tptp.bot_bot_set_real))) (=> (not _let_2) (= _let_1 tptp.top_top_set_real)))))) (= tptp.positive (tptp.map_fu5118516228767806217l_bool tptp.rep_Rat tptp.id_bool tptp.aTP_Lamm_xx)) (forall ((N tptp.nat) (X tptp.real)) (let ((_let_1 (tptp.aa_real_real (tptp.aa_nat_fun_real_real tptp.root N) X))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.zero_zero_real)) (=> (not _let_2) (= _let_1 (tptp.aa_real_real (tptp.the_in5290026491893676941l_real tptp.top_top_set_real (tptp.aa_nat_fun_real_real tptp.aTP_Lamm_xy N)) X))))))) (= (tptp.finite_card_char tptp.top_top_set_char) _let_26) (= tptp.top_top_set_char (tptp.image_nat_char tptp.unique3096191561947761185of_nat _let_27)) (forall ((C tptp.char)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_char_nat tptp.comm_s629917340098488124ar_nat C)) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit0 tptp.one)))))))))))) (= (tptp.image_char_nat tptp.comm_s629917340098488124ar_nat tptp.top_top_set_char) _let_27) (forall ((B0 tptp.bool) (B1 tptp.bool) (B22 tptp.bool) (B32 tptp.bool) (B42 tptp.bool) (B52 tptp.bool) (B62 tptp.bool) (B72 tptp.bool)) (let ((_let_1 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.integer_of_char (tptp.char2 B0 B1 B22 B32 B42 B52 B62 B72)) (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.zero_n356916108424825756nteger B72)) _let_1) (tptp.zero_n356916108424825756nteger B62))) _let_1) (tptp.zero_n356916108424825756nteger B52))) _let_1) (tptp.zero_n356916108424825756nteger B42))) _let_1) (tptp.zero_n356916108424825756nteger B32))) _let_1) (tptp.zero_n356916108424825756nteger B22))) _let_1) (tptp.zero_n356916108424825756nteger B1))) _let_1) (tptp.zero_n356916108424825756nteger B0))))) (forall ((X tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Y)) (exists ((Q3 tptp.rat)) (let ((_let_1 (tptp.aa_rat_real tptp.field_7254667332652039916t_real Q3))) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) _let_1)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real _let_1) Y))))))) (= tptp.plus_plus_rat (tptp.map_fu5968964422797239547at_rat tptp.rep_Rat _let_32 tptp.aTP_Lamm_xz)) (= tptp.inverse_inverse_rat (tptp.aa_fun7041730090766645614at_rat _let_32 tptp.aTP_Lamm_ya)) (forall ((C tptp.char)) (= (tptp.aa_char_nat tptp.comm_s629917340098488124ar_nat (tptp.ascii_of C)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se2925701944663578781it_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit1 tptp.one)))) (tptp.aa_char_nat tptp.comm_s629917340098488124ar_nat C)))) (= tptp.one_one_rat (tptp.aa_Pro6166618844887768661nt_rat tptp.abs_Rat _let_18)) (forall ((Xa2 tptp.int) (X tptp.int)) (= (tptp.aa_int_rat (tptp.aa_int_fun_int_rat tptp.fract Xa2) X) (tptp.aa_Pro6166618844887768661nt_rat tptp.abs_Rat (tptp.aa_Pro6970504127699319548nt_int (tptp.if_Pro3027730157355071871nt_int (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.fequal_int X) tptp.zero_zero_int) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int)) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int Xa2) X))))) (= tptp.zero_zero_rat (tptp.aa_Pro6166618844887768661nt_rat tptp.abs_Rat _let_17)) (= tptp.uminus_uminus_rat (tptp.aa_fun7041730090766645614at_rat _let_32 tptp.aTP_Lamm_yb)) (= tptp.times_times_rat (tptp.map_fu5968964422797239547at_rat tptp.rep_Rat _let_32 tptp.aTP_Lamm_yc)) (forall ((J tptp.int) (I tptp.int) (Js tptp.list_int)) (let ((_let_1 (tptp.upto_aux I J Js))) (let ((_let_2 (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int J) I)))) (and (=> _let_2 (= _let_1 Js)) (=> (not _let_2) (= _let_1 (tptp.upto_aux I (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int J) tptp.one_one_int) (tptp.cons_int J Js)))))))) (forall ((X tptp.int) (Xa2 tptp.int) (Y tptp.list_int)) (let ((_let_1 (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.accp_P1096762738010456898nt_int tptp.upto_rel) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int X) Xa2))))) (let ((_let_2 (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X) Xa2)))) (=> (= (tptp.upto X Xa2) Y) (=> _let_1 (not (=> (and (=> _let_2 (= Y (tptp.cons_int X (tptp.upto (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int X) tptp.one_one_int) Xa2)))) (=> (not _let_2) (= Y tptp.nil_int))) (not _let_1)))))))) (forall ((J tptp.int) (I tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int J) I)) (= (tptp.upto I J) tptp.nil_int))) (forall ((I tptp.int) (J tptp.int)) (= (= tptp.nil_int (tptp.upto I J)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int J) I)))) (forall ((I tptp.int) (J tptp.int)) (= (= (tptp.upto I J) tptp.nil_int) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int J) I)))) (forall ((I tptp.int) (K tptp.nat) (J tptp.int)) (let ((_let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int I) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int K)))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int _let_1) J)) (= (tptp.aa_nat_int (tptp.nth_int (tptp.upto I J)) K) _let_1)))) (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int N))) (let ((_let_2 (tptp.aa_num_int tptp.numeral_numeral_int M))) (let ((_let_3 (tptp.upto _let_2 _let_1))) (let ((_let_4 (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int _let_2) _let_1)))) (and (=> _let_4 (= _let_3 (tptp.cons_int _let_2 (tptp.upto (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int _let_2) tptp.one_one_int) _let_1)))) (=> (not _let_4) (= _let_3 tptp.nil_int)))))))) (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int N)))) (let ((_let_2 (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int M)))) (let ((_let_3 (tptp.upto _let_2 _let_1))) (let ((_let_4 (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int _let_2) _let_1)))) (and (=> _let_4 (= _let_3 (tptp.cons_int _let_2 (tptp.upto (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int _let_2) tptp.one_one_int) _let_1)))) (=> (not _let_4) (= _let_3 tptp.nil_int)))))))) (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int N))) (let ((_let_2 (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int M)))) (let ((_let_3 (tptp.upto _let_2 _let_1))) (let ((_let_4 (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int _let_2) _let_1)))) (and (=> _let_4 (= _let_3 (tptp.cons_int _let_2 (tptp.upto (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int _let_2) tptp.one_one_int) _let_1)))) (=> (not _let_4) (= _let_3 tptp.nil_int)))))))) (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int N)))) (let ((_let_2 (tptp.aa_num_int tptp.numeral_numeral_int M))) (let ((_let_3 (tptp.upto _let_2 _let_1))) (let ((_let_4 (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int _let_2) _let_1)))) (and (=> _let_4 (= _let_3 (tptp.cons_int _let_2 (tptp.upto (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int _let_2) tptp.one_one_int) _let_1)))) (=> (not _let_4) (= _let_3 tptp.nil_int)))))))) (forall ((I tptp.int) (J tptp.int)) (= (tptp.aa_int_set_int (tptp.aa_int8639817059373041269et_int tptp.set_or1266510415728281911st_int I) J) (tptp.set_int2 (tptp.upto I J)))) (forall ((I tptp.int) (J tptp.int) (K tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int I) J)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int J) K)) (= (tptp.upto I K) (tptp.append_int (tptp.upto I J) (tptp.upto (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int J) tptp.one_one_int) K)))))) (forall ((I tptp.int) (J tptp.int) (K tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int I) J)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int J) K)) (= (tptp.upto I K) (tptp.append_int (tptp.upto I (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int J) tptp.one_one_int)) (tptp.upto J K)))))) (forall ((I tptp.int) (J tptp.int)) (= (tptp.aa_int_set_int (tptp.aa_int8639817059373041269et_int tptp.set_or4662586982721622107an_int I) J) (tptp.set_int2 (tptp.upto I (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int J) tptp.one_one_int))))) (forall ((I tptp.int) (J tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int I) J)) (= (tptp.upto I J) (tptp.cons_int I (tptp.upto (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int I) tptp.one_one_int) J))))) (forall ((I tptp.int) (J tptp.int)) (let ((_let_1 (tptp.upto I J))) (let ((_let_2 (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int I) J)))) (and (=> _let_2 (= _let_1 (tptp.cons_int I (tptp.upto (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int I) tptp.one_one_int) J)))) (=> (not _let_2) (= _let_1 tptp.nil_int)))))) (forall ((X tptp.int) (Xa2 tptp.int) (Y tptp.list_int)) (let ((_let_1 (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X) Xa2)))) (=> (= (tptp.upto X Xa2) Y) (and (=> _let_1 (= Y (tptp.cons_int X (tptp.upto (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int X) tptp.one_one_int) Xa2)))) (=> (not _let_1) (= Y tptp.nil_int)))))) (forall ((I tptp.int) (J tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int I) J)) (= (tptp.upto I J) (tptp.append_int (tptp.upto I (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int J) tptp.one_one_int)) (tptp.cons_int J tptp.nil_int))))) (forall ((I tptp.int) (J tptp.int) (K tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int I) J)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int J) K)) (= (tptp.upto I K) (tptp.append_int (tptp.upto I (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int J) tptp.one_one_int)) (tptp.cons_int J (tptp.upto (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int J) tptp.one_one_int) K))))))) (forall ((I tptp.int) (J tptp.int)) (let ((_let_1 (tptp.upto I J))) (let ((_let_2 (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int I) J)))) (=> (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.accp_P1096762738010456898nt_int tptp.upto_rel) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int I) J))) (and (=> _let_2 (= _let_1 (tptp.cons_int I (tptp.upto (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int I) tptp.one_one_int) J)))) (=> (not _let_2) (= _let_1 tptp.nil_int))))))) (forall ((Xa2 tptp.product_prod_int_int) (X tptp.product_prod_int_int)) (let ((_let_1 (tptp.product_snd_int_int X))) (let ((_let_2 (tptp.product_snd_int_int Xa2))) (=> (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.aa_Pro1534211998248933470t_bool tptp.ratrel Xa2) Xa2)) (=> (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.aa_Pro1534211998248933470t_bool tptp.ratrel X) X)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_Pro6166618844887768661nt_rat tptp.abs_Rat Xa2)) (tptp.aa_Pro6166618844887768661nt_rat tptp.abs_Rat X)) (tptp.aa_Pro6166618844887768661nt_rat tptp.abs_Rat (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.product_fst_int_int Xa2)) _let_1)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.product_fst_int_int X)) _let_2))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int _let_2) _let_1))))))))) (forall ((X tptp.product_prod_int_int) (Y tptp.product_prod_int_int)) (let ((_let_1 (tptp.product_snd_int_int X))) (let ((_let_2 (tptp.product_snd_int_int Y))) (= (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.aa_Pro1534211998248933470t_bool tptp.ratrel X) Y)) (and (not (= _let_1 tptp.zero_zero_int)) (not (= _let_2 tptp.zero_zero_int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.product_fst_int_int X)) _let_2) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.product_fst_int_int Y)) _let_1))))))) (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.aa_Pro1534211998248933470t_bool tptp.ratrel _let_18) _let_18)) (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.aa_Pro1534211998248933470t_bool tptp.ratrel _let_17) _let_17)) (forall ((X5 tptp.product_prod_int_int) (Xa tptp.product_prod_int_int)) (let ((_let_1 (tptp.product_snd_int_int X5))) (let ((_let_2 (tptp.product_snd_int_int Xa))) (= (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.aa_Pro1534211998248933470t_bool tptp.ratrel X5) Xa)) (and (not (= _let_1 tptp.zero_zero_int)) (not (= _let_2 tptp.zero_zero_int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.product_fst_int_int X5)) _let_2) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.product_fst_int_int Xa)) _let_1))))))) (forall ((X tptp.product_prod_int_int)) (=> (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.aa_Pro1534211998248933470t_bool tptp.ratrel X) X)) (= (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_Pro6166618844887768661nt_rat tptp.abs_Rat X)) (tptp.aa_Pro6166618844887768661nt_rat tptp.abs_Rat (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.product_fst_int_int X))) (tptp.product_snd_int_int X)))))) (forall ((Xa2 tptp.product_prod_int_int) (X tptp.product_prod_int_int)) (=> (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.aa_Pro1534211998248933470t_bool tptp.ratrel Xa2) Xa2)) (=> (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.aa_Pro1534211998248933470t_bool tptp.ratrel X) X)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_Pro6166618844887768661nt_rat tptp.abs_Rat Xa2)) (tptp.aa_Pro6166618844887768661nt_rat tptp.abs_Rat X)) (tptp.aa_Pro6166618844887768661nt_rat tptp.abs_Rat (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.product_fst_int_int Xa2)) (tptp.product_fst_int_int X))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.product_snd_int_int Xa2)) (tptp.product_snd_int_int X)))))))) (forall ((X tptp.product_prod_int_int)) (=> (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.aa_Pro1534211998248933470t_bool tptp.ratrel X) X)) (= (tptp.pp (tptp.aa_rat_bool tptp.positive (tptp.aa_Pro6166618844887768661nt_rat tptp.abs_Rat X))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.product_fst_int_int X)) (tptp.product_snd_int_int X))))))) (forall ((X tptp.product_prod_int_int)) (let ((_let_1 (tptp.product_fst_int_int X))) (=> (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.aa_Pro1534211998248933470t_bool tptp.ratrel X) X)) (= (tptp.aa_rat_rat tptp.inverse_inverse_rat (tptp.aa_Pro6166618844887768661nt_rat tptp.abs_Rat X)) (tptp.aa_Pro6166618844887768661nt_rat tptp.abs_Rat (tptp.aa_Pro6970504127699319548nt_int (tptp.if_Pro3027730157355071871nt_int (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.fequal_int _let_1) tptp.zero_zero_int) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int)) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int (tptp.product_snd_int_int X)) _let_1))))))) (forall ((N tptp.nat) (X tptp.real)) (let ((_let_1 (tptp.aa_nat_fun_real_real tptp.root N))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) tptp.zero_zero_real)) (tptp.has_fi5821293074295781190e_real _let_1 (tptp.aa_real_real tptp.inverse_inverse_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real _let_1 X)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat))))) (tptp.topolo2177554685111907308n_real X tptp.top_top_set_real))))))) (forall ((N tptp.nat) (X tptp.real) (D4 tptp.real)) (let ((_let_1 (tptp.aa_nat_fun_real_real tptp.root N))) (let ((_let_2 (tptp.aa_real_real tptp.inverse_inverse_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real _let_1 X)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat))))))) (let ((_let_3 (= D4 _let_2))) (let ((_let_4 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N)))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (=> (not (= X tptp.zero_zero_real)) (=> (=> _let_4 (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) X)) _let_3)) (=> (=> _let_4 (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) tptp.zero_zero_real)) (= D4 (tptp.aa_real_real tptp.uminus_uminus_real _let_2)))) (=> (=> (not _let_4) _let_3) (tptp.has_fi5821293074295781190e_real _let_1 D4 (tptp.topolo2177554685111907308n_real X tptp.top_top_set_real)))))))))))) (forall ((A tptp.real) (B2 tptp.real) (F tptp.fun_real_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B2)) (=> (forall ((X4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) X4)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X4) B2)) (exists ((Y5 tptp.real)) (and (tptp.has_fi5821293074295781190e_real F Y5 (tptp.topolo2177554685111907308n_real X4 tptp.top_top_set_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y5) tptp.zero_zero_real))))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real F B2)) (tptp.aa_real_real F A)))))) (forall ((A tptp.real) (B2 tptp.real) (F tptp.fun_real_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B2)) (=> (forall ((X4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) X4)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X4) B2)) (exists ((Y5 tptp.real)) (and (tptp.has_fi5821293074295781190e_real F Y5 (tptp.topolo2177554685111907308n_real X4 tptp.top_top_set_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) Y5))))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real F A)) (tptp.aa_real_real F B2)))))) (forall ((A tptp.real) (B2 tptp.real) (G tptp.fun_real_real) (G2 tptp.fun_real_real)) (=> (forall ((X4 tptp.real)) (=> (tptp.member_real X4 (tptp.set_or1222579329274155063t_real A B2)) (tptp.has_fi5821293074295781190e_real G (tptp.aa_real_real G2 X4) (tptp.topolo2177554685111907308n_real X4 tptp.top_top_set_real)))) (=> (forall ((X4 tptp.real)) (=> (tptp.member_real X4 (tptp.set_or1222579329274155063t_real A B2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_real_real G2 X4))))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) B2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real G A)) (tptp.aa_real_real G B2))))))) (forall ((A tptp.real) (B2 tptp.real) (F tptp.fun_real_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) B2)) (=> (forall ((X4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) X4)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X4) B2)) (exists ((Y5 tptp.real)) (and (tptp.has_fi5821293074295781190e_real F Y5 (tptp.topolo2177554685111907308n_real X4 tptp.top_top_set_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) Y5))))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real F A)) (tptp.aa_real_real F B2)))))) (forall ((A tptp.real) (B2 tptp.real) (F tptp.fun_real_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) B2)) (=> (forall ((X4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) X4)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X4) B2)) (exists ((Y5 tptp.real)) (and (tptp.has_fi5821293074295781190e_real F Y5 (tptp.topolo2177554685111907308n_real X4 tptp.top_top_set_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y5) tptp.zero_zero_real))))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real F B2)) (tptp.aa_real_real F A)))))) (forall ((A tptp.real) (B2 tptp.real) (F tptp.fun_real_real) (K tptp.real)) (=> (not (= A B2)) (=> (forall ((X4 tptp.real)) (tptp.has_fi5821293074295781190e_real F K (tptp.topolo2177554685111907308n_real X4 tptp.top_top_set_real))) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real F B2)) (tptp.aa_real_real F A)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real B2) A)) K))))) (forall ((F tptp.fun_real_real) (L tptp.real) (X tptp.real) (S2 tptp.set_real)) (=> (tptp.has_fi5821293074295781190e_real F L (tptp.topolo2177554685111907308n_real X S2)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) L)) (exists ((D2 tptp.real)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) D2)) (forall ((H3 tptp.real)) (let ((_let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real X) H3))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) H3)) (=> (tptp.member_real _let_1 S2) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real H3) D2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real F _let_1)) (tptp.aa_real_real F X))))))))))))) (forall ((F tptp.fun_real_real) (L tptp.real) (X tptp.real) (S2 tptp.set_real)) (=> (tptp.has_fi5821293074295781190e_real F L (tptp.topolo2177554685111907308n_real X S2)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real L) tptp.zero_zero_real)) (exists ((D2 tptp.real)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) D2)) (forall ((H3 tptp.real)) (let ((_let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real X) H3))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) H3)) (=> (tptp.member_real _let_1 S2) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real H3) D2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real F X)) (tptp.aa_real_real F _let_1))))))))))))) (forall ((F tptp.fun_real_real) (L tptp.real) (X tptp.real) (S2 tptp.set_real)) (=> (tptp.has_fi5821293074295781190e_real F L (tptp.topolo2177554685111907308n_real X S2)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) L)) (exists ((D2 tptp.real)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) D2)) (forall ((H3 tptp.real)) (let ((_let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) H3))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) H3)) (=> (tptp.member_real _let_1 S2) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real H3) D2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real F X)) (tptp.aa_real_real F _let_1))))))))))))) (forall ((F tptp.fun_real_real) (L tptp.real) (X tptp.real) (S2 tptp.set_real)) (=> (tptp.has_fi5821293074295781190e_real F L (tptp.topolo2177554685111907308n_real X S2)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real L) tptp.zero_zero_real)) (exists ((D2 tptp.real)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) D2)) (forall ((H3 tptp.real)) (let ((_let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) H3))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) H3)) (=> (tptp.member_real _let_1 S2) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real H3) D2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real F _let_1)) (tptp.aa_real_real F X))))))))))))) (forall ((F tptp.fun_real_real) (L tptp.real) (X tptp.real)) (=> (tptp.has_fi5821293074295781190e_real F L (tptp.topolo2177554685111907308n_real X tptp.top_top_set_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) L)) (exists ((D2 tptp.real)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) D2)) (forall ((H3 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) H3)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real H3) D2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real F X)) (tptp.aa_real_real F (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) H3)))))))))))) (forall ((F tptp.fun_real_real) (L tptp.real) (X tptp.real)) (=> (tptp.has_fi5821293074295781190e_real F L (tptp.topolo2177554685111907308n_real X tptp.top_top_set_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real L) tptp.zero_zero_real)) (exists ((D2 tptp.real)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) D2)) (forall ((H3 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) H3)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real H3) D2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real F (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) H3))) (tptp.aa_real_real F X))))))))))) (forall ((F tptp.fun_real_real) (L tptp.real) (X tptp.real)) (=> (tptp.has_fi5821293074295781190e_real F L (tptp.topolo2177554685111907308n_real X tptp.top_top_set_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real L) tptp.zero_zero_real)) (exists ((D2 tptp.real)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) D2)) (forall ((H3 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) H3)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real H3) D2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real F X)) (tptp.aa_real_real F (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real X) H3)))))))))))) (forall ((F tptp.fun_real_real) (L tptp.real) (X tptp.real)) (=> (tptp.has_fi5821293074295781190e_real F L (tptp.topolo2177554685111907308n_real X tptp.top_top_set_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) L)) (exists ((D2 tptp.real)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) D2)) (forall ((H3 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) H3)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real H3) D2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real F (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real X) H3))) (tptp.aa_real_real F X))))))))))) (forall ((A tptp.real) (B2 tptp.real) (F tptp.fun_real_real) (F3 tptp.fun_real_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B2)) (=> (forall ((X4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) X4)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X4) B2)) (tptp.has_fi5821293074295781190e_real F (tptp.aa_real_real F3 X4) (tptp.topolo2177554685111907308n_real X4 tptp.top_top_set_real))))) (exists ((Z4 tptp.real)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) Z4)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Z4) B2)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real F B2)) (tptp.aa_real_real F A)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real B2) A)) (tptp.aa_real_real F3 Z4)))))))) (forall ((F tptp.fun_real_real) (L tptp.real) (X tptp.real) (D tptp.real)) (=> (tptp.has_fi5821293074295781190e_real F L (tptp.topolo2177554685111907308n_real X tptp.top_top_set_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) D)) (=> (forall ((Y4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real X) Y4))) D)) (= (tptp.aa_real_real F X) (tptp.aa_real_real F Y4)))) (= L tptp.zero_zero_real))))) (forall ((X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) X)) (tptp.has_fi5821293074295781190e_real tptp.ln_ln_real (tptp.aa_real_real tptp.inverse_inverse_real X) (tptp.topolo2177554685111907308n_real X tptp.top_top_set_real)))) (forall ((A tptp.real) (B2 tptp.real) (V tptp.fun_real_real) (K tptp.real)) (let ((_let_1 (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (not (= A B2)) (=> (forall ((X4 tptp.real)) (tptp.has_fi5821293074295781190e_real V K (tptp.topolo2177554685111907308n_real X4 tptp.top_top_set_real))) (= (tptp.aa_real_real V (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) B2)) _let_1)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real V A)) (tptp.aa_real_real V B2))) _let_1)))))) (forall ((F tptp.fun_real_real) (L tptp.real) (X tptp.real) (D tptp.real)) (=> (tptp.has_fi5821293074295781190e_real F L (tptp.topolo2177554685111907308n_real X tptp.top_top_set_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) D)) (=> (forall ((Y4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real X) Y4))) D)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real F Y4)) (tptp.aa_real_real F X))))) (= L tptp.zero_zero_real))))) (forall ((F tptp.fun_real_real) (L tptp.real) (X tptp.real) (D tptp.real)) (=> (tptp.has_fi5821293074295781190e_real F L (tptp.topolo2177554685111907308n_real X tptp.top_top_set_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) D)) (=> (forall ((Y4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real X) Y4))) D)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real F X)) (tptp.aa_real_real F Y4))))) (= L tptp.zero_zero_real))))) (forall ((X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) X)) (tptp.has_fi5821293074295781190e_real tptp.ln_ln_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.one_one_real) X) (tptp.topolo2177554685111907308n_real X tptp.top_top_set_real)))) (forall ((N tptp.nat) (X tptp.real) (S tptp.set_real)) (tptp.has_fi5821293074295781190e_real (tptp.aa_nat_fun_real_real tptp.aTP_Lamm_yd N) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)))) (tptp.topolo2177554685111907308n_real X S))) (forall ((G tptp.fun_real_real) (M tptp.real) (X tptp.real) (N tptp.nat)) (let ((_let_1 (tptp.topolo2177554685111907308n_real X tptp.top_top_set_real))) (=> (tptp.has_fi5821293074295781190e_real G M _let_1) (tptp.has_fi5821293074295781190e_real (tptp.aa_nat_fun_real_real (tptp.aTP_Lamm_ye G) N) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real G X)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) tptp.one_one_nat)))) M) _let_1)))) (forall ((Z tptp.real) (R tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) Z)) (tptp.has_fi5821293074295781190e_real (tptp.aa_rea7340605660300375871l_real tptp.aTP_Lamm_yf R) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real R) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.powr_real Z) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real R) tptp.one_one_real))) (tptp.topolo2177554685111907308n_real Z tptp.top_top_set_real)))) (forall ((X tptp.real) (B2 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) X)) (tptp.has_fi5821293074295781190e_real (tptp.aa_rea7340605660300375871l_real tptp.log B2) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.one_one_real) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real tptp.ln_ln_real B2)) X)) (tptp.topolo2177554685111907308n_real X tptp.top_top_set_real)))) (forall ((G tptp.fun_real_real) (M tptp.real) (X tptp.real) (R tptp.real)) (let ((_let_1 (tptp.topolo2177554685111907308n_real X tptp.top_top_set_real))) (let ((_let_2 (tptp.aa_real_real G X))) (=> (tptp.has_fi5821293074295781190e_real G M _let_1) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) _let_2)) (tptp.has_fi5821293074295781190e_real (tptp.aa_rea7340605660300375871l_real (tptp.aTP_Lamm_yg G) R) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real R) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.powr_real _let_2) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real R) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real tptp.one_one_nat))))) M) _let_1)))))) (forall ((G tptp.fun_real_real) (M tptp.real) (X tptp.real) (F tptp.fun_real_real) (R tptp.real)) (let ((_let_1 (tptp.topolo2177554685111907308n_real X tptp.top_top_set_real))) (let ((_let_2 (tptp.aa_real_real G X))) (let ((_let_3 (tptp.aa_real_real F X))) (=> (tptp.has_fi5821293074295781190e_real G M _let_1) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) _let_2)) (=> (tptp.has_fi5821293074295781190e_real F R _let_1) (tptp.has_fi5821293074295781190e_real (tptp.aa_fun6946558556880649704l_real (tptp.aTP_Lamm_yh G) F) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.powr_real _let_2) _let_3)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real R) (tptp.aa_real_real tptp.ln_ln_real _let_2))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real M) _let_3)) _let_2))) _let_1)))))))) (forall ((X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) X)) (tptp.has_fi5821293074295781190e_real tptp.sqrt (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real tptp.inverse_inverse_real (tptp.aa_real_real tptp.sqrt X))) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.topolo2177554685111907308n_real X tptp.top_top_set_real)))) (forall ((X tptp.real)) (tptp.has_fi5821293074295781190e_real tptp.arctan (tptp.aa_real_real tptp.inverse_inverse_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real tptp.one_one_real) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (tptp.topolo2177554685111907308n_real X tptp.top_top_set_real))) (forall ((X tptp.real) (A4 tptp.set_real)) (tptp.has_fi5821293074295781190e_real tptp.arsinh_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.one_one_real) (tptp.aa_real_real tptp.sqrt (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) tptp.one_one_real))) (tptp.topolo2177554685111907308n_real X A4))) (forall ((X tptp.real) (D4 tptp.real)) (let ((_let_1 (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_real_real tptp.inverse_inverse_real (tptp.aa_real_real tptp.sqrt X)))) (=> (not (= X tptp.zero_zero_real)) (=> (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) X)) (= D4 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real _let_2) _let_1))) (=> (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) tptp.zero_zero_real)) (= D4 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real tptp.uminus_uminus_real _let_2)) _let_1))) (tptp.has_fi5821293074295781190e_real tptp.sqrt D4 (tptp.topolo2177554685111907308n_real X tptp.top_top_set_real)))))))) (forall ((X tptp.real) (A4 tptp.set_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real) X)) (tptp.has_fi5821293074295781190e_real tptp.arcosh_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.one_one_real) (tptp.aa_real_real tptp.sqrt (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) tptp.one_one_real))) (tptp.topolo2177554685111907308n_real X A4)))) (forall ((X tptp.real) (A4 tptp.set_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.abs_abs_real X)) tptp.one_one_real)) (tptp.has_fi5821293074295781190e_real tptp.artanh_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.one_one_real) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real tptp.one_one_real) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (tptp.topolo2177554685111907308n_real X A4)))) (forall ((N tptp.nat) (X tptp.real)) (let ((_let_1 (tptp.aa_nat_fun_real_real tptp.root N))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) X)) (tptp.has_fi5821293074295781190e_real _let_1 (tptp.aa_real_real tptp.inverse_inverse_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real _let_1 X)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat))))) (tptp.topolo2177554685111907308n_real X tptp.top_top_set_real)))))) (forall ((X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) tptp.one_one_real)) (tptp.has_fi5821293074295781190e_real tptp.arccos (tptp.aa_real_real tptp.inverse_inverse_real (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_real_real tptp.sqrt (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real tptp.one_one_real) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))))) (tptp.topolo2177554685111907308n_real X tptp.top_top_set_real))))) (forall ((X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) tptp.one_one_real)) (tptp.has_fi5821293074295781190e_real tptp.arcsin (tptp.aa_real_real tptp.inverse_inverse_real (tptp.aa_real_real tptp.sqrt (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real tptp.one_one_real) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))))) (tptp.topolo2177554685111907308n_real X tptp.top_top_set_real))))) (forall ((Diff tptp.fun_na6724076748692969250l_real) (F tptp.fun_real_real) (X tptp.real) (N tptp.nat)) (=> (= (tptp.aa_nat_fun_real_real Diff tptp.zero_zero_nat) F) (=> (forall ((M3 tptp.nat) (X4 tptp.real)) (tptp.has_fi5821293074295781190e_real (tptp.aa_nat_fun_real_real Diff M3) (tptp.aa_real_real (tptp.aa_nat_fun_real_real Diff (tptp.aa_nat_nat tptp.suc M3)) X4) (tptp.topolo2177554685111907308n_real X4 tptp.top_top_set_real))) (exists ((T4 tptp.real)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real T4)) (tptp.aa_real_real tptp.abs_abs_real X))) (= (tptp.aa_real_real F X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_yi Diff) X) (tptp.set_ord_lessThan_nat N))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_nat_fun_real_real Diff N) T4)) (tptp.aa_nat_real tptp.semiri2265585572941072030t_real N))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) N))))))))) (forall ((Diff tptp.fun_na6724076748692969250l_real) (F tptp.fun_real_real) (X tptp.real) (N tptp.nat)) (=> (and (= (tptp.aa_nat_fun_real_real Diff tptp.zero_zero_nat) F) (forall ((M3 tptp.nat) (X4 tptp.real)) (tptp.has_fi5821293074295781190e_real (tptp.aa_nat_fun_real_real Diff M3) (tptp.aa_real_real (tptp.aa_nat_fun_real_real Diff (tptp.aa_nat_nat tptp.suc M3)) X4) (tptp.topolo2177554685111907308n_real X4 tptp.top_top_set_real)))) (exists ((T4 tptp.real)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real T4)) (tptp.aa_real_real tptp.abs_abs_real X))) (= (tptp.aa_real_real F X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_yi Diff) X) (tptp.set_ord_lessThan_nat N))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_nat_fun_real_real Diff N) T4)) (tptp.aa_nat_real tptp.semiri2265585572941072030t_real N))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) N)))))))) (forall ((N tptp.nat) (X tptp.real)) (let ((_let_1 (tptp.aa_nat_fun_real_real tptp.root N))) (=> (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N))) (=> (not (= X tptp.zero_zero_real)) (tptp.has_fi5821293074295781190e_real _let_1 (tptp.aa_real_real tptp.inverse_inverse_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real _let_1 X)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat))))) (tptp.topolo2177554685111907308n_real X tptp.top_top_set_real)))))) (forall ((H tptp.real) (N tptp.nat) (Diff tptp.fun_na6724076748692969250l_real) (F tptp.fun_real_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) H)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (=> (= (tptp.aa_nat_fun_real_real Diff tptp.zero_zero_nat) F) (=> (forall ((M3 tptp.nat) (T4 tptp.real)) (=> (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M3) N)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) T4)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real T4) H))) (tptp.has_fi5821293074295781190e_real (tptp.aa_nat_fun_real_real Diff M3) (tptp.aa_real_real (tptp.aa_nat_fun_real_real Diff (tptp.aa_nat_nat tptp.suc M3)) T4) (tptp.topolo2177554685111907308n_real T4 tptp.top_top_set_real)))) (exists ((T4 tptp.real)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) T4)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real T4) H)) (= (tptp.aa_real_real F H) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.groups6591440286371151544t_real (tptp.aa_fun1113820866546176217t_real (tptp.aTP_Lamm_mw H) Diff) (tptp.set_ord_lessThan_nat N))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_nat_fun_real_real Diff N) T4)) (tptp.aa_nat_real tptp.semiri2265585572941072030t_real N))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real H) N))))))))))) (forall ((H tptp.real) (Diff tptp.fun_na6724076748692969250l_real) (F tptp.fun_real_real) (N tptp.nat)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) H)) (=> (= (tptp.aa_nat_fun_real_real Diff tptp.zero_zero_nat) F) (=> (forall ((M3 tptp.nat) (T4 tptp.real)) (=> (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M3) N)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) T4)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real T4) H))) (tptp.has_fi5821293074295781190e_real (tptp.aa_nat_fun_real_real Diff M3) (tptp.aa_real_real (tptp.aa_nat_fun_real_real Diff (tptp.aa_nat_nat tptp.suc M3)) T4) (tptp.topolo2177554685111907308n_real T4 tptp.top_top_set_real)))) (exists ((T4 tptp.real)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) T4)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real T4) H)) (= (tptp.aa_real_real F H) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.groups6591440286371151544t_real (tptp.aa_fun1113820866546176217t_real (tptp.aTP_Lamm_mw H) Diff) (tptp.set_ord_lessThan_nat N))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_nat_fun_real_real Diff N) T4)) (tptp.aa_nat_real tptp.semiri2265585572941072030t_real N))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real H) N)))))))))) (forall ((H tptp.real) (N tptp.nat) (Diff tptp.fun_na6724076748692969250l_real) (F tptp.fun_real_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real H) tptp.zero_zero_real)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (=> (= (tptp.aa_nat_fun_real_real Diff tptp.zero_zero_nat) F) (=> (forall ((M3 tptp.nat) (T4 tptp.real)) (=> (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M3) N)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real H) T4)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real T4) tptp.zero_zero_real))) (tptp.has_fi5821293074295781190e_real (tptp.aa_nat_fun_real_real Diff M3) (tptp.aa_real_real (tptp.aa_nat_fun_real_real Diff (tptp.aa_nat_nat tptp.suc M3)) T4) (tptp.topolo2177554685111907308n_real T4 tptp.top_top_set_real)))) (exists ((T4 tptp.real)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real H) T4)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real T4) tptp.zero_zero_real)) (= (tptp.aa_real_real F H) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.groups6591440286371151544t_real (tptp.aa_fun1113820866546176217t_real (tptp.aTP_Lamm_mw H) Diff) (tptp.set_ord_lessThan_nat N))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_nat_fun_real_real Diff N) T4)) (tptp.aa_nat_real tptp.semiri2265585572941072030t_real N))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real H) N))))))))))) (forall ((Diff tptp.fun_na6724076748692969250l_real) (F tptp.fun_real_real) (N tptp.nat) (X tptp.real)) (=> (= (tptp.aa_nat_fun_real_real Diff tptp.zero_zero_nat) F) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (=> (not (= X tptp.zero_zero_real)) (=> (forall ((M3 tptp.nat) (X4 tptp.real)) (tptp.has_fi5821293074295781190e_real (tptp.aa_nat_fun_real_real Diff M3) (tptp.aa_real_real (tptp.aa_nat_fun_real_real Diff (tptp.aa_nat_nat tptp.suc M3)) X4) (tptp.topolo2177554685111907308n_real X4 tptp.top_top_set_real))) (exists ((T4 tptp.real)) (let ((_let_1 (tptp.aa_real_real tptp.abs_abs_real T4))) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) _let_1)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real _let_1) (tptp.aa_real_real tptp.abs_abs_real X))) (= (tptp.aa_real_real F X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_yi Diff) X) (tptp.set_ord_lessThan_nat N))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_nat_fun_real_real Diff N) T4)) (tptp.aa_nat_real tptp.semiri2265585572941072030t_real N))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) N)))))))))))) (forall ((Diff tptp.fun_na6724076748692969250l_real) (F tptp.fun_real_real) (N tptp.nat) (X tptp.real)) (=> (= (tptp.aa_nat_fun_real_real Diff tptp.zero_zero_nat) F) (=> (forall ((M3 tptp.nat) (T4 tptp.real)) (=> (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M3) N)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real T4)) (tptp.aa_real_real tptp.abs_abs_real X)))) (tptp.has_fi5821293074295781190e_real (tptp.aa_nat_fun_real_real Diff M3) (tptp.aa_real_real (tptp.aa_nat_fun_real_real Diff (tptp.aa_nat_nat tptp.suc M3)) T4) (tptp.topolo2177554685111907308n_real T4 tptp.top_top_set_real)))) (exists ((T4 tptp.real)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real T4)) (tptp.aa_real_real tptp.abs_abs_real X))) (= (tptp.aa_real_real F X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_yi Diff) X) (tptp.set_ord_lessThan_nat N))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_nat_fun_real_real Diff N) T4)) (tptp.aa_nat_real tptp.semiri2265585572941072030t_real N))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) N))))))))) (forall ((N tptp.nat) (Diff tptp.fun_na6724076748692969250l_real) (F tptp.fun_real_real) (A tptp.real) (B2 tptp.real) (C tptp.real) (X tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (=> (= (tptp.aa_nat_fun_real_real Diff tptp.zero_zero_nat) F) (=> (forall ((M3 tptp.nat) (T4 tptp.real)) (=> (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M3) N)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) T4)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real T4) B2))) (tptp.has_fi5821293074295781190e_real (tptp.aa_nat_fun_real_real Diff M3) (tptp.aa_real_real (tptp.aa_nat_fun_real_real Diff (tptp.aa_nat_nat tptp.suc M3)) T4) (tptp.topolo2177554685111907308n_real T4 tptp.top_top_set_real)))) (=> (tptp.pp (tptp.aa_real_bool _let_1 C)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real C) B2)) (=> (tptp.pp (tptp.aa_real_bool _let_1 X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) B2)) (=> (not (= X C)) (exists ((T4 tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real T4))) (let ((_let_2 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X))) (let ((_let_3 (tptp.pp (tptp.aa_real_bool _let_2 C)))) (and (=> _let_3 (and (tptp.pp (tptp.aa_real_bool _let_2 T4)) (tptp.pp (tptp.aa_real_bool _let_1 C)))) (=> (not _let_3) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real C) T4)) (tptp.pp (tptp.aa_real_bool _let_1 X)))) (= (tptp.aa_real_real F X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real (tptp.aa_rea7841385751566875788t_real (tptp.aTP_Lamm_yj Diff) C) X) (tptp.set_ord_lessThan_nat N))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_nat_fun_real_real Diff N) T4)) (tptp.aa_nat_real tptp.semiri2265585572941072030t_real N))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real X) C)) N))))))))))))))))))) (forall ((N tptp.nat) (Diff tptp.fun_na6724076748692969250l_real) (F tptp.fun_real_real) (A tptp.real) (B2 tptp.real) (C tptp.real)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (=> (= (tptp.aa_nat_fun_real_real Diff tptp.zero_zero_nat) F) (=> (forall ((M3 tptp.nat) (T4 tptp.real)) (=> (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M3) N)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) T4)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real T4) B2))) (tptp.has_fi5821293074295781190e_real (tptp.aa_nat_fun_real_real Diff M3) (tptp.aa_real_real (tptp.aa_nat_fun_real_real Diff (tptp.aa_nat_nat tptp.suc M3)) T4) (tptp.topolo2177554685111907308n_real T4 tptp.top_top_set_real)))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) C)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real C) B2)) (exists ((T4 tptp.real)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real C) T4)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real T4) B2)) (= (tptp.aa_real_real F B2) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real (tptp.aa_rea7841385751566875788t_real (tptp.aTP_Lamm_yk Diff) B2) C) (tptp.set_ord_lessThan_nat N))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_nat_fun_real_real Diff N) T4)) (tptp.aa_nat_real tptp.semiri2265585572941072030t_real N))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real B2) C)) N)))))))))))) (forall ((N tptp.nat) (Diff tptp.fun_na6724076748692969250l_real) (F tptp.fun_real_real) (A tptp.real) (B2 tptp.real) (C tptp.real)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (=> (= (tptp.aa_nat_fun_real_real Diff tptp.zero_zero_nat) F) (=> (forall ((M3 tptp.nat) (T4 tptp.real)) (=> (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M3) N)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) T4)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real T4) B2))) (tptp.has_fi5821293074295781190e_real (tptp.aa_nat_fun_real_real Diff M3) (tptp.aa_real_real (tptp.aa_nat_fun_real_real Diff (tptp.aa_nat_nat tptp.suc M3)) T4) (tptp.topolo2177554685111907308n_real T4 tptp.top_top_set_real)))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) C)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real C) B2)) (exists ((T4 tptp.real)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) T4)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real T4) C)) (= (tptp.aa_real_real F A) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real (tptp.aa_rea7841385751566875788t_real (tptp.aTP_Lamm_yk Diff) A) C) (tptp.set_ord_lessThan_nat N))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_nat_fun_real_real Diff N) T4)) (tptp.aa_nat_real tptp.semiri2265585572941072030t_real N))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A) C)) N)))))))))))) (forall ((N tptp.nat) (H tptp.real) (Diff tptp.fun_na6724076748692969250l_real) (K tptp.nat) (B4 tptp.real)) (=> (forall ((M3 tptp.nat) (T4 tptp.real)) (=> (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M3) N)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) T4)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real T4) H))) (tptp.has_fi5821293074295781190e_real (tptp.aa_nat_fun_real_real Diff M3) (tptp.aa_real_real (tptp.aa_nat_fun_real_real Diff (tptp.aa_nat_nat tptp.suc M3)) T4) (tptp.topolo2177554685111907308n_real T4 tptp.top_top_set_real)))) (=> (= N (tptp.aa_nat_nat tptp.suc K)) (forall ((M2 tptp.nat) (T5 tptp.real)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc M2))) (let ((_let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) _let_1))) (=> (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M2) N)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) T5)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real T5) H))) (tptp.has_fi5821293074295781190e_real (tptp.aa_nat_fun_real_real (tptp.aa_rea1103652080130114956l_real (tptp.aa_fun2567993205388704171l_real (tptp.aTP_Lamm_ym N) Diff) B4) M2) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real (tptp.aa_nat_fun_real_real Diff _let_1) T5)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real (tptp.aa_nat1308781354268537904t_real (tptp.aTP_Lamm_yn Diff) M2) T5) (tptp.set_ord_lessThan_nat _let_2))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real B4) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real T5) _let_2)) (tptp.aa_nat_real tptp.semiri2265585572941072030t_real _let_2))))) (tptp.topolo2177554685111907308n_real T5 tptp.top_top_set_real))))))))) (forall ((X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.abs_abs_real X)) tptp.one_one_real)) (tptp.has_fi5821293074295781190e_real tptp.aTP_Lamm_yo (tptp.suminf_real (tptp.aa_real_fun_nat_real tptp.aTP_Lamm_yp X)) (tptp.topolo2177554685111907308n_real X tptp.top_top_set_real)))) (forall ((R2 tptp.real) (F tptp.fun_nat_real) (X0 tptp.real)) (=> (forall ((X4 tptp.real)) (=> (tptp.member_real X4 (tptp.set_or1633881224788618240n_real (tptp.aa_real_real tptp.uminus_uminus_real R2) R2)) (tptp.summable_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_yq F) X4)))) (=> (tptp.member_real X0 (tptp.set_or1633881224788618240n_real (tptp.aa_real_real tptp.uminus_uminus_real R2) R2)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) R2)) (tptp.has_fi5821293074295781190e_real (tptp.aTP_Lamm_ys F) (tptp.suminf_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_yq F) X0)) (tptp.topolo2177554685111907308n_real X0 tptp.top_top_set_real)))))) (forall ((A tptp.real) (B2 tptp.real) (X tptp.real) (Y tptp.real) (F tptp.fun_real_real)) (let ((_let_1 (tptp.set_or1633881224788618240n_real A B2))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B2)) (=> (tptp.member_real X _let_1) (=> (tptp.member_real Y _let_1) (=> (forall ((X4 tptp.real)) (=> (tptp.member_real X4 (tptp.set_or1633881224788618240n_real A B2)) (tptp.has_fi5821293074295781190e_real F tptp.zero_zero_real (tptp.topolo2177554685111907308n_real X4 tptp.top_top_set_real)))) (= (tptp.aa_real_real F X) (tptp.aa_real_real F Y)))))))) (forall ((F tptp.fun_re4238438383274954274t_real) (F3 tptp.fun_re4238438383274954274t_real) (X0 tptp.real) (A tptp.real) (B2 tptp.real) (L5 tptp.fun_nat_real)) (let ((_let_1 (tptp.aa_real_fun_nat_real F3 X0))) (=> (forall ((N2 tptp.nat)) (tptp.has_fi5821293074295781190e_real (tptp.aa_nat_fun_real_real (tptp.aTP_Lamm_yt F) N2) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real F3 X0) N2) (tptp.topolo2177554685111907308n_real X0 tptp.top_top_set_real))) (=> (forall ((X4 tptp.real)) (=> (tptp.member_real X4 (tptp.set_or1633881224788618240n_real A B2)) (tptp.summable_real (tptp.aa_real_fun_nat_real F X4)))) (=> (tptp.member_real X0 (tptp.set_or1633881224788618240n_real A B2)) (=> (tptp.summable_real _let_1) (=> (tptp.summable_real L5) (=> (forall ((N2 tptp.nat) (X4 tptp.real) (Y4 tptp.real)) (let ((_let_1 (tptp.set_or1633881224788618240n_real A B2))) (=> (tptp.member_real X4 _let_1) (=> (tptp.member_real Y4 _let_1) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real F X4) N2)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real F Y4) N2)))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real L5 N2)) (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real X4) Y4))))))))) (tptp.has_fi5821293074295781190e_real (tptp.aTP_Lamm_yu F) (tptp.suminf_real _let_1) (tptp.topolo2177554685111907308n_real X0 tptp.top_top_set_real)))))))))) (forall ((L tptp.nat) (U tptp.nat)) (= (tptp.finite_card_nat (tptp.set_or5834768355832116004an_nat L U)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat U) (tptp.aa_nat_nat tptp.suc L)))) (forall ((A tptp.real) (B2 tptp.real) (F tptp.fun_real_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) B2)) (=> (forall ((X4 tptp.real)) (=> (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) X4)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X4) B2))) (tptp.topolo4422821103128117721l_real (tptp.topolo2177554685111907308n_real X4 tptp.top_top_set_real) F))) (exists ((L6 tptp.real) (M8 tptp.real)) (and (forall ((X5 tptp.real)) (let ((_let_1 (tptp.aa_real_real F X5))) (=> (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) X5)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X5) B2))) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real L6) _let_1)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real _let_1) M8)))))) (forall ((Y5 tptp.real)) (=> (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real L6) Y5)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y5) M8))) (exists ((X4 tptp.real)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) X4)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X4) B2)) (= (tptp.aa_real_real F X4) Y5)))))))))) (forall ((F tptp.fun_real_real) (L tptp.real) (C tptp.real)) (=> (tptp.filterlim_real_real F (tptp.topolo2815343760600316023s_real L) (tptp.topolo2177554685111907308n_real C tptp.top_top_set_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real L) tptp.zero_zero_real)) (exists ((R3 tptp.real)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) R3)) (forall ((X5 tptp.real)) (=> (and (not (= X5 C)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real C) X5))) R3))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real F X5)) tptp.zero_zero_real))))))))) (forall ((F tptp.fun_real_real) (L tptp.real) (C tptp.real)) (=> (tptp.filterlim_real_real F (tptp.topolo2815343760600316023s_real L) (tptp.topolo2177554685111907308n_real C tptp.top_top_set_real)) (=> (not (= L tptp.zero_zero_real)) (exists ((R3 tptp.real)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) R3)) (forall ((X5 tptp.real)) (=> (and (not (= X5 C)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real C) X5))) R3))) (not (= (tptp.aa_real_real F X5) tptp.zero_zero_real))))))))) (forall ((F tptp.fun_real_real) (L tptp.real) (C tptp.real)) (=> (tptp.filterlim_real_real F (tptp.topolo2815343760600316023s_real L) (tptp.topolo2177554685111907308n_real C tptp.top_top_set_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) L)) (exists ((R3 tptp.real)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) R3)) (forall ((X5 tptp.real)) (=> (and (not (= X5 C)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real C) X5))) R3))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) (tptp.aa_real_real F X5)))))))))) (forall ((X tptp.real)) (tptp.topolo4422821103128117721l_real (tptp.topolo2177554685111907308n_real X tptp.top_top_set_real) tptp.sqrt)) (forall ((X tptp.real) (N tptp.nat)) (tptp.topolo4422821103128117721l_real (tptp.topolo2177554685111907308n_real X tptp.top_top_set_real) (tptp.aa_nat_fun_real_real tptp.root N))) (forall ((A tptp.real) (X tptp.real) (B2 tptp.real) (G tptp.fun_real_real) (F tptp.fun_real_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) B2)) (=> (forall ((Z4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) Z4)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Z4) B2)) (= (tptp.aa_real_real G (tptp.aa_real_real F Z4)) Z4)))) (=> (forall ((Z4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) Z4)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Z4) B2)) (tptp.topolo4422821103128117721l_real (tptp.topolo2177554685111907308n_real Z4 tptp.top_top_set_real) F)))) (tptp.topolo4422821103128117721l_real (tptp.topolo2177554685111907308n_real (tptp.aa_real_real F X) tptp.top_top_set_real) G)))))) (forall ((X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real) X)) (tptp.topolo4422821103128117721l_real (tptp.topolo2177554685111907308n_real X tptp.top_top_set_real) tptp.arcosh_real))) (tptp.filterlim_real_real tptp.aTP_Lamm_yv (tptp.topolo2815343760600316023s_real tptp.zero_zero_real) (tptp.topolo2177554685111907308n_real _let_30 tptp.top_top_set_real)) (forall ((F tptp.fun_real_real) (D4 tptp.real) (G tptp.fun_real_real) (X tptp.real) (A tptp.real) (B2 tptp.real)) (let ((_let_1 (tptp.topolo2177554685111907308n_real X tptp.top_top_set_real))) (=> (tptp.has_fi5821293074295781190e_real F D4 (tptp.topolo2177554685111907308n_real (tptp.aa_real_real G X) tptp.top_top_set_real)) (=> (not (= D4 tptp.zero_zero_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) B2)) (=> (forall ((Y4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) Y4)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y4) B2)) (= (tptp.aa_real_real F (tptp.aa_real_real G Y4)) Y4)))) (=> (tptp.topolo4422821103128117721l_real _let_1 G) (tptp.has_fi5821293074295781190e_real G (tptp.aa_real_real tptp.inverse_inverse_real D4) _let_1))))))))) (forall ((X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) tptp.one_one_real)) (tptp.topolo4422821103128117721l_real (tptp.topolo2177554685111907308n_real X tptp.top_top_set_real) tptp.arccos)))) (forall ((X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) tptp.one_one_real)) (tptp.topolo4422821103128117721l_real (tptp.topolo2177554685111907308n_real X tptp.top_top_set_real) tptp.arcsin)))) (forall ((B2 tptp.real) (X tptp.real) (F tptp.fun_real_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B2) X)) (=> (forall ((X4 tptp.real)) (=> (tptp.member_real X4 (tptp.set_or1633881224788618240n_real B2 X)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_real_real F X4))))) (=> (tptp.topolo4422821103128117721l_real (tptp.topolo2177554685111907308n_real X tptp.top_top_set_real) F) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_real_real F X))))))) (forall ((X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) tptp.one_one_real)) (tptp.topolo4422821103128117721l_real (tptp.topolo2177554685111907308n_real X tptp.top_top_set_real) tptp.artanh_real)))) (forall ((I tptp.int) (J tptp.int)) (= (tptp.aa_int_set_int (tptp.aa_int8639817059373041269et_int tptp.set_or5832277885323065728an_int I) J) (tptp.set_int2 (tptp.upto (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int I) tptp.one_one_int) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int J) tptp.one_one_int))))) (forall ((D tptp.real) (X tptp.real) (G tptp.fun_real_real) (F tptp.fun_real_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) D)) (=> (forall ((Z4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real Z4) X))) D)) (= (tptp.aa_real_real G (tptp.aa_real_real F Z4)) Z4))) (=> (forall ((Z4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real Z4) X))) D)) (tptp.topolo4422821103128117721l_real (tptp.topolo2177554685111907308n_real Z4 tptp.top_top_set_real) F))) (tptp.topolo4422821103128117721l_real (tptp.topolo2177554685111907308n_real (tptp.aa_real_real F X) tptp.top_top_set_real) G))))) (forall ((A tptp.real) (B2 tptp.real) (F tptp.fun_real_real) (G tptp.fun_real_real) (G2 tptp.fun_real_real) (F3 tptp.fun_real_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B2)) (=> (forall ((Z4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) Z4)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Z4) B2)) (tptp.topolo4422821103128117721l_real (tptp.topolo2177554685111907308n_real Z4 tptp.top_top_set_real) F)))) (=> (forall ((Z4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) Z4)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Z4) B2)) (tptp.topolo4422821103128117721l_real (tptp.topolo2177554685111907308n_real Z4 tptp.top_top_set_real) G)))) (=> (forall ((Z4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) Z4)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Z4) B2)) (tptp.has_fi5821293074295781190e_real G (tptp.aa_real_real G2 Z4) (tptp.topolo2177554685111907308n_real Z4 tptp.top_top_set_real))))) (=> (forall ((Z4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) Z4)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Z4) B2)) (tptp.has_fi5821293074295781190e_real F (tptp.aa_real_real F3 Z4) (tptp.topolo2177554685111907308n_real Z4 tptp.top_top_set_real))))) (exists ((C2 tptp.real)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) C2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real C2) B2)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real F B2)) (tptp.aa_real_real F A))) (tptp.aa_real_real G2 C2)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real G B2)) (tptp.aa_real_real G A))) (tptp.aa_real_real F3 C2))))))))))) (forall ((A tptp.fun_nat_real)) (=> (tptp.filterlim_nat_real A (tptp.topolo2815343760600316023s_real tptp.zero_zero_real) tptp.at_top_nat) (=> (tptp.topolo6980174941875973593q_real A) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_nat_real A tptp.zero_zero_nat)) tptp.zero_zero_real)) (forall ((N8 tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N8))) (let ((_let_2 (tptp.aTP_Lamm_yw A))) (tptp.member_real (tptp.suminf_real _let_2) (tptp.set_or1222579329274155063t_real (tptp.groups6591440286371151544t_real _let_2 (tptp.set_ord_lessThan_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat _let_1) tptp.one_one_nat))) (tptp.groups6591440286371151544t_real _let_2 (tptp.set_ord_lessThan_nat _let_1))))))))))) (forall ((A tptp.fun_nat_real)) (=> (tptp.filterlim_nat_real A (tptp.topolo2815343760600316023s_real tptp.zero_zero_real) tptp.at_top_nat) (=> (tptp.topolo6980174941875973593q_real A) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) (tptp.aa_nat_real A tptp.zero_zero_nat))) (forall ((N8 tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N8))) (let ((_let_2 (tptp.aTP_Lamm_yw A))) (tptp.member_real (tptp.suminf_real _let_2) (tptp.set_or1222579329274155063t_real (tptp.groups6591440286371151544t_real _let_2 (tptp.set_ord_lessThan_nat _let_1)) (tptp.groups6591440286371151544t_real _let_2 (tptp.set_ord_lessThan_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat _let_1) tptp.one_one_nat)))))))))))) (forall ((C tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) C)) (tptp.filterlim_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat C) tptp.at_top_nat tptp.at_top_nat))) (forall ((C tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) C)) (tptp.filterlim_nat_nat (tptp.aa_nat_fun_nat_nat tptp.aTP_Lamm_ag C) tptp.at_top_nat tptp.at_top_nat))) (forall ((X7 tptp.fun_nat_real) (B4 tptp.real)) (=> (tptp.topolo6980174941875973593q_real X7) (=> (forall ((I3 tptp.nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_nat_real X7 I3))) B4))) (not (forall ((L6 tptp.real)) (not (tptp.filterlim_nat_real X7 (tptp.topolo2815343760600316023s_real L6) tptp.at_top_nat))))))) (tptp.filterlim_nat_real tptp.aTP_Lamm_yx (tptp.topolo2815343760600316023s_real tptp.one_one_real) tptp.at_top_nat) (forall ((F tptp.fun_nat_real) (G tptp.fun_nat_real)) (=> (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_nat_real F N2)) (tptp.aa_nat_real F (tptp.aa_nat_nat tptp.suc N2))))) (=> (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_nat_real G (tptp.aa_nat_nat tptp.suc N2))) (tptp.aa_nat_real G N2)))) (=> (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_nat_real F N2)) (tptp.aa_nat_real G N2)))) (=> (tptp.filterlim_nat_real (tptp.aa_fun1839206346889086768t_real (tptp.aTP_Lamm_gj F) G) (tptp.topolo2815343760600316023s_real tptp.zero_zero_real) tptp.at_top_nat) (exists ((L3 tptp.real)) (let ((_let_1 (tptp.topolo2815343760600316023s_real L3))) (and (forall ((N8 tptp.nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_nat_real F N8)) L3))) (tptp.filterlim_nat_real F _let_1 tptp.at_top_nat) (forall ((N8 tptp.nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real L3) (tptp.aa_nat_real G N8)))) (tptp.filterlim_nat_real G _let_1 tptp.at_top_nat))))))))) (forall ((X7 tptp.fun_nat_real)) (=> (forall ((R3 tptp.real)) (exists ((N6 tptp.nat)) (forall ((N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N6) N2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real R3) (tptp.aa_nat_real X7 N2))))))) (tptp.filterlim_nat_real (tptp.aTP_Lamm_yy X7) (tptp.topolo2815343760600316023s_real tptp.zero_zero_real) tptp.at_top_nat))) (forall ((C tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) C)) (tptp.filterlim_nat_real (tptp.aa_real_fun_nat_real tptp.aTP_Lamm_yz C) (tptp.topolo2815343760600316023s_real tptp.one_one_real) tptp.at_top_nat))) (forall ((F tptp.fun_nat_real) (L tptp.real)) (=> (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_nat_real F N2)) (tptp.aa_nat_real F (tptp.aa_nat_nat tptp.suc N2))))) (=> (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_nat_real F N2)) L))) (=> (forall ((E2 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) E2)) (exists ((N8 tptp.nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real L) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real F N8)) E2)))))) (tptp.filterlim_nat_real F (tptp.topolo2815343760600316023s_real L) tptp.at_top_nat))))) (forall ((X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) tptp.one_one_real)) (tptp.filterlim_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) (tptp.topolo2815343760600316023s_real tptp.zero_zero_real) tptp.at_top_nat)))) (forall ((X tptp.real) (A tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real) X)) (tptp.filterlim_nat_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_za X) A) (tptp.topolo2815343760600316023s_real tptp.zero_zero_real) tptp.at_top_nat))) (forall ((C tptp.real)) (let ((_let_1 (tptp.aa_real_real tptp.abs_abs_real C))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real _let_1) tptp.one_one_real)) (tptp.filterlim_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real _let_1) (tptp.topolo2815343760600316023s_real tptp.zero_zero_real) tptp.at_top_nat)))) (forall ((C tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.abs_abs_real C)) tptp.one_one_real)) (tptp.filterlim_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real C) (tptp.topolo2815343760600316023s_real tptp.zero_zero_real) tptp.at_top_nat))) (forall ((X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real) X)) (tptp.filterlim_nat_real (tptp.aa_real_fun_nat_real tptp.aTP_Lamm_zb X) (tptp.topolo2815343760600316023s_real tptp.zero_zero_real) tptp.at_top_nat))) (forall ((R tptp.real)) (tptp.filterlim_nat_real (tptp.aa_real_fun_nat_real tptp.aTP_Lamm_zc R) (tptp.topolo2815343760600316023s_real R) tptp.at_top_nat)) (forall ((A tptp.fun_nat_real)) (=> (tptp.filterlim_nat_real A (tptp.topolo2815343760600316023s_real tptp.zero_zero_real) tptp.at_top_nat) (=> (tptp.topolo6980174941875973593q_real A) (tptp.summable_real (tptp.aTP_Lamm_yw A))))) (forall ((A tptp.fun_nat_real)) (=> (tptp.filterlim_nat_real A (tptp.topolo2815343760600316023s_real tptp.zero_zero_real) tptp.at_top_nat) (=> (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_nat_real A N2)))) (=> (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_nat_real A (tptp.aa_nat_nat tptp.suc N2))) (tptp.aa_nat_real A N2)))) (tptp.summable_real (tptp.aTP_Lamm_yw A)))))) (forall ((Theta tptp.fun_nat_real) (Theta2 tptp.real)) (=> (tptp.filterlim_nat_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_zd Theta) Theta2) (tptp.topolo2815343760600316023s_real tptp.one_one_real) tptp.at_top_nat) (not (forall ((K3 tptp.fun_nat_int)) (not (tptp.filterlim_nat_real (tptp.aa_fun4551936527957760560t_real (tptp.aTP_Lamm_ze Theta) K3) (tptp.topolo2815343760600316023s_real Theta2) tptp.at_top_nat)))))) (forall ((Theta tptp.fun_nat_real)) (=> (tptp.filterlim_nat_real (tptp.aTP_Lamm_zf Theta) (tptp.topolo2815343760600316023s_real tptp.one_one_real) tptp.at_top_nat) (exists ((K3 tptp.fun_nat_int)) (tptp.filterlim_nat_real (tptp.aa_fun4551936527957760560t_real (tptp.aTP_Lamm_ze Theta) K3) (tptp.topolo2815343760600316023s_real tptp.zero_zero_real) tptp.at_top_nat)))) (forall ((A tptp.fun_nat_real)) (=> (tptp.filterlim_nat_real A (tptp.topolo2815343760600316023s_real tptp.zero_zero_real) tptp.at_top_nat) (=> (tptp.topolo6980174941875973593q_real A) (tptp.filterlim_nat_real (tptp.aTP_Lamm_zg A) (tptp.topolo2815343760600316023s_real (tptp.suminf_real (tptp.aTP_Lamm_yw A))) tptp.at_top_nat)))) (forall ((X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real X)) tptp.one_one_real)) (tptp.filterlim_nat_real (tptp.aa_real_fun_nat_real tptp.aTP_Lamm_jj X) (tptp.topolo2815343760600316023s_real tptp.zero_zero_real) tptp.at_top_nat))) (forall ((A tptp.fun_nat_real) (N tptp.nat)) (let ((_let_1 (tptp.aTP_Lamm_yw A))) (=> (tptp.filterlim_nat_real A (tptp.topolo2815343760600316023s_real tptp.zero_zero_real) tptp.at_top_nat) (=> (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_nat_real A N2)))) (=> (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_nat_real A (tptp.aa_nat_nat tptp.suc N2))) (tptp.aa_nat_real A N2)))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.groups6591440286371151544t_real _let_1 (tptp.set_ord_lessThan_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N)))) (tptp.suminf_real _let_1)))))))) (forall ((A tptp.fun_nat_real)) (=> (tptp.filterlim_nat_real A (tptp.topolo2815343760600316023s_real tptp.zero_zero_real) tptp.at_top_nat) (=> (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_nat_real A N2)))) (=> (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_nat_real A (tptp.aa_nat_nat tptp.suc N2))) (tptp.aa_nat_real A N2)))) (tptp.filterlim_nat_real (tptp.aTP_Lamm_zg A) (tptp.topolo2815343760600316023s_real (tptp.suminf_real (tptp.aTP_Lamm_yw A))) tptp.at_top_nat))))) (forall ((A tptp.fun_nat_real)) (=> (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_nat_real A (tptp.aa_nat_nat tptp.suc N2))) (tptp.aa_nat_real A N2)))) (=> (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_nat_real A N2)))) (=> (tptp.filterlim_nat_real A (tptp.topolo2815343760600316023s_real tptp.zero_zero_real) tptp.at_top_nat) (exists ((L3 tptp.real)) (let ((_let_1 (tptp.topolo2815343760600316023s_real L3))) (and (forall ((N8 tptp.nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.groups6591440286371151544t_real (tptp.aTP_Lamm_yw A) (tptp.set_ord_lessThan_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N8)))) L3))) (tptp.filterlim_nat_real (tptp.aTP_Lamm_zg A) _let_1 tptp.at_top_nat) (forall ((N8 tptp.nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real L3) (tptp.groups6591440286371151544t_real (tptp.aTP_Lamm_yw A) (tptp.set_ord_lessThan_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N8)) tptp.one_one_nat)))))) (tptp.filterlim_nat_real (tptp.aTP_Lamm_zh A) _let_1 tptp.at_top_nat)))))))) (forall ((A tptp.fun_nat_real)) (=> (tptp.filterlim_nat_real A (tptp.topolo2815343760600316023s_real tptp.zero_zero_real) tptp.at_top_nat) (=> (tptp.topolo6980174941875973593q_real A) (tptp.filterlim_nat_real (tptp.aTP_Lamm_zh A) (tptp.topolo2815343760600316023s_real (tptp.suminf_real (tptp.aTP_Lamm_yw A))) tptp.at_top_nat)))) (forall ((A tptp.fun_nat_real)) (=> (tptp.filterlim_nat_real A (tptp.topolo2815343760600316023s_real tptp.zero_zero_real) tptp.at_top_nat) (=> (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_nat_real A N2)))) (=> (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_nat_real A (tptp.aa_nat_nat tptp.suc N2))) (tptp.aa_nat_real A N2)))) (tptp.filterlim_nat_real (tptp.aTP_Lamm_zh A) (tptp.topolo2815343760600316023s_real (tptp.suminf_real (tptp.aTP_Lamm_yw A))) tptp.at_top_nat))))) (forall ((A tptp.fun_nat_real) (N tptp.nat)) (let ((_let_1 (tptp.aTP_Lamm_yw A))) (=> (tptp.filterlim_nat_real A (tptp.topolo2815343760600316023s_real tptp.zero_zero_real) tptp.at_top_nat) (=> (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_nat_real A N2)))) (=> (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_nat_real A (tptp.aa_nat_nat tptp.suc N2))) (tptp.aa_nat_real A N2)))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.suminf_real _let_1)) (tptp.groups6591440286371151544t_real _let_1 (tptp.set_ord_lessThan_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N)) tptp.one_one_nat)))))))))) (forall ((P tptp.fun_nat_bool) (K tptp.nat)) (= (tptp.eventually_nat (tptp.aa_nat_fun_nat_bool (tptp.aTP_Lamm_zi P) K) tptp.at_top_nat) (tptp.eventually_nat P tptp.at_top_nat))) (forall ((P tptp.fun_nat_bool) (K tptp.nat)) (=> (tptp.eventually_nat P tptp.at_top_nat) (tptp.eventually_nat (tptp.aa_nat_fun_nat_bool (tptp.aTP_Lamm_zi P) K) tptp.at_top_nat))) (forall ((P tptp.fun_nat_bool)) (= (tptp.eventually_nat P tptp.at_top_nat) (exists ((N9 tptp.nat)) (forall ((N5 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N9) N5)) (tptp.pp (tptp.aa_nat_bool P N5))))))) (forall ((C tptp.nat) (P tptp.fun_nat_bool)) (=> (forall ((X4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat C) X4)) (tptp.pp (tptp.aa_nat_bool P X4)))) (tptp.eventually_nat P tptp.at_top_nat))) (forall ((F4 tptp.filter_nat)) (= (tptp.ord_le2510731241096832064er_nat F4 tptp.at_top_nat) (forall ((N9 tptp.nat)) (tptp.eventually_nat (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N9) F4)))) (forall ((F tptp.fun_real_real)) (= (tptp.real_V5970128139526366754l_real F) (exists ((C3 tptp.real)) (forall ((X3 tptp.real)) (= (tptp.aa_real_real F X3) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real X3) C3)))))) (forall ((L tptp.nat) (U tptp.nat)) (= (tptp.finite_card_nat (tptp.set_or6659071591806873216st_nat L U)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat U) L))) (tptp.filterlim_real_real tptp.sqrt tptp.at_top_real tptp.at_top_real) (forall ((B2 tptp.real) (A tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B2) A)) (tptp.eventually_real (tptp.aa_rea7809428808904475482l_bool (tptp.aTP_Lamm_zj B2) A) (tptp.topolo2177554685111907308n_real A (tptp.set_or5984915006950818249n_real A))))) (tptp.filterlim_real_real tptp.tan_real tptp.at_top_real (tptp.topolo2177554685111907308n_real _let_30 (tptp.set_or5984915006950818249n_real _let_30))) (forall ((B2 tptp.real) (F tptp.fun_real_real) (Flim tptp.real)) (=> (forall ((X4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real B2) X4)) (exists ((Y5 tptp.real)) (and (tptp.has_fi5821293074295781190e_real F Y5 (tptp.topolo2177554685111907308n_real X4 tptp.top_top_set_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y5) tptp.zero_zero_real)))))) (=> (tptp.filterlim_real_real F (tptp.topolo2815343760600316023s_real Flim) tptp.at_top_real) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Flim) (tptp.aa_real_real F B2)))))) (tptp.filterlim_real_real tptp.arctan (tptp.topolo2815343760600316023s_real _let_30) tptp.at_top_real) (tptp.ord_le4104064031414453916r_real tptp.at_top_real tptp.at_infinity_real) (forall ((I tptp.int) (J tptp.int)) (= (tptp.aa_int_set_int (tptp.aa_int8639817059373041269et_int tptp.set_or6656581121297822940st_int I) J) (tptp.set_int2 (tptp.upto (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int I) tptp.one_one_int) J)))) (forall ((N tptp.nat) (F tptp.fun_real_real) (F4 tptp.filter_real)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (=> (tptp.filterlim_real_real F tptp.at_bot_real F4) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N)) (tptp.filterlim_real_real (tptp.aa_fun6946558556880649704l_real (tptp.aTP_Lamm_zk N) F) tptp.at_top_real F4))))) (tptp.ord_le4104064031414453916r_real tptp.at_bot_real tptp.at_infinity_real) (forall ((B2 tptp.real) (F tptp.fun_real_real) (Flim tptp.real)) (=> (forall ((X4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X4) B2)) (exists ((Y5 tptp.real)) (and (tptp.has_fi5821293074295781190e_real F Y5 (tptp.topolo2177554685111907308n_real X4 tptp.top_top_set_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) Y5)))))) (=> (tptp.filterlim_real_real F (tptp.topolo2815343760600316023s_real Flim) tptp.at_bot_real) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Flim) (tptp.aa_real_real F B2)))))) (forall ((N tptp.nat) (F tptp.fun_real_real) (F4 tptp.filter_real)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (=> (tptp.filterlim_real_real F tptp.at_bot_real F4) (=> (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N))) (tptp.filterlim_real_real (tptp.aa_fun6946558556880649704l_real (tptp.aTP_Lamm_zk N) F) tptp.at_bot_real F4))))) (tptp.filterlim_real_real tptp.arctan (tptp.topolo2815343760600316023s_real _let_31) tptp.at_bot_real) (forall ((F tptp.fun_nat_real) (A tptp.real) (B2 tptp.real)) (=> (tptp.ord_less_eq_set_real (tptp.image_nat_real F tptp.top_top_set_nat) (tptp.set_or1222579329274155063t_real A B2)) (tptp.bfun_nat_real F tptp.at_top_nat))) (forall ((X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) tptp.one_one_real)) (tptp.bfun_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) tptp.at_top_nat)))) (forall ((X tptp.real)) (tptp.filterlim_real_real (tptp.aa_rea7340605660300375871l_real tptp.aTP_Lamm_zl X) (tptp.topolo2815343760600316023s_real (tptp.aa_real_real tptp.exp_real X)) (tptp.topolo2177554685111907308n_real tptp.zero_zero_real (tptp.set_or5849166863359141190n_real tptp.zero_zero_real)))) (tptp.filterlim_real_real tptp.tan_real tptp.at_bot_real (tptp.topolo2177554685111907308n_real _let_31 (tptp.set_or5849166863359141190n_real _let_31))) (forall ((A tptp.real) (B2 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B2)) (tptp.eventually_real (tptp.aa_rea7809428808904475482l_bool (tptp.aTP_Lamm_zj A) B2) (tptp.topolo2177554685111907308n_real A (tptp.set_or5849166863359141190n_real A))))) (forall ((X7 tptp.fun_nat_real) (B4 tptp.real)) (=> (tptp.order_9091379641038594480t_real X7) (=> (forall ((I3 tptp.nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real B4) (tptp.aa_nat_real X7 I3)))) (tptp.bfun_nat_real X7 tptp.at_top_nat)))) (forall ((X7 tptp.fun_nat_real) (B4 tptp.real)) (=> (tptp.order_9091379641038594480t_real X7) (=> (forall ((I3 tptp.nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real B4) (tptp.aa_nat_real X7 I3)))) (not (forall ((L6 tptp.real)) (=> (tptp.filterlim_nat_real X7 (tptp.topolo2815343760600316023s_real L6) tptp.at_top_nat) (not (forall ((I2 tptp.nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real L6) (tptp.aa_nat_real X7 I2))))))))))) (forall ((A tptp.real) (B2 tptp.real) (F tptp.fun_real_real) (G tptp.fun_real_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B2)) (=> (forall ((X4 tptp.real)) (=> (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) X4)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X4) B2))) (tptp.topolo4422821103128117721l_real (tptp.topolo2177554685111907308n_real X4 tptp.top_top_set_real) F))) (=> (forall ((X4 tptp.real)) (=> (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) X4)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X4) B2))) (tptp.differ6690327859849518006l_real F (tptp.topolo2177554685111907308n_real X4 tptp.top_top_set_real)))) (=> (forall ((X4 tptp.real)) (=> (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) X4)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X4) B2))) (tptp.topolo4422821103128117721l_real (tptp.topolo2177554685111907308n_real X4 tptp.top_top_set_real) G))) (=> (forall ((X4 tptp.real)) (=> (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) X4)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X4) B2))) (tptp.differ6690327859849518006l_real G (tptp.topolo2177554685111907308n_real X4 tptp.top_top_set_real)))) (exists ((G_c tptp.real) (F_c tptp.real) (C2 tptp.real)) (let ((_let_1 (tptp.topolo2177554685111907308n_real C2 tptp.top_top_set_real))) (and (tptp.has_fi5821293074295781190e_real G G_c _let_1) (tptp.has_fi5821293074295781190e_real F F_c _let_1) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) C2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real C2) B2)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real F B2)) (tptp.aa_real_real F A))) G_c) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real G B2)) (tptp.aa_real_real G A))) F_c))))))))))) (forall ((A tptp.real) (B2 tptp.real) (F tptp.fun_real_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B2)) (=> (tptp.topolo5044208981011980120l_real (tptp.set_or1222579329274155063t_real A B2) F) (=> (forall ((X4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) X4)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X4) B2)) (tptp.differ6690327859849518006l_real F (tptp.topolo2177554685111907308n_real X4 tptp.top_top_set_real))))) (exists ((L3 tptp.real) (Z4 tptp.real)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) Z4)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Z4) B2)) (tptp.has_fi5821293074295781190e_real F L3 (tptp.topolo2177554685111907308n_real Z4 tptp.top_top_set_real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real F B2)) (tptp.aa_real_real F A)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real B2) A)) L3)))))))) (forall ((A4 tptp.set_real) (F tptp.fun_real_real)) (=> (tptp.topolo5044208981011980120l_real A4 F) (=> (forall ((X4 tptp.real)) (=> (tptp.member_real X4 A4) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.one_one_real) (tptp.aa_real_real F X4))))) (tptp.topolo5044208981011980120l_real A4 (tptp.aTP_Lamm_zm F))))) (forall ((A tptp.real) (B2 tptp.real) (F tptp.fun_real_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) B2)) (=> (tptp.topolo5044208981011980120l_real (tptp.set_or1222579329274155063t_real A B2) F) (exists ((C2 tptp.real) (D2 tptp.real)) (and (= (tptp.image_real_real F (tptp.set_or1222579329274155063t_real A B2)) (tptp.set_or1222579329274155063t_real C2 D2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real C2) D2))))))) (forall ((A4 tptp.set_real)) (=> (tptp.ord_less_eq_set_real A4 (tptp.set_ord_atLeast_real tptp.one_one_real)) (tptp.topolo5044208981011980120l_real A4 tptp.arcosh_real))) (forall ((A tptp.real) (B2 tptp.real) (F tptp.fun_real_real) (F3 tptp.fun_re7681423839302404990l_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B2)) (=> (= (tptp.aa_real_real F A) (tptp.aa_real_real F B2)) (=> (tptp.topolo5044208981011980120l_real (tptp.set_or1222579329274155063t_real A B2) F) (=> (forall ((X4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) X4)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X4) B2)) (tptp.has_de1759254742604945161l_real F (tptp.aa_rea7340605660300375871l_real F3 X4) (tptp.topolo2177554685111907308n_real X4 tptp.top_top_set_real))))) (exists ((Z4 tptp.real)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) Z4)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Z4) B2)) (forall ((X5 tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real F3 Z4) X5) tptp.zero_zero_real))))))))) (forall ((A tptp.real) (B2 tptp.real) (F tptp.fun_real_real) (F3 tptp.fun_re7681423839302404990l_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B2)) (=> (tptp.topolo5044208981011980120l_real (tptp.set_or1222579329274155063t_real A B2) F) (=> (forall ((X4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) X4)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X4) B2)) (tptp.has_de1759254742604945161l_real F (tptp.aa_rea7340605660300375871l_real F3 X4) (tptp.topolo2177554685111907308n_real X4 tptp.top_top_set_real))))) (not (forall ((Xi tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) Xi)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Xi) B2)) (not (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real F B2)) (tptp.aa_real_real F A)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real F3 Xi) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real B2) A)))))))))))) (forall ((A tptp.real) (B2 tptp.real) (F tptp.fun_real_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B2)) (=> (forall ((X4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) X4)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X4) B2)) (exists ((Y5 tptp.real)) (and (tptp.has_fi5821293074295781190e_real F Y5 (tptp.topolo2177554685111907308n_real X4 tptp.top_top_set_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) Y5))))))) (=> (tptp.topolo5044208981011980120l_real (tptp.set_or1222579329274155063t_real A B2) F) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real F A)) (tptp.aa_real_real F B2))))))) (forall ((A tptp.real) (B2 tptp.real) (F tptp.fun_real_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B2)) (=> (forall ((X4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) X4)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X4) B2)) (exists ((Y5 tptp.real)) (and (tptp.has_fi5821293074295781190e_real F Y5 (tptp.topolo2177554685111907308n_real X4 tptp.top_top_set_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y5) tptp.zero_zero_real))))))) (=> (tptp.topolo5044208981011980120l_real (tptp.set_or1222579329274155063t_real A B2) F) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real F B2)) (tptp.aa_real_real F A))))))) (forall ((A tptp.real) (B2 tptp.real) (F tptp.fun_real_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B2)) (=> (tptp.topolo5044208981011980120l_real (tptp.set_or1222579329274155063t_real A B2) F) (=> (forall ((X4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) X4)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X4) B2)) (tptp.has_fi5821293074295781190e_real F tptp.zero_zero_real (tptp.topolo2177554685111907308n_real X4 tptp.top_top_set_real))))) (= (tptp.aa_real_real F B2) (tptp.aa_real_real F A)))))) (forall ((A4 tptp.set_real)) (=> (tptp.ord_less_eq_set_real A4 (tptp.set_or1633881224788618240n_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real) tptp.one_one_real)) (tptp.topolo5044208981011980120l_real A4 tptp.artanh_real))) (forall ((A tptp.real) (B2 tptp.real) (F tptp.fun_real_real) (X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B2)) (=> (tptp.topolo5044208981011980120l_real (tptp.set_or1222579329274155063t_real A B2) F) (=> (forall ((X4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) X4)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X4) B2)) (tptp.has_fi5821293074295781190e_real F tptp.zero_zero_real (tptp.topolo2177554685111907308n_real X4 tptp.top_top_set_real))))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) B2)) (= (tptp.aa_real_real F X) (tptp.aa_real_real F A)))))))) (forall ((A tptp.real) (B2 tptp.real) (F tptp.fun_real_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B2)) (=> (= (tptp.aa_real_real F A) (tptp.aa_real_real F B2)) (=> (tptp.topolo5044208981011980120l_real (tptp.set_or1222579329274155063t_real A B2) F) (=> (forall ((X4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) X4)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X4) B2)) (tptp.differ6690327859849518006l_real F (tptp.topolo2177554685111907308n_real X4 tptp.top_top_set_real))))) (exists ((Z4 tptp.real)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) Z4)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Z4) B2)) (tptp.has_fi5821293074295781190e_real F tptp.zero_zero_real (tptp.topolo2177554685111907308n_real Z4 tptp.top_top_set_real))))))))) (tptp.order_mono_nat_nat tptp.suc) (forall ((N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (tptp.order_mono_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat N)))) (forall ((X7 tptp.fun_nat_real) (B4 tptp.real)) (=> (tptp.order_mono_nat_real X7) (=> (forall ((I3 tptp.nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_nat_real X7 I3)) B4))) (tptp.bfun_nat_real X7 tptp.at_top_nat)))) (forall ((X7 tptp.fun_nat_real) (B4 tptp.real)) (=> (tptp.order_mono_nat_real X7) (=> (forall ((I3 tptp.nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_nat_real X7 I3)) B4))) (not (forall ((L6 tptp.real)) (=> (tptp.filterlim_nat_real X7 (tptp.topolo2815343760600316023s_real L6) tptp.at_top_nat) (not (forall ((I2 tptp.nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_nat_real X7 I2)) L6)))))))))) (forall ((K tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) K)) (tptp.order_mono_nat_nat (tptp.aa_nat_fun_nat_nat tptp.aTP_Lamm_zn K)))) (forall ((F tptp.fun_nat_real) (G tptp.fun_nat_nat)) (=> (forall ((X4 tptp.nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_nat_real F X4)))) (=> (tptp.order_mono_nat_real F) (=> (tptp.order_5726023648592871131at_nat G) (= (tptp.bfun_nat_real (tptp.aa_fun1538629612289296340t_real (tptp.aTP_Lamm_zo F) G) tptp.at_top_nat) (tptp.bfun_nat_real F tptp.at_top_nat)))))) (forall ((F tptp.fun_nat_nat) (N tptp.nat)) (=> (tptp.order_5726023648592871131at_nat F) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N) (tptp.aa_nat_nat F N))))) (forall ((N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (tptp.inj_on_real_real (tptp.aa_nat_fun_real_real tptp.aTP_Lamm_xy N) tptp.top_top_set_real))) (forall ((X tptp.list_nat) (Y tptp.nat)) (=> (= (tptp.nat_list_encode X) Y) (=> (=> (= X tptp.nil_nat) (not (= Y tptp.zero_zero_nat))) (not (forall ((X4 tptp.nat) (Xs2 tptp.list_nat)) (=> (= X (tptp.cons_nat X4 Xs2)) (not (= Y (tptp.aa_nat_nat tptp.suc (tptp.aa_Pro4243173770044397973at_nat tptp.nat_prod_encode (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat X4) (tptp.nat_list_encode Xs2)))))))))))) (forall ((B2 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real) B2)) (tptp.inj_on_real_real (tptp.aa_rea7340605660300375871l_real tptp.log B2) (tptp.set_or5849166863359141190n_real tptp.zero_zero_real)))) (forall ((X tptp.nat) (Xs tptp.list_nat)) (= (tptp.nat_list_encode (tptp.cons_nat X Xs)) (tptp.aa_nat_nat tptp.suc (tptp.aa_Pro4243173770044397973at_nat tptp.nat_prod_encode (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat X) (tptp.nat_list_encode Xs)))))) (forall ((F tptp.fun_real_real) (F3 tptp.fun_real_real)) (=> (forall ((X4 tptp.real)) (tptp.has_fi5821293074295781190e_real F (tptp.aa_real_real F3 X4) (tptp.topolo2177554685111907308n_real X4 tptp.top_top_set_real))) (=> (forall ((X4 tptp.real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) (tptp.aa_real_real F3 X4)))) (tptp.order_7092887310737990675l_real F)))) (forall ((X tptp.list_nat) (Y tptp.nat)) (let ((_let_1 (tptp.accp_list_nat tptp.nat_list_encode_rel))) (=> (= (tptp.nat_list_encode X) Y) (=> (tptp.pp (tptp.aa_list_nat_bool _let_1 X)) (=> (=> (= X tptp.nil_nat) (=> (= Y tptp.zero_zero_nat) (not (tptp.pp (tptp.aa_list_nat_bool _let_1 tptp.nil_nat))))) (not (forall ((X4 tptp.nat) (Xs2 tptp.list_nat)) (let ((_let_1 (tptp.cons_nat X4 Xs2))) (=> (= X _let_1) (=> (= Y (tptp.aa_nat_nat tptp.suc (tptp.aa_Pro4243173770044397973at_nat tptp.nat_prod_encode (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat X4) (tptp.nat_list_encode Xs2))))) (not (tptp.pp (tptp.aa_list_nat_bool (tptp.accp_list_nat tptp.nat_list_encode_rel) _let_1))))))))))))) (forall ((N3 tptp.set_nat) (K tptp.nat)) (=> (forall ((N2 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat N2) N3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) N2)))) (tptp.pp (tptp.aa_set_nat_bool (tptp.inj_on_nat_nat (tptp.aa_nat_fun_nat_nat tptp.aTP_Lamm_xu K)) N3)))) (forall ((N3 tptp.set_nat)) (tptp.pp (tptp.aa_set_nat_bool (tptp.inj_on_nat_nat tptp.suc) N3))) (forall ((F tptp.fun_nat_real) (G tptp.fun_nat_nat)) (=> (tptp.summable_real F) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.inj_on_nat_nat G) tptp.top_top_set_nat)) (=> (forall ((X4 tptp.nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_nat_real F X4)))) (tptp.summable_real (tptp.comp_nat_real_nat F G)))))) (forall ((F tptp.fun_nat_real) (G tptp.fun_nat_nat)) (=> (tptp.summable_real F) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.inj_on_nat_nat G) tptp.top_top_set_nat)) (=> (forall ((X4 tptp.nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_nat_real F X4)))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.suminf_real (tptp.comp_nat_real_nat F G))) (tptp.suminf_real F))))))) (tptp.pp (tptp.aa_set_nat_bool (tptp.inj_on_nat_char tptp.unique3096191561947761185of_nat) _let_27)) (forall ((F tptp.fun_nat_real) (G tptp.fun_nat_nat)) (=> (tptp.summable_real F) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.inj_on_nat_nat G) tptp.top_top_set_nat)) (=> (forall ((X4 tptp.nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_nat_real F X4)))) (=> (forall ((X4 tptp.nat)) (=> (not (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X4) (tptp.image_nat_nat G tptp.top_top_set_nat)))) (= (tptp.aa_nat_real F X4) tptp.zero_zero_real))) (= (tptp.suminf_real (tptp.comp_nat_real_nat F G)) (tptp.suminf_real F))))))) (forall ((X tptp.real) (N tptp.int)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) X)) (=> (or (not (= X tptp.zero_zero_real)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) N))) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.powr_real X) (tptp.aa_int_real tptp.ring_1_of_int_real N)) (tptp.aa_int_real (tptp.aa_real_fun_int_real tptp.power_int_real X) N))))) (= tptp.topolo1511823702728130853y_real (tptp.comple2936214249959783750l_real (tptp.image_2178119161166701260l_real tptp.aTP_Lamm_zq _let_23))) (= tptp.topolo896644834953643431omplex (tptp.comple8358262395181532106omplex (tptp.image_5971271580939081552omplex tptp.aTP_Lamm_zs _let_23))) (forall ((P tptp.fun_Pr7757163693017731481t_bool)) (= (tptp.eventu1038000079068216329at_nat P (tptp.prod_filter_nat_nat tptp.at_top_nat tptp.at_top_nat)) (exists ((N9 tptp.nat)) (forall ((M6 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N9) M6)) (forall ((N5 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N9) N5)) (tptp.pp (tptp.aa_Pro2232559814647311250t_bool P (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat N5) M6)))))))))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_min_nat (tptp.aa_nat_nat tptp.suc M)) (tptp.aa_nat_nat tptp.suc N)) (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_min_nat M) N)))) (forall ((N tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_min_nat tptp.zero_zero_nat) N) tptp.zero_zero_nat)) (forall ((N tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_min_nat N) tptp.zero_zero_nat) tptp.zero_zero_nat)) (forall ((K tptp.num) (N tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_min_nat (tptp.aa_num_nat tptp.numeral_numeral_nat K)) (tptp.aa_nat_nat tptp.suc N)) (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_min_nat (tptp.aa_num_nat tptp.pred_numeral K)) N)))) (forall ((N tptp.nat) (K tptp.num)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_min_nat (tptp.aa_nat_nat tptp.suc N)) (tptp.aa_num_nat tptp.numeral_numeral_nat K)) (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_min_nat N) (tptp.aa_num_nat tptp.pred_numeral K))))) (= tptp.inf_inf_nat tptp.ord_min_nat) (forall ((M tptp.nat) (I tptp.nat) (N tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_min_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) I)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) I)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_min_nat M) N)) I))) (forall ((M tptp.nat) (N tptp.nat) (Q2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat M))) (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_min_nat N) Q2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_min_nat (tptp.aa_nat_nat _let_1 N)) (tptp.aa_nat_nat _let_1 Q2))))) (forall ((M tptp.nat) (N tptp.nat) (Q2 tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_min_nat M) N)) Q2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_min_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat M) Q2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat N) Q2)))) (forall ((M tptp.nat) (N tptp.nat) (K tptp.int) (L tptp.int) (R tptp.int)) (= (tptp.aa_int_int (tptp.bit_concat_bit M (tptp.aa_int_int (tptp.bit_concat_bit N K) L)) R) (tptp.aa_int_int (tptp.bit_concat_bit (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_min_nat M) N) K) (tptp.aa_int_int (tptp.bit_concat_bit (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) N) L) R)))) (forall ((M tptp.nat) (N tptp.nat) (K tptp.int) (L tptp.int)) (= (tptp.aa_int_int (tptp.bit_se2923211474154528505it_int M) (tptp.aa_int_int (tptp.bit_concat_bit N K) L)) (tptp.aa_int_int (tptp.bit_concat_bit (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_min_nat M) N) K) (tptp.aa_int_int (tptp.bit_se2923211474154528505it_int (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) N)) L)))) (forall ((N tptp.nat) (M tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_min_nat (tptp.aa_nat_nat tptp.suc N)) M) (tptp.aa_nat_nat (tptp.case_nat_nat tptp.zero_zero_nat (tptp.aa_nat_fun_nat_nat tptp.aTP_Lamm_zt N)) M))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_min_nat M) (tptp.aa_nat_nat tptp.suc N)) (tptp.aa_nat_nat (tptp.case_nat_nat tptp.zero_zero_nat (tptp.aa_nat_fun_nat_nat tptp.aTP_Lamm_zu N)) M))) (forall ((Q2 tptp.extended_enat)) (= (tptp.aa_Ext7969882492699152700d_enat (tptp.aa_Ext3475206891998675565d_enat tptp.ord_mi8085742599997312461d_enat tptp.zero_z5237406670263579293d_enat) Q2) tptp.zero_z5237406670263579293d_enat)) (forall ((Q2 tptp.extended_enat)) (= (tptp.aa_Ext7969882492699152700d_enat (tptp.aa_Ext3475206891998675565d_enat tptp.ord_mi8085742599997312461d_enat Q2) tptp.zero_z5237406670263579293d_enat) tptp.zero_z5237406670263579293d_enat)) (= tptp.inf_in1870772243966228564d_enat tptp.ord_mi8085742599997312461d_enat) (forall ((I tptp.nat) (J tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I) J)) (= (tptp.hd_nat (tptp.upt I J)) I))) (forall ((M tptp.nat) (I tptp.nat) (J tptp.nat)) (= (tptp.drop_nat M (tptp.upt I J)) (tptp.upt (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat I) M) J))) (forall ((I tptp.nat) (J tptp.nat)) (= (tptp.size_size_list_nat (tptp.upt I J)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat J) I))) (forall ((I tptp.nat) (K tptp.nat) (J tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat I) K))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_1) J)) (= (tptp.aa_nat_nat (tptp.nth_nat (tptp.upt I J)) K) _let_1)))) (forall ((I tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat I) M))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat _let_1) N)) (= (tptp.take_nat M (tptp.upt I N)) (tptp.upt I _let_1))))) (forall ((J tptp.nat) (I tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat J) I)) (= (tptp.upt I J) tptp.nil_nat))) (forall ((I tptp.nat) (J tptp.nat)) (= (= (tptp.upt I J) tptp.nil_nat) (or (= J tptp.zero_zero_nat) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat J) I))))) (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat N))) (let ((_let_2 (tptp.aa_num_nat tptp.numeral_numeral_nat M))) (let ((_let_3 (tptp.upt _let_2 _let_1))) (let ((_let_4 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_2) _let_1)))) (and (=> _let_4 (= _let_3 (tptp.cons_nat _let_2 (tptp.upt (tptp.aa_nat_nat tptp.suc _let_2) _let_1)))) (=> (not _let_4) (= _let_3 tptp.nil_nat)))))))) (forall ((N tptp.nat) (M tptp.nat)) (= (tptp.map_nat_nat (tptp.aa_nat_fun_nat_nat tptp.aTP_Lamm_zv N) (tptp.upt tptp.zero_zero_nat M)) (tptp.upt N (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) N)))) (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat J) K))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I) J)) (= (tptp.upt I _let_1) (tptp.append_nat (tptp.upt I J) (tptp.upt J _let_1)))))) (forall ((N tptp.nat) (M tptp.nat)) (= (tptp.set_or6659071591806873216st_nat N M) (tptp.set_nat2 (tptp.upt (tptp.aa_nat_nat tptp.suc N) (tptp.aa_nat_nat tptp.suc M))))) (forall ((N tptp.nat) (M tptp.nat)) (= (tptp.set_or5834768355832116004an_nat N M) (tptp.set_nat2 (tptp.upt (tptp.aa_nat_nat tptp.suc N) M)))) (forall ((N tptp.nat) (M tptp.nat)) (= (tptp.set_or1269000886237332187st_nat N M) (tptp.set_nat2 (tptp.upt N (tptp.aa_nat_nat tptp.suc M))))) (forall ((I tptp.nat) (J tptp.nat)) (= (tptp.set_or4665077453230672383an_nat I J) (tptp.set_nat2 (tptp.upt I J)))) (forall ((N tptp.nat)) (= (tptp.set_ord_lessThan_nat N) (tptp.set_nat2 (tptp.upt tptp.zero_zero_nat N)))) (forall ((N tptp.nat)) (= (tptp.set_ord_atMost_nat N) (tptp.set_nat2 (tptp.upt tptp.zero_zero_nat (tptp.aa_nat_nat tptp.suc N))))) (forall ((I tptp.nat) (J tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I) J)) (= (tptp.upt I J) (tptp.cons_nat I (tptp.upt (tptp.aa_nat_nat tptp.suc I) J))))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.map_nat_nat tptp.aTP_Lamm_zw (tptp.upt (tptp.aa_nat_nat tptp.suc M) (tptp.aa_nat_nat tptp.suc N))) (tptp.upt M N))) (forall ((I tptp.nat) (J tptp.nat) (X tptp.nat) (Xs tptp.list_nat)) (= (= (tptp.upt I J) (tptp.cons_nat X Xs)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I) J)) (= I X) (= (tptp.upt (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat I) tptp.one_one_nat) J) Xs)))) (forall ((I tptp.nat) (J tptp.nat)) (let ((_let_1 (tptp.upt I J))) (let ((_let_2 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I) J)))) (and (=> _let_2 (= _let_1 (tptp.cons_nat I (tptp.upt (tptp.aa_nat_nat tptp.suc I) J)))) (=> (not _let_2) (= _let_1 tptp.nil_nat)))))) (forall ((I tptp.nat) (J tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I) J)) (= (tptp.upt I (tptp.aa_nat_nat tptp.suc J)) (tptp.append_nat (tptp.upt I J) (tptp.cons_nat J tptp.nil_nat))))) (forall ((I tptp.nat) (J tptp.nat)) (let ((_let_1 (tptp.upt I (tptp.aa_nat_nat tptp.suc J)))) (let ((_let_2 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I) J)))) (and (=> _let_2 (= _let_1 (tptp.append_nat (tptp.upt I J) (tptp.cons_nat J tptp.nil_nat)))) (=> (not _let_2) (= _let_1 tptp.nil_nat)))))) (forall ((N tptp.nat) (J tptp.nat) (I tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat J) (tptp.aa_nat_nat tptp.suc I)))) (= (tptp.aa_nat_nat (tptp.nth_nat (tptp.linord2614967742042102400et_nat (tptp.set_or5834768355832116004an_nat I J))) N) (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat I) N))))) (forall ((N tptp.nat) (J tptp.nat) (I tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat J) I))) (= (tptp.aa_nat_nat (tptp.nth_nat (tptp.linord2614967742042102400et_nat (tptp.set_or6659071591806873216st_nat I J))) N) (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat I) N))))) (forall ((I tptp.nat) (J tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc I))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat _let_1) J)) (= (tptp.linord2614967742042102400et_nat (tptp.set_or6659071591806873216st_nat I J)) (tptp.cons_nat _let_1 (tptp.linord2614967742042102400et_nat (tptp.set_or6659071591806873216st_nat _let_1 J))))))) (forall ((I tptp.nat) (J tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc I))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_1) J)) (= (tptp.linord2614967742042102400et_nat (tptp.set_or5834768355832116004an_nat I J)) (tptp.cons_nat _let_1 (tptp.linord2614967742042102400et_nat (tptp.set_or5834768355832116004an_nat _let_1 J))))))) (forall ((M tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)) (= (tptp.groups4561878855575611511st_nat (tptp.upt M N)) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat tptp.aTP_Lamm_al) (tptp.set_or4665077453230672383an_nat M N))))) (forall ((M tptp.nat) (N3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.one_one_nat) M)) (= (tptp.finite_card_list_nat (tptp.collect_list_nat (tptp.aa_nat2079453845469346690t_bool (tptp.aTP_Lamm_zx M) N3))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.finite_card_list_nat (tptp.collect_list_nat (tptp.aa_nat2079453845469346690t_bool (tptp.aTP_Lamm_zy M) N3)))) (tptp.finite_card_list_nat (tptp.collect_list_nat (tptp.aa_nat2079453845469346690t_bool (tptp.aTP_Lamm_zz M) N3))))))) (forall ((M tptp.nat) (N3 tptp.nat)) (= (tptp.finite_card_list_nat (tptp.collect_list_nat (tptp.aa_nat2079453845469346690t_bool (tptp.aTP_Lamm_zx M) N3))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N3) M)) tptp.one_one_nat)) N3))) (forall ((M tptp.nat) (N tptp.nat)) (tptp.pp (tptp.aa_list_nat_bool (tptp.sorted_wrt_nat tptp.ord_less_eq_nat) (tptp.upt M N)))) (forall ((M tptp.nat) (N tptp.nat)) (tptp.pp (tptp.aa_list_nat_bool (tptp.sorted_wrt_nat tptp.ord_less_nat) (tptp.upt M N)))) (forall ((Ns tptp.list_nat) (I tptp.nat)) (=> (tptp.pp (tptp.aa_list_nat_bool (tptp.sorted_wrt_nat tptp.ord_less_nat) Ns)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I) (tptp.size_size_list_nat Ns))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I) (tptp.aa_nat_nat (tptp.nth_nat Ns) I)))))) (forall ((I tptp.int) (J tptp.int)) (tptp.sorted_wrt_int tptp.ord_less_int (tptp.upto I J))) (forall ((M tptp.int) (N tptp.int)) (tptp.sorted_wrt_int tptp.ord_less_eq_int (tptp.upto M N))) (forall ((X11 tptp.option4927543243414619207at_nat) (X12 tptp.nat) (X13 tptp.list_VEBT_VEBT) (X14 tptp.vEBT_VEBT)) (= (tptp.aa_VEBT_VEBT_nat tptp.size_size_VEBT_VEBT (tptp.vEBT_Node X11 X12 X13 X14)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.size_list_VEBT_VEBT tptp.size_size_VEBT_VEBT X13)) (tptp.aa_VEBT_VEBT_nat tptp.size_size_VEBT_VEBT X14))) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)))) (forall ((X11 tptp.option4927543243414619207at_nat) (X12 tptp.nat) (X13 tptp.list_VEBT_VEBT) (X14 tptp.vEBT_VEBT)) (= (tptp.aa_VEBT_VEBT_nat tptp.vEBT_size_VEBT (tptp.vEBT_Node X11 X12 X13 X14)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.size_list_VEBT_VEBT tptp.vEBT_size_VEBT X13)) (tptp.aa_VEBT_VEBT_nat tptp.vEBT_size_VEBT X14))) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)))) (forall ((S2 tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat S2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.finite_card_nat S2)) (tptp.aa_nat_nat tptp.suc (tptp.lattic8265883725875713057ax_nat S2)))))) (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat M) N))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.zero_zero_nat)) (=> (not _let_2) (= _let_1 (tptp.lattic8265883725875713057ax_nat (tptp.collect_nat (tptp.aa_nat_fun_nat_bool (tptp.aTP_Lamm_aaa N) M))))))))) (forall ((N tptp.nat) (M tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.gcd_gcd_nat M) N) (tptp.lattic8265883725875713057ax_nat (tptp.collect_nat (tptp.aa_nat_fun_nat_bool (tptp.aTP_Lamm_aab N) M)))))) (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat J) K))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I) J)) (= (tptp.set_or4665077453230672383an_nat I _let_1) (tptp.sup_sup_set_nat (tptp.set_or4665077453230672383an_nat I J) (tptp.set_or4665077453230672383an_nat J _let_1)))))) (= tptp.sup_sup_nat tptp.ord_max_nat) (= tptp.sup_su3973961784419623482d_enat tptp.ord_ma741700101516333627d_enat) (forall ((X tptp.rat)) (= (tptp.quotient_of X) (tptp.the_Pr4378521158711661632nt_int (tptp.aTP_Lamm_aac X)))) (forall ((K tptp.int) (L tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.algebr932160517623751201me_int (tptp.aa_int_int tptp.abs_abs_int K)) L)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.algebr932160517623751201me_int K) L)))) (forall ((K tptp.int) (L tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.algebr932160517623751201me_int K))) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int tptp.abs_abs_int L))) (tptp.pp (tptp.aa_int_bool _let_1 L))))) (forall ((Q2 tptp.int) (P2 tptp.int)) (let ((_let_1 (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int P2) Q2))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) Q2)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.algebr932160517623751201me_int P2) Q2)) (= (tptp.aa_Pro6970504127699319548nt_int tptp.normalize _let_1) _let_1))))) (forall ((Q2 tptp.rat)) (not (forall ((A3 tptp.int) (B3 tptp.int)) (=> (= Q2 (tptp.aa_int_rat (tptp.aa_int_fun_int_rat tptp.fract A3) B3)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) B3)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.algebr932160517623751201me_int A3) B3)))))))) (forall ((P tptp.fun_rat_bool) (Q2 tptp.rat)) (=> (forall ((A3 tptp.int) (B3 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) B3)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.algebr932160517623751201me_int A3) B3)) (tptp.pp (tptp.aa_rat_bool P (tptp.aa_int_rat (tptp.aa_int_fun_int_rat tptp.fract A3) B3)))))) (tptp.pp (tptp.aa_rat_bool P Q2)))) (forall ((R tptp.rat) (P2 tptp.int) (Q2 tptp.int)) (=> (= (tptp.quotient_of R) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int P2) Q2)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.algebr932160517623751201me_int P2) Q2)))) (forall ((R tptp.product_prod_int_int) (P2 tptp.int) (Q2 tptp.int)) (=> (= (tptp.aa_Pro6970504127699319548nt_int tptp.normalize R) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int P2) Q2)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.algebr932160517623751201me_int P2) Q2)))) (forall ((A tptp.int) (D tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_int tptp.abs_abs_int D))) (let ((_let_2 (tptp.aa_int_int tptp.abs_abs_int C))) (let ((_let_3 (tptp.aa_int_int tptp.abs_abs_int B2))) (let ((_let_4 (tptp.aa_int_int tptp.abs_abs_int A))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.algebr932160517623751201me_int A) D)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.algebr932160517623751201me_int B2) C)) (= (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int _let_4) _let_2) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int _let_3) _let_1)) (and (= _let_4 _let_3) (= _let_2 _let_1)))))))))) (forall ((A tptp.int) (B2 tptp.int) (X tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int X))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.algebr932160517623751201me_int A) B2)) (=> (tptp.pp (tptp.aa_int_bool _let_1 A)) (=> (tptp.pp (tptp.aa_int_bool _let_1 B2)) (= (tptp.aa_int_int tptp.abs_abs_int X) tptp.one_one_int)))))) (forall ((Q2 tptp.rat)) (=> (forall ((A3 tptp.int) (B3 tptp.int)) (=> (= Q2 (tptp.aa_int_rat (tptp.aa_int_fun_int_rat tptp.fract A3) B3)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) B3)) (=> (not (= A3 tptp.zero_zero_int)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.algebr932160517623751201me_int A3) B3))))))) (= Q2 tptp.zero_zero_rat))) (forall ((R tptp.rat)) (exists ((X4 tptp.product_prod_int_int)) (let ((_let_1 (tptp.product_snd_int_int X4))) (let ((_let_2 (tptp.product_fst_int_int X4))) (and (= R (tptp.aa_int_rat (tptp.aa_int_fun_int_rat tptp.fract _let_2) _let_1)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) _let_1)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.algebr932160517623751201me_int _let_2) _let_1)) (forall ((Y5 tptp.product_prod_int_int)) (let ((_let_1 (tptp.product_snd_int_int Y5))) (let ((_let_2 (tptp.product_fst_int_int Y5))) (=> (and (= R (tptp.aa_int_rat (tptp.aa_int_fun_int_rat tptp.fract _let_2) _let_1)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) _let_1)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.algebr932160517623751201me_int _let_2) _let_1))) (= Y5 X4)))))))))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.algebr932160517623751201me_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int M)) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.algebr934650988132801477me_nat M) N)))) (forall ((N tptp.nat) (K tptp.int)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.algebr934650988132801477me_nat N) (tptp.aa_int_nat tptp.nat2 (tptp.aa_int_int tptp.abs_abs_int K)))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.algebr932160517623751201me_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N)) K)))) (forall ((K tptp.int) (N tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.algebr934650988132801477me_nat (tptp.aa_int_nat tptp.nat2 (tptp.aa_int_int tptp.abs_abs_int K))) N)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.algebr932160517623751201me_int K) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N))))) (forall ((N tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.algebr934650988132801477me_nat (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)) N))) (forall ((N tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.algebr934650988132801477me_nat N) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)))) (forall ((A tptp.nat) (D tptp.nat) (B2 tptp.nat) (C tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.algebr934650988132801477me_nat A) D)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.algebr934650988132801477me_nat B2) C)) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) C) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B2) D)) (and (= A B2) (= C D)))))) (forall ((A tptp.nat) (B2 tptp.nat) (X tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat X))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.algebr934650988132801477me_nat A) B2)) (=> (tptp.pp (tptp.aa_nat_bool _let_1 A)) (=> (tptp.pp (tptp.aa_nat_bool _let_1 B2)) (= X tptp.one_one_nat)))))) (forall ((Xs tptp.list_int)) (= (tptp.gcd_Gcd_int (tptp.set_int2 Xs)) (tptp.aa_int_int (tptp.fold_int_int tptp.gcd_gcd_int Xs) tptp.zero_zero_int))) (forall ((Xs tptp.list_nat)) (= (tptp.gcd_Gcd_nat (tptp.set_nat2 Xs)) (tptp.aa_nat_nat (tptp.fold_nat_nat tptp.gcd_gcd_nat Xs) tptp.zero_zero_nat))) (forall ((K5 tptp.set_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.gcd_Gcd_int K5)))) (forall ((N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.algebr934650988132801477me_nat N) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) tptp.one_one_nat))))) (forall ((N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.algebr934650988132801477me_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) tptp.one_one_nat)) N)))) (forall ((X tptp.real)) (=> (tptp.member_real X tptp.field_5140801741446780682s_real) (not (forall ((M3 tptp.nat) (N2 tptp.nat)) (=> (not (= N2 tptp.zero_zero_nat)) (=> (= (tptp.aa_real_real tptp.abs_abs_real X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real M3)) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N2))) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.algebr934650988132801477me_nat M3) N2))))))))) (tptp.bNF_re1394333895916556125l_bool tptp.ratrel tptp.fequal_bool tptp.aTP_Lamm_xx tptp.aTP_Lamm_xx) (tptp.bNF_re5780769757191362231t_bool tptp.fequal_int _let_20 tptp.ord_less_eq_int tptp.ord_less_eq_int) (tptp.bNF_re1480548845665215743t_bool tptp.fequal_nat _let_21 tptp.ord_less_eq_nat tptp.ord_less_eq_nat) (tptp.bNF_re4734134812813710757nt_int tptp.ratrel _let_19 tptp.aTP_Lamm_xz tptp.aTP_Lamm_xz) (tptp.bNF_re4734134812813710757nt_int tptp.ratrel _let_19 tptp.aTP_Lamm_yc tptp.aTP_Lamm_yc) (tptp.bNF_re4808202430149235895nt_int tptp.fequal_int (tptp.bNF_re6250860962936578807nt_int tptp.fequal_int tptp.ratrel) tptp.aTP_Lamm_aad tptp.aTP_Lamm_aad) (tptp.bNF_re5162689864697376059at_nat tptp.fequal_nat _let_22 tptp.plus_plus_nat tptp.plus_plus_nat) (tptp.bNF_re5162689864697376059at_nat tptp.fequal_nat _let_22 tptp.minus_minus_nat tptp.minus_minus_nat) (tptp.bNF_re5162689864697376059at_nat tptp.fequal_nat _let_22 tptp.times_times_nat tptp.times_times_nat) (tptp.bNF_re5717476210804479843nt_int tptp.fequal_int (tptp.bNF_re4712519889275205905nt_int tptp.fequal_int tptp.fequal_int) tptp.times_times_int tptp.times_times_int) (tptp.bNF_re5162689864697376059at_nat tptp.fequal_nat _let_22 tptp.divide_divide_nat tptp.divide_divide_nat) (tptp.bNF_re6378542964492772123um_int tptp.fequal_num (tptp.bNF_re1822329894187522285nt_int tptp.fequal_num tptp.fequal_int) tptp.aTP_Lamm_aae tptp.aTP_Lamm_aae) (tptp.bNF_re1480548845665215743t_bool tptp.fequal_nat _let_21 tptp.ord_less_nat tptp.ord_less_nat) (tptp.bNF_re5780769757191362231t_bool tptp.fequal_int _let_20 tptp.ord_less_int tptp.ord_less_int) (tptp.pp (tptp.aa_fun1403452029515102102t_bool (tptp.aa_fun8298786006102058668t_bool _let_19 tptp.aTP_Lamm_yb) tptp.aTP_Lamm_yb)) (tptp.pp (tptp.aa_fun1403452029515102102t_bool (tptp.aa_fun8298786006102058668t_bool _let_19 tptp.aTP_Lamm_ya) tptp.aTP_Lamm_ya)) (tptp.bNF_re6323452265856231590at_rat tptp.pcr_rat _let_16 tptp.aTP_Lamm_xz tptp.plus_plus_rat) (tptp.pp (tptp.aa_rat_bool (tptp.aa_Pro6332413336323567195t_bool tptp.pcr_rat _let_18) tptp.one_one_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_Pro6332413336323567195t_bool tptp.pcr_rat _let_17) tptp.zero_zero_rat)) (tptp.bNF_re2486238095283335024nt_rat tptp.fequal_int (tptp.bNF_re2214769303045360666nt_rat tptp.fequal_int tptp.pcr_rat) tptp.aTP_Lamm_aad tptp.fract) (tptp.pp (tptp.aa_fun_rat_rat_bool (tptp.aa_fun2103967415933125506t_bool _let_16 tptp.aTP_Lamm_yb) tptp.uminus_uminus_rat)) (tptp.bNF_re6323452265856231590at_rat tptp.pcr_rat _let_16 tptp.aTP_Lamm_yc tptp.times_times_rat) (tptp.bNF_re3535474257078034868l_bool tptp.pcr_rat tptp.fequal_bool tptp.aTP_Lamm_xx tptp.positive) (tptp.pp (tptp.aa_fun_rat_rat_bool (tptp.aa_fun2103967415933125506t_bool _let_16 tptp.aTP_Lamm_ya) tptp.inverse_inverse_rat)) (tptp.bNF_re8869769828555196650nt_int tptp.pcr_int _let_14 _let_13 tptp.times_times_int) (tptp.pp (tptp.aa_int_bool (tptp.aa_Pro2928840338864870335t_bool tptp.pcr_int _let_9) tptp.zero_zero_int)) (tptp.bNF_re6830278522597306478at_int tptp.fequal_nat tptp.pcr_int tptp.aTP_Lamm_aaf tptp.semiri1314217659103216013at_int) (tptp.pp (tptp.aa_fun_int_int_bool (tptp.aa_fun7527181275634263258t_bool _let_14 _let_11) tptp.uminus_uminus_int)) (tptp.bNF_re4555766996558763186at_nat tptp.pcr_int tptp.fequal_nat _let_12 tptp.nat2) (tptp.pp (tptp.aa_int_bool (tptp.aa_Pro2928840338864870335t_bool tptp.pcr_int _let_10) tptp.one_one_int)) (tptp.bNF_re2632563231991741785t_bool tptp.pcr_int _let_15 _let_8 tptp.ord_less_int) (tptp.bNF_re2632563231991741785t_bool tptp.pcr_int _let_15 _let_6 tptp.ord_less_eq_int) (tptp.bNF_re8869769828555196650nt_int tptp.pcr_int _let_14 _let_3 tptp.plus_plus_int) (tptp.bNF_re8869769828555196650nt_int tptp.pcr_int _let_14 _let_5 tptp.minus_minus_int) (tptp.bNF_re6214786843070381989at_nat tptp.intrel _let_4 _let_13 _let_13) (forall ((X tptp.nat) (Y tptp.nat) (U tptp.nat) (V tptp.nat)) (= (tptp.pp (tptp.aa_Pro2232559814647311250t_bool (tptp.aa_Pro595088089689268830t_bool tptp.intrel (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat X) Y)) (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat U) V))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat X) V) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat U) Y)))) (tptp.bNF_re8246922863344978751at_nat tptp.intrel tptp.fequal_nat _let_12 _let_12) (tptp.pp (tptp.aa_fun4519828053337421206t_bool (tptp.aa_fun2399787666232550060t_bool _let_4 _let_11) _let_11)) (tptp.pp (tptp.aa_Pro2232559814647311250t_bool (tptp.aa_Pro595088089689268830t_bool tptp.intrel _let_10) _let_10)) (tptp.pp (tptp.aa_Pro2232559814647311250t_bool (tptp.aa_Pro595088089689268830t_bool tptp.intrel _let_9) _let_9)) (= tptp.intrel (tptp.produc5023667602222594023t_bool tptp.aTP_Lamm_aah)) (tptp.bNF_re2219331435504962769t_bool tptp.intrel _let_7 _let_8 _let_8) (tptp.bNF_re2219331435504962769t_bool tptp.intrel _let_7 _let_6 _let_6) (tptp.bNF_re6214786843070381989at_nat tptp.intrel _let_4 _let_5 _let_5) (tptp.bNF_re6214786843070381989at_nat tptp.intrel _let_4 _let_3 _let_3) (forall ((X7 tptp.fun_nat_rat) (Y6 tptp.fun_nat_rat)) (=> (exists ((A7 tptp.rat)) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) A7)) (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat tptp.abs_abs_rat (tptp.aa_nat_rat X7 N2))) A7))))) (=> (tptp.vanishes Y6) (tptp.vanishes (tptp.aa_fun765758790203053448at_rat (tptp.aTP_Lamm_aai X7) Y6))))) (forall ((C tptp.rat)) (= (tptp.vanishes (tptp.aTP_Lamm_aaj C)) (= C tptp.zero_zero_rat))) (forall ((X7 tptp.fun_nat_rat)) (=> (tptp.vanishes X7) (tptp.vanishes (tptp.aTP_Lamm_aak X7)))) (forall ((X7 tptp.fun_nat_rat) (Y6 tptp.fun_nat_rat)) (=> (tptp.vanishes X7) (=> (tptp.vanishes Y6) (tptp.vanishes (tptp.aa_fun765758790203053448at_rat (tptp.aTP_Lamm_aal X7) Y6))))) (forall ((X7 tptp.fun_nat_rat) (Y6 tptp.fun_nat_rat)) (=> (tptp.vanishes X7) (=> (tptp.vanishes Y6) (tptp.vanishes (tptp.aa_fun765758790203053448at_rat (tptp.aTP_Lamm_aam X7) Y6))))) (forall ((X7 tptp.fun_nat_rat)) (= (tptp.vanishes X7) (forall ((R5 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) R5)) (exists ((K2 tptp.nat)) (forall ((N5 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K2) N5)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat tptp.abs_abs_rat (tptp.aa_nat_rat X7 N5))) R5))))))))) (forall ((X7 tptp.fun_nat_rat)) (=> (forall ((R3 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) R3)) (exists ((K4 tptp.nat)) (forall ((N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K4) N2)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat tptp.abs_abs_rat (tptp.aa_nat_rat X7 N2))) R3))))))) (tptp.vanishes X7))) (forall ((X7 tptp.fun_nat_rat) (R tptp.rat)) (=> (tptp.vanishes X7) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) R)) (exists ((K3 tptp.nat)) (forall ((N8 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K3) N8)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat tptp.abs_abs_rat (tptp.aa_nat_rat X7 N8))) R)))))))) (forall ((N tptp.nat)) (= (tptp.field_nat (tptp.collec3392354462482085612at_nat (tptp.produc8955392012077580105t_bool (tptp.aTP_Lamm_aan N)))) (tptp.collect_nat (tptp.aa_nat_fun_nat_bool tptp.aTP_Lamm_br N)))) (= tptp.bNF_Ca8459412986667044542atLess (tptp.collec3392354462482085612at_nat (tptp.produc8955392012077580105t_bool tptp.ord_less_nat))) (forall ((Uu tptp.product_prod_int_int)) (let ((_let_1 (tptp.product_fst_int_int Uu))) (= (tptp.aa_Pro6970504127699319548nt_int tptp.aTP_Lamm_ya Uu) (tptp.aa_Pro6970504127699319548nt_int (tptp.if_Pro3027730157355071871nt_int (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.fequal_int _let_1) tptp.zero_zero_int) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int)) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int (tptp.product_snd_int_int Uu)) _let_1))))) (forall ((Uu tptp.nat)) (= (tptp.aa_nat_real tptp.aTP_Lamm_jp Uu) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)) Uu)) tptp.one_one_real)) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat Uu) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) tptp.one_one_nat))))) (forall ((Uu tptp.nat)) (= (tptp.aa_nat_real tptp.aTP_Lamm_mr Uu) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.one_one_real) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))) (tptp.aa_nat_nat tptp.suc Uu)))) (forall ((Uu tptp.real)) (= (tptp.pp (tptp.aa_real_bool tptp.aTP_Lamm_vn Uu)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) Uu)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Uu) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.aa_real_real tptp.cos_real Uu) tptp.zero_zero_real)))) (forall ((Uu tptp.product_prod_int_int)) (= (tptp.aa_Pro6970504127699319548nt_int tptp.aTP_Lamm_yb Uu) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.product_fst_int_int Uu))) (tptp.product_snd_int_int Uu)))) (forall ((Uu tptp.nat)) (= (tptp.aa_nat_real tptp.aTP_Lamm_md Uu) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real tptp.cos_coeff Uu)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real tptp.zero_zero_real) Uu)))) (forall ((Uu tptp.real)) (= (tptp.aa_real_real tptp.aTP_Lamm_yv Uu) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real tptp.cos_real Uu)) (tptp.aa_real_real tptp.sin_real Uu)))) (forall ((Uu tptp.nat)) (= (tptp.aa_nat_real tptp.aTP_Lamm_yx Uu) (tptp.aa_real_real (tptp.aa_nat_fun_real_real tptp.root Uu) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real Uu)))) (forall ((Uu tptp.nat)) (= (tptp.aa_nat_nat tptp.aTP_Lamm_zw Uu) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uu) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)))) (forall ((Uu tptp.complex)) (= (tptp.aa_complex_complex tptp.aTP_Lamm_ut Uu) (tptp.aa_complex_complex (tptp.plus_plus_complex Uu) tptp.one_one_complex))) (forall ((Uu tptp.real)) (= (tptp.aa_real_real tptp.aTP_Lamm_uw Uu) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real Uu) tptp.one_one_real))) (forall ((Uu tptp.rat)) (= (tptp.aa_rat_rat tptp.aTP_Lamm_uu Uu) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat Uu) tptp.one_one_rat))) (forall ((Uu tptp.nat)) (= (tptp.aa_nat_nat tptp.aTP_Lamm_ux Uu) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Uu) tptp.one_one_nat))) (forall ((Uu tptp.int)) (= (tptp.aa_int_int tptp.aTP_Lamm_uv Uu) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int Uu) tptp.one_one_int))) (forall ((Uu tptp.nat)) (= (tptp.aa_nat7603221163087113075at_nat tptp.aTP_Lamm_aaf Uu) (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Uu) tptp.zero_zero_nat))) (forall ((Uu tptp.product_prod_int_int)) (= (tptp.pp (tptp.aa_Pro4501881432599481050t_bool tptp.aTP_Lamm_xx Uu)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.product_fst_int_int Uu)) (tptp.product_snd_int_int Uu)))))) (forall ((Uu tptp.real)) (= (tptp.aa_real_real tptp.aTP_Lamm_yo Uu) (tptp.suminf_real (tptp.aa_real_fun_nat_real tptp.aTP_Lamm_jl Uu)))) (forall ((Uu tptp.real)) (= (tptp.aa_rea5117059003799598681omplex tptp.aTP_Lamm_zs Uu) (tptp.princi3496590319149328850omplex (tptp.collec8663557070575231912omplex (tptp.produc9214369023355538061x_bool (tptp.aTP_Lamm_zr Uu)))))) (forall ((Uu tptp.real)) (= (tptp.aa_rea5428163979925208277l_real tptp.aTP_Lamm_zq Uu) (tptp.princi6114159922880469582l_real (tptp.collec3799799289383736868l_real (tptp.produc5257810830037637649l_bool (tptp.aTP_Lamm_zp Uu)))))) (forall ((Uu tptp.num)) (= (tptp.aa_num_option_num tptp.aTP_Lamm_xn Uu) (tptp.some_num (tptp.aa_num_num tptp.bit1 Uu)))) (forall ((Uu tptp.num)) (= (tptp.aa_num_option_num tptp.aTP_Lamm_xj Uu) (tptp.some_num (tptp.aa_num_num tptp.bit0 Uu)))) (forall ((Uu tptp.int)) (= (tptp.aa_int2565445551602696444nt_int tptp.aTP_Lamm_wn Uu) (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int (tptp.aa_int_int tptp.uminus_uminus_int Uu)))) (forall ((Uu tptp.int)) (= (tptp.aa_int2565445551602696444nt_int tptp.aTP_Lamm_wo Uu) (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int (tptp.aa_int_int tptp.abs_abs_int Uu)))) (forall ((Uu tptp.nat)) (= (tptp.aa_nat8803788312118491388at_nat tptp.aTP_Lamm_iy Uu) (tptp.product_Pair_nat_nat (tptp.aa_nat_nat tptp.suc Uu)))) (forall ((Uu tptp.real)) (= (tptp.pp (tptp.aa_real_bool tptp.aTP_Lamm_xs Uu)) (exists ((I4 tptp.int) (N5 tptp.nat)) (and (= Uu (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_int_real tptp.ring_1_of_int_real I4)) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N5))) (not (= N5 tptp.zero_zero_nat)))))) (forall ((Uu tptp.real)) (= (tptp.pp (tptp.aa_real_bool tptp.aTP_Lamm_xt Uu)) (exists ((I4 tptp.int) (J3 tptp.int)) (and (= Uu (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_int_real tptp.ring_1_of_int_real I4)) (tptp.aa_int_real tptp.ring_1_of_int_real J3))) (not (= J3 tptp.zero_zero_int)))))) (forall ((Uu tptp.nat)) (= (tptp.aa_nat_option_num tptp.aTP_Lamm_xl Uu) (tptp.some_num tptp.one))) (forall ((Uu tptp.num) (Uua tptp.nat)) (= (tptp.aa_nat_option_num (tptp.aTP_Lamm_xq Uu) Uua) (tptp.case_num_option_num (tptp.some_num tptp.one) (tptp.aTP_Lamm_xo Uua) (tptp.aTP_Lamm_xp Uua) Uu))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat_complex (tptp.aTP_Lamm_of Uu) Uua) (tptp.aa_complex_complex (tptp.if_complex (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) Uua) (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial Uu) Uua))) tptp.zero_zero_complex))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_nat_fun_nat_real tptp.aTP_Lamm_oi Uu) Uua) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real (tptp.if_real (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) Uua)) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial Uu) Uua))) tptp.zero_zero_real))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat_rat (tptp.aTP_Lamm_og Uu) Uua) (tptp.aa_rat_rat (tptp.if_rat (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) Uua) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial Uu) Uua))) tptp.zero_zero_rat))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat_int (tptp.aa_nat_fun_nat_int tptp.aTP_Lamm_oh Uu) Uua) (tptp.aa_int_int (tptp.if_int (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) Uua) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial Uu) Uua))) tptp.zero_zero_int))) (forall ((Uu tptp.fun_nat_real) (Uua tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.aa_nat_real (tptp.aTP_Lamm_ms Uu) Uua) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real (tptp.if_real (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat _let_1) Uua)) tptp.zero_zero_real) (tptp.aa_nat_real Uu (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uua) tptp.one_one_nat)) _let_1)))))) (forall ((Uu tptp.code_integer) (Uua tptp.code_integer)) (let ((_let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.code_int_of_integer Uu)))) (= (tptp.aa_Code_integer_int (tptp.aa_Cod1242632294114111009er_int tptp.aTP_Lamm_vp Uu) Uua) (tptp.aa_int_int (tptp.if_int (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.fequal_Code_integer Uua) tptp.zero_z3403309356797280102nteger) _let_1) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int _let_1) tptp.one_one_int))))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (let ((_let_1 (tptp.aa_complex_complex (tptp.times_times_complex (tptp.numera6690914467698888265omplex (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex Uu)))) (= (tptp.aa_nat_complex (tptp.aa_nat6454746962644518025omplex tptp.aTP_Lamm_je Uu) Uua) (tptp.aa_complex_complex (tptp.if_complex (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.fequal_nat Uua) tptp.zero_zero_nat) _let_1) (tptp.aa_complex_complex (tptp.plus_plus_complex _let_1) tptp.one_one_complex))))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (let ((_let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real Uu)))) (= (tptp.aa_nat_real (tptp.aa_nat_fun_nat_real tptp.aTP_Lamm_jh Uu) Uua) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real (tptp.if_real (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.fequal_nat Uua) tptp.zero_zero_nat)) _let_1) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real _let_1) tptp.one_one_real))))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (let ((_let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_num_rat tptp.numeral_numeral_rat (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat Uu)))) (= (tptp.aa_nat_rat (tptp.aa_nat_fun_nat_rat tptp.aTP_Lamm_jf Uu) Uua) (tptp.aa_rat_rat (tptp.if_rat (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.fequal_nat Uua) tptp.zero_zero_nat) _let_1) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat _let_1) tptp.one_one_rat))))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat Uu)))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.aTP_Lamm_ji Uu) Uua) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.if_nat (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.fequal_nat Uua) tptp.zero_zero_nat)) _let_1) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat _let_1) tptp.one_one_nat))))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (let ((_let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int Uu)))) (= (tptp.aa_nat_int (tptp.aa_nat_fun_nat_int tptp.aTP_Lamm_jg Uu) Uua) (tptp.aa_int_int (tptp.if_int (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.fequal_nat Uua) tptp.zero_zero_nat) _let_1) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int _let_1) tptp.one_one_int))))) (forall ((Uu tptp.code_integer) (Uua tptp.code_integer)) (let ((_let_1 (tptp.code_num_of_integer Uu))) (let ((_let_2 (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num _let_1) _let_1))) (= (tptp.aa_Code_integer_num (tptp.aa_Cod6128727250572145423er_num tptp.aTP_Lamm_vq Uu) Uua) (tptp.aa_num_num (tptp.aa_num_fun_num_num (tptp.if_num (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.fequal_Code_integer Uua) tptp.zero_z3403309356797280102nteger)) _let_2) (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num _let_2) tptp.one)))))) (forall ((Uu tptp.code_integer) (Uua tptp.code_integer)) (let ((_let_1 (tptp.code_nat_of_integer Uu))) (let ((_let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat _let_1) _let_1))) (= (tptp.aa_Code_integer_nat (tptp.aa_Cod5420483313623307717er_nat tptp.aTP_Lamm_vs Uu) Uua) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.if_nat (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.fequal_Code_integer Uua) tptp.zero_z3403309356797280102nteger)) _let_2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat _let_2) tptp.one_one_nat)))))) (forall ((Uu tptp.int) (Uua tptp.int)) (= (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.aTP_Lamm_we Uu) Uua) (tptp.aa_Pro6970504127699319548nt_int (tptp.if_Pro3027730157355071871nt_int (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.fequal_int Uu) tptp.zero_zero_int) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int)) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int tptp.sgn_sgn_int Uu)) Uua)) (tptp.aa_int_int tptp.abs_abs_int Uu))))) (forall ((Uu tptp.int) (Uua tptp.int)) (= (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.aTP_Lamm_aad Uu) Uua) (tptp.aa_Pro6970504127699319548nt_int (tptp.if_Pro3027730157355071871nt_int (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.fequal_int Uua) tptp.zero_zero_int) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int)) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int Uu) Uua)))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat_complex (tptp.aTP_Lamm_ob Uu) Uua) (tptp.aa_complex_complex (tptp.if_complex (tptp.aa_bool_bool tptp.fNot (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) Uua)) (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial Uu) Uua))) tptp.zero_zero_complex))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_nat_fun_nat_real tptp.aTP_Lamm_oe Uu) Uua) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real (tptp.if_real (tptp.aa_bool_bool tptp.fNot (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) Uua))) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial Uu) Uua))) tptp.zero_zero_real))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat_rat (tptp.aTP_Lamm_oc Uu) Uua) (tptp.aa_rat_rat (tptp.if_rat (tptp.aa_bool_bool tptp.fNot (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) Uua)) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial Uu) Uua))) tptp.zero_zero_rat))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat_int (tptp.aa_nat_fun_nat_int tptp.aTP_Lamm_od Uu) Uua) (tptp.aa_int_int (tptp.if_int (tptp.aa_bool_bool tptp.fNot (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) Uua)) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial Uu) Uua))) tptp.zero_zero_int))) (forall ((Uu tptp.nat) (Uua tptp.num)) (= (tptp.aa_num_option_num (tptp.aa_nat3713591252005393295on_num tptp.aTP_Lamm_xr Uu) Uua) (tptp.case_nat_option_num tptp.none_num (tptp.aTP_Lamm_xq Uua) Uu))) (forall ((Uu tptp.nat) (Uua tptp.num)) (= (tptp.aa_num_option_num (tptp.aTP_Lamm_xo Uu) Uua) (tptp.case_o6005452278849405969um_num tptp.none_num tptp.aTP_Lamm_xj (tptp.bit_take_bit_num Uu Uua)))) (forall ((Uu tptp.num) (Uua tptp.nat)) (= (tptp.aa_nat_option_num (tptp.aTP_Lamm_xk Uu) Uua) (tptp.case_o6005452278849405969um_num tptp.none_num tptp.aTP_Lamm_xj (tptp.bit_take_bit_num Uua Uu)))) (forall ((Uu tptp.fun_nat_fun_nat_int) (Uua tptp.nat)) (= (tptp.aa_nat_int (tptp.aTP_Lamm_ts Uu) Uua) (tptp.groups705719431365010083at_int (tptp.aa_nat_fun_nat_int (tptp.aTP_Lamm_tr Uu) Uua) (tptp.set_ord_atMost_nat Uua)))) (forall ((Uu tptp.fun_nat_fun_nat_nat) (Uua tptp.nat)) (= (tptp.aa_nat_nat (tptp.aTP_Lamm_tq Uu) Uua) (tptp.groups708209901874060359at_nat (tptp.aa_nat_fun_nat_nat (tptp.aTP_Lamm_qg Uu) Uua) (tptp.set_ord_atMost_nat Uua)))) (forall ((Uu tptp.fun_nat_fun_nat_real) (Uua tptp.nat)) (= (tptp.aa_nat_real (tptp.aTP_Lamm_qj Uu) Uua) (tptp.groups6591440286371151544t_real (tptp.aa_nat_fun_nat_real (tptp.aTP_Lamm_qi Uu) Uua) (tptp.set_ord_atMost_nat Uua)))) (forall ((Uu tptp.fun_nat_fun_nat_nat) (Uua tptp.nat)) (= (tptp.aa_nat_nat (tptp.aTP_Lamm_qh Uu) Uua) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_nat_fun_nat_nat (tptp.aTP_Lamm_qg Uu) Uua)) (tptp.set_ord_atMost_nat Uua)))) (forall ((Uu tptp.product_prod_int_int) (Uua tptp.product_prod_int_int)) (let ((_let_1 (tptp.product_snd_int_int Uua))) (let ((_let_2 (tptp.product_snd_int_int Uu))) (= (tptp.aa_Pro6970504127699319548nt_int (tptp.aa_Pro4124234152028750080nt_int tptp.aTP_Lamm_xz Uu) Uua) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.product_fst_int_int Uu)) _let_1)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.product_fst_int_int Uua)) _let_2))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int _let_2) _let_1)))))) (forall ((Uu tptp.real) (Uua tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.aTP_Lamm_jk Uu) Uua) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)) Uua)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.one_one_real) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Uua) tptp.one_one_nat))))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real Uu) tptp.one_one_real)) (tptp.aa_nat_nat tptp.suc Uua))))) (forall ((Uu tptp.real) (Uua tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) Uua)) tptp.one_one_nat))) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.aTP_Lamm_nc Uu) Uua) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)) Uua)) (tptp.aa_nat_real tptp.semiri2265585572941072030t_real _let_1))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Uu) _let_1))))) (forall ((Uu tptp.real) (Uua tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) Uua))) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.aTP_Lamm_nb Uu) Uua) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)) Uua)) (tptp.aa_nat_real tptp.semiri2265585572941072030t_real _let_1))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Uu) _let_1))))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat_Code_integer (tptp.aTP_Lamm_sg Uu) Uua) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) Uua)) (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger Uua))) (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial Uu) Uua))))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat_complex (tptp.aTP_Lamm_sf Uu) Uua) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_nat_complex (tptp.power_power_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex tptp.one_one_complex)) Uua)) (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex Uua))) (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial Uu) Uua))))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_nat_fun_nat_real tptp.aTP_Lamm_sj Uu) Uua) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)) Uua)) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real Uua))) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial Uu) Uua))))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat_rat (tptp.aTP_Lamm_sh Uu) Uua) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat tptp.one_one_rat)) Uua)) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat Uua))) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial Uu) Uua))))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat_int (tptp.aa_nat_fun_nat_int tptp.aTP_Lamm_si Uu) Uua) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int)) Uua)) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int Uua))) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial Uu) Uua))))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat_complex (tptp.aTP_Lamm_uk Uu) Uua) (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex (tptp.aa_nat_complex (tptp.gbinomial_complex (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Uu) Uua))) Uua)) (tptp.aa_nat_complex (tptp.power_power_complex (tptp.numera6690914467698888265omplex (tptp.aa_num_num tptp.bit0 tptp.one))) Uua)))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_nat_fun_nat_real tptp.aTP_Lamm_um Uu) Uua) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.gbinomial_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Uu) Uua))) Uua)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))) Uua)))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat_rat (tptp.aTP_Lamm_ul Uu) Uua) (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_nat_rat (tptp.gbinomial_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Uu) Uua))) Uua)) (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_num_rat tptp.numeral_numeral_rat (tptp.aa_num_num tptp.bit0 tptp.one))) Uua)))) (forall ((Uu tptp.real) (Uua tptp.real)) (let ((_let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.aTP_Lamm_vk Uu) Uua)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real _let_1)) Uua)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Uua) _let_1)) (= (tptp.aa_real_real tptp.sin_real Uua) Uu))))) (forall ((Uu tptp.real) (Uua tptp.real)) (let ((_let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.aTP_Lamm_vj Uu) Uua)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.uminus_uminus_real _let_1)) Uua)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Uua) _let_1)) (= (tptp.aa_real_real tptp.tan_real Uua) Uu))))) (forall ((Uu tptp.complex) (Uua tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_com8943241093633526360l_bool tptp.aTP_Lamm_vo Uu) Uua)) (and (= (tptp.aa_complex_complex tptp.sgn_sgn_complex Uu) (tptp.aa_real_complex tptp.cis Uua)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.pi)) Uua)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Uua) tptp.pi))))) (forall ((Uu tptp.product_prod_int_int) (Uua tptp.product_prod_int_int)) (= (tptp.aa_Pro6970504127699319548nt_int (tptp.aa_Pro4124234152028750080nt_int tptp.aTP_Lamm_yc Uu) Uua) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.product_fst_int_int Uu)) (tptp.product_fst_int_int Uua))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.product_snd_int_int Uu)) (tptp.product_snd_int_int Uua))))) (forall ((Uu tptp.real) (Uua tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_real_fun_int_bool tptp.aTP_Lamm_wc Uu) Uua)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_int_real tptp.ring_1_of_int_real Uua)) Uu)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Uu) (tptp.aa_int_real tptp.ring_1_of_int_real (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int Uua) tptp.one_one_int))))))) (forall ((Uu tptp.rat) (Uua tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aTP_Lamm_wd Uu) Uua)) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_int_rat tptp.ring_1_of_int_rat Uua)) Uu)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Uu) (tptp.aa_int_rat tptp.ring_1_of_int_rat (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int Uua) tptp.one_one_int))))))) (forall ((Uu tptp.real) (Uua tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat Uua) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) tptp.one_one_nat))) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.aTP_Lamm_jl Uu) Uua) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)) Uua)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.one_one_real) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real _let_1))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Uu) _let_1)))))) (forall ((Uu tptp.real) (Uua tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.aTP_Lamm_yp Uu) Uua) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)) Uua)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Uu) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat Uua) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))))) (forall ((Uu tptp.fun_nat_real) (Uua tptp.nat)) (= (tptp.aa_nat_real (tptp.aTP_Lamm_yw Uu) Uua) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)) Uua)) (tptp.aa_nat_real Uu Uua)))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat_Code_integer (tptp.aTP_Lamm_su Uu) Uua) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) Uua)) (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial Uu) Uua))))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat_complex (tptp.aTP_Lamm_st Uu) Uua) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_nat_complex (tptp.power_power_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex tptp.one_one_complex)) Uua)) (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial Uu) Uua))))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_nat_fun_nat_real tptp.aTP_Lamm_sx Uu) Uua) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)) Uua)) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial Uu) Uua))))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat_rat (tptp.aTP_Lamm_sv Uu) Uua) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat tptp.one_one_rat)) Uua)) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial Uu) Uua))))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat_int (tptp.aa_nat_fun_nat_int tptp.aTP_Lamm_sw Uu) Uua) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int)) Uua)) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial Uu) Uua))))) (forall ((Uu tptp.rat) (Uua tptp.product_prod_int_int)) (let ((_let_1 (tptp.product_snd_int_int Uua))) (let ((_let_2 (tptp.product_fst_int_int Uua))) (= (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.aTP_Lamm_aac Uu) Uua)) (and (= Uu (tptp.aa_int_rat (tptp.aa_int_fun_int_rat tptp.fract _let_2) _let_1)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) _let_1)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.algebr932160517623751201me_int _let_2) _let_1))))))) (forall ((Uu tptp.complex) (Uua tptp.nat)) (= (tptp.aa_nat_complex (tptp.aTP_Lamm_tn Uu) Uua) (tptp.aa_nat_complex (tptp.gbinomial_complex (tptp.aa_complex_complex (tptp.plus_plus_complex Uu) (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex Uua))) Uua))) (forall ((Uu tptp.real) (Uua tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.aTP_Lamm_tp Uu) Uua) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.gbinomial_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real Uu) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real Uua))) Uua))) (forall ((Uu tptp.rat) (Uua tptp.nat)) (= (tptp.aa_nat_rat (tptp.aTP_Lamm_to Uu) Uua) (tptp.aa_nat_rat (tptp.gbinomial_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat Uu) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat Uua))) Uua))) (forall ((Uu tptp.complex) (Uua tptp.nat)) (= (tptp.aa_nat_complex (tptp.aTP_Lamm_tg Uu) Uua) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_nat_complex (tptp.gbinomial_complex Uu) Uua)) (tptp.aa_complex_complex (tptp.minus_minus_complex (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex Uu) (tptp.numera6690914467698888265omplex (tptp.aa_num_num tptp.bit0 tptp.one)))) (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex Uua))))) (forall ((Uu tptp.real) (Uua tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.aTP_Lamm_ti Uu) Uua) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.gbinomial_real Uu) Uua)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real Uu) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real Uua))))) (forall ((Uu tptp.rat) (Uua tptp.nat)) (= (tptp.aa_nat_rat (tptp.aTP_Lamm_th Uu) Uua) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat (tptp.gbinomial_rat Uu) Uua)) (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_rat_rat (tptp.divide_divide_rat Uu) (tptp.aa_num_rat tptp.numeral_numeral_rat (tptp.aa_num_num tptp.bit0 tptp.one)))) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat Uua))))) (forall ((Uu tptp.complex) (Uua tptp.nat)) (= (tptp.aa_nat_complex (tptp.aTP_Lamm_tt Uu) Uua) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_nat_complex (tptp.gbinomial_complex Uu) Uua)) (tptp.aa_nat_complex (tptp.power_power_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex tptp.one_one_complex)) Uua)))) (forall ((Uu tptp.real) (Uua tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.aTP_Lamm_tv Uu) Uua) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.gbinomial_real Uu) Uua)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)) Uua)))) (forall ((Uu tptp.rat) (Uua tptp.nat)) (= (tptp.aa_nat_rat (tptp.aTP_Lamm_tu Uu) Uua) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat (tptp.gbinomial_rat Uu) Uua)) (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat tptp.one_one_rat)) Uua)))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.aTP_Lamm_ru Uu) Uua) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial Uu) Uua)) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (forall ((Uu tptp.set_int) (Uua tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aTP_Lamm_xh Uu) Uua)) (and (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Uua) Uu)) (forall ((X3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X3) Uu)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X3) Uua))))))) (forall ((Uu tptp.real) (Uua tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.aTP_Lamm_nn Uu) Uua) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Uu) Uua)) (tptp.aa_nat_real tptp.semiri2265585572941072030t_real Uua)))) (forall ((Uu tptp.set_complex) (Uua tptp.set_complex)) (= (tptp.pp (tptp.aa_set_complex_bool (tptp.aa_set6592632205191297002x_bool tptp.aTP_Lamm_ns Uu) Uua)) (and (tptp.pp (tptp.aa_set_complex_bool (tptp.ord_less_set_complex Uu) Uua)) (tptp.pp (tptp.aa_set_complex_bool tptp.finite3207457112153483333omplex Uua))))) (forall ((Uu tptp.set_nat) (Uua tptp.set_nat)) (= (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.aTP_Lamm_nq Uu) Uua)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_set_nat Uu) Uua)) (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat Uua))))) (forall ((Uu tptp.set_int) (Uua tptp.set_int)) (= (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.aTP_Lamm_nr Uu) Uua)) (and (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_set_int Uu) Uua)) (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int Uua))))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.aTP_Lamm_zn Uu) Uua) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat Uu) Uua)) Uua))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.aTP_Lamm_pw Uu) Uua) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Uu) Uua)) Uu))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.aTP_Lamm_pv Uu) Uua) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Uu) Uua)) Uua))) (forall ((Uu tptp.nat) (Uua tptp.complex)) (= (tptp.pp (tptp.aa_complex_bool (tptp.aTP_Lamm_cq Uu) Uua)) (= (tptp.aa_nat_complex (tptp.power_power_complex Uua) Uu) tptp.one_one_complex))) (forall ((Uu tptp.nat) (Uua tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_nat_fun_real_bool tptp.aTP_Lamm_cp Uu) Uua)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Uua) Uu) tptp.one_one_real))) (forall ((Uu tptp.real) (Uua tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.aTP_Lamm_zl Uu) Uua) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.powr_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real tptp.one_one_real) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real Uu) Uua))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.one_one_real) Uua)))) (forall ((Uu tptp.real) (Uua tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat Uua) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) tptp.one_one_nat))) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.aTP_Lamm_jj Uu) Uua) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.one_one_real) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real _let_1))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Uu) _let_1))))) (forall ((Uu tptp.real) (Uua tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.aTP_Lamm_vm Uu) Uua)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) Uua)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Uua) tptp.pi)) (= (tptp.aa_real_real tptp.cos_real Uua) Uu)))) (forall ((Uu tptp.fun_nat_real) (Uua tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) Uua))) (= (tptp.aa_nat_real (tptp.aTP_Lamm_pa Uu) Uua) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real Uu _let_1)) (tptp.aa_nat_real Uu (tptp.aa_nat_nat tptp.suc _let_1)))))) (forall ((Uu tptp.fun_nat_rat) (Uua tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) Uua))) (= (tptp.aa_nat_rat (tptp.aTP_Lamm_pb Uu) Uua) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat Uu _let_1)) (tptp.aa_nat_rat Uu (tptp.aa_nat_nat tptp.suc _let_1)))))) (forall ((Uu tptp.fun_nat_nat) (Uua tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) Uua))) (= (tptp.aa_nat_nat (tptp.aTP_Lamm_pc Uu) Uua) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat Uu _let_1)) (tptp.aa_nat_nat Uu (tptp.aa_nat_nat tptp.suc _let_1)))))) (forall ((Uu tptp.fun_nat_int) (Uua tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) Uua))) (= (tptp.aa_nat_int (tptp.aTP_Lamm_pd Uu) Uua) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int Uu _let_1)) (tptp.aa_nat_int Uu (tptp.aa_nat_nat tptp.suc _let_1)))))) (forall ((Uu tptp.fun_nat_real) (Uua tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) Uua))) (= (tptp.aa_nat_real (tptp.aTP_Lamm_iw Uu) Uua) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real Uu _let_1)) (tptp.aa_nat_real Uu (tptp.aa_nat_nat tptp.suc _let_1)))))) (forall ((Uu tptp.fun_nat_rat) (Uua tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) Uua))) (= (tptp.aa_nat_rat (tptp.aTP_Lamm_it Uu) Uua) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_nat_rat Uu _let_1)) (tptp.aa_nat_rat Uu (tptp.aa_nat_nat tptp.suc _let_1)))))) (forall ((Uu tptp.fun_nat_nat) (Uua tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) Uua))) (= (tptp.aa_nat_nat (tptp.aTP_Lamm_iv Uu) Uua) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat Uu _let_1)) (tptp.aa_nat_nat Uu (tptp.aa_nat_nat tptp.suc _let_1)))))) (forall ((Uu tptp.fun_nat_int) (Uua tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) Uua))) (= (tptp.aa_nat_int (tptp.aTP_Lamm_iu Uu) Uua) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_nat_int Uu _let_1)) (tptp.aa_nat_int Uu (tptp.aa_nat_nat tptp.suc _let_1)))))) (forall ((Uu tptp.fun_nat_complex) (Uua tptp.nat)) (= (tptp.aa_nat_complex (tptp.aTP_Lamm_hx Uu) Uua) (tptp.aa_complex_complex (tptp.minus_minus_complex (tptp.aa_nat_complex Uu (tptp.aa_nat_nat tptp.suc Uua))) (tptp.aa_nat_complex Uu Uua)))) (forall ((Uu tptp.fun_nat_real) (Uua tptp.nat)) (= (tptp.aa_nat_real (tptp.aTP_Lamm_ia Uu) Uua) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_nat_real Uu (tptp.aa_nat_nat tptp.suc Uua))) (tptp.aa_nat_real Uu Uua)))) (forall ((Uu tptp.fun_nat_rat) (Uua tptp.nat)) (= (tptp.aa_nat_rat (tptp.aTP_Lamm_hy Uu) Uua) (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_nat_rat Uu (tptp.aa_nat_nat tptp.suc Uua))) (tptp.aa_nat_rat Uu Uua)))) (forall ((Uu tptp.fun_nat_int) (Uua tptp.nat)) (= (tptp.aa_nat_int (tptp.aTP_Lamm_hz Uu) Uua) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_nat_int Uu (tptp.aa_nat_nat tptp.suc Uua))) (tptp.aa_nat_int Uu Uua)))) (forall ((Uu tptp.fun_nat_complex) (Uua tptp.nat)) (= (tptp.aa_nat_complex (tptp.aTP_Lamm_gy Uu) Uua) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_nat_complex Uu Uua)) (tptp.aa_nat_complex (tptp.power_power_complex tptp.zero_zero_complex) Uua)))) (forall ((Uu tptp.fun_nat_real) (Uua tptp.nat)) (= (tptp.aa_nat_real (tptp.aTP_Lamm_ha Uu) Uua) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real Uu Uua)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real tptp.zero_zero_real) Uua)))) (forall ((Uu tptp.fun_nat_rat) (Uua tptp.nat)) (= (tptp.aa_nat_rat (tptp.aTP_Lamm_gz Uu) Uua) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat Uu Uua)) (tptp.aa_nat_rat (tptp.power_power_rat tptp.zero_zero_rat) Uua)))) (forall ((Uu tptp.fun_nat_int) (Uua tptp.nat)) (= (tptp.aa_nat_int (tptp.aTP_Lamm_kp Uu) Uua) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int Uu Uua)) (tptp.aa_nat_int (tptp.power_power_int tptp.zero_zero_int) Uua)))) (forall ((Uu tptp.fun_nat_complex) (Uua tptp.nat)) (= (tptp.aa_nat_complex (tptp.aTP_Lamm_ip Uu) Uua) (tptp.aa_complex_complex (tptp.minus_minus_complex (tptp.aa_nat_complex Uu Uua)) (tptp.aa_nat_complex Uu (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uua) tptp.one_one_nat))))) (forall ((Uu tptp.fun_nat_real) (Uua tptp.nat)) (= (tptp.aa_nat_real (tptp.aTP_Lamm_is Uu) Uua) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_nat_real Uu Uua)) (tptp.aa_nat_real Uu (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uua) tptp.one_one_nat))))) (forall ((Uu tptp.fun_nat_rat) (Uua tptp.nat)) (= (tptp.aa_nat_rat (tptp.aTP_Lamm_iq Uu) Uua) (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_nat_rat Uu Uua)) (tptp.aa_nat_rat Uu (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uua) tptp.one_one_nat))))) (forall ((Uu tptp.fun_nat_int) (Uua tptp.nat)) (= (tptp.aa_nat_int (tptp.aTP_Lamm_ir Uu) Uua) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_nat_int Uu Uua)) (tptp.aa_nat_int Uu (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uua) tptp.one_one_nat))))) (forall ((Uu tptp.fun_nat_complex) (Uua tptp.nat)) (= (tptp.aa_nat_complex (tptp.aTP_Lamm_il Uu) Uua) (tptp.aa_complex_complex (tptp.minus_minus_complex (tptp.aa_nat_complex Uu Uua)) (tptp.aa_nat_complex Uu (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Uua) tptp.one_one_nat))))) (forall ((Uu tptp.fun_nat_real) (Uua tptp.nat)) (= (tptp.aa_nat_real (tptp.aTP_Lamm_io Uu) Uua) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_nat_real Uu Uua)) (tptp.aa_nat_real Uu (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Uua) tptp.one_one_nat))))) (forall ((Uu tptp.fun_nat_rat) (Uua tptp.nat)) (= (tptp.aa_nat_rat (tptp.aTP_Lamm_im Uu) Uua) (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_nat_rat Uu Uua)) (tptp.aa_nat_rat Uu (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Uua) tptp.one_one_nat))))) (forall ((Uu tptp.fun_nat_int) (Uua tptp.nat)) (= (tptp.aa_nat_int (tptp.aTP_Lamm_in Uu) Uua) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_nat_int Uu Uua)) (tptp.aa_nat_int Uu (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Uua) tptp.one_one_nat))))) (forall ((Uu tptp.fun_nat_complex) (Uua tptp.nat)) (= (tptp.aa_nat_complex (tptp.aTP_Lamm_lb Uu) Uua) (tptp.aa_complex_complex (tptp.minus_minus_complex (tptp.aa_nat_complex Uu Uua)) (tptp.aa_nat_complex Uu (tptp.aa_nat_nat tptp.suc Uua))))) (forall ((Uu tptp.fun_nat_real) (Uua tptp.nat)) (= (tptp.aa_nat_real (tptp.aTP_Lamm_le Uu) Uua) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_nat_real Uu Uua)) (tptp.aa_nat_real Uu (tptp.aa_nat_nat tptp.suc Uua))))) (forall ((Uu tptp.fun_nat_rat) (Uua tptp.nat)) (= (tptp.aa_nat_rat (tptp.aTP_Lamm_lc Uu) Uua) (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_nat_rat Uu Uua)) (tptp.aa_nat_rat Uu (tptp.aa_nat_nat tptp.suc Uua))))) (forall ((Uu tptp.fun_nat_int) (Uua tptp.nat)) (= (tptp.aa_nat_int (tptp.aTP_Lamm_ld Uu) Uua) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_nat_int Uu Uua)) (tptp.aa_nat_int Uu (tptp.aa_nat_nat tptp.suc Uua))))) (forall ((Uu tptp.fun_nat_real) (Uua tptp.nat)) (= (tptp.aa_nat_real (tptp.aTP_Lamm_zh Uu) Uua) (tptp.groups6591440286371151544t_real (tptp.aTP_Lamm_yw Uu) (tptp.set_ord_lessThan_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) Uua)) tptp.one_one_nat))))) (forall ((Uu tptp.fun_nat_real) (Uua tptp.nat)) (= (tptp.aa_nat_real (tptp.aTP_Lamm_zg Uu) Uua) (tptp.groups6591440286371151544t_real (tptp.aTP_Lamm_yw Uu) (tptp.set_ord_lessThan_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) Uua))))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.aTP_Lamm_xf Uu) Uua) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat tptp.nat_triangle (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Uu) Uua))) Uu))) (forall ((Uu tptp.complex) (Uua tptp.nat)) (= (tptp.aa_nat_complex (tptp.aTP_Lamm_mf Uu) Uua) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex (tptp.aa_nat_nat tptp.suc Uua))) (tptp.aa_nat_complex (tptp.power_power_complex Uu) Uua)))) (forall ((Uu tptp.real) (Uua tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.aTP_Lamm_me Uu) Uua) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real (tptp.aa_nat_nat tptp.suc Uua))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Uu) Uua)))) (forall ((Uu tptp.num) (Uua tptp.num)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat Uu))) (= (tptp.aa_num_int (tptp.aTP_Lamm_xi Uu) Uua) (tptp.aa_int_int (tptp.bit_se2923211474154528505it_int _let_1) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) _let_1)) (tptp.aa_num_int tptp.numeral_numeral_int Uua)))))) (forall ((Uu tptp.nat) (Uua tptp.real)) (= (tptp.aa_real_real (tptp.aa_nat_fun_real_real tptp.aTP_Lamm_xy Uu) Uua) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real tptp.sgn_sgn_real Uua)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real tptp.abs_abs_real Uua)) Uu)))) (forall ((Uu tptp.real) (Uua tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.aTP_Lamm_nd Uu) Uua) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real tptp.sin_coeff Uua)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Uu) Uua)))) (forall ((Uu tptp.real) (Uua tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.aTP_Lamm_mu Uu) Uua) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real tptp.cos_coeff Uua)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Uu) Uua)))) (forall ((Uu tptp.num) (Uua tptp.num)) (= (tptp.aa_num_int (tptp.aa_num_fun_num_int tptp.aTP_Lamm_aae Uu) Uua) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_num_int tptp.numeral_numeral_int Uu)) (tptp.aa_num_int tptp.numeral_numeral_int Uua)))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat_complex (tptp.aTP_Lamm_uc Uu) Uua) (tptp.aa_nat_complex (tptp.gbinomial_complex (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex Uua)) Uu))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_nat_fun_nat_real tptp.aTP_Lamm_ue Uu) Uua) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.gbinomial_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real Uua)) Uu))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat_rat (tptp.aTP_Lamm_ud Uu) Uua) (tptp.aa_nat_rat (tptp.gbinomial_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat Uua)) Uu))) (forall ((Uu tptp.code_integer) (Uua tptp.code_integer)) (= (tptp.aa_Cod6977894654539884864nteger (tptp.aa_Cod8380929501330563836nteger tptp.aTP_Lamm_gv Uu) Uua) (tptp.produc1086072967326762835nteger Uu (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))) Uua) tptp.one_one_Code_integer)))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat7603221163087113075at_nat (tptp.aa_nat8803788312118491388at_nat tptp.aTP_Lamm_gu Uu) Uua) (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Uu) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) Uua)) tptp.one_one_nat)))) (forall ((Uu tptp.int) (Uua tptp.int)) (= (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.aTP_Lamm_gt Uu) Uua) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int Uu) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) Uua)) tptp.one_one_int)))) (forall ((Uu tptp.code_integer) (Uua tptp.code_integer)) (= (tptp.aa_Cod6977894654539884864nteger (tptp.aa_Cod8380929501330563836nteger tptp.aTP_Lamm_hg Uu) Uua) (tptp.produc1086072967326762835nteger Uu (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))) Uua)))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat7603221163087113075at_nat (tptp.aa_nat8803788312118491388at_nat tptp.aTP_Lamm_hf Uu) Uua) (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Uu) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) Uua)))) (forall ((Uu tptp.int) (Uua tptp.int)) (= (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.aTP_Lamm_he Uu) Uua) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int Uu) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) Uua)))) (forall ((Uu tptp.complex) (Uua tptp.nat)) (= (tptp.aa_nat_complex (tptp.aTP_Lamm_ny Uu) Uua) (tptp.aa_complex_complex (tptp.plus_plus_complex Uu) (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex Uua)) (tptp.numera6690914467698888265omplex (tptp.aa_num_num tptp.bit0 tptp.one)))))) (forall ((Uu tptp.real) (Uua tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.aTP_Lamm_oa Uu) Uua) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real Uu) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real Uua)) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))))) (forall ((Uu tptp.rat) (Uua tptp.nat)) (= (tptp.aa_nat_rat (tptp.aTP_Lamm_nz Uu) Uua) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat Uu) (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat Uua)) (tptp.aa_num_rat tptp.numeral_numeral_rat (tptp.aa_num_num tptp.bit0 tptp.one)))))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.aTP_Lamm_ss Uu) Uua) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat Uua) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial Uu) Uua)))) (forall ((Uu tptp.real) (Uua tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.aTP_Lamm_zc Uu) Uua) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real Uu) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real tptp.one_one_real) (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_real_real tptp.inverse_inverse_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real (tptp.aa_nat_nat tptp.suc Uua)))))))) (forall ((Uu tptp.fun_nat_real) (Uua tptp.nat)) (= (tptp.aa_nat_real (tptp.aTP_Lamm_xv Uu) Uua) (tptp.groups6591440286371151544t_real Uu (tptp.set_ord_lessThan_nat Uua)))) (forall ((Uu tptp.complex) (Uua tptp.nat)) (= (tptp.aa_nat_complex (tptp.aTP_Lamm_uf Uu) Uua) (tptp.aa_complex_complex (tptp.minus_minus_complex Uu) (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex Uua)))) (forall ((Uu tptp.real) (Uua tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.aTP_Lamm_uh Uu) Uua) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real Uu) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real Uua)))) (forall ((Uu tptp.rat) (Uua tptp.nat)) (= (tptp.aa_nat_rat (tptp.aTP_Lamm_ug Uu) Uua) (tptp.aa_rat_rat (tptp.minus_minus_rat Uu) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat Uua)))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.aTP_Lamm_ui Uu) Uua) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uu) (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat Uua)))) (forall ((Uu tptp.int) (Uua tptp.nat)) (= (tptp.aa_nat_int (tptp.aTP_Lamm_uj Uu) Uua) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int Uu) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int Uua)))) (forall ((Uu tptp.real) (Uua tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.aTP_Lamm_qp Uu) Uua) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real Uu) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real Uua)))) (forall ((Uu tptp.rat) (Uua tptp.nat)) (= (tptp.aa_nat_rat (tptp.aTP_Lamm_qo Uu) Uua) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat Uu) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat Uua)))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.aTP_Lamm_qq Uu) Uua) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Uu) (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat Uua)))) (forall ((Uu tptp.int) (Uua tptp.nat)) (= (tptp.aa_nat_int (tptp.aTP_Lamm_qr Uu) Uua) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int Uu) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int Uua)))) (forall ((Uu tptp.real) (Uua tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.aTP_Lamm_oq Uu) Uua)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Uua) Uu)))) (forall ((Uu tptp.set_complex) (Uua tptp.set_complex)) (= (tptp.pp (tptp.aa_set_complex_bool (tptp.aTP_Lamm_bt Uu) Uua)) (tptp.pp (tptp.aa_set_complex_bool (tptp.ord_le211207098394363844omplex Uua) Uu)))) (forall ((Uu tptp.set_nat) (Uua tptp.set_nat)) (= (tptp.pp (tptp.aa_set_nat_bool (tptp.aTP_Lamm_bs Uu) Uua)) (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat Uua) Uu)))) (forall ((Uu tptp.set_int) (Uua tptp.set_int)) (= (tptp.pp (tptp.aa_set_int_bool (tptp.aTP_Lamm_bu Uu) Uua)) (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int Uua) Uu)))) (forall ((Uu tptp.rat) (Uua tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.aTP_Lamm_or Uu) Uua)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat Uua) Uu)))) (forall ((Uu tptp.num) (Uua tptp.num)) (= (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.aTP_Lamm_os Uu) Uua)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num Uua) Uu)))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.aTP_Lamm_bq Uu) Uua)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Uua) Uu)))) (forall ((Uu tptp.int) (Uua tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.aTP_Lamm_ot Uu) Uua)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Uua) Uu)))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.aTP_Lamm_xw Uu) Uua) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat Uua) Uu))) (forall ((Uu tptp.real) (Uua tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.aTP_Lamm_kj Uu) Uua)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Uua) Uu)))) (forall ((Uu tptp.rat) (Uua tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.aTP_Lamm_kg Uu) Uua)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Uua) Uu)))) (forall ((Uu tptp.num) (Uua tptp.num)) (= (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.aTP_Lamm_kh Uu) Uua)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num Uua) Uu)))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.aTP_Lamm_br Uu) Uua)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Uua) Uu)))) (forall ((Uu tptp.int) (Uua tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.aTP_Lamm_ki Uu) Uua)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Uua) Uu)))) (forall ((Uu tptp.real) (Uua tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.aTP_Lamm_ae Uu) Uua) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real Uua) Uu))) (forall ((Uu tptp.rat) (Uua tptp.rat)) (= (tptp.aa_rat_rat (tptp.aTP_Lamm_af Uu) Uua) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat Uua) Uu))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.aTP_Lamm_ag Uu) Uua) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat Uua) Uu))) (forall ((Uu tptp.int) (Uua tptp.int)) (= (tptp.aa_int_int (tptp.aTP_Lamm_ah Uu) Uua) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int Uua) Uu))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.aTP_Lamm_xu Uu) Uua) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uua) Uu))) (forall ((Uu tptp.nat) (Uua tptp.real)) (= (tptp.aa_real_real (tptp.aa_nat_fun_real_real tptp.aTP_Lamm_yd Uu) Uua) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Uua) Uu))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.aTP_Lamm_zv Uu) Uua) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Uua) Uu))) (forall ((Uu tptp.real) (Uua tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.aTP_Lamm_yf Uu) Uua) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.powr_real Uua) Uu))) (forall ((Uu tptp.code_integer) (Uua tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.aTP_Lamm_fh Uu) Uua)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer Uua) Uu)))) (forall ((Uu tptp.complex) (Uua tptp.complex)) (= (tptp.pp (tptp.aa_complex_bool (tptp.aa_com1553036987509291606x_bool tptp.aTP_Lamm_fe Uu) Uua)) (tptp.pp (tptp.aa_complex_bool (tptp.aa_com1553036987509291606x_bool tptp.dvd_dvd_complex Uua) Uu)))) (forall ((Uu tptp.real) (Uua tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.aTP_Lamm_ff Uu) Uua)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.dvd_dvd_real Uua) Uu)))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.aTP_Lamm_fg Uu) Uua)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat Uua) Uu)))) (forall ((Uu tptp.int) (Uua tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.aTP_Lamm_fi Uu) Uua)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int Uua) Uu)))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat7603221163087113075at_nat (tptp.aa_nat8803788312118491388at_nat tptp.aTP_Lamm_ww Uu) Uua) (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Uua) Uu))) (forall ((Uu tptp.real) (Uua tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.aTP_Lamm_yz Uu) Uua) (tptp.aa_real_real (tptp.aa_nat_fun_real_real tptp.root Uua) Uu))) (forall ((Uu tptp.set_complex) (Uua tptp.complex)) (= (tptp.pp (tptp.aa_complex_bool (tptp.aTP_Lamm_a Uu) Uua)) (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex Uua) Uu)))) (forall ((Uu tptp.set_real) (Uua tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aTP_Lamm_aa Uu) Uua)) (tptp.member_real Uua Uu))) (forall ((Uu tptp.set_list_nat) (Uua tptp.list_nat)) (= (tptp.pp (tptp.aa_list_nat_bool (tptp.aTP_Lamm_ab Uu) Uua)) (tptp.member_list_nat Uua Uu))) (forall ((Uu tptp.set_nat) (Uua tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aTP_Lamm_ac Uu) Uua)) (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat Uua) Uu)))) (forall ((Uu tptp.set_int) (Uua tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aTP_Lamm_ad Uu) Uua)) (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Uua) Uu)))) (forall ((Uu tptp.fun_nat_real) (Uua tptp.nat)) (= (tptp.aa_nat_real (tptp.aTP_Lamm_mc Uu) Uua) (tptp.aa_nat_real Uu (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) Uua)) tptp.one_one_nat)))) (forall ((Uu tptp.fun_nat_real) (Uua tptp.nat)) (= (tptp.aa_nat_real (tptp.aTP_Lamm_mb Uu) Uua) (tptp.aa_nat_real Uu (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) Uua)))) (forall ((Uu tptp.fun_nat_complex) (Uua tptp.nat)) (= (tptp.aa_nat_complex (tptp.aTP_Lamm_ku Uu) Uua) (tptp.aa_nat_complex Uu (tptp.aa_nat_nat tptp.suc Uua)))) (forall ((Uu tptp.fun_nat_real) (Uua tptp.nat)) (= (tptp.aa_nat_real (tptp.aTP_Lamm_hw Uu) Uua) (tptp.aa_nat_real Uu (tptp.aa_nat_nat tptp.suc Uua)))) (forall ((Uu tptp.fun_nat_rat) (Uua tptp.nat)) (= (tptp.aa_nat_rat (tptp.aTP_Lamm_ht Uu) Uua) (tptp.aa_nat_rat Uu (tptp.aa_nat_nat tptp.suc Uua)))) (forall ((Uu tptp.fun_nat_nat) (Uua tptp.nat)) (= (tptp.aa_nat_nat (tptp.aTP_Lamm_hv Uu) Uua) (tptp.aa_nat_nat Uu (tptp.aa_nat_nat tptp.suc Uua)))) (forall ((Uu tptp.fun_nat_int) (Uua tptp.nat)) (= (tptp.aa_nat_int (tptp.aTP_Lamm_hu Uu) Uua) (tptp.aa_nat_int Uu (tptp.aa_nat_nat tptp.suc Uua)))) (forall ((Uu tptp.nat) (Uua tptp.num)) (= (tptp.aa_num_option_num (tptp.aTP_Lamm_xp Uu) Uua) (tptp.some_num (tptp.case_option_num_num tptp.one tptp.bit1 (tptp.bit_take_bit_num Uu Uua))))) (forall ((Uu tptp.num) (Uua tptp.nat)) (= (tptp.aa_nat_option_num (tptp.aTP_Lamm_xm Uu) Uua) (tptp.some_num (tptp.case_option_num_num tptp.one tptp.bit1 (tptp.bit_take_bit_num Uua Uu))))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat4401263874371387303t_bool (tptp.aa_nat4909001760120733684t_bool tptp.aTP_Lamm_aah Uu) Uua) (tptp.produc8955392012077580105t_bool (tptp.aa_nat8637530788439456283t_bool (tptp.aTP_Lamm_aag Uu) Uua)))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat7997280740862404369at_nat (tptp.aa_nat5682243440470347102at_nat tptp.aTP_Lamm_xe Uu) Uua) (tptp.produc2626176000494625587at_nat (tptp.aa_nat4158579785191972357at_nat (tptp.aTP_Lamm_xd Uu) Uua)))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat7997280740862404369at_nat (tptp.aa_nat5682243440470347102at_nat tptp.aTP_Lamm_xc Uu) Uua) (tptp.produc2626176000494625587at_nat (tptp.aa_nat4158579785191972357at_nat (tptp.aTP_Lamm_xb Uu) Uua)))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat4401263874371387303t_bool (tptp.aa_nat4909001760120733684t_bool tptp.aTP_Lamm_xa Uu) Uua) (tptp.produc8955392012077580105t_bool (tptp.aa_nat8637530788439456283t_bool (tptp.aTP_Lamm_wz Uu) Uua)))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat4401263874371387303t_bool (tptp.aa_nat4909001760120733684t_bool tptp.aTP_Lamm_wy Uu) Uua) (tptp.produc8955392012077580105t_bool (tptp.aa_nat8637530788439456283t_bool (tptp.aTP_Lamm_wx Uu) Uua)))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat7997280740862404369at_nat (tptp.aa_nat5682243440470347102at_nat tptp.aTP_Lamm_wv Uu) Uua) (tptp.produc2626176000494625587at_nat (tptp.aa_nat4158579785191972357at_nat (tptp.aTP_Lamm_wu Uu) Uua)))) (forall ((Uu tptp.fun_nat_real) (Uua tptp.real)) (= (tptp.aa_real_real (tptp.aTP_Lamm_ys Uu) Uua) (tptp.suminf_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_yr Uu) Uua)))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat_complex (tptp.aTP_Lamm_vg Uu) Uua) (tptp.aa_real_complex tptp.cis (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))) tptp.pi)) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real Uua))) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real Uu))))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.aTP_Lamm_fj Uu) Uua)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat _let_1) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat Uu) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat _let_1) Uua)))))))) (forall ((Uu tptp.complex) (Uua tptp.nat)) (= (tptp.aa_nat3829984526574172007omplex (tptp.aTP_Lamm_uq Uu) Uua) (tptp.times_times_complex (tptp.aa_complex_complex (tptp.minus_minus_complex Uu) (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex Uua))))) (forall ((Uu tptp.real) (Uua tptp.nat)) (= (tptp.aa_nat_fun_real_real (tptp.aTP_Lamm_us Uu) Uua) (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real Uu) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real Uua))))) (forall ((Uu tptp.rat) (Uua tptp.nat)) (= (tptp.aa_nat_fun_rat_rat (tptp.aTP_Lamm_ur Uu) Uua) (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat (tptp.minus_minus_rat Uu) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat Uua))))) (forall ((Uu tptp.complex) (Uua tptp.nat)) (= (tptp.aa_nat3829984526574172007omplex (tptp.aTP_Lamm_nt Uu) Uua) (tptp.times_times_complex (tptp.aa_complex_complex (tptp.plus_plus_complex Uu) (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex Uua))))) (forall ((Uu tptp.real) (Uua tptp.nat)) (= (tptp.aa_nat_fun_real_real (tptp.aTP_Lamm_nw Uu) Uua) (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real Uu) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real Uua))))) (forall ((Uu tptp.rat) (Uua tptp.nat)) (= (tptp.aa_nat_fun_rat_rat (tptp.aTP_Lamm_nu Uu) Uua) (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat Uu) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat Uua))))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat_fun_nat_nat (tptp.aTP_Lamm_nx Uu) Uua) (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Uu) (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat Uua))))) (forall ((Uu tptp.int) (Uua tptp.nat)) (= (tptp.aa_nat_fun_int_int (tptp.aTP_Lamm_nv Uu) Uua) (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int Uu) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int Uua))))) (forall ((Uu tptp.real) (Uua tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.aTP_Lamm_zb Uu) Uua) (tptp.aa_real_real tptp.inverse_inverse_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Uu) Uua)))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.aTP_Lamm_zt Uu) Uua) (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_min_nat Uu) Uua)))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.aTP_Lamm_zu Uu) Uua) (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_min_nat Uua) Uu)))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.aTP_Lamm_wb Uu) Uua) (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat Uu) Uua)))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.aTP_Lamm_wa Uu) Uua) (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat Uua) Uu)))) (forall ((Uu tptp.fun_complex_complex) (Uua tptp.complex)) (= (tptp.aa_complex_real (tptp.aTP_Lamm_jn Uu) Uua) (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.aa_complex_complex Uu Uua)))) (forall ((Uu tptp.fun_nat_complex) (Uua tptp.nat)) (= (tptp.aa_nat_real (tptp.aTP_Lamm_jm Uu) Uua) (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.aa_nat_complex Uu Uua)))) (forall ((Uu tptp.fun_nat_real) (Uua tptp.nat)) (= (tptp.aa_nat_real (tptp.aTP_Lamm_jo Uu) Uua) (tptp.aa_real_real tptp.real_V7735802525324610683m_real (tptp.aa_nat_real Uu Uua)))) (forall ((Uu tptp.fun_nat_real) (Uua tptp.nat)) (= (tptp.aa_nat_real (tptp.aTP_Lamm_yy Uu) Uua) (tptp.aa_real_real tptp.inverse_inverse_real (tptp.aa_nat_real Uu Uua)))) (forall ((Uu tptp.fun_complex_real) (Uua tptp.complex)) (= (tptp.aa_complex_real (tptp.aTP_Lamm_tl Uu) Uua) (tptp.aa_real_real tptp.ln_ln_real (tptp.aa_complex_real Uu Uua)))) (forall ((Uu tptp.fun_real_real) (Uua tptp.real)) (= (tptp.aa_real_real (tptp.aTP_Lamm_tj Uu) Uua) (tptp.aa_real_real tptp.ln_ln_real (tptp.aa_real_real Uu Uua)))) (forall ((Uu tptp.fun_nat_real) (Uua tptp.nat)) (= (tptp.aa_nat_real (tptp.aTP_Lamm_tm Uu) Uua) (tptp.aa_real_real tptp.ln_ln_real (tptp.aa_nat_real Uu Uua)))) (forall ((Uu tptp.fun_int_real) (Uua tptp.int)) (= (tptp.aa_int_real (tptp.aTP_Lamm_tk Uu) Uua) (tptp.aa_real_real tptp.ln_ln_real (tptp.aa_int_real Uu Uua)))) (forall ((Uu tptp.fun_nat_rat) (Uua tptp.nat)) (= (tptp.aa_nat_rat (tptp.aTP_Lamm_aak Uu) Uua) (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_nat_rat Uu Uua)))) (forall ((Uu tptp.fun_nat_complex) (Uua tptp.nat)) (= (tptp.aa_nat3829984526574172007omplex (tptp.aTP_Lamm_pq Uu) Uua) (tptp.times_times_complex (tptp.aa_nat_complex Uu Uua)))) (forall ((Uu tptp.fun_nat_real) (Uua tptp.nat)) (= (tptp.aa_nat_fun_real_real (tptp.aTP_Lamm_pr Uu) Uua) (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real Uu Uua)))) (forall ((Uu tptp.fun_nat_rat) (Uua tptp.nat)) (= (tptp.aa_nat_fun_rat_rat (tptp.aTP_Lamm_ps Uu) Uua) (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat Uu Uua)))) (forall ((Uu tptp.fun_nat_nat) (Uua tptp.nat)) (= (tptp.aa_nat_fun_nat_nat (tptp.aTP_Lamm_pt Uu) Uua) (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat Uu Uua)))) (forall ((Uu tptp.fun_nat_int) (Uua tptp.nat)) (= (tptp.aa_nat_fun_int_int (tptp.aTP_Lamm_pu Uu) Uua) (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int Uu Uua)))) (forall ((Uu tptp.fun_nat_complex) (Uua tptp.nat)) (= (tptp.aa_nat3829984526574172007omplex (tptp.aTP_Lamm_ne Uu) Uua) (tptp.plus_plus_complex (tptp.aa_nat_complex Uu Uua)))) (forall ((Uu tptp.fun_nat_real) (Uua tptp.nat)) (= (tptp.aa_nat_fun_real_real (tptp.aTP_Lamm_ni Uu) Uua) (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real Uu Uua)))) (forall ((Uu tptp.fun_nat_rat) (Uua tptp.nat)) (= (tptp.aa_nat_fun_rat_rat (tptp.aTP_Lamm_nf Uu) Uua) (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_nat_rat Uu Uua)))) (forall ((Uu tptp.fun_nat_nat) (Uua tptp.nat)) (= (tptp.aa_nat_fun_nat_nat (tptp.aTP_Lamm_nh Uu) Uua) (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat Uu Uua)))) (forall ((Uu tptp.fun_nat_int) (Uua tptp.nat)) (= (tptp.aa_nat_fun_int_int (tptp.aTP_Lamm_ng Uu) Uua) (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_nat_int Uu Uua)))) (forall ((Uu tptp.fun_real_real) (Uua tptp.real)) (= (tptp.aa_real_real (tptp.aTP_Lamm_zm Uu) Uua) (tptp.aa_real_real tptp.arcosh_real (tptp.aa_real_real Uu Uua)))) (forall ((Uu tptp.fun_nat_real) (Uua tptp.nat)) (= (tptp.aa_nat_real (tptp.aTP_Lamm_gx Uu) Uua) (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_nat_real Uu Uua)))) (forall ((Uu tptp.fun_int_int) (Uua tptp.int)) (= (tptp.aa_int_int (tptp.aTP_Lamm_gw Uu) Uua) (tptp.aa_int_int tptp.abs_abs_int (tptp.aa_int_int Uu Uua)))) (forall ((Uu tptp.fun_nat_real) (Uua tptp.nat)) (= (tptp.aa_nat_real (tptp.aTP_Lamm_zf Uu) Uua) (tptp.aa_real_real tptp.cos_real (tptp.aa_nat_real Uu Uua)))) (forall ((Uu tptp.fun_re4238438383274954274t_real) (Uua tptp.real)) (= (tptp.aa_real_real (tptp.aTP_Lamm_yu Uu) Uua) (tptp.suminf_real (tptp.aa_real_fun_nat_real Uu Uua)))) (forall ((Uu tptp.list_VEBT_VEBT) (Uua tptp.vEBT_VEBT)) (= (tptp.pp (tptp.aa_VEBT_VEBT_bool (tptp.aTP_Lamm_ar Uu) Uua)) (exists ((I4 tptp.nat)) (and (= Uua (tptp.nth_VEBT_VEBT Uu I4)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I4) (tptp.size_s6755466524823107622T_VEBT Uu))))))) (forall ((Uu tptp.list_complex) (Uua tptp.complex)) (= (tptp.pp (tptp.aa_complex_bool (tptp.aTP_Lamm_an Uu) Uua)) (exists ((I4 tptp.nat)) (and (= Uua (tptp.aa_nat_complex (tptp.nth_complex Uu) I4)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I4) (tptp.size_s3451745648224563538omplex Uu))))))) (forall ((Uu tptp.list_real) (Uua tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aTP_Lamm_ao Uu) Uua)) (exists ((I4 tptp.nat)) (and (= Uua (tptp.aa_nat_real (tptp.nth_real Uu) I4)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I4) (tptp.size_size_list_real Uu))))))) (forall ((Uu tptp.list_list_nat) (Uua tptp.list_nat)) (= (tptp.pp (tptp.aa_list_nat_bool (tptp.aTP_Lamm_ap Uu) Uua)) (exists ((I4 tptp.nat)) (and (= Uua (tptp.nth_list_nat Uu I4)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I4) (tptp.size_s3023201423986296836st_nat Uu))))))) (forall ((Uu tptp.list_bool) (Uua tptp.bool)) (= (tptp.pp (tptp.aa_bool_bool (tptp.aTP_Lamm_as Uu) Uua)) (exists ((I4 tptp.nat)) (and (= (tptp.pp Uua) (tptp.pp (tptp.aa_nat_bool (tptp.nth_bool Uu) I4))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I4) (tptp.size_size_list_bool Uu))))))) (forall ((Uu tptp.list_nat) (Uua tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aTP_Lamm_at Uu) Uua)) (exists ((I4 tptp.nat)) (and (= Uua (tptp.aa_nat_nat (tptp.nth_nat Uu) I4)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I4) (tptp.size_size_list_nat Uu))))))) (forall ((Uu tptp.list_int) (Uua tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aTP_Lamm_aq Uu) Uua)) (exists ((I4 tptp.nat)) (and (= Uua (tptp.aa_nat_int (tptp.nth_int Uu) I4)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I4) (tptp.size_size_list_int Uu))))))) (forall ((Uu tptp.fun_nat_real) (Uua tptp.fun_nat_real) (Uub tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.aa_nat_real (tptp.aa_fun1839206346889086768t_real (tptp.aTP_Lamm_mt Uu) Uua) Uub) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real (tptp.if_real (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat _let_1) Uub)) (tptp.aa_nat_real Uua (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat Uub) _let_1))) (tptp.aa_nat_real Uu (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uub) tptp.one_one_nat)) _let_1)))))) (forall ((Uu tptp.fun_nat_real) (Uua tptp.fun_nat_real) (Uub tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_fun1839206346889086768t_real (tptp.aTP_Lamm_ma Uu) Uua) Uub) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real (tptp.if_real (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) Uub)) (tptp.aa_nat_real Uu Uub)) (tptp.aa_nat_real Uua Uub)))) (forall ((Uu tptp.num) (Uua tptp.code_integer) (Uub tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))) Uua))) (let ((_let_2 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger Uu))) (= (tptp.aa_Cod6977894654539884864nteger (tptp.aa_Cod8380929501330563836nteger (tptp.aTP_Lamm_fm Uu) Uua) Uub) (tptp.if_Pro6119634080678213985nteger (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger _let_2) Uub) (tptp.produc1086072967326762835nteger (tptp.plus_p5714425477246183910nteger _let_1 tptp.one_one_Code_integer) (tptp.minus_8373710615458151222nteger Uub _let_2)) (tptp.produc1086072967326762835nteger _let_1 Uub)))))) (forall ((Uu tptp.num) (Uua tptp.nat) (Uub tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) Uua))) (let ((_let_2 (tptp.aa_num_nat tptp.numeral_numeral_nat Uu))) (= (tptp.aa_nat7603221163087113075at_nat (tptp.aa_nat8803788312118491388at_nat (tptp.aTP_Lamm_fk Uu) Uua) Uub) (tptp.aa_Pro262675715343573244at_nat (tptp.aa_Pro8023792847356852296at_nat (tptp.if_Pro6206227464963214023at_nat (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat _let_2) Uub)) (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat _let_1) tptp.one_one_nat)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uub) _let_2))) (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat _let_1) Uub)))))) (forall ((Uu tptp.num) (Uua tptp.int) (Uub tptp.int)) (let ((_let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) Uua))) (let ((_let_2 (tptp.aa_num_int tptp.numeral_numeral_int Uu))) (= (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int (tptp.aTP_Lamm_fl Uu) Uua) Uub) (tptp.aa_Pro6970504127699319548nt_int (tptp.if_Pro3027730157355071871nt_int (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int _let_2) Uub) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int _let_1) tptp.one_one_int)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int Uub) _let_2))) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int _let_1) Uub)))))) (forall ((Uu tptp.code_integer) (Uua tptp.code_integer) (Uub tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger Uua))) (= (tptp.aa_Cod6977894654539884864nteger (tptp.aa_Cod8380929501330563836nteger (tptp.aTP_Lamm_vu Uu) Uua) Uub) (tptp.if_Pro6119634080678213985nteger (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.fequal_Code_integer Uub) tptp.zero_z3403309356797280102nteger) (tptp.produc1086072967326762835nteger _let_1 tptp.zero_z3403309356797280102nteger) (tptp.produc1086072967326762835nteger (tptp.minus_8373710615458151222nteger _let_1 tptp.one_one_Code_integer) (tptp.minus_8373710615458151222nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger Uu) Uub)))))) (forall ((Uu tptp.code_integer) (Uua tptp.code_integer) (Uub tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger Uua))) (= (tptp.aa_Cod6977894654539884864nteger (tptp.aa_Cod8380929501330563836nteger (tptp.aTP_Lamm_wt Uu) Uua) Uub) (tptp.if_Pro6119634080678213985nteger (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.fequal_Code_integer Uub) tptp.zero_z3403309356797280102nteger) (tptp.produc1086072967326762835nteger _let_1 tptp.zero_z3403309356797280102nteger) (tptp.produc1086072967326762835nteger (tptp.minus_8373710615458151222nteger _let_1 tptp.one_one_Code_integer) (tptp.minus_8373710615458151222nteger (tptp.abs_abs_Code_integer Uu) Uub)))))) (forall ((Uu tptp.code_integer) (Uua tptp.code_integer) (Uub tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger Uua))) (= (tptp.aa_Cod6977894654539884864nteger (tptp.aa_Cod8380929501330563836nteger (tptp.aTP_Lamm_vt Uu) Uua) Uub) (tptp.if_Pro6119634080678213985nteger (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.fequal_Code_integer Uub) tptp.zero_z3403309356797280102nteger) (tptp.produc1086072967326762835nteger _let_1 tptp.zero_z3403309356797280102nteger) (tptp.produc1086072967326762835nteger (tptp.minus_8373710615458151222nteger _let_1 tptp.one_one_Code_integer) (tptp.minus_8373710615458151222nteger Uu Uub)))))) (forall ((Uu tptp.fun_nat_fun_nat_real) (Uua tptp.nat) (Uub tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_nat_fun_nat_real (tptp.aTP_Lamm_qi Uu) Uua) Uub) (tptp.aa_nat_real (tptp.aa_nat_fun_nat_real Uu Uub) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uua) Uub)))) (forall ((Uu tptp.fun_nat_fun_nat_nat) (Uua tptp.nat) (Uub tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.aTP_Lamm_qg Uu) Uua) Uub) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat Uu Uub) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uua) Uub)))) (forall ((Uu tptp.fun_nat_fun_nat_int) (Uua tptp.nat) (Uub tptp.nat)) (= (tptp.aa_nat_int (tptp.aa_nat_fun_nat_int (tptp.aTP_Lamm_tr Uu) Uua) Uub) (tptp.aa_nat_int (tptp.aa_nat_fun_nat_int Uu Uub) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uua) Uub)))) (forall ((Uu tptp.fun_co2286642472385812463l_bool) (Uua tptp.real) (Uub tptp.complex)) (= (tptp.pp (tptp.aa_complex_bool (tptp.aa_rea5887071448072802392x_bool (tptp.aTP_Lamm_cc Uu) Uua) Uub)) (tptp.pp (tptp.aa_real_bool (tptp.aa_com8943241093633526360l_bool Uu Uub) Uua)))) (forall ((Uu tptp.fun_co2841405903858895691t_bool) (Uua tptp.nat) (Uub tptp.complex)) (= (tptp.pp (tptp.aa_complex_bool (tptp.aa_nat5545486172511849908x_bool (tptp.aTP_Lamm_ck Uu) Uua) Uub)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_com5335841084339320244t_bool Uu Uub) Uua)))) (forall ((Uu tptp.fun_re1255401033344146673l_bool) (Uua tptp.real) (Uub tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool (tptp.aTP_Lamm_bw Uu) Uua) Uub)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool Uu Uub) Uua)))) (forall ((Uu tptp.fun_re4238438383274954274t_real) (Uua tptp.nat) (Uub tptp.real)) (= (tptp.aa_real_real (tptp.aa_nat_fun_real_real (tptp.aTP_Lamm_yt Uu) Uua) Uub) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real Uu Uub) Uua))) (forall ((Uu tptp.fun_re9121486324101951821t_bool) (Uua tptp.nat) (Uub tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_nat_fun_real_bool (tptp.aTP_Lamm_ce Uu) Uua) Uub)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_real_fun_nat_bool Uu Uub) Uua)))) (forall ((Uu tptp.fun_re8661203372455305201t_bool) (Uua tptp.int) (Uub tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_int_fun_real_bool (tptp.aTP_Lamm_cm Uu) Uua) Uub)) (tptp.pp (tptp.aa_int_bool (tptp.aa_real_fun_int_bool Uu Uub) Uua)))) (forall ((Uu tptp.fun_na6801867027684862029l_bool) (Uua tptp.real) (Uub tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_real_fun_nat_bool (tptp.aTP_Lamm_by Uu) Uua) Uub)) (tptp.pp (tptp.aa_real_bool (tptp.aa_nat_fun_real_bool Uu Uub) Uua)))) (forall ((Uu tptp.fun_nat_fun_nat_bool) (Uua tptp.nat) (Uub tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool (tptp.aTP_Lamm_cg Uu) Uua) Uub)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool Uu Uub) Uua)))) (forall ((Uu tptp.fun_nat_fun_int_bool) (Uua tptp.int) (Uub tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_int_fun_nat_bool (tptp.aTP_Lamm_co Uu) Uua) Uub)) (tptp.pp (tptp.aa_int_bool (tptp.aa_nat_fun_int_bool Uu Uub) Uua)))) (forall ((Uu tptp.fun_in3970322703178350321l_bool) (Uua tptp.real) (Uub tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_real_fun_int_bool (tptp.aTP_Lamm_ca Uu) Uua) Uub)) (tptp.pp (tptp.aa_real_bool (tptp.aa_int_fun_real_bool Uu Uub) Uua)))) (forall ((Uu tptp.fun_int_fun_nat_bool) (Uua tptp.nat) (Uub tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_nat_fun_int_bool (tptp.aTP_Lamm_ci Uu) Uua) Uub)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_int_fun_nat_bool Uu Uub) Uua)))) (forall ((Uu tptp.complex) (Uua tptp.complex) (Uub tptp.nat)) (= (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex (tptp.aTP_Lamm_vf Uu) Uua) Uub) (tptp.groups2073611262835488442omplex (tptp.aa_nat6454746962644518025omplex (tptp.aa_com4347742694490471604omplex (tptp.aTP_Lamm_ve Uu) Uua) Uub) (tptp.set_ord_atMost_nat Uub)))) (forall ((Uu tptp.real) (Uua tptp.real) (Uub tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_vd Uu) Uua) Uub) (tptp.groups6591440286371151544t_real (tptp.aa_nat_fun_nat_real (tptp.aa_rea6853821027689443120t_real (tptp.aTP_Lamm_vc Uu) Uua) Uub) (tptp.set_ord_atMost_nat Uub)))) (forall ((Uu tptp.complex) (Uua tptp.complex) (Uub tptp.nat)) (= (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex (tptp.aTP_Lamm_vb Uu) Uua) Uub) (tptp.groups2073611262835488442omplex (tptp.aa_nat6454746962644518025omplex (tptp.aa_com4347742694490471604omplex (tptp.aTP_Lamm_va Uu) Uua) Uub) (tptp.set_ord_atMost_nat Uub)))) (forall ((Uu tptp.real) (Uua tptp.real) (Uub tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_uz Uu) Uua) Uub) (tptp.groups6591440286371151544t_real (tptp.aa_nat_fun_nat_real (tptp.aa_rea6853821027689443120t_real (tptp.aTP_Lamm_uy Uu) Uua) Uub) (tptp.set_ord_atMost_nat Uub)))) (forall ((Uu tptp.fun_nat_real) (Uua tptp.fun_nat_real) (Uub tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_fun1839206346889086768t_real (tptp.aTP_Lamm_rc Uu) Uua) Uub) (tptp.groups6591440286371151544t_real (tptp.aa_nat_fun_nat_real (tptp.aa_fun3023522663955195517t_real (tptp.aTP_Lamm_rb Uu) Uua) Uub) (tptp.set_ord_atMost_nat Uub)))) (forall ((Uu tptp.fun_nat_complex) (Uua tptp.fun_nat_complex) (Uub tptp.nat)) (= (tptp.aa_nat_complex (tptp.aa_fun2955221450537884980omplex (tptp.aTP_Lamm_ra Uu) Uua) Uub) (tptp.groups2073611262835488442omplex (tptp.aa_nat6454746962644518025omplex (tptp.aa_fun5379041630539201665omplex (tptp.aTP_Lamm_qz Uu) Uua) Uub) (tptp.set_ord_atMost_nat Uub)))) (forall ((Uu tptp.nat) (Uua tptp.complex) (Uub tptp.nat)) (= (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex (tptp.aTP_Lamm_mk Uu) Uua) Uub) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_complex_complex (tptp.if_complex (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.fequal_nat Uub) Uu) tptp.one_one_complex) tptp.zero_zero_complex)) (tptp.aa_nat_complex (tptp.power_power_complex Uua) Uub)))) (forall ((Uu tptp.nat) (Uua tptp.real) (Uub tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_ml Uu) Uua) Uub) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real (tptp.if_real (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.fequal_nat Uub) Uu)) tptp.one_one_real) tptp.zero_zero_real)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Uua) Uub)))) (forall ((Uu tptp.nat) (Uua tptp.int) (Uub tptp.nat)) (= (tptp.aa_nat_int (tptp.aa_int_fun_nat_int (tptp.aTP_Lamm_mm Uu) Uua) Uub) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.if_int (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.fequal_nat Uub) Uu) tptp.one_one_int) tptp.zero_zero_int)) (tptp.aa_nat_int (tptp.power_power_int Uua) Uub)))) (forall ((Uu tptp.code_integer) (Uua tptp.code_integer) (Uub tptp.code_integer)) (= (tptp.aa_Cod2825494507867081354r_bool (tptp.aa_Cod4981436349852597092r_bool (tptp.aTP_Lamm_vr Uu) Uua) Uub) (tptp.produc5135875973608410785r_bool (tptp.if_Code_integer (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) Uu) Uua (tptp.minus_8373710615458151222nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger Uua) Uub)) (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.fequal_Code_integer Uub) tptp.one_one_Code_integer)))) (forall ((Uu tptp.rat) (Uua tptp.int) (Uub tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool (tptp.aTP_Lamm_ws Uu) Uua) Uub)) (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.produc8560705615207772305t_bool (tptp.aa_int2327297053056786951t_bool (tptp.aTP_Lamm_wr Uua) Uub)) (tptp.quotient_of Uu))))) (forall ((Uu tptp.rat) (Uua tptp.int) (Uub tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool (tptp.aTP_Lamm_wq Uu) Uua) Uub)) (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.produc8560705615207772305t_bool (tptp.aa_int2327297053056786951t_bool (tptp.aTP_Lamm_wp Uua) Uub)) (tptp.quotient_of Uu))))) (forall ((Uu tptp.rat) (Uua tptp.int) (Uub tptp.int)) (= (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int (tptp.aTP_Lamm_wm Uu) Uua) Uub) (tptp.aa_Pro6970504127699319548nt_int (tptp.produc4245557441103728435nt_int (tptp.aa_int1966403025003302569nt_int (tptp.aTP_Lamm_wl Uua) Uub)) (tptp.quotient_of Uu)))) (forall ((Uu tptp.rat) (Uua tptp.int) (Uub tptp.int)) (= (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int (tptp.aTP_Lamm_wk Uu) Uua) Uub) (tptp.aa_Pro6970504127699319548nt_int (tptp.produc4245557441103728435nt_int (tptp.aa_int1966403025003302569nt_int (tptp.aTP_Lamm_wj Uua) Uub)) (tptp.quotient_of Uu)))) (forall ((Uu tptp.rat) (Uua tptp.int) (Uub tptp.int)) (= (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int (tptp.aTP_Lamm_wi Uu) Uua) Uub) (tptp.aa_Pro6970504127699319548nt_int (tptp.produc4245557441103728435nt_int (tptp.aa_int1966403025003302569nt_int (tptp.aTP_Lamm_wh Uua) Uub)) (tptp.quotient_of Uu)))) (forall ((Uu tptp.rat) (Uua tptp.int) (Uub tptp.int)) (= (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int (tptp.aTP_Lamm_wg Uu) Uua) Uub) (tptp.aa_Pro6970504127699319548nt_int (tptp.produc4245557441103728435nt_int (tptp.aa_int1966403025003302569nt_int (tptp.aTP_Lamm_wf Uua) Uub)) (tptp.quotient_of Uu)))) (forall ((Uu tptp.fun_na6724076748692969250l_real) (Uua tptp.real) (Uub tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_yi Uu) Uua) Uub) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_nat_fun_real_real Uu Uub) tptp.zero_zero_real)) (tptp.aa_nat_real tptp.semiri2265585572941072030t_real Uub))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Uua) Uub)))) (forall ((Uu tptp.real) (Uua tptp.fun_na5723442673449079972x_real) (Uub tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_fun5746040925223427547t_real (tptp.aTP_Lamm_mv Uu) Uua) Uub) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_complex_real (tptp.aa_nat480766339200631653x_real Uua Uub) tptp.zero_zero_complex)) (tptp.aa_nat_real tptp.semiri2265585572941072030t_real Uub))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Uu) Uub)))) (forall ((Uu tptp.real) (Uua tptp.fun_na6724076748692969250l_real) (Uub tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_fun1113820866546176217t_real (tptp.aTP_Lamm_mw Uu) Uua) Uub) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_nat_fun_real_real Uua Uub) tptp.zero_zero_real)) (tptp.aa_nat_real tptp.semiri2265585572941072030t_real Uub))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Uu) Uub)))) (forall ((Uu tptp.real) (Uua tptp.fun_nat_fun_rat_real) (Uub tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_fun507281639146497029t_real (tptp.aTP_Lamm_mx Uu) Uua) Uub) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_rat_real (tptp.aa_nat_fun_rat_real Uua Uub) tptp.zero_zero_rat)) (tptp.aa_nat_real tptp.semiri2265585572941072030t_real Uub))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Uu) Uub)))) (forall ((Uu tptp.real) (Uua tptp.fun_nat_fun_nat_real) (Uub tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_fun7039663905532832253t_real (tptp.aTP_Lamm_my Uu) Uua) Uub) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_nat_real (tptp.aa_nat_fun_nat_real Uua Uub) tptp.zero_zero_nat)) (tptp.aa_nat_real tptp.semiri2265585572941072030t_real Uub))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Uu) Uub)))) (forall ((Uu tptp.real) (Uua tptp.fun_nat_fun_int_real) (Uub tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_fun241848180832411225t_real (tptp.aTP_Lamm_mz Uu) Uua) Uub) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_int_real (tptp.aa_nat_fun_int_real Uua Uub) tptp.zero_zero_int)) (tptp.aa_nat_real tptp.semiri2265585572941072030t_real Uub))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Uu) Uub)))) (forall ((Uu tptp.fun_nat_complex) (Uua tptp.nat) (Uub tptp.complex)) (= (tptp.pp (tptp.aa_complex_bool (tptp.aa_nat5545486172511849908x_bool (tptp.aTP_Lamm_qm Uu) Uua) Uub)) (= (tptp.groups2073611262835488442omplex (tptp.aa_com8181001469867462503omplex (tptp.aTP_Lamm_kn Uu) Uub) (tptp.set_ord_atMost_nat Uua)) tptp.zero_zero_complex))) (forall ((Uu tptp.fun_nat_real) (Uua tptp.nat) (Uub tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_nat_fun_real_bool (tptp.aTP_Lamm_qn Uu) Uua) Uub)) (= (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_kl Uu) Uub) (tptp.set_ord_atMost_nat Uua)) tptp.zero_zero_real))) (forall ((Uu tptp.fun_nat_complex) (Uua tptp.fun_nat_complex) (Uub tptp.nat)) (= (tptp.aa_nat_complex (tptp.aa_fun2955221450537884980omplex (tptp.aTP_Lamm_hb Uu) Uua) Uub) (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_nat_complex Uu Uub)) (tptp.aa_nat_complex (tptp.power_power_complex tptp.zero_zero_complex) Uub))) (tptp.aa_nat_complex Uua Uub)))) (forall ((Uu tptp.fun_nat_real) (Uua tptp.fun_nat_real) (Uub tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_fun1839206346889086768t_real (tptp.aTP_Lamm_hd Uu) Uua) Uub) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real Uu Uub)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real tptp.zero_zero_real) Uub))) (tptp.aa_nat_real Uua Uub)))) (forall ((Uu tptp.fun_nat_rat) (Uua tptp.fun_nat_rat) (Uub tptp.nat)) (= (tptp.aa_nat_rat (tptp.aa_fun765758790203053448at_rat (tptp.aTP_Lamm_hc Uu) Uua) Uub) (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat Uu Uub)) (tptp.aa_nat_rat (tptp.power_power_rat tptp.zero_zero_rat) Uub))) (tptp.aa_nat_rat Uua Uub)))) (forall ((Uu tptp.fun_nat_real) (Uua tptp.real) (Uub tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_yq Uu) Uua) Uub) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real Uu Uub)) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real (tptp.aa_nat_nat tptp.suc Uub)))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Uua) Uub)))) (forall ((Uu tptp.real) (Uua tptp.fun_nat_real) (Uub tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_fun1839206346889086768t_real (tptp.aTP_Lamm_na Uu) Uua) Uub) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_nat_real Uua Uub)) (tptp.aa_nat_real tptp.semiri2265585572941072030t_real Uub))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Uu) Uub)))) (forall ((Uu tptp.nat) (Uua tptp.nat) (Uub tptp.list_nat)) (= (tptp.pp (tptp.aa_list_nat_bool (tptp.aa_nat2079453845469346690t_bool (tptp.aTP_Lamm_zy Uu) Uua) Uub)) (and (= (tptp.size_size_list_nat Uub) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uu) tptp.one_one_nat)) (= (tptp.groups4561878855575611511st_nat Uub) Uua)))) (forall ((Uu tptp.fun_nat_complex) (Uua tptp.complex) (Uub tptp.nat)) (= (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex (tptp.aTP_Lamm_nk Uu) Uua) Uub) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex Uub)) (tptp.aa_nat_complex Uu Uub))) (tptp.aa_nat_complex (tptp.power_power_complex Uua) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uub) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)))))) (forall ((Uu tptp.fun_nat_real) (Uua tptp.real) (Uub tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_nm Uu) Uua) Uub) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real Uub)) (tptp.aa_nat_real Uu Uub))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Uua) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uub) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)))))) (forall ((Uu tptp.nat) (Uua tptp.nat) (Uub tptp.list_nat)) (= (tptp.pp (tptp.aa_list_nat_bool (tptp.aa_nat2079453845469346690t_bool (tptp.aTP_Lamm_zz Uu) Uua) Uub)) (and (= (tptp.size_size_list_nat Uub) Uu) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.groups4561878855575611511st_nat Uub)) tptp.one_one_nat) Uua)))) (forall ((Uu tptp.set_VEBT_VEBT) (Uua tptp.nat) (Uub tptp.list_VEBT_VEBT)) (= (tptp.pp (tptp.aa_lis2822252094023462681T_bool (tptp.aa_nat1297483763028037422T_bool (tptp.aTP_Lamm_bm Uu) Uua) Uub)) (and (tptp.ord_le4337996190870823476T_VEBT (tptp.set_VEBT_VEBT2 Uub) Uu) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.size_s6755466524823107622T_VEBT Uub)) Uua))))) (forall ((Uu tptp.set_complex) (Uua tptp.nat) (Uub tptp.list_complex)) (= (tptp.pp (tptp.aa_list_complex_bool (tptp.aa_nat8039161444313734436x_bool (tptp.aTP_Lamm_bl Uu) Uua) Uub)) (and (tptp.pp (tptp.aa_set_complex_bool (tptp.ord_le211207098394363844omplex (tptp.set_complex2 Uub)) Uu)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.size_s3451745648224563538omplex Uub)) Uua))))) (forall ((Uu tptp.set_bool) (Uua tptp.nat) (Uub tptp.list_bool)) (= (tptp.pp (tptp.aa_list_bool_bool (tptp.aa_nat4862889769322786699l_bool (tptp.aTP_Lamm_bn Uu) Uua) Uub)) (and (tptp.ord_less_eq_set_bool (tptp.set_bool2 Uub) Uu) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.size_size_list_bool Uub)) Uua))))) (forall ((Uu tptp.set_nat) (Uua tptp.nat) (Uub tptp.list_nat)) (= (tptp.pp (tptp.aa_list_nat_bool (tptp.aa_nat2079453845469346690t_bool (tptp.aTP_Lamm_bo Uu) Uua) Uub)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat (tptp.set_nat2 Uub)) Uu)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.size_size_list_nat Uub)) Uua))))) (forall ((Uu tptp.set_int) (Uua tptp.nat) (Uub tptp.list_int)) (= (tptp.pp (tptp.aa_list_int_bool (tptp.aa_nat1619170893822700070t_bool (tptp.aTP_Lamm_bp Uu) Uua) Uub)) (and (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int (tptp.set_int2 Uub)) Uu)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.size_size_list_int Uub)) Uua))))) (forall ((Uu tptp.set_VEBT_VEBT) (Uua tptp.nat) (Uub tptp.list_VEBT_VEBT)) (= (tptp.pp (tptp.aa_lis2822252094023462681T_bool (tptp.aa_nat1297483763028037422T_bool (tptp.aTP_Lamm_bh Uu) Uua) Uub)) (and (tptp.ord_le4337996190870823476T_VEBT (tptp.set_VEBT_VEBT2 Uub) Uu) (= (tptp.size_s6755466524823107622T_VEBT Uub) Uua)))) (forall ((Uu tptp.set_complex) (Uua tptp.nat) (Uub tptp.list_complex)) (= (tptp.pp (tptp.aa_list_complex_bool (tptp.aa_nat8039161444313734436x_bool (tptp.aTP_Lamm_bg Uu) Uua) Uub)) (and (tptp.pp (tptp.aa_set_complex_bool (tptp.ord_le211207098394363844omplex (tptp.set_complex2 Uub)) Uu)) (= (tptp.size_s3451745648224563538omplex Uub) Uua)))) (forall ((Uu tptp.set_bool) (Uua tptp.nat) (Uub tptp.list_bool)) (= (tptp.pp (tptp.aa_list_bool_bool (tptp.aa_nat4862889769322786699l_bool (tptp.aTP_Lamm_bi Uu) Uua) Uub)) (and (tptp.ord_less_eq_set_bool (tptp.set_bool2 Uub) Uu) (= (tptp.size_size_list_bool Uub) Uua)))) (forall ((Uu tptp.set_nat) (Uua tptp.nat) (Uub tptp.list_nat)) (= (tptp.pp (tptp.aa_list_nat_bool (tptp.aa_nat2079453845469346690t_bool (tptp.aTP_Lamm_bj Uu) Uua) Uub)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat (tptp.set_nat2 Uub)) Uu)) (= (tptp.size_size_list_nat Uub) Uua)))) (forall ((Uu tptp.set_int) (Uua tptp.nat) (Uub tptp.list_int)) (= (tptp.pp (tptp.aa_list_int_bool (tptp.aa_nat1619170893822700070t_bool (tptp.aTP_Lamm_bk Uu) Uua) Uub)) (and (tptp.pp (tptp.aa_set_int_bool (tptp.ord_less_eq_set_int (tptp.set_int2 Uub)) Uu)) (= (tptp.size_size_list_int Uub) Uua)))) (forall ((Uu tptp.nat) (Uua tptp.nat) (Uub tptp.list_nat)) (= (tptp.pp (tptp.aa_list_nat_bool (tptp.aa_nat2079453845469346690t_bool (tptp.aTP_Lamm_zx Uu) Uua) Uub)) (and (= (tptp.size_size_list_nat Uub) Uu) (= (tptp.groups4561878855575611511st_nat Uub) Uua)))) (forall ((Uu tptp.set_nat) (Uua tptp.nat) (Uub tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool (tptp.aTP_Lamm_vv Uu) Uua) Uub)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat (tptp.aa_nat_nat tptp.suc Uub)) Uu)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Uub) Uua))))) (forall ((Uu tptp.nat) (Uua tptp.nat) (Uub tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool (tptp.aTP_Lamm_aan Uu) Uua) Uub)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Uua) Uu)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Uub) Uu)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Uua) Uub))))) (forall ((Uu tptp.set_nat) (Uua tptp.nat) (Uub tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool (tptp.aTP_Lamm_vw Uu) Uua) Uub)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat Uub) Uu)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Uub) (tptp.aa_nat_nat tptp.suc Uua)))))) (forall ((Uu tptp.fun_nat_complex) (Uua tptp.complex) (Uub tptp.nat)) (= (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex (tptp.aTP_Lamm_nj Uu) Uua) Uub) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_nat_complex (tptp.diffs_complex Uu) Uub)) (tptp.aa_nat_complex (tptp.power_power_complex Uua) Uub)))) (forall ((Uu tptp.fun_nat_real) (Uua tptp.real) (Uub tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_nl Uu) Uua) Uub) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real (tptp.diffs_real Uu) Uub)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Uua) Uub)))) (forall ((Uu tptp.complex) (Uua tptp.fun_nat_complex) (Uub tptp.nat)) (= (tptp.aa_nat_complex (tptp.aa_fun2955221450537884980omplex (tptp.aTP_Lamm_np Uu) Uua) Uub) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_nat_complex (tptp.diffs_complex Uua) Uub)) (tptp.aa_nat_complex (tptp.power_power_complex Uu) Uub)))) (forall ((Uu tptp.real) (Uua tptp.fun_nat_real) (Uub tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_fun1839206346889086768t_real (tptp.aTP_Lamm_no Uu) Uua) Uub) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real (tptp.diffs_real Uua) Uub)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Uu) Uub)))) (forall ((Uu tptp.nat) (Uua tptp.nat) (Uub tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.aTP_Lamm_qk Uu) Uua) Uub) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uua) Uub)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uu) Uub)))) (forall ((Uu tptp.int) (Uua tptp.int) (Uub tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool (tptp.aTP_Lamm_vi Uu) Uua) Uub)) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Uu) Uua)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Uua) Uub))))) (forall ((Uu tptp.int) (Uua tptp.int) (Uub tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool (tptp.aTP_Lamm_ef Uu) Uua) Uub)) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Uu) Uub)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Uub) Uua))))) (forall ((Uu tptp.int) (Uua tptp.int) (Uub tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool (tptp.aTP_Lamm_vh Uu) Uua) Uub)) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Uu) Uub)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Uua) Uub))))) (forall ((Uu tptp.int) (Uua tptp.int) (Uub tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool (tptp.aTP_Lamm_ei Uu) Uua) Uub)) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Uu) Uub)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Uub) Uua))))) (forall ((Uu tptp.int) (Uua tptp.int) (Uub tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool (tptp.aTP_Lamm_eh Uu) Uua) Uub)) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Uu) Uub)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Uub) Uua))))) (forall ((Uu tptp.int) (Uua tptp.int) (Uub tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool (tptp.aTP_Lamm_eg Uu) Uua) Uub)) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Uu) Uub)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Uub) Uua))))) (forall ((Uu tptp.nat) (Uua tptp.nat) (Uub tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat Uub))) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool (tptp.aTP_Lamm_aab Uu) Uua) Uub)) (and (tptp.pp (tptp.aa_nat_bool _let_1 Uua)) (tptp.pp (tptp.aa_nat_bool _let_1 Uu)))))) (forall ((Uu tptp.set_complex) (Uua tptp.fun_complex_bool) (Uub tptp.complex)) (= (tptp.pp (tptp.aa_complex_bool (tptp.aa_fun1096865461735438652x_bool (tptp.aTP_Lamm_az Uu) Uua) Uub)) (and (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex Uub) Uu)) (tptp.pp (tptp.aa_complex_bool Uua Uub))))) (forall ((Uu tptp.set_real) (Uua tptp.fun_real_bool) (Uub tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_fun6476784834714468668l_bool (tptp.aTP_Lamm_ba Uu) Uua) Uub)) (and (tptp.member_real Uub Uu) (tptp.pp (tptp.aa_real_bool Uua Uub))))) (forall ((Uu tptp.set_list_nat) (Uua tptp.fun_list_nat_bool) (Uub tptp.list_nat)) (= (tptp.pp (tptp.aa_list_nat_bool (tptp.aa_fun6009467934925565500t_bool (tptp.aTP_Lamm_bb Uu) Uua) Uub)) (and (tptp.member_list_nat Uub Uu) (tptp.pp (tptp.aa_list_nat_bool Uua Uub))))) (forall ((Uu tptp.set_nat) (Uua tptp.fun_nat_bool) (Uub tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_fun3878383735219268284t_bool (tptp.aTP_Lamm_bc Uu) Uua) Uub)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat Uub) Uu)) (tptp.pp (tptp.aa_nat_bool Uua Uub))))) (forall ((Uu tptp.set_int) (Uua tptp.fun_int_bool) (Uub tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_fun5146555767781538748t_bool (tptp.aTP_Lamm_bd Uu) Uua) Uub)) (and (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Uub) Uu)) (tptp.pp (tptp.aa_int_bool Uua Uub))))) (forall ((Uu tptp.set_complex) (Uua tptp.fun_complex_complex) (Uub tptp.complex)) (= (tptp.pp (tptp.aa_complex_bool (tptp.aa_fun9073502203726719595x_bool (tptp.aTP_Lamm_dr Uu) Uua) Uub)) (and (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex Uub) Uu)) (not (= (tptp.aa_complex_complex Uua Uub) tptp.zero_zero_complex))))) (forall ((Uu tptp.set_complex) (Uua tptp.fun_complex_real) (Uub tptp.complex)) (= (tptp.pp (tptp.aa_complex_bool (tptp.aa_fun2898354424061222765x_bool (tptp.aTP_Lamm_dz Uu) Uua) Uub)) (and (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex Uub) Uu)) (not (= (tptp.aa_complex_real Uua Uub) tptp.zero_zero_real))))) (forall ((Uu tptp.set_real) (Uua tptp.fun_real_complex) (Uub tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_fun3813300650643916655l_bool (tptp.aTP_Lamm_dl Uu) Uua) Uub)) (and (tptp.member_real Uub Uu) (not (= (tptp.aa_real_complex Uua Uub) tptp.zero_zero_complex))))) (forall ((Uu tptp.set_real) (Uua tptp.fun_real_real) (Uub tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_fun9137271176455094897l_bool (tptp.aTP_Lamm_dt Uu) Uua) Uub)) (and (tptp.member_real Uub Uu) (not (= (tptp.aa_real_real Uua Uub) tptp.zero_zero_real))))) (forall ((Uu tptp.set_real) (Uua tptp.fun_real_rat) (Uub tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_fun8987621170725249221l_bool (tptp.aTP_Lamm_eb Uu) Uua) Uub)) (and (tptp.member_real Uub Uu) (not (= (tptp.aa_real_rat Uua Uub) tptp.zero_zero_rat))))) (forall ((Uu tptp.set_nat) (Uua tptp.fun_nat_complex) (Uub tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_fun8004580481347240231t_bool (tptp.aTP_Lamm_dn Uu) Uua) Uub)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat Uub) Uu)) (not (= (tptp.aa_nat_complex Uua Uub) tptp.zero_zero_complex))))) (forall ((Uu tptp.set_nat) (Uua tptp.fun_nat_real) (Uub tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_fun1349230436907296553t_bool (tptp.aTP_Lamm_dv Uu) Uua) Uub)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat Uub) Uu)) (not (= (tptp.aa_nat_real Uua Uub) tptp.zero_zero_real))))) (forall ((Uu tptp.set_nat) (Uua tptp.fun_nat_rat) (Uub tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_fun5637262893798792573t_bool (tptp.aTP_Lamm_ed Uu) Uua) Uub)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat Uub) Uu)) (not (= (tptp.aa_nat_rat Uua Uub) tptp.zero_zero_rat))))) (forall ((Uu tptp.set_int) (Uua tptp.fun_int_complex) (Uub tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_fun8146511558608327279t_bool (tptp.aTP_Lamm_dp Uu) Uua) Uub)) (and (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Uub) Uu)) (not (= (tptp.aa_int_complex Uua Uub) tptp.zero_zero_complex))))) (forall ((Uu tptp.set_int) (Uua tptp.fun_int_real) (Uub tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_fun1262781554902806129t_bool (tptp.aTP_Lamm_dx Uu) Uua) Uub)) (and (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Uub) Uu)) (not (= (tptp.aa_int_real Uua Uub) tptp.zero_zero_real))))) (forall ((Uu tptp.set_complex) (Uua tptp.fun_complex_complex) (Uub tptp.complex)) (= (tptp.pp (tptp.aa_complex_bool (tptp.aa_fun9073502203726719595x_bool (tptp.aTP_Lamm_cx Uu) Uua) Uub)) (and (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex Uub) Uu)) (not (= (tptp.aa_complex_complex Uua Uub) tptp.one_one_complex))))) (forall ((Uu tptp.set_complex) (Uua tptp.fun_complex_real) (Uub tptp.complex)) (= (tptp.pp (tptp.aa_complex_bool (tptp.aa_fun2898354424061222765x_bool (tptp.aTP_Lamm_df Uu) Uua) Uub)) (and (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex Uub) Uu)) (not (= (tptp.aa_complex_real Uua Uub) tptp.one_one_real))))) (forall ((Uu tptp.set_real) (Uua tptp.fun_real_complex) (Uub tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_fun3813300650643916655l_bool (tptp.aTP_Lamm_cr Uu) Uua) Uub)) (and (tptp.member_real Uub Uu) (not (= (tptp.aa_real_complex Uua Uub) tptp.one_one_complex))))) (forall ((Uu tptp.set_real) (Uua tptp.fun_real_real) (Uub tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_fun9137271176455094897l_bool (tptp.aTP_Lamm_cz Uu) Uua) Uub)) (and (tptp.member_real Uub Uu) (not (= (tptp.aa_real_real Uua Uub) tptp.one_one_real))))) (forall ((Uu tptp.set_real) (Uua tptp.fun_real_rat) (Uub tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_fun8987621170725249221l_bool (tptp.aTP_Lamm_dh Uu) Uua) Uub)) (and (tptp.member_real Uub Uu) (not (= (tptp.aa_real_rat Uua Uub) tptp.one_one_rat))))) (forall ((Uu tptp.set_nat) (Uua tptp.fun_nat_complex) (Uub tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_fun8004580481347240231t_bool (tptp.aTP_Lamm_ct Uu) Uua) Uub)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat Uub) Uu)) (not (= (tptp.aa_nat_complex Uua Uub) tptp.one_one_complex))))) (forall ((Uu tptp.set_nat) (Uua tptp.fun_nat_real) (Uub tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_fun1349230436907296553t_bool (tptp.aTP_Lamm_db Uu) Uua) Uub)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat Uub) Uu)) (not (= (tptp.aa_nat_real Uua Uub) tptp.one_one_real))))) (forall ((Uu tptp.set_nat) (Uua tptp.fun_nat_rat) (Uub tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_fun5637262893798792573t_bool (tptp.aTP_Lamm_dj Uu) Uua) Uub)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat Uub) Uu)) (not (= (tptp.aa_nat_rat Uua Uub) tptp.one_one_rat))))) (forall ((Uu tptp.set_int) (Uua tptp.fun_int_complex) (Uub tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_fun8146511558608327279t_bool (tptp.aTP_Lamm_cv Uu) Uua) Uub)) (and (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Uub) Uu)) (not (= (tptp.aa_int_complex Uua Uub) tptp.one_one_complex))))) (forall ((Uu tptp.set_int) (Uua tptp.fun_int_real) (Uub tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_fun1262781554902806129t_bool (tptp.aTP_Lamm_dd Uu) Uua) Uub)) (and (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Uub) Uu)) (not (= (tptp.aa_int_real Uua Uub) tptp.one_one_real))))) (forall ((Uu tptp.nat) (Uua tptp.nat) (Uub tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool (tptp.aTP_Lamm_aaa Uu) Uua) Uub)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat Uub) Uu)) Uua)))) (forall ((Uu tptp.nat) (Uua tptp.nat) (Uub tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool (tptp.aTP_Lamm_qf Uu) Uua) Uub)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Uua) Uub)) Uu)))) (forall ((Uu tptp.real) (Uua tptp.complex) (Uub tptp.complex)) (= (tptp.pp (tptp.aa_complex_bool (tptp.aa_com1553036987509291606x_bool (tptp.aTP_Lamm_zr Uu) Uua) Uub)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_complex_real (tptp.real_V3694042436643373181omplex Uua) Uub)) Uu)))) (forall ((Uu tptp.real) (Uua tptp.real) (Uub tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool (tptp.aTP_Lamm_zp Uu) Uua) Uub)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.real_V975177566351809787t_real Uua) Uub)) Uu)))) (forall ((Uu tptp.nat) (Uua tptp.nat) (Uub tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool (tptp.aTP_Lamm_qy Uu) Uua) Uub)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Uua) Uub)) Uu)))) (forall ((Uu tptp.set_Pr958786334691620121nt_int) (Uua tptp.int) (Uub tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool (tptp.aTP_Lamm_jw Uu) Uua) Uub)) (tptp.member5262025264175285858nt_int (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int Uua) Uub) Uu))) (forall ((Uu tptp.set_Pr7592006421409863191nteger) (Uua tptp.fun_Co6545587727236015215e_term) (Uub tptp.produc8923325533196201883nteger)) (= (tptp.pp (tptp.aa_Pro5843519176478241656r_bool (tptp.aa_fun5646951941296221740r_bool (tptp.aTP_Lamm_jx Uu) Uua) Uub)) (tptp.member4581088367259704696nteger (tptp.produc4282985567423050387nteger Uua Uub) Uu))) (forall ((Uu tptp.set_Pr5663546166630115725nteger) (Uua tptp.fun_Pr272337284026993017e_term) (Uub tptp.produc8923325533196201883nteger)) (= (tptp.pp (tptp.aa_Pro5843519176478241656r_bool (tptp.aa_fun5449300841655810358r_bool (tptp.aTP_Lamm_jy Uu) Uua) Uub)) (tptp.member6423679177046879214nteger (tptp.produc7384524951051686153nteger Uua Uub) Uu))) (forall ((Uu tptp.set_Pr233528076387193594nt_int) (Uua tptp.fun_Pr9164807099015279978e_term) (Uub tptp.product_prod_int_int)) (= (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.aa_fun5300525129335604105t_bool (tptp.aTP_Lamm_jz Uu) Uua) Uub)) (tptp.member690604328116145115nt_int (tptp.produc1560874099174258678nt_int Uua Uub) Uu))) (forall ((Uu tptp.set_Pr5033440245338114598nt_int) (Uua tptp.fun_in6429348457993719614e_term) (Uub tptp.product_prod_int_int)) (= (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.aa_fun4446166836006121821t_bool (tptp.aTP_Lamm_ka Uu) Uua) Uub)) (tptp.member500491123954006279nt_int (tptp.produc4852315488734385442nt_int Uua Uub) Uu))) (forall ((Uu tptp.nat) (Uua tptp.complex) (Uub tptp.complex)) (= (tptp.pp (tptp.aa_complex_bool (tptp.aa_com1553036987509291606x_bool (tptp.aTP_Lamm_fd Uu) Uua) Uub)) (= (tptp.aa_nat_complex (tptp.power_power_complex Uub) Uu) Uua))) (forall ((Uu tptp.complex) (Uua tptp.nat) (Uub tptp.complex)) (= (tptp.pp (tptp.aa_complex_bool (tptp.aa_nat5545486172511849908x_bool (tptp.aTP_Lamm_vx Uu) Uua) Uub)) (= (tptp.aa_nat_complex (tptp.power_power_complex Uub) Uua) Uu))) (forall ((Uu tptp.fun_nat_complex) (Uua tptp.complex) (Uub tptp.nat)) (= (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex (tptp.aTP_Lamm_kq Uu) Uua) Uub) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_nat_complex Uu (tptp.aa_nat_nat tptp.suc Uub))) (tptp.aa_nat_complex (tptp.power_power_complex Uua) Uub)))) (forall ((Uu tptp.fun_nat_real) (Uua tptp.real) (Uub tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_kr Uu) Uua) Uub) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real Uu (tptp.aa_nat_nat tptp.suc Uub))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Uua) Uub)))) (forall ((Uu tptp.fun_nat_real) (Uua tptp.fun_nat_int) (Uub tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_fun4551936527957760560t_real (tptp.aTP_Lamm_ze Uu) Uua) Uub) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_nat_real Uu Uub)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_int_real tptp.ring_1_of_int_real (tptp.aa_nat_int Uua Uub))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))) tptp.pi))))) (forall ((Uu tptp.fun_nat_real) (Uua tptp.real) (Uub tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_yr Uu) Uua) Uub) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real Uu Uub)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Uua) (tptp.aa_nat_nat tptp.suc Uub))))) (forall ((Uu tptp.fun_nat_complex) (Uua tptp.complex) (Uub tptp.nat)) (= (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex (tptp.aTP_Lamm_kn Uu) Uua) Uub) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_nat_complex Uu Uub)) (tptp.aa_nat_complex (tptp.power_power_complex Uua) Uub)))) (forall ((Uu tptp.fun_nat_real) (Uua tptp.real) (Uub tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_kl Uu) Uua) Uub) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real Uu Uub)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Uua) Uub)))) (forall ((Uu tptp.fun_nat_rat) (Uua tptp.rat) (Uub tptp.nat)) (= (tptp.aa_nat_rat (tptp.aa_rat_fun_nat_rat (tptp.aTP_Lamm_qs Uu) Uua) Uub) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat Uu Uub)) (tptp.aa_nat_rat (tptp.power_power_rat Uua) Uub)))) (forall ((Uu tptp.fun_nat_nat) (Uua tptp.nat) (Uub tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.aTP_Lamm_rr Uu) Uua) Uub) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat Uu Uub)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat Uua) Uub)))) (forall ((Uu tptp.fun_nat_int) (Uua tptp.int) (Uub tptp.nat)) (= (tptp.aa_nat_int (tptp.aa_int_fun_nat_int (tptp.aTP_Lamm_qt Uu) Uua) Uub) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int Uu Uub)) (tptp.aa_nat_int (tptp.power_power_int Uua) Uub)))) (forall ((Uu tptp.fun_nat_bool) (Uua tptp.nat) (Uub tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool (tptp.aTP_Lamm_be Uu) Uua) Uub)) (and (tptp.pp (tptp.aa_nat_bool Uu Uub)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Uub) Uua))))) (forall ((Uu tptp.fun_nat_rat) (Uua tptp.fun_nat_rat) (Uub tptp.nat)) (= (tptp.aa_nat_rat (tptp.aa_fun765758790203053448at_rat (tptp.aTP_Lamm_aai Uu) Uua) Uub) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat Uu Uub)) (tptp.aa_nat_rat Uua Uub)))) (forall ((Uu tptp.fun_nat_nat) (Uua tptp.fun_nat_nat) (Uub tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_fun5791449513213591928at_nat (tptp.aTP_Lamm_oj Uu) Uua) Uub) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat Uu Uub)) (tptp.aa_nat_nat Uua Uub)))) (forall ((Uu tptp.fun_nat_int) (Uua tptp.fun_nat_int) (Uub tptp.nat)) (= (tptp.aa_nat_int (tptp.aa_fun5565043122120104496at_int (tptp.aTP_Lamm_ok Uu) Uua) Uub) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int Uu Uub)) (tptp.aa_nat_int Uua Uub)))) (forall ((Uu tptp.fun_int_int) (Uua tptp.fun_int_int) (Uub tptp.int)) (= (tptp.aa_int_int (tptp.aa_fun6280345759651049192nt_int (tptp.aTP_Lamm_ol Uu) Uua) Uub) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int Uu Uub)) (tptp.aa_int_int Uua Uub)))) (forall ((Uu tptp.fun_co8153928105989009288nteger) (Uua tptp.fun_co8153928105989009288nteger) (Uub tptp.complex)) (= (tptp.aa_com4217951221296830281nteger (tptp.aa_fun5267417455630836558nteger (tptp.aTP_Lamm_ie Uu) Uua) Uub) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_com4217951221296830281nteger Uua Uub)) (tptp.aa_com4217951221296830281nteger Uu Uub)))) (forall ((Uu tptp.fun_complex_real) (Uua tptp.fun_complex_real) (Uub tptp.complex)) (= (tptp.aa_complex_real (tptp.aa_fun8933909628229591020x_real (tptp.aTP_Lamm_ih Uu) Uua) Uub) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_complex_real Uua Uub)) (tptp.aa_complex_real Uu Uub)))) (forall ((Uu tptp.fun_re6978948838062957830nteger) (Uua tptp.fun_re6978948838062957830nteger) (Uub tptp.real)) (= (tptp.aa_real_Code_integer (tptp.aa_fun7923231501384339402nteger (tptp.aTP_Lamm_ic Uu) Uua) Uub) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_real_Code_integer Uua Uub)) (tptp.aa_real_Code_integer Uu Uub)))) (forall ((Uu tptp.fun_real_real) (Uua tptp.fun_real_real) (Uub tptp.real)) (= (tptp.aa_real_real (tptp.aa_fun6946558556880649704l_real (tptp.aTP_Lamm_if Uu) Uua) Uub) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real Uua Uub)) (tptp.aa_real_real Uu Uub)))) (forall ((Uu tptp.fun_real_rat) (Uua tptp.fun_real_rat) (Uub tptp.real)) (= (tptp.aa_real_rat (tptp.aa_fun2468082234287226944al_rat (tptp.aTP_Lamm_ij Uu) Uua) Uub) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_real_rat Uua Uub)) (tptp.aa_real_rat Uu Uub)))) (forall ((Uu tptp.fun_nat_Code_integer) (Uua tptp.fun_nat_Code_integer) (Uub tptp.nat)) (= (tptp.aa_nat_Code_integer (tptp.aa_fun589076786913273746nteger (tptp.aTP_Lamm_ib Uu) Uua) Uub) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_nat_Code_integer Uua Uub)) (tptp.aa_nat_Code_integer Uu Uub)))) (forall ((Uu tptp.fun_nat_rat) (Uua tptp.fun_nat_rat) (Uub tptp.nat)) (= (tptp.aa_nat_rat (tptp.aa_fun765758790203053448at_rat (tptp.aTP_Lamm_ii Uu) Uua) Uub) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat Uua Uub)) (tptp.aa_nat_rat Uu Uub)))) (forall ((Uu tptp.fun_int_Code_integer) (Uua tptp.fun_int_Code_integer) (Uub tptp.int)) (= (tptp.aa_int_Code_integer (tptp.aa_fun5304498221708291146nteger (tptp.aTP_Lamm_id Uu) Uua) Uub) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_int_Code_integer Uua Uub)) (tptp.aa_int_Code_integer Uu Uub)))) (forall ((Uu tptp.fun_int_real) (Uua tptp.fun_int_real) (Uub tptp.int)) (= (tptp.aa_int_real (tptp.aa_fun3252798400008884712t_real (tptp.aTP_Lamm_ig Uu) Uua) Uub) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_int_real Uua Uub)) (tptp.aa_int_real Uu Uub)))) (forall ((Uu tptp.fun_int_rat) (Uua tptp.fun_int_rat) (Uub tptp.int)) (= (tptp.aa_int_rat (tptp.aa_fun1481061427733998144nt_rat (tptp.aTP_Lamm_ik Uu) Uua) Uub) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_int_rat Uua Uub)) (tptp.aa_int_rat Uu Uub)))) (forall ((Uu tptp.fun_complex_complex) (Uua tptp.fun_complex_complex) (Uub tptp.complex)) (= (tptp.aa_complex_complex (tptp.aa_fun3187328805393345264omplex (tptp.aTP_Lamm_gi Uu) Uua) Uub) (tptp.aa_complex_complex (tptp.minus_minus_complex (tptp.aa_complex_complex Uu Uub)) (tptp.aa_complex_complex Uua Uub)))) (forall ((Uu tptp.fun_nat_complex) (Uua tptp.fun_nat_complex) (Uub tptp.nat)) (= (tptp.aa_nat_complex (tptp.aa_fun2955221450537884980omplex (tptp.aTP_Lamm_ke Uu) Uua) Uub) (tptp.aa_complex_complex (tptp.minus_minus_complex (tptp.aa_nat_complex Uu Uub)) (tptp.aa_nat_complex Uua Uub)))) (forall ((Uu tptp.fun_nat_real) (Uua tptp.fun_nat_real) (Uub tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_fun1839206346889086768t_real (tptp.aTP_Lamm_gj Uu) Uua) Uub) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_nat_real Uu Uub)) (tptp.aa_nat_real Uua Uub)))) (forall ((Uu tptp.fun_nat_rat) (Uua tptp.fun_nat_rat) (Uub tptp.nat)) (= (tptp.aa_nat_rat (tptp.aa_fun765758790203053448at_rat (tptp.aTP_Lamm_aam Uu) Uua) Uub) (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_nat_rat Uu Uub)) (tptp.aa_nat_rat Uua Uub)))) (forall ((Uu tptp.fun_int_int) (Uua tptp.fun_int_int) (Uub tptp.int)) (= (tptp.aa_int_int (tptp.aa_fun6280345759651049192nt_int (tptp.aTP_Lamm_gh Uu) Uua) Uub) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_int_int Uu Uub)) (tptp.aa_int_int Uua Uub)))) (forall ((Uu tptp.fun_complex_nat) (Uua tptp.fun_complex_nat) (Uub tptp.complex)) (= (tptp.aa_complex_nat (tptp.aa_fun2465681967280144180ex_nat (tptp.aTP_Lamm_hj Uu) Uua) Uub) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_complex_nat Uua Uub)) (tptp.aa_complex_nat Uu Uub)))) (forall ((Uu tptp.fun_real_nat) (Uua tptp.fun_real_nat) (Uub tptp.real)) (= (tptp.aa_real_nat (tptp.aa_fun211602392931233840al_nat (tptp.aTP_Lamm_hh Uu) Uua) Uub) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_real_nat Uua Uub)) (tptp.aa_real_nat Uu Uub)))) (forall ((Uu tptp.fun_nat_complex) (Uua tptp.fun_nat_complex) (Uub tptp.nat)) (= (tptp.aa_nat_complex (tptp.aa_fun2955221450537884980omplex (tptp.aTP_Lamm_mn Uu) Uua) Uub) (tptp.aa_complex_complex (tptp.minus_minus_complex (tptp.aa_nat_complex Uua Uub)) (tptp.aa_nat_complex Uu Uub)))) (forall ((Uu tptp.fun_nat_real) (Uua tptp.fun_nat_real) (Uub tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_fun1839206346889086768t_real (tptp.aTP_Lamm_mp Uu) Uua) Uub) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_nat_real Uua Uub)) (tptp.aa_nat_real Uu Uub)))) (forall ((Uu tptp.fun_nat_nat) (Uua tptp.fun_nat_nat) (Uub tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_fun5791449513213591928at_nat (tptp.aTP_Lamm_hk Uu) Uua) Uub) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat Uua Uub)) (tptp.aa_nat_nat Uu Uub)))) (forall ((Uu tptp.fun_int_nat) (Uua tptp.fun_int_nat) (Uub tptp.int)) (= (tptp.aa_int_nat (tptp.aa_fun6506752150744536624nt_nat (tptp.aTP_Lamm_hi Uu) Uua) Uub) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_int_nat Uua Uub)) (tptp.aa_int_nat Uu Uub)))) (forall ((Uu tptp.fun_complex_complex) (Uua tptp.fun_complex_complex) (Uub tptp.complex)) (= (tptp.aa_complex_complex (tptp.aa_fun3187328805393345264omplex (tptp.aTP_Lamm_ge Uu) Uua) Uub) (tptp.aa_complex_complex (tptp.plus_plus_complex (tptp.aa_complex_complex Uu Uub)) (tptp.aa_complex_complex Uua Uub)))) (forall ((Uu tptp.fun_nat_real) (Uua tptp.fun_nat_real) (Uub tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_fun1839206346889086768t_real (tptp.aTP_Lamm_gg Uu) Uua) Uub) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real Uu Uub)) (tptp.aa_nat_real Uua Uub)))) (forall ((Uu tptp.fun_nat_rat) (Uua tptp.fun_nat_rat) (Uub tptp.nat)) (= (tptp.aa_nat_rat (tptp.aa_fun765758790203053448at_rat (tptp.aTP_Lamm_aal Uu) Uua) Uub) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_nat_rat Uu Uub)) (tptp.aa_nat_rat Uua Uub)))) (forall ((Uu tptp.fun_nat_nat) (Uua tptp.fun_nat_nat) (Uub tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_fun5791449513213591928at_nat (tptp.aTP_Lamm_gf Uu) Uua) Uub) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat Uu Uub)) (tptp.aa_nat_nat Uua Uub)))) (forall ((Uu tptp.fun_nat_int) (Uua tptp.fun_nat_int) (Uub tptp.nat)) (= (tptp.aa_nat_int (tptp.aa_fun5565043122120104496at_int (tptp.aTP_Lamm_kd Uu) Uua) Uub) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_nat_int Uu Uub)) (tptp.aa_nat_int Uua Uub)))) (forall ((Uu tptp.fun_int_int) (Uua tptp.fun_int_int) (Uub tptp.int)) (= (tptp.aa_int_int (tptp.aa_fun6280345759651049192nt_int (tptp.aTP_Lamm_gd Uu) Uua) Uub) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int Uu Uub)) (tptp.aa_int_int Uua Uub)))) (forall ((Uu tptp.fun_real_real) (Uua tptp.fun_real_real) (Uub tptp.real)) (= (tptp.aa_real_real (tptp.aa_fun6946558556880649704l_real (tptp.aTP_Lamm_yh Uu) Uua) Uub) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.powr_real (tptp.aa_real_real Uu Uub)) (tptp.aa_real_real Uua Uub)))) (forall ((Uu tptp.fun_nat_nat) (Uua tptp.nat) (Uub tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool (tptp.aTP_Lamm_bf Uu) Uua) Uub)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat Uu Uub)) Uua)))) (forall ((Uu tptp.fun_nat_nat) (Uua tptp.nat) (Uub tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.aTP_Lamm_gn Uu) Uua) Uub) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat Uu Uub)) Uua))) (forall ((Uu tptp.fun_nat_int) (Uua tptp.int) (Uub tptp.nat)) (= (tptp.aa_nat_int (tptp.aa_int_fun_nat_int (tptp.aTP_Lamm_op Uu) Uua) Uub) (tptp.aa_int_int (tptp.modulo_modulo_int (tptp.aa_nat_int Uu Uub)) Uua))) (forall ((Uu tptp.fun_int_int) (Uua tptp.int) (Uub tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int (tptp.aTP_Lamm_gm Uu) Uua) Uub) (tptp.aa_int_int (tptp.modulo_modulo_int (tptp.aa_int_int Uu Uub)) Uua))) (forall ((Uu tptp.fun_complex_complex) (Uua tptp.complex) (Uub tptp.complex)) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex (tptp.aTP_Lamm_gk Uu) Uua) Uub) (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex (tptp.aa_complex_complex Uu Uub)) Uua))) (forall ((Uu tptp.fun_nat_complex) (Uua tptp.complex) (Uub tptp.nat)) (= (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex (tptp.aTP_Lamm_kc Uu) Uua) Uub) (tptp.aa_complex_complex (tptp.divide1717551699836669952omplex (tptp.aa_nat_complex Uu Uub)) Uua))) (forall ((Uu tptp.fun_nat_real) (Uua tptp.real) (Uub tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_gl Uu) Uua) Uub) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_nat_real Uu Uub)) Uua))) (forall ((Uu tptp.fun_complex_complex) (Uua tptp.complex) (Uub tptp.complex)) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex (tptp.aTP_Lamm_fw Uu) Uua) Uub) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_complex_complex Uu Uub)) Uua))) (forall ((Uu tptp.fun_nat_real) (Uua tptp.real) (Uub tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_fy Uu) Uua) Uub) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real Uu Uub)) Uua))) (forall ((Uu tptp.fun_nat_nat) (Uua tptp.nat) (Uub tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.aTP_Lamm_fx Uu) Uua) Uub) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat Uu Uub)) Uua))) (forall ((Uu tptp.fun_int_int) (Uua tptp.int) (Uub tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int (tptp.aTP_Lamm_fv Uu) Uua) Uub) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int Uu Uub)) Uua))) (forall ((Uu tptp.complex) (Uua tptp.fun_nat_complex) (Uub tptp.nat)) (= (tptp.aa_nat_complex (tptp.aa_fun2955221450537884980omplex (tptp.aTP_Lamm_mg Uu) Uua) Uub) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_nat_complex Uua Uub)) Uu))) (forall ((Uu tptp.real) (Uua tptp.fun_nat_real) (Uub tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_fun1839206346889086768t_real (tptp.aTP_Lamm_mh Uu) Uua) Uub) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real Uua Uub)) Uu))) (forall ((Uu tptp.fun_nat_complex) (Uua tptp.complex) (Uub tptp.nat)) (= (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex (tptp.aTP_Lamm_kx Uu) Uua) Uub) (tptp.aa_complex_complex (tptp.minus_minus_complex (tptp.aa_nat_complex Uu Uub)) Uua))) (forall ((Uu tptp.fun_nat_real) (Uua tptp.real) (Uub tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_la Uu) Uua) Uub) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_nat_real Uu Uub)) Uua))) (forall ((Uu tptp.fun_nat_rat) (Uua tptp.rat) (Uub tptp.nat)) (= (tptp.aa_nat_rat (tptp.aa_rat_fun_nat_rat (tptp.aTP_Lamm_ky Uu) Uua) Uub) (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_nat_rat Uu Uub)) Uua))) (forall ((Uu tptp.fun_nat_int) (Uua tptp.int) (Uub tptp.nat)) (= (tptp.aa_nat_int (tptp.aa_int_fun_nat_int (tptp.aTP_Lamm_kz Uu) Uua) Uub) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_nat_int Uu Uub)) Uua))) (forall ((Uu tptp.fun_real_real) (Uua tptp.nat) (Uub tptp.real)) (= (tptp.aa_real_real (tptp.aa_nat_fun_real_real (tptp.aTP_Lamm_ye Uu) Uua) Uub) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real Uu Uub)) Uua))) (forall ((Uu tptp.fun_nat_nat) (Uua tptp.nat) (Uub tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.aTP_Lamm_om Uu) Uua) Uub) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_nat_nat Uu Uub)) Uua))) (forall ((Uu tptp.fun_nat_int) (Uua tptp.nat) (Uub tptp.nat)) (= (tptp.aa_nat_int (tptp.aa_nat_fun_nat_int (tptp.aTP_Lamm_on Uu) Uua) Uub) (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_nat_int Uu Uub)) Uua))) (forall ((Uu tptp.fun_int_int) (Uua tptp.nat) (Uub tptp.int)) (= (tptp.aa_int_int (tptp.aa_nat_fun_int_int (tptp.aTP_Lamm_oo Uu) Uua) Uub) (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_int_int Uu Uub)) Uua))) (forall ((Uu tptp.nat) (Uua tptp.fun_real_real) (Uub tptp.real)) (= (tptp.aa_real_real (tptp.aa_fun6946558556880649704l_real (tptp.aTP_Lamm_zk Uu) Uua) Uub) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real Uua Uub)) Uu))) (forall ((Uu tptp.fun_real_real) (Uua tptp.real) (Uub tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real (tptp.aTP_Lamm_yg Uu) Uua) Uub) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.powr_real (tptp.aa_real_real Uu Uub)) Uua))) (forall ((Uu tptp.real) (Uua tptp.fun_nat_complex) (Uub tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_fun7054779078796324018t_real (tptp.aTP_Lamm_lf Uu) Uua) Uub) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.aa_nat_complex Uua Uub))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Uu) Uub)))) (forall ((Uu tptp.complex) (Uua tptp.complex) (Uub tptp.nat)) (= (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex (tptp.aTP_Lamm_iz Uu) Uua) Uub) (tptp.aa_complex_complex (tptp.plus_plus_complex Uu) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex Uub)) Uua)))) (forall ((Uu tptp.real) (Uua tptp.real) (Uub tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_jd Uu) Uua) Uub) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real Uu) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real Uub)) Uua)))) (forall ((Uu tptp.rat) (Uua tptp.rat) (Uub tptp.nat)) (= (tptp.aa_nat_rat (tptp.aa_rat_fun_nat_rat (tptp.aTP_Lamm_ja Uu) Uua) Uub) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat Uu) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat Uub)) Uua)))) (forall ((Uu tptp.nat) (Uua tptp.nat) (Uub tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.aTP_Lamm_jc Uu) Uua) Uub) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Uu) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat Uub)) Uua)))) (forall ((Uu tptp.int) (Uua tptp.int) (Uub tptp.nat)) (= (tptp.aa_nat_int (tptp.aa_int_fun_nat_int (tptp.aTP_Lamm_jb Uu) Uua) Uub) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int Uu) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int Uub)) Uua)))) (forall ((Uu tptp.complex) (Uua tptp.nat) (Uub tptp.nat)) (= (tptp.aa_nat_complex (tptp.aa_nat6454746962644518025omplex (tptp.aTP_Lamm_lw Uu) Uua) Uub) (tptp.aa_nat_complex (tptp.power_power_complex Uu) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uua) (tptp.aa_nat_nat tptp.suc Uub))))) (forall ((Uu tptp.real) (Uua tptp.nat) (Uub tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_nat_fun_nat_real (tptp.aTP_Lamm_lz Uu) Uua) Uub) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Uu) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uua) (tptp.aa_nat_nat tptp.suc Uub))))) (forall ((Uu tptp.rat) (Uua tptp.nat) (Uub tptp.nat)) (= (tptp.aa_nat_rat (tptp.aa_nat_fun_nat_rat (tptp.aTP_Lamm_lx Uu) Uua) Uub) (tptp.aa_nat_rat (tptp.power_power_rat Uu) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uua) (tptp.aa_nat_nat tptp.suc Uub))))) (forall ((Uu tptp.int) (Uua tptp.nat) (Uub tptp.nat)) (= (tptp.aa_nat_int (tptp.aa_nat_fun_nat_int (tptp.aTP_Lamm_ly Uu) Uua) Uub) (tptp.aa_nat_int (tptp.power_power_int Uu) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uua) (tptp.aa_nat_nat tptp.suc Uub))))) (forall ((Uu tptp.real) (Uua tptp.real) (Uub tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_za Uu) Uua) Uub) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real Uua) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Uu) Uub)))) (forall ((Uu tptp.complex) (Uua tptp.nat) (Uub tptp.nat)) (= (tptp.aa_nat_complex (tptp.aa_nat6454746962644518025omplex (tptp.aTP_Lamm_hn Uu) Uua) Uub) (tptp.aa_nat_complex (tptp.power_power_complex Uu) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Uua) Uub)))) (forall ((Uu tptp.real) (Uua tptp.nat) (Uub tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_nat_fun_nat_real (tptp.aTP_Lamm_hq Uu) Uua) Uub) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Uu) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Uua) Uub)))) (forall ((Uu tptp.rat) (Uua tptp.nat) (Uub tptp.nat)) (= (tptp.aa_nat_rat (tptp.aa_nat_fun_nat_rat (tptp.aTP_Lamm_ho Uu) Uua) Uub) (tptp.aa_nat_rat (tptp.power_power_rat Uu) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Uua) Uub)))) (forall ((Uu tptp.int) (Uua tptp.nat) (Uub tptp.nat)) (= (tptp.aa_nat_int (tptp.aa_nat_fun_nat_int (tptp.aTP_Lamm_hp Uu) Uua) Uub) (tptp.aa_nat_int (tptp.power_power_int Uu) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Uua) Uub)))) (forall ((Uu tptp.nat) (Uua tptp.nat) (Uub tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.aTP_Lamm_ix Uu) Uua) Uub) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Uu) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat Uub) Uua)))) (forall ((Uu tptp.real) (Uua tptp.real) (Uub tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool (tptp.aTP_Lamm_zj Uu) Uua) Uub)) (tptp.member_real Uub (tptp.set_or1633881224788618240n_real Uu Uua)))) (forall ((Uu tptp.complex) (Uua tptp.fun_complex_complex) (Uub tptp.complex)) (= (tptp.aa_complex_complex (tptp.aa_fun3187328805393345264omplex (tptp.aTP_Lamm_ga Uu) Uua) Uub) (tptp.aa_complex_complex (tptp.times_times_complex Uu) (tptp.aa_complex_complex Uua Uub)))) (forall ((Uu tptp.complex) (Uua tptp.fun_nat_complex) (Uub tptp.nat)) (= (tptp.aa_nat_complex (tptp.aa_fun2955221450537884980omplex (tptp.aTP_Lamm_kb Uu) Uua) Uub) (tptp.aa_complex_complex (tptp.times_times_complex Uu) (tptp.aa_nat_complex Uua Uub)))) (forall ((Uu tptp.real) (Uua tptp.fun_nat_real) (Uub tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_fun1839206346889086768t_real (tptp.aTP_Lamm_gc Uu) Uua) Uub) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real Uu) (tptp.aa_nat_real Uua Uub)))) (forall ((Uu tptp.nat) (Uua tptp.fun_nat_nat) (Uub tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_fun5791449513213591928at_nat (tptp.aTP_Lamm_gb Uu) Uua) Uub) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat Uu) (tptp.aa_nat_nat Uua Uub)))) (forall ((Uu tptp.int) (Uua tptp.fun_int_int) (Uub tptp.int)) (= (tptp.aa_int_int (tptp.aa_fun6280345759651049192nt_int (tptp.aTP_Lamm_fz Uu) Uua) Uub) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int Uu) (tptp.aa_int_int Uua Uub)))) (forall ((Uu tptp.fun_nat_real) (Uua tptp.real) (Uub tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_kf Uu) Uua) Uub) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real Uua) (tptp.aa_nat_real Uu Uub)))) (forall ((Uu tptp.complex) (Uua tptp.fun_nat_nat) (Uub tptp.nat)) (= (tptp.aa_nat_complex (tptp.aa_fun1958354139826840918omplex (tptp.aTP_Lamm_ov Uu) Uua) Uub) (tptp.aa_nat_complex (tptp.power_power_complex Uu) (tptp.aa_nat_nat Uua Uub)))) (forall ((Uu tptp.real) (Uua tptp.fun_nat_nat) (Uub tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_fun1538629612289296340t_real (tptp.aTP_Lamm_ou Uu) Uua) Uub) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Uu) (tptp.aa_nat_nat Uua Uub)))) (forall ((Uu tptp.nat) (Uua tptp.fun_nat_nat) (Uub tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_fun5791449513213591928at_nat (tptp.aTP_Lamm_ow Uu) Uua) Uub) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat Uu) (tptp.aa_nat_nat Uua Uub)))) (forall ((Uu tptp.int) (Uua tptp.fun_nat_nat) (Uub tptp.nat)) (= (tptp.aa_nat_int (tptp.aa_fun1613598493704395220at_int (tptp.aTP_Lamm_ox Uu) Uua) Uub) (tptp.aa_nat_int (tptp.power_power_int Uu) (tptp.aa_nat_nat Uua Uub)))) (forall ((Uu tptp.int) (Uua tptp.fun_int_nat) (Uub tptp.int)) (= (tptp.aa_int_int (tptp.aa_fun2328901131235339916nt_int (tptp.aTP_Lamm_oy Uu) Uua) Uub) (tptp.aa_nat_int (tptp.power_power_int Uu) (tptp.aa_int_nat Uua Uub)))) (forall ((Uu tptp.real) (Uua tptp.nat) (Uub tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_nat_fun_nat_real (tptp.aTP_Lamm_qv Uu) Uua) Uub) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real Uu) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uua) Uub))))) (forall ((Uu tptp.rat) (Uua tptp.nat) (Uub tptp.nat)) (= (tptp.aa_nat_rat (tptp.aa_nat_fun_nat_rat (tptp.aTP_Lamm_qu Uu) Uua) Uub) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat Uu) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uua) Uub))))) (forall ((Uu tptp.nat) (Uua tptp.nat) (Uub tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.aTP_Lamm_qw Uu) Uua) Uub) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Uu) (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uua) Uub))))) (forall ((Uu tptp.int) (Uua tptp.nat) (Uub tptp.nat)) (= (tptp.aa_nat_int (tptp.aa_nat_fun_nat_int (tptp.aTP_Lamm_qx Uu) Uua) Uub) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int Uu) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uua) Uub))))) (forall ((Uu tptp.fun_nat_real) (Uua tptp.nat) (Uub tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_nat_fun_nat_real (tptp.aTP_Lamm_kw Uu) Uua) Uub) (tptp.aa_nat_real Uu (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uua) (tptp.aa_nat_nat tptp.suc Uub))))) (forall ((Uu tptp.fun_nat_nat) (Uua tptp.nat) (Uub tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.aTP_Lamm_kv Uu) Uua) Uub) (tptp.aa_nat_nat Uu (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uua) (tptp.aa_nat_nat tptp.suc Uub))))) (forall ((Uu tptp.fun_nat_int) (Uua tptp.nat) (Uub tptp.nat)) (= (tptp.aa_nat_int (tptp.aa_nat_fun_nat_int (tptp.aTP_Lamm_pe Uu) Uua) Uub) (tptp.aa_nat_int Uu (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uua) (tptp.aa_nat_nat tptp.suc Uub))))) (forall ((Uu tptp.fun_nat_complex) (Uua tptp.nat) (Uub tptp.nat)) (= (tptp.aa_nat_complex (tptp.aa_nat6454746962644518025omplex (tptp.aTP_Lamm_kk Uu) Uua) Uub) (tptp.aa_nat_complex Uu (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Uub) Uua)))) (forall ((Uu tptp.fun_nat_real) (Uua tptp.nat) (Uub tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_nat_fun_nat_real (tptp.aTP_Lamm_hm Uu) Uua) Uub) (tptp.aa_nat_real Uu (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Uub) Uua)))) (forall ((Uu tptp.fun_nat_bool) (Uua tptp.nat) (Uub tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool (tptp.aTP_Lamm_zi Uu) Uua) Uub)) (tptp.pp (tptp.aa_nat_bool Uu (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Uub) Uua))))) (forall ((Uu tptp.fun_nat_nat) (Uua tptp.nat) (Uub tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.aTP_Lamm_hl Uu) Uua) Uub) (tptp.aa_nat_nat Uu (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Uub) Uua)))) (forall ((Uu tptp.fun_nat_int) (Uua tptp.nat) (Uub tptp.nat)) (= (tptp.aa_nat_int (tptp.aa_nat_fun_nat_int (tptp.aTP_Lamm_oz Uu) Uua) Uub) (tptp.aa_nat_int Uu (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Uub) Uua)))) (forall ((Uu tptp.fun_Pr2602117396471556196at_nat) (Uua tptp.nat) (Uub tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.aTP_Lamm_go Uu) Uua) Uub) (tptp.aa_Pro4243173770044397973at_nat Uu (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Uua) Uub)))) (forall ((Uu tptp.fun_Pr2477239776880934807at_nat) (Uua tptp.nat) (Uub tptp.nat)) (= (tptp.aa_nat7997280740862404369at_nat (tptp.aa_nat5682243440470347102at_nat (tptp.aTP_Lamm_gp Uu) Uua) Uub) (tptp.aa_Pro8023792847356852296at_nat Uu (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Uua) Uub)))) (forall ((Uu tptp.fun_Pr248683899324676269t_bool) (Uua tptp.nat) (Uub tptp.nat)) (= (tptp.aa_nat4401263874371387303t_bool (tptp.aa_nat4909001760120733684t_bool (tptp.aTP_Lamm_gq Uu) Uua) Uub) (tptp.aa_Pro595088089689268830t_bool Uu (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Uua) Uub)))) (forall ((Uu tptp.fun_Pr2478283820680522243nt_int) (Uua tptp.int) (Uub tptp.int)) (= (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int (tptp.aTP_Lamm_gr Uu) Uua) Uub) (tptp.aa_Pro6970504127699319548nt_int Uu (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int Uua) Uub)))) (forall ((Uu tptp.fun_Pr803113274115125473t_bool) (Uua tptp.int) (Uub tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool (tptp.aTP_Lamm_gs Uu) Uua) Uub)) (tptp.pp (tptp.aa_Pro4501881432599481050t_bool Uu (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int Uua) Uub))))) (forall ((Uu tptp.nat) (Uua tptp.fun_nat_complex) (Uub tptp.nat)) (= (tptp.aa_nat_complex (tptp.aa_fun2955221450537884980omplex (tptp.aTP_Lamm_mi Uu) Uua) Uub) (tptp.aa_nat_complex Uua (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Uub) Uu)))) (forall ((Uu tptp.nat) (Uua tptp.fun_nat_real) (Uub tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_fun1839206346889086768t_real (tptp.aTP_Lamm_mj Uu) Uua) Uub) (tptp.aa_nat_real Uua (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Uub) Uu)))) (forall ((Uu tptp.fun_nat_real) (Uua tptp.fun_nat_nat) (Uub tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_fun1538629612289296340t_real (tptp.aTP_Lamm_zo Uu) Uua) Uub) (tptp.aa_nat_real Uu (tptp.aa_nat_nat Uua Uub)))) (forall ((Uu tptp.fun_nat_complex) (Uua tptp.complex) (Uub tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_com20334259897932645t_real (tptp.aTP_Lamm_ko Uu) Uua) Uub) (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_nat_complex Uu Uub)) (tptp.aa_nat_complex (tptp.power_power_complex Uua) Uub))))) (forall ((Uu tptp.fun_nat_real) (Uua tptp.real) (Uub tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_km Uu) Uua) Uub) (tptp.aa_real_real tptp.real_V7735802525324610683m_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real Uu Uub)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Uua) Uub))))) (forall ((Uu tptp.fun_complex_complex) (Uua tptp.fun_complex_complex) (Uub tptp.complex)) (= (tptp.aa_complex_real (tptp.aa_fun1953249243402654830x_real (tptp.aTP_Lamm_qc Uu) Uua) Uub) (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.aa_complex_complex (tptp.minus_minus_complex (tptp.aa_complex_complex Uu Uub)) (tptp.aa_complex_complex Uua Uub))))) (forall ((Uu tptp.fun_complex_real) (Uua tptp.fun_complex_real) (Uub tptp.complex)) (= (tptp.aa_complex_real (tptp.aa_fun8933909628229591020x_real (tptp.aTP_Lamm_pz Uu) Uua) Uub) (tptp.aa_real_real tptp.real_V7735802525324610683m_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_complex_real Uu Uub)) (tptp.aa_complex_real Uua Uub))))) (forall ((Uu tptp.fun_real_complex) (Uua tptp.fun_real_complex) (Uub tptp.real)) (= (tptp.aa_real_real (tptp.aa_fun2786211375485122666l_real (tptp.aTP_Lamm_qa Uu) Uua) Uub) (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.aa_complex_complex (tptp.minus_minus_complex (tptp.aa_real_complex Uu Uub)) (tptp.aa_real_complex Uua Uub))))) (forall ((Uu tptp.fun_real_real) (Uua tptp.fun_real_real) (Uub tptp.real)) (= (tptp.aa_real_real (tptp.aa_fun6946558556880649704l_real (tptp.aTP_Lamm_px Uu) Uua) Uub) (tptp.aa_real_real tptp.real_V7735802525324610683m_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real Uu Uub)) (tptp.aa_real_real Uua Uub))))) (forall ((Uu tptp.fun_nat_complex) (Uua tptp.fun_nat_complex) (Uub tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_fun7054779078796324018t_real (tptp.aTP_Lamm_qe Uu) Uua) Uub) (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.aa_complex_complex (tptp.minus_minus_complex (tptp.aa_nat_complex Uu Uub)) (tptp.aa_nat_complex Uua Uub))))) (forall ((Uu tptp.fun_nat_real) (Uua tptp.fun_nat_real) (Uub tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_fun1839206346889086768t_real (tptp.aTP_Lamm_qd Uu) Uua) Uub) (tptp.aa_real_real tptp.real_V7735802525324610683m_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_nat_real Uu Uub)) (tptp.aa_nat_real Uua Uub))))) (forall ((Uu tptp.fun_int_complex) (Uua tptp.fun_int_complex) (Uub tptp.int)) (= (tptp.aa_int_real (tptp.aa_fun1985759105522019690t_real (tptp.aTP_Lamm_qb Uu) Uua) Uub) (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.aa_complex_complex (tptp.minus_minus_complex (tptp.aa_int_complex Uu Uub)) (tptp.aa_int_complex Uua Uub))))) (forall ((Uu tptp.fun_int_real) (Uua tptp.fun_int_real) (Uub tptp.int)) (= (tptp.aa_int_real (tptp.aa_fun3252798400008884712t_real (tptp.aTP_Lamm_py Uu) Uua) Uub) (tptp.aa_real_real tptp.real_V7735802525324610683m_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_int_real Uu Uub)) (tptp.aa_int_real Uua Uub))))) (forall ((Uu tptp.fun_nat_real) (Uua tptp.real) (Uub tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_zd Uu) Uua) Uub) (tptp.aa_real_real tptp.cos_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_nat_real Uu Uub)) Uua)))) (forall ((Uu tptp.fun_real_bool) (Uua tptp.fun_real_complex) (Uub tptp.complex)) (= (tptp.pp (tptp.aa_complex_bool (tptp.aa_fun6713666175893136621x_bool (tptp.aTP_Lamm_em Uu) Uua) Uub)) (exists ((X3 tptp.real)) (and (= Uub (tptp.aa_real_complex Uua X3)) (tptp.pp (tptp.aa_real_bool Uu X3)))))) (forall ((Uu tptp.fun_real_bool) (Uua tptp.fun_real_real) (Uub tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_fun9137271176455094897l_bool (tptp.aTP_Lamm_ej Uu) Uua) Uub)) (exists ((X3 tptp.real)) (and (= Uub (tptp.aa_real_real Uua X3)) (tptp.pp (tptp.aa_real_bool Uu X3)))))) (forall ((Uu tptp.fun_real_bool) (Uua tptp.fun_real_nat) (Uub tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_fun3670751239728173737t_bool (tptp.aTP_Lamm_ek Uu) Uua) Uub)) (exists ((X3 tptp.real)) (and (= Uub (tptp.aa_real_nat Uua X3)) (tptp.pp (tptp.aa_real_bool Uu X3)))))) (forall ((Uu tptp.fun_real_bool) (Uua tptp.fun_real_int) (Uub tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_fun6938287985607813617t_bool (tptp.aTP_Lamm_el Uu) Uua) Uub)) (exists ((X3 tptp.real)) (and (= Uub (tptp.aa_real_int Uua X3)) (tptp.pp (tptp.aa_real_bool Uu X3)))))) (forall ((Uu tptp.fun_nat_bool) (Uua tptp.fun_nat_complex) (Uub tptp.complex)) (= (tptp.pp (tptp.aa_complex_bool (tptp.aa_fun678042768005816265x_bool (tptp.aTP_Lamm_eq Uu) Uua) Uub)) (exists ((X3 tptp.nat)) (and (= Uub (tptp.aa_nat_complex Uua X3)) (tptp.pp (tptp.aa_nat_bool Uu X3)))))) (forall ((Uu tptp.fun_nat_bool) (Uua tptp.fun_nat_real) (Uub tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_fun2369234836118212941l_bool (tptp.aTP_Lamm_en Uu) Uua) Uub)) (exists ((X3 tptp.nat)) (and (= Uub (tptp.aa_nat_real Uua X3)) (tptp.pp (tptp.aa_nat_bool Uu X3)))))) (forall ((Uu tptp.fun_nat_bool) (Uua tptp.fun_nat_nat) (Uub tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_fun1783405840085286277t_bool (tptp.aTP_Lamm_eo Uu) Uua) Uub)) (exists ((X3 tptp.nat)) (and (= Uub (tptp.aa_nat_nat Uua X3)) (tptp.pp (tptp.aa_nat_bool Uu X3)))))) (forall ((Uu tptp.fun_nat_bool) (Uua tptp.fun_nat_int) (Uub tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_fun5050942585964926157t_bool (tptp.aTP_Lamm_ep Uu) Uua) Uub)) (exists ((X3 tptp.nat)) (and (= Uub (tptp.aa_nat_int Uua X3)) (tptp.pp (tptp.aa_nat_bool Uu X3)))))) (forall ((Uu tptp.fun_int_bool) (Uua tptp.fun_int_real) (Uub tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_fun1272151855474214385l_bool (tptp.aTP_Lamm_er Uu) Uua) Uub)) (exists ((X3 tptp.int)) (and (= Uub (tptp.aa_int_real Uua X3)) (tptp.pp (tptp.aa_int_bool Uu X3)))))) (forall ((Uu tptp.fun_int_bool) (Uua tptp.fun_int_nat) (Uub tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_fun8751864718750488105t_bool (tptp.aTP_Lamm_es Uu) Uua) Uub)) (exists ((X3 tptp.int)) (and (= Uub (tptp.aa_int_nat Uua X3)) (tptp.pp (tptp.aa_int_bool Uu X3)))))) (forall ((Uu tptp.fun_real_bool) (Uua tptp.fun_co2286642472385812463l_bool) (Uub tptp.complex)) (= (tptp.pp (tptp.aa_complex_bool (tptp.aa_fun6039685132559610447x_bool (tptp.aTP_Lamm_cb Uu) Uua) Uub)) (exists ((Y3 tptp.real)) (and (tptp.pp (tptp.aa_real_bool Uu Y3)) (tptp.pp (tptp.aa_real_bool (tptp.aa_com8943241093633526360l_bool Uua Uub) Y3)))))) (forall ((Uu tptp.fun_real_bool) (Uua tptp.fun_re1255401033344146673l_bool) (Uub tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_fun4964148113266127823l_bool (tptp.aTP_Lamm_bv Uu) Uua) Uub)) (exists ((Y3 tptp.real)) (and (tptp.pp (tptp.aa_real_bool Uu Y3)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool Uua Uub) Y3)))))) (forall ((Uu tptp.fun_real_bool) (Uua tptp.fun_na6801867027684862029l_bool) (Uub tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_fun7391232120346184911t_bool (tptp.aTP_Lamm_bx Uu) Uua) Uub)) (exists ((Y3 tptp.real)) (and (tptp.pp (tptp.aa_real_bool Uu Y3)) (tptp.pp (tptp.aa_real_bool (tptp.aa_nat_fun_real_bool Uua Uub) Y3)))))) (forall ((Uu tptp.fun_real_bool) (Uua tptp.fun_in3970322703178350321l_bool) (Uub tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_fun69789402421856207t_bool (tptp.aTP_Lamm_bz Uu) Uua) Uub)) (exists ((Y3 tptp.real)) (and (tptp.pp (tptp.aa_real_bool Uu Y3)) (tptp.pp (tptp.aa_real_bool (tptp.aa_int_fun_real_bool Uua Uub) Y3)))))) (forall ((Uu tptp.fun_nat_bool) (Uua tptp.fun_co2841405903858895691t_bool) (Uub tptp.complex)) (= (tptp.pp (tptp.aa_complex_bool (tptp.aa_fun6682930621474858099x_bool (tptp.aTP_Lamm_cj Uu) Uua) Uub)) (exists ((Y3 tptp.nat)) (and (tptp.pp (tptp.aa_nat_bool Uu Y3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_com5335841084339320244t_bool Uua Uub) Y3)))))) (forall ((Uu tptp.fun_nat_bool) (Uua tptp.fun_re9121486324101951821t_bool) (Uub tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_fun4927090880566115059l_bool (tptp.aTP_Lamm_cd Uu) Uua) Uub)) (exists ((Y3 tptp.nat)) (and (tptp.pp (tptp.aa_nat_bool Uu Y3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_real_fun_nat_bool Uua Uub) Y3)))))) (forall ((Uu tptp.fun_nat_bool) (Uua tptp.fun_nat_fun_nat_bool) (Uub tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_fun8399658544460314611t_bool (tptp.aTP_Lamm_cf Uu) Uua) Uub)) (exists ((Y3 tptp.nat)) (and (tptp.pp (tptp.aa_nat_bool Uu Y3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool Uua Uub) Y3)))))) (forall ((Uu tptp.fun_nat_bool) (Uua tptp.fun_int_fun_nat_bool) (Uub tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_fun6484551404966387955t_bool (tptp.aTP_Lamm_ch Uu) Uua) Uub)) (exists ((Y3 tptp.nat)) (and (tptp.pp (tptp.aa_nat_bool Uu Y3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_int_fun_nat_bool Uua Uub) Y3)))))) (forall ((Uu tptp.fun_int_bool) (Uua tptp.fun_re8661203372455305201t_bool) (Uub tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_fun7352647192720469839l_bool (tptp.aTP_Lamm_cl Uu) Uua) Uub)) (exists ((Y3 tptp.int)) (and (tptp.pp (tptp.aa_int_bool Uu Y3)) (tptp.pp (tptp.aa_int_bool (tptp.aa_real_fun_int_bool Uua Uub) Y3)))))) (forall ((Uu tptp.fun_int_bool) (Uua tptp.fun_nat_fun_int_bool) (Uub tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_fun7626329022887090767t_bool (tptp.aTP_Lamm_cn Uu) Uua) Uub)) (exists ((Y3 tptp.int)) (and (tptp.pp (tptp.aa_int_bool Uu Y3)) (tptp.pp (tptp.aa_int_bool (tptp.aa_nat_fun_int_bool Uua Uub) Y3)))))) (forall ((Uu tptp.complex) (Uua tptp.complex) (Uub tptp.nat) (Uuc tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat _let_1))) (= (tptp.aa_nat_complex (tptp.aa_nat6454746962644518025omplex (tptp.aa_com4347742694490471604omplex (tptp.aTP_Lamm_va Uu) Uua) Uub) Uuc) (tptp.aa_complex_complex (tptp.if_complex (tptp.aa_bool_bool (tptp.fconj (tptp.aa_nat_bool _let_2 Uub)) (tptp.aa_bool_bool tptp.fNot (tptp.aa_nat_bool _let_2 Uuc))) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_complex_complex (tptp.real_V2046097035970521341omplex (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_int_real tptp.ring_1_of_int_real (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat Uub) _let_1))) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial Uub) Uuc))))) (tptp.aa_nat_real tptp.semiri2265585572941072030t_real Uub)))) (tptp.aa_nat_complex (tptp.power_power_complex Uu) Uuc))) (tptp.aa_nat_complex (tptp.power_power_complex Uua) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uub) Uuc)))) tptp.zero_zero_complex))))) (forall ((Uu tptp.real) (Uua tptp.real) (Uub tptp.nat) (Uuc tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat _let_1))) (= (tptp.aa_nat_real (tptp.aa_nat_fun_nat_real (tptp.aa_rea6853821027689443120t_real (tptp.aTP_Lamm_uy Uu) Uua) Uub) Uuc) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real (tptp.if_real (tptp.aa_bool_bool (tptp.fconj (tptp.aa_nat_bool _let_2 Uub)) (tptp.aa_bool_bool tptp.fNot (tptp.aa_nat_bool _let_2 Uuc)))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.real_V1485227260804924795R_real (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_int_real tptp.ring_1_of_int_real (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat Uub) _let_1))) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial Uub) Uuc))))) (tptp.aa_nat_real tptp.semiri2265585572941072030t_real Uub)))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Uu) Uuc))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Uua) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uub) Uuc)))) tptp.zero_zero_real))))) (forall ((Uu tptp.complex) (Uua tptp.complex) (Uub tptp.nat) (Uuc tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.aa_nat_complex (tptp.aa_nat6454746962644518025omplex (tptp.aa_com4347742694490471604omplex (tptp.aTP_Lamm_ve Uu) Uua) Uub) Uuc) (tptp.aa_complex_complex (tptp.if_complex (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat _let_1) Uub) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_complex_complex (tptp.real_V2046097035970521341omplex (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_int_real tptp.ring_1_of_int_real (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat Uub) _let_1))) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial Uub) Uuc))))) (tptp.aa_nat_real tptp.semiri2265585572941072030t_real Uub))) (tptp.aa_nat_complex (tptp.power_power_complex Uu) Uuc))) (tptp.aa_nat_complex (tptp.power_power_complex Uua) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uub) Uuc)))) tptp.zero_zero_complex)))) (forall ((Uu tptp.real) (Uua tptp.real) (Uub tptp.nat) (Uuc tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.aa_nat_real (tptp.aa_nat_fun_nat_real (tptp.aa_rea6853821027689443120t_real (tptp.aTP_Lamm_vc Uu) Uua) Uub) Uuc) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real (tptp.if_real (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat _let_1) Uub)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.real_V1485227260804924795R_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_int_real tptp.ring_1_of_int_real (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat Uub) _let_1))) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial Uub) Uuc))))) (tptp.aa_nat_real tptp.semiri2265585572941072030t_real Uub))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Uu) Uuc))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Uua) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uub) Uuc)))) tptp.zero_zero_real)))) (forall ((Uu tptp.nat) (Uua tptp.fun_nat_complex) (Uub tptp.fun_nat_complex) (Uuc tptp.nat)) (= (tptp.aa_nat_complex (tptp.aa_fun2955221450537884980omplex (tptp.aa_fun7497765718855568684omplex (tptp.aTP_Lamm_rv Uu) Uua) Uub) Uuc) (tptp.aa_complex_complex (tptp.if_complex (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Uuc) Uu) (tptp.aa_nat_complex Uua Uuc)) (tptp.aa_complex_complex (tptp.if_complex (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.fequal_nat Uuc) Uu) tptp.zero_zero_complex) (tptp.aa_nat_complex Uub (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uuc) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat))))))) (forall ((Uu tptp.nat) (Uua tptp.fun_nat_real) (Uub tptp.fun_nat_real) (Uuc tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_fun1839206346889086768t_real (tptp.aa_fun8674848580393814182t_real (tptp.aTP_Lamm_rz Uu) Uua) Uub) Uuc) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real (tptp.if_real (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Uuc) Uu)) (tptp.aa_nat_real Uua Uuc)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real (tptp.if_real (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.fequal_nat Uuc) Uu)) tptp.zero_zero_real) (tptp.aa_nat_real Uub (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uuc) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat))))))) (forall ((Uu tptp.nat) (Uua tptp.fun_nat_rat) (Uub tptp.fun_nat_rat) (Uuc tptp.nat)) (= (tptp.aa_nat_rat (tptp.aa_fun765758790203053448at_rat (tptp.aa_fun3638354034882855594at_rat (tptp.aTP_Lamm_rw Uu) Uua) Uub) Uuc) (tptp.aa_rat_rat (tptp.if_rat (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Uuc) Uu) (tptp.aa_nat_rat Uua Uuc)) (tptp.aa_rat_rat (tptp.if_rat (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.fequal_nat Uuc) Uu) tptp.zero_zero_rat) (tptp.aa_nat_rat Uub (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uuc) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat))))))) (forall ((Uu tptp.nat) (Uua tptp.fun_nat_nat) (Uub tptp.fun_nat_nat) (Uuc tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_fun5791449513213591928at_nat (tptp.aa_fun6854695580826382482at_nat (tptp.aTP_Lamm_ry Uu) Uua) Uub) Uuc) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.if_nat (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Uuc) Uu)) (tptp.aa_nat_nat Uua Uuc)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.if_nat (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.fequal_nat Uuc) Uu)) tptp.zero_zero_nat) (tptp.aa_nat_nat Uub (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uuc) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat))))))) (forall ((Uu tptp.nat) (Uua tptp.fun_nat_int) (Uub tptp.fun_nat_int) (Uuc tptp.nat)) (= (tptp.aa_nat_int (tptp.aa_fun5565043122120104496at_int (tptp.aa_fun5140708168904641446at_int (tptp.aTP_Lamm_rx Uu) Uua) Uub) Uuc) (tptp.aa_int_int (tptp.if_int (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Uuc) Uu) (tptp.aa_nat_int Uua Uuc)) (tptp.aa_int_int (tptp.if_int (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.fequal_nat Uuc) Uu) tptp.zero_zero_int) (tptp.aa_nat_int Uub (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uuc) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat))))))) (forall ((Uu tptp.nat) (Uua tptp.fun_nat_complex) (Uub tptp.fun_nat_complex) (Uuc tptp.nat)) (= (tptp.aa_nat_complex (tptp.aa_fun2955221450537884980omplex (tptp.aa_fun7497765718855568684omplex (tptp.aTP_Lamm_pg Uu) Uua) Uub) Uuc) (tptp.aa_complex_complex (tptp.if_complex (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Uuc) Uu) (tptp.aa_nat_complex Uua Uuc)) (tptp.aa_complex_complex (tptp.if_complex (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.fequal_nat Uuc) Uu) tptp.one_one_complex) (tptp.aa_nat_complex Uub (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uuc) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat))))))) (forall ((Uu tptp.nat) (Uua tptp.fun_nat_real) (Uub tptp.fun_nat_real) (Uuc tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_fun1839206346889086768t_real (tptp.aa_fun8674848580393814182t_real (tptp.aTP_Lamm_pi Uu) Uua) Uub) Uuc) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real (tptp.if_real (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Uuc) Uu)) (tptp.aa_nat_real Uua Uuc)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real (tptp.if_real (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.fequal_nat Uuc) Uu)) tptp.one_one_real) (tptp.aa_nat_real Uub (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uuc) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat))))))) (forall ((Uu tptp.nat) (Uua tptp.fun_nat_rat) (Uub tptp.fun_nat_rat) (Uuc tptp.nat)) (= (tptp.aa_nat_rat (tptp.aa_fun765758790203053448at_rat (tptp.aa_fun3638354034882855594at_rat (tptp.aTP_Lamm_pk Uu) Uua) Uub) Uuc) (tptp.aa_rat_rat (tptp.if_rat (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Uuc) Uu) (tptp.aa_nat_rat Uua Uuc)) (tptp.aa_rat_rat (tptp.if_rat (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.fequal_nat Uuc) Uu) tptp.one_one_rat) (tptp.aa_nat_rat Uub (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uuc) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat))))))) (forall ((Uu tptp.nat) (Uua tptp.fun_nat_nat) (Uub tptp.fun_nat_nat) (Uuc tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_fun5791449513213591928at_nat (tptp.aa_fun6854695580826382482at_nat (tptp.aTP_Lamm_pm Uu) Uua) Uub) Uuc) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.if_nat (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Uuc) Uu)) (tptp.aa_nat_nat Uua Uuc)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.if_nat (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.fequal_nat Uuc) Uu)) tptp.one_one_nat) (tptp.aa_nat_nat Uub (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uuc) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat))))))) (forall ((Uu tptp.nat) (Uua tptp.fun_nat_int) (Uub tptp.fun_nat_int) (Uuc tptp.nat)) (= (tptp.aa_nat_int (tptp.aa_fun5565043122120104496at_int (tptp.aa_fun5140708168904641446at_int (tptp.aTP_Lamm_po Uu) Uua) Uub) Uuc) (tptp.aa_int_int (tptp.if_int (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Uuc) Uu) (tptp.aa_nat_int Uua Uuc)) (tptp.aa_int_int (tptp.if_int (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.fequal_nat Uuc) Uu) tptp.one_one_int) (tptp.aa_nat_int Uub (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uuc) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat))))))) (forall ((Uu tptp.nat) (Uua tptp.fun_nat_complex) (Uub tptp.fun_nat_complex) (Uuc tptp.nat)) (= (tptp.aa_nat_complex (tptp.aa_fun2955221450537884980omplex (tptp.aa_fun7497765718855568684omplex (tptp.aTP_Lamm_ph Uu) Uua) Uub) Uuc) (tptp.aa_complex_complex (tptp.if_complex (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Uuc) Uu) (tptp.aa_nat_complex Uua Uuc)) (tptp.aa_nat_complex Uub Uuc)))) (forall ((Uu tptp.nat) (Uua tptp.fun_nat_real) (Uub tptp.fun_nat_real) (Uuc tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_fun1839206346889086768t_real (tptp.aa_fun8674848580393814182t_real (tptp.aTP_Lamm_pj Uu) Uua) Uub) Uuc) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real (tptp.if_real (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Uuc) Uu)) (tptp.aa_nat_real Uua Uuc)) (tptp.aa_nat_real Uub Uuc)))) (forall ((Uu tptp.nat) (Uua tptp.fun_nat_rat) (Uub tptp.fun_nat_rat) (Uuc tptp.nat)) (= (tptp.aa_nat_rat (tptp.aa_fun765758790203053448at_rat (tptp.aa_fun3638354034882855594at_rat (tptp.aTP_Lamm_pl Uu) Uua) Uub) Uuc) (tptp.aa_rat_rat (tptp.if_rat (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Uuc) Uu) (tptp.aa_nat_rat Uua Uuc)) (tptp.aa_nat_rat Uub Uuc)))) (forall ((Uu tptp.nat) (Uua tptp.fun_nat_nat) (Uub tptp.fun_nat_nat) (Uuc tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_fun5791449513213591928at_nat (tptp.aa_fun6854695580826382482at_nat (tptp.aTP_Lamm_pn Uu) Uua) Uub) Uuc) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.if_nat (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Uuc) Uu)) (tptp.aa_nat_nat Uua Uuc)) (tptp.aa_nat_nat Uub Uuc)))) (forall ((Uu tptp.nat) (Uua tptp.fun_nat_int) (Uub tptp.fun_nat_int) (Uuc tptp.nat)) (= (tptp.aa_nat_int (tptp.aa_fun5565043122120104496at_int (tptp.aa_fun5140708168904641446at_int (tptp.aTP_Lamm_pp Uu) Uua) Uub) Uuc) (tptp.aa_int_int (tptp.if_int (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Uuc) Uu) (tptp.aa_nat_int Uua Uuc)) (tptp.aa_nat_int Uub Uuc)))) (forall ((Uu tptp.fun_nat_complex) (Uua tptp.set_nat) (Uub tptp.fun_nat_complex) (Uuc tptp.nat)) (= (tptp.aa_nat_complex (tptp.aa_fun2955221450537884980omplex (tptp.aa_set5115289136882354743omplex (tptp.aTP_Lamm_mo Uu) Uua) Uub) Uuc) (tptp.aa_complex_complex (tptp.if_complex (tptp.aa_set_nat_bool (tptp.member_nat Uuc) Uua) (tptp.aa_nat_complex Uub Uuc)) (tptp.aa_nat_complex Uu Uuc)))) (forall ((Uu tptp.fun_nat_real) (Uua tptp.set_nat) (Uub tptp.fun_nat_real) (Uuc tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_fun1839206346889086768t_real (tptp.aa_set1316517696749040435t_real (tptp.aTP_Lamm_mq Uu) Uua) Uub) Uuc) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real (tptp.if_real (tptp.aa_set_nat_bool (tptp.member_nat Uuc) Uua)) (tptp.aa_nat_real Uub Uuc)) (tptp.aa_nat_real Uu Uuc)))) (forall ((Uu tptp.real) (Uua tptp.real) (Uub tptp.nat) (Uuc tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_nat_fun_nat_real (tptp.aa_rea6853821027689443120t_real (tptp.aTP_Lamm_jv Uu) Uua) Uub) Uuc) (tptp.groups6591440286371151544t_real (tptp.aa_nat_fun_nat_real (tptp.aa_rea6853821027689443120t_real (tptp.aTP_Lamm_ju Uu) Uua) Uub) (tptp.set_ord_lessThan_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uub) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat))) Uuc))))) (forall ((Uu tptp.rat) (Uua tptp.rat) (Uub tptp.nat) (Uuc tptp.nat)) (= (tptp.aa_nat_rat (tptp.aa_nat_fun_nat_rat (tptp.aa_rat250263598611652360at_rat (tptp.aTP_Lamm_jt Uu) Uua) Uub) Uuc) (tptp.groups2906978787729119204at_rat (tptp.aa_nat_fun_nat_rat (tptp.aa_rat250263598611652360at_rat (tptp.aTP_Lamm_js Uu) Uua) Uub) (tptp.set_ord_lessThan_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uub) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat))) Uuc))))) (forall ((Uu tptp.complex) (Uua tptp.complex) (Uub tptp.nat) (Uuc tptp.nat)) (= (tptp.aa_nat_complex (tptp.aa_nat6454746962644518025omplex (tptp.aa_com4347742694490471604omplex (tptp.aTP_Lamm_jr Uu) Uua) Uub) Uuc) (tptp.groups2073611262835488442omplex (tptp.aa_nat6454746962644518025omplex (tptp.aa_com4347742694490471604omplex (tptp.aTP_Lamm_jq Uu) Uua) Uub) (tptp.set_ord_lessThan_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uub) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat))) Uuc))))) (forall ((Uu tptp.fun_nat_real) (Uua tptp.fun_nat_real) (Uub tptp.set_nat) (Uuc tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_set1166323925324055613t_real (tptp.aa_fun1400677770452585267t_real (tptp.aTP_Lamm_fu Uu) Uua) Uub) Uuc) (tptp.groups6591440286371151544t_real (tptp.aa_nat_fun_nat_real (tptp.aa_fun3023522663955195517t_real (tptp.aTP_Lamm_ft Uu) Uua) Uuc) Uub))) (forall ((Uu tptp.fun_nat_nat) (Uua tptp.fun_nat_nat) (Uub tptp.set_nat) (Uuc tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_set6537093552120046177at_nat (tptp.aa_fun4561837934398617467at_nat (tptp.aTP_Lamm_fs Uu) Uua) Uub) Uuc) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_nat_fun_nat_nat (tptp.aa_fun6650658898577385413at_nat (tptp.aTP_Lamm_fr Uu) Uua) Uuc)) Uub))) (forall ((Uu tptp.fun_complex_complex) (Uua tptp.fun_complex_complex) (Uub tptp.set_complex) (Uuc tptp.complex)) (= (tptp.aa_complex_complex (tptp.aa_set7743095458595710203omplex (tptp.aa_fun1583801116089702097omplex (tptp.aTP_Lamm_fq Uu) Uua) Uub) Uuc) (tptp.groups7754918857620584856omplex (tptp.aa_com3342990543769683525omplex (tptp.aa_fun6995112137416684571omplex (tptp.aTP_Lamm_fp Uu) Uua) Uuc) Uub))) (forall ((Uu tptp.fun_int_int) (Uua tptp.fun_int_int) (Uub tptp.set_int) (Uuc tptp.int)) (= (tptp.aa_int_int (tptp.aa_set7310040872927613301nt_int (tptp.aa_fun8076508010538293575nt_int (tptp.aTP_Lamm_fo Uu) Uua) Uub) Uuc) (tptp.groups4538972089207619220nt_int (tptp.aa_int_fun_int_int (tptp.aa_fun5911324870756489105nt_int (tptp.aTP_Lamm_fn Uu) Uua) Uuc) Uub))) (forall ((Uu tptp.nat) (Uua tptp.code_integer) (Uub tptp.code_integer) (Uuc tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.fequal_nat Uuc))) (= (tptp.aa_nat_Code_integer (tptp.aa_Cod1578151519121547077nteger (tptp.aa_Cod6397266357770349983nteger (tptp.aTP_Lamm_sc Uu) Uua) Uub) Uuc) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.if_Code_integer (tptp.aa_nat_bool _let_1 tptp.zero_zero_nat) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger Uub) (tptp.if_Code_integer (tptp.aa_nat_bool _let_1 Uu) tptp.one_one_Code_integer tptp.zero_z3403309356797280102nteger))) (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger Uua) Uuc))))) (forall ((Uu tptp.nat) (Uua tptp.complex) (Uub tptp.complex) (Uuc tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.fequal_nat Uuc))) (= (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex (tptp.aa_com8177640530696437650omplex (tptp.aTP_Lamm_sb Uu) Uua) Uub) Uuc) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_complex_complex (tptp.if_complex (tptp.aa_nat_bool _let_1 tptp.zero_zero_nat) (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex Uub)) (tptp.aa_complex_complex (tptp.if_complex (tptp.aa_nat_bool _let_1 Uu) tptp.one_one_complex) tptp.zero_zero_complex))) (tptp.aa_nat_complex (tptp.power_power_complex Uua) Uuc))))) (forall ((Uu tptp.nat) (Uua tptp.real) (Uub tptp.real) (Uuc tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.fequal_nat Uuc))) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real (tptp.aa_rea7841385751566875788t_real (tptp.aTP_Lamm_se Uu) Uua) Uub) Uuc) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real (tptp.if_real (tptp.aa_nat_bool _let_1 tptp.zero_zero_nat)) (tptp.aa_real_real tptp.uminus_uminus_real Uub)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real (tptp.if_real (tptp.aa_nat_bool _let_1 Uu)) tptp.one_one_real) tptp.zero_zero_real))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Uua) Uuc))))) (forall ((Uu tptp.nat) (Uua tptp.rat) (Uub tptp.rat) (Uuc tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.fequal_nat Uuc))) (= (tptp.aa_nat_rat (tptp.aa_rat_fun_nat_rat (tptp.aa_rat3146053865535587600at_rat (tptp.aTP_Lamm_sd Uu) Uua) Uub) Uuc) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat (tptp.if_rat (tptp.aa_nat_bool _let_1 tptp.zero_zero_nat) (tptp.aa_rat_rat tptp.uminus_uminus_rat Uub)) (tptp.aa_rat_rat (tptp.if_rat (tptp.aa_nat_bool _let_1 Uu) tptp.one_one_rat) tptp.zero_zero_rat))) (tptp.aa_nat_rat (tptp.power_power_rat Uua) Uuc))))) (forall ((Uu tptp.nat) (Uua tptp.int) (Uub tptp.int) (Uuc tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.fequal_nat Uuc))) (= (tptp.aa_nat_int (tptp.aa_int_fun_nat_int (tptp.aa_int5842867502692063756at_int (tptp.aTP_Lamm_sa Uu) Uua) Uub) Uuc) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.if_int (tptp.aa_nat_bool _let_1 tptp.zero_zero_nat) (tptp.aa_int_int tptp.uminus_uminus_int Uub)) (tptp.aa_int_int (tptp.if_int (tptp.aa_nat_bool _let_1 Uu) tptp.one_one_int) tptp.zero_zero_int))) (tptp.aa_nat_int (tptp.power_power_int Uua) Uuc))))) (forall ((Uu tptp.fun_nat_nat) (Uua tptp.fun_nat_nat) (Uub tptp.nat) (Uuc tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.aa_fun6650658898577385413at_nat (tptp.aTP_Lamm_rt Uu) Uua) Uub) Uuc) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_nat_fun_nat_nat (tptp.aa_fun6650658898577385413at_nat (tptp.aTP_Lamm_rs Uu) Uua) Uuc)) (tptp.set_ord_atMost_nat Uuc))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat Uub) Uuc)))) (forall ((Uu tptp.fun_nat_int) (Uua tptp.fun_nat_int) (Uub tptp.int) (Uuc tptp.nat)) (= (tptp.aa_nat_int (tptp.aa_int_fun_nat_int (tptp.aa_fun2315716387381795033at_int (tptp.aTP_Lamm_ri Uu) Uua) Uub) Uuc) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.groups3539618377306564664at_int (tptp.aa_nat_fun_nat_int (tptp.aa_fun6128006242533108349at_int (tptp.aTP_Lamm_rh Uu) Uua) Uuc) (tptp.set_ord_atMost_nat Uuc))) (tptp.aa_nat_int (tptp.power_power_int Uub) Uuc)))) (forall ((Uu tptp.fun_nat_rat) (Uua tptp.fun_nat_rat) (Uub tptp.rat) (Uuc tptp.nat)) (= (tptp.aa_nat_rat (tptp.aa_rat_fun_nat_rat (tptp.aa_fun5559679822142647773at_rat (tptp.aTP_Lamm_rg Uu) Uua) Uub) Uuc) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.groups2906978787729119204at_rat (tptp.aa_nat_fun_nat_rat (tptp.aa_fun2663889555218712533at_rat (tptp.aTP_Lamm_rf Uu) Uua) Uuc) (tptp.set_ord_atMost_nat Uuc))) (tptp.aa_nat_rat (tptp.power_power_rat Uub) Uuc)))) (forall ((Uu tptp.fun_nat_real) (Uua tptp.fun_nat_real) (Uub tptp.real) (Uuc tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real (tptp.aa_fun4732485501138722137t_real (tptp.aTP_Lamm_rj Uu) Uua) Uub) Uuc) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.groups6591440286371151544t_real (tptp.aa_nat_fun_nat_real (tptp.aa_fun3023522663955195517t_real (tptp.aTP_Lamm_rb Uu) Uua) Uuc) (tptp.set_ord_atMost_nat Uuc))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Uub) Uuc)))) (forall ((Uu tptp.fun_nat_complex) (Uua tptp.fun_nat_complex) (Uub tptp.complex) (Uuc tptp.nat)) (= (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex (tptp.aa_fun3721018923249493343omplex (tptp.aTP_Lamm_re Uu) Uua) Uub) Uuc) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.groups2073611262835488442omplex (tptp.aa_nat6454746962644518025omplex (tptp.aa_fun5379041630539201665omplex (tptp.aTP_Lamm_qz Uu) Uua) Uuc) (tptp.set_ord_atMost_nat Uuc))) (tptp.aa_nat_complex (tptp.power_power_complex Uub) Uuc)))) (forall ((Uu tptp.fun_na6724076748692969250l_real) (Uua tptp.nat) (Uub tptp.real) (Uuc tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real (tptp.aa_nat1308781354268537904t_real (tptp.aTP_Lamm_yn Uu) Uua) Uub) Uuc) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_nat_fun_real_real Uu (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat tptp.suc Uua)) Uuc)) tptp.zero_zero_real)) (tptp.aa_nat_real tptp.semiri2265585572941072030t_real Uuc))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Uub) Uuc)))) (forall ((Uu tptp.fun_na6724076748692969250l_real) (Uua tptp.nat) (Uub tptp.real) (Uuc tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real (tptp.aa_nat1308781354268537904t_real (tptp.aTP_Lamm_yl Uu) Uua) Uub) Uuc) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_nat_fun_real_real Uu (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Uua) Uuc)) tptp.zero_zero_real)) (tptp.aa_nat_real tptp.semiri2265585572941072030t_real Uuc))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Uub) Uuc)))) (forall ((Uu tptp.fun_na6724076748692969250l_real) (Uua tptp.real) (Uub tptp.real) (Uuc tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real (tptp.aa_rea7841385751566875788t_real (tptp.aTP_Lamm_yj Uu) Uua) Uub) Uuc) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_nat_fun_real_real Uu Uuc) Uua)) (tptp.aa_nat_real tptp.semiri2265585572941072030t_real Uuc))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real Uub) Uua)) Uuc)))) (forall ((Uu tptp.fun_na6724076748692969250l_real) (Uua tptp.real) (Uub tptp.real) (Uuc tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real (tptp.aa_rea7841385751566875788t_real (tptp.aTP_Lamm_yk Uu) Uua) Uub) Uuc) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_nat_fun_real_real Uu Uuc) Uub)) (tptp.aa_nat_real tptp.semiri2265585572941072030t_real Uuc))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real Uua) Uub)) Uuc)))) (forall ((Uu tptp.complex) (Uua tptp.complex) (Uub tptp.nat) (Uuc tptp.nat)) (let ((_let_1 (tptp.power_power_complex Uu))) (= (tptp.aa_nat_complex (tptp.aa_nat6454746962644518025omplex (tptp.aa_com4347742694490471604omplex (tptp.aTP_Lamm_lg Uu) Uua) Uub) Uuc) (tptp.aa_complex_complex (tptp.minus_minus_complex (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_nat_complex (tptp.power_power_complex (tptp.aa_complex_complex (tptp.plus_plus_complex Uu) Uua)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uub) Uuc))) (tptp.aa_nat_complex _let_1 Uuc))) (tptp.aa_nat_complex _let_1 Uub))))) (forall ((Uu tptp.real) (Uua tptp.real) (Uub tptp.nat) (Uuc tptp.nat)) (let ((_let_1 (tptp.aa_real_fun_nat_real tptp.power_power_real Uu))) (= (tptp.aa_nat_real (tptp.aa_nat_fun_nat_real (tptp.aa_rea6853821027689443120t_real (tptp.aTP_Lamm_lm Uu) Uua) Uub) Uuc) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real Uu) Uua)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uub) Uuc))) (tptp.aa_nat_real _let_1 Uuc))) (tptp.aa_nat_real _let_1 Uub))))) (forall ((Uu tptp.rat) (Uua tptp.rat) (Uub tptp.nat) (Uuc tptp.nat)) (let ((_let_1 (tptp.power_power_rat Uu))) (= (tptp.aa_nat_rat (tptp.aa_nat_fun_nat_rat (tptp.aa_rat250263598611652360at_rat (tptp.aTP_Lamm_li Uu) Uua) Uub) Uuc) (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat Uu) Uua)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uub) Uuc))) (tptp.aa_nat_rat _let_1 Uuc))) (tptp.aa_nat_rat _let_1 Uub))))) (forall ((Uu tptp.int) (Uua tptp.int) (Uub tptp.nat) (Uuc tptp.nat)) (let ((_let_1 (tptp.power_power_int Uu))) (= (tptp.aa_nat_int (tptp.aa_nat_fun_nat_int (tptp.aa_int431785320988601264at_int (tptp.aTP_Lamm_lk Uu) Uua) Uub) Uuc) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int Uu) Uua)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uub) Uuc))) (tptp.aa_nat_int _let_1 Uuc))) (tptp.aa_nat_int _let_1 Uub))))) (forall ((Uu tptp.nat) (Uua tptp.nat) (Uub tptp.nat) (Uuc tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat Uua))) (let ((_let_2 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat Uu))) (= (tptp.aa_nat7603221163087113075at_nat (tptp.aa_nat8803788312118491388at_nat (tptp.aa_nat4158579785191972357at_nat (tptp.aTP_Lamm_wu Uu) Uua) Uub) Uuc) (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat _let_2 Uub)) (tptp.aa_nat_nat _let_1 Uuc))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat _let_2 Uuc)) (tptp.aa_nat_nat _let_1 Uub))))))) (forall ((Uu tptp.complex) (Uua tptp.complex) (Uub tptp.nat) (Uuc tptp.nat)) (= (tptp.aa_nat_complex (tptp.aa_nat6454746962644518025omplex (tptp.aa_com4347742694490471604omplex (tptp.aTP_Lamm_jq Uu) Uua) Uub) Uuc) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_nat_complex (tptp.power_power_complex (tptp.aa_complex_complex (tptp.plus_plus_complex Uua) Uu)) Uuc)) (tptp.aa_nat_complex (tptp.power_power_complex Uua) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uub) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) Uuc))))) (forall ((Uu tptp.real) (Uua tptp.real) (Uub tptp.nat) (Uuc tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_nat_fun_nat_real (tptp.aa_rea6853821027689443120t_real (tptp.aTP_Lamm_ju Uu) Uua) Uub) Uuc) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real Uua) Uu)) Uuc)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Uua) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uub) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) Uuc))))) (forall ((Uu tptp.rat) (Uua tptp.rat) (Uub tptp.nat) (Uuc tptp.nat)) (= (tptp.aa_nat_rat (tptp.aa_nat_fun_nat_rat (tptp.aa_rat250263598611652360at_rat (tptp.aTP_Lamm_js Uu) Uua) Uub) Uuc) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat Uua) Uu)) Uuc)) (tptp.aa_nat_rat (tptp.power_power_rat Uua) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uub) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) Uuc))))) (forall ((Uu tptp.real) (Uua tptp.real) (Uub tptp.nat) (Uuc tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_nat_fun_nat_real (tptp.aa_rea6853821027689443120t_real (tptp.aTP_Lamm_rq Uu) Uua) Uub) Uuc) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial Uub) Uuc))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.comm_s7457072308508201937r_real Uu) Uuc))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.comm_s7457072308508201937r_real Uua) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uub) Uuc))))) (forall ((Uu tptp.rat) (Uua tptp.rat) (Uub tptp.nat) (Uuc tptp.nat)) (= (tptp.aa_nat_rat (tptp.aa_nat_fun_nat_rat (tptp.aa_rat250263598611652360at_rat (tptp.aTP_Lamm_ro Uu) Uua) Uub) Uuc) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial Uub) Uuc))) (tptp.aa_nat_rat (tptp.comm_s4028243227959126397er_rat Uu) Uuc))) (tptp.aa_nat_rat (tptp.comm_s4028243227959126397er_rat Uua) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uub) Uuc))))) (forall ((Uu tptp.int) (Uua tptp.int) (Uub tptp.nat) (Uuc tptp.nat)) (= (tptp.aa_nat_int (tptp.aa_nat_fun_nat_int (tptp.aa_int431785320988601264at_int (tptp.aTP_Lamm_rp Uu) Uua) Uub) Uuc) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial Uub) Uuc))) (tptp.aa_nat_int (tptp.comm_s4660882817536571857er_int Uu) Uuc))) (tptp.aa_nat_int (tptp.comm_s4660882817536571857er_int Uua) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uub) Uuc))))) (forall ((Uu tptp.complex) (Uua tptp.complex) (Uub tptp.nat) (Uuc tptp.nat)) (= (tptp.aa_nat_complex (tptp.aa_nat6454746962644518025omplex (tptp.aa_com4347742694490471604omplex (tptp.aTP_Lamm_rk Uu) Uua) Uub) Uuc) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial Uub) Uuc))) (tptp.aa_nat_complex (tptp.power_power_complex Uu) Uuc))) (tptp.aa_nat_complex (tptp.power_power_complex Uua) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uub) Uuc))))) (forall ((Uu tptp.real) (Uua tptp.real) (Uub tptp.nat) (Uuc tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_nat_fun_nat_real (tptp.aa_rea6853821027689443120t_real (tptp.aTP_Lamm_rn Uu) Uua) Uub) Uuc) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial Uub) Uuc))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Uu) Uuc))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Uua) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uub) Uuc))))) (forall ((Uu tptp.rat) (Uua tptp.rat) (Uub tptp.nat) (Uuc tptp.nat)) (= (tptp.aa_nat_rat (tptp.aa_nat_fun_nat_rat (tptp.aa_rat250263598611652360at_rat (tptp.aTP_Lamm_rl Uu) Uua) Uub) Uuc) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial Uub) Uuc))) (tptp.aa_nat_rat (tptp.power_power_rat Uu) Uuc))) (tptp.aa_nat_rat (tptp.power_power_rat Uua) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uub) Uuc))))) (forall ((Uu tptp.nat) (Uua tptp.nat) (Uub tptp.nat) (Uuc tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.aa_nat3783148529270815480at_nat (tptp.aTP_Lamm_rd Uu) Uua) Uub) Uuc) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial Uub) Uuc))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat Uu) Uuc))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat Uua) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uub) Uuc))))) (forall ((Uu tptp.int) (Uua tptp.int) (Uub tptp.nat) (Uuc tptp.nat)) (= (tptp.aa_nat_int (tptp.aa_nat_fun_nat_int (tptp.aa_int431785320988601264at_int (tptp.aTP_Lamm_rm Uu) Uua) Uub) Uuc) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial Uub) Uuc))) (tptp.aa_nat_int (tptp.power_power_int Uu) Uuc))) (tptp.aa_nat_int (tptp.power_power_int Uua) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uub) Uuc))))) (forall ((Uu tptp.complex) (Uua tptp.nat) (Uub tptp.complex) (Uuc tptp.nat)) (= (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex (tptp.aa_nat2301396582920332468omplex (tptp.aTP_Lamm_lo Uu) Uua) Uub) Uuc) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_nat_complex (tptp.power_power_complex Uub) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uua) (tptp.aa_nat_nat tptp.suc Uuc)))) (tptp.aa_nat_complex (tptp.power_power_complex Uu) Uuc)))) (forall ((Uu tptp.real) (Uua tptp.nat) (Uub tptp.real) (Uuc tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real (tptp.aa_nat1308781354268537904t_real (tptp.aTP_Lamm_lr Uu) Uua) Uub) Uuc) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Uub) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uua) (tptp.aa_nat_nat tptp.suc Uuc)))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Uu) Uuc)))) (forall ((Uu tptp.rat) (Uua tptp.nat) (Uub tptp.rat) (Uuc tptp.nat)) (= (tptp.aa_nat_rat (tptp.aa_rat_fun_nat_rat (tptp.aa_nat298952458717073160at_rat (tptp.aTP_Lamm_lp Uu) Uua) Uub) Uuc) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat (tptp.power_power_rat Uub) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uua) (tptp.aa_nat_nat tptp.suc Uuc)))) (tptp.aa_nat_rat (tptp.power_power_rat Uu) Uuc)))) (forall ((Uu tptp.int) (Uua tptp.nat) (Uub tptp.int) (Uuc tptp.nat)) (= (tptp.aa_nat_int (tptp.aa_int_fun_nat_int (tptp.aa_nat6704147566042551216at_int (tptp.aTP_Lamm_lq Uu) Uua) Uub) Uuc) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int (tptp.power_power_int Uub) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uua) (tptp.aa_nat_nat tptp.suc Uuc)))) (tptp.aa_nat_int (tptp.power_power_int Uu) Uuc)))) (forall ((Uu tptp.complex) (Uua tptp.complex) (Uub tptp.nat) (Uuc tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uub) Uuc))) (let ((_let_2 (tptp.power_power_complex Uu))) (= (tptp.aa_nat_complex (tptp.aa_nat6454746962644518025omplex (tptp.aa_com4347742694490471604omplex (tptp.aTP_Lamm_lh Uu) Uua) Uub) Uuc) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_nat_complex _let_2 Uuc)) (tptp.aa_complex_complex (tptp.minus_minus_complex (tptp.aa_nat_complex (tptp.power_power_complex (tptp.aa_complex_complex (tptp.plus_plus_complex Uu) Uua)) _let_1)) (tptp.aa_nat_complex _let_2 _let_1))))))) (forall ((Uu tptp.real) (Uua tptp.real) (Uub tptp.nat) (Uuc tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uub) Uuc))) (let ((_let_2 (tptp.aa_real_fun_nat_real tptp.power_power_real Uu))) (= (tptp.aa_nat_real (tptp.aa_nat_fun_nat_real (tptp.aa_rea6853821027689443120t_real (tptp.aTP_Lamm_ln Uu) Uua) Uub) Uuc) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real _let_2 Uuc)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real Uu) Uua)) _let_1)) (tptp.aa_nat_real _let_2 _let_1))))))) (forall ((Uu tptp.rat) (Uua tptp.rat) (Uub tptp.nat) (Uuc tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uub) Uuc))) (let ((_let_2 (tptp.power_power_rat Uu))) (= (tptp.aa_nat_rat (tptp.aa_nat_fun_nat_rat (tptp.aa_rat250263598611652360at_rat (tptp.aTP_Lamm_lj Uu) Uua) Uub) Uuc) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat _let_2 Uuc)) (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat Uu) Uua)) _let_1)) (tptp.aa_nat_rat _let_2 _let_1))))))) (forall ((Uu tptp.int) (Uua tptp.int) (Uub tptp.nat) (Uuc tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uub) Uuc))) (let ((_let_2 (tptp.power_power_int Uu))) (= (tptp.aa_nat_int (tptp.aa_nat_fun_nat_int (tptp.aa_int431785320988601264at_int (tptp.aTP_Lamm_ll Uu) Uua) Uub) Uuc) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int _let_2 Uuc)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int Uu) Uua)) _let_1)) (tptp.aa_nat_int _let_2 _let_1))))))) (forall ((Uu tptp.complex) (Uua tptp.nat) (Uub tptp.complex) (Uuc tptp.nat)) (= (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex (tptp.aa_nat2301396582920332468omplex (tptp.aTP_Lamm_ls Uu) Uua) Uub) Uuc) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_nat_complex (tptp.power_power_complex Uu) Uuc)) (tptp.aa_nat_complex (tptp.power_power_complex Uub) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uua) Uuc))))) (forall ((Uu tptp.real) (Uua tptp.nat) (Uub tptp.real) (Uuc tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real (tptp.aa_nat1308781354268537904t_real (tptp.aTP_Lamm_lv Uu) Uua) Uub) Uuc) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Uu) Uuc)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Uub) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uua) Uuc))))) (forall ((Uu tptp.rat) (Uua tptp.nat) (Uub tptp.rat) (Uuc tptp.nat)) (= (tptp.aa_nat_rat (tptp.aa_rat_fun_nat_rat (tptp.aa_nat298952458717073160at_rat (tptp.aTP_Lamm_lt Uu) Uua) Uub) Uuc) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat (tptp.power_power_rat Uu) Uuc)) (tptp.aa_nat_rat (tptp.power_power_rat Uub) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uua) Uuc))))) (forall ((Uu tptp.int) (Uua tptp.nat) (Uub tptp.int) (Uuc tptp.nat)) (= (tptp.aa_nat_int (tptp.aa_int_fun_nat_int (tptp.aa_nat6704147566042551216at_int (tptp.aTP_Lamm_lu Uu) Uua) Uub) Uuc) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int (tptp.power_power_int Uu) Uuc)) (tptp.aa_nat_int (tptp.power_power_int Uub) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uua) Uuc))))) (forall ((Uu tptp.nat) (Uua tptp.nat) (Uub tptp.nat) (Uuc tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.aa_nat3783148529270815480at_nat (tptp.aTP_Lamm_ql Uu) Uua) Uub) Uuc) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial Uu) Uuc)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial Uua) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uub) Uuc))))) (forall ((Uu tptp.int) (Uua tptp.int) (Uub tptp.int) (Uuc tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool (tptp.aa_int2327297053056786951t_bool (tptp.aTP_Lamm_wr Uu) Uua) Uub) Uuc)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int Uu) Uuc)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int Uua) Uub))))) (forall ((Uu tptp.nat) (Uua tptp.nat) (Uub tptp.nat) (Uuc tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool (tptp.aa_nat8637530788439456283t_bool (tptp.aTP_Lamm_wz Uu) Uua) Uub) Uuc)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Uu) Uuc)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Uub) Uua))))) (forall ((Uu tptp.int) (Uua tptp.int) (Uub tptp.int) (Uuc tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool (tptp.aa_int2327297053056786951t_bool (tptp.aTP_Lamm_wp Uu) Uua) Uub) Uuc)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int Uu) Uuc)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int Uua) Uub))))) (forall ((Uu tptp.nat) (Uua tptp.nat) (Uub tptp.nat) (Uuc tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool (tptp.aa_nat8637530788439456283t_bool (tptp.aTP_Lamm_wx Uu) Uua) Uub) Uuc)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Uu) Uuc)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Uub) Uua))))) (forall ((Uu tptp.nat) (Uua tptp.nat) (Uub tptp.nat) (Uuc tptp.nat)) (= (tptp.aa_nat7603221163087113075at_nat (tptp.aa_nat8803788312118491388at_nat (tptp.aa_nat4158579785191972357at_nat (tptp.aTP_Lamm_xb Uu) Uua) Uub) Uuc) (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Uu) Uub)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Uua) Uuc)))) (forall ((Uu tptp.nat) (Uua tptp.nat) (Uub tptp.nat) (Uuc tptp.nat)) (= (tptp.aa_nat7603221163087113075at_nat (tptp.aa_nat8803788312118491388at_nat (tptp.aa_nat4158579785191972357at_nat (tptp.aTP_Lamm_xd Uu) Uua) Uub) Uuc) (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Uu) Uuc)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Uua) Uub)))) (forall ((Uu tptp.nat) (Uua tptp.nat) (Uub tptp.nat) (Uuc tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool (tptp.aa_nat8637530788439456283t_bool (tptp.aTP_Lamm_aag Uu) Uua) Uub) Uuc)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Uu) Uuc) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Uub) Uua)))) (forall ((Uu tptp.set_complex) (Uua tptp.fun_complex_complex) (Uub tptp.fun_complex_complex) (Uuc tptp.complex)) (= (tptp.pp (tptp.aa_complex_bool (tptp.aa_fun9073502203726719595x_bool (tptp.aa_fun6641798613628721963x_bool (tptp.aTP_Lamm_cy Uu) Uua) Uub) Uuc)) (and (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex Uuc) Uu)) (not (= (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_complex_complex Uua Uuc)) (tptp.aa_complex_complex Uub Uuc)) tptp.one_one_complex))))) (forall ((Uu tptp.set_complex) (Uua tptp.fun_complex_real) (Uub tptp.fun_complex_real) (Uuc tptp.complex)) (= (tptp.pp (tptp.aa_complex_bool (tptp.aa_fun2898354424061222765x_bool (tptp.aa_fun2094807616088678831x_bool (tptp.aTP_Lamm_dg Uu) Uua) Uub) Uuc)) (and (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex Uuc) Uu)) (not (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_complex_real Uua Uuc)) (tptp.aa_complex_real Uub Uuc)) tptp.one_one_real))))) (forall ((Uu tptp.set_real) (Uua tptp.fun_real_complex) (Uub tptp.fun_real_complex) (Uuc tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_fun3813300650643916655l_bool (tptp.aa_fun5520078544946397361l_bool (tptp.aTP_Lamm_cs Uu) Uua) Uub) Uuc)) (and (tptp.member_real Uuc Uu) (not (= (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_real_complex Uua Uuc)) (tptp.aa_real_complex Uub Uuc)) tptp.one_one_complex))))) (forall ((Uu tptp.set_real) (Uua tptp.fun_real_real) (Uub tptp.fun_real_real) (Uuc tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_fun9137271176455094897l_bool (tptp.aa_fun334843040499603765l_bool (tptp.aTP_Lamm_da Uu) Uua) Uub) Uuc)) (and (tptp.member_real Uuc Uu) (not (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real Uua Uuc)) (tptp.aa_real_real Uub Uuc)) tptp.one_one_real))))) (forall ((Uu tptp.set_real) (Uua tptp.fun_real_rat) (Uub tptp.fun_real_rat) (Uuc tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_fun8987621170725249221l_bool (tptp.aa_fun8530242357055030877l_bool (tptp.aTP_Lamm_di Uu) Uua) Uub) Uuc)) (and (tptp.member_real Uuc Uu) (not (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_real_rat Uua Uuc)) (tptp.aa_real_rat Uub Uuc)) tptp.one_one_rat))))) (forall ((Uu tptp.set_nat) (Uua tptp.fun_nat_complex) (Uub tptp.fun_nat_complex) (Uuc tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_fun8004580481347240231t_bool (tptp.aa_fun5430245816583273541t_bool (tptp.aTP_Lamm_cu Uu) Uua) Uub) Uuc)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat Uuc) Uu)) (not (= (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_nat_complex Uua Uuc)) (tptp.aa_nat_complex Uub Uuc)) tptp.one_one_complex))))) (forall ((Uu tptp.set_nat) (Uua tptp.fun_nat_real) (Uub tptp.fun_nat_real) (Uuc tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_fun1349230436907296553t_bool (tptp.aa_fun849216055071118793t_bool (tptp.aTP_Lamm_dc Uu) Uua) Uub) Uuc)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat Uuc) Uu)) (not (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real Uua Uuc)) (tptp.aa_nat_real Uub Uuc)) tptp.one_one_real))))) (forall ((Uu tptp.set_nat) (Uua tptp.fun_nat_rat) (Uub tptp.fun_nat_rat) (Uuc tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_fun5637262893798792573t_bool (tptp.aa_fun2107527232086395633t_bool (tptp.aTP_Lamm_dk Uu) Uua) Uub) Uuc)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat Uuc) Uu)) (not (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat Uua Uuc)) (tptp.aa_nat_rat Uub Uuc)) tptp.one_one_rat))))) (forall ((Uu tptp.set_int) (Uua tptp.fun_int_complex) (Uub tptp.fun_int_complex) (Uuc tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_fun8146511558608327279t_bool (tptp.aa_fun3850298374753145905t_bool (tptp.aTP_Lamm_cw Uu) Uua) Uub) Uuc)) (and (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Uuc) Uu)) (not (= (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_int_complex Uua Uuc)) (tptp.aa_int_complex Uub Uuc)) tptp.one_one_complex))))) (forall ((Uu tptp.set_int) (Uua tptp.fun_int_real) (Uub tptp.fun_int_real) (Uuc tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_fun1262781554902806129t_bool (tptp.aa_fun6205147705862377397t_bool (tptp.aTP_Lamm_de Uu) Uua) Uub) Uuc)) (and (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Uuc) Uu)) (not (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_int_real Uua Uuc)) (tptp.aa_int_real Uub Uuc)) tptp.one_one_real))))) (forall ((Uu tptp.set_complex) (Uua tptp.fun_complex_complex) (Uub tptp.fun_complex_complex) (Uuc tptp.complex)) (= (tptp.pp (tptp.aa_complex_bool (tptp.aa_fun9073502203726719595x_bool (tptp.aa_fun6641798613628721963x_bool (tptp.aTP_Lamm_ds Uu) Uua) Uub) Uuc)) (and (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex Uuc) Uu)) (not (= (tptp.aa_complex_complex (tptp.plus_plus_complex (tptp.aa_complex_complex Uua Uuc)) (tptp.aa_complex_complex Uub Uuc)) tptp.zero_zero_complex))))) (forall ((Uu tptp.set_complex) (Uua tptp.fun_complex_real) (Uub tptp.fun_complex_real) (Uuc tptp.complex)) (= (tptp.pp (tptp.aa_complex_bool (tptp.aa_fun2898354424061222765x_bool (tptp.aa_fun2094807616088678831x_bool (tptp.aTP_Lamm_ea Uu) Uua) Uub) Uuc)) (and (tptp.pp (tptp.aa_set_complex_bool (tptp.member_complex Uuc) Uu)) (not (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_complex_real Uua Uuc)) (tptp.aa_complex_real Uub Uuc)) tptp.zero_zero_real))))) (forall ((Uu tptp.set_real) (Uua tptp.fun_real_complex) (Uub tptp.fun_real_complex) (Uuc tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_fun3813300650643916655l_bool (tptp.aa_fun5520078544946397361l_bool (tptp.aTP_Lamm_dm Uu) Uua) Uub) Uuc)) (and (tptp.member_real Uuc Uu) (not (= (tptp.aa_complex_complex (tptp.plus_plus_complex (tptp.aa_real_complex Uua Uuc)) (tptp.aa_real_complex Uub Uuc)) tptp.zero_zero_complex))))) (forall ((Uu tptp.set_real) (Uua tptp.fun_real_real) (Uub tptp.fun_real_real) (Uuc tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_fun9137271176455094897l_bool (tptp.aa_fun334843040499603765l_bool (tptp.aTP_Lamm_du Uu) Uua) Uub) Uuc)) (and (tptp.member_real Uuc Uu) (not (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real Uua Uuc)) (tptp.aa_real_real Uub Uuc)) tptp.zero_zero_real))))) (forall ((Uu tptp.set_real) (Uua tptp.fun_real_rat) (Uub tptp.fun_real_rat) (Uuc tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_fun8987621170725249221l_bool (tptp.aa_fun8530242357055030877l_bool (tptp.aTP_Lamm_ec Uu) Uua) Uub) Uuc)) (and (tptp.member_real Uuc Uu) (not (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_real_rat Uua Uuc)) (tptp.aa_real_rat Uub Uuc)) tptp.zero_zero_rat))))) (forall ((Uu tptp.set_nat) (Uua tptp.fun_nat_complex) (Uub tptp.fun_nat_complex) (Uuc tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_fun8004580481347240231t_bool (tptp.aa_fun5430245816583273541t_bool (tptp.aTP_Lamm_do Uu) Uua) Uub) Uuc)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat Uuc) Uu)) (not (= (tptp.aa_complex_complex (tptp.plus_plus_complex (tptp.aa_nat_complex Uua Uuc)) (tptp.aa_nat_complex Uub Uuc)) tptp.zero_zero_complex))))) (forall ((Uu tptp.set_nat) (Uua tptp.fun_nat_real) (Uub tptp.fun_nat_real) (Uuc tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_fun1349230436907296553t_bool (tptp.aa_fun849216055071118793t_bool (tptp.aTP_Lamm_dw Uu) Uua) Uub) Uuc)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat Uuc) Uu)) (not (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real Uua Uuc)) (tptp.aa_nat_real Uub Uuc)) tptp.zero_zero_real))))) (forall ((Uu tptp.set_nat) (Uua tptp.fun_nat_rat) (Uub tptp.fun_nat_rat) (Uuc tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_fun5637262893798792573t_bool (tptp.aa_fun2107527232086395633t_bool (tptp.aTP_Lamm_ee Uu) Uua) Uub) Uuc)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat Uuc) Uu)) (not (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_nat_rat Uua Uuc)) (tptp.aa_nat_rat Uub Uuc)) tptp.zero_zero_rat))))) (forall ((Uu tptp.set_int) (Uua tptp.fun_int_complex) (Uub tptp.fun_int_complex) (Uuc tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_fun8146511558608327279t_bool (tptp.aa_fun3850298374753145905t_bool (tptp.aTP_Lamm_dq Uu) Uua) Uub) Uuc)) (and (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Uuc) Uu)) (not (= (tptp.aa_complex_complex (tptp.plus_plus_complex (tptp.aa_int_complex Uua Uuc)) (tptp.aa_int_complex Uub Uuc)) tptp.zero_zero_complex))))) (forall ((Uu tptp.set_int) (Uua tptp.fun_int_real) (Uub tptp.fun_int_real) (Uuc tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_fun1262781554902806129t_bool (tptp.aa_fun6205147705862377397t_bool (tptp.aTP_Lamm_dy Uu) Uua) Uub) Uuc)) (and (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Uuc) Uu)) (not (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_int_real Uua Uuc)) (tptp.aa_int_real Uub Uuc)) tptp.zero_zero_real))))) (forall ((Uu tptp.fun_nat_complex) (Uua tptp.nat) (Uub tptp.complex) (Uuc tptp.nat)) (= (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex (tptp.aa_nat2301396582920332468omplex (tptp.aTP_Lamm_ks Uu) Uua) Uub) Uuc) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_nat_complex Uu (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Uuc) Uua))) (tptp.aa_nat_complex (tptp.power_power_complex Uub) Uuc)))) (forall ((Uu tptp.fun_nat_real) (Uua tptp.nat) (Uub tptp.real) (Uuc tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real (tptp.aa_nat1308781354268537904t_real (tptp.aTP_Lamm_kt Uu) Uua) Uub) Uuc) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real Uu (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Uuc) Uua))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Uub) Uuc)))) (forall ((Uu tptp.fun_nat_complex) (Uua tptp.complex) (Uub tptp.nat) (Uuc tptp.nat)) (= (tptp.aa_nat_complex (tptp.aa_nat6454746962644518025omplex (tptp.aa_com4347742694490471604omplex (tptp.aTP_Lamm_sy Uu) Uua) Uub) Uuc) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_nat_complex Uu Uuc)) (tptp.aa_nat_complex (tptp.power_power_complex Uua) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uuc) Uub)) tptp.one_one_nat))))) (forall ((Uu tptp.fun_nat_real) (Uua tptp.real) (Uub tptp.nat) (Uuc tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_nat_fun_nat_real (tptp.aa_rea6853821027689443120t_real (tptp.aTP_Lamm_te Uu) Uua) Uub) Uuc) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real Uu Uuc)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Uua) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uuc) Uub)) tptp.one_one_nat))))) (forall ((Uu tptp.fun_nat_rat) (Uua tptp.rat) (Uub tptp.nat) (Uuc tptp.nat)) (= (tptp.aa_nat_rat (tptp.aa_nat_fun_nat_rat (tptp.aa_rat250263598611652360at_rat (tptp.aTP_Lamm_ta Uu) Uua) Uub) Uuc) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat Uu Uuc)) (tptp.aa_nat_rat (tptp.power_power_rat Uua) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uuc) Uub)) tptp.one_one_nat))))) (forall ((Uu tptp.fun_nat_int) (Uua tptp.int) (Uub tptp.nat) (Uuc tptp.nat)) (= (tptp.aa_nat_int (tptp.aa_nat_fun_nat_int (tptp.aa_int431785320988601264at_int (tptp.aTP_Lamm_tc Uu) Uua) Uub) Uuc) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int Uu Uuc)) (tptp.aa_nat_int (tptp.power_power_int Uua) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uuc) Uub)) tptp.one_one_nat))))) (forall ((Uu tptp.fun_nat_complex) (Uua tptp.fun_nat_complex) (Uub tptp.nat) (Uuc tptp.nat)) (= (tptp.aa_nat_complex (tptp.aa_nat6454746962644518025omplex (tptp.aa_fun5379041630539201665omplex (tptp.aTP_Lamm_qz Uu) Uua) Uub) Uuc) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_nat_complex Uu Uuc)) (tptp.aa_nat_complex Uua (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uub) Uuc))))) (forall ((Uu tptp.fun_nat_real) (Uua tptp.fun_nat_real) (Uub tptp.nat) (Uuc tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_nat_fun_nat_real (tptp.aa_fun3023522663955195517t_real (tptp.aTP_Lamm_rb Uu) Uua) Uub) Uuc) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real Uu Uuc)) (tptp.aa_nat_real Uua (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uub) Uuc))))) (forall ((Uu tptp.fun_nat_rat) (Uua tptp.fun_nat_rat) (Uub tptp.nat) (Uuc tptp.nat)) (= (tptp.aa_nat_rat (tptp.aa_nat_fun_nat_rat (tptp.aa_fun2663889555218712533at_rat (tptp.aTP_Lamm_rf Uu) Uua) Uub) Uuc) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat Uu Uuc)) (tptp.aa_nat_rat Uua (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uub) Uuc))))) (forall ((Uu tptp.fun_nat_nat) (Uua tptp.fun_nat_nat) (Uub tptp.nat) (Uuc tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.aa_fun6650658898577385413at_nat (tptp.aTP_Lamm_rs Uu) Uua) Uub) Uuc) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat Uu Uuc)) (tptp.aa_nat_nat Uua (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uub) Uuc))))) (forall ((Uu tptp.fun_nat_int) (Uua tptp.fun_nat_int) (Uub tptp.nat) (Uuc tptp.nat)) (= (tptp.aa_nat_int (tptp.aa_nat_fun_nat_int (tptp.aa_fun6128006242533108349at_int (tptp.aTP_Lamm_rh Uu) Uua) Uub) Uuc) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int Uu Uuc)) (tptp.aa_nat_int Uua (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uub) Uuc))))) (forall ((Uu tptp.fun_complex_complex) (Uua tptp.fun_complex_complex) (Uub tptp.complex) (Uuc tptp.complex)) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex (tptp.aa_fun6995112137416684571omplex (tptp.aTP_Lamm_fp Uu) Uua) Uub) Uuc) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_complex_complex Uu Uub)) (tptp.aa_complex_complex Uua Uuc)))) (forall ((Uu tptp.fun_nat_real) (Uua tptp.fun_nat_real) (Uub tptp.nat) (Uuc tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_nat_fun_nat_real (tptp.aa_fun3023522663955195517t_real (tptp.aTP_Lamm_ft Uu) Uua) Uub) Uuc) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real Uu Uub)) (tptp.aa_nat_real Uua Uuc)))) (forall ((Uu tptp.fun_nat_nat) (Uua tptp.fun_nat_nat) (Uub tptp.nat) (Uuc tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.aa_fun6650658898577385413at_nat (tptp.aTP_Lamm_fr Uu) Uua) Uub) Uuc) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat Uu Uub)) (tptp.aa_nat_nat Uua Uuc)))) (forall ((Uu tptp.fun_int_int) (Uua tptp.fun_int_int) (Uub tptp.int) (Uuc tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int (tptp.aa_fun5911324870756489105nt_int (tptp.aTP_Lamm_fn Uu) Uua) Uub) Uuc) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int Uu Uub)) (tptp.aa_int_int Uua Uuc)))) (forall ((Uu tptp.fun_nat_real) (Uua tptp.nat) (Uub tptp.nat) (Uuc tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_nat_fun_nat_real (tptp.aa_nat4085805313368488148t_real (tptp.aTP_Lamm_hs Uu) Uua) Uub) Uuc) (tptp.aa_nat_real Uu (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Uub) Uua)) Uuc)))) (forall ((Uu tptp.fun_nat_nat) (Uua tptp.nat) (Uub tptp.nat) (Uuc tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.aa_nat3783148529270815480at_nat (tptp.aTP_Lamm_hr Uu) Uua) Uub) Uuc) (tptp.aa_nat_nat Uu (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Uub) Uua)) Uuc)))) (forall ((Uu tptp.fun_nat_int) (Uua tptp.nat) (Uub tptp.nat) (Uuc tptp.nat)) (= (tptp.aa_nat_int (tptp.aa_nat_fun_nat_int (tptp.aa_nat1293065384339088724at_int (tptp.aTP_Lamm_pf Uu) Uua) Uub) Uuc) (tptp.aa_nat_int Uu (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Uub) Uua)) Uuc)))) (forall ((Uu tptp.int) (Uua tptp.int) (Uub tptp.int) (Uuc tptp.int)) (= (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int (tptp.aa_int1966403025003302569nt_int (tptp.aTP_Lamm_wl Uu) Uua) Uub) Uuc) (tptp.aa_Pro6970504127699319548nt_int tptp.normalize (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int Uu) Uuc)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int Uub) Uua))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int Uua) Uuc))))) (forall ((Uu tptp.int) (Uua tptp.int) (Uub tptp.int) (Uuc tptp.int)) (= (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int (tptp.aa_int1966403025003302569nt_int (tptp.aTP_Lamm_wj Uu) Uua) Uub) Uuc) (tptp.aa_Pro6970504127699319548nt_int tptp.normalize (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int Uu) Uuc)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int Uub) Uua))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int Uua) Uuc))))) (forall ((Uu tptp.int) (Uua tptp.int) (Uub tptp.int) (Uuc tptp.int)) (= (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int (tptp.aa_int1966403025003302569nt_int (tptp.aTP_Lamm_wh Uu) Uua) Uub) Uuc) (tptp.aa_Pro6970504127699319548nt_int tptp.normalize (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int Uu) Uub)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int Uua) Uuc))))) (forall ((Uu tptp.int) (Uua tptp.int) (Uub tptp.int) (Uuc tptp.int)) (= (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int (tptp.aa_int1966403025003302569nt_int (tptp.aTP_Lamm_wf Uu) Uua) Uub) Uuc) (tptp.aa_Pro6970504127699319548nt_int tptp.normalize (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int Uu) Uuc)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int Uua) Uub))))) (forall ((Uu tptp.fun_real_bool) (Uua tptp.fun_real_bool) (Uub tptp.fun_re7812779276277946752omplex) (Uuc tptp.complex)) (= (tptp.pp (tptp.aa_complex_bool (tptp.aa_fun8363404835654190852x_bool (tptp.aa_fun7464652376466389139x_bool (tptp.aTP_Lamm_ew Uu) Uua) Uub) Uuc)) (exists ((X3 tptp.real) (Y3 tptp.real)) (and (= Uuc (tptp.aa_real_complex (tptp.aa_rea2649881322057434177omplex Uub X3) Y3)) (tptp.pp (tptp.aa_real_bool Uu X3)) (tptp.pp (tptp.aa_real_bool Uua Y3)))))) (forall ((Uu tptp.fun_real_bool) (Uua tptp.fun_real_bool) (Uub tptp.fun_re7681423839302404990l_real) (Uuc tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_fun955784922888763656l_bool (tptp.aa_fun2902298374912565143l_bool (tptp.aTP_Lamm_et Uu) Uua) Uub) Uuc)) (exists ((X3 tptp.real) (Y3 tptp.real)) (and (= Uuc (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real Uub X3) Y3)) (tptp.pp (tptp.aa_real_bool Uu X3)) (tptp.pp (tptp.aa_real_bool Uua Y3)))))) (forall ((Uu tptp.fun_real_bool) (Uua tptp.fun_real_bool) (Uub tptp.fun_re7428432522468557474al_nat) (Uuc tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_fun528418799539591104t_bool (tptp.aa_fun8259732966411813455t_bool (tptp.aTP_Lamm_eu Uu) Uua) Uub) Uuc)) (exists ((X3 tptp.real) (Y3 tptp.real)) (and (= Uuc (tptp.aa_real_nat (tptp.aa_real_fun_real_nat Uub X3) Y3)) (tptp.pp (tptp.aa_real_bool Uu X3)) (tptp.pp (tptp.aa_real_bool Uua Y3)))))) (forall ((Uu tptp.fun_real_bool) (Uua tptp.fun_real_bool) (Uub tptp.fun_re4938349377536830718al_int) (Uuc tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_fun1238366933954993416t_bool (tptp.aa_fun2410317078794417559t_bool (tptp.aTP_Lamm_ev Uu) Uua) Uub) Uuc)) (exists ((X3 tptp.real) (Y3 tptp.real)) (and (= Uuc (tptp.aa_real_int (tptp.aa_real_fun_real_int Uub X3) Y3)) (tptp.pp (tptp.aa_real_bool Uu X3)) (tptp.pp (tptp.aa_real_bool Uua Y3)))))) (forall ((Uu tptp.fun_real_bool) (Uua tptp.fun_nat_bool) (Uub tptp.fun_re2084383175013312036omplex) (Uuc tptp.complex)) (= (tptp.pp (tptp.aa_complex_bool (tptp.aa_fun9170867047750497504x_bool (tptp.aa_fun2493215948360222867x_bool (tptp.aTP_Lamm_fa Uu) Uua) Uub) Uuc)) (exists ((X3 tptp.real) (Y3 tptp.nat)) (and (= Uuc (tptp.aa_nat_complex (tptp.aa_rea1531280491672885477omplex Uub X3) Y3)) (tptp.pp (tptp.aa_real_bool Uu X3)) (tptp.pp (tptp.aa_nat_bool Uua Y3)))))) (forall ((Uu tptp.fun_real_bool) (Uua tptp.fun_nat_bool) (Uub tptp.fun_re4238438383274954274t_real) (Uuc tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_fun5008594764412271332l_bool (tptp.aa_fun7835077198776561559l_bool (tptp.aTP_Lamm_ex Uu) Uua) Uub) Uuc)) (exists ((X3 tptp.real) (Y3 tptp.nat)) (and (= Uuc (tptp.aa_nat_real (tptp.aa_real_fun_nat_real Uub X3) Y3)) (tptp.pp (tptp.aa_real_bool Uu X3)) (tptp.pp (tptp.aa_nat_bool Uua Y3)))))) (forall ((Uu tptp.fun_real_bool) (Uua tptp.fun_nat_bool) (Uub tptp.fun_real_fun_nat_nat) (Uuc tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_fun3685766209695167900t_bool (tptp.aa_fun2965812958138651215t_bool (tptp.aTP_Lamm_ey Uu) Uua) Uub) Uuc)) (exists ((X3 tptp.real) (Y3 tptp.nat)) (and (= Uuc (tptp.aa_nat_nat (tptp.aa_real_fun_nat_nat Uub X3) Y3)) (tptp.pp (tptp.aa_real_bool Uu X3)) (tptp.pp (tptp.aa_nat_bool Uua Y3)))))) (forall ((Uu tptp.fun_real_bool) (Uua tptp.fun_nat_bool) (Uub tptp.fun_real_fun_nat_int) (Uuc tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_fun4395714344110570212t_bool (tptp.aa_fun6339769107376031127t_bool (tptp.aTP_Lamm_ez Uu) Uua) Uub) Uuc)) (exists ((X3 tptp.real) (Y3 tptp.nat)) (and (= Uuc (tptp.aa_nat_int (tptp.aa_real_fun_nat_int Uub X3) Y3)) (tptp.pp (tptp.aa_real_bool Uu X3)) (tptp.pp (tptp.aa_nat_bool Uua Y3)))))) (forall ((Uu tptp.fun_real_bool) (Uua tptp.fun_int_bool) (Uub tptp.fun_re7457141977439324286t_real) (Uuc tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_fun6686107996194020744l_bool (tptp.aa_fun7698435294645330071l_bool (tptp.aTP_Lamm_fb Uu) Uua) Uub) Uuc)) (exists ((X3 tptp.real) (Y3 tptp.int)) (and (= Uuc (tptp.aa_int_real (tptp.aa_real_fun_int_real Uub X3) Y3)) (tptp.pp (tptp.aa_real_bool Uu X3)) (tptp.pp (tptp.aa_int_bool Uua Y3)))))) (forall ((Uu tptp.fun_real_bool) (Uua tptp.fun_int_bool) (Uub tptp.fun_real_fun_int_nat) (Uuc tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_fun6723608294159301696t_bool (tptp.aa_fun543251173574902607t_bool (tptp.aTP_Lamm_fc Uu) Uua) Uub) Uuc)) (exists ((X3 tptp.real) (Y3 tptp.int)) (and (= Uuc (tptp.aa_int_nat (tptp.aa_real_fun_int_nat Uub X3) Y3)) (tptp.pp (tptp.aa_real_bool Uu X3)) (tptp.pp (tptp.aa_int_bool Uua Y3)))))) (forall ((Uu tptp.nat) (Uua tptp.fun_nat_real) (Uub tptp.real) (Uuc tptp.real) (Uud tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real (tptp.aa_rea7841385751566875788t_real (tptp.aa_fun2548873334967081986t_real (tptp.aTP_Lamm_sr Uu) Uua) Uub) Uuc) Uud) (tptp.groups6591440286371151544t_real (tptp.aa_nat_fun_nat_real (tptp.aa_rea6853821027689443120t_real (tptp.aa_rea6454571821648764761t_real (tptp.aTP_Lamm_sq Uua) Uub) Uuc) Uud) (tptp.set_ord_lessThan_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uu) Uud))))) (forall ((Uu tptp.nat) (Uua tptp.fun_nat_int) (Uub tptp.int) (Uuc tptp.int) (Uud tptp.nat)) (= (tptp.aa_nat_int (tptp.aa_int_fun_nat_int (tptp.aa_int5842867502692063756at_int (tptp.aa_fun7421131748584218370at_int (tptp.aTP_Lamm_sp Uu) Uua) Uub) Uuc) Uud) (tptp.groups3539618377306564664at_int (tptp.aa_nat_fun_nat_int (tptp.aa_int431785320988601264at_int (tptp.aa_int6823550873765277145at_int (tptp.aTP_Lamm_so Uua) Uub) Uuc) Uud) (tptp.set_ord_lessThan_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uu) Uud))))) (forall ((Uu tptp.nat) (Uua tptp.fun_nat_rat) (Uub tptp.rat) (Uuc tptp.rat) (Uud tptp.nat)) (= (tptp.aa_nat_rat (tptp.aa_rat_fun_nat_rat (tptp.aa_rat3146053865535587600at_rat (tptp.aa_fun8528462509625601970at_rat (tptp.aTP_Lamm_sn Uu) Uua) Uub) Uuc) Uud) (tptp.groups2906978787729119204at_rat (tptp.aa_nat_fun_nat_rat (tptp.aa_rat250263598611652360at_rat (tptp.aa_rat8984911954100663005at_rat (tptp.aTP_Lamm_sm Uua) Uub) Uuc) Uud) (tptp.set_ord_lessThan_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uu) Uud))))) (forall ((Uu tptp.nat) (Uua tptp.fun_nat_complex) (Uub tptp.complex) (Uuc tptp.complex) (Uud tptp.nat)) (= (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex (tptp.aa_com8177640530696437650omplex (tptp.aa_fun5031706661949900810omplex (tptp.aTP_Lamm_sl Uu) Uua) Uub) Uuc) Uud) (tptp.groups2073611262835488442omplex (tptp.aa_nat6454746962644518025omplex (tptp.aa_com4347742694490471604omplex (tptp.aa_com7713930848417683039omplex (tptp.aTP_Lamm_sk Uua) Uub) Uuc) Uud) (tptp.set_ord_lessThan_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uu) Uud))))) (forall ((Uu tptp.nat) (Uua tptp.fun_na6724076748692969250l_real) (Uub tptp.real) (Uuc tptp.nat) (Uud tptp.real)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uu) Uuc))) (= (tptp.aa_real_real (tptp.aa_nat_fun_real_real (tptp.aa_rea1103652080130114956l_real (tptp.aa_fun2567993205388704171l_real (tptp.aTP_Lamm_ym Uu) Uua) Uub) Uuc) Uud) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real (tptp.aa_nat_fun_real_real Uua Uuc) Uud)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real (tptp.aa_nat1308781354268537904t_real (tptp.aTP_Lamm_yl Uua) Uuc) Uud) (tptp.set_ord_lessThan_nat _let_1))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real Uub) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Uud) _let_1)) (tptp.aa_nat_real tptp.semiri2265585572941072030t_real _let_1)))))))) (forall ((Uu tptp.nat) (Uua tptp.fun_nat_real) (Uub tptp.real) (Uuc tptp.real) (Uud tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real (tptp.aa_rea7841385751566875788t_real (tptp.aa_fun2548873334967081986t_real (tptp.aTP_Lamm_tf Uu) Uua) Uub) Uuc) Uud) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.groups6591440286371151544t_real (tptp.aa_nat_fun_nat_real (tptp.aa_rea6853821027689443120t_real (tptp.aTP_Lamm_te Uua) Uuc) Uud) (tptp.set_or1269000886237332187st_nat (tptp.aa_nat_nat tptp.suc Uud) Uu))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Uub) Uud)))) (forall ((Uu tptp.nat) (Uua tptp.fun_nat_int) (Uub tptp.int) (Uuc tptp.int) (Uud tptp.nat)) (= (tptp.aa_nat_int (tptp.aa_int_fun_nat_int (tptp.aa_int5842867502692063756at_int (tptp.aa_fun7421131748584218370at_int (tptp.aTP_Lamm_td Uu) Uua) Uub) Uuc) Uud) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.groups3539618377306564664at_int (tptp.aa_nat_fun_nat_int (tptp.aa_int431785320988601264at_int (tptp.aTP_Lamm_tc Uua) Uuc) Uud) (tptp.set_or1269000886237332187st_nat (tptp.aa_nat_nat tptp.suc Uud) Uu))) (tptp.aa_nat_int (tptp.power_power_int Uub) Uud)))) (forall ((Uu tptp.nat) (Uua tptp.fun_nat_rat) (Uub tptp.rat) (Uuc tptp.rat) (Uud tptp.nat)) (= (tptp.aa_nat_rat (tptp.aa_rat_fun_nat_rat (tptp.aa_rat3146053865535587600at_rat (tptp.aa_fun8528462509625601970at_rat (tptp.aTP_Lamm_tb Uu) Uua) Uub) Uuc) Uud) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.groups2906978787729119204at_rat (tptp.aa_nat_fun_nat_rat (tptp.aa_rat250263598611652360at_rat (tptp.aTP_Lamm_ta Uua) Uuc) Uud) (tptp.set_or1269000886237332187st_nat (tptp.aa_nat_nat tptp.suc Uud) Uu))) (tptp.aa_nat_rat (tptp.power_power_rat Uub) Uud)))) (forall ((Uu tptp.nat) (Uua tptp.fun_nat_complex) (Uub tptp.complex) (Uuc tptp.complex) (Uud tptp.nat)) (= (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex (tptp.aa_com8177640530696437650omplex (tptp.aa_fun5031706661949900810omplex (tptp.aTP_Lamm_sz Uu) Uua) Uub) Uuc) Uud) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.groups2073611262835488442omplex (tptp.aa_nat6454746962644518025omplex (tptp.aa_com4347742694490471604omplex (tptp.aTP_Lamm_sy Uua) Uuc) Uud) (tptp.set_or1269000886237332187st_nat (tptp.aa_nat_nat tptp.suc Uud) Uu))) (tptp.aa_nat_complex (tptp.power_power_complex Uub) Uud)))) (forall ((Uu tptp.nat) (Uua tptp.complex) (Uub tptp.complex) (Uuc tptp.complex) (Uud tptp.nat)) (= (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex (tptp.aa_com8177640530696437650omplex (tptp.aa_com177695874307951165omplex (tptp.aTP_Lamm_un Uu) Uua) Uub) Uuc) Uud) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_nat_complex (tptp.gbinomial_complex (tptp.aa_complex_complex (tptp.minus_minus_complex (tptp.aa_complex_complex (tptp.plus_plus_complex (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex Uud)) Uua)) tptp.one_one_complex)) Uud)) (tptp.aa_nat_complex (tptp.power_power_complex Uub) Uud))) (tptp.aa_nat_complex (tptp.power_power_complex (tptp.aa_complex_complex (tptp.plus_plus_complex Uub) Uuc)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uu) Uud))))) (forall ((Uu tptp.nat) (Uua tptp.real) (Uub tptp.real) (Uuc tptp.real) (Uud tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real (tptp.aa_rea7841385751566875788t_real (tptp.aa_rea1729780184207679413t_real (tptp.aTP_Lamm_up Uu) Uua) Uub) Uuc) Uud) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.gbinomial_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real Uud)) Uua)) tptp.one_one_real)) Uud)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Uub) Uud))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real Uub) Uuc)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uu) Uud))))) (forall ((Uu tptp.nat) (Uua tptp.rat) (Uub tptp.rat) (Uuc tptp.rat) (Uud tptp.nat)) (= (tptp.aa_nat_rat (tptp.aa_rat_fun_nat_rat (tptp.aa_rat3146053865535587600at_rat (tptp.aa_rat7467449789483521253at_rat (tptp.aTP_Lamm_uo Uu) Uua) Uub) Uuc) Uud) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat (tptp.gbinomial_rat (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat Uud)) Uua)) tptp.one_one_rat)) Uud)) (tptp.aa_nat_rat (tptp.power_power_rat Uub) Uud))) (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat Uub) Uuc)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uu) Uud))))) (forall ((Uu tptp.nat) (Uua tptp.complex) (Uub tptp.complex) (Uuc tptp.complex) (Uud tptp.nat)) (= (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex (tptp.aa_com8177640530696437650omplex (tptp.aa_com177695874307951165omplex (tptp.aTP_Lamm_tw Uu) Uua) Uub) Uuc) Uud) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_nat_complex (tptp.gbinomial_complex (tptp.aa_complex_complex (tptp.plus_plus_complex (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex Uu)) Uua)) Uud)) (tptp.aa_nat_complex (tptp.power_power_complex Uub) Uud))) (tptp.aa_nat_complex (tptp.power_power_complex Uuc) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uu) Uud))))) (forall ((Uu tptp.nat) (Uua tptp.real) (Uub tptp.real) (Uuc tptp.real) (Uud tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real (tptp.aa_rea7841385751566875788t_real (tptp.aa_rea1729780184207679413t_real (tptp.aTP_Lamm_ua Uu) Uua) Uub) Uuc) Uud) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.gbinomial_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real Uu)) Uua)) Uud)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Uub) Uud))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Uuc) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uu) Uud))))) (forall ((Uu tptp.nat) (Uua tptp.rat) (Uub tptp.rat) (Uuc tptp.rat) (Uud tptp.nat)) (= (tptp.aa_nat_rat (tptp.aa_rat_fun_nat_rat (tptp.aa_rat3146053865535587600at_rat (tptp.aa_rat7467449789483521253at_rat (tptp.aTP_Lamm_ty Uu) Uua) Uub) Uuc) Uud) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat (tptp.gbinomial_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat Uu)) Uua)) Uud)) (tptp.aa_nat_rat (tptp.power_power_rat Uub) Uud))) (tptp.aa_nat_rat (tptp.power_power_rat Uuc) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uu) Uud))))) (forall ((Uu tptp.nat) (Uua tptp.complex) (Uub tptp.complex) (Uuc tptp.complex) (Uud tptp.nat)) (= (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex (tptp.aa_com8177640530696437650omplex (tptp.aa_com177695874307951165omplex (tptp.aTP_Lamm_tx Uu) Uua) Uub) Uuc) Uud) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_nat_complex (tptp.gbinomial_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex Uua)) Uud)) (tptp.aa_nat_complex (tptp.power_power_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex Uub)) Uud))) (tptp.aa_nat_complex (tptp.power_power_complex (tptp.aa_complex_complex (tptp.plus_plus_complex Uub) Uuc)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uu) Uud))))) (forall ((Uu tptp.nat) (Uua tptp.real) (Uub tptp.real) (Uuc tptp.real) (Uud tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real (tptp.aa_rea7841385751566875788t_real (tptp.aa_rea1729780184207679413t_real (tptp.aTP_Lamm_ub Uu) Uua) Uub) Uuc) Uud) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.gbinomial_real (tptp.aa_real_real tptp.uminus_uminus_real Uua)) Uud)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real tptp.uminus_uminus_real Uub)) Uud))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real Uub) Uuc)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uu) Uud))))) (forall ((Uu tptp.nat) (Uua tptp.rat) (Uub tptp.rat) (Uuc tptp.rat) (Uud tptp.nat)) (= (tptp.aa_nat_rat (tptp.aa_rat_fun_nat_rat (tptp.aa_rat3146053865535587600at_rat (tptp.aa_rat7467449789483521253at_rat (tptp.aTP_Lamm_tz Uu) Uua) Uub) Uuc) Uud) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat (tptp.gbinomial_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat Uua)) Uud)) (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat Uub)) Uud))) (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat Uub) Uuc)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uu) Uud))))) (forall ((Uu tptp.fun_nat_complex) (Uua tptp.complex) (Uub tptp.complex) (Uuc tptp.nat) (Uud tptp.nat)) (= (tptp.aa_nat_complex (tptp.aa_nat6454746962644518025omplex (tptp.aa_com4347742694490471604omplex (tptp.aa_com7713930848417683039omplex (tptp.aTP_Lamm_sk Uu) Uua) Uub) Uuc) Uud) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_nat_complex Uu (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Uuc) Uud)) tptp.one_one_nat))) (tptp.aa_nat_complex (tptp.power_power_complex Uub) Uud))) (tptp.aa_nat_complex (tptp.power_power_complex Uua) Uuc)))) (forall ((Uu tptp.fun_nat_real) (Uua tptp.real) (Uub tptp.real) (Uuc tptp.nat) (Uud tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_nat_fun_nat_real (tptp.aa_rea6853821027689443120t_real (tptp.aa_rea6454571821648764761t_real (tptp.aTP_Lamm_sq Uu) Uua) Uub) Uuc) Uud) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real Uu (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Uuc) Uud)) tptp.one_one_nat))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Uub) Uud))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Uua) Uuc)))) (forall ((Uu tptp.fun_nat_rat) (Uua tptp.rat) (Uub tptp.rat) (Uuc tptp.nat) (Uud tptp.nat)) (= (tptp.aa_nat_rat (tptp.aa_nat_fun_nat_rat (tptp.aa_rat250263598611652360at_rat (tptp.aa_rat8984911954100663005at_rat (tptp.aTP_Lamm_sm Uu) Uua) Uub) Uuc) Uud) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat Uu (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Uuc) Uud)) tptp.one_one_nat))) (tptp.aa_nat_rat (tptp.power_power_rat Uub) Uud))) (tptp.aa_nat_rat (tptp.power_power_rat Uua) Uuc)))) (forall ((Uu tptp.fun_nat_int) (Uua tptp.int) (Uub tptp.int) (Uuc tptp.nat) (Uud tptp.nat)) (= (tptp.aa_nat_int (tptp.aa_nat_fun_nat_int (tptp.aa_int431785320988601264at_int (tptp.aa_int6823550873765277145at_int (tptp.aTP_Lamm_so Uu) Uua) Uub) Uuc) Uud) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int Uu (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Uuc) Uud)) tptp.one_one_nat))) (tptp.aa_nat_int (tptp.power_power_int Uub) Uud))) (tptp.aa_nat_int (tptp.power_power_int Uua) Uuc)))) (forall ((Uu tptp.nat) (Uua tptp.list_VEBT_VEBT) (Uub tptp.vEBT_VEBT) (Uuc tptp.nat) (Uud tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (= Uuc Uud))) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool (tptp.aa_VEB1917483692448707121t_bool (tptp.aa_lis1179741779018426550t_bool (tptp.aTP_Lamm_xg Uu) Uua) Uub) Uuc) Uud)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Uuc) Uud)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Uud) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat _let_1) Uu))) (forall ((I4 tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I4) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat _let_1) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uu) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat Uu) _let_1))))) (= (exists ((X_1 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions (tptp.nth_VEBT_VEBT Uua I4)) X_1))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions Uub) I4)))))) (=> _let_2 (forall ((X3 tptp.vEBT_VEBT)) (=> (tptp.pp (tptp.aa_set8260762808118238015T_bool (tptp.aa_VEB289770264548726718T_bool tptp.member_VEBT_VEBT X3) (tptp.set_VEBT_VEBT2 Uua))) (not (exists ((X_1 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions X3) X_1))))))) (=> (not _let_2) (and (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_V5917875025757280293ildren (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat Uu) _let_1) Uua) Uud)) (forall ((X3 tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X3) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat _let_1) Uu))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_V5917875025757280293ildren (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat Uu) _let_1) Uua) X3)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Uuc) X3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X3) Uud)))))))))))))) (forall ((Uu tptp.rat) (Uua tptp.nat)) (= (tptp.aa_nat_rat (tptp.aTP_Lamm_aaj Uu) Uua) Uu)) (forall ((Uu tptp.complex)) (= (tptp.aa_complex_complex tptp.aTP_Lamm_ai Uu) Uu)) (forall ((Uu tptp.real)) (= (tptp.aa_real_real tptp.aTP_Lamm_aj Uu) Uu)) (forall ((Uu tptp.rat)) (= (tptp.aa_rat_rat tptp.aTP_Lamm_ak Uu) Uu)) (forall ((Uu tptp.nat)) (= (tptp.aa_nat_nat tptp.aTP_Lamm_al Uu) Uu)) (forall ((Uu tptp.int)) (= (tptp.aa_int_int tptp.aTP_Lamm_am Uu) Uu)) (forall ((Uu tptp.complex)) (= (tptp.aa_complex_complex tptp.aTP_Lamm_au Uu) tptp.zero_zero_complex)) (forall ((Uu tptp.real)) (= (tptp.aa_real_real tptp.aTP_Lamm_av Uu) tptp.zero_zero_real)) (forall ((Uu tptp.rat)) (= (tptp.aa_rat_rat tptp.aTP_Lamm_aw Uu) tptp.zero_zero_rat)) (forall ((Uu tptp.nat)) (= (tptp.aa_nat_nat tptp.aTP_Lamm_ax Uu) tptp.zero_zero_nat)) (forall ((Uu tptp.int)) (= (tptp.aa_int_int tptp.aTP_Lamm_ay Uu) tptp.zero_zero_int)) (forall ((Uu tptp.real)) (= (tptp.pp (tptp.aa_real_bool tptp.aTP_Lamm_vl Uu)) false)) (forall ((Uu tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool tptp.aTP_Lamm_vz Uu)) false)) (forall ((Uu tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool tptp.aTP_Lamm_vy Uu)) true)) (forall ((P tptp.bool)) (or (tptp.pp P) (tptp.pp (tptp.aa_bool_bool tptp.fNot P)))) (forall ((P tptp.bool)) (or (not (tptp.pp (tptp.aa_bool_bool tptp.fNot P))) (not (tptp.pp P)))) (tptp.pp tptp.fTrue) (forall ((P tptp.bool) (Q tptp.bool)) (or (not (tptp.pp (tptp.aa_bool_bool (tptp.fconj P) Q))) (tptp.pp Q))) (forall ((P tptp.bool) (Q tptp.bool)) (or (not (tptp.pp (tptp.aa_bool_bool (tptp.fconj P) Q))) (tptp.pp P))) (forall ((P tptp.bool) (Q tptp.bool)) (or (not (tptp.pp P)) (not (tptp.pp Q)) (tptp.pp (tptp.aa_bool_bool (tptp.fconj P) Q)))) (forall ((P tptp.bool) (Q tptp.bool)) (or (not (tptp.pp (tptp.aa_bool_bool (tptp.fdisj P) Q))) (tptp.pp P) (tptp.pp Q))) (forall ((Q tptp.bool) (P tptp.bool)) (or (not (tptp.pp Q)) (tptp.pp (tptp.aa_bool_bool (tptp.fdisj P) Q)))) (forall ((P tptp.bool) (Q tptp.bool)) (or (not (tptp.pp P)) (tptp.pp (tptp.aa_bool_bool (tptp.fdisj P) Q)))) (not (tptp.pp tptp.fFalse)) (forall ((P tptp.bool) (Q tptp.bool)) (or (not (tptp.pp (tptp.aa_bool_bool (tptp.aa_boo8970175072276269406l_bool tptp.fimplies P) Q))) (not (tptp.pp P)) (tptp.pp Q))) (forall ((Q tptp.bool) (P tptp.bool)) (or (not (tptp.pp Q)) (tptp.pp (tptp.aa_bool_bool (tptp.aa_boo8970175072276269406l_bool tptp.fimplies P) Q)))) (forall ((P tptp.bool) (Q tptp.bool)) (or (tptp.pp P) (tptp.pp (tptp.aa_bool_bool (tptp.aa_boo8970175072276269406l_bool tptp.fimplies P) Q)))) (forall ((X tptp.int) (Y tptp.int)) (= (tptp.aa_int_int (tptp.if_int tptp.fFalse X) Y) Y)) (forall ((X tptp.int) (Y tptp.int)) (= (tptp.aa_int_int (tptp.if_int tptp.fTrue X) Y) X)) (forall ((X tptp.nat) (Y tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.if_nat tptp.fFalse) X) Y) Y)) (forall ((X tptp.nat) (Y tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.if_nat tptp.fTrue) X) Y) X)) (forall ((X tptp.num) (Y tptp.num)) (= (tptp.aa_num_num (tptp.aa_num_fun_num_num (tptp.if_num tptp.fFalse) X) Y) Y)) (forall ((X tptp.num) (Y tptp.num)) (= (tptp.aa_num_num (tptp.aa_num_fun_num_num (tptp.if_num tptp.fTrue) X) Y) X)) (forall ((X tptp.rat) (Y tptp.rat)) (= (tptp.aa_rat_rat (tptp.if_rat tptp.fFalse X) Y) Y)) (forall ((X tptp.rat) (Y tptp.rat)) (= (tptp.aa_rat_rat (tptp.if_rat tptp.fTrue X) Y) X)) (forall ((P tptp.fun_nat_bool) (X tptp.nat)) (or (not (tptp.pp (tptp.aa_nat_bool P X))) (tptp.pp (tptp.aa_fun_nat_bool_bool tptp.fEx_nat P)))) (forall ((X tptp.real) (Y tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real (tptp.if_real tptp.fFalse) X) Y) Y)) (forall ((X tptp.real) (Y tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real (tptp.if_real tptp.fTrue) X) Y) X)) (forall ((X tptp.int) (Y tptp.int)) (or (not (= X Y)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.fequal_int X) Y)))) (forall ((X tptp.int) (Y tptp.int)) (or (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.fequal_int X) Y))) (= X Y))) (forall ((X tptp.nat) (Y tptp.nat)) (or (not (= X Y)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.fequal_nat X) Y)))) (forall ((X tptp.nat) (Y tptp.nat)) (or (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.fequal_nat X) Y))) (= X Y))) (forall ((X tptp.num) (Y tptp.num)) (or (not (= X Y)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.fequal_num X) Y)))) (forall ((X tptp.num) (Y tptp.num)) (or (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.fequal_num X) Y))) (= X Y))) (forall ((X tptp.bool) (Y tptp.bool)) (or (not (= X Y)) (tptp.pp (tptp.aa_bool_bool (tptp.aa_boo8970175072276269406l_bool tptp.fequal_bool X) Y)))) (forall ((X tptp.bool) (Y tptp.bool)) (or (not (tptp.pp (tptp.aa_bool_bool (tptp.aa_boo8970175072276269406l_bool tptp.fequal_bool X) Y))) (= X Y))) (forall ((X tptp.real) (Y tptp.real)) (or (not (= X Y)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.fequal_real X) Y)))) (forall ((X tptp.real) (Y tptp.real)) (or (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.fequal_real X) Y))) (= X Y))) (forall ((P tptp.fun_real_bool)) (= (tptp.aa_real_bool P (tptp.fChoice_real P)) (tptp.aa_fun3352386287069783311l_bool tptp.fEx_real P))) (forall ((X tptp.complex) (Y tptp.complex)) (= (tptp.aa_complex_complex (tptp.if_complex tptp.fFalse X) Y) Y)) (forall ((X tptp.complex) (Y tptp.complex)) (= (tptp.aa_complex_complex (tptp.if_complex tptp.fTrue X) Y) X)) (forall ((X tptp.code_integer) (Y tptp.code_integer)) (= (tptp.if_Code_integer tptp.fFalse X Y) Y)) (forall ((X tptp.code_integer) (Y tptp.code_integer)) (= (tptp.if_Code_integer tptp.fTrue X Y) X)) (forall ((X tptp.vEBT_VEBT) (Y tptp.vEBT_VEBT)) (= (tptp.if_VEBT_VEBT tptp.fFalse X Y) Y)) (forall ((X tptp.vEBT_VEBT) (Y tptp.vEBT_VEBT)) (= (tptp.if_VEBT_VEBT tptp.fTrue X Y) X)) (forall ((P tptp.fun_VEBT_VEBT_bool) (X tptp.vEBT_VEBT)) (or (not (tptp.pp (tptp.fAll_VEBT_VEBT P))) (tptp.pp (tptp.aa_VEBT_VEBT_bool P X)))) (forall ((X tptp.code_integer) (Y tptp.code_integer)) (or (not (= X Y)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.fequal_Code_integer X) Y)))) (forall ((X tptp.code_integer) (Y tptp.code_integer)) (or (not (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.fequal_Code_integer X) Y))) (= X Y))) (forall ((X tptp.option_nat) (Y tptp.option_nat)) (= (tptp.if_option_nat tptp.fFalse X Y) Y)) (forall ((X tptp.option_nat) (Y tptp.option_nat)) (= (tptp.if_option_nat tptp.fTrue X Y) X)) (forall ((X tptp.option_nat) (Y tptp.option_nat)) (or (not (= X Y)) (tptp.pp (tptp.aa_option_nat_bool (tptp.aa_opt7943525813896274546t_bool tptp.fequal_option_nat X) Y)))) (forall ((X tptp.option_nat) (Y tptp.option_nat)) (or (not (tptp.pp (tptp.aa_option_nat_bool (tptp.aa_opt7943525813896274546t_bool tptp.fequal_option_nat X) Y))) (= X Y))) (forall ((X tptp.product_prod_int_int) (Y tptp.product_prod_int_int)) (= (tptp.aa_Pro6970504127699319548nt_int (tptp.if_Pro3027730157355071871nt_int tptp.fFalse X) Y) Y)) (forall ((X tptp.product_prod_int_int) (Y tptp.product_prod_int_int)) (= (tptp.aa_Pro6970504127699319548nt_int (tptp.if_Pro3027730157355071871nt_int tptp.fTrue X) Y) X)) (forall ((X tptp.product_prod_nat_nat) (Y tptp.product_prod_nat_nat)) (= (tptp.aa_Pro262675715343573244at_nat (tptp.aa_Pro8023792847356852296at_nat (tptp.if_Pro6206227464963214023at_nat tptp.fFalse) X) Y) Y)) (forall ((X tptp.product_prod_nat_nat) (Y tptp.product_prod_nat_nat)) (= (tptp.aa_Pro262675715343573244at_nat (tptp.aa_Pro8023792847356852296at_nat (tptp.if_Pro6206227464963214023at_nat tptp.fTrue) X) Y) X)) (forall ((P tptp.fun_bool_bool) (Q tptp.fun_VEBT_VEBT_bool) (R2 tptp.vEBT_VEBT)) (= (tptp.aa_VEBT_VEBT_bool (tptp.cOMBB_3745307990312268622T_VEBT P Q) R2) (tptp.aa_bool_bool P (tptp.aa_VEBT_VEBT_bool Q R2)))) (forall ((P tptp.fun_VE2066785035971159626l_bool) (Q tptp.fun_VEBT_VEBT_bool) (R2 tptp.vEBT_VEBT)) (= (tptp.aa_VEBT_VEBT_bool (tptp.cOMBS_6222329278419335549l_bool P Q) R2) (tptp.aa_bool_bool (tptp.aa_VEB8047906998784800507l_bool P R2) (tptp.aa_VEBT_VEBT_bool Q R2)))) (forall ((P tptp.bool)) (or (= P tptp.fTrue) (= P tptp.fFalse))) (forall ((X tptp.produc8923325533196201883nteger) (Y tptp.produc8923325533196201883nteger)) (= (tptp.if_Pro6119634080678213985nteger tptp.fFalse X Y) Y)) (forall ((X tptp.produc8923325533196201883nteger) (Y tptp.produc8923325533196201883nteger)) (= (tptp.if_Pro6119634080678213985nteger tptp.fTrue X Y) X)) (forall ((P tptp.fun_fu7168253649841883962l_bool) (Q tptp.fun_VE3763956218935105199t_bool) (R2 tptp.vEBT_VEBT)) (= (tptp.aa_VEBT_VEBT_bool (tptp.cOMBB_2885587777813823575T_VEBT P Q) R2) (tptp.aa_fun_nat_bool_bool P (tptp.aa_VEB4832260192069861672t_bool Q R2)))) (forall ((P tptp.fun_bo1841576699660343469l_bool) (Q tptp.fun_VEBT_VEBT_bool) (R2 tptp.vEBT_VEBT)) (= (tptp.aa_VEB8047906998784800507l_bool (tptp.cOMBB_3438363824644082366T_VEBT P Q) R2) (tptp.aa_boo8970175072276269406l_bool P (tptp.aa_VEBT_VEBT_bool Q R2)))) (forall ((P tptp.fun_VE7346385682144900493T_bool) (Q tptp.set_VEBT_VEBT) (R2 tptp.vEBT_VEBT)) (= (tptp.aa_VEBT_VEBT_bool (tptp.cOMBC_771164880915498576T_bool P Q) R2) (tptp.aa_set8260762808118238015T_bool (tptp.aa_VEB289770264548726718T_bool P R2) Q))) _let_2 _let_1 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 26.60/26.78 )
% 26.60/26.78 % SZS output end Proof for ITP238_1
% 26.60/26.79 % cvc5---1.0.5 exiting
% 26.60/26.79 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------