TSTP Solution File: ITP280_1 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : ITP280_1 : TPTP v8.1.2. Released v8.0.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n017.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 03:31:01 EDT 2023
% Result : Theorem 19.17s 19.50s
% Output : Proof 19.17s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 3.85/3.98 % Problem : ITP280_1 : TPTP v8.1.2. Released v8.0.0.
% 3.85/3.99 % Command : do_cvc5 %s %d
% 3.99/4.20 % Computer : n017.cluster.edu
% 3.99/4.20 % Model : x86_64 x86_64
% 3.99/4.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 3.99/4.20 % Memory : 8042.1875MB
% 3.99/4.20 % OS : Linux 3.10.0-693.el7.x86_64
% 3.99/4.20 % CPULimit : 300
% 3.99/4.20 % WCLimit : 300
% 3.99/4.20 % DateTime : Sun Aug 27 12:18:15 EDT 2023
% 3.99/4.21 % CPUTime :
% 7.89/8.07 %----Proving TF0_NAR, FOF, or CNF
% 19.17/19.50 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.3yGePsytJ2/cvc5---1.0.5_7015.p...
% 19.17/19.50 ------- get file name : TPTP file name is ITP280_1
% 19.17/19.50 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_7015.smt2...
% 19.17/19.50 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 19.17/19.50 % SZS status Theorem for ITP280_1
% 19.17/19.50 % SZS output start Proof for ITP280_1
% 19.17/19.50 (
% 19.17/19.50 (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.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat tptp.va) _let_2)))) (let ((_let_4 (tptp.aa_nat_nat tptp.suc _let_3))) (let ((_let_5 (tptp.aa_num_num tptp.bit1 tptp.one))) (let ((_let_6 (tptp.aa_num_num tptp.bit0 _let_5))) (let ((_let_7 (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit1 _let_6)))) (let ((_let_8 (tptp.aa_rea7340605660300375871l_real tptp.times_times_real _let_7))) (let ((_let_9 (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.vEBT_V8646137997579335489_i_l_d _let_4))) (tptp.aa_real_real _let_8 (tptp.aa_VEBT_VEBT_real tptp.vEBT_VEBT_cnt (tptp.vEBT_vebt_buildup _let_4))))))) (let ((_let_10 (not _let_9))) (let ((_let_11 (tptp.set_or5849166863359141190n_real tptp.zero_zero_real))) (let ((_let_12 (tptp.topolo2177554685111907308n_real tptp.zero_zero_real _let_11))) (let ((_let_13 (tptp.map_fu3926683916856352828t_real tptp.rep_real tptp.real2))) (let ((_let_14 (tptp.bNF_re9178625837396562677at_rat tptp.realrel tptp.realrel))) (let ((_let_15 (tptp.bNF_re1458715823057739248l_bool tptp.pcr_real tptp.fequal_bool))) (let ((_let_16 (tptp.produc4528391901023682385at_nat tptp.aTP_Lamm_ef))) (let ((_let_17 (tptp.bNF_re2241393799969408733at_nat tptp.intrel tptp.intrel))) (let ((_let_18 (tptp.produc4528391901023682385at_nat tptp.aTP_Lamm_ed))) (let ((_let_19 (tptp.bNF_re1498568104593929552l_bool tptp.pcr_int tptp.fequal_bool))) (let ((_let_20 (tptp.produc5023667602222594023t_bool tptp.aTP_Lamm_eb))) (let ((_let_21 (tptp.bNF_re3189209160384574813l_bool tptp.intrel tptp.fequal_bool))) (let ((_let_22 (tptp.produc5023667602222594023t_bool tptp.aTP_Lamm_dz))) (let ((_let_23 (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat tptp.one_one_nat) tptp.zero_zero_nat))) (let ((_let_24 (tptp.produc6842872674320459806at_nat tptp.minus_minus_nat))) (let ((_let_25 (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat tptp.zero_zero_nat) tptp.zero_zero_nat))) (let ((_let_26 (tptp.produc2626176000494625587at_nat tptp.aTP_Lamm_dx))) (let ((_let_27 (tptp.produc4528391901023682385at_nat tptp.aTP_Lamm_dw))) (let ((_let_28 (tptp.bNF_re237660433471117187t_real tptp.pcr_real tptp.pcr_real))) (let ((_let_29 (tptp.bNF_re7400052026677387805at_int tptp.pcr_int tptp.pcr_int))) (let ((_let_30 (tptp.bNF_re8279943556446156061nt_rat tptp.pcr_rat tptp.pcr_rat))) (let ((_let_31 (tptp.product_Pair_int_int tptp.zero_zero_int tptp.one_one_int))) (let ((_let_32 (tptp.bNF_re7145576690424134365nt_int tptp.ratrel tptp.ratrel))) (let ((_let_33 (tptp.bNF_re5653821019739307937at_nat tptp.fequal_nat tptp.fequal_nat))) (let ((_let_34 (tptp.bNF_re4712519889275205905nt_int tptp.fequal_int tptp.fequal_int))) (let ((_let_35 (tptp.map_fu5673905371560938248nt_rat tptp.rep_Rat tptp.abs_Rat))) (let ((_let_36 (tptp.map_fu6608131713810608381l_bool tptp.rep_Integ tptp.id_bool))) (let ((_let_37 (tptp.aa_num_num tptp.bit0 _let_1))) (let ((_let_38 (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_37))))))))) (let ((_let_39 (tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat _let_38))) (let ((_let_40 (tptp.aa_num_real tptp.numeral_numeral_real _let_1))) (let ((_let_41 (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi))) (let ((_let_42 (tptp.aa_real_real _let_41 _let_40))) (let ((_let_43 (tptp.topolo2815343760600316023s_real tptp.zero_zero_real))) (let ((_let_44 (tptp.image_nat_nat tptp.suc tptp.top_top_set_nat))) (let ((_let_45 (tptp.aa_real_real tptp.uminus_uminus_real _let_42))) (let ((_let_46 (tptp.map_fu3667384564859982768at_int tptp.rep_Integ tptp.abs_Integ))) (let ((_let_47 (tptp.comp_nat_nat_nat tptp.suc tptp.suc))) (let ((_let_48 (tptp.numera6620942414471956472nteger _let_1))) (let ((_let_49 (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger))) (let ((_let_50 (= (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger))) (let ((_let_51 (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (let ((_let_52 (tptp.power_power_nat _let_2))) (let ((_let_53 (tptp.the_real tptp.aTP_Lamm_bz))) (let ((_let_54 (tptp.aa_rea7340605660300375871l_real tptp.times_times_real _let_40))) (let ((_let_55 (tptp.aa_num_real tptp.numeral_numeral_real _let_37))) (let ((_let_56 (tptp.aa_real_real _let_41 _let_55))) (let ((_let_57 (tptp.vEBT_Leaf tptp.fFalse tptp.fFalse))) (let ((_let_58 (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat))) (let ((_let_59 (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int))) (let ((_let_60 (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (let ((_let_61 (tptp.aa_int_int tptp.bit_ri7919022796975470100ot_int tptp.zero_zero_int))) (let ((_let_62 (tptp.aa_int_int tptp.bit_ri7919022796975470100ot_int tptp.one_one_int))) (let ((_let_63 (tptp.aa_num_int tptp.numeral_numeral_int _let_1))) (let ((_let_64 (tptp.aa_int_int tptp.uminus_uminus_int _let_63))) (let ((_let_65 (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger _let_48))) (let ((_let_66 (tptp.aa_num_rat tptp.numeral_numeral_rat tptp.one))) (let ((_let_67 (tptp.numera6690914467698888265omplex tptp.one))) (let ((_let_68 (tptp.aa_num_real tptp.numeral_numeral_real tptp.one))) (let ((_let_69 (= (tptp.aa_rat_rat tptp.inverse_inverse_rat tptp.zero_zero_rat) tptp.zero_zero_rat))) (let ((_let_70 (= (tptp.invers8013647133539491842omplex tptp.zero_zero_complex) tptp.zero_zero_complex))) (let ((_let_71 (= (tptp.aa_real_real tptp.inverse_inverse_real tptp.zero_zero_real) tptp.zero_zero_real))) (let ((_let_72 (tptp.aa_real_real _let_54 tptp.pi))) (let ((_let_73 (tptp.uminus1482373934393186551omplex tptp.imaginary_unit))) (let ((_let_74 (tptp.aa_real_real tptp.sqrt _let_40))) (let ((_let_75 (tptp.uminus1482373934393186551omplex tptp.one_one_complex))) (let ((_let_76 (tptp.numera6690914467698888265omplex _let_1))) (let ((_let_77 (tptp.real_V4546457046886955230omplex tptp.pi))) (let ((_let_78 (tptp.divide1717551699836669952omplex _let_77 _let_76))) (let ((_let_79 (tptp.aa_real_real tptp.real_V1803761363581548252l_real tptp.pi))) (let ((_let_80 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real _let_79) _let_40))) (let ((_let_81 (tptp.aa_num_real tptp.numeral_numeral_real _let_5))) (let ((_let_82 (tptp.aa_real_real tptp.sqrt _let_81))) (let ((_let_83 (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.one_one_real))) (let ((_let_84 (tptp.aa_real_real _let_41 (tptp.aa_num_real tptp.numeral_numeral_real _let_6)))) (let ((_let_85 (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real))) (let ((_let_86 (tptp.aa_real_real _let_41 _let_81))) (let ((_let_87 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real _let_82) _let_40))) (let ((_let_88 (tptp.aa_real_real _let_83 _let_40))) (let ((_let_89 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real _let_74) _let_40))) (let ((_let_90 (tptp.aa_real_real tptp.cos_real _let_40))) (let ((_let_91 (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real _let_81))) (let ((_let_92 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real _let_91 _let_40)) tptp.pi))) (let ((_let_93 (tptp.aa_num_num tptp.bit1 _let_5))) (let ((_let_94 (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit1 _let_1)))) (let ((_let_95 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (let ((_let_96 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real))) (let ((_let_97 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.pi))) (let ((_let_98 (tptp.aa_nat_nat tptp.suc _let_58))) (let ((_let_99 (tptp.aa_int_nat tptp.nat2 tptp.one_one_int))) (let ((_let_100 (tptp.aa_rat_rat tptp.uminus_uminus_rat tptp.one_one_rat))) (let ((_let_101 (= (tptp.aa_real_real tptp.sgn_sgn_real tptp.zero_zero_real) tptp.zero_zero_real))) (let ((_let_102 (= (tptp.sgn_sgn_complex tptp.zero_zero_complex) tptp.zero_zero_complex))) (let ((_let_103 (tptp.aa_num_rat tptp.numeral_numeral_rat _let_5))) (let ((_let_104 (tptp.numera6690914467698888265omplex _let_5))) (let ((_let_105 (tptp.aa_num_int tptp.numeral_numeral_int _let_5))) (let ((_let_106 (tptp.aa_num_int tptp.numeral_numeral_int tptp.one))) (let ((_let_107 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat _let_100))) (let ((_let_108 (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger _let_60))) (let ((_let_109 (tptp.aa_int_fun_int_bool tptp.ord_less_int _let_59))) (let ((_let_110 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real _let_85))) (let ((_let_111 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat))) (let ((_let_112 (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int))) (let ((_let_113 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_114 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat))) (let ((_let_115 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real _let_85))) (let ((_let_116 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int _let_59))) (let ((_let_117 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat _let_100))) (let ((_let_118 (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger _let_60))) (let ((_let_119 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.one_one_rat))) (let ((_let_120 (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.one_one_int))) (let ((_let_121 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real))) (let ((_let_122 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.one_one_real))) (let ((_let_123 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.one_one_int))) (let ((_let_124 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.one_one_rat))) (let ((_let_125 (= (tptp.aa_int_int tptp.uminus_uminus_int tptp.zero_zero_int) tptp.zero_zero_int))) (let ((_let_126 (= (tptp.aa_int_int tptp.abs_abs_int tptp.one_one_int) tptp.one_one_int))) (let ((_let_127 (= (tptp.aa_rat_rat tptp.abs_abs_rat tptp.one_one_rat) tptp.one_one_rat))) (let ((_let_128 (= (tptp.aa_real_real tptp.abs_abs_real tptp.one_one_real) tptp.one_one_real))) (let ((_let_129 (= (tptp.abs_abs_Code_integer tptp.one_one_Code_integer) tptp.one_one_Code_integer))) (let ((_let_130 (tptp.aa_num_rat tptp.numeral_numeral_rat _let_1))) (let ((_let_131 (tptp.aa_rat_rat tptp.uminus_uminus_rat _let_130))) (let ((_let_132 (tptp.uminus1482373934393186551omplex _let_76))) (let ((_let_133 (tptp.aa_real_real tptp.uminus_uminus_real _let_40))) (let ((_let_134 (= (tptp.modulo364778990260209775nteger _let_60 _let_48) tptp.one_one_Code_integer))) (let ((_let_135 (= (tptp.modulo_modulo_int _let_59 _let_63) tptp.one_one_int))) (let ((_let_136 (tptp.minus_minus_rat _let_100))) (let ((_let_137 (tptp.aa_int_fun_int_int tptp.minus_minus_int _let_59))) (let ((_let_138 (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real _let_85))) (let ((_let_139 (tptp.minus_minus_rat tptp.one_one_rat))) (let ((_let_140 (tptp.aa_int_fun_int_int tptp.minus_minus_int tptp.one_one_int))) (let ((_let_141 (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real tptp.one_one_real))) (let ((_let_142 (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat _let_100))) (let ((_let_143 (tptp.aa_int_fun_int_int tptp.plus_plus_int _let_59))) (let ((_let_144 (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real _let_85))) (let ((_let_145 (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat tptp.one_one_rat))) (let ((_let_146 (tptp.aa_int_fun_int_int tptp.plus_plus_int tptp.one_one_int))) (let ((_let_147 (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real tptp.one_one_real))) (let ((_let_148 (= (tptp.aa_int_int tptp.abs_abs_int tptp.zero_zero_int) tptp.zero_zero_int))) (let ((_let_149 (= (tptp.aa_rat_rat tptp.abs_abs_rat tptp.zero_zero_rat) tptp.zero_zero_rat))) (let ((_let_150 (= (tptp.aa_real_real tptp.abs_abs_real tptp.zero_zero_real) tptp.zero_zero_real))) (let ((_let_151 (= (tptp.abs_abs_Code_integer tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger))) (let ((_let_152 (tptp.vEBT_vebt_buildup _let_3))) (let ((_let_153 (= (tptp.modulo364778990260209775nteger tptp.one_one_Code_integer _let_48) tptp.one_one_Code_integer))) (let ((_let_154 (= (tptp.modulo_modulo_int tptp.one_one_int _let_63) tptp.one_one_int))) (let ((_let_155 (tptp.aa_nat_nat (tptp.modulo_modulo_nat tptp.one_one_nat) _let_2))) (let ((_let_156 (= _let_155 tptp.one_one_nat))) (let ((_let_157 (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat tptp.one_one_nat))) (let ((_let_158 (tptp.aa_nat_nat _let_157 tptp.one_one_nat))) (let ((_let_159 (= _let_158 _let_2))) (let ((_let_160 (tptp.aa_int_int _let_146 tptp.one_one_int))) (let ((_let_161 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat))) (let ((_let_162 (tptp.aa_rat_rat _let_145 tptp.one_one_rat))) (let ((_let_163 (tptp.aa_real_real _let_147 tptp.one_one_real))) (let ((_let_164 (= _let_157 tptp.suc))) (let ((_let_165 (= (tptp.aa_nat_int tptp.semiri1314217659103216013at_int tptp.one_one_nat) tptp.one_one_int))) (let ((_let_166 (not (tptp.pp (tptp.aa_int_bool _let_112 tptp.zero_zero_int))))) (let ((_let_167 (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int _let_63))) (let ((_let_168 (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat _let_2))) (let ((_let_169 (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer _let_48))) (let ((_let_170 (tptp.aa_num_nat tptp.numeral_numeral_nat tptp.one))) (let ((_let_171 (= _let_170 tptp.one_one_nat))) (let ((_let_172 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.one_one_nat))) (let ((_let_173 (tptp.pp (tptp.aa_real_bool _let_95 tptp.one_one_real)))) (let ((_let_174 (tptp.pp (tptp.aa_int_bool _let_113 tptp.one_one_int)))) (let ((_let_175 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat))) (let ((_let_176 (tptp.pp (tptp.aa_nat_bool _let_175 tptp.one_one_nat)))) (let ((_let_177 (tptp.pp (tptp.aa_rat_bool _let_114 tptp.one_one_rat)))) (let ((_let_178 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.one_one_nat))) (let ((_let_179 (tptp.pp (tptp.aa_int_bool _let_112 tptp.one_one_int)))) (let ((_let_180 (tptp.pp (tptp.aa_nat_bool _let_161 tptp.one_one_nat)))) (let ((_let_181 (tptp.pp (tptp.aa_rat_bool _let_111 tptp.one_one_rat)))) (let ((_let_182 (tptp.pp (tptp.aa_real_bool _let_96 tptp.one_one_real)))) (let ((_let_183 (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int tptp.one_one_int) _let_63) tptp.zero_zero_int))) (let ((_let_184 (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat tptp.one_one_nat) _let_2) tptp.zero_zero_nat))) (let ((_let_185 (tptp.aa_num_nat tptp.numeral_numeral_nat _let_5))) (let ((_let_186 (forall ((A tptp.real) (B tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) B) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real B) A))))) (let ((_let_187 (= (tptp.aa_nat_int tptp.semiri1314217659103216013at_int tptp.zero_zero_nat) tptp.zero_zero_int))) (let ((_let_188 (tptp.pp (tptp.aa_int_bool _let_113 tptp.zero_zero_int)))) (let ((_let_189 (tptp.aa_num_nat tptp.numeral_numeral_nat _let_37))) (let ((_let_190 (= _let_170 _let_58))) (let ((_let_191 (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))))))) (let ((_let_192 (forall ((X tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc X))) (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.suc (tptp.aa_nat_nat tptp.suc tptp.va)))) (=> (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat _let_2) _let_3))) (=> (= X (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat _let_3) _let_2)) (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.vEBT_V8646137997579335489_i_l_d _let_1))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_VEBT_VEBT_real tptp.vEBT_VEBT_cnt (tptp.vEBT_vebt_buildup _let_1))) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit1 tptp.one))))))))))))))) (let ((_let_193 (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat tptp.suc tptp.va)))) (let ((_let_194 (tptp.pp (tptp.aa_nat_bool _let_168 _let_193)))) (let ((_let_195 (not _let_194))) (let ((_let_196 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat _let_193) _let_2))) (let ((_let_197 (tptp.aa_nat_nat tptp.suc _let_196))) (let ((_let_198 (tptp.aa_VEBT_VEBT_real tptp.vEBT_VEBT_cnt (tptp.vEBT_vebt_buildup _let_197)))) (let ((_let_199 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real _let_198) _let_7))) (let ((_let_200 (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.vEBT_V8646137997579335489_i_l_d _let_197))) _let_199)))) (let ((_let_201 (= tptp.one_one_nat _let_170))) (let ((_let_202 (= tptp.suc _let_157))) (let ((_let_203 (= tptp.one_one_nat _let_155))) (let ((_let_204 (= _let_196 _let_3))) (let ((_let_205 (= _let_199 (tptp.aa_real_real _let_8 _let_198)))) (let ((_let_206 (ASSUME :args (_let_190)))) (let ((_let_207 (SYMM (ASSUME :args (_let_171))))) (let ((_let_208 (SYMM (ASSUME :args (_let_164))))) (let ((_let_209 (SYMM (ASSUME :args (_let_156))))) (let ((_let_210 (ASSUME :args (_let_10)))) (let ((_let_211 (_let_191))) (let ((_let_212 (ASSUME :args _let_211))) (let ((_let_213 (_let_186))) (let ((_let_214 (ASSUME :args _let_213))) (let ((_let_215 (not _let_205))) (let ((_let_216 (not _let_204))) (let ((_let_217 (not _let_203))) (let ((_let_218 (not _let_202))) (let ((_let_219 (not _let_201))) (let ((_let_220 (not _let_190))) (let ((_let_221 (not _let_200))) (let ((_let_222 (APPLY_UF tptp.aa_nat_nat))) (let ((_let_223 (SYMM _let_208))) (let ((_let_224 (CONG _let_223 (REFL :args (_let_3)) :args _let_222))) (let ((_let_225 (ASSUME :args (_let_204)))) (let ((_let_226 (APPLY_UF tptp.aa_nat_fun_nat_nat))) (let ((_let_227 (REFL :args (tptp.plus_plus_nat)))) (let ((_let_228 (CONG _let_227 (TRANS (SYMM _let_206) (SYMM _let_207)) :args _let_226))) (let ((_let_229 (CONG _let_228 (SYMM (SYMM _let_225)) :args _let_222))) (let ((_let_230 (REFL :args (_let_196)))) (let ((_let_231 (TRANS (CONG _let_227 (SYMM _let_209) :args _let_226) _let_223))) (let ((_let_232 (CONG (TRANS _let_231 (SYMM (TRANS _let_228 _let_223))) _let_230 :args _let_222))) (let ((_let_233 (CONG (SYMM _let_231) _let_230 :args _let_222))) (let ((_let_234 (ASSUME :args (_let_205)))) (let ((_let_235 (CONG _let_223 _let_230 :args _let_222))) (let ((_let_236 (REFL :args (tptp.vEBT_V8646137997579335489_i_l_d)))) (let ((_let_237 (ASSUME :args (_let_200)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_210 _let_208 _let_207 _let_206 _let_225 _let_209 _let_234 _let_237) :args (_let_190 _let_10 _let_200 _let_201 _let_202 _let_203 _let_204 _let_205)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (TRUE_INTRO _let_237)) (CONG (CONG (CONG (REFL :args (tptp.ord_less_eq_real)) (CONG (REFL :args (tptp.semiri5074537144036343181t_real)) (TRANS (CONG _let_236 (SYMM _let_235) :args _let_222) (CONG _let_236 (TRANS _let_235 _let_233 _let_232 _let_229 _let_224) :args _let_222)) :args (APPLY_UF tptp.aa_nat_real)) :args (APPLY_UF tptp.aa_rea7809428808904475482l_bool)) (TRANS (SYMM (SYMM _let_234)) (CONG (REFL :args (_let_8)) (CONG (REFL :args (tptp.vEBT_VEBT_cnt)) (CONG (TRANS _let_233 _let_232 _let_229 _let_224) :args (APPLY_UF tptp.vEBT_vebt_buildup)) :args (APPLY_UF tptp.aa_VEBT_VEBT_real)) :args (APPLY_UF tptp.aa_real_real))) :args (APPLY_UF tptp.aa_real_bool)) :args (APPLY_UF tptp.pp)) (FALSE_INTRO _let_210))) :args (_let_10 _let_202 _let_201 _let_190 _let_204 _let_203 _let_205 _let_200)) :args ((not (and _let_190 _let_10 _let_200 _let_201 _let_202 _let_203 _let_204 _let_205)) SB_LITERAL))) (CONG (REFL :args (_let_220)) (MACRO_SR_PRED_INTRO :args ((= (not _let_10) _let_9))) (REFL :args (_let_221)) (REFL :args (_let_219)) (REFL :args (_let_218)) (REFL :args (_let_217)) (REFL :args (_let_216)) (REFL :args (_let_215)) :args (or))) :args ((or _let_9 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_214 :args (_let_198 _let_7 QUANTIFIERS_INST_E_MATCHING ((tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) B)))) :args _let_213)) _let_214 :args (_let_205 false _let_186)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_212 :args (tptp.va QUANTIFIERS_INST_E_MATCHING ((tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat tptp.suc M))))) :args _let_211)) _let_212 :args (_let_204 false _let_191)) _let_210 _let_209 _let_208 _let_207 _let_206 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (ASSUME :args (_let_192)) (MACRO_SR_EQ_INTRO :args (_let_192 SB_DEFAULT SBA_FIXPOINT))) (ASSUME :args (_let_195)) :args (_let_200 true _let_194)) :args (false false _let_205 false _let_204 true _let_9 false _let_203 false _let_202 false _let_201 false _let_190 false _let_200)) :args (_let_195 _let_192 (forall ((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.suc (tptp.aa_nat_nat tptp.suc tptp.va)))) (=> (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat _let_1) _let_2))) (=> (= X (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat _let_2) _let_1)) (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.vEBT_V8646137997579335489_i_l_d X))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_VEBT_VEBT_real tptp.vEBT_VEBT_cnt (tptp.vEBT_vebt_buildup X))) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit1 tptp.one)))))))))))) (forall ((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.suc (tptp.aa_nat_nat tptp.suc tptp.va)))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat _let_1) _let_2)) (=> (= X (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat _let_2) _let_1)) (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.vEBT_V8646137997579335489_i_l_d X))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_VEBT_VEBT_real tptp.vEBT_VEBT_cnt (tptp.vEBT_vebt_buildup X))) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit1 tptp.one)))))))))))) (forall ((T tptp.vEBT_VEBT)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real (tptp.aa_VEBT_VEBT_nat tptp.vEBT_VEBT_space2 T))) (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.bit1 tptp.one)))) (tptp.aa_VEBT_VEBT_real tptp.vEBT_VEBT_cnt T))))) _let_191 (forall ((B 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 B) _let_1)) A)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real B) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) _let_1)))))) (forall ((B 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 B) _let_1)) A)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) _let_1)))))) (forall ((A tptp.real) (B 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 B) _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)) B))))) (forall ((A tptp.rat) (B 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 B) _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)) B))))) (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_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)) (= (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)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat N))) (= (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat _let_1) _let_1))) (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.num)) (not (= (tptp.aa_num_num tptp.bit1 M) tptp.one))) (forall ((N tptp.num)) (not (= tptp.one (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 ((M tptp.num) (N tptp.num)) (not (= (tptp.aa_num_num tptp.bit0 M) (tptp.aa_num_num tptp.bit1 N)))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat M) N)) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex M)) (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex 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_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_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 ((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 ((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.aa_int_fun_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 ((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.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.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.aa_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.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.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) (N tptp.num)) (= (= (tptp.aa_num_num tptp.bit0 M) (tptp.aa_num_num tptp.bit0 N)) (= M N))) (forall ((M tptp.num)) (= (tptp.aa_num_num (tptp.times_times_num M) tptp.one) M)) (forall ((N tptp.num)) (= (tptp.aa_num_num (tptp.times_times_num tptp.one) N) N)) (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 ((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 ((M tptp.nat) (N tptp.nat)) (= (= (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex M) (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex 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_rat tptp.semiri681578069525770553at_rat M) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat 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) (N tptp.nat)) (= (= (tptp.aa_nat_int tptp.semiri1314217659103216013at_int M) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N)) (= 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.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.aa_num_num tptp.bit1 M) (tptp.aa_num_num tptp.bit1 N)) (= 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_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 ((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.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.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.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.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.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.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.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.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.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.times_times_num M) N)))) (forall ((N tptp.num)) (= (tptp.aa_num_num (tptp.times_times_num (tptp.aa_num_num tptp.bit0 tptp.one)) N) (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 ((N tptp.num)) (not (= tptp.one (tptp.aa_num_num tptp.bit0 N)))) (forall ((M tptp.num)) (not (= (tptp.aa_num_num tptp.bit0 M) tptp.one))) (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit1 N))) (= (tptp.aa_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.times_times_num M) _let_1))))) (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (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)) (= (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)) (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.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)) (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 ((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 ((A tptp.complex) (P tptp.fun_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.set_nat) (P tptp.fun_set_nat_bool)) (= (tptp.member_set_nat A (tptp.collect_set_nat P)) (tptp.pp (tptp.aa_set_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.member_int A (tptp.collect_int P)) (tptp.pp (tptp.aa_int_bool P A)))) (forall ((A2 tptp.set_complex)) (= (tptp.collect_complex (tptp.aTP_Lamm_a A2)) A2)) (forall ((A2 tptp.set_real)) (= (tptp.collect_real (tptp.aTP_Lamm_aa A2)) A2)) (forall ((A2 tptp.set_list_nat)) (= (tptp.collect_list_nat (tptp.aTP_Lamm_ab A2)) A2)) (forall ((A2 tptp.set_set_nat)) (= (tptp.collect_set_nat (tptp.aTP_Lamm_ac A2)) A2)) (forall ((A2 tptp.set_nat)) (= (tptp.collect_nat (tptp.aTP_Lamm_ad A2)) A2)) (forall ((A2 tptp.set_int)) (= (tptp.collect_int (tptp.aTP_Lamm_ae A2)) A2)) (forall ((P tptp.fun_real_bool) (Q tptp.fun_real_bool)) (=> (forall ((X3 tptp.real)) (= (tptp.pp (tptp.aa_real_bool P X3)) (tptp.pp (tptp.aa_real_bool Q X3)))) (= (tptp.collect_real P) (tptp.collect_real Q)))) (forall ((P tptp.fun_list_nat_bool) (Q tptp.fun_list_nat_bool)) (=> (forall ((X3 tptp.list_nat)) (= (tptp.pp (tptp.aa_list_nat_bool P X3)) (tptp.pp (tptp.aa_list_nat_bool Q X3)))) (= (tptp.collect_list_nat P) (tptp.collect_list_nat Q)))) (forall ((P tptp.fun_set_nat_bool) (Q tptp.fun_set_nat_bool)) (=> (forall ((X3 tptp.set_nat)) (= (tptp.pp (tptp.aa_set_nat_bool P X3)) (tptp.pp (tptp.aa_set_nat_bool Q X3)))) (= (tptp.collect_set_nat P) (tptp.collect_set_nat Q)))) (forall ((P tptp.fun_nat_bool) (Q tptp.fun_nat_bool)) (=> (forall ((X3 tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool P X3)) (tptp.pp (tptp.aa_nat_bool Q X3)))) (= (tptp.collect_nat P) (tptp.collect_nat Q)))) (forall ((P tptp.fun_int_bool) (Q tptp.fun_int_bool)) (=> (forall ((X3 tptp.int)) (= (tptp.pp (tptp.aa_int_bool P X3)) (tptp.pp (tptp.aa_int_bool Q X3)))) (= (tptp.collect_int P) (tptp.collect_int Q)))) (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)) (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) (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)) (=> (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 ((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 ((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)) (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 ((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 ((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 ((P tptp.fun_nat_bool) (K tptp.nat) (B tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool P K)) (=> (forall ((Y tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool P Y)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Y) B)))) (exists ((X3 tptp.nat)) (and (tptp.pp (tptp.aa_nat_bool P X3)) (forall ((Y3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool P Y3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Y3) X3))))))))) (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 ((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 ((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 ((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 ((M tptp.nat) (N tptp.nat) (R 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 ((X3 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool R X3) X3))) (=> (forall ((X3 tptp.nat) (Y tptp.nat) (Z2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool R X3))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 Y)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool R Y) Z2)) (tptp.pp (tptp.aa_nat_bool _let_1 Z2)))))) (=> (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool R N2) (tptp.aa_nat_nat tptp.suc N2)))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool R M) 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 ((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)) (= (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 ((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)) (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) (M3 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)) M3)) (exists ((M4 tptp.nat)) (= M3 (tptp.aa_nat_nat tptp.suc M4))))) (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 ((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)) (=> (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) (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 ((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))))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.semiri4939895301339042750nteger M)) (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_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)))) (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 ((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.times_times_num K) L)))))) (forall ((A tptp.int) (K tptp.num) (L tptp.num)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.divide_divide_int A))) (= (tptp.aa_int_int (tptp.aa_int_fun_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.times_times_num K) 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.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)) (not (= N (tptp.aa_nat_nat tptp.suc N)))) (forall ((X tptp.nat) (Y4 tptp.nat)) (=> (= (tptp.aa_nat_nat tptp.suc X) (tptp.aa_nat_nat tptp.suc Y4)) (= X Y4))) (forall ((F tptp.fun_nat_set_int) (N tptp.nat) (N3 tptp.nat)) (=> (forall ((N2 tptp.nat)) (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) N3)) (tptp.ord_less_eq_set_int (tptp.aa_nat_set_int F N3) (tptp.aa_nat_set_int F N))))) (forall ((F tptp.fun_nat_rat) (N tptp.nat) (N3 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) N3)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat F N3)) (tptp.aa_nat_rat F N)))))) (forall ((F tptp.fun_nat_num) (N tptp.nat) (N3 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) N3)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_nat_num F N3)) (tptp.aa_nat_num F N)))))) (forall ((F tptp.fun_nat_nat) (N tptp.nat) (N3 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) N3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat F N3)) (tptp.aa_nat_nat F N)))))) (forall ((F tptp.fun_nat_int) (N tptp.nat) (N3 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) N3)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int F N3)) (tptp.aa_nat_int F N)))))) (forall ((F tptp.fun_nat_real) (N tptp.nat) (N3 tptp.nat)) (=> (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_nat_real F (tptp.aa_nat_nat tptp.suc N2))) (tptp.aa_nat_real F N2)))) (=> (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.aa_nat_real F N3)) (tptp.aa_nat_real F N)))))) (forall ((F tptp.fun_nat_set_int) (N tptp.nat) (N3 tptp.nat)) (=> (forall ((N2 tptp.nat)) (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) N3)) (tptp.ord_less_eq_set_int (tptp.aa_nat_set_int F N) (tptp.aa_nat_set_int F N3))))) (forall ((F tptp.fun_nat_rat) (N tptp.nat) (N3 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) N3)) (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 N3)))))) (forall ((F tptp.fun_nat_num) (N tptp.nat) (N3 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) N3)) (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 N3)))))) (forall ((F tptp.fun_nat_nat) (N tptp.nat) (N3 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) N3)) (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 N3)))))) (forall ((F tptp.fun_nat_int) (N tptp.nat) (N3 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) N3)) (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 N3)))))) (forall ((F tptp.fun_nat_real) (N tptp.nat) (N3 tptp.nat)) (=> (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))))) (=> (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.aa_nat_real F N)) (tptp.aa_nat_real F N3)))))) (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 ((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 ((X tptp.nat) (Y4 tptp.complex)) (let ((_let_1 (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex X))) (= (tptp.aa_complex_complex (tptp.times_times_complex _let_1) Y4) (tptp.aa_complex_complex (tptp.times_times_complex Y4) _let_1)))) (forall ((X tptp.nat) (Y4 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) Y4) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real Y4) _let_1)))) (forall ((X tptp.nat) (Y4 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) Y4) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat Y4) _let_1)))) (forall ((X tptp.nat) (Y4 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) Y4) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat Y4) _let_1)))) (forall ((X tptp.nat) (Y4 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) Y4) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int Y4) _let_1)))) (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 ((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.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 ((Y4 tptp.num)) (=> (not (= Y4 tptp.one)) (=> (forall ((X22 tptp.num)) (not (= Y4 (tptp.aa_num_num tptp.bit0 X22)))) (not (forall ((X32 tptp.num)) (not (= Y4 (tptp.aa_num_num tptp.bit1 X32)))))))) (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 ((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.aa_int_fun_int_int 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.aa_int_fun_int_int tptp.divide_divide_int (tptp.aa_int_int _let_3 _let_2)) _let_1)))))) (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.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.aa_int_fun_int_int tptp.divide_divide_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int M)) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N)))) (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.aa_int_fun_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 ((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 ((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.numera6620942414471956472nteger _let_1)) (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_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 ((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_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.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)) (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 ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_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) B))) (or (tptp.pp (tptp.aa_Code_integer_bool _let_1 A)) (tptp.pp (tptp.aa_Code_integer_bool _let_1 B)))))) (forall ((A tptp.nat) (B 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) B))) (or (tptp.pp (tptp.aa_nat_bool _let_1 A)) (tptp.pp (tptp.aa_nat_bool _let_1 B)))))) (forall ((A tptp.int) (B 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) B))) (or (tptp.pp (tptp.aa_int_bool _let_1 A)) (tptp.pp (tptp.aa_int_bool _let_1 B)))))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer A) B)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) (tptp.divide6298287555418463151nteger B A)) B))) (forall ((A tptp.nat) (B tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat A) B)) (= (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 B) A)) B))) (forall ((A tptp.int) (B tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int A) B)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int B) A)) B))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer A) B)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.divide6298287555418463151nteger B A)) A) B))) (forall ((A tptp.nat) (B tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat A) B)) (= (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 B) A)) A) B))) (forall ((A tptp.int) (B tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int A) B)) (= (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.divide_divide_int B) A)) A) B))) (forall ((A tptp.code_integer)) (let ((_let_1 (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.aa_int_fun_int_int tptp.divide_divide_int A) _let_1)) A)))) (forall ((X tptp.nat) (Y4 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 Y4) _let_1)) (=> (= (tptp.pp (tptp.aa_nat_bool _let_2 X)) (tptp.pp (tptp.aa_nat_bool _let_2 Y4))) (= X Y4)))))) (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 ((A tptp.code_integer) (B 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 B)) (=> (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 B A)) (tptp.divide6298287555418463151nteger C A))) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer B) C))))))) (forall ((A tptp.nat) (B 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 B)) (=> (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 B) 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 B) C))))))) (forall ((A tptp.int) (B 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 B)) (=> (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.aa_int_fun_int_int tptp.divide_divide_int B) A)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int C) A))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int B) C))))))) (forall ((A tptp.nat) (B 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 B)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat B) C)) (tptp.pp (tptp.aa_nat_bool _let_1 C)))))) (forall ((A tptp.int) (B 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 B)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int B) C)) (tptp.pp (tptp.aa_int_bool _let_1 C)))))) (forall ((A tptp.code_integer) (B 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 B)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer B) 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 ((S tptp.set_real)) (=> (exists ((X4 tptp.real)) (tptp.member_real X4 S)) (=> (exists ((Z3 tptp.real)) (forall ((X3 tptp.real)) (=> (tptp.member_real X3 S) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X3) Z3))))) (exists ((Y tptp.real)) (and (forall ((X4 tptp.real)) (=> (tptp.member_real X4 S) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X4) Y)))) (forall ((Z3 tptp.real)) (=> (forall ((X3 tptp.real)) (=> (tptp.member_real X3 S) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X3) Z3)))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y) Z3))))))))) (forall ((B tptp.code_integer) (A tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer B) A)) (not (forall ((K2 tptp.code_integer)) (not (= A (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B) K2))))))) (forall ((B tptp.real) (A tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.dvd_dvd_real B) A)) (not (forall ((K2 tptp.real)) (not (= A (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real B) K2))))))) (forall ((B tptp.rat) (A tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.dvd_dvd_rat B) A)) (not (forall ((K2 tptp.rat)) (not (= A (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat B) K2))))))) (forall ((B tptp.nat) (A tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat B) A)) (not (forall ((K2 tptp.nat)) (not (= A (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B) K2))))))) (forall ((B tptp.int) (A tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int B) A)) (not (forall ((K2 tptp.int)) (not (= A (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B) K2))))))) (forall ((A tptp.code_integer) (B tptp.code_integer) (K tptp.code_integer)) (=> (= A (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B) K)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer B) A)))) (forall ((A tptp.real) (B tptp.real) (K tptp.real)) (=> (= A (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real B) K)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.dvd_dvd_real B) A)))) (forall ((A tptp.rat) (B tptp.rat) (K tptp.rat)) (=> (= A (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat B) K)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.dvd_dvd_rat B) A)))) (forall ((A tptp.nat) (B tptp.nat) (K tptp.nat)) (=> (= A (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B) K)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat B) A)))) (forall ((A tptp.int) (B tptp.int) (K tptp.int)) (=> (= A (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B) K)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int B) A)))) (forall ((B tptp.code_integer) (A tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer B) A)) (exists ((K3 tptp.code_integer)) (= A (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B) K3))))) (forall ((B tptp.real) (A tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.dvd_dvd_real B) A)) (exists ((K3 tptp.real)) (= A (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real B) K3))))) (forall ((B tptp.rat) (A tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.dvd_dvd_rat B) A)) (exists ((K3 tptp.rat)) (= A (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat B) K3))))) (forall ((B tptp.nat) (A tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat B) A)) (exists ((K3 tptp.nat)) (= A (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B) K3))))) (forall ((B tptp.int) (A tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int B) A)) (exists ((K3 tptp.int)) (= A (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B) K3))))) (forall ((A tptp.code_integer) (C tptp.code_integer) (B 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 B) C)))))) (forall ((A tptp.real) (C tptp.real) (B 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 B) C)))))) (forall ((A tptp.rat) (C tptp.rat) (B 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 B) C)))))) (forall ((A tptp.nat) (C tptp.nat) (B 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 B) C)))))) (forall ((A tptp.int) (C tptp.int) (B 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 B) C)))))) (forall ((A tptp.code_integer) (B 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 B)) (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B) C)))))) (forall ((A tptp.real) (B 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 B)) (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real B) C)))))) (forall ((A tptp.rat) (B 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 B)) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat B) C)))))) (forall ((A tptp.nat) (B 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 B)) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B) C)))))) (forall ((A tptp.int) (B 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 B)) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B) C)))))) (forall ((A tptp.code_integer) (B 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) B)) C)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer A) C)))) (forall ((A tptp.real) (B 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) B)) C)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.dvd_dvd_real A) C)))) (forall ((A tptp.rat) (B 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) B)) C)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.dvd_dvd_rat A) C)))) (forall ((A tptp.nat) (B 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) B)) C)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat A) C)))) (forall ((A tptp.int) (B 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) B)) C)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int A) C)))) (forall ((A tptp.code_integer) (B 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) B)))) (forall ((A tptp.real) (B 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) B)))) (forall ((A tptp.rat) (B 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) B)))) (forall ((A tptp.nat) (B 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) B)))) (forall ((A tptp.int) (B 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) B)))) (forall ((A tptp.code_integer) (B 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) B)) (=> (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 B) D)))))) (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.dvd_dvd_real A) B)) (=> (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 B) D)))))) (forall ((A tptp.rat) (B 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) B)) (=> (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 B) D)))))) (forall ((A tptp.nat) (B 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) B)) (=> (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 B) D)))))) (forall ((A tptp.int) (B 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) B)) (=> (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 B) D)))))) (forall ((A tptp.code_integer) (B 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) B)) C)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer B) C)))) (forall ((A tptp.real) (B 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) B)) C)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.dvd_dvd_real B) C)))) (forall ((A tptp.rat) (B 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) B)) C)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.dvd_dvd_rat B) C)))) (forall ((A tptp.nat) (B 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) B)) C)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat B) C)))) (forall ((A tptp.int) (B 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) B)) C)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int B) C)))) (forall ((A tptp.code_integer) (B 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 B) A)))) (forall ((A tptp.real) (B 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 B) A)))) (forall ((A tptp.rat) (B 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 B) A)))) (forall ((A tptp.nat) (B 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 B) A)))) (forall ((A tptp.int) (B 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 B) A)))) (forall ((C tptp.code_integer) (A tptp.code_integer) (B 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 B)) (= (= (tptp.divide6298287555418463151nteger A C) (tptp.divide6298287555418463151nteger B C)) (= A B)))))) (forall ((C tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (tptp.dvd_dvd_complex C))) (=> (tptp.pp (tptp.aa_complex_bool _let_1 A)) (=> (tptp.pp (tptp.aa_complex_bool _let_1 B)) (= (= (tptp.divide1717551699836669952omplex A C) (tptp.divide1717551699836669952omplex B C)) (= A B)))))) (forall ((C tptp.real) (A tptp.real) (B 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 B)) (= (= (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 B) C)) (= A B)))))) (forall ((C tptp.rat) (A tptp.rat) (B 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 B)) (= (= (tptp.aa_rat_rat (tptp.divide_divide_rat A) C) (tptp.aa_rat_rat (tptp.divide_divide_rat B) C)) (= A B)))))) (forall ((C tptp.nat) (A tptp.nat) (B 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 B)) (= (= (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 B) C)) (= A B)))))) (forall ((C tptp.int) (A tptp.int) (B 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 B)) (= (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A) C) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int B) C)) (= A B)))))) (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer C))) (=> (= (tptp.divide6298287555418463151nteger A C) (tptp.divide6298287555418463151nteger B C)) (=> (tptp.pp (tptp.aa_Code_integer_bool _let_1 A)) (=> (tptp.pp (tptp.aa_Code_integer_bool _let_1 B)) (= A B)))))) (forall ((A tptp.complex) (C tptp.complex) (B tptp.complex)) (let ((_let_1 (tptp.dvd_dvd_complex C))) (=> (= (tptp.divide1717551699836669952omplex A C) (tptp.divide1717551699836669952omplex B C)) (=> (tptp.pp (tptp.aa_complex_bool _let_1 A)) (=> (tptp.pp (tptp.aa_complex_bool _let_1 B)) (= A B)))))) (forall ((A tptp.real) (C tptp.real) (B 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 B) C)) (=> (tptp.pp (tptp.aa_real_bool _let_1 A)) (=> (tptp.pp (tptp.aa_real_bool _let_1 B)) (= A B)))))) (forall ((A tptp.rat) (C tptp.rat) (B 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 B) C)) (=> (tptp.pp (tptp.aa_rat_bool _let_1 A)) (=> (tptp.pp (tptp.aa_rat_bool _let_1 B)) (= A B)))))) (forall ((A tptp.nat) (C tptp.nat) (B 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 B) C)) (=> (tptp.pp (tptp.aa_nat_bool _let_1 A)) (=> (tptp.pp (tptp.aa_nat_bool _let_1 B)) (= A B)))))) (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int C))) (=> (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A) C) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int B) C)) (=> (tptp.pp (tptp.aa_int_bool _let_1 A)) (=> (tptp.pp (tptp.aa_int_bool _let_1 B)) (= A B)))))) (forall ((D tptp.code_integer) (B tptp.code_integer) (A tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer D) B)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer B) A)) (= (tptp.divide6298287555418463151nteger (tptp.divide6298287555418463151nteger A D) (tptp.divide6298287555418463151nteger B D)) (tptp.divide6298287555418463151nteger A B))))) (forall ((D tptp.nat) (B 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) B)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat B) 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 B) D)) (tptp.aa_nat_nat _let_1 B)))))) (forall ((D tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.divide_divide_int A))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int D) B)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int B) A)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int (tptp.aa_int_int _let_1 D)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int B) D)) (tptp.aa_int_int _let_1 B)))))) (forall ((C tptp.code_integer) (B tptp.code_integer) (A tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer C) B)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.divide6298287555418463151nteger B C)) A) (tptp.divide6298287555418463151nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B) A) C)))) (forall ((C tptp.nat) (B tptp.nat) (A tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat C) B)) (= (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 B) 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 B) A)) C)))) (forall ((C tptp.int) (B tptp.int) (A tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int C) B)) (= (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.divide_divide_int B) C)) A) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B) A)) C)))) (forall ((C tptp.code_integer) (B 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) B)) (= (tptp.aa_Cod1783974652533396728nteger _let_1 (tptp.divide6298287555418463151nteger B C)) (tptp.divide6298287555418463151nteger (tptp.aa_Cod1783974652533396728nteger _let_1 B) C))))) (forall ((C tptp.nat) (B 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) B)) (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat B) C)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat _let_1 B)) C))))) (forall ((C tptp.int) (B 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) B)) (= (tptp.aa_int_int _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int B) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int (tptp.aa_int_int _let_1 B)) C))))) (forall ((C tptp.code_integer) (B tptp.code_integer) (A tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer C) B)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer B) A)) (= (tptp.divide6298287555418463151nteger A (tptp.divide6298287555418463151nteger B C)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.divide6298287555418463151nteger A B)) C))))) (forall ((C tptp.nat) (B 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) B)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat B) A)) (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat B) C)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat _let_1 B)) C)))))) (forall ((C tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.divide_divide_int A))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int C) B)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int B) A)) (= (tptp.aa_int_int _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int B) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int _let_1 B)) C)))))) (forall ((B tptp.code_integer) (C tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B) 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 B) C))))) (forall ((B 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 B) 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 B)) C)))))) (forall ((B tptp.int) (C tptp.int) (A tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.divide_divide_int A))) (let ((_let_2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B) 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.aa_int_fun_int_int tptp.divide_divide_int (tptp.aa_int_int _let_1 B)) C)))))) (forall ((A tptp.code_integer) (C tptp.code_integer) (B 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)) B)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer A) (tptp.divide6298287555418463151nteger B C))))) (forall ((A tptp.nat) (C tptp.nat) (B 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)) B)) (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 B) C))))) (forall ((A tptp.int) (C tptp.int) (B 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)) B)) (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.divide_divide_int B) C))))) (forall ((B 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 B) 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 B)) (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 B) D)))))) (forall ((B 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 B) 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) B)) (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 B) D)))))) (forall ((B 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 B) 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.aa_int_fun_int_int tptp.divide_divide_int A) B)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int C) D)) (tptp.aa_int_int (tptp.aa_int_fun_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 B) D)))))) (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 ((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 ((N tptp.num)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))) (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 ((A tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))) A)) (not (forall ((B2 tptp.code_integer)) (not (= A (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))) B2))))))) (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 ((B2 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))) B2))))))) (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 ((B2 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))) B2))))))) (forall ((N tptp.num)) (not (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))) (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 ((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 ((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 ((V tptp.num) (W tptp.num)) (= (tptp.aa_int_int (tptp.aa_int_fun_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.aa_int_fun_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 ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (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 B) (and (= (tptp.pp (tptp.aa_Code_integer_bool _let_2 A)) (tptp.pp (tptp.aa_Code_integer_bool _let_2 B))) (= (tptp.divide6298287555418463151nteger A _let_1) (tptp.divide6298287555418463151nteger B _let_1))))))) (forall ((A tptp.nat) (B 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 B) (and (= (tptp.pp (tptp.aa_nat_bool _let_2 A)) (tptp.pp (tptp.aa_nat_bool _let_2 B))) (= (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 B) _let_1))))))) (forall ((A tptp.int) (B 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 B) (and (= (tptp.pp (tptp.aa_int_bool _let_2 A)) (tptp.pp (tptp.aa_int_bool _let_2 B))) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A) _let_1) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int B) _let_1))))))) (forall ((B tptp.complex) (C tptp.complex) (A tptp.complex)) (= (tptp.aa_complex_complex (tptp.times_times_complex (tptp.divide1717551699836669952omplex B C)) A) (tptp.divide1717551699836669952omplex (tptp.aa_complex_complex (tptp.times_times_complex B) A) C))) (forall ((B 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 B) 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 B) A)) C))) (forall ((B 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 B) C)) A) (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat B) A)) C))) (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (= (tptp.divide1717551699836669952omplex (tptp.divide1717551699836669952omplex A B) C) (tptp.divide1717551699836669952omplex A (tptp.aa_complex_complex (tptp.times_times_complex B) C)))) (forall ((A tptp.real) (B 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 B)) C) (tptp.aa_real_real _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real B) C))))) (forall ((A tptp.rat) (B 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 B)) C) (tptp.aa_rat_rat _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat B) C))))) (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (= (tptp.divide1717551699836669952omplex A (tptp.divide1717551699836669952omplex B C)) (tptp.divide1717551699836669952omplex (tptp.aa_complex_complex (tptp.times_times_complex A) C) B))) (forall ((A tptp.real) (B 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 B) 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)) B))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (= (tptp.aa_rat_rat (tptp.divide_divide_rat A) (tptp.aa_rat_rat (tptp.divide_divide_rat B) 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)) B))) (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (tptp.times_times_complex A))) (= (tptp.aa_complex_complex _let_1 (tptp.divide1717551699836669952omplex B C)) (tptp.divide1717551699836669952omplex (tptp.aa_complex_complex _let_1 B) C)))) (forall ((A tptp.real) (B 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 B) C)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real _let_1 B)) C)))) (forall ((A tptp.rat) (B 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 B) C)) (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_rat_rat _let_1 B)) C)))) (forall ((N tptp.nat) (X tptp.nat)) (not (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_V5719532721284313246member (tptp.vEBT_vebt_buildup N)) X)))) (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 ((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 ((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 ((R2 tptp.real) (A tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.times_times_real R2))) (= (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 R2)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real A) R2)))) (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 ((V tptp.num) (W tptp.num)) (= (tptp.aa_int_int (tptp.aa_int_fun_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.aa_int_fun_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 ((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.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 ((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) (B tptp.nat)) (= (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) B)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int A)) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int B)))) (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (= (tptp.divide1717551699836669952omplex (tptp.divide1717551699836669952omplex A B) C) (tptp.divide1717551699836669952omplex A (tptp.aa_complex_complex (tptp.times_times_complex C) B)))) (forall ((A tptp.real) (B 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 B)) C) (tptp.aa_real_real _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real C) B))))) (forall ((A tptp.rat) (B 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 B)) C) (tptp.aa_rat_rat _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat C) B))))) (forall ((X tptp.complex) (Y4 tptp.complex) (Z tptp.complex) (W tptp.complex)) (= (tptp.divide1717551699836669952omplex (tptp.divide1717551699836669952omplex X Y4) (tptp.divide1717551699836669952omplex Z W)) (tptp.divide1717551699836669952omplex (tptp.aa_complex_complex (tptp.times_times_complex X) W) (tptp.aa_complex_complex (tptp.times_times_complex Y4) Z)))) (forall ((X tptp.real) (Y4 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) Y4)) (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 Y4) Z)))) (forall ((X tptp.rat) (Y4 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) Y4)) (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 Y4) Z)))) (forall ((X tptp.complex) (Y4 tptp.complex) (Z tptp.complex) (W tptp.complex)) (= (tptp.aa_complex_complex (tptp.times_times_complex (tptp.divide1717551699836669952omplex X Y4)) (tptp.divide1717551699836669952omplex Z W)) (tptp.divide1717551699836669952omplex (tptp.aa_complex_complex (tptp.times_times_complex X) Z) (tptp.aa_complex_complex (tptp.times_times_complex Y4) W)))) (forall ((X tptp.real) (Y4 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) Y4)) (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 Y4) W)))) (forall ((X tptp.rat) (Y4 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) Y4)) (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 Y4) W)))) (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 ((X33 tptp.num) (Y32 tptp.num)) (= (= (tptp.aa_num_num tptp.bit1 X33) (tptp.aa_num_num tptp.bit1 Y32)) (= X33 Y32))) (forall ((X2 tptp.num) (Y2 tptp.num)) (= (= (tptp.aa_num_num tptp.bit0 X2) (tptp.aa_num_num tptp.bit0 Y2)) (= X2 Y2))) (forall ((A tptp.set_int)) (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)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) A))) (forall ((X tptp.set_int)) (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 ((X tptp.real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) X))) (forall ((T tptp.vEBT_VEBT)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_VEBT_VEBT_real tptp.vEBT_VEBT_cnt T)))) (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 ((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))))) (forall ((A tptp.nat) (B tptp.nat)) (= (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) B)) (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 B)))) (forall ((A tptp.nat) (B tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B)) (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 B))))) (forall ((X33 tptp.num)) (not (= tptp.one (tptp.aa_num_num tptp.bit1 X33)))) (forall ((X2 tptp.num) (X33 tptp.num)) (not (= (tptp.aa_num_num tptp.bit0 X2) (tptp.aa_num_num tptp.bit1 X33)))) (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) (B tptp.complex)) (= (= (tptp.aa_complex_complex (tptp.times_times_complex A) B) tptp.zero_zero_complex) (or (= A tptp.zero_zero_complex) (= B tptp.zero_zero_complex)))) (forall ((A tptp.real) (B tptp.real)) (= (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) B) tptp.zero_zero_real) (or (= A tptp.zero_zero_real) (= B tptp.zero_zero_real)))) (forall ((A tptp.rat) (B tptp.rat)) (= (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) B) tptp.zero_zero_rat) (or (= A tptp.zero_zero_rat) (= B tptp.zero_zero_rat)))) (forall ((A tptp.nat) (B tptp.nat)) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) B) tptp.zero_zero_nat) (or (= A tptp.zero_zero_nat) (= B tptp.zero_zero_nat)))) (forall ((A tptp.int) (B tptp.int)) (= (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) B) tptp.zero_zero_int) (or (= A tptp.zero_zero_int) (= B tptp.zero_zero_int)))) (forall ((C tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (tptp.times_times_complex C))) (= (= (tptp.aa_complex_complex _let_1 A) (tptp.aa_complex_complex _let_1 B)) (or (= C tptp.zero_zero_complex) (= A B))))) (forall ((C tptp.real) (A tptp.real) (B 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 B)) (or (= C tptp.zero_zero_real) (= A B))))) (forall ((C tptp.rat) (A tptp.rat) (B 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 B)) (or (= C tptp.zero_zero_rat) (= A B))))) (forall ((C tptp.nat) (A tptp.nat) (B 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 B)) (or (= C tptp.zero_zero_nat) (= A B))))) (forall ((C tptp.int) (A tptp.int) (B 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 B)) (or (= C tptp.zero_zero_int) (= A B))))) (forall ((A tptp.complex) (C tptp.complex) (B tptp.complex)) (= (= (tptp.aa_complex_complex (tptp.times_times_complex A) C) (tptp.aa_complex_complex (tptp.times_times_complex B) C)) (or (= C tptp.zero_zero_complex) (= A B)))) (forall ((A tptp.real) (C tptp.real) (B 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 B) C)) (or (= C tptp.zero_zero_real) (= A B)))) (forall ((A tptp.rat) (C tptp.rat) (B 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 B) C)) (or (= C tptp.zero_zero_rat) (= A B)))) (forall ((A tptp.nat) (C tptp.nat) (B 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 B) C)) (or (= C tptp.zero_zero_nat) (= A B)))) (forall ((A tptp.int) (C tptp.int) (B 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 B) C)) (or (= C tptp.zero_zero_int) (= A B)))) (forall ((A tptp.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.aa_int_fun_int_int tptp.divide_divide_int tptp.zero_zero_int) A) tptp.zero_zero_int)) (forall ((A tptp.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.aa_int_fun_int_int tptp.divide_divide_int A) tptp.zero_zero_int) tptp.zero_zero_int)) (forall ((A tptp.complex) (B tptp.complex)) (= (= (tptp.divide1717551699836669952omplex A B) tptp.zero_zero_complex) (or (= A tptp.zero_zero_complex) (= B tptp.zero_zero_complex)))) (forall ((A tptp.real) (B tptp.real)) (= (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real A) B) tptp.zero_zero_real) (or (= A tptp.zero_zero_real) (= B tptp.zero_zero_real)))) (forall ((A tptp.rat) (B tptp.rat)) (= (= (tptp.aa_rat_rat (tptp.divide_divide_rat A) B) tptp.zero_zero_rat) (or (= A tptp.zero_zero_rat) (= B tptp.zero_zero_rat)))) (forall ((C tptp.complex) (A tptp.complex) (B tptp.complex)) (= (= (tptp.divide1717551699836669952omplex C A) (tptp.divide1717551699836669952omplex C B)) (or (= C tptp.zero_zero_complex) (= A B)))) (forall ((C tptp.real) (A tptp.real) (B 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 B)) (or (= C tptp.zero_zero_real) (= A B))))) (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (tptp.divide_divide_rat C))) (= (= (tptp.aa_rat_rat _let_1 A) (tptp.aa_rat_rat _let_1 B)) (or (= C tptp.zero_zero_rat) (= A B))))) (forall ((A tptp.complex) (C tptp.complex) (B tptp.complex)) (= (= (tptp.divide1717551699836669952omplex A C) (tptp.divide1717551699836669952omplex B C)) (or (= C tptp.zero_zero_complex) (= A B)))) (forall ((A tptp.real) (C tptp.real) (B 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 B) C)) (or (= C tptp.zero_zero_real) (= A B)))) (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (= (= (tptp.aa_rat_rat (tptp.divide_divide_rat A) C) (tptp.aa_rat_rat (tptp.divide_divide_rat B) C)) (or (= C tptp.zero_zero_rat) (= A B)))) (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.aa_int_fun_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.aa_int_fun_int_int tptp.divide_divide_int A) tptp.zero_zero_int) tptp.zero_zero_int)) (forall ((A tptp.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.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.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.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 ((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 ((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 ((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)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat M) tptp.zero_zero_nat) 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)))) (= (tptp.aa_nat_nat tptp.nat_triangle tptp.zero_zero_nat) tptp.zero_zero_nat) (forall ((A tptp.complex) (B tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (tptp.divide1717551699836669952omplex (tptp.aa_complex_complex (tptp.times_times_complex A) B) A) B))) (forall ((A tptp.real) (B 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) B)) A) B))) (forall ((A tptp.rat) (B 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) B)) A) B))) (forall ((A tptp.nat) (B 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) B)) A) B))) (forall ((A tptp.int) (B tptp.int)) (=> (not (= A tptp.zero_zero_int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) B)) A) B))) (forall ((B tptp.complex) (A tptp.complex)) (=> (not (= B tptp.zero_zero_complex)) (= (tptp.divide1717551699836669952omplex (tptp.aa_complex_complex (tptp.times_times_complex A) B) B) A))) (forall ((B tptp.real) (A tptp.real)) (=> (not (= B 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) B)) B) A))) (forall ((B tptp.rat) (A tptp.rat)) (=> (not (= B 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) B)) B) A))) (forall ((B tptp.nat) (A tptp.nat)) (=> (not (= B 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) B)) B) A))) (forall ((B tptp.int) (A tptp.int)) (=> (not (= B tptp.zero_zero_int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) B)) B) A))) (forall ((C tptp.nat) (A tptp.nat) (B 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 B)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) B))))) (forall ((C tptp.int) (A tptp.int) (B 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.aa_int_fun_int_int tptp.divide_divide_int (tptp.aa_int_int _let_1 A)) (tptp.aa_int_int _let_1 B)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A) B))))) (forall ((C tptp.nat) (A tptp.nat) (B 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 B) C)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) B)))) (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (=> (not (= C tptp.zero_zero_int)) (= (tptp.aa_int_int (tptp.aa_int_fun_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 B) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A) B)))) (forall ((C tptp.nat) (A tptp.nat) (B 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 B)))) (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) B)))))))) (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.times_times_int C))) (let ((_let_2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int (tptp.aa_int_int _let_1 A)) (tptp.aa_int_int _let_1 B)))) (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.aa_int_fun_int_int tptp.divide_divide_int A) B)))))))) (forall ((C tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (tptp.times_times_complex C))) (let ((_let_2 (tptp.divide1717551699836669952omplex (tptp.aa_complex_complex _let_1 A) (tptp.aa_complex_complex _let_1 B)))) (let ((_let_3 (= C tptp.zero_zero_complex))) (and (=> _let_3 (= _let_2 tptp.zero_zero_complex)) (=> (not _let_3) (= _let_2 (tptp.divide1717551699836669952omplex A B)))))))) (forall ((C tptp.real) (A tptp.real) (B 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 B)))) (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) B)))))))) (forall ((C tptp.rat) (A tptp.rat) (B 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 B)))) (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) B)))))))) (forall ((C tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (tptp.times_times_complex C))) (=> (not (= C tptp.zero_zero_complex)) (= (tptp.divide1717551699836669952omplex (tptp.aa_complex_complex _let_1 A) (tptp.aa_complex_complex _let_1 B)) (tptp.divide1717551699836669952omplex A B))))) (forall ((C tptp.real) (A tptp.real) (B 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 B)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real A) B))))) (forall ((C tptp.rat) (A tptp.rat) (B 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 B)) (tptp.aa_rat_rat (tptp.divide_divide_rat A) B))))) (forall ((C tptp.complex) (A tptp.complex) (B tptp.complex)) (=> (not (= C tptp.zero_zero_complex)) (= (tptp.divide1717551699836669952omplex (tptp.aa_complex_complex (tptp.times_times_complex C) A) (tptp.aa_complex_complex (tptp.times_times_complex B) C)) (tptp.divide1717551699836669952omplex A B)))) (forall ((C tptp.real) (A tptp.real) (B 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 B) C)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real A) B)))) (forall ((C tptp.rat) (A tptp.rat) (B 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 B) C)) (tptp.aa_rat_rat (tptp.divide_divide_rat A) B)))) (forall ((C tptp.complex) (A tptp.complex) (B tptp.complex)) (=> (not (= C tptp.zero_zero_complex)) (= (tptp.divide1717551699836669952omplex (tptp.aa_complex_complex (tptp.times_times_complex A) C) (tptp.aa_complex_complex (tptp.times_times_complex B) C)) (tptp.divide1717551699836669952omplex A B)))) (forall ((C tptp.real) (A tptp.real) (B 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 B) C)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real A) B)))) (forall ((C tptp.rat) (A tptp.rat) (B 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 B) C)) (tptp.aa_rat_rat (tptp.divide_divide_rat A) B)))) (forall ((C tptp.complex) (A tptp.complex) (B tptp.complex)) (=> (not (= C tptp.zero_zero_complex)) (= (tptp.divide1717551699836669952omplex (tptp.aa_complex_complex (tptp.times_times_complex A) C) (tptp.aa_complex_complex (tptp.times_times_complex C) B)) (tptp.divide1717551699836669952omplex A B)))) (forall ((C tptp.real) (A tptp.real) (B 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) B)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real A) B)))) (forall ((C tptp.rat) (A tptp.rat) (B 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) B)) (tptp.aa_rat_rat (tptp.divide_divide_rat A) B)))) (forall ((C tptp.code_integer) (A tptp.code_integer) (B 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 B))) (or (= C tptp.zero_z3403309356797280102nteger) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer A) B)))))) (forall ((C tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (tptp.times_times_complex C))) (= (tptp.pp (tptp.aa_complex_bool (tptp.dvd_dvd_complex (tptp.aa_complex_complex _let_1 A)) (tptp.aa_complex_complex _let_1 B))) (or (= C tptp.zero_zero_complex) (tptp.pp (tptp.aa_complex_bool (tptp.dvd_dvd_complex A) B)))))) (forall ((C tptp.real) (A tptp.real) (B 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 B))) (or (= C tptp.zero_zero_real) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.dvd_dvd_real A) B)))))) (forall ((C tptp.rat) (A tptp.rat) (B 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 B))) (or (= C tptp.zero_zero_rat) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.dvd_dvd_rat A) B)))))) (forall ((C tptp.int) (A tptp.int) (B 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 B))) (or (= C tptp.zero_zero_int) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int A) B)))))) (forall ((A tptp.code_integer) (C tptp.code_integer) (B 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 B) C))) (or (= C tptp.zero_z3403309356797280102nteger) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer A) B))))) (forall ((A tptp.complex) (C tptp.complex) (B tptp.complex)) (= (tptp.pp (tptp.aa_complex_bool (tptp.dvd_dvd_complex (tptp.aa_complex_complex (tptp.times_times_complex A) C)) (tptp.aa_complex_complex (tptp.times_times_complex B) C))) (or (= C tptp.zero_zero_complex) (tptp.pp (tptp.aa_complex_bool (tptp.dvd_dvd_complex A) B))))) (forall ((A tptp.real) (C tptp.real) (B 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 B) C))) (or (= C tptp.zero_zero_real) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.dvd_dvd_real A) B))))) (forall ((A tptp.rat) (C tptp.rat) (B 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 B) C))) (or (= C tptp.zero_zero_rat) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.dvd_dvd_rat A) B))))) (forall ((A tptp.int) (C tptp.int) (B 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 B) C))) (or (= C tptp.zero_zero_int) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int A) B))))) (forall ((A tptp.code_integer) (B 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 B)) (tptp.aa_Cod1783974652533396728nteger _let_1 C))) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer B) C)))))) (forall ((A tptp.nat) (B 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 B)) (tptp.aa_nat_nat _let_1 C))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat B) C)))))) (forall ((A tptp.int) (B 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 B)) (tptp.aa_int_int _let_1 C))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int B) C)))))) (forall ((A tptp.code_integer) (B 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 B) 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 B) C))))) (forall ((A tptp.nat) (B 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 B) 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 B) C))))) (forall ((A tptp.int) (B 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 B) 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 B) C))))) (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_real tptp.semiri5074537144036343181t_real M) tptp.zero_zero_real) (= 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_nat tptp.semiri1316708129612266289at_nat M) tptp.zero_zero_nat) (= 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 ((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_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real 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_nat (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat 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))) (= (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex tptp.zero_zero_nat) tptp.zero_zero_complex) (= (tptp.aa_nat_real tptp.semiri5074537144036343181t_real tptp.zero_zero_nat) tptp.zero_zero_real) (= (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat tptp.zero_zero_nat) tptp.zero_zero_rat) (= (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat tptp.zero_zero_nat) tptp.zero_zero_nat) _let_187 (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 ((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 ((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 ((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 ((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.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 ((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 ((B tptp.complex) (W tptp.num) (A tptp.complex)) (let ((_let_1 (tptp.numera6690914467698888265omplex W))) (let ((_let_2 (= _let_1 tptp.zero_zero_complex))) (= (= (tptp.divide1717551699836669952omplex B _let_1) A) (and (=> (not _let_2) (= B (tptp.aa_complex_complex (tptp.times_times_complex A) _let_1))) (=> _let_2 (= A tptp.zero_zero_complex))))))) (forall ((B 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 B) _let_1) A) (and (=> (not _let_2) (= B (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) _let_1))) (=> _let_2 (= A tptp.zero_zero_real))))))) (forall ((B 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 B) _let_1) A) (and (=> (not _let_2) (= B (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) (B tptp.complex) (W tptp.num)) (let ((_let_1 (tptp.numera6690914467698888265omplex W))) (let ((_let_2 (= _let_1 tptp.zero_zero_complex))) (= (= A (tptp.divide1717551699836669952omplex B _let_1)) (and (=> (not _let_2) (= (tptp.aa_complex_complex (tptp.times_times_complex A) _let_1) B)) (=> _let_2 (= A tptp.zero_zero_complex))))))) (forall ((A tptp.real) (B 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 B) _let_1)) (and (=> (not _let_2) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) _let_1) B)) (=> _let_2 (= A tptp.zero_zero_real))))))) (forall ((A tptp.rat) (B 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 B) _let_1)) (and (=> (not _let_2) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) _let_1) B)) (=> _let_2 (= A tptp.zero_zero_rat))))))) (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.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) (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 ((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)))) (tptp.pp (tptp.aa_rat_bool _let_114 tptp.zero_zero_rat)) (tptp.pp (tptp.aa_nat_bool _let_175 tptp.zero_zero_nat)) _let_188 (tptp.pp (tptp.aa_real_bool _let_95 tptp.zero_zero_real)) (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) (B tptp.complex)) (=> (not (= (tptp.aa_complex_complex (tptp.times_times_complex A) B) tptp.zero_zero_complex)) (and (not (= A tptp.zero_zero_complex)) (not (= B tptp.zero_zero_complex))))) (forall ((A tptp.real) (B tptp.real)) (=> (not (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) B) tptp.zero_zero_real)) (and (not (= A tptp.zero_zero_real)) (not (= B tptp.zero_zero_real))))) (forall ((A tptp.rat) (B tptp.rat)) (=> (not (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) B) tptp.zero_zero_rat)) (and (not (= A tptp.zero_zero_rat)) (not (= B tptp.zero_zero_rat))))) (forall ((A tptp.nat) (B tptp.nat)) (=> (not (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) B) tptp.zero_zero_nat)) (and (not (= A tptp.zero_zero_nat)) (not (= B tptp.zero_zero_nat))))) (forall ((A tptp.int) (B tptp.int)) (=> (not (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) B) tptp.zero_zero_int)) (and (not (= A tptp.zero_zero_int)) (not (= B tptp.zero_zero_int))))) (forall ((A tptp.complex) (B tptp.complex)) (=> (= (tptp.aa_complex_complex (tptp.times_times_complex A) B) tptp.zero_zero_complex) (or (= A tptp.zero_zero_complex) (= B tptp.zero_zero_complex)))) (forall ((A tptp.real) (B tptp.real)) (=> (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) B) tptp.zero_zero_real) (or (= A tptp.zero_zero_real) (= B tptp.zero_zero_real)))) (forall ((A tptp.rat) (B tptp.rat)) (=> (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) B) tptp.zero_zero_rat) (or (= A tptp.zero_zero_rat) (= B tptp.zero_zero_rat)))) (forall ((A tptp.nat) (B tptp.nat)) (=> (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) B) tptp.zero_zero_nat) (or (= A tptp.zero_zero_nat) (= B tptp.zero_zero_nat)))) (forall ((A tptp.int) (B tptp.int)) (=> (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) B) tptp.zero_zero_int) (or (= A tptp.zero_zero_int) (= B tptp.zero_zero_int)))) (forall ((A tptp.complex) (B tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (=> (not (= B tptp.zero_zero_complex)) (not (= (tptp.aa_complex_complex (tptp.times_times_complex A) B) tptp.zero_zero_complex))))) (forall ((A tptp.real) (B tptp.real)) (=> (not (= A tptp.zero_zero_real)) (=> (not (= B tptp.zero_zero_real)) (not (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) B) tptp.zero_zero_real))))) (forall ((A tptp.rat) (B tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (=> (not (= B tptp.zero_zero_rat)) (not (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) B) tptp.zero_zero_rat))))) (forall ((A tptp.nat) (B tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (=> (not (= B tptp.zero_zero_nat)) (not (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) B) tptp.zero_zero_nat))))) (forall ((A tptp.int) (B tptp.int)) (=> (not (= A tptp.zero_zero_int)) (=> (not (= B tptp.zero_zero_int)) (not (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) B) tptp.zero_zero_int))))) (forall ((C tptp.complex) (A tptp.complex) (B 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 B)) (= A B))))) (forall ((C tptp.real) (A tptp.real) (B 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 B)) (= A B))))) (forall ((C tptp.rat) (A tptp.rat) (B 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 B)) (= A B))))) (forall ((C tptp.nat) (A tptp.nat) (B 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 B)) (= A B))))) (forall ((C tptp.int) (A tptp.int) (B 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 B)) (= A B))))) (forall ((C tptp.complex) (A tptp.complex) (B 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 B) C)) (= A B)))) (forall ((C tptp.real) (A tptp.real) (B 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 B) C)) (= A B)))) (forall ((C tptp.rat) (A tptp.rat) (B 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 B) C)) (= A B)))) (forall ((C tptp.nat) (A tptp.nat) (B 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 B) C)) (= A B)))) (forall ((C tptp.int) (A tptp.int) (B 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 B) C)) (= A B)))) (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.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.complex) (B tptp.complex)) (= (tptp.pp (tptp.aa_complex_bool (tptp.dvd_dvd_complex A) B)) (=> (= A tptp.zero_zero_complex) (= B tptp.zero_zero_complex)))) (forall ((A tptp.real) (B tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.dvd_dvd_real A) B)) (=> (= A tptp.zero_zero_real) (= B tptp.zero_zero_real)))) (forall ((A tptp.rat) (B tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.dvd_dvd_rat A) B)) (=> (= A tptp.zero_zero_rat) (= B tptp.zero_zero_rat)))) (forall ((X tptp.nat)) (=> (not (= X tptp.zero_zero_nat)) (not (forall ((N2 tptp.nat)) (not (= X (tptp.aa_nat_nat tptp.suc N2))))))) (forall ((X tptp.nat)) (=> (not (= X tptp.zero_zero_nat)) (=> (not (= X (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat))) (not (forall ((Va tptp.nat)) (not (= X (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat tptp.suc Va))))))))) (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 ((Y4 tptp.nat)) (=> (not (= Y4 tptp.zero_zero_nat)) (not (forall ((Nat3 tptp.nat)) (not (= Y4 (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 ((X3 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool P X3) tptp.zero_zero_nat))) (=> (forall ((Y 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 Y)))) (=> (forall ((X3 tptp.nat) (Y tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool P X3) Y)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool P (tptp.aa_nat_nat tptp.suc X3)) (tptp.aa_nat_nat tptp.suc Y))))) (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 ((M4 tptp.nat)) (= N (tptp.aa_nat_nat tptp.suc M4))))) (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 ((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 ((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 ((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 ((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)) (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)) (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 ((A tptp.rat) (B 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) B)) (=> (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 B)) (=> (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 B) D))))))))) (forall ((A tptp.nat) (B 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) B)) (=> (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 B)) (=> (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 B) D))))))))) (forall ((A tptp.int) (B 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) B)) (=> (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 B)) (=> (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 B) D))))))))) (forall ((A tptp.real) (B 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) B)) (=> (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 B)) (=> (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 B) D))))))))) (forall ((A tptp.rat) (B 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) B)) (=> (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 B) D))))))))) (forall ((A tptp.nat) (B 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) B)) (=> (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 B) D))))))))) (forall ((A tptp.int) (B 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) B)) (=> (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 B) D))))))))) (forall ((A tptp.real) (B 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) B)) (=> (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 B) D))))))))) (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)) (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) (B 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 B))) (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 B) 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) B)))))) (forall ((A tptp.int) (B 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 B))) (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 B) 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) B)))))) (forall ((A tptp.real) (B 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 B))) (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 B) 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) B)))))) (forall ((B 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 B) 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 B))))))) (forall ((B 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 B) 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 B))))))) (forall ((B 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 B) 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 B))))))) (forall ((A tptp.rat) (B 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 B) 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) B)))))) (forall ((A tptp.int) (B 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 B) 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) B)))))) (forall ((A tptp.real) (B 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 B) 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) B)))))) (forall ((A tptp.rat) (B 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) B)) (=> (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 B))))))) (forall ((A tptp.nat) (B 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) B)) (=> (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 B))))))) (forall ((A tptp.int) (B 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) B)) (=> (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 B))))))) (forall ((A tptp.real) (B 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) B)) (=> (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 B))))))) (forall ((B 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 B) 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 B) C)))))) (forall ((B 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 B) 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 B) C)))))) (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real B) 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 B) C)))))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B)) (=> (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 B) C)))))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B)) (=> (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 B) C)))))) (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B)) (=> (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 B) C)))))) (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) B)) (=> (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 B) C)))))) (forall ((A tptp.rat) (B 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) B)) 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 B) 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 B))))))) (forall ((A tptp.int) (B 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) B)) 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 B) 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 B))))))) (forall ((A tptp.real) (B 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) B)) 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 B) 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 B))))))) (forall ((A tptp.rat) (B 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 B) 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 B)))) (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) B)) tptp.zero_zero_rat))))) (forall ((A tptp.nat) (B 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 B) 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 B)))) (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) B)) tptp.zero_zero_nat))))) (forall ((A tptp.int) (B 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 B) 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 B)))) (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) B)) tptp.zero_zero_int))))) (forall ((A tptp.real) (B 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 B) 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 B)))) (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) B)) tptp.zero_zero_real))))) (forall ((A tptp.rat) (B 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 B)) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) B))))))) (forall ((A tptp.nat) (B 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 B)) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) B))))))) (forall ((A tptp.int) (B 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 B)) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) B))))))) (forall ((A tptp.real) (B 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 B)) (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) B))))))) (forall ((A tptp.rat) (B 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 B) 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) B)) tptp.zero_zero_rat))))) (forall ((A tptp.nat) (B 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 B) 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) B)) tptp.zero_zero_nat))))) (forall ((A tptp.int) (B 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 B) 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) B)) tptp.zero_zero_int))))) (forall ((A tptp.real) (B 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 B) 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) B)) tptp.zero_zero_real))))) (forall ((A tptp.rat) (B 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) B)) (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) B)) tptp.zero_zero_rat))))) (forall ((A tptp.nat) (B 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) B)) (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) B)) tptp.zero_zero_nat))))) (forall ((A tptp.int) (B 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) B)) (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) B)) tptp.zero_zero_int))))) (forall ((A tptp.real) (B 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) B)) (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) B)) tptp.zero_zero_real))))) (forall ((A tptp.rat) (B 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 B) 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 B) A)) tptp.zero_zero_rat))))) (forall ((A tptp.nat) (B 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 B) 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 B) A)) tptp.zero_zero_nat))))) (forall ((A tptp.int) (B 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 B) 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 B) A)) tptp.zero_zero_int))))) (forall ((A tptp.real) (B 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 B) 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 B) A)) tptp.zero_zero_real))))) (forall ((A tptp.rat) (B 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) B))) (or (and (tptp.pp (tptp.aa_rat_bool _let_1 A)) (tptp.pp (tptp.aa_rat_bool _let_1 B))) (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 B) tptp.zero_zero_rat))))))) (forall ((A tptp.int) (B 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) B))) (or (and (tptp.pp (tptp.aa_int_bool _let_1 A)) (tptp.pp (tptp.aa_int_bool _let_1 B))) (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 B) tptp.zero_zero_int))))))) (forall ((A tptp.real) (B 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) B))) (or (and (tptp.pp (tptp.aa_real_bool _let_1 A)) (tptp.pp (tptp.aa_real_bool _let_1 B))) (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 B) tptp.zero_zero_real))))))) (forall ((A tptp.rat) (B 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) B)) (=> (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 B))))))) (forall ((A tptp.nat) (B 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) B)) (=> (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 B))))))) (forall ((A tptp.int) (B 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) B)) (=> (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 B))))))) (forall ((A tptp.real) (B 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) B)) (=> (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 B))))))) (forall ((A tptp.rat) (B 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) B)) 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 B) 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 B))))))) (forall ((A tptp.real) (B 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) B)) 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 B) 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 B))))))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B)) (=> (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 B) C)))))) (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) B)) (=> (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 B) C)))))) (forall ((A tptp.rat) (B 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) B))) (or (and (tptp.pp (tptp.aa_rat_bool _let_1 A)) (tptp.pp (tptp.aa_rat_bool _let_1 B))) (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 B) tptp.zero_zero_rat))))))) (forall ((A tptp.real) (B 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) B))) (or (and (tptp.pp (tptp.aa_real_bool _let_1 A)) (tptp.pp (tptp.aa_real_bool _let_1 B))) (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 B) tptp.zero_zero_real))))))) (forall ((X tptp.rat) (Y4 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 Y4)) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat (tptp.divide_divide_rat X) Y4))))))) (forall ((X tptp.real) (Y4 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 Y4)) (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real X) Y4))))))) (forall ((X tptp.rat) (Y4 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 Y4) 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) Y4)) tptp.zero_zero_rat))))) (forall ((X tptp.real) (Y4 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 Y4) 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) Y4)) tptp.zero_zero_real))))) (forall ((X tptp.rat) (Y4 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) Y4)) (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) Y4)) tptp.zero_zero_rat))))) (forall ((X tptp.real) (Y4 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) Y4)) (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) Y4)) tptp.zero_zero_real))))) (forall ((X tptp.rat) (Y4 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 Y4) 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) Y4)))))) (forall ((X tptp.real) (Y4 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 Y4) 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) Y4)))))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B)) (=> (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 B) C)) (tptp.aa_rat_rat (tptp.divide_divide_rat A) C)))))) (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) B)) (=> (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 B) C)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real A) C)))))) (forall ((Y4 tptp.complex) (Z tptp.complex) (X tptp.complex) (W tptp.complex)) (=> (not (= Y4 tptp.zero_zero_complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (= (tptp.divide1717551699836669952omplex X Y4) (tptp.divide1717551699836669952omplex W Z)) (= (tptp.aa_complex_complex (tptp.times_times_complex X) Z) (tptp.aa_complex_complex (tptp.times_times_complex W) Y4)))))) (forall ((Y4 tptp.real) (Z tptp.real) (X tptp.real) (W tptp.real)) (=> (not (= Y4 tptp.zero_zero_real)) (=> (not (= Z tptp.zero_zero_real)) (= (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real X) Y4) (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) Y4)))))) (forall ((Y4 tptp.rat) (Z tptp.rat) (X tptp.rat) (W tptp.rat)) (=> (not (= Y4 tptp.zero_zero_rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (= (tptp.aa_rat_rat (tptp.divide_divide_rat X) Y4) (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) Y4)))))) (forall ((B tptp.complex) (C tptp.complex) (A tptp.complex)) (let ((_let_1 (= C tptp.zero_zero_complex))) (= (= (tptp.divide1717551699836669952omplex B C) A) (and (=> (not _let_1) (= B (tptp.aa_complex_complex (tptp.times_times_complex A) C))) (=> _let_1 (= A tptp.zero_zero_complex)))))) (forall ((B 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 B) C) A) (and (=> (not _let_1) (= B (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) C))) (=> _let_1 (= A tptp.zero_zero_real)))))) (forall ((B tptp.rat) (C tptp.rat) (A tptp.rat)) (let ((_let_1 (= C tptp.zero_zero_rat))) (= (= (tptp.aa_rat_rat (tptp.divide_divide_rat B) C) A) (and (=> (not _let_1) (= B (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) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (= C tptp.zero_zero_complex))) (= (= A (tptp.divide1717551699836669952omplex B C)) (and (=> (not _let_1) (= (tptp.aa_complex_complex (tptp.times_times_complex A) C) B)) (=> _let_1 (= A tptp.zero_zero_complex)))))) (forall ((A tptp.real) (B 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 B) C)) (and (=> (not _let_1) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) C) B)) (=> _let_1 (= A tptp.zero_zero_real)))))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (= C tptp.zero_zero_rat))) (= (= A (tptp.aa_rat_rat (tptp.divide_divide_rat B) C)) (and (=> (not _let_1) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) C) B)) (=> _let_1 (= A tptp.zero_zero_rat)))))) (forall ((C tptp.complex) (B tptp.complex) (A tptp.complex)) (=> (not (= C tptp.zero_zero_complex)) (=> (= B (tptp.aa_complex_complex (tptp.times_times_complex A) C)) (= (tptp.divide1717551699836669952omplex B C) A)))) (forall ((C tptp.real) (B tptp.real) (A tptp.real)) (=> (not (= C tptp.zero_zero_real)) (=> (= B (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 B) C) A)))) (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (not (= C tptp.zero_zero_rat)) (=> (= B (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) C)) (= (tptp.aa_rat_rat (tptp.divide_divide_rat B) C) A)))) (forall ((C tptp.complex) (A tptp.complex) (B tptp.complex)) (=> (not (= C tptp.zero_zero_complex)) (=> (= (tptp.aa_complex_complex (tptp.times_times_complex A) C) B) (= A (tptp.divide1717551699836669952omplex B C))))) (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (not (= C tptp.zero_zero_real)) (=> (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) C) B) (= A (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real B) C))))) (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (not (= C tptp.zero_zero_rat)) (=> (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) C) B) (= A (tptp.aa_rat_rat (tptp.divide_divide_rat B) C))))) (forall ((C tptp.complex) (B tptp.complex) (A tptp.complex)) (=> (not (= C tptp.zero_zero_complex)) (= (= (tptp.divide1717551699836669952omplex B C) A) (= B (tptp.aa_complex_complex (tptp.times_times_complex A) C))))) (forall ((C tptp.real) (B tptp.real) (A tptp.real)) (=> (not (= C tptp.zero_zero_real)) (= (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real B) C) A) (= B (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) C))))) (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (not (= C tptp.zero_zero_rat)) (= (= (tptp.aa_rat_rat (tptp.divide_divide_rat B) C) A) (= B (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) C))))) (forall ((C tptp.complex) (A tptp.complex) (B tptp.complex)) (=> (not (= C tptp.zero_zero_complex)) (= (= A (tptp.divide1717551699836669952omplex B C)) (= (tptp.aa_complex_complex (tptp.times_times_complex A) C) B)))) (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (not (= C tptp.zero_zero_real)) (= (= A (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real B) C)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) C) B)))) (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (not (= C tptp.zero_zero_rat)) (= (= A (tptp.aa_rat_rat (tptp.divide_divide_rat B) C)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) C) B)))) (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 ((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 ((B tptp.code_integer) (A tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer B) A)) (= (= (tptp.divide6298287555418463151nteger A B) tptp.zero_z3403309356797280102nteger) (= A tptp.zero_z3403309356797280102nteger)))) (forall ((B tptp.complex) (A tptp.complex)) (=> (tptp.pp (tptp.aa_complex_bool (tptp.dvd_dvd_complex B) A)) (= (= (tptp.divide1717551699836669952omplex A B) tptp.zero_zero_complex) (= A tptp.zero_zero_complex)))) (forall ((B tptp.real) (A tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.dvd_dvd_real B) A)) (= (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real A) B) tptp.zero_zero_real) (= A tptp.zero_zero_real)))) (forall ((B tptp.rat) (A tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.dvd_dvd_rat B) A)) (= (= (tptp.aa_rat_rat (tptp.divide_divide_rat A) B) tptp.zero_zero_rat) (= A tptp.zero_zero_rat)))) (forall ((B tptp.nat) (A tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat B) A)) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) B) tptp.zero_zero_nat) (= A tptp.zero_zero_nat)))) (forall ((B tptp.int) (A tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int B) A)) (= (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A) B) tptp.zero_zero_int) (= A tptp.zero_zero_int)))) (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_real tptp.semiri5074537144036343181t_real (tptp.aa_nat_nat tptp.suc N)) tptp.zero_zero_real))) (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_nat tptp.semiri1316708129612266289at_nat (tptp.aa_nat_nat tptp.suc N)) tptp.zero_zero_nat))) (forall ((N tptp.nat)) (not (= (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_nat tptp.suc N)) tptp.zero_zero_int))) (forall ((A tptp.set_int)) (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)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) A))) (forall ((A tptp.rat) (B tptp.rat)) (= (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B))) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) A)) (not (= B A))))) (forall ((A tptp.num) (B tptp.num)) (= (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A) B))) (and (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num B) A)) (not (= B A))))) (forall ((A tptp.nat) (B tptp.nat)) (= (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B))) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B) A)) (not (= B A))))) (forall ((A tptp.int) (B tptp.int)) (= (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B))) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B) A)) (not (= B A))))) (forall ((A tptp.real) (B tptp.real)) (= (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) B))) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real B) A)) (not (= B A))))) (forall ((X tptp.rat) (Y4 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 Y4)))) (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 Y4))) (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 Y4)))) (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) (Y4 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 Y4)))) (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 Y4))) (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 Y4)))) (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) (Y4 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 Y4)))) (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 Y4))) (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 Y4)))) (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) (Y4 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 Y4)))) (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 Y4))) (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 Y4)))) (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.real) (Y4 tptp.real) (Z tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X))) (let ((_let_2 (tptp.pp (tptp.aa_real_bool _let_1 Y4)))) (let ((_let_3 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Z))) (let ((_let_4 (tptp.pp (tptp.aa_real_bool _let_3 X)))) (let ((_let_5 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y4))) (let ((_let_6 (tptp.pp (tptp.aa_real_bool _let_5 Z)))) (let ((_let_7 (tptp.pp (tptp.aa_real_bool _let_5 X)))) (let ((_let_8 (tptp.pp (tptp.aa_real_bool _let_3 Y4)))) (let ((_let_9 (tptp.pp (tptp.aa_real_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) (Y4 tptp.set_int)) (= (= X Y4) (and (tptp.ord_less_eq_set_int X Y4) (tptp.ord_less_eq_set_int Y4 X)))) (forall ((X tptp.rat) (Y4 tptp.rat)) (= (= X Y4) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) Y4)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat Y4) X))))) (forall ((X tptp.num) (Y4 tptp.num)) (= (= X Y4) (and (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X) Y4)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num Y4) X))))) (forall ((X tptp.nat) (Y4 tptp.nat)) (= (= X Y4) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X) Y4)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Y4) X))))) (forall ((X tptp.int) (Y4 tptp.int)) (= (= X Y4) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X) Y4)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Y4) X))))) (forall ((X tptp.real) (Y4 tptp.real)) (= (= X Y4) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) Y4)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y4) X))))) (forall ((A tptp.set_int) (B tptp.set_int) (C tptp.set_int)) (=> (= A B) (=> (tptp.ord_less_eq_set_int B C) (tptp.ord_less_eq_set_int A C)))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (= A B) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) C)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) C))))) (forall ((A tptp.num) (B tptp.num) (C tptp.num)) (=> (= A B) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num B) C)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A) C))))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (= A B) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B) C)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) C))))) (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (= A B) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B) C)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) C))))) (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (=> (= A B) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real B) C)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) C))))) (forall ((A tptp.set_int) (B tptp.set_int) (C tptp.set_int)) (=> (tptp.ord_less_eq_set_int A B) (=> (= B C) (tptp.ord_less_eq_set_int A C)))) (forall ((A tptp.rat) (B 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 B)) (=> (= B C) (tptp.pp (tptp.aa_rat_bool _let_1 C)))))) (forall ((A tptp.num) (B 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 B)) (=> (= B C) (tptp.pp (tptp.aa_num_bool _let_1 C)))))) (forall ((A tptp.nat) (B 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 B)) (=> (= B C) (tptp.pp (tptp.aa_nat_bool _let_1 C)))))) (forall ((A tptp.int) (B 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 B)) (=> (= B C) (tptp.pp (tptp.aa_int_bool _let_1 C)))))) (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A))) (=> (tptp.pp (tptp.aa_real_bool _let_1 B)) (=> (= B C) (tptp.pp (tptp.aa_real_bool _let_1 C)))))) (forall ((X tptp.set_int) (Y4 tptp.set_int)) (=> (tptp.ord_less_eq_set_int X Y4) (=> (tptp.ord_less_eq_set_int Y4 X) (= X Y4)))) (forall ((X tptp.rat) (Y4 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) Y4)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat Y4) X)) (= X Y4)))) (forall ((X tptp.num) (Y4 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X) Y4)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num Y4) X)) (= X Y4)))) (forall ((X tptp.nat) (Y4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X) Y4)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Y4) X)) (= X Y4)))) (forall ((X tptp.int) (Y4 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X) Y4)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Y4) X)) (= X Y4)))) (forall ((X tptp.real) (Y4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) Y4)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y4) X)) (= X Y4)))) (forall ((A tptp.set_int) (B tptp.set_int) (C tptp.set_int)) (=> (tptp.ord_less_eq_set_int A B) (=> (tptp.ord_less_eq_set_int B C) (tptp.ord_less_eq_set_int A C)))) (forall ((A tptp.rat) (B 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 B)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) C)) (tptp.pp (tptp.aa_rat_bool _let_1 C)))))) (forall ((A tptp.num) (B 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 B)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num B) C)) (tptp.pp (tptp.aa_num_bool _let_1 C)))))) (forall ((A tptp.nat) (B 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 B)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B) C)) (tptp.pp (tptp.aa_nat_bool _let_1 C)))))) (forall ((A tptp.int) (B 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 B)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B) C)) (tptp.pp (tptp.aa_int_bool _let_1 C)))))) (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A))) (=> (tptp.pp (tptp.aa_real_bool _let_1 B)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real B) C)) (tptp.pp (tptp.aa_real_bool _let_1 C)))))) (forall ((X tptp.set_int) (Y4 tptp.set_int) (Z tptp.set_int)) (=> (tptp.ord_less_eq_set_int X Y4) (=> (tptp.ord_less_eq_set_int Y4 Z) (tptp.ord_less_eq_set_int X Z)))) (forall ((X tptp.rat) (Y4 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 Y4)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat Y4) Z)) (tptp.pp (tptp.aa_rat_bool _let_1 Z)))))) (forall ((X tptp.num) (Y4 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 Y4)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num Y4) Z)) (tptp.pp (tptp.aa_num_bool _let_1 Z)))))) (forall ((X tptp.nat) (Y4 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 Y4)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Y4) Z)) (tptp.pp (tptp.aa_nat_bool _let_1 Z)))))) (forall ((X tptp.int) (Y4 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 Y4)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Y4) Z)) (tptp.pp (tptp.aa_int_bool _let_1 Z)))))) (forall ((X tptp.real) (Y4 tptp.real) (Z tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X))) (=> (tptp.pp (tptp.aa_real_bool _let_1 Y4)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y4) Z)) (tptp.pp (tptp.aa_real_bool _let_1 Z)))))) (forall ((P tptp.fun_rat_fun_rat_bool) (A tptp.rat) (B tptp.rat)) (=> (forall ((A3 tptp.rat) (B2 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A3) B2)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool P A3) B2)))) (=> (forall ((A3 tptp.rat) (B2 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool P B2) A3)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool P A3) B2)))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool P A) B))))) (forall ((P tptp.fun_num_fun_num_bool) (A tptp.num) (B tptp.num)) (=> (forall ((A3 tptp.num) (B2 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A3) B2)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool P A3) B2)))) (=> (forall ((A3 tptp.num) (B2 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool P B2) A3)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool P A3) B2)))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool P A) B))))) (forall ((P tptp.fun_nat_fun_nat_bool) (A tptp.nat) (B tptp.nat)) (=> (forall ((A3 tptp.nat) (B2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A3) B2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool P A3) B2)))) (=> (forall ((A3 tptp.nat) (B2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool P B2) A3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool P A3) B2)))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool P A) B))))) (forall ((P tptp.fun_int_fun_int_bool) (A tptp.int) (B tptp.int)) (=> (forall ((A3 tptp.int) (B2 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A3) B2)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool P A3) B2)))) (=> (forall ((A3 tptp.int) (B2 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool P B2) A3)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool P A3) B2)))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool P A) B))))) (forall ((P tptp.fun_re1255401033344146673l_bool) (A tptp.real) (B tptp.real)) (=> (forall ((A3 tptp.real) (B2 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A3) B2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool P A3) B2)))) (=> (forall ((A3 tptp.real) (B2 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool P B2) A3)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool P A3) B2)))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool P A) B))))) (forall ((A tptp.set_int) (B tptp.set_int)) (= (= A B) (and (tptp.ord_less_eq_set_int B A) (tptp.ord_less_eq_set_int A B)))) (forall ((A tptp.rat) (B tptp.rat)) (= (= A B) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) A)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B))))) (forall ((A tptp.num) (B tptp.num)) (= (= A B) (and (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num B) A)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A) B))))) (forall ((A tptp.nat) (B tptp.nat)) (= (= A B) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B) A)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B))))) (forall ((A tptp.int) (B tptp.int)) (= (= A B) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B) A)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B))))) (forall ((A tptp.real) (B tptp.real)) (= (= A B) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real B) A)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) B))))) (forall ((B tptp.set_int) (A tptp.set_int)) (=> (tptp.ord_less_eq_set_int B A) (=> (tptp.ord_less_eq_set_int A B) (= A B)))) (forall ((B tptp.rat) (A tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) A)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B)) (= A B)))) (forall ((B tptp.num) (A tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num B) A)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A) B)) (= A B)))) (forall ((B tptp.nat) (A tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B) A)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B)) (= A B)))) (forall ((B tptp.int) (A tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B) A)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B)) (= A B)))) (forall ((B tptp.real) (A tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real B) A)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) B)) (= A B)))) (forall ((B tptp.set_int) (A tptp.set_int) (C tptp.set_int)) (=> (tptp.ord_less_eq_set_int B A) (=> (tptp.ord_less_eq_set_int C B) (tptp.ord_less_eq_set_int C A)))) (forall ((B 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 B) A)) (=> (tptp.pp (tptp.aa_rat_bool _let_1 B)) (tptp.pp (tptp.aa_rat_bool _let_1 A)))))) (forall ((B 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 B) A)) (=> (tptp.pp (tptp.aa_num_bool _let_1 B)) (tptp.pp (tptp.aa_num_bool _let_1 A)))))) (forall ((B 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 B) A)) (=> (tptp.pp (tptp.aa_nat_bool _let_1 B)) (tptp.pp (tptp.aa_nat_bool _let_1 A)))))) (forall ((B 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 B) A)) (=> (tptp.pp (tptp.aa_int_bool _let_1 B)) (tptp.pp (tptp.aa_int_bool _let_1 A)))))) (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real C))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real B) A)) (=> (tptp.pp (tptp.aa_real_bool _let_1 B)) (tptp.pp (tptp.aa_real_bool _let_1 A)))))) (forall ((A tptp.set_int) (B tptp.set_int)) (=> (tptp.ord_less_eq_set_int A B) (=> (tptp.ord_less_eq_set_int B A) (= A B)))) (forall ((A tptp.rat) (B tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) A)) (= A B)))) (forall ((A tptp.num) (B tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A) B)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num B) A)) (= A B)))) (forall ((A tptp.nat) (B tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B) A)) (= A B)))) (forall ((A tptp.int) (B tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B) A)) (= A B)))) (forall ((A tptp.real) (B tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) B)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real B) A)) (= A B)))) (forall ((A tptp.set_int) (B tptp.set_int)) (= (= A B) (and (tptp.ord_less_eq_set_int A B) (tptp.ord_less_eq_set_int B A)))) (forall ((A tptp.rat) (B tptp.rat)) (= (= A B) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) A))))) (forall ((A tptp.num) (B tptp.num)) (= (= A B) (and (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A) B)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num B) A))))) (forall ((A tptp.nat) (B tptp.nat)) (= (= A B) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B) A))))) (forall ((A tptp.int) (B tptp.int)) (= (= A B) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B) A))))) (forall ((A tptp.real) (B tptp.real)) (= (= A B) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) B)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real B) A))))) (forall ((A tptp.rat) (F tptp.fun_rat_rat) (B 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 B))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) C)) (=> (forall ((X3 tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X3) Y)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat F X3)) (tptp.aa_rat_rat F Y))))) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat F C)))))))) (forall ((A tptp.rat) (F tptp.fun_num_rat) (B 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 B))) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num B) C)) (=> (forall ((X3 tptp.num) (Y tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X3) Y)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_num_rat F X3)) (tptp.aa_num_rat F Y))))) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_num_rat F C)))))))) (forall ((A tptp.rat) (F tptp.fun_nat_rat) (B 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 B))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B) C)) (=> (forall ((X3 tptp.nat) (Y tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X3) Y)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat F X3)) (tptp.aa_nat_rat F Y))))) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_nat_rat F C)))))))) (forall ((A tptp.rat) (F tptp.fun_int_rat) (B 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 B))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B) C)) (=> (forall ((X3 tptp.int) (Y tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X3) Y)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_int_rat F X3)) (tptp.aa_int_rat F Y))))) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_int_rat F C)))))))) (forall ((A tptp.rat) (F tptp.fun_real_rat) (B tptp.real) (C tptp.real)) (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_real_rat F B))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real B) C)) (=> (forall ((X3 tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X3) Y)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_real_rat F X3)) (tptp.aa_real_rat F Y))))) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_real_rat F C)))))))) (forall ((A tptp.num) (F tptp.fun_rat_num) (B 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 B))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) C)) (=> (forall ((X3 tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X3) Y)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_rat_num F X3)) (tptp.aa_rat_num F Y))))) (tptp.pp (tptp.aa_num_bool _let_1 (tptp.aa_rat_num F C)))))))) (forall ((A tptp.num) (F tptp.fun_num_num) (B 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 B))) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num B) C)) (=> (forall ((X3 tptp.num) (Y tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X3) Y)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_num_num F X3)) (tptp.aa_num_num F Y))))) (tptp.pp (tptp.aa_num_bool _let_1 (tptp.aa_num_num F C)))))))) (forall ((A tptp.num) (F tptp.fun_nat_num) (B 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 B))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B) C)) (=> (forall ((X3 tptp.nat) (Y tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X3) Y)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_nat_num F X3)) (tptp.aa_nat_num F Y))))) (tptp.pp (tptp.aa_num_bool _let_1 (tptp.aa_nat_num F C)))))))) (forall ((A tptp.num) (F tptp.fun_int_num) (B 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 B))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B) C)) (=> (forall ((X3 tptp.int) (Y tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X3) Y)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_int_num F X3)) (tptp.aa_int_num F Y))))) (tptp.pp (tptp.aa_num_bool _let_1 (tptp.aa_int_num F C)))))))) (forall ((A tptp.num) (F tptp.fun_real_num) (B tptp.real) (C tptp.real)) (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_real_num F B))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real B) C)) (=> (forall ((X3 tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X3) Y)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_real_num F X3)) (tptp.aa_real_num F Y))))) (tptp.pp (tptp.aa_num_bool _let_1 (tptp.aa_real_num F C)))))))) (forall ((A tptp.rat) (B 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) B)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat F B)) C)) (=> (forall ((X3 tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X3) Y)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat F X3)) (tptp.aa_rat_rat F Y))))) (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) (B 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) B)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_rat_num F B)) C)) (=> (forall ((X3 tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X3) Y)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_rat_num F X3)) (tptp.aa_rat_num F Y))))) (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) (B 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) B)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_rat_nat F B)) C)) (=> (forall ((X3 tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X3) Y)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_rat_nat F X3)) (tptp.aa_rat_nat F Y))))) (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) (B 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) B)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_rat_int F B)) C)) (=> (forall ((X3 tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X3) Y)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_rat_int F X3)) (tptp.aa_rat_int F Y))))) (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.rat) (B 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) B)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_rat_real F B)) C)) (=> (forall ((X3 tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X3) Y)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_rat_real F X3)) (tptp.aa_rat_real F Y))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_rat_real F A)) C)))))) (forall ((A tptp.num) (B 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) B)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_num_rat F B)) C)) (=> (forall ((X3 tptp.num) (Y tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X3) Y)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_num_rat F X3)) (tptp.aa_num_rat F Y))))) (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) (B 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) B)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_num_num F B)) C)) (=> (forall ((X3 tptp.num) (Y tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X3) Y)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_num_num F X3)) (tptp.aa_num_num F Y))))) (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) (B 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) B)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_num_nat F B)) C)) (=> (forall ((X3 tptp.num) (Y tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X3) Y)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_num_nat F X3)) (tptp.aa_num_nat F Y))))) (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) (B 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) B)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_num_int F B)) C)) (=> (forall ((X3 tptp.num) (Y tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X3) Y)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_num_int F X3)) (tptp.aa_num_int F Y))))) (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.num) (B 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) B)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_num_real F B)) C)) (=> (forall ((X3 tptp.num) (Y tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X3) Y)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_num_real F X3)) (tptp.aa_num_real F Y))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_num_real F A)) C)))))) (forall ((X tptp.set_int) (Y4 tptp.set_int)) (=> (= X Y4) (tptp.ord_less_eq_set_int X Y4))) (forall ((X tptp.rat) (Y4 tptp.rat)) (=> (= X Y4) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) Y4)))) (forall ((X tptp.num) (Y4 tptp.num)) (=> (= X Y4) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X) Y4)))) (forall ((X tptp.nat) (Y4 tptp.nat)) (=> (= X Y4) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X) Y4)))) (forall ((X tptp.int) (Y4 tptp.int)) (=> (= X Y4) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X) Y4)))) (forall ((X tptp.real) (Y4 tptp.real)) (=> (= X Y4) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) Y4)))) (forall ((A tptp.rat) (B tptp.rat)) (or (= A B) (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B))) (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) A))))) (forall ((A tptp.num) (B tptp.num)) (or (= A B) (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A) B))) (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num B) A))))) (forall ((A tptp.nat) (B tptp.nat)) (or (= A B) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B))) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B) A))))) (forall ((A tptp.int) (B tptp.int)) (or (= A B) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B))) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B) A))))) (forall ((A tptp.real) (B tptp.real)) (or (= A B) (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) B))) (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real B) A))))) (forall ((X tptp.rat) (Y4 tptp.rat)) (or (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) Y4)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat Y4) X)))) (forall ((X tptp.num) (Y4 tptp.num)) (or (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X) Y4)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num Y4) X)))) (forall ((X tptp.nat) (Y4 tptp.nat)) (or (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X) Y4)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Y4) X)))) (forall ((X tptp.int) (Y4 tptp.int)) (or (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X) Y4)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Y4) X)))) (forall ((X tptp.real) (Y4 tptp.real)) (or (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) Y4)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y4) X)))) (forall ((A tptp.rat) (F tptp.fun_rat_rat) (B tptp.rat) (C tptp.rat)) (=> (= A (tptp.aa_rat_rat F B)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) C)) (=> (forall ((X3 tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X3) Y)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat F X3)) (tptp.aa_rat_rat F Y))))) (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) (B tptp.rat) (C tptp.rat)) (=> (= A (tptp.aa_rat_num F B)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) C)) (=> (forall ((X3 tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X3) Y)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_rat_num F X3)) (tptp.aa_rat_num F Y))))) (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) (B tptp.rat) (C tptp.rat)) (=> (= A (tptp.aa_rat_nat F B)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) C)) (=> (forall ((X3 tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X3) Y)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_rat_nat F X3)) (tptp.aa_rat_nat F Y))))) (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) (B tptp.rat) (C tptp.rat)) (=> (= A (tptp.aa_rat_int F B)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) C)) (=> (forall ((X3 tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X3) Y)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_rat_int F X3)) (tptp.aa_rat_int F Y))))) (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.real) (F tptp.fun_rat_real) (B tptp.rat) (C tptp.rat)) (=> (= A (tptp.aa_rat_real F B)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) C)) (=> (forall ((X3 tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X3) Y)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_rat_real F X3)) (tptp.aa_rat_real F Y))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) (tptp.aa_rat_real F C))))))) (forall ((A tptp.rat) (F tptp.fun_num_rat) (B tptp.num) (C tptp.num)) (=> (= A (tptp.aa_num_rat F B)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num B) C)) (=> (forall ((X3 tptp.num) (Y tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X3) Y)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_num_rat F X3)) (tptp.aa_num_rat F Y))))) (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) (B tptp.num) (C tptp.num)) (=> (= A (tptp.aa_num_num F B)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num B) C)) (=> (forall ((X3 tptp.num) (Y tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X3) Y)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_num_num F X3)) (tptp.aa_num_num F Y))))) (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) (B tptp.num) (C tptp.num)) (=> (= A (tptp.aa_num_nat F B)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num B) C)) (=> (forall ((X3 tptp.num) (Y tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X3) Y)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_num_nat F X3)) (tptp.aa_num_nat F Y))))) (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) (B tptp.num) (C tptp.num)) (=> (= A (tptp.aa_num_int F B)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num B) C)) (=> (forall ((X3 tptp.num) (Y tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X3) Y)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_num_int F X3)) (tptp.aa_num_int F Y))))) (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.real) (F tptp.fun_num_real) (B tptp.num) (C tptp.num)) (=> (= A (tptp.aa_num_real F B)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num B) C)) (=> (forall ((X3 tptp.num) (Y tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X3) Y)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_num_real F X3)) (tptp.aa_num_real F Y))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) (tptp.aa_num_real F C))))))) (forall ((A tptp.rat) (B 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) B)) (=> (= (tptp.aa_rat_rat F B) C) (=> (forall ((X3 tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X3) Y)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat F X3)) (tptp.aa_rat_rat F Y))))) (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) (B 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) B)) (=> (= (tptp.aa_rat_num F B) C) (=> (forall ((X3 tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X3) Y)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_rat_num F X3)) (tptp.aa_rat_num F Y))))) (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) (B 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) B)) (=> (= (tptp.aa_rat_nat F B) C) (=> (forall ((X3 tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X3) Y)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_rat_nat F X3)) (tptp.aa_rat_nat F Y))))) (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) (B 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) B)) (=> (= (tptp.aa_rat_int F B) C) (=> (forall ((X3 tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X3) Y)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_rat_int F X3)) (tptp.aa_rat_int F Y))))) (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.rat) (B 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) B)) (=> (= (tptp.aa_rat_real F B) C) (=> (forall ((X3 tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X3) Y)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_rat_real F X3)) (tptp.aa_rat_real F Y))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_rat_real F A)) C)))))) (forall ((A tptp.num) (B 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) B)) (=> (= (tptp.aa_num_rat F B) C) (=> (forall ((X3 tptp.num) (Y tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X3) Y)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_num_rat F X3)) (tptp.aa_num_rat F Y))))) (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) (B 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) B)) (=> (= (tptp.aa_num_num F B) C) (=> (forall ((X3 tptp.num) (Y tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X3) Y)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_num_num F X3)) (tptp.aa_num_num F Y))))) (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) (B 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) B)) (=> (= (tptp.aa_num_nat F B) C) (=> (forall ((X3 tptp.num) (Y tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X3) Y)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_num_nat F X3)) (tptp.aa_num_nat F Y))))) (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) (B 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) B)) (=> (= (tptp.aa_num_int F B) C) (=> (forall ((X3 tptp.num) (Y tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X3) Y)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_num_int F X3)) (tptp.aa_num_int F Y))))) (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.num) (B 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) B)) (=> (= (tptp.aa_num_real F B) C) (=> (forall ((X3 tptp.num) (Y tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X3) Y)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_num_real F X3)) (tptp.aa_num_real F Y))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_num_real F A)) C)))))) (forall ((X tptp.rat) (Y4 tptp.rat)) (=> (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) Y4))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat Y4) X)))) (forall ((X tptp.num) (Y4 tptp.num)) (=> (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X) Y4))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num Y4) X)))) (forall ((X tptp.nat) (Y4 tptp.nat)) (=> (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X) Y4))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Y4) X)))) (forall ((X tptp.int) (Y4 tptp.int)) (=> (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X) Y4))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Y4) X)))) (forall ((X tptp.real) (Y4 tptp.real)) (=> (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) Y4))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y4) X)))) (forall ((Y4 tptp.set_int) (X tptp.set_int)) (=> (tptp.ord_less_eq_set_int Y4 X) (= (tptp.ord_less_eq_set_int X Y4) (= X Y4)))) (forall ((Y4 tptp.rat) (X tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat Y4) X)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) Y4)) (= X Y4)))) (forall ((Y4 tptp.num) (X tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num Y4) X)) (= (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X) Y4)) (= X Y4)))) (forall ((Y4 tptp.nat) (X tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Y4) X)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X) Y4)) (= X Y4)))) (forall ((Y4 tptp.int) (X tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Y4) X)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X) Y4)) (= X Y4)))) (forall ((Y4 tptp.real) (X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y4) X)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) Y4)) (= X Y4)))) (forall ((C tptp.nat) (A tptp.nat) (B 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 B) C)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat _let_1 B)) C))))) (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int 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 B) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int (tptp.aa_int_int _let_1 B)) C))))) (forall ((B tptp.complex) (C tptp.complex) (W tptp.num)) (let ((_let_1 (tptp.numera6690914467698888265omplex W))) (let ((_let_2 (= C tptp.zero_zero_complex))) (= (= (tptp.divide1717551699836669952omplex B C) _let_1) (and (=> (not _let_2) (= B (tptp.aa_complex_complex (tptp.times_times_complex _let_1) C))) (=> _let_2 (= _let_1 tptp.zero_zero_complex))))))) (forall ((B 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 B) C) _let_1) (and (=> (not _let_2) (= B (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real _let_1) C))) (=> _let_2 (= _let_1 tptp.zero_zero_real))))))) (forall ((B 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 B) C) _let_1) (and (=> (not _let_2) (= B (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) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (tptp.numera6690914467698888265omplex W))) (let ((_let_2 (= C tptp.zero_zero_complex))) (= (= _let_1 (tptp.divide1717551699836669952omplex B C)) (and (=> (not _let_2) (= (tptp.aa_complex_complex (tptp.times_times_complex _let_1) C) B)) (=> _let_2 (= _let_1 tptp.zero_zero_complex))))))) (forall ((W tptp.num) (B 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 B) C)) (and (=> (not _let_2) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real _let_1) C) B)) (=> _let_2 (= _let_1 tptp.zero_zero_real))))))) (forall ((W tptp.num) (B 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 B) C)) (and (=> (not _let_2) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat _let_1) C) B)) (=> _let_2 (= _let_1 tptp.zero_zero_rat))))))) (forall ((A tptp.code_integer) (B 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) B)) (= (= (tptp.divide6298287555418463151nteger B A) C) (= B (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger C) A)))))) (forall ((A tptp.nat) (B 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) B)) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat B) A) C) (= B (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat C) A)))))) (forall ((A tptp.int) (B 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) B)) (= (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int B) A) C) (= B (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int C) A)))))) (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (=> (not (= B tptp.zero_z3403309356797280102nteger)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer B) A)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.divide6298287555418463151nteger A B)) 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) B))))))) (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (not (= B tptp.zero_zero_nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat B) 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) B)) 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) B))))))) (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (=> (not (= B tptp.zero_zero_int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int B) A)) (= (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.divide_divide_int A) B)) 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) B))))))) (forall ((C tptp.code_integer) (B 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) B)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer A) (tptp.divide6298287555418463151nteger B 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)) B)))))) (forall ((C tptp.nat) (B 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) B)) (= (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 B) 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)) B)))))) (forall ((C tptp.int) (B 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) B)) (= (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.divide_divide_int B) 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)) B)))))) (forall ((A tptp.code_integer) (C tptp.code_integer) (B 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) B)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer C) D)) (= (= (tptp.divide6298287555418463151nteger B A) (tptp.divide6298287555418463151nteger D C)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B) C) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) D)))))))) (forall ((A tptp.nat) (C tptp.nat) (B 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) B)) (=> (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 B) 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 B) C) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) D)))))))) (forall ((A tptp.int) (C tptp.int) (B 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) B)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int C) D)) (= (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int B) A) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int D) C)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B) C) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) D)))))))) _let_190 (forall ((A tptp.nat) (B tptp.nat)) (= (= A B) (= (tptp.aa_nat_int tptp.semiri1314217659103216013at_int A) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int B)))) (forall ((P tptp.bool) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_nat (tptp.if_nat P A) B)))) (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 B))))))) (tptp.pp (tptp.aa_Code_integer_bool _let_169 tptp.zero_z3403309356797280102nteger)) (tptp.pp (tptp.aa_nat_bool _let_168 tptp.zero_zero_nat)) (tptp.pp (tptp.aa_int_bool _let_167 tptp.zero_zero_int)) (= _let_2 _let_98) (= _let_185 (tptp.aa_nat_nat tptp.suc _let_98)) (= (tptp.aa_nat_nat tptp.vEBT_V8646137997579335489_i_l_d tptp.zero_zero_nat) _let_189) (= (tptp.aa_nat_nat tptp.vEBT_V8646137997579335489_i_l_d _let_58) _let_189) (forall ((X2 tptp.num)) (not (= tptp.one (tptp.aa_num_num tptp.bit0 X2)))) (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.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.aa_nat_fun_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.aa_int_fun_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 ((A tptp.code_integer)) (let ((_let_1 (tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_nat6383147911832638789nteger tptp.bit_se8260200283734997820nteger tptp.zero_zero_nat) A) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger _let_1) (tptp.divide6298287555418463151nteger A _let_1))))) (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.aa_nat_fun_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.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.aa_Cod1783974652533396728nteger (tptp.aa_nat6383147911832638789nteger 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.aa_nat_fun_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 ((M tptp.nat) (A tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_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.aa_nat_fun_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.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.aa_Cod1783974652533396728nteger (tptp.aa_nat6383147911832638789nteger tptp.bit_se8260200283734997820nteger M) A))) (or (tptp.pp (tptp.aa_Code_integer_bool _let_1 A)) (= M tptp.zero_zero_nat))))) (forall ((A2 tptp.set_int) (B3 tptp.set_int)) (=> (tptp.ord_less_eq_set_int A2 B3) (=> (tptp.ord_less_eq_set_int B3 A2) (= A2 B3)))) (forall ((A2 tptp.set_complex) (B3 tptp.set_complex)) (=> (forall ((X3 tptp.complex)) (=> (tptp.member_complex X3 A2) (tptp.member_complex X3 B3))) (tptp.ord_le211207098394363844omplex A2 B3))) (forall ((A2 tptp.set_real) (B3 tptp.set_real)) (=> (forall ((X3 tptp.real)) (=> (tptp.member_real X3 A2) (tptp.member_real X3 B3))) (tptp.ord_less_eq_set_real A2 B3))) (forall ((A2 tptp.set_set_nat) (B3 tptp.set_set_nat)) (=> (forall ((X3 tptp.set_nat)) (=> (tptp.member_set_nat X3 A2) (tptp.member_set_nat X3 B3))) (tptp.ord_le6893508408891458716et_nat A2 B3))) (forall ((A2 tptp.set_nat) (B3 tptp.set_nat)) (=> (forall ((X3 tptp.nat)) (let ((_let_1 (tptp.member_nat X3))) (=> (tptp.pp (tptp.aa_set_nat_bool _let_1 A2)) (tptp.pp (tptp.aa_set_nat_bool _let_1 B3))))) (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat A2) B3)))) (forall ((A2 tptp.set_int) (B3 tptp.set_int)) (=> (forall ((X3 tptp.int)) (=> (tptp.member_int X3 A2) (tptp.member_int X3 B3))) (tptp.ord_less_eq_set_int A2 B3))) (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))) (= (tptp.aa_nat_nat tptp.vEBT_V8346862874174094_d_u_p _let_58) _let_185) (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.aa_nat_fun_int_int tptp.bit_se4203085406695923979it_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.aa_nat_fun_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.aa_nat_fun_int_int tptp.bit_se2159334234014336723it_int N) K))) (tptp.pp (tptp.aa_int_bool _let_1 K))))) (forall ((A tptp.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)) (= (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.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.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.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 ((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)) (= (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)) (= (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 ((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 ((A tptp.rat) (B 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) B))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) A)))) (forall ((A tptp.int) (B 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) B))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B) A)))) (forall ((A tptp.real) (B 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) B))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real B) A)))) (forall ((V tptp.num) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (tptp.times_times_complex (tptp.numera6690914467698888265omplex V)))) (= (tptp.aa_complex_complex _let_1 (tptp.minus_minus_complex B C)) (tptp.minus_minus_complex (tptp.aa_complex_complex _let_1 B) (tptp.aa_complex_complex _let_1 C))))) (forall ((V tptp.num) (B 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 B) C)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real _let_1 B)) (tptp.aa_real_real _let_1 C))))) (forall ((V tptp.num) (B 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 B) C)) (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_rat_rat _let_1 B)) (tptp.aa_rat_rat _let_1 C))))) (forall ((V tptp.num) (B 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 B) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_int_int _let_1 B)) (tptp.aa_int_int _let_1 C))))) (forall ((A tptp.complex) (B tptp.complex) (V tptp.num)) (let ((_let_1 (tptp.numera6690914467698888265omplex V))) (= (tptp.aa_complex_complex (tptp.times_times_complex (tptp.minus_minus_complex A B)) _let_1) (tptp.minus_minus_complex (tptp.aa_complex_complex (tptp.times_times_complex A) _let_1) (tptp.aa_complex_complex (tptp.times_times_complex B) _let_1))))) (forall ((A tptp.real) (B 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) B)) _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 B) _let_1))))) (forall ((A tptp.rat) (B 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) B)) _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 B) _let_1))))) (forall ((A tptp.int) (B 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) B)) _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 B) _let_1))))) (forall ((C tptp.code_integer) (A tptp.code_integer) (B 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 B)) (= (tptp.divide6298287555418463151nteger (tptp.minus_8373710615458151222nteger A B) C) (tptp.minus_8373710615458151222nteger (tptp.divide6298287555418463151nteger A C) (tptp.divide6298287555418463151nteger B C))))))) (forall ((C tptp.int) (A tptp.int) (B 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 B)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) B)) 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.divide_divide_int A) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int B) C))))))) (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 ((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.aa_int_fun_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 ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (=> (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A) B) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real C) D)) (= (= A B) (= C D)))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (=> (= (tptp.aa_rat_rat (tptp.minus_minus_rat A) B) (tptp.aa_rat_rat (tptp.minus_minus_rat C) D)) (= (= A B) (= C D)))) (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (=> (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) B) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int C) D)) (= (= A B) (= C D)))) (forall ((A tptp.real) (C tptp.real) (B 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)) B) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real _let_1 B)) C)))) (forall ((A tptp.rat) (C tptp.rat) (B 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)) B) (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_rat_rat _let_1 B)) C)))) (forall ((A tptp.nat) (C tptp.nat) (B 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)) B) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat _let_1 B)) C)))) (forall ((A tptp.int) (C tptp.int) (B 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)) B) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_int_int _let_1 B)) C)))) (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.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (=> (= (tptp.aa_rat_rat (tptp.minus_minus_rat A) B) (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) B)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat C) D))))) (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (=> (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) B) (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) B)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int C) D))))) (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (=> (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A) B) (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) B)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real C) D))))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B)) (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 B) C))))) (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B)) (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 B) C))))) (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) B)) (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 B) C))))) (forall ((B 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 B) 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 B)))))) (forall ((B 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 B) 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 B)))))) (forall ((B 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 B) 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 B)))))) (forall ((A tptp.rat) (B 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) B)) (=> (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 B) D)))))) (forall ((A tptp.int) (B 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) B)) (=> (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 B) D)))))) (forall ((A tptp.real) (B tptp.real) (D tptp.real) (C tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) B)) (=> (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 B) D)))))) (forall ((A tptp.complex) (B tptp.complex)) (= (= A B) (= (tptp.minus_minus_complex A B) tptp.zero_zero_complex))) (forall ((A tptp.real) (B tptp.real)) (= (= A B) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A) B) tptp.zero_zero_real))) (forall ((A tptp.rat) (B tptp.rat)) (= (= A B) (= (tptp.aa_rat_rat (tptp.minus_minus_rat A) B) tptp.zero_zero_rat))) (forall ((A tptp.int) (B tptp.int)) (= (= A B) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) B) tptp.zero_zero_int))) (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.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_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_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_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 ((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 ((A tptp.real) (B 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 B) C)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real _let_1 B)) (tptp.aa_real_real _let_1 C))))) (forall ((A tptp.rat) (B 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 B) C)) (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_rat_rat _let_1 B)) (tptp.aa_rat_rat _let_1 C))))) (forall ((A tptp.nat) (B 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 B) C)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat _let_1 B)) (tptp.aa_nat_nat _let_1 C))))) (forall ((A tptp.int) (B 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 B) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_int_int _let_1 B)) (tptp.aa_int_int _let_1 C))))) (forall ((B 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 B) 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 B) A)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real C) A)))) (forall ((B 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 B) C)) A) (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat B) A)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat C) A)))) (forall ((B 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 B) 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 B) A)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat C) A)))) (forall ((B 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 B) 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 B) A)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int C) A)))) (forall ((A tptp.real) (B 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 B) C)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real _let_1 B)) (tptp.aa_real_real _let_1 C))))) (forall ((A tptp.rat) (B 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 B) C)) (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_rat_rat _let_1 B)) (tptp.aa_rat_rat _let_1 C))))) (forall ((A tptp.int) (B 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 B) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_int_int _let_1 B)) (tptp.aa_int_int _let_1 C))))) (forall ((A tptp.real) (B 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) B)) 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 B) C)))) (forall ((A tptp.rat) (B 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) B)) 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 B) C)))) (forall ((A tptp.int) (B 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) B)) 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 B) C)))) (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (= (tptp.divide1717551699836669952omplex (tptp.minus_minus_complex A B) C) (tptp.minus_minus_complex (tptp.divide1717551699836669952omplex A C) (tptp.divide1717551699836669952omplex B C)))) (forall ((A tptp.real) (B 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) B)) 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 B) C)))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (= (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_rat_rat (tptp.minus_minus_rat A) B)) 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 B) C)))) (forall ((A tptp.code_integer) (C tptp.code_integer) (B 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 B))) (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.minus_8373710615458151222nteger B C)))))) (forall ((A tptp.int) (C tptp.int) (B 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) B))) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int B) C)))))) (forall ((X tptp.code_integer) (Y4 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 Y4)) (=> (tptp.pp (tptp.aa_Code_integer_bool _let_1 Z)) (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.minus_8373710615458151222nteger Y4 Z))))))) (forall ((X tptp.real) (Y4 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 Y4)) (=> (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 Y4) Z))))))) (forall ((X tptp.rat) (Y4 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 Y4)) (=> (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 Y4) Z))))))) (forall ((X tptp.int) (Y4 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 Y4)) (=> (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 Y4) Z))))))) (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 ((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 ((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) (B tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B))) (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 B))) (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 ((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 ((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 ((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 ((A tptp.rat) (B tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B)) (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) B)) tptp.zero_zero_rat)))) (forall ((A tptp.int) (B tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B)) (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) B)) tptp.zero_zero_int)))) (forall ((A tptp.real) (B tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) B)) (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) B)) tptp.zero_zero_real)))) _let_188 (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 ((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 ((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.extended_enat)) (tptp.pp (tptp.aa_Ext2772979874139974381t_bool (tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) N))) (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.aa_nat_fun_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.aa_nat_fun_int_int tptp.bit_se7879613467334960850it_int N) 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 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_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 ((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 ((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))))))) _let_187 (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.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 ((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 ((Z tptp.complex) (X tptp.complex) (Y4 tptp.complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (tptp.minus_minus_complex (tptp.divide1717551699836669952omplex X Z) Y4) (tptp.divide1717551699836669952omplex (tptp.minus_minus_complex X (tptp.aa_complex_complex (tptp.times_times_complex Y4) Z)) Z)))) (forall ((Z tptp.real) (X tptp.real) (Y4 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)) Y4) (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 Y4) Z))) Z)))) (forall ((Z tptp.rat) (X tptp.rat) (Y4 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)) Y4) (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 Y4) Z))) Z)))) (forall ((Z tptp.complex) (X tptp.complex) (Y4 tptp.complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (tptp.minus_minus_complex X (tptp.divide1717551699836669952omplex Y4 Z)) (tptp.divide1717551699836669952omplex (tptp.minus_minus_complex (tptp.aa_complex_complex (tptp.times_times_complex X) Z) Y4) Z)))) (forall ((Z tptp.real) (X tptp.real) (Y4 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 Y4) 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)) Y4)) Z)))) (forall ((Z tptp.rat) (X tptp.rat) (Y4 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 Y4) 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)) Y4)) Z)))) (forall ((Y4 tptp.complex) (Z tptp.complex) (X tptp.complex) (W tptp.complex)) (=> (not (= Y4 tptp.zero_zero_complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (tptp.minus_minus_complex (tptp.divide1717551699836669952omplex X Y4) (tptp.divide1717551699836669952omplex W Z)) (tptp.divide1717551699836669952omplex (tptp.minus_minus_complex (tptp.aa_complex_complex (tptp.times_times_complex X) Z) (tptp.aa_complex_complex (tptp.times_times_complex W) Y4)) (tptp.aa_complex_complex (tptp.times_times_complex Y4) Z)))))) (forall ((Y4 tptp.real) (Z tptp.real) (X tptp.real) (W tptp.real)) (=> (not (= Y4 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) Y4)) (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) Y4))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real Y4) Z)))))) (forall ((Y4 tptp.rat) (Z tptp.rat) (X tptp.rat) (W tptp.rat)) (=> (not (= Y4 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) Y4)) (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) Y4))) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat Y4) Z)))))) (forall ((Z tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (tptp.minus_minus_complex A (tptp.divide1717551699836669952omplex B Z)))) (let ((_let_2 (= Z tptp.zero_zero_complex))) (and (=> _let_2 (= _let_1 A)) (=> (not _let_2) (= _let_1 (tptp.divide1717551699836669952omplex (tptp.minus_minus_complex (tptp.aa_complex_complex (tptp.times_times_complex A) Z) B) Z))))))) (forall ((Z tptp.real) (A tptp.real) (B 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 B) 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)) B)) Z))))))) (forall ((Z tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (tptp.aa_rat_rat (tptp.minus_minus_rat A) (tptp.aa_rat_rat (tptp.divide_divide_rat B) 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)) B)) Z))))))) (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 ((B tptp.real) (A tptp.real) (C tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.times_times_real B))) (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 ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_rat tptp.times_times_rat B))) (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 ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B))) (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 ((B tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.times_times_int B))) (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)))))) _let_186 (forall ((A tptp.rat) (B tptp.rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) B) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat B) A))) (forall ((A tptp.nat) (B tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) B) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B) A))) (forall ((A tptp.int) (B tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) B) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B) A))) (forall ((A tptp.real) (B 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 B)) C) (tptp.aa_real_real _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real B) C))))) (forall ((A tptp.rat) (B 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 B)) C) (tptp.aa_rat_rat _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat B) C))))) (forall ((A tptp.nat) (B 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 B)) C) (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B) C))))) (forall ((A tptp.int) (B 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 B)) C) (tptp.aa_int_int _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B) C))))) (forall ((A tptp.real) (B 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 B)) C) (tptp.aa_real_real _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real B) C))))) (forall ((A tptp.rat) (B 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 B)) C) (tptp.aa_rat_rat _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat B) C))))) (forall ((A tptp.nat) (B 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 B)) C) (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B) C))))) (forall ((A tptp.int) (B 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 B)) C) (tptp.aa_int_int _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B) C))))) (forall ((A2 tptp.set_complex) (B3 tptp.set_complex) (X tptp.complex)) (=> (tptp.ord_le211207098394363844omplex A2 B3) (=> (tptp.member_complex X A2) (tptp.member_complex X B3)))) (forall ((A2 tptp.set_real) (B3 tptp.set_real) (X tptp.real)) (=> (tptp.ord_less_eq_set_real A2 B3) (=> (tptp.member_real X A2) (tptp.member_real X B3)))) (forall ((A2 tptp.set_set_nat) (B3 tptp.set_set_nat) (X tptp.set_nat)) (=> (tptp.ord_le6893508408891458716et_nat A2 B3) (=> (tptp.member_set_nat X A2) (tptp.member_set_nat X B3)))) (forall ((A2 tptp.set_nat) (B3 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 A2) B3)) (=> (tptp.pp (tptp.aa_set_nat_bool _let_1 A2)) (tptp.pp (tptp.aa_set_nat_bool _let_1 B3)))))) (forall ((A2 tptp.set_int) (B3 tptp.set_int) (X tptp.int)) (=> (tptp.ord_less_eq_set_int A2 B3) (=> (tptp.member_int X A2) (tptp.member_int X B3)))) (forall ((A2 tptp.set_complex) (B3 tptp.set_complex) (C tptp.complex)) (=> (tptp.ord_le211207098394363844omplex A2 B3) (=> (tptp.member_complex C A2) (tptp.member_complex C B3)))) (forall ((A2 tptp.set_real) (B3 tptp.set_real) (C tptp.real)) (=> (tptp.ord_less_eq_set_real A2 B3) (=> (tptp.member_real C A2) (tptp.member_real C B3)))) (forall ((A2 tptp.set_set_nat) (B3 tptp.set_set_nat) (C tptp.set_nat)) (=> (tptp.ord_le6893508408891458716et_nat A2 B3) (=> (tptp.member_set_nat C A2) (tptp.member_set_nat C B3)))) (forall ((A2 tptp.set_nat) (B3 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 A2) B3)) (=> (tptp.pp (tptp.aa_set_nat_bool _let_1 A2)) (tptp.pp (tptp.aa_set_nat_bool _let_1 B3)))))) (forall ((A2 tptp.set_int) (B3 tptp.set_int) (C tptp.int)) (=> (tptp.ord_less_eq_set_int A2 B3) (=> (tptp.member_int C A2) (tptp.member_int C B3)))) (forall ((A2 tptp.set_int) (B3 tptp.set_int)) (=> (= A2 B3) (not (=> (tptp.ord_less_eq_set_int A2 B3) (not (tptp.ord_less_eq_set_int B3 A2)))))) (forall ((A2 tptp.set_complex) (B3 tptp.set_complex)) (= (tptp.ord_le211207098394363844omplex A2 B3) (forall ((X5 tptp.complex)) (=> (tptp.member_complex X5 A2) (tptp.member_complex X5 B3))))) (forall ((A2 tptp.set_real) (B3 tptp.set_real)) (= (tptp.ord_less_eq_set_real A2 B3) (forall ((X5 tptp.real)) (=> (tptp.member_real X5 A2) (tptp.member_real X5 B3))))) (forall ((A2 tptp.set_set_nat) (B3 tptp.set_set_nat)) (= (tptp.ord_le6893508408891458716et_nat A2 B3) (forall ((X5 tptp.set_nat)) (=> (tptp.member_set_nat X5 A2) (tptp.member_set_nat X5 B3))))) (forall ((A2 tptp.set_nat) (B3 tptp.set_nat)) (= (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat A2) B3)) (forall ((X5 tptp.nat)) (let ((_let_1 (tptp.member_nat X5))) (=> (tptp.pp (tptp.aa_set_nat_bool _let_1 A2)) (tptp.pp (tptp.aa_set_nat_bool _let_1 B3))))))) (forall ((A2 tptp.set_int) (B3 tptp.set_int)) (= (tptp.ord_less_eq_set_int A2 B3) (forall ((X5 tptp.int)) (=> (tptp.member_int X5 A2) (tptp.member_int X5 B3))))) (forall ((A2 tptp.set_int) (B3 tptp.set_int)) (=> (= A2 B3) (tptp.ord_less_eq_set_int A2 B3))) (forall ((A2 tptp.set_int) (B3 tptp.set_int)) (=> (= A2 B3) (tptp.ord_less_eq_set_int B3 A2))) (forall ((A2 tptp.set_complex) (B3 tptp.set_complex)) (= (tptp.ord_le211207098394363844omplex A2 B3) (forall ((T2 tptp.complex)) (=> (tptp.member_complex T2 A2) (tptp.member_complex T2 B3))))) (forall ((A2 tptp.set_real) (B3 tptp.set_real)) (= (tptp.ord_less_eq_set_real A2 B3) (forall ((T2 tptp.real)) (=> (tptp.member_real T2 A2) (tptp.member_real T2 B3))))) (forall ((A2 tptp.set_set_nat) (B3 tptp.set_set_nat)) (= (tptp.ord_le6893508408891458716et_nat A2 B3) (forall ((T2 tptp.set_nat)) (=> (tptp.member_set_nat T2 A2) (tptp.member_set_nat T2 B3))))) (forall ((A2 tptp.set_nat) (B3 tptp.set_nat)) (= (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat A2) B3)) (forall ((T2 tptp.nat)) (let ((_let_1 (tptp.member_nat T2))) (=> (tptp.pp (tptp.aa_set_nat_bool _let_1 A2)) (tptp.pp (tptp.aa_set_nat_bool _let_1 B3))))))) (forall ((A2 tptp.set_int) (B3 tptp.set_int)) (= (tptp.ord_less_eq_set_int A2 B3) (forall ((T2 tptp.int)) (=> (tptp.member_int T2 A2) (tptp.member_int T2 B3))))) (forall ((A2 tptp.set_int)) (tptp.ord_less_eq_set_int A2 A2)) (forall ((P tptp.fun_real_bool) (Q tptp.fun_real_bool)) (=> (forall ((X3 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool P X3)) (tptp.pp (tptp.aa_real_bool Q X3)))) (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 ((X3 tptp.list_nat)) (=> (tptp.pp (tptp.aa_list_nat_bool P X3)) (tptp.pp (tptp.aa_list_nat_bool Q X3)))) (tptp.ord_le6045566169113846134st_nat (tptp.collect_list_nat P) (tptp.collect_list_nat Q)))) (forall ((P tptp.fun_set_nat_bool) (Q tptp.fun_set_nat_bool)) (=> (forall ((X3 tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool P X3)) (tptp.pp (tptp.aa_set_nat_bool Q X3)))) (tptp.ord_le6893508408891458716et_nat (tptp.collect_set_nat P) (tptp.collect_set_nat Q)))) (forall ((P tptp.fun_nat_bool) (Q tptp.fun_nat_bool)) (=> (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool P X3)) (tptp.pp (tptp.aa_nat_bool Q X3)))) (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 ((X3 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool P X3)) (tptp.pp (tptp.aa_int_bool Q X3)))) (tptp.ord_less_eq_set_int (tptp.collect_int P) (tptp.collect_int Q)))) (forall ((A2 tptp.set_int) (B3 tptp.set_int) (C2 tptp.set_int)) (=> (tptp.ord_less_eq_set_int A2 B3) (=> (tptp.ord_less_eq_set_int B3 C2) (tptp.ord_less_eq_set_int A2 C2)))) (forall ((A2 tptp.set_int) (B3 tptp.set_int)) (= (= A2 B3) (and (tptp.ord_less_eq_set_int A2 B3) (tptp.ord_less_eq_set_int B3 A2)))) (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 ((X5 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool P X5)) (tptp.pp (tptp.aa_real_bool Q X5)))))) (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 ((X5 tptp.list_nat)) (=> (tptp.pp (tptp.aa_list_nat_bool P X5)) (tptp.pp (tptp.aa_list_nat_bool Q X5)))))) (forall ((P tptp.fun_set_nat_bool) (Q tptp.fun_set_nat_bool)) (= (tptp.ord_le6893508408891458716et_nat (tptp.collect_set_nat P) (tptp.collect_set_nat Q)) (forall ((X5 tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool P X5)) (tptp.pp (tptp.aa_set_nat_bool Q X5)))))) (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 ((X5 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool P X5)) (tptp.pp (tptp.aa_nat_bool Q X5)))))) (forall ((P tptp.fun_int_bool) (Q tptp.fun_int_bool)) (= (tptp.ord_less_eq_set_int (tptp.collect_int P) (tptp.collect_int Q)) (forall ((X5 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool P X5)) (tptp.pp (tptp.aa_int_bool Q X5)))))) (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int 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 B) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int (tptp.aa_int_int _let_1 B)) C))))) (forall ((Y4 tptp.rat) (Z tptp.rat) (X tptp.rat) (W tptp.rat)) (=> (not (= Y4 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) Y4)) (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) Y4))) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat Y4) Z))) tptp.zero_zero_rat)))))) (forall ((Y4 tptp.real) (Z tptp.real) (X tptp.real) (W tptp.real)) (=> (not (= Y4 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) Y4)) (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) Y4))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real Y4) Z))) tptp.zero_zero_real)))))) (= (tptp.aa_nat_nat tptp.vEBT_V8346862874174094_d_u_p tptp.zero_zero_nat) _let_185) (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))) (forall ((A tptp.nat) (B tptp.nat)) (exists ((D2 tptp.nat) (X3 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 B))) (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 B)) (or (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat _let_1 X3)) (tptp.aa_nat_nat _let_2 Y)) D2) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat _let_2 X3)) (tptp.aa_nat_nat _let_1 Y)) D2)))))))) (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 ((N tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat tptp.vEBT_V8346862874174094_d_u_p N)) (tptp.aa_nat_nat tptp.vEBT_V8646137997579335489_i_l_d N)))) (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 ((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_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.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.nat)) (not (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat tptp.zero_zero_nat) A)) (not (= tptp.zero_zero_nat A))))) (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.nat)) (let ((_let_1 (not (= A tptp.zero_zero_nat)))) (= _let_1 (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat A) tptp.zero_zero_nat)) _let_1)))) (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 ((N tptp.extended_enat)) (= (tptp.minus_3235023915231533773d_enat tptp.zero_z5237406670263579293d_enat N) tptp.zero_z5237406670263579293d_enat)) (forall ((N tptp.extended_enat)) (= (tptp.minus_3235023915231533773d_enat N tptp.zero_z5237406670263579293d_enat) N)) (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 ((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 ((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 ((A tptp.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.aa_int_fun_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.aa_int_fun_int_int tptp.divide_divide_int A) tptp.one_one_int) A)) (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 ((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)) (= (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.nat)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_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.one_one_nat) (and (= M tptp.one_one_nat) (= N tptp.one_one_nat)))) (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)) (= (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.real) (B 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) B))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B) A)))) (forall ((A tptp.rat) (B 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) B))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) A)))) (forall ((A tptp.int) (B 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) B))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B) A)))) (forall ((C tptp.complex) (B tptp.complex)) (= (= C (tptp.aa_complex_complex (tptp.times_times_complex C) B)) (or (= C tptp.zero_zero_complex) (= B tptp.one_one_complex)))) (forall ((C tptp.real) (B tptp.real)) (= (= C (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real C) B)) (or (= C tptp.zero_zero_real) (= B tptp.one_one_real)))) (forall ((C tptp.rat) (B tptp.rat)) (= (= C (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat C) B)) (or (= C tptp.zero_zero_rat) (= B tptp.one_one_rat)))) (forall ((C tptp.int) (B tptp.int)) (= (= C (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int C) B)) (or (= C tptp.zero_zero_int) (= B 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) (B tptp.complex)) (= (= C (tptp.aa_complex_complex (tptp.times_times_complex B) C)) (or (= C tptp.zero_zero_complex) (= B tptp.one_one_complex)))) (forall ((C tptp.real) (B tptp.real)) (= (= C (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real B) C)) (or (= C tptp.zero_zero_real) (= B tptp.one_one_real)))) (forall ((C tptp.rat) (B tptp.rat)) (= (= C (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat B) C)) (or (= C tptp.zero_zero_rat) (= B tptp.one_one_rat)))) (forall ((C tptp.int) (B tptp.int)) (= (= C (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B) C)) (or (= C tptp.zero_zero_int) (= B 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)))) (= (tptp.minus_minus_complex tptp.one_one_complex tptp.one_one_complex) tptp.zero_zero_complex) (= (tptp.aa_real_real _let_141 tptp.one_one_real) tptp.zero_zero_real) (= (tptp.aa_rat_rat _let_139 tptp.one_one_rat) tptp.zero_zero_rat) (= (tptp.aa_int_int _let_140 tptp.one_one_int) tptp.zero_zero_int) (forall ((A tptp.complex)) (=> (not (= A tptp.zero_zero_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.aa_int_fun_int_int tptp.divide_divide_int A) A) tptp.one_one_int))) (forall ((A tptp.complex) (B tptp.complex)) (= (= (tptp.divide1717551699836669952omplex A B) tptp.one_one_complex) (and (not (= B tptp.zero_zero_complex)) (= A B)))) (forall ((A tptp.real) (B tptp.real)) (= (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real A) B) tptp.one_one_real) (and (not (= B tptp.zero_zero_real)) (= A B)))) (forall ((A tptp.rat) (B tptp.rat)) (= (= (tptp.aa_rat_rat (tptp.divide_divide_rat A) B) tptp.one_one_rat) (and (not (= B tptp.zero_zero_rat)) (= A B)))) (forall ((A tptp.complex) (B tptp.complex)) (= (= tptp.one_one_complex (tptp.divide1717551699836669952omplex A B)) (and (not (= B tptp.zero_zero_complex)) (= A B)))) (forall ((A tptp.real) (B tptp.real)) (= (= tptp.one_one_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real A) B)) (and (not (= B tptp.zero_zero_real)) (= A B)))) (forall ((A tptp.rat) (B tptp.rat)) (= (= tptp.one_one_rat (tptp.aa_rat_rat (tptp.divide_divide_rat A) B)) (and (not (= B tptp.zero_zero_rat)) (= A B)))) (forall ((A tptp.complex)) (=> (not (= A tptp.zero_zero_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.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 ((B tptp.real) (A tptp.real)) (= (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real B) A) tptp.one_one_real) (and (not (= A tptp.zero_zero_real)) (= A B)))) (forall ((B tptp.rat) (A tptp.rat)) (= (= (tptp.aa_rat_rat (tptp.divide_divide_rat B) A) tptp.one_one_rat) (and (not (= A tptp.zero_zero_rat)) (= A B)))) (forall ((B tptp.real) (A tptp.real)) (= (= tptp.one_one_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real B) A)) (and (not (= A tptp.zero_zero_real)) (= A B)))) (forall ((B tptp.rat) (A tptp.rat)) (= (= tptp.one_one_rat (tptp.aa_rat_rat (tptp.divide_divide_rat B) A)) (and (not (= A tptp.zero_zero_rat)) (= A B)))) (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 ((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.code_integer) (B 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 B) 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) B)) tptp.one_one_Code_integer))))) (forall ((A tptp.nat) (B 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 B) 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) B)) tptp.one_one_nat))))) (forall ((A tptp.int) (B 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 B) 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) B)) tptp.one_one_int))))) (forall ((A tptp.code_integer) (B 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 B) tptp.one_one_Code_integer)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.divide6298287555418463151nteger A B)) tptp.one_one_Code_integer))))) (forall ((A tptp.nat) (B 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 B) 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) B)) tptp.one_one_nat))))) (forall ((A tptp.int) (B 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 B) 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.divide_divide_int A) B)) tptp.one_one_int))))) (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.aa_int_fun_int_int tptp.divide_divide_int tptp.one_one_int) A)) tptp.one_one_int)))) (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.aa_int_fun_int_int 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 ((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_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_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 ((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 ((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 ((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 ((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 ((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_real tptp.semiri5074537144036343181t_real N) tptp.one_one_real) (= 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_nat tptp.semiri1316708129612266289at_nat N) tptp.one_one_nat) (= 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.one_one_complex (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex 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_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat 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))) (forall ((N tptp.nat)) (= (= tptp.one_one_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N)) (= N tptp.one_one_nat))) (= (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex tptp.one_one_nat) tptp.one_one_complex) (= (tptp.aa_nat_real tptp.semiri5074537144036343181t_real tptp.one_one_nat) tptp.one_one_real) (= (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat tptp.one_one_nat) tptp.one_one_rat) (= (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat tptp.one_one_nat) tptp.one_one_nat) _let_165 (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 ((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.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 ((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)) (= (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)) (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)) (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.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) (B 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 B) A))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B))))) (forall ((A tptp.rat) (B 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 B) A))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B))))) (forall ((A tptp.real) (B 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 B) A))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B) A))))) (forall ((A tptp.rat) (B 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 B) A))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) A))))) (forall ((A tptp.real) (B 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 B) A)) tptp.one_one_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B) A))))) (forall ((A tptp.rat) (B 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 B) A)) tptp.one_one_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) A))))) (forall ((A tptp.real) (B 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 B) A)) tptp.one_one_real)) (tptp.pp (tptp.aa_real_bool _let_1 B)))))) (forall ((A tptp.rat) (B 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 B) A)) tptp.one_one_rat)) (tptp.pp (tptp.aa_rat_bool _let_1 B)))))) (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 ((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 ((B 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 B) _let_1)) A)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) _let_1)))))) (forall ((B 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 B) _let_1)) A)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) _let_1)))))) (forall ((A tptp.real) (B 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 B) _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)) B))))) (forall ((A tptp.rat) (B 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 B) _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)) B))))) (forall ((A tptp.complex) (B tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (tptp.divide1717551699836669952omplex A (tptp.aa_complex_complex (tptp.times_times_complex A) B)) (tptp.divide1717551699836669952omplex tptp.one_one_complex B)))) (forall ((A tptp.real) (B 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) B)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.one_one_real) B)))) (forall ((A tptp.rat) (B 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) B)) (tptp.aa_rat_rat (tptp.divide_divide_rat tptp.one_one_rat) B)))) (forall ((B tptp.complex) (A tptp.complex)) (=> (not (= B tptp.zero_zero_complex)) (= (tptp.divide1717551699836669952omplex B (tptp.aa_complex_complex (tptp.times_times_complex A) B)) (tptp.divide1717551699836669952omplex tptp.one_one_complex A)))) (forall ((B tptp.real) (A tptp.real)) (=> (not (= B tptp.zero_zero_real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real B) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) B)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.one_one_real) A)))) (forall ((B tptp.rat) (A tptp.rat)) (=> (not (= B tptp.zero_zero_rat)) (= (tptp.aa_rat_rat (tptp.divide_divide_rat B) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) B)) (tptp.aa_rat_rat (tptp.divide_divide_rat tptp.one_one_rat) A)))) (forall ((A tptp.code_integer) (B 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 B) (tptp.divide6298287555418463151nteger tptp.one_one_Code_integer A)) (tptp.divide6298287555418463151nteger B A)))) (forall ((A tptp.nat) (B 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 B) (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 B) A)))) (forall ((A tptp.int) (B 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 B) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int tptp.one_one_int) A)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int B) A)))) (forall ((A tptp.code_integer) (B 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 B A)) A) B))) (forall ((A tptp.nat) (B 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 B) A)) A) B))) (forall ((A tptp.int) (B 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.aa_int_fun_int_int tptp.divide_divide_int B) A)) A) B))) (forall ((N tptp.nat) (A tptp.int) (B 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 B) N))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int A) B))))) (forall ((N tptp.nat) (A tptp.nat) (B 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.power_power_nat A) N)) (tptp.aa_nat_nat (tptp.power_power_nat B) N))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat A) B))))) (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 ((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 ((A tptp.rat) (B 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 B) A)) tptp.one_one_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B))))) (forall ((A tptp.real) (B 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 B) A)) tptp.one_one_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) B))))) (forall ((A tptp.rat) (B 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 B) A)) tptp.one_one_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) A))))) (forall ((A tptp.real) (B 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 B) A)) tptp.one_one_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real B) A))))) (forall ((A tptp.rat) (B 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 B) A))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) A))))) (forall ((A tptp.real) (B 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 B) A))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real B) A))))) (forall ((A tptp.rat) (B 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 B) A))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B))))) (forall ((A tptp.real) (B 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 B) A))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) B))))) (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)) (= (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)) (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 ((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)))) (= (tptp.aa_nat_nat tptp.suc tptp.one_one_nat) _let_2) (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 ((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_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)))) _let_184 _let_183 _let_184 _let_183 (forall ((A tptp.code_integer) (N tptp.nat)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.pp (tptp.aa_Code_integer_bool _let_1 (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.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 ((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.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 ((N tptp.nat)) (let ((_let_1 (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.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.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.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.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 ((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 ((K tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int K) tptp.zero_zero_int) K)) (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 ((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 ((X4 tptp.real)) (exists ((Y tptp.real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y) X4)))) (forall ((X4 tptp.rat)) (exists ((Y tptp.rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Y) X4)))) (forall ((X4 tptp.real)) (exists ((X_1 tptp.real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X4) X_1)))) (forall ((X4 tptp.rat)) (exists ((X_1 tptp.rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X4) X_1)))) (not (tptp.pp (tptp.aa_real_bool _let_121 tptp.one_one_real))) (not (tptp.pp (tptp.aa_rat_bool _let_119 tptp.one_one_rat))) (not (tptp.pp (tptp.aa_nat_bool _let_178 tptp.one_one_nat))) (not (tptp.pp (tptp.aa_int_bool _let_120 tptp.one_one_int))) (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 ((S2 tptp.nat) (T tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat S2) T)) (not (= S2 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) (Y4 tptp.nat)) (=> (not (= X Y4)) (=> (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Y4))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Y4) X))))) (forall ((X tptp.real) (Y4 tptp.real)) (=> (not (= X Y4)) (=> (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Y4))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y4) X))))) (forall ((X tptp.rat) (Y4 tptp.rat)) (=> (not (= X Y4)) (=> (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) Y4))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Y4) X))))) (forall ((X tptp.int) (Y4 tptp.int)) (=> (not (= X Y4)) (=> (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) Y4))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Y4) X))))) (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 ((X tptp.real)) (exists ((Y tptp.real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y) X)))) (forall ((X tptp.rat)) (exists ((Y tptp.rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Y) X)))) (forall ((X tptp.int)) (exists ((Y tptp.int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Y) X)))) (forall ((X tptp.real)) (exists ((X_1 tptp.real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) X_1)))) (forall ((X tptp.rat)) (exists ((X_1 tptp.rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) X_1)))) (forall ((X tptp.nat)) (exists ((X_1 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) X_1)))) (forall ((X tptp.int)) (exists ((X_1 tptp.int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) X_1)))) (forall ((X tptp.real) (Y4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Y4)) (exists ((Z2 tptp.real)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Z2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Z2) Y4)))))) (forall ((X tptp.rat) (Y4 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) Y4)) (exists ((Z2 tptp.rat)) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) Z2)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Z2) Y4)))))) (forall ((X tptp.real) (Y4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Y4)) (not (= X Y4)))) (forall ((X tptp.rat) (Y4 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) Y4)) (not (= X Y4)))) (forall ((X tptp.num) (Y4 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X) Y4)) (not (= X Y4)))) (forall ((X tptp.nat) (Y4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Y4)) (not (= X Y4)))) (forall ((X tptp.int) (Y4 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) Y4)) (not (= X Y4)))) (forall ((A tptp.real) (B tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B)) (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B) A))))) (forall ((A tptp.rat) (B tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B)) (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) A))))) (forall ((A tptp.num) (B tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num A) B)) (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num B) A))))) (forall ((A tptp.nat) (B tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) B)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat B) A))))) (forall ((A tptp.int) (B tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B) A))))) (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (=> (= A B) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B) C)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) C))))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (= A B) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) C)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) C))))) (forall ((A tptp.num) (B tptp.num) (C tptp.num)) (=> (= A B) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num B) C)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num A) C))))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (= A B) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat B) C)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) C))))) (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (= A B) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B) C)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) C))))) (forall ((A tptp.real) (B 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 B)) (=> (= B C) (tptp.pp (tptp.aa_real_bool _let_1 C)))))) (forall ((A tptp.rat) (B 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 B)) (=> (= B C) (tptp.pp (tptp.aa_rat_bool _let_1 C)))))) (forall ((A tptp.num) (B 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 B)) (=> (= B C) (tptp.pp (tptp.aa_num_bool _let_1 C)))))) (forall ((A tptp.nat) (B 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 B)) (=> (= B C) (tptp.pp (tptp.aa_nat_bool _let_1 C)))))) (forall ((A tptp.int) (B 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 B)) (=> (= B C) (tptp.pp (tptp.aa_int_bool _let_1 C)))))) (forall ((P tptp.fun_nat_bool) (A tptp.nat)) (=> (forall ((X3 tptp.nat)) (=> (forall ((Y3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Y3) X3)) (tptp.pp (tptp.aa_nat_bool P Y3)))) (tptp.pp (tptp.aa_nat_bool P X3)))) (tptp.pp (tptp.aa_nat_bool P A)))) (forall ((Y4 tptp.real) (X tptp.real)) (=> (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y4) X))) (= (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Y4))) (= X Y4)))) (forall ((Y4 tptp.rat) (X tptp.rat)) (=> (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Y4) X))) (= (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) Y4))) (= X Y4)))) (forall ((Y4 tptp.num) (X tptp.num)) (=> (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num Y4) X))) (= (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X) Y4))) (= X Y4)))) (forall ((Y4 tptp.nat) (X tptp.nat)) (=> (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Y4) X))) (= (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Y4))) (= X Y4)))) (forall ((Y4 tptp.int) (X tptp.int)) (=> (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Y4) X))) (= (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) Y4))) (= X Y4)))) (forall ((X tptp.real) (Y4 tptp.real)) (=> (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Y4))) (=> (not (= X Y4)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y4) X))))) (forall ((X tptp.rat) (Y4 tptp.rat)) (=> (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) Y4))) (=> (not (= X Y4)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Y4) X))))) (forall ((X tptp.num) (Y4 tptp.num)) (=> (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X) Y4))) (=> (not (= X Y4)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num Y4) X))))) (forall ((X tptp.nat) (Y4 tptp.nat)) (=> (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Y4))) (=> (not (= X Y4)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Y4) X))))) (forall ((X tptp.int) (Y4 tptp.int)) (=> (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) Y4))) (=> (not (= X Y4)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Y4) X))))) (forall ((B tptp.real) (A tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B) A)) (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B))))) (forall ((B tptp.rat) (A tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) A)) (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B))))) (forall ((B tptp.num) (A tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num B) A)) (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num A) B))))) (forall ((B tptp.nat) (A tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat B) A)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) B))))) (forall ((B tptp.int) (A tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B) A)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B))))) (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_12 tptp.nat)) (tptp.pp (tptp.aa_nat_bool P X_12))) (exists ((N4 tptp.nat)) (and (tptp.pp (tptp.aa_nat_bool P N4)) (forall ((M5 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M5) N4)) (not (tptp.pp (tptp.aa_nat_bool P M5))))))))) (forall ((P tptp.fun_re1255401033344146673l_bool) (A tptp.real) (B tptp.real)) (=> (forall ((A3 tptp.real) (B2 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A3) B2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool P A3) B2)))) (=> (forall ((A3 tptp.real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool P A3) A3))) (=> (forall ((A3 tptp.real) (B2 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool P B2) A3)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool P A3) B2)))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool P A) B)))))) (forall ((P tptp.fun_rat_fun_rat_bool) (A tptp.rat) (B tptp.rat)) (=> (forall ((A3 tptp.rat) (B2 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A3) B2)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool P A3) B2)))) (=> (forall ((A3 tptp.rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool P A3) A3))) (=> (forall ((A3 tptp.rat) (B2 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool P B2) A3)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool P A3) B2)))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool P A) B)))))) (forall ((P tptp.fun_num_fun_num_bool) (A tptp.num) (B tptp.num)) (=> (forall ((A3 tptp.num) (B2 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num A3) B2)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool P A3) B2)))) (=> (forall ((A3 tptp.num)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool P A3) A3))) (=> (forall ((A3 tptp.num) (B2 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool P B2) A3)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool P A3) B2)))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool P A) B)))))) (forall ((P tptp.fun_nat_fun_nat_bool) (A tptp.nat) (B tptp.nat)) (=> (forall ((A3 tptp.nat) (B2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A3) B2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool P A3) B2)))) (=> (forall ((A3 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool P A3) A3))) (=> (forall ((A3 tptp.nat) (B2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool P B2) A3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool P A3) B2)))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool P A) B)))))) (forall ((P tptp.fun_int_fun_int_bool) (A tptp.int) (B tptp.int)) (=> (forall ((A3 tptp.int) (B2 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A3) B2)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool P A3) B2)))) (=> (forall ((A3 tptp.int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool P A3) A3))) (=> (forall ((A3 tptp.int) (B2 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool P B2) A3)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool P A3) B2)))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool P A) B)))))) (forall ((A tptp.real) (B 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 B)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B) C)) (tptp.pp (tptp.aa_real_bool _let_1 C)))))) (forall ((A tptp.rat) (B 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 B)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) C)) (tptp.pp (tptp.aa_rat_bool _let_1 C)))))) (forall ((A tptp.num) (B 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 B)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num B) C)) (tptp.pp (tptp.aa_num_bool _let_1 C)))))) (forall ((A tptp.nat) (B 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 B)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat B) C)) (tptp.pp (tptp.aa_nat_bool _let_1 C)))))) (forall ((A tptp.int) (B 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 B)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B) C)) (tptp.pp (tptp.aa_int_bool _let_1 C)))))) (forall ((X tptp.real) (Y4 tptp.real)) (= (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Y4))) (or (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y4) X)) (= X Y4)))) (forall ((X tptp.rat) (Y4 tptp.rat)) (= (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) Y4))) (or (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Y4) X)) (= X Y4)))) (forall ((X tptp.num) (Y4 tptp.num)) (= (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X) Y4))) (or (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num Y4) X)) (= X Y4)))) (forall ((X tptp.nat) (Y4 tptp.nat)) (= (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Y4))) (or (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Y4) X)) (= X Y4)))) (forall ((X tptp.int) (Y4 tptp.int)) (= (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) Y4))) (or (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Y4) X)) (= X Y4)))) (forall ((B 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 B) A)) (=> (tptp.pp (tptp.aa_real_bool _let_1 B)) (tptp.pp (tptp.aa_real_bool _let_1 A)))))) (forall ((B 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 B) A)) (=> (tptp.pp (tptp.aa_rat_bool _let_1 B)) (tptp.pp (tptp.aa_rat_bool _let_1 A)))))) (forall ((B 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 B) A)) (=> (tptp.pp (tptp.aa_num_bool _let_1 B)) (tptp.pp (tptp.aa_num_bool _let_1 A)))))) (forall ((B 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 B) A)) (=> (tptp.pp (tptp.aa_nat_bool _let_1 B)) (tptp.pp (tptp.aa_nat_bool _let_1 A)))))) (forall ((B 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 B) A)) (=> (tptp.pp (tptp.aa_int_bool _let_1 B)) (tptp.pp (tptp.aa_int_bool _let_1 A)))))) (forall ((A tptp.real) (B tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B)) (not (= A B)))) (forall ((A tptp.rat) (B tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B)) (not (= A B)))) (forall ((A tptp.num) (B tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num A) B)) (not (= A B)))) (forall ((A tptp.nat) (B tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) B)) (not (= A B)))) (forall ((A tptp.int) (B tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B)) (not (= A B)))) (forall ((B tptp.real) (A tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B) A)) (not (= A B)))) (forall ((B tptp.rat) (A tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) A)) (not (= A B)))) (forall ((B tptp.num) (A tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num B) A)) (not (= A B)))) (forall ((B tptp.nat) (A tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat B) A)) (not (= A B)))) (forall ((B tptp.int) (A tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B) A)) (not (= A B)))) (forall ((X tptp.real) (Y4 tptp.real)) (=> (not (= X Y4)) (=> (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Y4))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y4) X))))) (forall ((X tptp.rat) (Y4 tptp.rat)) (=> (not (= X Y4)) (=> (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) Y4))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Y4) X))))) (forall ((X tptp.num) (Y4 tptp.num)) (=> (not (= X Y4)) (=> (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X) Y4))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num Y4) X))))) (forall ((X tptp.nat) (Y4 tptp.nat)) (=> (not (= X Y4)) (=> (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Y4))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Y4) X))))) (forall ((X tptp.int) (Y4 tptp.int)) (=> (not (= X Y4)) (=> (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) Y4))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Y4) X))))) (forall ((X tptp.real) (Y4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Y4)) (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y4) X))))) (forall ((X tptp.rat) (Y4 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) Y4)) (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Y4) X))))) (forall ((X tptp.num) (Y4 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X) Y4)) (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num Y4) X))))) (forall ((X tptp.nat) (Y4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Y4)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Y4) X))))) (forall ((X tptp.int) (Y4 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) Y4)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Y4) X))))) (forall ((X tptp.real) (Y4 tptp.real)) (= (not (= X Y4)) (or (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Y4)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y4) X))))) (forall ((X tptp.rat) (Y4 tptp.rat)) (= (not (= X Y4)) (or (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) Y4)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Y4) X))))) (forall ((X tptp.num) (Y4 tptp.num)) (= (not (= X Y4)) (or (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X) Y4)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num Y4) X))))) (forall ((X tptp.nat) (Y4 tptp.nat)) (= (not (= X Y4)) (or (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Y4)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Y4) X))))) (forall ((X tptp.int) (Y4 tptp.int)) (= (not (= X Y4)) (or (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) Y4)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Y4) X))))) (forall ((A tptp.real) (B tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B)) (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B) A))))) (forall ((A tptp.rat) (B tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B)) (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) A))))) (forall ((A tptp.num) (B tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num A) B)) (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num B) A))))) (forall ((A tptp.nat) (B tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) B)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat B) A))))) (forall ((A tptp.int) (B tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B) A))))) (forall ((X tptp.real) (Y4 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 Y4)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y4) Z)) (tptp.pp (tptp.aa_real_bool _let_1 Z)))))) (forall ((X tptp.rat) (Y4 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 Y4)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Y4) Z)) (tptp.pp (tptp.aa_rat_bool _let_1 Z)))))) (forall ((X tptp.num) (Y4 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 Y4)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num Y4) Z)) (tptp.pp (tptp.aa_num_bool _let_1 Z)))))) (forall ((X tptp.nat) (Y4 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 Y4)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Y4) Z)) (tptp.pp (tptp.aa_nat_bool _let_1 Z)))))) (forall ((X tptp.int) (Y4 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 Y4)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Y4) Z)) (tptp.pp (tptp.aa_int_bool _let_1 Z)))))) (forall ((A tptp.real) (F tptp.fun_real_real) (B tptp.real) (C tptp.real)) (=> (= A (tptp.aa_real_real F B)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B) C)) (=> (forall ((X3 tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X3) Y)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real F X3)) (tptp.aa_real_real F Y))))) (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) (B tptp.real) (C tptp.real)) (=> (= A (tptp.aa_real_rat F B)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B) C)) (=> (forall ((X3 tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X3) Y)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_real_rat F X3)) (tptp.aa_real_rat F Y))))) (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) (B tptp.real) (C tptp.real)) (=> (= A (tptp.aa_real_num F B)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B) C)) (=> (forall ((X3 tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X3) Y)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num (tptp.aa_real_num F X3)) (tptp.aa_real_num F Y))))) (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) (B tptp.real) (C tptp.real)) (=> (= A (tptp.aa_real_nat F B)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B) C)) (=> (forall ((X3 tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X3) Y)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_real_nat F X3)) (tptp.aa_real_nat F Y))))) (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) (B tptp.real) (C tptp.real)) (=> (= A (tptp.aa_real_int F B)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B) C)) (=> (forall ((X3 tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X3) Y)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_real_int F X3)) (tptp.aa_real_int F Y))))) (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) (B tptp.rat) (C tptp.rat)) (=> (= A (tptp.aa_rat_real F B)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) C)) (=> (forall ((X3 tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X3) Y)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_rat_real F X3)) (tptp.aa_rat_real F Y))))) (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) (B tptp.rat) (C tptp.rat)) (=> (= A (tptp.aa_rat_rat F B)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) C)) (=> (forall ((X3 tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X3) Y)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat F X3)) (tptp.aa_rat_rat F Y))))) (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) (B tptp.rat) (C tptp.rat)) (=> (= A (tptp.aa_rat_num F B)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) C)) (=> (forall ((X3 tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X3) Y)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num (tptp.aa_rat_num F X3)) (tptp.aa_rat_num F Y))))) (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) (B tptp.rat) (C tptp.rat)) (=> (= A (tptp.aa_rat_nat F B)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) C)) (=> (forall ((X3 tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X3) Y)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_rat_nat F X3)) (tptp.aa_rat_nat F Y))))) (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) (B tptp.rat) (C tptp.rat)) (=> (= A (tptp.aa_rat_int F B)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) C)) (=> (forall ((X3 tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X3) Y)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_rat_int F X3)) (tptp.aa_rat_int F Y))))) (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) (B 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) B)) (=> (= (tptp.aa_real_real F B) C) (=> (forall ((X3 tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X3) Y)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real F X3)) (tptp.aa_real_real F Y))))) (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) (B 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) B)) (=> (= (tptp.aa_real_rat F B) C) (=> (forall ((X3 tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X3) Y)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_real_rat F X3)) (tptp.aa_real_rat F Y))))) (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) (B 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) B)) (=> (= (tptp.aa_real_num F B) C) (=> (forall ((X3 tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X3) Y)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num (tptp.aa_real_num F X3)) (tptp.aa_real_num F Y))))) (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) (B 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) B)) (=> (= (tptp.aa_real_nat F B) C) (=> (forall ((X3 tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X3) Y)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_real_nat F X3)) (tptp.aa_real_nat F Y))))) (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) (B 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) B)) (=> (= (tptp.aa_real_int F B) C) (=> (forall ((X3 tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X3) Y)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_real_int F X3)) (tptp.aa_real_int F Y))))) (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) (B 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) B)) (=> (= (tptp.aa_rat_real F B) C) (=> (forall ((X3 tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X3) Y)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_rat_real F X3)) (tptp.aa_rat_real F Y))))) (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) (B 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) B)) (=> (= (tptp.aa_rat_rat F B) C) (=> (forall ((X3 tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X3) Y)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat F X3)) (tptp.aa_rat_rat F Y))))) (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) (B 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) B)) (=> (= (tptp.aa_rat_num F B) C) (=> (forall ((X3 tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X3) Y)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num (tptp.aa_rat_num F X3)) (tptp.aa_rat_num F Y))))) (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) (B 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) B)) (=> (= (tptp.aa_rat_nat F B) C) (=> (forall ((X3 tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X3) Y)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_rat_nat F X3)) (tptp.aa_rat_nat F Y))))) (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) (B 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) B)) (=> (= (tptp.aa_rat_int F B) C) (=> (forall ((X3 tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X3) Y)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_rat_int F X3)) (tptp.aa_rat_int F Y))))) (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) (B 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 B))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B) C)) (=> (forall ((X3 tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X3) Y)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real F X3)) (tptp.aa_real_real F Y))))) (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real F C)))))))) (forall ((A tptp.real) (F tptp.fun_rat_real) (B 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 B))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) C)) (=> (forall ((X3 tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X3) Y)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_rat_real F X3)) (tptp.aa_rat_real F Y))))) (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_rat_real F C)))))))) (forall ((A tptp.real) (F tptp.fun_num_real) (B 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 B))) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num B) C)) (=> (forall ((X3 tptp.num) (Y tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X3) Y)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_num_real F X3)) (tptp.aa_num_real F Y))))) (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_num_real F C)))))))) (forall ((A tptp.real) (F tptp.fun_nat_real) (B 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 B))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat B) C)) (=> (forall ((X3 tptp.nat) (Y tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X3) Y)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_nat_real F X3)) (tptp.aa_nat_real F Y))))) (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_nat_real F C)))))))) (forall ((A tptp.real) (F tptp.fun_int_real) (B 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 B))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B) C)) (=> (forall ((X3 tptp.int) (Y tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X3) Y)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_int_real F X3)) (tptp.aa_int_real F Y))))) (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_int_real F C)))))))) (forall ((A tptp.rat) (F tptp.fun_real_rat) (B 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 B))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B) C)) (=> (forall ((X3 tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X3) Y)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_real_rat F X3)) (tptp.aa_real_rat F Y))))) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_real_rat F C)))))))) (forall ((A tptp.rat) (F tptp.fun_rat_rat) (B 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 B))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) C)) (=> (forall ((X3 tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X3) Y)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat F X3)) (tptp.aa_rat_rat F Y))))) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat F C)))))))) (forall ((A tptp.rat) (F tptp.fun_num_rat) (B 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 B))) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num B) C)) (=> (forall ((X3 tptp.num) (Y tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X3) Y)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_num_rat F X3)) (tptp.aa_num_rat F Y))))) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_num_rat F C)))))))) (forall ((A tptp.rat) (F tptp.fun_nat_rat) (B 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 B))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat B) C)) (=> (forall ((X3 tptp.nat) (Y tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X3) Y)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_nat_rat F X3)) (tptp.aa_nat_rat F Y))))) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_nat_rat F C)))))))) (forall ((A tptp.rat) (F tptp.fun_int_rat) (B 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 B))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B) C)) (=> (forall ((X3 tptp.int) (Y tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X3) Y)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_int_rat F X3)) (tptp.aa_int_rat F Y))))) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_int_rat F C)))))))) (forall ((A tptp.real) (B 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) B)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real F B)) C)) (=> (forall ((X3 tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X3) Y)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real F X3)) (tptp.aa_real_real F Y))))) (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) (B 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) B)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_real_rat F B)) C)) (=> (forall ((X3 tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X3) Y)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_real_rat F X3)) (tptp.aa_real_rat F Y))))) (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) (B 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) B)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num (tptp.aa_real_num F B)) C)) (=> (forall ((X3 tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X3) Y)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num (tptp.aa_real_num F X3)) (tptp.aa_real_num F Y))))) (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) (B 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) B)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_real_nat F B)) C)) (=> (forall ((X3 tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X3) Y)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_real_nat F X3)) (tptp.aa_real_nat F Y))))) (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) (B 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) B)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_real_int F B)) C)) (=> (forall ((X3 tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X3) Y)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_real_int F X3)) (tptp.aa_real_int F Y))))) (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) (B 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) B)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_rat_real F B)) C)) (=> (forall ((X3 tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X3) Y)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_rat_real F X3)) (tptp.aa_rat_real F Y))))) (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) (B 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) B)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat F B)) C)) (=> (forall ((X3 tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X3) Y)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat F X3)) (tptp.aa_rat_rat F Y))))) (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) (B 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) B)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num (tptp.aa_rat_num F B)) C)) (=> (forall ((X3 tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X3) Y)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num (tptp.aa_rat_num F X3)) (tptp.aa_rat_num F Y))))) (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) (B 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) B)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_rat_nat F B)) C)) (=> (forall ((X3 tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X3) Y)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_rat_nat F X3)) (tptp.aa_rat_nat F Y))))) (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) (B 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) B)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_rat_int F B)) C)) (=> (forall ((X3 tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X3) Y)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_rat_int F X3)) (tptp.aa_rat_int F Y))))) (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) (Y4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Y4)) (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y4) X))))) (forall ((X tptp.rat) (Y4 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) Y4)) (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Y4) X))))) (forall ((X tptp.num) (Y4 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X) Y4)) (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num Y4) X))))) (forall ((X tptp.nat) (Y4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Y4)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Y4) X))))) (forall ((X tptp.int) (Y4 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) Y4)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Y4) X))))) (forall ((X tptp.real) (Y4 tptp.real) (P tptp.bool)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Y4)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y4) X)) (tptp.pp P)))) (forall ((X tptp.rat) (Y4 tptp.rat) (P tptp.bool)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) Y4)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Y4) X)) (tptp.pp P)))) (forall ((X tptp.num) (Y4 tptp.num) (P tptp.bool)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X) Y4)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num Y4) X)) (tptp.pp P)))) (forall ((X tptp.nat) (Y4 tptp.nat) (P tptp.bool)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Y4)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Y4) X)) (tptp.pp P)))) (forall ((X tptp.int) (Y4 tptp.int) (P tptp.bool)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) Y4)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Y4) X)) (tptp.pp P)))) (forall ((X tptp.real) (Y4 tptp.real)) (or (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Y4)) (= X Y4) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y4) X)))) (forall ((X tptp.rat) (Y4 tptp.rat)) (or (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) Y4)) (= X Y4) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Y4) X)))) (forall ((X tptp.num) (Y4 tptp.num)) (or (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X) Y4)) (= X Y4) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num Y4) X)))) (forall ((X tptp.nat) (Y4 tptp.nat)) (or (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Y4)) (= X Y4) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Y4) X)))) (forall ((X tptp.int) (Y4 tptp.int)) (or (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) Y4)) (= X Y4) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Y4) X)))) (forall ((X tptp.real) (Y4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Y4)) (not (= X Y4)))) (forall ((X tptp.rat) (Y4 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) Y4)) (not (= X Y4)))) (forall ((X tptp.num) (Y4 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X) Y4)) (not (= X Y4)))) (forall ((X tptp.nat) (Y4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Y4)) (not (= X Y4)))) (forall ((X tptp.int) (Y4 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) Y4)) (not (= X Y4)))) (forall ((X tptp.real) (Y4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Y4)) (not (= Y4 X)))) (forall ((X tptp.rat) (Y4 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) Y4)) (not (= Y4 X)))) (forall ((X tptp.num) (Y4 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X) Y4)) (not (= Y4 X)))) (forall ((X tptp.nat) (Y4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Y4)) (not (= Y4 X)))) (forall ((X tptp.int) (Y4 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) Y4)) (not (= Y4 X)))) (forall ((X tptp.real) (Y4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Y4)) (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y4) X))))) (forall ((X tptp.rat) (Y4 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) Y4)) (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Y4) X))))) (forall ((X tptp.num) (Y4 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X) Y4)) (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num Y4) X))))) (forall ((X tptp.nat) (Y4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Y4)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Y4) X))))) (forall ((X tptp.int) (Y4 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) Y4)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Y4) X))))) _let_182 _let_181 _let_180 _let_179 _let_182 _let_181 _let_180 _let_179 (not (tptp.pp (tptp.aa_real_bool _let_121 tptp.zero_zero_real))) (not (tptp.pp (tptp.aa_rat_bool _let_119 tptp.zero_zero_rat))) (not (tptp.pp (tptp.aa_nat_bool _let_178 tptp.zero_zero_nat))) (not (tptp.pp (tptp.aa_int_bool _let_120 tptp.zero_zero_int))) (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 ((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 ((F tptp.fun_nat_real) (N tptp.nat) (N3 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) N3)) (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 N3)))))) (forall ((F tptp.fun_nat_rat) (N tptp.nat) (N3 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) N3)) (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 N3)))))) (forall ((F tptp.fun_nat_num) (N tptp.nat) (N3 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) N3)) (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 N3)))))) (forall ((F tptp.fun_nat_nat) (N tptp.nat) (N3 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) N3)) (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 N3)))))) (forall ((F tptp.fun_nat_int) (N tptp.nat) (N3 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) N3)) (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 N3)))))) (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_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_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 ((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_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_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_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_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 ((T tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X4 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X4) Z2)) (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat T) X4))))))) (forall ((T tptp.num)) (exists ((Z2 tptp.num)) (forall ((X4 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X4) Z2)) (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num T) X4))))))) (forall ((T tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X4) Z2)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat T) X4))))))) (forall ((T tptp.int)) (exists ((Z2 tptp.int)) (forall ((X4 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X4) Z2)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int T) X4))))))) (forall ((T tptp.real)) (exists ((Z2 tptp.real)) (forall ((X4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X4) Z2)) (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real T) X4))))))) (forall ((T tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X4 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X4) Z2)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X4) T)))))) (forall ((T tptp.num)) (exists ((Z2 tptp.num)) (forall ((X4 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X4) Z2)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X4) T)))))) (forall ((T tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X4) Z2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X4) T)))))) (forall ((T tptp.int)) (exists ((Z2 tptp.int)) (forall ((X4 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X4) Z2)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X4) T)))))) (forall ((T tptp.real)) (exists ((Z2 tptp.real)) (forall ((X4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X4) Z2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X4) T)))))) (forall ((T tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X4 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Z2) X4)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat T) X4)))))) (forall ((T tptp.num)) (exists ((Z2 tptp.num)) (forall ((X4 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num Z2) X4)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num T) X4)))))) (forall ((T tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Z2) X4)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat T) X4)))))) (forall ((T tptp.int)) (exists ((Z2 tptp.int)) (forall ((X4 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Z2) X4)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int T) X4)))))) (forall ((T tptp.real)) (exists ((Z2 tptp.real)) (forall ((X4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Z2) X4)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real T) X4)))))) (forall ((T tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X4 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Z2) X4)) (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X4) T))))))) (forall ((T tptp.num)) (exists ((Z2 tptp.num)) (forall ((X4 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num Z2) X4)) (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X4) T))))))) (forall ((T tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Z2) X4)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X4) T))))))) (forall ((T tptp.int)) (exists ((Z2 tptp.int)) (forall ((X4 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Z2) X4)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X4) T))))))) (forall ((T tptp.real)) (exists ((Z2 tptp.real)) (forall ((X4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Z2) X4)) (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X4) T))))))) (forall ((B 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 B) 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 B))) (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 B) A))))))) (forall ((B 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 B) 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 B))) (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 B) A))))))) (forall ((B 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 B) 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 B) A))) (and (tptp.pp (tptp.aa_real_bool _let_1 tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool _let_1 B))) (= A tptp.zero_zero_real))))) (forall ((B 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 B) 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 B) A))) (and (tptp.pp (tptp.aa_rat_bool _let_1 tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool _let_1 B))) (= A tptp.zero_zero_rat))))) (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 ((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 ((B4 tptp.rat) (A4 tptp.rat)) (= (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B4) A4))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A4) B4)))) (forall ((B4 tptp.num) (A4 tptp.num)) (= (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num B4) A4))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num A4) B4)))) (forall ((B4 tptp.nat) (A4 tptp.nat)) (= (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B4) A4))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A4) B4)))) (forall ((B4 tptp.int) (A4 tptp.int)) (= (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B4) A4))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A4) B4)))) (forall ((B4 tptp.real) (A4 tptp.real)) (= (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real B4) A4))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A4) B4)))) (forall ((Y4 tptp.set_int) (X tptp.set_int)) (=> (tptp.ord_less_eq_set_int Y4 X) (not (tptp.ord_less_set_int X Y4)))) (forall ((Y4 tptp.rat) (X tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat Y4) X)) (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) Y4))))) (forall ((Y4 tptp.num) (X tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num Y4) X)) (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X) Y4))))) (forall ((Y4 tptp.nat) (X tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Y4) X)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Y4))))) (forall ((Y4 tptp.int) (X tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Y4) X)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) Y4))))) (forall ((Y4 tptp.real) (X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y4) X)) (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Y4))))) (forall ((X tptp.rat) (Y4 tptp.rat)) (=> (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) Y4))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat Y4) X)))) (forall ((X tptp.num) (Y4 tptp.num)) (=> (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X) Y4))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num Y4) X)))) (forall ((X tptp.nat) (Y4 tptp.nat)) (=> (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Y4))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Y4) X)))) (forall ((X tptp.int) (Y4 tptp.int)) (=> (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) Y4))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Y4) X)))) (forall ((X tptp.real) (Y4 tptp.real)) (=> (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Y4))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y4) X)))) (forall ((A tptp.set_int) (B tptp.set_int)) (= (not (tptp.ord_less_set_int A B)) (or (not (tptp.ord_less_eq_set_int A B)) (= A B)))) (forall ((A tptp.rat) (B tptp.rat)) (= (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B))) (or (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B))) (= A B)))) (forall ((A tptp.num) (B tptp.num)) (= (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num A) B))) (or (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A) B))) (= A B)))) (forall ((A tptp.nat) (B tptp.nat)) (= (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) B))) (or (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B))) (= A B)))) (forall ((A tptp.int) (B tptp.int)) (= (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B))) (or (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B))) (= A B)))) (forall ((A tptp.real) (B tptp.real)) (= (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B))) (or (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) B))) (= A B)))) (forall ((X tptp.set_int) (Y4 tptp.set_int)) (=> (not (tptp.ord_less_set_int X Y4)) (= (tptp.ord_less_eq_set_int X Y4) (= X Y4)))) (forall ((X tptp.rat) (Y4 tptp.rat)) (=> (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) Y4))) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) Y4)) (= X Y4)))) (forall ((X tptp.num) (Y4 tptp.num)) (=> (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X) Y4))) (= (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X) Y4)) (= X Y4)))) (forall ((X tptp.nat) (Y4 tptp.nat)) (=> (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Y4))) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X) Y4)) (= X Y4)))) (forall ((X tptp.int) (Y4 tptp.int)) (=> (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) Y4))) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X) Y4)) (= X Y4)))) (forall ((X tptp.real) (Y4 tptp.real)) (=> (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Y4))) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) Y4)) (= X Y4)))) (forall ((X tptp.set_int) (Y4 tptp.set_int)) (=> (tptp.ord_less_eq_set_int X Y4) (= (not (tptp.ord_less_set_int X Y4)) (= X Y4)))) (forall ((X tptp.rat) (Y4 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) Y4)) (= (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) Y4))) (= X Y4)))) (forall ((X tptp.num) (Y4 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X) Y4)) (= (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X) Y4))) (= X Y4)))) (forall ((X tptp.nat) (Y4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X) Y4)) (= (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Y4))) (= X Y4)))) (forall ((X tptp.int) (Y4 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X) Y4)) (= (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) Y4))) (= X Y4)))) (forall ((X tptp.real) (Y4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) Y4)) (= (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Y4))) (= X Y4)))) (forall ((Z tptp.rat) (Y4 tptp.rat)) (=> (forall ((X3 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Z) X3)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat Y4) X3)))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat Y4) Z)))) (forall ((Z tptp.real) (Y4 tptp.real)) (=> (forall ((X3 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Z) X3)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y4) X3)))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y4) Z)))) (forall ((Y4 tptp.rat) (Z tptp.rat)) (=> (forall ((X3 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X3) Y4)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X3) Z)))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat Y4) Z)))) (forall ((Y4 tptp.real) (Z tptp.real)) (=> (forall ((X3 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X3) Y4)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X3) Z)))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y4) Z)))) (forall ((X tptp.set_int) (Y4 tptp.set_int)) (= (tptp.ord_less_set_int X Y4) (and (tptp.ord_less_eq_set_int X Y4) (not (tptp.ord_less_eq_set_int Y4 X))))) (forall ((X tptp.rat) (Y4 tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) Y4)) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) Y4)) (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat Y4) X)))))) (forall ((X tptp.num) (Y4 tptp.num)) (= (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X) Y4)) (and (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X) Y4)) (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num Y4) X)))))) (forall ((X tptp.nat) (Y4 tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Y4)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X) Y4)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Y4) X)))))) (forall ((X tptp.int) (Y4 tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) Y4)) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X) Y4)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Y4) X)))))) (forall ((X tptp.real) (Y4 tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Y4)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) Y4)) (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y4) X)))))) (forall ((Y4 tptp.rat) (X tptp.rat)) (=> (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat Y4) X))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) Y4)))) (forall ((Y4 tptp.num) (X tptp.num)) (=> (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num Y4) X))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X) Y4)))) (forall ((Y4 tptp.nat) (X tptp.nat)) (=> (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Y4) X))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Y4)))) (forall ((Y4 tptp.int) (X tptp.int)) (=> (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Y4) X))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) Y4)))) (forall ((Y4 tptp.real) (X tptp.real)) (=> (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y4) X))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Y4)))) (forall ((A tptp.set_int) (B tptp.set_int)) (= (tptp.ord_less_eq_set_int A B) (or (tptp.ord_less_set_int A B) (= A B)))) (forall ((A tptp.rat) (B tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B)) (or (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B)) (= A B)))) (forall ((A tptp.num) (B tptp.num)) (= (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A) B)) (or (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num A) B)) (= A B)))) (forall ((A tptp.nat) (B tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B)) (or (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) B)) (= A B)))) (forall ((A tptp.int) (B tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B)) (or (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B)) (= A B)))) (forall ((A tptp.real) (B tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) B)) (or (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B)) (= A B)))) (forall ((A tptp.set_int) (B tptp.set_int)) (= (tptp.ord_less_set_int A B) (and (tptp.ord_less_eq_set_int A B) (not (= A B))))) (forall ((A tptp.rat) (B tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B)) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B)) (not (= A B))))) (forall ((A tptp.num) (B tptp.num)) (= (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num A) B)) (and (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A) B)) (not (= A B))))) (forall ((A tptp.nat) (B tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) B)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B)) (not (= A B))))) (forall ((A tptp.int) (B tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B)) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B)) (not (= A B))))) (forall ((A tptp.real) (B tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) B)) (not (= A B))))) (forall ((A tptp.set_int) (B tptp.set_int) (C tptp.set_int)) (=> (tptp.ord_less_eq_set_int A B) (=> (tptp.ord_less_set_int B C) (tptp.ord_less_set_int A C)))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) C)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) C))))) (forall ((A tptp.num) (B tptp.num) (C tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A) B)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num B) C)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num A) C))))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat B) C)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) C))))) (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B) C)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) C))))) (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) B)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B) C)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) C))))) (forall ((A tptp.set_int) (B tptp.set_int) (C tptp.set_int)) (=> (tptp.ord_less_set_int A B) (=> (tptp.ord_less_eq_set_int B C) (tptp.ord_less_set_int A C)))) (forall ((A tptp.rat) (B 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 B)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) C)) (tptp.pp (tptp.aa_rat_bool _let_1 C)))))) (forall ((A tptp.num) (B 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 B)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num B) C)) (tptp.pp (tptp.aa_num_bool _let_1 C)))))) (forall ((A tptp.nat) (B 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 B)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B) C)) (tptp.pp (tptp.aa_nat_bool _let_1 C)))))) (forall ((A tptp.int) (B 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 B)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B) C)) (tptp.pp (tptp.aa_int_bool _let_1 C)))))) (forall ((A tptp.real) (B 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 B)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real B) C)) (tptp.pp (tptp.aa_real_bool _let_1 C)))))) (forall ((A tptp.set_int) (B tptp.set_int)) (= (tptp.ord_less_set_int A B) (and (tptp.ord_less_eq_set_int A B) (not (tptp.ord_less_eq_set_int B A))))) (forall ((A tptp.rat) (B tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B)) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B)) (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) A)))))) (forall ((A tptp.num) (B tptp.num)) (= (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num A) B)) (and (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A) B)) (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num B) A)))))) (forall ((A tptp.nat) (B tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) B)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B) A)))))) (forall ((A tptp.int) (B tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B)) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B) A)))))) (forall ((A tptp.real) (B tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) B)) (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real B) A)))))) (forall ((Z tptp.rat) (X tptp.rat) (Y4 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 Y4) W2))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat Y4) Z))))) (forall ((Z tptp.real) (X tptp.real) (Y4 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 Y4) W2))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y4) Z))))) (forall ((X tptp.rat) (Y4 tptp.rat) (Z tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) Y4)) (=> (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) Y4)) (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 Y4) Z))))) (forall ((X tptp.real) (Y4 tptp.real) (Z tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Y4)) (=> (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) Y4)) (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 Y4) Z))))) (forall ((B tptp.set_int) (A tptp.set_int)) (= (tptp.ord_less_eq_set_int B A) (or (tptp.ord_less_set_int B A) (= A B)))) (forall ((B tptp.rat) (A tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) A)) (or (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) A)) (= A B)))) (forall ((B tptp.num) (A tptp.num)) (= (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num B) A)) (or (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num B) A)) (= A B)))) (forall ((B tptp.nat) (A tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B) A)) (or (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat B) A)) (= A B)))) (forall ((B tptp.int) (A tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B) A)) (or (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B) A)) (= A B)))) (forall ((B tptp.real) (A tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real B) A)) (or (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B) A)) (= A B)))) (forall ((B tptp.set_int) (A tptp.set_int)) (= (tptp.ord_less_set_int B A) (and (tptp.ord_less_eq_set_int B A) (not (= A B))))) (forall ((B tptp.rat) (A tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) A)) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) A)) (not (= A B))))) (forall ((B tptp.num) (A tptp.num)) (= (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num B) A)) (and (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num B) A)) (not (= A B))))) (forall ((B tptp.nat) (A tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat B) A)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B) A)) (not (= A B))))) (forall ((B tptp.int) (A tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B) A)) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B) A)) (not (= A B))))) (forall ((B tptp.real) (A tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B) A)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real B) A)) (not (= A B))))) (forall ((B tptp.set_int) (A tptp.set_int) (C tptp.set_int)) (=> (tptp.ord_less_eq_set_int B A) (=> (tptp.ord_less_set_int C B) (tptp.ord_less_set_int C A)))) (forall ((B 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 B) A)) (=> (tptp.pp (tptp.aa_rat_bool _let_1 B)) (tptp.pp (tptp.aa_rat_bool _let_1 A)))))) (forall ((B 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 B) A)) (=> (tptp.pp (tptp.aa_num_bool _let_1 B)) (tptp.pp (tptp.aa_num_bool _let_1 A)))))) (forall ((B 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 B) A)) (=> (tptp.pp (tptp.aa_nat_bool _let_1 B)) (tptp.pp (tptp.aa_nat_bool _let_1 A)))))) (forall ((B 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 B) A)) (=> (tptp.pp (tptp.aa_int_bool _let_1 B)) (tptp.pp (tptp.aa_int_bool _let_1 A)))))) (forall ((B 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 B) A)) (=> (tptp.pp (tptp.aa_real_bool _let_1 B)) (tptp.pp (tptp.aa_real_bool _let_1 A)))))) (forall ((B tptp.set_int) (A tptp.set_int) (C tptp.set_int)) (=> (tptp.ord_less_set_int B A) (=> (tptp.ord_less_eq_set_int C B) (tptp.ord_less_set_int C A)))) (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) A)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat C) B)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat C) A))))) (forall ((B tptp.num) (A tptp.num) (C tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num B) A)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num C) B)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num C) A))))) (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat B) A)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat C) B)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat C) A))))) (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B) A)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int C) B)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int C) A))))) (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B) A)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real C) B)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real C) A))))) (forall ((B tptp.set_int) (A tptp.set_int)) (= (tptp.ord_less_set_int B A) (and (tptp.ord_less_eq_set_int B A) (not (tptp.ord_less_eq_set_int A B))))) (forall ((B tptp.rat) (A tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) A)) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) A)) (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B)))))) (forall ((B tptp.num) (A tptp.num)) (= (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num B) A)) (and (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num B) A)) (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A) B)))))) (forall ((B tptp.nat) (A tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat B) A)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B) A)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B)))))) (forall ((B tptp.int) (A tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B) A)) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B) A)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B)))))) (forall ((B tptp.real) (A tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B) A)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real B) A)) (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) B)))))) (forall ((A tptp.set_int) (B tptp.set_int)) (=> (tptp.ord_less_set_int A B) (tptp.ord_less_eq_set_int A B))) (forall ((A tptp.rat) (B tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B)))) (forall ((A tptp.num) (B tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num A) B)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A) B)))) (forall ((A tptp.nat) (B tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) B)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B)))) (forall ((A tptp.int) (B tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B)))) (forall ((A tptp.real) (B tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) B)))) (forall ((B tptp.set_int) (A tptp.set_int)) (=> (tptp.ord_less_set_int B A) (tptp.ord_less_eq_set_int B A))) (forall ((B tptp.rat) (A tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) A)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) A)))) (forall ((B tptp.num) (A tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num B) A)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num B) A)))) (forall ((B tptp.nat) (A tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat B) A)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B) A)))) (forall ((B tptp.int) (A tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B) A)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B) A)))) (forall ((B tptp.real) (A tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B) A)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real B) A)))) (forall ((X tptp.set_int) (Y4 tptp.set_int)) (= (tptp.ord_less_eq_set_int X Y4) (or (tptp.ord_less_set_int X Y4) (= X Y4)))) (forall ((X tptp.rat) (Y4 tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) Y4)) (or (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) Y4)) (= X Y4)))) (forall ((X tptp.num) (Y4 tptp.num)) (= (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X) Y4)) (or (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X) Y4)) (= X Y4)))) (forall ((X tptp.nat) (Y4 tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X) Y4)) (or (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Y4)) (= X Y4)))) (forall ((X tptp.int) (Y4 tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X) Y4)) (or (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) Y4)) (= X Y4)))) (forall ((X tptp.real) (Y4 tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) Y4)) (or (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Y4)) (= X Y4)))) (forall ((X tptp.set_int) (Y4 tptp.set_int)) (= (tptp.ord_less_set_int X Y4) (and (tptp.ord_less_eq_set_int X Y4) (not (= X Y4))))) (forall ((X tptp.rat) (Y4 tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) Y4)) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) Y4)) (not (= X Y4))))) (forall ((X tptp.num) (Y4 tptp.num)) (= (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X) Y4)) (and (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X) Y4)) (not (= X Y4))))) (forall ((X tptp.nat) (Y4 tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Y4)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X) Y4)) (not (= X Y4))))) (forall ((X tptp.int) (Y4 tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) Y4)) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X) Y4)) (not (= X Y4))))) (forall ((X tptp.real) (Y4 tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Y4)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) Y4)) (not (= X Y4))))) (forall ((X tptp.rat) (Y4 tptp.rat)) (= (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) Y4))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Y4) X)))) (forall ((X tptp.num) (Y4 tptp.num)) (= (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X) Y4))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num Y4) X)))) (forall ((X tptp.nat) (Y4 tptp.nat)) (= (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X) Y4))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Y4) X)))) (forall ((X tptp.int) (Y4 tptp.int)) (= (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X) Y4))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Y4) X)))) (forall ((X tptp.real) (Y4 tptp.real)) (= (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) Y4))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y4) X)))) (forall ((X tptp.rat) (Y4 tptp.rat)) (= (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) Y4))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat Y4) X)))) (forall ((X tptp.num) (Y4 tptp.num)) (= (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X) Y4))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num Y4) X)))) (forall ((X tptp.nat) (Y4 tptp.nat)) (= (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Y4))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Y4) X)))) (forall ((X tptp.int) (Y4 tptp.int)) (= (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) Y4))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Y4) X)))) (forall ((X tptp.real) (Y4 tptp.real)) (= (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Y4))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y4) X)))) (forall ((X tptp.set_int) (Y4 tptp.set_int)) (=> (tptp.ord_less_set_int X Y4) (tptp.ord_less_eq_set_int X Y4))) (forall ((X tptp.rat) (Y4 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) Y4)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) Y4)))) (forall ((X tptp.num) (Y4 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X) Y4)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X) Y4)))) (forall ((X tptp.nat) (Y4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Y4)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X) Y4)))) (forall ((X tptp.int) (Y4 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) Y4)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X) Y4)))) (forall ((X tptp.real) (Y4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Y4)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) Y4)))) (forall ((A tptp.set_int) (B tptp.set_int)) (=> (tptp.ord_less_eq_set_int A B) (=> (not (= A B)) (tptp.ord_less_set_int A B)))) (forall ((A tptp.rat) (B tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B)) (=> (not (= A B)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B))))) (forall ((A tptp.num) (B tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A) B)) (=> (not (= A B)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num A) B))))) (forall ((A tptp.nat) (B tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B)) (=> (not (= A B)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) B))))) (forall ((A tptp.int) (B tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B)) (=> (not (= A B)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B))))) (forall ((A tptp.real) (B tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) B)) (=> (not (= A B)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B))))) (forall ((A tptp.set_int) (B tptp.set_int)) (=> (not (= A B)) (=> (tptp.ord_less_eq_set_int A B) (tptp.ord_less_set_int A B)))) (forall ((A tptp.rat) (B tptp.rat)) (=> (not (= A B)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B))))) (forall ((A tptp.num) (B tptp.num)) (=> (not (= A B)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A) B)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num A) B))))) (forall ((A tptp.nat) (B tptp.nat)) (=> (not (= A B)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) B))))) (forall ((A tptp.int) (B tptp.int)) (=> (not (= A B)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B))))) (forall ((A tptp.real) (B tptp.real)) (=> (not (= A B)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) B)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B))))) (forall ((X tptp.set_int) (Y4 tptp.set_int) (Z tptp.set_int)) (=> (tptp.ord_less_eq_set_int X Y4) (=> (tptp.ord_less_set_int Y4 Z) (tptp.ord_less_set_int X Z)))) (forall ((X tptp.rat) (Y4 tptp.rat) (Z tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) Y4)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Y4) Z)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) Z))))) (forall ((X tptp.num) (Y4 tptp.num) (Z tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X) Y4)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num Y4) Z)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X) Z))))) (forall ((X tptp.nat) (Y4 tptp.nat) (Z tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X) Y4)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Y4) Z)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Z))))) (forall ((X tptp.int) (Y4 tptp.int) (Z tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X) Y4)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Y4) Z)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) Z))))) (forall ((X tptp.real) (Y4 tptp.real) (Z tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) Y4)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y4) Z)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Z))))) (forall ((X tptp.set_int) (Y4 tptp.set_int) (Z tptp.set_int)) (=> (tptp.ord_less_set_int X Y4) (=> (tptp.ord_less_eq_set_int Y4 Z) (tptp.ord_less_set_int X Z)))) (forall ((X tptp.rat) (Y4 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 Y4)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat Y4) Z)) (tptp.pp (tptp.aa_rat_bool _let_1 Z)))))) (forall ((X tptp.num) (Y4 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 Y4)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num Y4) Z)) (tptp.pp (tptp.aa_num_bool _let_1 Z)))))) (forall ((X tptp.nat) (Y4 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 Y4)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Y4) Z)) (tptp.pp (tptp.aa_nat_bool _let_1 Z)))))) (forall ((X tptp.int) (Y4 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 Y4)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Y4) Z)) (tptp.pp (tptp.aa_int_bool _let_1 Z)))))) (forall ((X tptp.real) (Y4 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 Y4)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y4) Z)) (tptp.pp (tptp.aa_real_bool _let_1 Z)))))) (forall ((A tptp.rat) (F tptp.fun_real_rat) (B 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 B))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B) C)) (=> (forall ((X3 tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X3) Y)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_real_rat F X3)) (tptp.aa_real_rat F Y))))) (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) (B 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 B))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) C)) (=> (forall ((X3 tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X3) Y)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat F X3)) (tptp.aa_rat_rat F Y))))) (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) (B 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 B))) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num B) C)) (=> (forall ((X3 tptp.num) (Y tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X3) Y)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_num_rat F X3)) (tptp.aa_num_rat F Y))))) (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) (B 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 B))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat B) C)) (=> (forall ((X3 tptp.nat) (Y tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X3) Y)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_nat_rat F X3)) (tptp.aa_nat_rat F Y))))) (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) (B 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 B))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B) C)) (=> (forall ((X3 tptp.int) (Y tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X3) Y)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_int_rat F X3)) (tptp.aa_int_rat F Y))))) (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.num) (F tptp.fun_real_num) (B tptp.real) (C tptp.real)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A) (tptp.aa_real_num F B))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B) C)) (=> (forall ((X3 tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X3) Y)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num (tptp.aa_real_num F X3)) (tptp.aa_real_num F Y))))) (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.num) (F tptp.fun_rat_num) (B tptp.rat) (C tptp.rat)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A) (tptp.aa_rat_num F B))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) C)) (=> (forall ((X3 tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X3) Y)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num (tptp.aa_rat_num F X3)) (tptp.aa_rat_num F Y))))) (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.num) (F tptp.fun_num_num) (B tptp.num) (C tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A) (tptp.aa_num_num F B))) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num B) C)) (=> (forall ((X3 tptp.num) (Y tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X3) Y)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num (tptp.aa_num_num F X3)) (tptp.aa_num_num F Y))))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num A) (tptp.aa_num_num F C))))))) (forall ((A tptp.num) (F tptp.fun_nat_num) (B tptp.nat) (C tptp.nat)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A) (tptp.aa_nat_num F B))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat B) C)) (=> (forall ((X3 tptp.nat) (Y tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X3) Y)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num (tptp.aa_nat_num F X3)) (tptp.aa_nat_num F Y))))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num A) (tptp.aa_nat_num F C))))))) (forall ((A tptp.num) (F tptp.fun_int_num) (B tptp.int) (C tptp.int)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A) (tptp.aa_int_num F B))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B) C)) (=> (forall ((X3 tptp.int) (Y tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X3) Y)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num (tptp.aa_int_num F X3)) (tptp.aa_int_num F Y))))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num A) (tptp.aa_int_num F C))))))) (forall ((A tptp.rat) (B 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) B)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat F B)) C)) (=> (forall ((X3 tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X3) Y)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat F X3)) (tptp.aa_rat_rat F Y))))) (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) (B 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) B)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num (tptp.aa_rat_num F B)) C)) (=> (forall ((X3 tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X3) Y)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_rat_num F X3)) (tptp.aa_rat_num F Y))))) (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) (B 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) B)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_rat_nat F B)) C)) (=> (forall ((X3 tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X3) Y)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_rat_nat F X3)) (tptp.aa_rat_nat F Y))))) (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) (B 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) B)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_rat_int F B)) C)) (=> (forall ((X3 tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X3) Y)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_rat_int F X3)) (tptp.aa_rat_int F Y))))) (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.rat) (B 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) B)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_rat_real F B)) C)) (=> (forall ((X3 tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X3) Y)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_rat_real F X3)) (tptp.aa_rat_real F Y))))) (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) (B 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) B)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_num_rat F B)) C)) (=> (forall ((X3 tptp.num) (Y tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X3) Y)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_num_rat F X3)) (tptp.aa_num_rat F Y))))) (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) (B 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) B)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num (tptp.aa_num_num F B)) C)) (=> (forall ((X3 tptp.num) (Y tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X3) Y)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_num_num F X3)) (tptp.aa_num_num F Y))))) (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) (B 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) B)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_num_nat F B)) C)) (=> (forall ((X3 tptp.num) (Y tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X3) Y)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_num_nat F X3)) (tptp.aa_num_nat F Y))))) (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) (B 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) B)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_num_int F B)) C)) (=> (forall ((X3 tptp.num) (Y tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X3) Y)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_num_int F X3)) (tptp.aa_num_int F Y))))) (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.num) (B 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) B)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_num_real F B)) C)) (=> (forall ((X3 tptp.num) (Y tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X3) Y)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_num_real F X3)) (tptp.aa_num_real F Y))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_num_real F A)) C)))))) (forall ((A tptp.rat) (F tptp.fun_rat_rat) (B 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 B))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) C)) (=> (forall ((X3 tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X3) Y)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat F X3)) (tptp.aa_rat_rat F Y))))) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat F C)))))))) (forall ((A tptp.num) (F tptp.fun_rat_num) (B 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 B))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) C)) (=> (forall ((X3 tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X3) Y)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_rat_num F X3)) (tptp.aa_rat_num F Y))))) (tptp.pp (tptp.aa_num_bool _let_1 (tptp.aa_rat_num F C)))))))) (forall ((A tptp.nat) (F tptp.fun_rat_nat) (B 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 B))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) C)) (=> (forall ((X3 tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X3) Y)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_rat_nat F X3)) (tptp.aa_rat_nat F Y))))) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_rat_nat F C)))))))) (forall ((A tptp.int) (F tptp.fun_rat_int) (B 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 B))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) C)) (=> (forall ((X3 tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X3) Y)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_rat_int F X3)) (tptp.aa_rat_int F Y))))) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_rat_int F C)))))))) (forall ((A tptp.real) (F tptp.fun_rat_real) (B 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 B))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) C)) (=> (forall ((X3 tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X3) Y)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_rat_real F X3)) (tptp.aa_rat_real F Y))))) (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_rat_real F C)))))))) (forall ((A tptp.rat) (F tptp.fun_num_rat) (B 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 B))) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num B) C)) (=> (forall ((X3 tptp.num) (Y tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X3) Y)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_num_rat F X3)) (tptp.aa_num_rat F Y))))) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_num_rat F C)))))))) (forall ((A tptp.num) (F tptp.fun_num_num) (B 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 B))) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num B) C)) (=> (forall ((X3 tptp.num) (Y tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X3) Y)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_num_num F X3)) (tptp.aa_num_num F Y))))) (tptp.pp (tptp.aa_num_bool _let_1 (tptp.aa_num_num F C)))))))) (forall ((A tptp.nat) (F tptp.fun_num_nat) (B 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 B))) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num B) C)) (=> (forall ((X3 tptp.num) (Y tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X3) Y)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_num_nat F X3)) (tptp.aa_num_nat F Y))))) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_num_nat F C)))))))) (forall ((A tptp.int) (F tptp.fun_num_int) (B 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 B))) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num B) C)) (=> (forall ((X3 tptp.num) (Y tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X3) Y)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_num_int F X3)) (tptp.aa_num_int F Y))))) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_num_int F C)))))))) (forall ((A tptp.real) (F tptp.fun_num_real) (B 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 B))) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num B) C)) (=> (forall ((X3 tptp.num) (Y tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X3) Y)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_num_real F X3)) (tptp.aa_num_real F Y))))) (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_num_real F C)))))))) (forall ((A tptp.real) (B 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) B)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_real_rat F B)) C)) (=> (forall ((X3 tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X3) Y)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_real_rat F X3)) (tptp.aa_real_rat F Y))))) (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) (B 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) B)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat F B)) C)) (=> (forall ((X3 tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X3) Y)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat F X3)) (tptp.aa_rat_rat F Y))))) (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) (B 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) B)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_num_rat F B)) C)) (=> (forall ((X3 tptp.num) (Y tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X3) Y)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_num_rat F X3)) (tptp.aa_num_rat F Y))))) (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) (B 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) B)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat F B)) C)) (=> (forall ((X3 tptp.nat) (Y tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X3) Y)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_nat_rat F X3)) (tptp.aa_nat_rat F Y))))) (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) (B 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) B)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_int_rat F B)) C)) (=> (forall ((X3 tptp.int) (Y tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X3) Y)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_int_rat F X3)) (tptp.aa_int_rat F Y))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_int_rat F A)) C)))))) (forall ((A tptp.real) (B 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) B)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_real_num F B)) C)) (=> (forall ((X3 tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X3) Y)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num (tptp.aa_real_num F X3)) (tptp.aa_real_num F Y))))) (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.rat) (B 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) B)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_rat_num F B)) C)) (=> (forall ((X3 tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X3) Y)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num (tptp.aa_rat_num F X3)) (tptp.aa_rat_num F Y))))) (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.num) (B 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_num A) B)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_num_num F B)) C)) (=> (forall ((X3 tptp.num) (Y tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X3) Y)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num (tptp.aa_num_num F X3)) (tptp.aa_num_num F Y))))) (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.nat) (B 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_nat A) B)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_nat_num F B)) C)) (=> (forall ((X3 tptp.nat) (Y tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X3) Y)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num (tptp.aa_nat_num F X3)) (tptp.aa_nat_num F Y))))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num (tptp.aa_nat_num F A)) C)))))) (forall ((A tptp.int) (B tptp.int) (F tptp.fun_int_num) (C tptp.num)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_int_num F B)) C)) (=> (forall ((X3 tptp.int) (Y tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X3) Y)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num (tptp.aa_int_num F X3)) (tptp.aa_int_num F Y))))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num (tptp.aa_int_num F A)) C)))))) (forall ((X tptp.rat) (Y4 tptp.rat)) (or (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) Y4)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Y4) X)))) (forall ((X tptp.num) (Y4 tptp.num)) (or (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X) Y4)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num Y4) X)))) (forall ((X tptp.nat) (Y4 tptp.nat)) (or (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X) Y4)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Y4) X)))) (forall ((X tptp.int) (Y4 tptp.int)) (or (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X) Y4)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Y4) X)))) (forall ((X tptp.real) (Y4 tptp.real)) (or (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) Y4)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y4) X)))) (forall ((X tptp.set_int) (Y4 tptp.set_int)) (=> (tptp.ord_less_eq_set_int X Y4) (or (tptp.ord_less_set_int X Y4) (= X Y4)))) (forall ((X tptp.rat) (Y4 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) Y4)) (or (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) Y4)) (= X Y4)))) (forall ((X tptp.num) (Y4 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X) Y4)) (or (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X) Y4)) (= X Y4)))) (forall ((X tptp.nat) (Y4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X) Y4)) (or (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Y4)) (= X Y4)))) (forall ((X tptp.int) (Y4 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X) Y4)) (or (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) Y4)) (= X Y4)))) (forall ((X tptp.real) (Y4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) Y4)) (or (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Y4)) (= X Y4)))) (not (tptp.pp (tptp.aa_real_bool _let_96 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_161 tptp.zero_zero_nat))) _let_166 (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 ((E tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real E))) (and (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 _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 ((E tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat E))) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) E)) (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 ((P tptp.fun_int_bool) (X tptp.nat) (Y4 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) Y4)))) (and (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Y4) 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 Y4))))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Y4)) (tptp.pp (tptp.aa_int_bool P tptp.zero_zero_int)))))) (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B)) (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 B) C))))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B)) (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 B) C))))) (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B)) (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 B) C))))) (forall ((B 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 B) 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 B)))))) (forall ((B 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 B) 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 B)))))) (forall ((B 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 B) 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 B)))))) (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (=> (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A) B) (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) B)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real C) D))))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (=> (= (tptp.aa_rat_rat (tptp.minus_minus_rat A) B) (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) B)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat C) D))))) (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (=> (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) B) (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) B)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int C) D))))) (forall ((A tptp.real) (B tptp.real) (D tptp.real) (C tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B)) (=> (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 B) D)))))) (forall ((A tptp.rat) (B 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) B)) (=> (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 B) D)))))) (forall ((A tptp.int) (B 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) B)) (=> (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 B) D)))))) (forall ((A2 tptp.set_nat) (B3 tptp.set_nat) (C2 tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat A2) B3)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat B3) C2)) (= (tptp.minus_minus_set_nat B3 (tptp.minus_minus_set_nat C2 A2)) A2)))) (forall ((A2 tptp.set_int) (B3 tptp.set_int) (C2 tptp.set_int)) (=> (tptp.ord_less_eq_set_int A2 B3) (=> (tptp.ord_less_eq_set_int B3 C2) (= (tptp.minus_minus_set_int B3 (tptp.minus_minus_set_int C2 A2)) A2)))) (forall ((A2 tptp.set_nat) (B3 tptp.set_nat)) (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat (tptp.minus_minus_set_nat A2 B3)) A2))) (forall ((A2 tptp.set_int) (B3 tptp.set_int)) (tptp.ord_less_eq_set_int (tptp.minus_minus_set_int A2 B3) A2)) (forall ((A2 tptp.set_nat) (C2 tptp.set_nat) (D3 tptp.set_nat) (B3 tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat A2) C2)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat D3) B3)) (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat (tptp.minus_minus_set_nat A2 B3)) (tptp.minus_minus_set_nat C2 D3)))))) (forall ((A2 tptp.set_int) (C2 tptp.set_int) (D3 tptp.set_int) (B3 tptp.set_int)) (=> (tptp.ord_less_eq_set_int A2 C2) (=> (tptp.ord_less_eq_set_int D3 B3) (tptp.ord_less_eq_set_int (tptp.minus_minus_set_int A2 B3) (tptp.minus_minus_set_int C2 D3))))) (tptp.pp (tptp.aa_rat_bool _let_124 tptp.one_one_rat)) (tptp.pp (tptp.aa_nat_bool _let_172 tptp.one_one_nat)) (tptp.pp (tptp.aa_int_bool _let_123 tptp.one_one_int)) (tptp.pp (tptp.aa_real_bool _let_122 tptp.one_one_real)) (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 ((I2 tptp.nat)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I2) (tptp.aa_nat_nat tptp.suc N))) (tptp.pp (tptp.aa_nat_bool P I2)))) (or (tptp.pp (tptp.aa_nat_bool P N)) (exists ((I2 tptp.nat)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I2) N)) (tptp.pp (tptp.aa_nat_bool P I2))))))) (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 ((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.suc N))) (tptp.pp (tptp.aa_nat_bool P I2)))) (and (tptp.pp (tptp.aa_nat_bool P N)) (forall ((I2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I2) N)) (tptp.pp (tptp.aa_nat_bool P I2))))))) (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 ((M6 tptp.nat)) (and (= M (tptp.aa_nat_nat tptp.suc M6)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N) M6)))))) (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) (K2 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) K2)) (=> (tptp.pp (tptp.aa_nat_bool _let_1 J2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool P J2) K2)) (tptp.pp (tptp.aa_nat_bool _let_1 K2)))))))) (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))))) (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.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)) (=> (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.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 (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 ((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 ((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 ((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 ((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 ((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 ((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 ((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)) (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)) (=> (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_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 ((Z tptp.int)) (not (forall ((M4 tptp.nat) (N2 tptp.nat)) (not (= Z (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int M4)) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N2))))))) (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 ((A tptp.code_integer) (B 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 B)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer)) (tptp.pp (tptp.aa_Code_integer_bool _let_1 tptp.one_one_Code_integer)))))) (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat A))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 B)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat B) tptp.one_one_nat)) (tptp.pp (tptp.aa_nat_bool _let_1 tptp.one_one_nat)))))) (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int A))) (=> (tptp.pp (tptp.aa_int_bool _let_1 B)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int B) tptp.one_one_int)) (tptp.pp (tptp.aa_int_bool _let_1 tptp.one_one_int)))))) (forall ((B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer B))) (=> (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 ((B tptp.nat) (A tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat B))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 tptp.one_one_nat)) (tptp.pp (tptp.aa_nat_bool _let_1 A))))) (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int B))) (=> (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.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 ((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 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int M) N))) (=> (tptp.pp (tptp.aa_int_bool _let_1 N)) (tptp.pp (tptp.aa_int_bool _let_1 M)))))) (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 ((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) (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 ((C tptp.rat) (B 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) B))) (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) B))) (=> (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 B) tptp.one_one_rat)))))) (forall ((C tptp.int) (B 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) B))) (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) B))) (=> (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 B) tptp.one_one_int)))))) (forall ((C tptp.real) (B 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) B))) (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) B))) (=> (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 B) tptp.one_one_real)))))) (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) (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) (B 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 B) 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) B))) (=> (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 B) tptp.one_one_rat)))))) (forall ((C tptp.int) (B 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 B) 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) B))) (=> (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 B) tptp.one_one_int)))))) (forall ((C tptp.real) (B 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 B) 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) B))) (=> (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 B) tptp.one_one_real)))))) (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 ((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 ((C tptp.rat) (B 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) B))) (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) B))) (=> (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 B) tptp.one_one_rat)))))) (forall ((C tptp.int) (B 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) B))) (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) B))) (=> (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 B) tptp.one_one_int)))))) (forall ((C tptp.real) (B 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) B))) (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) B))) (=> (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 B) tptp.one_one_real)))))) (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) (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) (B 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 B) 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) B))) (=> (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 B) tptp.one_one_rat)))))) (forall ((C tptp.int) (B 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 B) 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) B))) (=> (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 B) tptp.one_one_int)))))) (forall ((C tptp.real) (B 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 B) 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) B))) (=> (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 B) tptp.one_one_real)))))) (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 ((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 ((X tptp.rat) (Y4 tptp.rat)) (=> (forall ((Z2 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) Z2)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Z2) 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 Z2) X)) Y4))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) Y4)))) (forall ((X tptp.real) (Y4 tptp.real)) (=> (forall ((Z2 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) Z2)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Z2) 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 Z2) X)) Y4))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) Y4)))) (forall ((B 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 B) 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 B) 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) B))) (= A tptp.zero_zero_rat)))) (forall ((B 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 B) 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 B) 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) B))) (= A tptp.zero_zero_real)))) (forall ((B 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 B) 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) B))) (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 B) A)))))) (forall ((B 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 B) 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) B))) (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 B) A)))))) (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)) (=> (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 ((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)) (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 ((A tptp.nat) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (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.aa_int_fun_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.aa_int_fun_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.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)))) (forall ((A tptp.real) (B 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 B) 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) B)))))) (forall ((A tptp.rat) (B 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 B) 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) B)))))) (forall ((A tptp.int) (B 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 B) 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) B)))))) (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) (B 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) B)) 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 B) 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 B))))))) (forall ((A tptp.rat) (B 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) B)) 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 B) 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 B))))))) (forall ((A tptp.int) (B 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) B)) 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 B) 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 B))))))) (forall ((A tptp.real) (B 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) B)) (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) B)) tptp.zero_zero_real))))) (forall ((A tptp.rat) (B 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) B)) (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) B)) tptp.zero_zero_rat))))) (forall ((A tptp.nat) (B 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) B)) (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) B)) tptp.zero_zero_nat))))) (forall ((A tptp.int) (B 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) B)) (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) B)) tptp.zero_zero_int))))) (forall ((A tptp.real) (B 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 B) 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) B)) tptp.zero_zero_real))))) (forall ((A tptp.rat) (B 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 B) 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) B)) tptp.zero_zero_rat))))) (forall ((A tptp.nat) (B 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 B) 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) B)) tptp.zero_zero_nat))))) (forall ((A tptp.int) (B 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 B) 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) B)) tptp.zero_zero_int))))) (forall ((A tptp.real) (B 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 B)) (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) B))))))) (forall ((A tptp.rat) (B 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 B)) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) B))))))) (forall ((A tptp.nat) (B 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 B)) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) B))))))) (forall ((A tptp.int) (B 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 B)) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) B))))))) (forall ((A tptp.real) (B 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 B) 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 B) A)) tptp.zero_zero_real))))) (forall ((A tptp.rat) (B 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 B) 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 B) A)) tptp.zero_zero_rat))))) (forall ((A tptp.nat) (B 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 B) 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 B) A)) tptp.zero_zero_nat))))) (forall ((A tptp.int) (B 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 B) 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 B) A)) tptp.zero_zero_int))))) (forall ((A tptp.real) (B 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) B))) (or (and (tptp.pp (tptp.aa_real_bool _let_1 A)) (tptp.pp (tptp.aa_real_bool _let_1 B))) (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 B) tptp.zero_zero_real))))))) (forall ((A tptp.rat) (B 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) B))) (or (and (tptp.pp (tptp.aa_rat_bool _let_1 A)) (tptp.pp (tptp.aa_rat_bool _let_1 B))) (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 B) tptp.zero_zero_rat))))))) (forall ((A tptp.int) (B 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) B))) (or (and (tptp.pp (tptp.aa_int_bool _let_1 A)) (tptp.pp (tptp.aa_int_bool _let_1 B))) (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 B) tptp.zero_zero_int))))))) (forall ((A tptp.real) (B 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) B))) (=> (tptp.pp (tptp.aa_real_bool _let_1 A)) (tptp.pp (tptp.aa_real_bool _let_1 B)))))) (forall ((A tptp.rat) (B 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) B))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 A)) (tptp.pp (tptp.aa_rat_bool _let_1 B)))))) (forall ((A tptp.nat) (B 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) B))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 A)) (tptp.pp (tptp.aa_nat_bool _let_1 B)))))) (forall ((A tptp.int) (B 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) B))) (=> (tptp.pp (tptp.aa_int_bool _let_1 A)) (tptp.pp (tptp.aa_int_bool _let_1 B)))))) (forall ((B 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 B) A))) (=> (tptp.pp (tptp.aa_real_bool _let_1 A)) (tptp.pp (tptp.aa_real_bool _let_1 B)))))) (forall ((B 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 B) A))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 A)) (tptp.pp (tptp.aa_rat_bool _let_1 B)))))) (forall ((B 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 B) A))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 A)) (tptp.pp (tptp.aa_nat_bool _let_1 B)))))) (forall ((B 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 B) A))) (=> (tptp.pp (tptp.aa_int_bool _let_1 A)) (tptp.pp (tptp.aa_int_bool _let_1 B)))))) (forall ((C tptp.real) (A tptp.real) (B 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 B))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B) A)))))) (forall ((C tptp.rat) (A tptp.rat) (B 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 B))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) A)))))) (forall ((C tptp.int) (A tptp.int) (B 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 B))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B) A)))))) (forall ((C tptp.real) (A tptp.real) (B 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 B))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B)))))) (forall ((C tptp.rat) (A tptp.rat) (B 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 B))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B)))))) (forall ((C tptp.int) (A tptp.int) (B 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 B))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B)))))) (forall ((B 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 B) 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 B))))))) (forall ((B 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 B) 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 B))))))) (forall ((B 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 B) 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 B))))))) (forall ((A tptp.real) (B 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) B)) (=> (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 B))))))) (forall ((A tptp.rat) (B 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) B)) (=> (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 B))))))) (forall ((A tptp.nat) (B 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) B)) (=> (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 B))))))) (forall ((A tptp.int) (B 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) B)) (=> (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 B))))))) (forall ((C tptp.real) (A tptp.real) (B 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 B))) (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) B))) (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 B) A))))))) (forall ((C tptp.rat) (A tptp.rat) (B 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 B))) (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) B))) (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 B) A))))))) (forall ((C tptp.int) (A tptp.int) (B 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 B))) (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) B))) (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 B) A))))))) (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B) 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 B) C)))))) (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) 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 B) C)))))) (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B) 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 B) C)))))) (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B)) (=> (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 B) C)))))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B)) (=> (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 B) C)))))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) B)) (=> (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 B) C)))))) (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B)) (=> (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 B) C)))))) (forall ((A tptp.real) (C tptp.real) (B 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 B) 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) B))) (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 B) A)))))) (forall ((A tptp.rat) (C tptp.rat) (B 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 B) 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) B))) (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 B) A)))))) (forall ((A tptp.int) (C tptp.int) (B 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 B) 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) B))) (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 B) A)))))) (forall ((A tptp.real) (B 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) B)) (=> (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 B))))))) (forall ((A tptp.rat) (B 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) B)) (=> (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 B))))))) (forall ((A tptp.nat) (B 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) B)) (=> (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 B))))))) (forall ((A tptp.int) (B 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) B)) (=> (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 B))))))) (forall ((A tptp.real) (B tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B)) (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) B)) tptp.zero_zero_real)))) (forall ((A tptp.rat) (B tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B)) (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) B)) tptp.zero_zero_rat)))) (forall ((A tptp.int) (B tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B)) (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) B)) tptp.zero_zero_int)))) (forall ((X tptp.real) (Y4 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 Y4) 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) Y4)))))) (forall ((X tptp.rat) (Y4 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 Y4) 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) Y4)))))) (forall ((X tptp.real) (Y4 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) Y4)) (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) Y4)) tptp.zero_zero_real))))) (forall ((X tptp.rat) (Y4 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) Y4)) (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) Y4)) tptp.zero_zero_rat))))) (forall ((X tptp.real) (Y4 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 Y4) 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) Y4)) tptp.zero_zero_real))))) (forall ((X tptp.rat) (Y4 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 Y4) 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) Y4)) tptp.zero_zero_rat))))) (forall ((X tptp.real) (Y4 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 Y4)) (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real X) Y4))))))) (forall ((X tptp.rat) (Y4 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 Y4)) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat (tptp.divide_divide_rat X) Y4))))))) (forall ((A tptp.real) (B 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) B)) 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 B) 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 B))))))) (forall ((A tptp.rat) (B 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) B)) 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 B) 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 B))))))) (forall ((A tptp.real) (C tptp.real) (B 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 B) 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) B))) (=> (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 B) A))) (not (= C tptp.zero_zero_real))))) (forall ((A tptp.rat) (C tptp.rat) (B 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 B) 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) B))) (=> (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 B) A))) (not (= C tptp.zero_zero_rat))))) (forall ((A tptp.real) (B 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) B))) (or (and (tptp.pp (tptp.aa_real_bool _let_1 A)) (tptp.pp (tptp.aa_real_bool _let_1 B))) (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 B) tptp.zero_zero_real))))))) (forall ((A tptp.rat) (B 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) B))) (or (and (tptp.pp (tptp.aa_rat_bool _let_1 A)) (tptp.pp (tptp.aa_rat_bool _let_1 B))) (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 B) tptp.zero_zero_rat))))))) (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B)) (=> (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 B) C)))))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B)) (=> (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 B) C)))))) (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B) 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 B) C)))))) (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) 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 B) C)))))) (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_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_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 ((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)))) _let_177 _let_176 _let_174 _let_173 _let_177 _let_176 _let_174 _let_173 (not (tptp.pp (tptp.aa_rat_bool _let_124 tptp.zero_zero_rat))) (not (tptp.pp (tptp.aa_nat_bool _let_172 tptp.zero_zero_nat))) (not (tptp.pp (tptp.aa_int_bool _let_123 tptp.zero_zero_int))) (not (tptp.pp (tptp.aa_real_bool _let_122 tptp.zero_zero_real))) (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)) (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 ((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 ((M4 tptp.nat)) (= N (tptp.aa_nat_nat tptp.suc M4))))) (forall ((N tptp.nat) (P tptp.fun_nat_bool)) (= (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.suc N))) (tptp.pp (tptp.aa_nat_bool P I2)))) (and (tptp.pp (tptp.aa_nat_bool P tptp.zero_zero_nat)) (forall ((I2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I2) N)) (tptp.pp (tptp.aa_nat_bool P (tptp.aa_nat_nat tptp.suc I2)))))))) (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 ((M5 tptp.nat)) (= N (tptp.aa_nat_nat tptp.suc M5))))) (forall ((N tptp.nat) (P tptp.fun_nat_bool)) (= (exists ((I2 tptp.nat)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I2) (tptp.aa_nat_nat tptp.suc N))) (tptp.pp (tptp.aa_nat_bool P I2)))) (or (tptp.pp (tptp.aa_nat_bool P tptp.zero_zero_nat)) (exists ((I2 tptp.nat)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I2) N)) (tptp.pp (tptp.aa_nat_bool P (tptp.aa_nat_nat tptp.suc I2)))))))) (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 ((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_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 ((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_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 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 ((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 ((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_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 ((B tptp.complex) (A tptp.complex)) (=> (not (= B tptp.zero_zero_complex)) (= (= (tptp.divide1717551699836669952omplex A B) tptp.one_one_complex) (= A B)))) (forall ((B tptp.real) (A tptp.real)) (=> (not (= B tptp.zero_zero_real)) (= (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real A) B) tptp.one_one_real) (= A B)))) (forall ((B tptp.rat) (A tptp.rat)) (=> (not (= B tptp.zero_zero_rat)) (= (= (tptp.aa_rat_rat (tptp.divide_divide_rat A) B) tptp.one_one_rat) (= A B)))) (= _let_67 tptp.one_one_complex) (= _let_68 tptp.one_one_real) (= _let_66 tptp.one_one_rat) _let_171 (= _let_106 tptp.one_one_int) (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 ((K2 tptp.nat)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K2) N)) (forall ((I4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I4) K2)) (not (tptp.pp (tptp.aa_nat_bool P I4))))) (tptp.pp (tptp.aa_nat_bool P K2))))))) (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 ((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)) (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)))))) (forall ((A tptp.code_integer) (B 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) B)) 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 B) tptp.one_one_Code_integer))))) (forall ((A tptp.nat) (B 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) B)) 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 B) tptp.one_one_nat))))) (forall ((A tptp.int) (B 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) B)) 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 B) tptp.one_one_int))))) (forall ((B 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 B) tptp.one_one_Code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger C) B))) (tptp.pp (tptp.aa_Code_integer_bool _let_1 C)))))) (forall ((B 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 B) 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) B))) (tptp.pp (tptp.aa_nat_bool _let_1 C)))))) (forall ((B 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 B) 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) B))) (tptp.pp (tptp.aa_int_bool _let_1 C)))))) (forall ((B 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 B) 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) B)) C)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer A) C))))) (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat B) 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) B)) C)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat A) C))))) (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int B) 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) B)) C)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int A) C))))) (forall ((B 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 B) tptp.one_one_Code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B) C))) (tptp.pp (tptp.aa_Code_integer_bool _let_1 C)))))) (forall ((B 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 B) 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 B) C))) (tptp.pp (tptp.aa_nat_bool _let_1 C)))))) (forall ((B 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 B) 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 B) C))) (tptp.pp (tptp.aa_int_bool _let_1 C)))))) (forall ((A tptp.code_integer) (B 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) B)) C)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer B) C))))) (forall ((A tptp.nat) (B 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) B)) C)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat B) C))))) (forall ((A tptp.int) (B 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) B)) C)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int B) C))))) (forall ((A tptp.code_integer) (B 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 B) (tptp.aa_Cod1783974652533396728nteger _let_1 C)) (= B C))))) (forall ((A tptp.nat) (B 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 B) (tptp.aa_nat_nat _let_1 C)) (= B C))))) (forall ((A tptp.int) (B 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 B) (tptp.aa_int_int _let_1 C)) (= B C))))) (forall ((A tptp.code_integer) (B 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 B) A) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger C) A)) (= B C)))) (forall ((A tptp.nat) (B 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 B) A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat C) A)) (= B C)))) (forall ((A tptp.int) (B 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 B) A) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int C) A)) (= B C)))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) B)) (=> (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 B) C)))))) (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 ((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 ((A tptp.code_integer) (B 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 B A) (tptp.divide6298287555418463151nteger C A)) (= B C)))) (forall ((A tptp.nat) (B 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 B) A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat C) A)) (= B C)))) (forall ((A tptp.int) (B 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.divide_divide_int B) A) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int C) A)) (= B C)))) (forall ((B 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 B) tptp.one_one_Code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.divide6298287555418463151nteger A B)) C)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer A) C))))) (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat B) 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) B)) C)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat A) C))))) (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int B) 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.divide_divide_int A) B)) C)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int A) C))))) (forall ((B 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 B) tptp.one_one_Code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.divide6298287555418463151nteger C B))) (tptp.pp (tptp.aa_Code_integer_bool _let_1 C)))))) (forall ((B 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 B) 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) B))) (tptp.pp (tptp.aa_nat_bool _let_1 C)))))) (forall ((B 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 B) tptp.one_one_int)) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int C) B))) (tptp.pp (tptp.aa_int_bool _let_1 C)))))) (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)))) _let_171 (= tptp.one_one_nat _let_58) (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.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 ((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 ((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 ((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 ((C tptp.rat) (A tptp.rat) (B 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 B))) (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) B))) (=> (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 B) A))))))) (forall ((C tptp.int) (A tptp.int) (B 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 B))) (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) B))) (=> (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 B) A))))))) (forall ((C tptp.real) (A tptp.real) (B 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 B))) (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) B))) (=> (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 B) A))))))) (forall ((A tptp.rat) (C tptp.rat) (B 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 B) 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) B))) (=> (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 B) A)))))) (forall ((A tptp.int) (C tptp.int) (B 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 B) 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) B))) (=> (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 B) A)))))) (forall ((A tptp.real) (C tptp.real) (B 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 B) 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) B))) (=> (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 B) A)))))) (forall ((C tptp.rat) (A tptp.rat) (B 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 B))) (=> (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) B)))))) (forall ((C tptp.nat) (A tptp.nat) (B 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 B))) (=> (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) B)))))) (forall ((C tptp.int) (A tptp.int) (B 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 B))) (=> (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) B)))))) (forall ((C tptp.real) (A tptp.real) (B 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 B))) (=> (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) B)))))) (forall ((A tptp.rat) (B 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) B)) (=> (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) B)) (=> (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 B) D)))))))) (forall ((A tptp.nat) (B 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) B)) (=> (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) B)) (=> (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 B) D)))))))) (forall ((A tptp.int) (B 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) B)) (=> (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) B)) (=> (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 B) D)))))))) (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B)) (=> (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) B)) (=> (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 B) D)))))))) (forall ((C tptp.rat) (A tptp.rat) (B 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 B))) (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) B))) (=> (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 B) A))))))) (forall ((C tptp.int) (A tptp.int) (B 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 B))) (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) B))) (=> (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 B) A))))))) (forall ((C tptp.real) (A tptp.real) (B 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 B))) (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) B))) (=> (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 B) A))))))) (forall ((A tptp.rat) (C tptp.rat) (B 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 B) 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) B))))) (forall ((A tptp.nat) (C tptp.nat) (B 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 B) 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) B))))) (forall ((A tptp.int) (C tptp.int) (B 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 B) 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) B))))) (forall ((A tptp.real) (C tptp.real) (B 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 B) 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) B))))) (forall ((A tptp.rat) (B 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) B)) (=> (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 B) D))))))))) (forall ((A tptp.nat) (B 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) B)) (=> (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 B) D))))))))) (forall ((A tptp.int) (B 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) B)) (=> (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 B) D))))))))) (forall ((A tptp.real) (B 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) B)) (=> (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 B) D))))))))) (forall ((A tptp.rat) (C tptp.rat) (B 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 B) 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) B))) (=> (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 B) A)))))) (forall ((A tptp.int) (C tptp.int) (B 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 B) 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) B))) (=> (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 B) A)))))) (forall ((A tptp.real) (C tptp.real) (B 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 B) 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) B))) (=> (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 B) A)))))) (forall ((C tptp.rat) (A tptp.rat) (B 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 B))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) A)))))) (forall ((C tptp.int) (A tptp.int) (B 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 B))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B) A)))))) (forall ((C tptp.real) (A tptp.real) (B 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 B))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real B) A)))))) (forall ((C tptp.rat) (A tptp.rat) (B 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 B))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B)))))) (forall ((C tptp.int) (A tptp.int) (B 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 B))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B)))))) (forall ((C tptp.real) (A tptp.real) (B 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 B))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) B)))))) (forall ((C tptp.rat) (A tptp.rat) (B 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 B))) (=> (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) B)))))) (forall ((C tptp.nat) (A tptp.nat) (B 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 B))) (=> (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) B)))))) (forall ((C tptp.int) (A tptp.int) (B 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 B))) (=> (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) B)))))) (forall ((C tptp.real) (A tptp.real) (B 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 B))) (=> (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) B)))))) (forall ((A tptp.rat) (C tptp.rat) (B 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 B) 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) B))))) (forall ((A tptp.nat) (C tptp.nat) (B 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 B) 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) B))))) (forall ((A tptp.int) (C tptp.int) (B 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 B) 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) B))))) (forall ((A tptp.real) (C tptp.real) (B 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 B) 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) B))))) (forall ((A tptp.rat) (B 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) B)) (=> (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 B) D)))))))) (forall ((A tptp.nat) (B 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) B)) (=> (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 B) D)))))))) (forall ((A tptp.int) (B 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) B)) (=> (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 B) D)))))))) (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) B)) (=> (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 B) D)))))))) (forall ((A tptp.rat) (B 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) B)) (=> (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 B) D)))))))) (forall ((A tptp.nat) (B 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) B)) (=> (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 B) D)))))))) (forall ((A tptp.int) (B 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) B)) (=> (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 B) D)))))))) (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B)) (=> (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 B) D)))))))) (forall ((Y4 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) Y4)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) Y4)) (=> (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 Y4) W)))))))) (forall ((Y4 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) Y4)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) Y4)) (=> (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 Y4) W)))))))) (forall ((X tptp.rat) (Y4 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) Y4)) (=> (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 Y4) W)))))))) (forall ((X tptp.real) (Y4 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) Y4)) (=> (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 Y4) W)))))))) (forall ((X tptp.rat) (Y4 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) Y4)) (=> (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 Y4) W))))))))) (forall ((X tptp.real) (Y4 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) Y4)) (=> (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 Y4) W))))))))) (forall ((A tptp.rat) (C tptp.rat) (B 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 B) 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) B))) (=> (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 B) A)))))) (forall ((A tptp.real) (C tptp.real) (B 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 B) 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) B))) (=> (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 B) A)))))) (forall ((X tptp.rat) (Y4 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 Y4) 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) Y4)) tptp.zero_zero_rat))))) (forall ((X tptp.real) (Y4 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 Y4) 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) Y4)) tptp.zero_zero_real))))) (forall ((X tptp.rat) (Y4 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) Y4)) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat (tptp.divide_divide_rat X) Y4))))))) (forall ((X tptp.real) (Y4 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) Y4)) (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real X) Y4))))))) (forall ((X tptp.rat) (Y4 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 Y4) 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) Y4)))))) (forall ((X tptp.real) (Y4 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 Y4) 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) Y4)))))) (forall ((X tptp.rat) (Y4 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) Y4)) (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) Y4)) tptp.zero_zero_rat))))) (forall ((X tptp.real) (Y4 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) Y4)) (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) Y4)) tptp.zero_zero_real))))) (forall ((A tptp.nat) (B 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) B)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) B) tptp.zero_zero_nat)))) (forall ((A tptp.int) (B 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) B)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A) B) tptp.zero_zero_int)))) (forall ((B 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 B)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B) A)) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) B))))))) (forall ((B 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 B)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B) A)) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A) B))))))) (forall ((B 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 B) C)) A)) (and (=> _let_4 (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B) _let_3))) (=> (not _let_4) (and (=> _let_2 (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real _let_3) B))) (=> (not _let_2) (tptp.pp (tptp.aa_real_bool _let_1 A)))))))))))) (forall ((B 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 B) C)) A)) (and (=> _let_4 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) _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) B))) (=> (not _let_2) (tptp.pp (tptp.aa_rat_bool _let_1 A)))))))))))) (forall ((A tptp.real) (B 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 B) C))) (and (=> _let_4 (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real _let_3) B))) (=> (not _let_4) (and (=> _let_2 (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B) _let_3))) (=> (not _let_2) (tptp.pp (tptp.aa_real_bool _let_1 tptp.zero_zero_real)))))))))))) (forall ((A tptp.rat) (B 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 B) C))) (and (=> _let_4 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat _let_3) B))) (=> (not _let_4) (and (=> _let_2 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) _let_3))) (=> (not _let_2) (tptp.pp (tptp.aa_rat_bool _let_1 tptp.zero_zero_rat)))))))))))) (forall ((C tptp.real) (B 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 B) 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)) B))))) (forall ((C tptp.rat) (B 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 B) 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)) B))))) (forall ((C tptp.real) (A tptp.real) (B 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 B) C))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) C)))))) (forall ((C tptp.rat) (A tptp.rat) (B 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 B) C))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) C)))))) (forall ((C tptp.real) (B 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 B) C)) A)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) C)))))) (forall ((C tptp.rat) (B 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 B) C)) A)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) C)))))) (forall ((C tptp.real) (A tptp.real) (B 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 B) 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)) B))))) (forall ((C tptp.rat) (A tptp.rat) (B 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 B) 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)) B))))) (forall ((Y4 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) Y4)) (=> (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) Y4))) (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) Y4)) Z))))) (forall ((Y4 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) Y4)) (=> (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) Y4))) (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) Y4)) Z))))) (forall ((Y4 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) Y4)) (=> (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) Y4)) 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) Y4)))))) (forall ((Y4 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) Y4)) (=> (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) Y4)) 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) Y4)))))) (forall ((B 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 B) 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) B))) (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 B))))))))) (forall ((B 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 B) 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) B))) (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 B))))))))) (forall ((A tptp.real) (B 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) B)) (=> (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) B))) (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 B)))))))) (forall ((A tptp.rat) (B 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) B)) (=> (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) B))) (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 B)))))))) (forall ((X tptp.rat) (Y4 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 Y4)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat Y4) 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 Y4) X)) X))))))) (forall ((X tptp.int) (Y4 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 Y4)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Y4) 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 Y4) X)) X))))))) (forall ((X tptp.real) (Y4 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 Y4)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y4) 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 Y4) X)) X))))))) (forall ((X tptp.rat) (Y4 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 Y4)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat Y4) 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) Y4)) X))))))) (forall ((X tptp.int) (Y4 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 Y4)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Y4) 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) Y4)) X))))))) (forall ((X tptp.real) (Y4 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 Y4)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y4) 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) Y4)) X))))))) (forall ((A tptp.rat) (B 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) B)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) 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) B)) tptp.one_one_rat)))))) (forall ((A tptp.nat) (B 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) B)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B) 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) B)) tptp.one_one_nat)))))) (forall ((A tptp.int) (B 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) B)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B) 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) B)) tptp.one_one_int)))))) (forall ((A tptp.real) (B 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) B)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real B) 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) B)) tptp.one_one_real)))))) (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 ((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 ((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 ((K2 tptp.nat)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat K2) N)) (forall ((I4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I4) K2)) (not (tptp.pp (tptp.aa_nat_bool P I4))))) (tptp.pp (tptp.aa_nat_bool P (tptp.aa_nat_nat tptp.suc K2)))))))) (forall ((A tptp.code_integer) (B 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 ((C3 tptp.code_integer)) (not (= B (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) C3)))))))) (forall ((A tptp.nat) (B 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 ((C3 tptp.nat)) (not (= B (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) C3)))))))) (forall ((A tptp.int) (B 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 ((C3 tptp.int)) (not (= B (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) C3)))))))) (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)) (=> (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 ((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)) (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 ((B tptp.code_integer) (A tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer)) (= (= (tptp.divide6298287555418463151nteger A B) tptp.zero_z3403309356797280102nteger) (= A tptp.zero_z3403309356797280102nteger)))) (forall ((B tptp.nat) (A tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat B) tptp.one_one_nat)) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) B) tptp.zero_zero_nat) (= A tptp.zero_zero_nat)))) (forall ((B tptp.int) (A tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int B) tptp.one_one_int)) (= (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A) B) tptp.zero_zero_int) (= A tptp.zero_zero_int)))) (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 ((B 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 B) tptp.one_one_Code_integer)) (= (= (tptp.divide6298287555418463151nteger A B) C) (= A (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger C) B))))) (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat B) tptp.one_one_nat)) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) B) C) (= A (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat C) B))))) (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int B) tptp.one_one_int)) (= (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A) B) C) (= A (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int C) B))))) (forall ((B 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 B) tptp.one_one_Code_integer)) (= (= A (tptp.divide6298287555418463151nteger C B)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) B) C)))) (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat B) tptp.one_one_nat)) (= (= A (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat C) B)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) B) C)))) (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int B) tptp.one_one_int)) (= (= A (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int C) B)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) B) C)))) (forall ((C tptp.code_integer) (B 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 B) A)) (= (tptp.divide6298287555418463151nteger A (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B) C)) (tptp.divide6298287555418463151nteger (tptp.divide6298287555418463151nteger A B) C))))) (forall ((C tptp.nat) (B 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 B) A)) (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B) C)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat _let_1 B)) C)))))) (forall ((C tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int 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 B) A)) (= (tptp.aa_int_int _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int (tptp.aa_int_int _let_1 B)) C)))))) (forall ((B 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 B) tptp.one_one_Code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.divide6298287555418463151nteger A B)) C) (tptp.divide6298287555418463151nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) C) B)))) (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat B) 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) B)) 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)) B)))) (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int B) 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.divide_divide_int A) B)) C) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) C)) B)))) (forall ((C tptp.code_integer) (A tptp.code_integer) (B 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 B C)) (tptp.divide6298287555418463151nteger (tptp.aa_Cod1783974652533396728nteger _let_1 B) C))))) (forall ((C tptp.nat) (A tptp.nat) (B 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 B) C)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat _let_1 B)) C))))) (forall ((C tptp.int) (A tptp.int) (B 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.aa_int_fun_int_int tptp.divide_divide_int B) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int (tptp.aa_int_int _let_1 B)) C))))) (forall ((B 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 B) 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 B) C)) (tptp.divide6298287555418463151nteger (tptp.divide6298287555418463151nteger A B) C))))) (forall ((B 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 B) 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 B) C)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat _let_1 B)) C)))))) (forall ((B tptp.int) (C tptp.int) (A tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.divide_divide_int A))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int B) 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 B) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int (tptp.aa_int_int _let_1 B)) C)))))) (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 ((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 ((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 ((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 ((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 ((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 ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (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.divide6298287555418463151nteger (tptp.minus_8373710615458151222nteger (tptp.power_8256067586552552935nteger _let_1 M) tptp.one_one_Code_integer) (tptp.power_8256067586552552935nteger _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)) (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_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.aa_int_fun_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 ((X tptp.int) (X6 tptp.int) (P tptp.bool) (P2 tptp.bool)) (let ((_let_1 (tptp.pp P2))) (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 ((X tptp.int) (X6 tptp.int) (P tptp.bool) (P2 tptp.bool)) (let ((_let_1 (tptp.pp P2))) (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 ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (not (= A B)))) (let ((_let_2 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat A) B)))) (=> _let_1 (=> _let_2 (and _let_2 _let_1)))))) (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (not (= A B)))) (=> (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat A) B)) _let_1) _let_1))) (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat A) B)))) (=> (and _let_1 (not (= A B))) _let_1))) (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat A) B)) (not (= A B))))) (= _let_1 _let_1))) (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (= A B))) (let ((_let_2 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat A) B)))) (= _let_2 (or (and _let_2 (not _let_1)) _let_1))))) (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat A) B)))) (= (and _let_1 (not (= A B))) (and _let_1 (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat B) A))))))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat A))) (=> (and (tptp.pp (tptp.aa_nat_bool _let_1 B)) (not (= A B))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat B) C)) (and (tptp.pp (tptp.aa_nat_bool _let_1 C)) (not (= A C))))))) (forall ((A tptp.nat) (B 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 B)) (=> (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat B) C)) (not (= B C))) (and (tptp.pp (tptp.aa_nat_bool _let_1 C)) (not (= A C))))))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat A))) (=> (and (tptp.pp (tptp.aa_nat_bool _let_1 B)) (not (= A B))) (=> (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat B) C)) (not (= B C))) (and (tptp.pp (tptp.aa_nat_bool _let_1 C)) (not (= A C))))))) (forall ((A tptp.nat) (B tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat A) B)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat B) A)) (= A B)))) (forall ((A tptp.nat)) (not (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat A) A)) (not (= A A))))) (forall ((A tptp.nat) (B tptp.nat)) (= (= A B) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat A) B)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat B) A))))) (forall ((A tptp.nat) (B 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 B)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat B) C)) (tptp.pp (tptp.aa_nat_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.nat) (B tptp.nat)) (=> (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat A) B)) (not (= A B))) (not (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat B) A)) (not (= B A)))))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.power_8256067586552552935nteger _let_1 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.power_8256067586552552935nteger _let_1 M) tptp.one_one_Code_integer) _let_2))) (or (= _let_2 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.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.aa_int_fun_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 ((B 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 B) C)) A)) (and (=> _let_3 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) _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) B))) (=> (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 ((B 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 B) C)) A)) (and (=> _let_3 (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real B) _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) B))) (=> (not _let_1) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) A))))))))))) (forall ((A tptp.rat) (B 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 B) C))) (and (=> _let_4 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat _let_3) B))) (=> (not _let_4) (and (=> _let_2 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) _let_3))) (=> (not _let_2) (tptp.pp (tptp.aa_rat_bool _let_1 tptp.zero_zero_rat)))))))))))) (forall ((A tptp.real) (B 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 B) C))) (and (=> _let_4 (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real _let_3) B))) (=> (not _let_4) (and (=> _let_2 (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real B) _let_3))) (=> (not _let_2) (tptp.pp (tptp.aa_real_bool _let_1 tptp.zero_zero_real)))))))))))) (forall ((B 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 B) 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) B))) (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 B)))))))) (forall ((B 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 B) 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) B))) (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 B)))))))) (forall ((C tptp.rat) (B 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 B) 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)) B))))) (forall ((C tptp.real) (B 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 B) 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)) B))))) (forall ((C tptp.rat) (A tptp.rat) (B 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 B) C))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) C)))))) (forall ((C tptp.real) (A tptp.real) (B 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 B) C))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real B) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) C)))))) (forall ((C tptp.rat) (B 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 B) C)) A)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) C)))))) (forall ((C tptp.real) (B 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 B) C)) A)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real B) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) C)))))) (forall ((C tptp.rat) (A tptp.rat) (B 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 B) 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)) B))))) (forall ((C tptp.real) (A tptp.real) (B 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 B) 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)) B))))) (forall ((Y4 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) Y4)) (=> (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) Y4))) (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) Y4)) Z))))) (forall ((Y4 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) Y4)) (=> (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) Y4))) (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) Y4)) Z))))) (forall ((Y4 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) Y4)) (=> (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) Y4)) 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) Y4)))))) (forall ((Y4 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) Y4)) (=> (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) Y4)) 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) Y4)))))) (forall ((A tptp.rat) (B 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) B)) (=> (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) B))) (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 B)))))))) (forall ((A tptp.real) (B 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) B)) (=> (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) B))) (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 B)))))))) (forall ((B 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 B) C)) _let_1)) (and (=> _let_5 (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B) _let_4))) (=> (not _let_5) (and (=> _let_3 (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real _let_4) B))) (=> (not _let_3) (tptp.pp (tptp.aa_real_bool _let_2 _let_1))))))))))))) (forall ((B 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 B) C)) _let_1)) (and (=> _let_5 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) _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) B))) (=> (not _let_3) (tptp.pp (tptp.aa_rat_bool _let_2 _let_1))))))))))))) (forall ((W tptp.num) (B 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 B) C))) (and (=> _let_5 (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real _let_4) B))) (=> (not _let_5) (and (=> _let_3 (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B) _let_4))) (=> (not _let_3) (tptp.pp (tptp.aa_real_bool _let_2 tptp.zero_zero_real))))))))))))) (forall ((W tptp.num) (B 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 B) C))) (and (=> _let_5 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat _let_4) B))) (=> (not _let_5) (and (=> _let_3 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) _let_4))) (=> (not _let_3) (tptp.pp (tptp.aa_rat_bool _let_2 tptp.zero_zero_rat))))))))))))) (forall ((Y4 tptp.real) (Z tptp.real) (X tptp.real) (W tptp.real)) (=> (not (= Y4 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) Y4)) (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) Y4))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real Y4) Z))) tptp.zero_zero_real)))))) (forall ((Y4 tptp.rat) (Z tptp.rat) (X tptp.rat) (W tptp.rat)) (=> (not (= Y4 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) Y4)) (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) Y4))) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat Y4) Z))) tptp.zero_zero_rat)))))) (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)))) (tptp.pp (tptp.aa_nat_bool _let_161 _let_2)) (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 ((B2 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) tptp.one_one_Code_integer)) (=> (= (tptp.divide6298287555418463151nteger tptp.one_one_Code_integer A) B2) (=> (= (tptp.divide6298287555418463151nteger tptp.one_one_Code_integer B2) A) (=> (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) B2) tptp.one_one_Code_integer) (not (= (tptp.divide6298287555418463151nteger C A) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger C) B2))))))))))))) (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 ((B2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat tptp.one_one_nat))) (=> (not (= B2 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 _let_1 A) B2) (=> (= (tptp.aa_nat_nat _let_1 B2) A) (=> (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) B2) 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) B2)))))))))))))) (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 ((B2 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.divide_divide_int tptp.one_one_int))) (=> (not (= B2 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 _let_1 A) B2) (=> (= (tptp.aa_int_int _let_1 B2) A) (=> (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) B2) tptp.one_one_int) (not (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int C) A) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int C) B2)))))))))))))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (not (= A tptp.zero_z3403309356797280102nteger)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer)) (= (tptp.divide6298287555418463151nteger A (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) B)) (tptp.divide6298287555418463151nteger tptp.one_one_Code_integer B))))) (forall ((A tptp.nat) (B tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat B) 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) B)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat tptp.one_one_nat) B))))) (forall ((A tptp.int) (B tptp.int)) (=> (not (= A tptp.zero_zero_int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int B) tptp.one_one_int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) B)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int tptp.one_one_int) B))))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (not (= A tptp.zero_z3403309356797280102nteger)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer)) (= (tptp.divide6298287555418463151nteger A (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B) A)) (tptp.divide6298287555418463151nteger tptp.one_one_Code_integer B))))) (forall ((A tptp.nat) (B tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat B) 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 B) A)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat tptp.one_one_nat) B))))) (forall ((A tptp.int) (B tptp.int)) (=> (not (= A tptp.zero_zero_int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int B) tptp.one_one_int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B) A)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int tptp.one_one_int) B))))) (not (tptp.pp (tptp.aa_Code_integer_bool _let_169 tptp.one_one_Code_integer))) (not (tptp.pp (tptp.aa_nat_bool _let_168 tptp.one_one_nat))) (not (tptp.pp (tptp.aa_int_bool _let_167 tptp.one_one_int))) (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) (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 ((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 ((A tptp.code_integer) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer _let_1))) (let ((_let_3 (tptp.power_8256067586552552935nteger _let_1 N))) (= (tptp.pp (tptp.aa_Code_integer_bool _let_2 (tptp.divide6298287555418463151nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) (tptp.power_8256067586552552935nteger _let_1 M)) _let_3))) (or (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N) M)) (= _let_3 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_2 (tptp.divide6298287555418463151nteger A (tptp.power_8256067586552552935nteger _let_1 (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.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.aa_int_fun_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.aa_int_fun_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 ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (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 ((N tptp.nat) (A tptp.rat) (B 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) B)) (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 B) N)))))) (forall ((N tptp.nat) (A tptp.int) (B 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) B)) (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 B) N)))))) (forall ((N tptp.nat) (A tptp.real) (B 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) B)) (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 B) N)))))) (forall ((B 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 B) C)) _let_1)) (and (=> _let_4 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) _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) B))) (=> (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 ((B 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 B) C)) _let_1)) (and (=> _let_4 (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real B) _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) B))) (=> (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 ((W tptp.num) (B 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 B) C))) (and (=> _let_5 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat _let_4) B))) (=> (not _let_5) (and (=> _let_3 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) _let_4))) (=> (not _let_3) (tptp.pp (tptp.aa_rat_bool _let_2 tptp.zero_zero_rat))))))))))))) (forall ((W tptp.num) (B 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 B) C))) (and (=> _let_5 (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real _let_4) B))) (=> (not _let_5) (and (=> _let_3 (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real B) _let_4))) (=> (not _let_3) (tptp.pp (tptp.aa_real_bool _let_2 tptp.zero_zero_real))))))))))))) (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 ((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 ((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 ((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)) (=> (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 ((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 ((Q3 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 Q3)) 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 Q3)))) (tptp.pp (tptp.aa_nat_bool P Q3)))))))) (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 ((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 ((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 ((M4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) M4)) (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 M4)) X)) C)))) (= X tptp.zero_zero_real)))))) (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 ((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 ((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 ((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)) (=> (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)) (=> (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 ((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 ((P tptp.fun_real_bool) (D3 tptp.real) (Q tptp.fun_real_bool)) (=> (forall ((X3 tptp.real) (K2 tptp.real)) (= (tptp.pp (tptp.aa_real_bool P X3)) (tptp.pp (tptp.aa_real_bool P (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real X3) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real K2) D3)))))) (=> (forall ((X3 tptp.real) (K2 tptp.real)) (= (tptp.pp (tptp.aa_real_bool Q X3)) (tptp.pp (tptp.aa_real_bool Q (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real X3) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real K2) D3)))))) (forall ((X4 tptp.real) (K4 tptp.real)) (let ((_let_1 (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 K4) D3)))) (= (or (tptp.pp (tptp.aa_real_bool P X4)) (tptp.pp (tptp.aa_real_bool Q X4))) (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) (D3 tptp.rat) (Q tptp.fun_rat_bool)) (=> (forall ((X3 tptp.rat) (K2 tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool P X3)) (tptp.pp (tptp.aa_rat_bool P (tptp.aa_rat_rat (tptp.minus_minus_rat X3) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat K2) D3)))))) (=> (forall ((X3 tptp.rat) (K2 tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool Q X3)) (tptp.pp (tptp.aa_rat_bool Q (tptp.aa_rat_rat (tptp.minus_minus_rat X3) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat K2) D3)))))) (forall ((X4 tptp.rat) (K4 tptp.rat)) (let ((_let_1 (tptp.aa_rat_rat (tptp.minus_minus_rat X4) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat K4) D3)))) (= (or (tptp.pp (tptp.aa_rat_bool P X4)) (tptp.pp (tptp.aa_rat_bool Q X4))) (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) (D3 tptp.int) (Q tptp.fun_int_bool)) (=> (forall ((X3 tptp.int) (K2 tptp.int)) (= (tptp.pp (tptp.aa_int_bool P X3)) (tptp.pp (tptp.aa_int_bool P (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int X3) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int K2) D3)))))) (=> (forall ((X3 tptp.int) (K2 tptp.int)) (= (tptp.pp (tptp.aa_int_bool Q X3)) (tptp.pp (tptp.aa_int_bool Q (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int X3) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int K2) D3)))))) (forall ((X4 tptp.int) (K4 tptp.int)) (let ((_let_1 (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 K4) D3)))) (= (or (tptp.pp (tptp.aa_int_bool P X4)) (tptp.pp (tptp.aa_int_bool Q X4))) (or (tptp.pp (tptp.aa_int_bool P _let_1)) (tptp.pp (tptp.aa_int_bool Q _let_1))))))))) (forall ((P tptp.fun_real_bool) (D3 tptp.real) (Q tptp.fun_real_bool)) (=> (forall ((X3 tptp.real) (K2 tptp.real)) (= (tptp.pp (tptp.aa_real_bool P X3)) (tptp.pp (tptp.aa_real_bool P (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real X3) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real K2) D3)))))) (=> (forall ((X3 tptp.real) (K2 tptp.real)) (= (tptp.pp (tptp.aa_real_bool Q X3)) (tptp.pp (tptp.aa_real_bool Q (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real X3) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real K2) D3)))))) (forall ((X4 tptp.real) (K4 tptp.real)) (let ((_let_1 (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 K4) D3)))) (= (and (tptp.pp (tptp.aa_real_bool P X4)) (tptp.pp (tptp.aa_real_bool Q X4))) (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) (D3 tptp.rat) (Q tptp.fun_rat_bool)) (=> (forall ((X3 tptp.rat) (K2 tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool P X3)) (tptp.pp (tptp.aa_rat_bool P (tptp.aa_rat_rat (tptp.minus_minus_rat X3) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat K2) D3)))))) (=> (forall ((X3 tptp.rat) (K2 tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool Q X3)) (tptp.pp (tptp.aa_rat_bool Q (tptp.aa_rat_rat (tptp.minus_minus_rat X3) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat K2) D3)))))) (forall ((X4 tptp.rat) (K4 tptp.rat)) (let ((_let_1 (tptp.aa_rat_rat (tptp.minus_minus_rat X4) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat K4) D3)))) (= (and (tptp.pp (tptp.aa_rat_bool P X4)) (tptp.pp (tptp.aa_rat_bool Q X4))) (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) (D3 tptp.int) (Q tptp.fun_int_bool)) (=> (forall ((X3 tptp.int) (K2 tptp.int)) (= (tptp.pp (tptp.aa_int_bool P X3)) (tptp.pp (tptp.aa_int_bool P (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int X3) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int K2) D3)))))) (=> (forall ((X3 tptp.int) (K2 tptp.int)) (= (tptp.pp (tptp.aa_int_bool Q X3)) (tptp.pp (tptp.aa_int_bool Q (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int X3) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int K2) D3)))))) (forall ((X4 tptp.int) (K4 tptp.int)) (let ((_let_1 (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 K4) D3)))) (= (and (tptp.pp (tptp.aa_int_bool P X4)) (tptp.pp (tptp.aa_int_bool Q X4))) (and (tptp.pp (tptp.aa_int_bool P _let_1)) (tptp.pp (tptp.aa_int_bool Q _let_1))))))))) (forall ((P3 tptp.nat) (A tptp.nat) (B tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat P3) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) B))) (not (forall ((X3 tptp.nat) (Y tptp.nat)) (=> (= P3 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat X3) Y)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat X3) A)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat Y) B))))))))) (forall ((P3 tptp.int) (A tptp.int) (B tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int P3) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) B))) (not (forall ((X3 tptp.int) (Y tptp.int)) (=> (= P3 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int X3) Y)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int X3) A)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int Y) B))))))))) (forall ((A tptp.nat) (B 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 B) C))) (exists ((B5 tptp.nat) (C4 tptp.nat)) (and (= A (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B5) C4)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat B5) B)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat C4) C)))))) (forall ((A tptp.int) (B 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 B) C))) (exists ((B5 tptp.int) (C4 tptp.int)) (and (= A (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B5) C4)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int B5) B)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int C4) C)))))) (forall ((T tptp.vEBT_VEBT)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_VEBT_VEBT_nat tptp.vEBT_VEBT_space T)) (tptp.aa_VEBT_VEBT_nat tptp.vEBT_VEBT_space2 T)))) (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.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.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.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_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.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_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.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.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.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_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.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat I)) N))))) (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.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_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.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.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_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.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_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.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_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.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.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 ((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.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat I)) N))))) (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)) (= (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)) (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.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 ((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 ((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 ((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 ((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 ((X tptp.rat) (Y4 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 Y4)) (= (= (tptp.aa_nat_rat (tptp.power_power_rat X) _let_1) (tptp.aa_nat_rat (tptp.power_power_rat Y4) _let_1)) (= X Y4))))))) (forall ((X tptp.nat) (Y4 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 Y4)) (= (= (tptp.aa_nat_nat (tptp.power_power_nat X) _let_1) (tptp.aa_nat_nat (tptp.power_power_nat Y4) _let_1)) (= X Y4))))))) (forall ((X tptp.int) (Y4 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 Y4)) (= (= (tptp.aa_nat_int (tptp.power_power_int X) _let_1) (tptp.aa_nat_int (tptp.power_power_int Y4) _let_1)) (= X Y4))))))) (forall ((X tptp.real) (Y4 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 Y4)) (= (= (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 Y4) _let_1)) (= X Y4))))))) (forall ((B tptp.rat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.power_power_rat B))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) B)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) 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 ((B tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.power_power_nat B))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) B)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat B) 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 ((B tptp.int) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.power_power_int 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 (tptp.aa_int_fun_int_bool tptp.ord_less_int B) 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 ((B tptp.real) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_real_fun_nat_real tptp.power_power_real B))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) B)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B) 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 ((A tptp.rat) (B 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 B)) (=> (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 B) N))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B)))))))) (forall ((A tptp.nat) (B 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 B)) (=> (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.power_power_nat A) N)) (tptp.aa_nat_nat (tptp.power_power_nat B) N))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B)))))))) (forall ((A tptp.int) (B 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 B)) (=> (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 B) N))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B)))))))) (forall ((A tptp.real) (B 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 B)) (=> (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 B) N))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) B)))))))) (forall ((A2 tptp.set_int) (B3 tptp.set_int)) (=> (tptp.ord_less_eq_set_int A2 B3) (=> (not (= A2 B3)) (tptp.ord_less_set_int A2 B3)))) (forall ((C tptp.complex) (A2 tptp.set_complex) (B3 tptp.set_complex)) (=> (tptp.member_complex C A2) (=> (not (tptp.member_complex C B3)) (tptp.member_complex C (tptp.minus_811609699411566653omplex A2 B3))))) (forall ((C tptp.real) (A2 tptp.set_real) (B3 tptp.set_real)) (=> (tptp.member_real C A2) (=> (not (tptp.member_real C B3)) (tptp.member_real C (tptp.minus_minus_set_real A2 B3))))) (forall ((C tptp.set_nat) (A2 tptp.set_set_nat) (B3 tptp.set_set_nat)) (=> (tptp.member_set_nat C A2) (=> (not (tptp.member_set_nat C B3)) (tptp.member_set_nat C (tptp.minus_2163939370556025621et_nat A2 B3))))) (forall ((C tptp.int) (A2 tptp.set_int) (B3 tptp.set_int)) (=> (tptp.member_int C A2) (=> (not (tptp.member_int C B3)) (tptp.member_int C (tptp.minus_minus_set_int A2 B3))))) (forall ((C tptp.nat) (A2 tptp.set_nat) (B3 tptp.set_nat)) (let ((_let_1 (tptp.member_nat C))) (=> (tptp.pp (tptp.aa_set_nat_bool _let_1 A2)) (=> (not (tptp.pp (tptp.aa_set_nat_bool _let_1 B3))) (tptp.pp (tptp.aa_set_nat_bool _let_1 (tptp.minus_minus_set_nat A2 B3))))))) (forall ((C tptp.complex) (A2 tptp.set_complex) (B3 tptp.set_complex)) (= (tptp.member_complex C (tptp.minus_811609699411566653omplex A2 B3)) (and (tptp.member_complex C A2) (not (tptp.member_complex C B3))))) (forall ((C tptp.real) (A2 tptp.set_real) (B3 tptp.set_real)) (= (tptp.member_real C (tptp.minus_minus_set_real A2 B3)) (and (tptp.member_real C A2) (not (tptp.member_real C B3))))) (forall ((C tptp.set_nat) (A2 tptp.set_set_nat) (B3 tptp.set_set_nat)) (= (tptp.member_set_nat C (tptp.minus_2163939370556025621et_nat A2 B3)) (and (tptp.member_set_nat C A2) (not (tptp.member_set_nat C B3))))) (forall ((C tptp.int) (A2 tptp.set_int) (B3 tptp.set_int)) (= (tptp.member_int C (tptp.minus_minus_set_int A2 B3)) (and (tptp.member_int C A2) (not (tptp.member_int C B3))))) (forall ((C tptp.nat) (A2 tptp.set_nat) (B3 tptp.set_nat)) (let ((_let_1 (tptp.member_nat C))) (= (tptp.pp (tptp.aa_set_nat_bool _let_1 (tptp.minus_minus_set_nat A2 B3))) (and (tptp.pp (tptp.aa_set_nat_bool _let_1 A2)) (not (tptp.pp (tptp.aa_set_nat_bool _let_1 B3))))))) (forall ((A2 tptp.set_nat) (B3 tptp.set_nat)) (let ((_let_1 (tptp.minus_minus_set_nat A2 B3))) (= (tptp.minus_minus_set_nat _let_1 B3) _let_1))) (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.nat)) (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.one_one_real) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N))) (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 _let_1) N)))))) (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 ((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 ((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)) (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num 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_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 ((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.aa_nat_fun_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 ((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.aa_nat_fun_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.aa_nat_fun_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)) (= (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_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_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_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_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_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_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_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_complex (tptp.power_power_complex tptp.zero_zero_complex) (tptp.aa_num_nat tptp.numeral_numeral_nat K)) tptp.zero_zero_complex)) (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.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.nat)) (= (tptp.aa_nat_nat (tptp.power_power_nat 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 ((N tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat))) (= (tptp.aa_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.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.power_power_nat X) N))) (or (tptp.pp (tptp.aa_nat_bool _let_1 X)) (= N tptp.zero_zero_nat))))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex (tptp.aa_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_real tptp.semiri5074537144036343181t_real (tptp.aa_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_rat tptp.semiri681578069525770553at_rat (tptp.aa_nat_nat (tptp.power_power_nat M) N)) (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat M)) N))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat (tptp.aa_nat_nat (tptp.power_power_nat M) N)) (tptp.aa_nat_nat (tptp.power_power_nat (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat M)) N))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_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 ((B tptp.nat) (W tptp.nat) (X tptp.nat)) (= (= (tptp.aa_nat_complex (tptp.power_power_complex (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex B)) W) (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex X)) (= (tptp.aa_nat_nat (tptp.power_power_nat B) W) X))) (forall ((B 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 B)) W) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real X)) (= (tptp.aa_nat_nat (tptp.power_power_nat B) W) X))) (forall ((B tptp.nat) (W tptp.nat) (X tptp.nat)) (= (= (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat B)) W) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat X)) (= (tptp.aa_nat_nat (tptp.power_power_nat B) W) X))) (forall ((B tptp.nat) (W tptp.nat) (X tptp.nat)) (= (= (tptp.aa_nat_nat (tptp.power_power_nat (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat B)) W) (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat X)) (= (tptp.aa_nat_nat (tptp.power_power_nat B) W) X))) (forall ((B tptp.nat) (W tptp.nat) (X tptp.nat)) (= (= (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int B)) W) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int X)) (= (tptp.aa_nat_nat (tptp.power_power_nat B) W) X))) (forall ((X tptp.nat) (B 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 B)) W)) (= X (tptp.aa_nat_nat (tptp.power_power_nat B) W)))) (forall ((X tptp.nat) (B 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 B)) W)) (= X (tptp.aa_nat_nat (tptp.power_power_nat B) W)))) (forall ((X tptp.nat) (B tptp.nat) (W tptp.nat)) (= (= (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat X) (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat B)) W)) (= X (tptp.aa_nat_nat (tptp.power_power_nat B) W)))) (forall ((X tptp.nat) (B tptp.nat) (W tptp.nat)) (= (= (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat X) (tptp.aa_nat_nat (tptp.power_power_nat (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat B)) W)) (= X (tptp.aa_nat_nat (tptp.power_power_nat B) W)))) (forall ((X tptp.nat) (B 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 B)) W)) (= X (tptp.aa_nat_nat (tptp.power_power_nat B) W)))) (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.aa_int_fun_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 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.aa_int_fun_int_int tptp.divide_divide_int K) L) tptp.zero_zero_int)))) (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.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.times_times_num M) N)))))) (forall ((A tptp.nat) (M tptp.num) (N tptp.num)) (let ((_let_1 (tptp.power_power_nat A))) (= (tptp.aa_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.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.times_times_num M) 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) (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 ((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 ((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.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.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.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.nat) (N tptp.nat)) (= (= (tptp.aa_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.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) (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 ((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 ((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 ((B tptp.real) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_real_fun_nat_real tptp.power_power_real B))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) B)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B) 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 ((B tptp.rat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.power_power_rat B))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) B)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) 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 ((B tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.power_power_nat B))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) B)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat B) 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 ((B tptp.int) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.power_power_int 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 (tptp.aa_int_fun_int_bool tptp.ord_less_int B) 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 ((B tptp.rat) (X tptp.nat) (Y4 tptp.nat)) (let ((_let_1 (tptp.power_power_rat B))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.one_one_rat) B)) (= (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 Y4))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X) Y4)))))) (forall ((B tptp.nat) (X tptp.nat) (Y4 tptp.nat)) (let ((_let_1 (tptp.power_power_nat B))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.one_one_nat) B)) (= (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 Y4))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X) Y4)))))) (forall ((B tptp.int) (X tptp.nat) (Y4 tptp.nat)) (let ((_let_1 (tptp.power_power_int B))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.one_one_int) B)) (= (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 Y4))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X) Y4)))))) (forall ((B tptp.real) (X tptp.nat) (Y4 tptp.nat)) (let ((_let_1 (tptp.aa_real_fun_nat_real tptp.power_power_real B))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real) B)) (= (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 Y4))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X) Y4)))))) (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.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.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.nat)) (= (= (tptp.aa_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.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))) (forall ((B 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 B)) 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.power_power_nat B) W)) X)))) (forall ((B 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 B)) 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.power_power_nat B) W)) X)))) (forall ((B 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.power_power_nat (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat B)) 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.power_power_nat B) W)) X)))) (forall ((B 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 B)) 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.power_power_nat B) W)) X)))) (forall ((X tptp.nat) (B 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 B)) W))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) (tptp.aa_nat_nat (tptp.power_power_nat B) W))))) (forall ((X tptp.nat) (B 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 B)) W))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) (tptp.aa_nat_nat (tptp.power_power_nat B) W))))) (forall ((X tptp.nat) (B 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.power_power_nat (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat B)) W))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) (tptp.aa_nat_nat (tptp.power_power_nat B) W))))) (forall ((X tptp.nat) (B 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 B)) W))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) (tptp.aa_nat_nat (tptp.power_power_nat B) W))))) (forall ((X tptp.nat) (B 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 B)) W))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X) (tptp.aa_nat_nat (tptp.power_power_nat B) W))))) (forall ((X tptp.nat) (B 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.power_power_nat (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat B)) W))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X) (tptp.aa_nat_nat (tptp.power_power_nat B) W))))) (forall ((X tptp.nat) (B 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 B)) W))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X) (tptp.aa_nat_nat (tptp.power_power_nat B) W))))) (forall ((X tptp.nat) (B 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 B)) W))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X) (tptp.aa_nat_nat (tptp.power_power_nat B) W))))) (forall ((B 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 B)) 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.power_power_nat B) W)) X)))) (forall ((B 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.power_power_nat (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat B)) 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.power_power_nat B) W)) X)))) (forall ((B 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 B)) 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.power_power_nat B) W)) X)))) (forall ((B 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 B)) 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.power_power_nat B) W)) X)))) (forall ((Y4 tptp.nat) (X tptp.num) (N tptp.nat)) (= (= (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex Y4) (tptp.aa_nat_complex (tptp.power_power_complex (tptp.numera6690914467698888265omplex X)) N)) (= Y4 (tptp.aa_nat_nat (tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat X)) N)))) (forall ((Y4 tptp.nat) (X tptp.num) (N tptp.nat)) (= (= (tptp.aa_nat_real tptp.semiri5074537144036343181t_real Y4) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_num_real tptp.numeral_numeral_real X)) N)) (= Y4 (tptp.aa_nat_nat (tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat X)) N)))) (forall ((Y4 tptp.nat) (X tptp.num) (N tptp.nat)) (= (= (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat Y4) (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_num_rat tptp.numeral_numeral_rat X)) N)) (= Y4 (tptp.aa_nat_nat (tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat X)) N)))) (forall ((Y4 tptp.nat) (X tptp.num) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat X)) N))) (= (= (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat Y4) _let_1) (= Y4 _let_1)))) (forall ((Y4 tptp.nat) (X tptp.num) (N tptp.nat)) (= (= (tptp.aa_nat_int tptp.semiri1314217659103216013at_int Y4) (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int X)) N)) (= Y4 (tptp.aa_nat_nat (tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat X)) N)))) (forall ((X tptp.num) (N tptp.nat) (Y4 tptp.nat)) (= (= (tptp.aa_nat_complex (tptp.power_power_complex (tptp.numera6690914467698888265omplex X)) N) (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex Y4)) (= (tptp.aa_nat_nat (tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat X)) N) Y4))) (forall ((X tptp.num) (N tptp.nat) (Y4 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 Y4)) (= (tptp.aa_nat_nat (tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat X)) N) Y4))) (forall ((X tptp.num) (N tptp.nat) (Y4 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 Y4)) (= (tptp.aa_nat_nat (tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat X)) N) Y4))) (forall ((X tptp.num) (N tptp.nat) (Y4 tptp.nat)) (let ((_let_1 (tptp.aa_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 Y4)) (= _let_1 Y4)))) (forall ((X tptp.num) (N tptp.nat) (Y4 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 Y4)) (= (tptp.aa_nat_nat (tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat X)) N) Y4))) (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.aa_int_fun_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 ((C tptp.complex) (A2 tptp.set_complex) (B3 tptp.set_complex)) (=> (tptp.member_complex C (tptp.minus_811609699411566653omplex A2 B3)) (not (=> (tptp.member_complex C A2) (tptp.member_complex C B3))))) (forall ((C tptp.real) (A2 tptp.set_real) (B3 tptp.set_real)) (=> (tptp.member_real C (tptp.minus_minus_set_real A2 B3)) (not (=> (tptp.member_real C A2) (tptp.member_real C B3))))) (forall ((C tptp.set_nat) (A2 tptp.set_set_nat) (B3 tptp.set_set_nat)) (=> (tptp.member_set_nat C (tptp.minus_2163939370556025621et_nat A2 B3)) (not (=> (tptp.member_set_nat C A2) (tptp.member_set_nat C B3))))) (forall ((C tptp.int) (A2 tptp.set_int) (B3 tptp.set_int)) (=> (tptp.member_int C (tptp.minus_minus_set_int A2 B3)) (not (=> (tptp.member_int C A2) (tptp.member_int C B3))))) (forall ((C tptp.nat) (A2 tptp.set_nat) (B3 tptp.set_nat)) (let ((_let_1 (tptp.member_nat C))) (=> (tptp.pp (tptp.aa_set_nat_bool _let_1 (tptp.minus_minus_set_nat A2 B3))) (not (=> (tptp.pp (tptp.aa_set_nat_bool _let_1 A2)) (tptp.pp (tptp.aa_set_nat_bool _let_1 B3))))))) (forall ((C tptp.complex) (A2 tptp.set_complex) (B3 tptp.set_complex)) (=> (tptp.member_complex C (tptp.minus_811609699411566653omplex A2 B3)) (tptp.member_complex C A2))) (forall ((C tptp.real) (A2 tptp.set_real) (B3 tptp.set_real)) (=> (tptp.member_real C (tptp.minus_minus_set_real A2 B3)) (tptp.member_real C A2))) (forall ((C tptp.set_nat) (A2 tptp.set_set_nat) (B3 tptp.set_set_nat)) (=> (tptp.member_set_nat C (tptp.minus_2163939370556025621et_nat A2 B3)) (tptp.member_set_nat C A2))) (forall ((C tptp.int) (A2 tptp.set_int) (B3 tptp.set_int)) (=> (tptp.member_int C (tptp.minus_minus_set_int A2 B3)) (tptp.member_int C A2))) (forall ((C tptp.nat) (A2 tptp.set_nat) (B3 tptp.set_nat)) (let ((_let_1 (tptp.member_nat C))) (=> (tptp.pp (tptp.aa_set_nat_bool _let_1 (tptp.minus_minus_set_nat A2 B3))) (tptp.pp (tptp.aa_set_nat_bool _let_1 A2))))) (forall ((C tptp.complex) (A2 tptp.set_complex) (B3 tptp.set_complex)) (=> (tptp.member_complex C (tptp.minus_811609699411566653omplex A2 B3)) (not (tptp.member_complex C B3)))) (forall ((C tptp.real) (A2 tptp.set_real) (B3 tptp.set_real)) (=> (tptp.member_real C (tptp.minus_minus_set_real A2 B3)) (not (tptp.member_real C B3)))) (forall ((C tptp.set_nat) (A2 tptp.set_set_nat) (B3 tptp.set_set_nat)) (=> (tptp.member_set_nat C (tptp.minus_2163939370556025621et_nat A2 B3)) (not (tptp.member_set_nat C B3)))) (forall ((C tptp.int) (A2 tptp.set_int) (B3 tptp.set_int)) (=> (tptp.member_int C (tptp.minus_minus_set_int A2 B3)) (not (tptp.member_int C B3)))) (forall ((C tptp.nat) (A2 tptp.set_nat) (B3 tptp.set_nat)) (let ((_let_1 (tptp.member_nat C))) (=> (tptp.pp (tptp.aa_set_nat_bool _let_1 (tptp.minus_minus_set_nat A2 B3))) (not (tptp.pp (tptp.aa_set_nat_bool _let_1 B3)))))) (forall ((A2 tptp.set_complex) (B3 tptp.set_complex)) (=> (tptp.ord_less_set_complex A2 B3) (exists ((B2 tptp.complex)) (tptp.member_complex B2 (tptp.minus_811609699411566653omplex B3 A2))))) (forall ((A2 tptp.set_real) (B3 tptp.set_real)) (=> (tptp.ord_less_set_real A2 B3) (exists ((B2 tptp.real)) (tptp.member_real B2 (tptp.minus_minus_set_real B3 A2))))) (forall ((A2 tptp.set_set_nat) (B3 tptp.set_set_nat)) (=> (tptp.ord_less_set_set_nat A2 B3) (exists ((B2 tptp.set_nat)) (tptp.member_set_nat B2 (tptp.minus_2163939370556025621et_nat B3 A2))))) (forall ((A2 tptp.set_int) (B3 tptp.set_int)) (=> (tptp.ord_less_set_int A2 B3) (exists ((B2 tptp.int)) (tptp.member_int B2 (tptp.minus_minus_set_int B3 A2))))) (forall ((A2 tptp.set_nat) (B3 tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_set_nat A2) B3)) (exists ((B2 tptp.nat)) (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat B2) (tptp.minus_minus_set_nat B3 A2)))))) (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 ((X tptp.real) (Y4 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 Y4) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) N2)))))) (forall ((Y4 tptp.real) (X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) Y4)) (=> (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)) Y4)))))) (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) (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 ((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.aa_int_fun_int_int tptp.divide_divide_int X) K)) X))))) (forall ((A2 tptp.set_int) (B3 tptp.set_int)) (=> (tptp.ord_less_set_int A2 B3) (not (=> (tptp.ord_less_eq_set_int A2 B3) (tptp.ord_less_eq_set_int B3 A2))))) (forall ((A2 tptp.set_int) (B3 tptp.set_int)) (= (tptp.ord_less_set_int A2 B3) (and (tptp.ord_less_eq_set_int A2 B3) (not (= A2 B3))))) (forall ((A2 tptp.set_int) (B3 tptp.set_int)) (=> (tptp.ord_less_set_int A2 B3) (tptp.ord_less_eq_set_int A2 B3))) (forall ((A2 tptp.set_int) (B3 tptp.set_int) (C2 tptp.set_int)) (=> (tptp.ord_less_set_int A2 B3) (=> (tptp.ord_less_eq_set_int B3 C2) (tptp.ord_less_set_int A2 C2)))) (forall ((A2 tptp.set_int) (B3 tptp.set_int)) (= (tptp.ord_less_set_int A2 B3) (and (tptp.ord_less_eq_set_int A2 B3) (not (tptp.ord_less_eq_set_int B3 A2))))) (forall ((A2 tptp.set_int) (B3 tptp.set_int) (C2 tptp.set_int)) (=> (tptp.ord_less_eq_set_int A2 B3) (=> (tptp.ord_less_set_int B3 C2) (tptp.ord_less_set_int A2 C2)))) (forall ((A2 tptp.set_int) (B3 tptp.set_int)) (= (tptp.ord_less_eq_set_int A2 B3) (or (tptp.ord_less_set_int A2 B3) (= A2 B3)))) _let_166 (forall ((X tptp.real) (Y4 tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) Y4)) (or (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Y4)) (= X Y4)))) (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 ((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)))) (not (= tptp.zero_z5237406670263579293d_enat tptp.one_on7984719198319812577d_enat)) (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 ((A tptp.nat) (B tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) B)) (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 B))))) (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 ((D tptp.int) (P2 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 ((X3 tptp.int) (K2 tptp.int)) (= (tptp.pp (tptp.aa_int_bool P2 X3)) (tptp.pp (tptp.aa_int_bool P2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int X3) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int K2) D)))))) (=> (exists ((Z3 tptp.int)) (forall ((X3 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Z3) X3)) (= (tptp.pp (tptp.aa_int_bool P X3)) (tptp.pp (tptp.aa_int_bool P2 X3)))))) (=> (exists ((X_13 tptp.int)) (tptp.pp (tptp.aa_int_bool P2 X_13))) (exists ((X_1 tptp.int)) (tptp.pp (tptp.aa_int_bool P X_1)))))))) (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 ((X3 tptp.int) (K2 tptp.int)) (= (tptp.pp (tptp.aa_int_bool P1 X3)) (tptp.pp (tptp.aa_int_bool P1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int X3) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int K2) D)))))) (=> (exists ((Z3 tptp.int)) (forall ((X3 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X3) Z3)) (= (tptp.pp (tptp.aa_int_bool P X3)) (tptp.pp (tptp.aa_int_bool P1 X3)))))) (=> (exists ((X_13 tptp.int)) (tptp.pp (tptp.aa_int_bool P1 X_13))) (exists ((X_1 tptp.int)) (tptp.pp (tptp.aa_int_bool P X_1)))))))) (forall ((B 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) B)) (= (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.divide_divide_int A) B)) 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 ((B tptp.int) (A tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B) 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.divide_divide_int A) B)) 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.int) (B 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) B)) (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.divide_divide_int A) B)) tptp.zero_zero_int))))) (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)))))) _let_165 (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 ((X3 tptp.real)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) X3)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X3) N) A) (forall ((Y3 tptp.real)) (=> (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) Y3)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Y3) N) A)) (= Y3 X3)))))))) (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.nat) (B tptp.nat)) (let ((_let_1 (tptp.aa_nat_int tptp.semiri1314217659103216013at_int B))) (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) B)))) (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 ((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 ((X3 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool P X3)) (tptp.pp (tptp.aa_int_bool P (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int X3) D))))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) K)) (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) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int K) D)))))))))) (forall ((X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) X)) (forall ((Y3 tptp.real)) (exists ((N2 tptp.nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y3) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N2)) X))))))) (forall ((A tptp.int) (A4 tptp.int) (B tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) A4)) (=> (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 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A) B)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A4) B)))))) (forall ((A tptp.int) (B4 tptp.int) (B tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int 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) B4)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B4) B)) (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 B4)))))))) (forall ((I tptp.int) (K tptp.int)) (= (= (tptp.aa_int_int (tptp.aa_int_fun_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) (A4 tptp.int) (B tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) A4)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B) 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.divide_divide_int A4) B)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A) B)))))) (forall ((A tptp.int) (B4 tptp.int) (B tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int 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) B4)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B4) B)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int _let_1 B4)) (tptp.aa_int_int _let_1 B)))))))) (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.aa_int_fun_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 ((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.aa_int_fun_int_int tptp.divide_divide_int K) L))))))) (forall ((A tptp.int) (B 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 B) 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.divide_divide_int A) B)) tptp.zero_zero_int))))) (forall ((A tptp.int) (B 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) B)) (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.divide_divide_int A) B)) 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.aa_int_fun_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 ((B tptp.int) (A tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B) 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.divide_divide_int A) B))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) tptp.zero_zero_int))))) (forall ((B 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) B)) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A) B))) (tptp.pp (tptp.aa_int_bool _let_1 A)))))) (forall ((A tptp.int) (B 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.aa_int_fun_int_int tptp.divide_divide_int A) B))) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B) A)) (tptp.pp (tptp.aa_int_bool _let_1 B))))))) (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 ((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 ((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 ((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 ((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 ((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.aa_int_fun_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 ((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.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.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.nat) (N tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (not (= (tptp.aa_nat_nat (tptp.power_power_nat A) N) tptp.zero_zero_nat)))) (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 ((X tptp.complex) (Y4 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 Y4))) (=> (= (tptp.aa_complex_complex (tptp.times_times_complex X) Y4) (tptp.aa_complex_complex _let_2 X)) (= (tptp.aa_complex_complex (tptp.times_times_complex _let_1) Y4) (tptp.aa_complex_complex _let_2 _let_1)))))) (forall ((X tptp.real) (Y4 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 Y4))) (=> (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real X) Y4) (tptp.aa_real_real _let_2 X)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real _let_1) Y4) (tptp.aa_real_real _let_2 _let_1)))))) (forall ((X tptp.rat) (Y4 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 Y4))) (=> (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat X) Y4) (tptp.aa_rat_rat _let_2 X)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat _let_1) Y4) (tptp.aa_rat_rat _let_2 _let_1)))))) (forall ((X tptp.nat) (Y4 tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.power_power_nat X) N))) (let ((_let_2 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat Y4))) (=> (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat X) Y4) (tptp.aa_nat_nat _let_2 X)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat _let_1) Y4) (tptp.aa_nat_nat _let_2 _let_1)))))) (forall ((X tptp.int) (Y4 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 Y4))) (=> (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int X) Y4) (tptp.aa_int_int _let_2 X)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int _let_1) Y4) (tptp.aa_int_int _let_2 _let_1)))))) (forall ((A tptp.complex) (B tptp.complex) (N tptp.nat)) (= (tptp.aa_nat_complex (tptp.power_power_complex (tptp.aa_complex_complex (tptp.times_times_complex A) B)) 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 B) N)))) (forall ((A tptp.real) (B 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) B)) 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 B) N)))) (forall ((A tptp.rat) (B 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) B)) 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 B) N)))) (forall ((A tptp.nat) (B tptp.nat) (N tptp.nat)) (= (tptp.aa_nat_nat (tptp.power_power_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) B)) N) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.power_power_nat A) N)) (tptp.aa_nat_nat (tptp.power_power_nat B) N)))) (forall ((A tptp.int) (B 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) B)) 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 B) 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.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.complex) (B tptp.complex) (N tptp.nat)) (= (tptp.aa_nat_complex (tptp.power_power_complex (tptp.divide1717551699836669952omplex A B)) N) (tptp.divide1717551699836669952omplex (tptp.aa_nat_complex (tptp.power_power_complex A) N) (tptp.aa_nat_complex (tptp.power_power_complex B) N)))) (forall ((A tptp.real) (B 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) B)) 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 B) N)))) (forall ((A tptp.rat) (B tptp.rat) (N tptp.nat)) (= (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_rat_rat (tptp.divide_divide_rat A) B)) 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 B) N)))) (forall ((X tptp.code_integer) (Y4 tptp.code_integer) (N tptp.nat)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer X) Y4)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.power_8256067586552552935nteger X N)) (tptp.power_8256067586552552935nteger Y4 N))))) (forall ((X tptp.int) (Y4 tptp.int) (N tptp.nat)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int X) Y4)) (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 Y4) N))))) (forall ((X tptp.real) (Y4 tptp.real) (N tptp.nat)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.dvd_dvd_real X) Y4)) (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 Y4) N))))) (forall ((X tptp.nat) (Y4 tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat X) Y4)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_nat_nat (tptp.power_power_nat X) N)) (tptp.aa_nat_nat (tptp.power_power_nat Y4) N))))) (forall ((X tptp.complex) (Y4 tptp.complex) (N tptp.nat)) (=> (tptp.pp (tptp.aa_complex_bool (tptp.dvd_dvd_complex X) Y4)) (tptp.pp (tptp.aa_complex_bool (tptp.dvd_dvd_complex (tptp.aa_nat_complex (tptp.power_power_complex X) N)) (tptp.aa_nat_complex (tptp.power_power_complex Y4) N))))) (forall ((I tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (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 ((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.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.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (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.power_power_nat (tptp.aa_nat_nat _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 ((A tptp.rat) (B tptp.rat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B)) (=> (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 B) N)))))) (forall ((A tptp.nat) (B tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B)) (=> (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.power_power_nat A) N)) (tptp.aa_nat_nat (tptp.power_power_nat B) N)))))) (forall ((A tptp.int) (B tptp.int) (N tptp.nat)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B)) (=> (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 B) N)))))) (forall ((A tptp.real) (B tptp.real) (N tptp.nat)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) B)) (=> (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 B) 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.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) (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.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.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 ((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.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 ((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 ((X tptp.complex) (Y4 tptp.complex) (N tptp.nat)) (=> (= (tptp.aa_complex_complex (tptp.times_times_complex X) Y4) 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 Y4) N)) tptp.one_one_complex))) (forall ((X tptp.real) (Y4 tptp.real) (N tptp.nat)) (=> (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real X) Y4) 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 Y4) N)) tptp.one_one_real))) (forall ((X tptp.rat) (Y4 tptp.rat) (N tptp.nat)) (=> (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat X) Y4) 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 Y4) N)) tptp.one_one_rat))) (forall ((X tptp.nat) (Y4 tptp.nat) (N tptp.nat)) (=> (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat X) Y4) tptp.one_one_nat) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.power_power_nat X) N)) (tptp.aa_nat_nat (tptp.power_power_nat Y4) N)) tptp.one_one_nat))) (forall ((X tptp.int) (Y4 tptp.int) (N tptp.nat)) (=> (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int X) Y4) 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 Y4) N)) tptp.one_one_int))) (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.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.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 ((A tptp.complex) (N tptp.nat)) (= (tptp.aa_nat_complex (tptp.power_power_complex (tptp.divide1717551699836669952omplex tptp.one_one_complex A)) N) (tptp.divide1717551699836669952omplex tptp.one_one_complex (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))))) (forall ((A tptp.rat)) (= (tptp.aa_nat_rat (tptp.power_power_rat A) tptp.zero_zero_nat) tptp.one_one_rat)) (forall ((A tptp.int)) (= (tptp.aa_nat_int (tptp.power_power_int A) tptp.zero_zero_nat) tptp.one_one_int)) (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.nat)) (= (tptp.aa_nat_nat (tptp.power_power_nat A) tptp.zero_zero_nat) tptp.one_one_nat)) (forall ((A tptp.complex)) (= (tptp.aa_nat_complex (tptp.power_power_complex A) tptp.zero_zero_nat) tptp.one_one_complex)) (forall ((B 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 B) A)) (= (tptp.power_8256067586552552935nteger (tptp.divide6298287555418463151nteger A B) N) (tptp.divide6298287555418463151nteger (tptp.power_8256067586552552935nteger A N) (tptp.power_8256067586552552935nteger B N))))) (forall ((B tptp.nat) (A tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat B) A)) (= (tptp.aa_nat_nat (tptp.power_power_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) B)) N) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat (tptp.power_power_nat A) N)) (tptp.aa_nat_nat (tptp.power_power_nat B) N))))) (forall ((B tptp.int) (A tptp.int) (N tptp.nat)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int B) A)) (= (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A) B)) N) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int (tptp.aa_nat_int (tptp.power_power_int A) N)) (tptp.aa_nat_int (tptp.power_power_int B) N))))) (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.power_power_nat N) K))))) (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.power_power_nat I) N)))))) (forall ((X tptp.code_integer) (Y4 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) Y4)) (=> (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.power_8256067586552552935nteger X N)) (tptp.power_8256067586552552935nteger Y4 M)))))) (forall ((X tptp.int) (Y4 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) Y4)) (=> (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 Y4) M)))))) (forall ((X tptp.real) (Y4 tptp.real) (N tptp.nat) (M tptp.nat)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.dvd_dvd_real X) Y4)) (=> (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 Y4) M)))))) (forall ((X tptp.nat) (Y4 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) Y4)) (=> (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.power_power_nat X) N)) (tptp.aa_nat_nat (tptp.power_power_nat Y4) M)))))) (forall ((X tptp.complex) (Y4 tptp.complex) (N tptp.nat) (M tptp.nat)) (=> (tptp.pp (tptp.aa_complex_bool (tptp.dvd_dvd_complex X) Y4)) (=> (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.dvd_dvd_complex (tptp.aa_nat_complex (tptp.power_power_complex X) N)) (tptp.aa_nat_complex (tptp.power_power_complex Y4) M)))))) (forall ((A tptp.code_integer) (N tptp.nat) (B tptp.code_integer) (M tptp.nat)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.power_8256067586552552935nteger A N)) B)) (=> (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.power_8256067586552552935nteger A M)) B))))) (forall ((A tptp.int) (N tptp.nat) (B 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)) B)) (=> (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)) B)))))) (forall ((A tptp.real) (N tptp.nat) (B 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)) B)) (=> (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)) B)))))) (forall ((A tptp.nat) (N tptp.nat) (B tptp.nat) (M tptp.nat)) (let ((_let_1 (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)) B)) (=> (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)) B)))))) (forall ((A tptp.complex) (N tptp.nat) (B tptp.complex) (M tptp.nat)) (let ((_let_1 (tptp.power_power_complex A))) (=> (tptp.pp (tptp.aa_complex_bool (tptp.dvd_dvd_complex (tptp.aa_nat_complex _let_1 N)) B)) (=> (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.dvd_dvd_complex (tptp.aa_nat_complex _let_1 M)) B)))))) (forall ((M tptp.nat) (N tptp.nat) (A tptp.code_integer)) (=> (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.power_8256067586552552935nteger A M)) (tptp.power_8256067586552552935nteger A 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.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.nat)) (let ((_let_1 (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.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.dvd_dvd_complex (tptp.aa_nat_complex _let_1 M)) (tptp.aa_nat_complex _let_1 N)))))) (forall ((A tptp.rat) (N tptp.nat) (B 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 B) N))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) B)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B))))) (forall ((A tptp.nat) (N tptp.nat) (B tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.power_power_nat A) N)) (tptp.aa_nat_nat (tptp.power_power_nat B) N))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) B)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) B))))) (forall ((A tptp.int) (N tptp.nat) (B 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 B) N))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) B)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B))))) (forall ((A tptp.real) (N tptp.nat) (B 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 B) N))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) B)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B))))) (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.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 ((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) (B 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 B) _let_1))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) B)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B)))))) (forall ((A tptp.nat) (N tptp.nat) (B 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.power_power_nat A) _let_1)) (tptp.aa_nat_nat (tptp.power_power_nat B) _let_1))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) B)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B)))))) (forall ((A tptp.int) (N tptp.nat) (B 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 B) _let_1))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) B)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B)))))) (forall ((A tptp.real) (N tptp.nat) (B 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 B) _let_1))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) B)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) B)))))) (forall ((A tptp.rat) (N tptp.nat) (B 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 B) _let_2)) (=> (tptp.pp (tptp.aa_rat_bool _let_1 A)) (=> (tptp.pp (tptp.aa_rat_bool _let_1 B)) (= A B))))))) (forall ((A tptp.nat) (N tptp.nat) (B 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.power_power_nat A) _let_2) (tptp.aa_nat_nat (tptp.power_power_nat B) _let_2)) (=> (tptp.pp (tptp.aa_nat_bool _let_1 A)) (=> (tptp.pp (tptp.aa_nat_bool _let_1 B)) (= A B))))))) (forall ((A tptp.int) (N tptp.nat) (B 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 B) _let_2)) (=> (tptp.pp (tptp.aa_int_bool _let_1 A)) (=> (tptp.pp (tptp.aa_int_bool _let_1 B)) (= A B))))))) (forall ((A tptp.real) (N tptp.nat) (B 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 B) _let_2)) (=> (tptp.pp (tptp.aa_real_bool _let_1 A)) (=> (tptp.pp (tptp.aa_real_bool _let_1 B)) (= A B))))))) (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.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.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 ((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_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_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_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_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 ((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.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 ((N tptp.nat) (N5 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) N5)) (=> (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 N5))))))) (forall ((N tptp.nat) (N5 tptp.nat) (A tptp.nat)) (let ((_let_1 (tptp.power_power_nat A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N) N5)) (=> (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 N5))))))) (forall ((N tptp.nat) (N5 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) N5)) (=> (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 N5))))))) (forall ((N tptp.nat) (N5 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) N5)) (=> (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 N5))))))) (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_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_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_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_complex (tptp.power_power_complex tptp.zero_zero_complex) 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 N) (tptp.aa_nat_nat (tptp.power_power_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)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_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.power_power_nat M) _let_1)) (tptp.aa_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.power_power_nat K) M))))) (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.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.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 ((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.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 ((I tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (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 ((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.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.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.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_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.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.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) (N5 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) N5)) (=> (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 N5)) (tptp.aa_nat_real _let_1 N)))))))) (forall ((N tptp.nat) (N5 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) N5)) (=> (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 N5)) (tptp.aa_nat_rat _let_1 N)))))))) (forall ((N tptp.nat) (N5 tptp.nat) (A tptp.nat)) (let ((_let_1 (tptp.power_power_nat A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N) N5)) (=> (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 N5)) (tptp.aa_nat_nat _let_1 N)))))))) (forall ((N tptp.nat) (N5 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) N5)) (=> (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 N5)) (tptp.aa_nat_int _let_1 N)))))))) (forall ((N tptp.nat) (N5 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) N5)) (=> (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 N5)) (tptp.aa_nat_rat _let_1 N)))))))) (forall ((N tptp.nat) (N5 tptp.nat) (A tptp.nat)) (let ((_let_1 (tptp.power_power_nat A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N) N5)) (=> (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 N5)) (tptp.aa_nat_nat _let_1 N)))))))) (forall ((N tptp.nat) (N5 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) N5)) (=> (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 N5)) (tptp.aa_nat_int _let_1 N)))))))) (forall ((N tptp.nat) (N5 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) N5)) (=> (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 N5)) (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.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.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)))))) (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)))))) (= (tptp.aa_nat_rat (tptp.power_power_rat tptp.zero_zero_rat) _let_2) tptp.zero_zero_rat) (= (tptp.aa_nat_int (tptp.power_power_int tptp.zero_zero_int) _let_2) tptp.zero_zero_int) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real tptp.zero_zero_real) _let_2) tptp.zero_zero_real) (= (tptp.aa_nat_nat (tptp.power_power_nat tptp.zero_zero_nat) _let_2) tptp.zero_zero_nat) (= (tptp.aa_nat_complex (tptp.power_power_complex tptp.zero_zero_complex) _let_2) tptp.zero_zero_complex) (forall ((N tptp.nat) (A tptp.rat) (B 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 B)) (= (= (tptp.aa_nat_rat (tptp.power_power_rat A) N) (tptp.aa_nat_rat (tptp.power_power_rat B) N)) (= A B))))))) (forall ((N tptp.nat) (A tptp.nat) (B 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 B)) (= (= (tptp.aa_nat_nat (tptp.power_power_nat A) N) (tptp.aa_nat_nat (tptp.power_power_nat B) N)) (= A B))))))) (forall ((N tptp.nat) (A tptp.int) (B 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 B)) (= (= (tptp.aa_nat_int (tptp.power_power_int A) N) (tptp.aa_nat_int (tptp.power_power_int B) N)) (= A B))))))) (forall ((N tptp.nat) (A tptp.real) (B 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 B)) (= (= (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 B) N)) (= A B))))))) (forall ((A tptp.rat) (N tptp.nat) (B 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 B) N)) (=> (tptp.pp (tptp.aa_rat_bool _let_1 A)) (=> (tptp.pp (tptp.aa_rat_bool _let_1 B)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (= A B))))))) (forall ((A tptp.nat) (N tptp.nat) (B 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.power_power_nat A) N) (tptp.aa_nat_nat (tptp.power_power_nat B) N)) (=> (tptp.pp (tptp.aa_nat_bool _let_1 A)) (=> (tptp.pp (tptp.aa_nat_bool _let_1 B)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (= A B))))))) (forall ((A tptp.int) (N tptp.nat) (B 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 B) N)) (=> (tptp.pp (tptp.aa_int_bool _let_1 A)) (=> (tptp.pp (tptp.aa_int_bool _let_1 B)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (= A B))))))) (forall ((A tptp.real) (N tptp.nat) (B 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 B) N)) (=> (tptp.pp (tptp.aa_real_bool _let_1 A)) (=> (tptp.pp (tptp.aa_real_bool _let_1 B)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (= A B))))))) (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.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 ((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.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))) (= (tptp.aa_nat_rat (tptp.power_power_rat tptp.one_one_rat) _let_2) tptp.one_one_rat) (= (tptp.aa_nat_int (tptp.power_power_int tptp.one_one_int) _let_2) tptp.one_one_int) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real tptp.one_one_real) _let_2) tptp.one_one_real) (= (tptp.aa_nat_nat (tptp.power_power_nat tptp.one_one_nat) _let_2) tptp.one_one_nat) (= (tptp.aa_nat_complex (tptp.power_power_complex tptp.one_one_complex) _let_2) tptp.one_one_complex) (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.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)) (=> (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 ((X tptp.complex) (Y4 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.minus_minus_complex X Y4)) _let_1) (tptp.aa_nat_complex (tptp.power_power_complex (tptp.minus_minus_complex Y4 X)) _let_1)))) (forall ((X tptp.real) (Y4 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) Y4)) _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 Y4) X)) _let_1)))) (forall ((X tptp.rat) (Y4 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) Y4)) _let_1) (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_rat_rat (tptp.minus_minus_rat Y4) X)) _let_1)))) (forall ((X tptp.int) (Y4 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) Y4)) _let_1) (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int Y4) X)) _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_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.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))))))) (forall ((X tptp.code_integer) (M tptp.nat) (N tptp.nat)) (=> (not (= X tptp.zero_z3403309356797280102nteger)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.power_8256067586552552935nteger X M)) (tptp.power_8256067586552552935nteger X 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.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 ((X tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (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 ((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.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))) (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.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.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.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.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.power_power_nat 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.dvd_dvd_complex X) (tptp.aa_nat_complex (tptp.power_power_complex X) N))))) (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.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.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.aa_int_fun_int_int tptp.divide_divide_int (tptp.aa_nat_int _let_1 M)) (tptp.aa_nat_int _let_1 N))))))) (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.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.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.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.power_power_nat (tptp.aa_nat_nat _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 ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (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 ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (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 ((X tptp.rat) (Y4 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 Y4) _let_1))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) Y4)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) Y4)))))) (forall ((X tptp.nat) (Y4 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.power_power_nat X) _let_1)) (tptp.aa_nat_nat (tptp.power_power_nat Y4) _let_1))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) Y4)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X) Y4)))))) (forall ((X tptp.int) (Y4 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 Y4) _let_1))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) Y4)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X) Y4)))))) (forall ((X tptp.real) (Y4 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 Y4) _let_1))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) Y4)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) Y4)))))) (forall ((X tptp.rat) (Y4 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 Y4) _let_2)) (=> (tptp.pp (tptp.aa_rat_bool _let_1 X)) (=> (tptp.pp (tptp.aa_rat_bool _let_1 Y4)) (= X Y4))))))) (forall ((X tptp.nat) (Y4 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.power_power_nat X) _let_2) (tptp.aa_nat_nat (tptp.power_power_nat Y4) _let_2)) (=> (tptp.pp (tptp.aa_nat_bool _let_1 X)) (=> (tptp.pp (tptp.aa_nat_bool _let_1 Y4)) (= X Y4))))))) (forall ((X tptp.int) (Y4 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 Y4) _let_2)) (=> (tptp.pp (tptp.aa_int_bool _let_1 X)) (=> (tptp.pp (tptp.aa_int_bool _let_1 Y4)) (= X Y4))))))) (forall ((X tptp.real) (Y4 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 Y4) _let_2)) (=> (tptp.pp (tptp.aa_real_bool _let_1 X)) (=> (tptp.pp (tptp.aa_real_bool _let_1 Y4)) (= X Y4))))))) (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 ((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.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 ((A tptp.rat) (B tptp.rat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B)) (=> (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 B) N))))))) (forall ((A tptp.nat) (B tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) B)) (=> (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.power_power_nat A) N)) (tptp.aa_nat_nat (tptp.power_power_nat B) N))))))) (forall ((A tptp.int) (B tptp.int) (N tptp.nat)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B)) (=> (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 B) N))))))) (forall ((A tptp.real) (B tptp.real) (N tptp.nat)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B)) (=> (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 B) N))))))) (forall ((M tptp.nat) (P3 tptp.complex)) (let ((_let_1 (tptp.power_power_complex P3))) (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 P3) (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) (P3 tptp.real)) (let ((_let_1 (tptp.aa_real_fun_nat_real tptp.power_power_real P3))) (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 P3) (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) (P3 tptp.rat)) (let ((_let_1 (tptp.power_power_rat P3))) (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 P3) (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) (P3 tptp.nat)) (let ((_let_1 (tptp.power_power_nat P3))) (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 P3) (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) (P3 tptp.int)) (let ((_let_1 (tptp.power_power_int P3))) (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 P3) (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.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 ((X tptp.rat) (Y4 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 Y4) _let_1))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) Y4)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) Y4)))))) (forall ((X tptp.nat) (Y4 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.power_power_nat X) _let_1)) (tptp.aa_nat_nat (tptp.power_power_nat Y4) _let_1))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) Y4)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Y4)))))) (forall ((X tptp.int) (Y4 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 Y4) _let_1))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) Y4)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) Y4)))))) (forall ((X tptp.real) (Y4 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 Y4) _let_1))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) Y4)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Y4)))))) (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 ((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.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.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.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 ((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)) (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.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 ((T tptp.vEBT_VEBT) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt T) N)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real (tptp.aa_VEBT_VEBT_nat tptp.vEBT_VEBT_space2 T))) (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.aa_num_num tptp.bit1 tptp.one))))) (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_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))) N)) tptp.one_one_real)))))) (forall ((T tptp.vEBT_VEBT) (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))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt T) N)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_VEBT_VEBT_real tptp.vEBT_VEBT_cnt T)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real _let_2) (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_2) N)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (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.one))))) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit1 _let_1)))))))))))) (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (U tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt T) N)) (=> (= U (tptp.aa_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_eq_nat (tptp.aa_VEBT_VEBT_nat tptp.vEBT_VEBT_space T)) (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.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit1 tptp.one))))) U)))))) (forall ((T tptp.vEBT_VEBT) (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.vEBT_invar_vebt T) N)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_VEBT_VEBT_real tptp.vEBT_VEBT_cnt T)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real _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 _let_1) N)) tptp.one_one_real))))))) (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (U tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt T) N)) (=> (= U (tptp.aa_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_eq_nat (tptp.aa_VEBT_VEBT_nat tptp.vEBT_VEBT_space2 T)) (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.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit1 tptp.one))))) U)))))) (forall ((E2 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) E2)) (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)))) E2))))))) (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)) (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)))) E2))))))) (forall ((X tptp.nat) (N tptp.nat)) (= (tptp.aa_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.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N)))) (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (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) B))) (tptp.aa_nat_nat _let_1 A)) (tptp.aa_nat_nat _let_1 B)))) (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) (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 ((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.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A))) (= (= (tptp.aa_real_real _let_1 B) (tptp.aa_real_real _let_1 C)) (= B C)))) (forall ((A tptp.rat) (B 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 B) (tptp.aa_rat_rat _let_1 C)) (= B C)))) (forall ((A tptp.nat) (B 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 B) (tptp.aa_nat_nat _let_1 C)) (= B C)))) (forall ((A tptp.int) (B 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 B) (tptp.aa_int_int _let_1 C)) (= B C)))) (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (= (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real B) A) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real C) A)) (= B C))) (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (= (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat B) A) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat C) A)) (= B C))) (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat B) A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat C) A)) (= B C))) (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (= (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int B) A) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int C) A)) (= B C))) (forall ((Ma tptp.nat) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (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.vEBT_VEBT_high Ma) N)) (tptp.aa_nat_nat _let_1 M)))))) (forall ((C tptp.rat) (A tptp.rat) (B 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 B))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B))))) (forall ((C tptp.nat) (A tptp.nat) (B 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 B))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B))))) (forall ((C tptp.int) (A tptp.int) (B 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 B))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B))))) (forall ((C tptp.real) (A tptp.real) (B 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 B))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) B))))) (forall ((A tptp.rat) (C tptp.rat) (B 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 B) C))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B)))) (forall ((A tptp.nat) (C tptp.nat) (B 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 B) C))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B)))) (forall ((A tptp.int) (C tptp.int) (B 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 B) C))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B)))) (forall ((A tptp.real) (C tptp.real) (B 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 B) C))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) B)))) (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.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) (Y4 tptp.nat)) (= (= tptp.zero_zero_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat X) Y4)) (and (= X tptp.zero_zero_nat) (= Y4 tptp.zero_zero_nat)))) (forall ((X tptp.nat) (Y4 tptp.nat)) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat X) Y4) tptp.zero_zero_nat) (and (= X tptp.zero_zero_nat) (= Y4 tptp.zero_zero_nat)))) (forall ((A tptp.complex) (B tptp.complex)) (= (= A (tptp.plus_plus_complex A B)) (= B tptp.zero_zero_complex))) (forall ((A tptp.real) (B tptp.real)) (= (= A (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) B)) (= B tptp.zero_zero_real))) (forall ((A tptp.rat) (B tptp.rat)) (= (= A (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) B)) (= B tptp.zero_zero_rat))) (forall ((A tptp.nat) (B tptp.nat)) (= (= A (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) B)) (= B tptp.zero_zero_nat))) (forall ((A tptp.int) (B tptp.int)) (= (= A (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) B)) (= B tptp.zero_zero_int))) (forall ((A tptp.complex) (B tptp.complex)) (= (= A (tptp.plus_plus_complex B A)) (= B tptp.zero_zero_complex))) (forall ((A tptp.real) (B tptp.real)) (= (= A (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real B) A)) (= B tptp.zero_zero_real))) (forall ((A tptp.rat) (B tptp.rat)) (= (= A (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat B) A)) (= B tptp.zero_zero_rat))) (forall ((A tptp.nat) (B tptp.nat)) (= (= A (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat B) A)) (= B tptp.zero_zero_nat))) (forall ((A tptp.int) (B tptp.int)) (= (= A (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int B) A)) (= B tptp.zero_zero_int))) (forall ((A tptp.complex) (B tptp.complex)) (= (= (tptp.plus_plus_complex A B) A) (= B tptp.zero_zero_complex))) (forall ((A tptp.real) (B tptp.real)) (= (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) B) A) (= B tptp.zero_zero_real))) (forall ((A tptp.rat) (B tptp.rat)) (= (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) B) A) (= B tptp.zero_zero_rat))) (forall ((A tptp.nat) (B tptp.nat)) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) B) A) (= B tptp.zero_zero_nat))) (forall ((A tptp.int) (B tptp.int)) (= (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) B) A) (= B tptp.zero_zero_int))) (forall ((B tptp.complex) (A tptp.complex)) (= (= (tptp.plus_plus_complex B A) A) (= B tptp.zero_zero_complex))) (forall ((B tptp.real) (A tptp.real)) (= (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real B) A) A) (= B tptp.zero_zero_real))) (forall ((B tptp.rat) (A tptp.rat)) (= (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat B) A) A) (= B tptp.zero_zero_rat))) (forall ((B tptp.nat) (A tptp.nat)) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat B) A) A) (= B tptp.zero_zero_nat))) (forall ((B tptp.int) (A tptp.int)) (= (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int B) A) A) (= B 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.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 ((C tptp.real) (A tptp.real) (B 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 B))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B))))) (forall ((C tptp.rat) (A tptp.rat) (B 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 B))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B))))) (forall ((C tptp.nat) (A tptp.nat) (B 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 B))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) B))))) (forall ((C tptp.int) (A tptp.int) (B 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 B))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B))))) (forall ((A tptp.real) (C tptp.real) (B 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 B) C))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B)))) (forall ((A tptp.rat) (C tptp.rat) (B 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 B) C))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B)))) (forall ((A tptp.nat) (C tptp.nat) (B 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 B) C))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) B)))) (forall ((A tptp.int) (C tptp.int) (B 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 B) C))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B)))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.plus_plus_complex (tptp.numera6690914467698888265omplex M) (tptp.numera6690914467698888265omplex N)) (tptp.numera6690914467698888265omplex (tptp.aa_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.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.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.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.plus_plus_num M) N)))) (forall ((V tptp.num) (W tptp.num) (Z tptp.complex)) (= (tptp.plus_plus_complex (tptp.numera6690914467698888265omplex V) (tptp.plus_plus_complex (tptp.numera6690914467698888265omplex W) Z)) (tptp.plus_plus_complex (tptp.numera6690914467698888265omplex (tptp.aa_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.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.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.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.plus_plus_num V) W))) Z))) (forall ((A tptp.real) (B 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) B)) B) A)) (forall ((A tptp.rat) (B 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) B)) B) A)) (forall ((A tptp.nat) (B 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) B)) B) A)) (forall ((A tptp.int) (B 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) B)) B) A)) (forall ((A tptp.real) (C tptp.real) (B 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 B) C)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A) B))) (forall ((A tptp.rat) (C tptp.rat) (B 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 B) C)) (tptp.aa_rat_rat (tptp.minus_minus_rat A) B))) (forall ((A tptp.nat) (C tptp.nat) (B 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 B) C)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat A) B))) (forall ((A tptp.int) (C tptp.int) (B 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 B) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) B))) (forall ((A tptp.real) (B 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) B)) A) B)) (forall ((A tptp.rat) (B 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) B)) A) B)) (forall ((A tptp.nat) (B 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) B)) A) B)) (forall ((A tptp.int) (B 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) B)) A) B)) (forall ((C tptp.real) (A tptp.real) (B 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 B)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A) B)))) (forall ((C tptp.rat) (A tptp.rat) (B 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 B)) (tptp.aa_rat_rat (tptp.minus_minus_rat A) B)))) (forall ((C tptp.nat) (A tptp.nat) (B 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 B)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat A) B)))) (forall ((C tptp.int) (A tptp.int) (B 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 B)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) B)))) (forall ((A tptp.real) (B 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) B)) B) A)) (forall ((A tptp.rat) (B 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) B)) B) A)) (forall ((A tptp.int) (B 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) B)) B) A)) (forall ((A tptp.real) (B 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) B)) B) A)) (forall ((A tptp.rat) (B 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) B)) B) A)) (forall ((A tptp.int) (B 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) B)) B) A)) (forall ((X tptp.nat) (N tptp.nat) (Y4 tptp.nat)) (let ((_let_1 (tptp.aa_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.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 Y4) _let_1)) X)) N) Y4)))) (forall ((A tptp.code_integer) (B 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 B A))) (tptp.pp (tptp.aa_Code_integer_bool _let_1 B))))) (forall ((A tptp.real) (B 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 B) A))) (tptp.pp (tptp.aa_real_bool _let_1 B))))) (forall ((A tptp.rat) (B 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 B) A))) (tptp.pp (tptp.aa_rat_bool _let_1 B))))) (forall ((A tptp.nat) (B 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 B) A))) (tptp.pp (tptp.aa_nat_bool _let_1 B))))) (forall ((A tptp.int) (B 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 B) A))) (tptp.pp (tptp.aa_int_bool _let_1 B))))) (forall ((A tptp.code_integer) (B 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 B))) (tptp.pp (tptp.aa_Code_integer_bool _let_1 B))))) (forall ((A tptp.real) (B 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) B))) (tptp.pp (tptp.aa_real_bool _let_1 B))))) (forall ((A tptp.rat) (B 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) B))) (tptp.pp (tptp.aa_rat_bool _let_1 B))))) (forall ((A tptp.nat) (B 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) B))) (tptp.pp (tptp.aa_nat_bool _let_1 B))))) (forall ((A tptp.int) (B 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) B))) (tptp.pp (tptp.aa_int_bool _let_1 B))))) (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.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.plus_plus_nat M) 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.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) (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 ((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)) (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)) (= (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)) (= (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) (B 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 B) A))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) B)))) (forall ((A tptp.nat) (B 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 B) A))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) B)))) (forall ((A tptp.int) (B 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 B) A))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) B)))) (forall ((A tptp.real) (B 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 B) A))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) B)))) (forall ((A tptp.rat) (B 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) B))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) B)))) (forall ((A tptp.nat) (B 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) B))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) B)))) (forall ((A tptp.int) (B 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) B))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) B)))) (forall ((A tptp.real) (B 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) B))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) B)))) (forall ((A tptp.rat) (B 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) B)) B)) (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) (B 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) B)) B)) (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) (B 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) B)) B)) (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) (B 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) B)) B)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) tptp.zero_zero_real)))) (forall ((B 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 B) A)) B)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) tptp.zero_zero_rat)))) (forall ((B 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 B) A)) B)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) tptp.zero_zero_nat)))) (forall ((B 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 B) A)) B)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) tptp.zero_zero_int)))) (forall ((B 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 B) A)) B)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) tptp.zero_zero_real)))) (forall ((B 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 B) A)) B)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) tptp.zero_zero_real)))) (forall ((B 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 B) A)) B)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) tptp.zero_zero_rat)))) (forall ((B 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 B) A)) B)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) tptp.zero_zero_nat)))) (forall ((B 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 B) A)) B)) (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) (B 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) B)) B)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) tptp.zero_zero_real)))) (forall ((A tptp.rat) (B 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) B)) B)) (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) (B 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) B)) B)) (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) (B 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) B)) B)) (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) (B 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) B))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) B)))) (forall ((A tptp.rat) (B 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) B))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) B)))) (forall ((A tptp.nat) (B 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) B))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) B)))) (forall ((A tptp.int) (B 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) B))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) B)))) (forall ((A tptp.real) (B 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 B) A))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) B)))) (forall ((A tptp.rat) (B 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 B) A))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) B)))) (forall ((A tptp.nat) (B 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 B) A))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) B)))) (forall ((A tptp.int) (B 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 B) A))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) B)))) (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 ((X tptp.real) (Y4 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 Y4) Y4)) tptp.zero_zero_real) (and (= X tptp.zero_zero_real) (= Y4 tptp.zero_zero_real)))) (forall ((X tptp.rat) (Y4 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 Y4) Y4)) tptp.zero_zero_rat) (and (= X tptp.zero_zero_rat) (= Y4 tptp.zero_zero_rat)))) (forall ((X tptp.int) (Y4 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 Y4) Y4)) tptp.zero_zero_int) (and (= X tptp.zero_zero_int) (= Y4 tptp.zero_zero_int)))) (forall ((B tptp.rat) (A tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) A)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat B) (tptp.aa_rat_rat (tptp.minus_minus_rat A) B)) A))) (forall ((B tptp.nat) (A tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B) A)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat B) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat A) B)) A))) (forall ((B tptp.int) (A tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B) A)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int B) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) B)) A))) (forall ((B tptp.real) (A tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real B) A)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real B) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A) B)) A))) (forall ((B tptp.rat) (A tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) A)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.minus_minus_rat A) B)) B) A))) (forall ((B tptp.nat) (A tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B) 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) B)) B) A))) (forall ((B tptp.int) (A tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B) 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) B)) B) A))) (forall ((B tptp.real) (A tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real B) 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) B)) B) A))) (forall ((A tptp.nat) (B 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) B)) tptp.zero_zero_nat)) (forall ((V tptp.num) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (tptp.times_times_complex (tptp.numera6690914467698888265omplex V)))) (= (tptp.aa_complex_complex _let_1 (tptp.plus_plus_complex B C)) (tptp.plus_plus_complex (tptp.aa_complex_complex _let_1 B) (tptp.aa_complex_complex _let_1 C))))) (forall ((V tptp.num) (B 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 B) C)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real _let_1 B)) (tptp.aa_real_real _let_1 C))))) (forall ((V tptp.num) (B 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 B) C)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat _let_1 B)) (tptp.aa_rat_rat _let_1 C))))) (forall ((V tptp.num) (B 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 B) C)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat _let_1 B)) (tptp.aa_nat_nat _let_1 C))))) (forall ((V tptp.num) (B 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 B) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int _let_1 B)) (tptp.aa_int_int _let_1 C))))) (forall ((A tptp.complex) (B tptp.complex) (V tptp.num)) (let ((_let_1 (tptp.numera6690914467698888265omplex V))) (= (tptp.aa_complex_complex (tptp.times_times_complex (tptp.plus_plus_complex A B)) _let_1) (tptp.plus_plus_complex (tptp.aa_complex_complex (tptp.times_times_complex A) _let_1) (tptp.aa_complex_complex (tptp.times_times_complex B) _let_1))))) (forall ((A tptp.real) (B 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) B)) _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 B) _let_1))))) (forall ((A tptp.rat) (B 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) B)) _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 B) _let_1))))) (forall ((A tptp.nat) (B 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) B)) _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 B) _let_1))))) (forall ((A tptp.int) (B 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) B)) _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 B) _let_1))))) (forall ((A tptp.code_integer) (C tptp.code_integer) (B 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) B))) (tptp.pp (tptp.aa_Code_integer_bool _let_1 B))))) (forall ((A tptp.real) (C tptp.real) (B 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)) B))) (tptp.pp (tptp.aa_real_bool _let_1 B))))) (forall ((A tptp.rat) (C tptp.rat) (B 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)) B))) (tptp.pp (tptp.aa_rat_bool _let_1 B))))) (forall ((A tptp.nat) (C tptp.nat) (B 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)) B))) (tptp.pp (tptp.aa_nat_bool _let_1 B))))) (forall ((A tptp.int) (C tptp.int) (B 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)) B))) (tptp.pp (tptp.aa_int_bool _let_1 B))))) (forall ((A tptp.code_integer) (B 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 B (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger C) A)))) (tptp.pp (tptp.aa_Code_integer_bool _let_1 B))))) (forall ((A tptp.real) (B 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 B) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real C) A)))) (tptp.pp (tptp.aa_real_bool _let_1 B))))) (forall ((A tptp.rat) (B 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 B) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat C) A)))) (tptp.pp (tptp.aa_rat_bool _let_1 B))))) (forall ((A tptp.nat) (B 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 B) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat C) A)))) (tptp.pp (tptp.aa_nat_bool _let_1 B))))) (forall ((A tptp.int) (B 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 B) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int C) A)))) (tptp.pp (tptp.aa_int_bool _let_1 B))))) (forall ((C tptp.code_integer) (A tptp.code_integer) (B 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 B)) (= (tptp.divide6298287555418463151nteger (tptp.plus_p5714425477246183910nteger A B) C) (tptp.plus_p5714425477246183910nteger (tptp.divide6298287555418463151nteger A C) (tptp.divide6298287555418463151nteger B C))))))) (forall ((C tptp.nat) (A tptp.nat) (B 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 B)) (= (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) B)) 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 B) C))))))) (forall ((C tptp.int) (A tptp.int) (B 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 B)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) B)) 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.divide_divide_int A) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int B) C))))))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) N)) (tptp.plus_plus_complex (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex M) (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex 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_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_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_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)) (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_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 ((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 ((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)) (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 ((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)))) (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (not (= B 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) B))) B) (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) B))))) (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (=> (not (= B tptp.zero_zero_int)) (= (tptp.aa_int_int (tptp.aa_int_fun_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) B))) B) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int C) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A) B))))) (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (not (= B 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 B) C))) B) (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) B))))) (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (=> (not (= B tptp.zero_zero_int)) (= (tptp.aa_int_int (tptp.aa_int_fun_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 B) C))) B) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int C) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A) B))))) (forall ((B tptp.nat) (C tptp.nat) (A tptp.nat)) (=> (not (= B 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) B)) A)) B) (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) B))))) (forall ((B tptp.int) (C tptp.int) (A tptp.int)) (=> (not (= B tptp.zero_zero_int)) (= (tptp.aa_int_int (tptp.aa_int_fun_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) B)) A)) B) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int C) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A) B))))) (forall ((B tptp.nat) (C tptp.nat) (A tptp.nat)) (=> (not (= B 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 B) C)) A)) B) (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) B))))) (forall ((B tptp.int) (C tptp.int) (A tptp.int)) (=> (not (= B tptp.zero_zero_int)) (= (tptp.aa_int_int (tptp.aa_int_fun_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 B) C)) A)) B) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int C) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A) B))))) (forall ((N tptp.num)) (= (tptp.plus_plus_complex (tptp.numera6690914467698888265omplex N) tptp.one_one_complex) (tptp.numera6690914467698888265omplex (tptp.aa_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.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.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.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.plus_plus_num N) tptp.one)))) (forall ((N tptp.num)) (= (tptp.plus_plus_complex tptp.one_one_complex (tptp.numera6690914467698888265omplex N)) (tptp.numera6690914467698888265omplex (tptp.aa_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.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.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.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.plus_plus_num tptp.one) N)))) (forall ((M tptp.nat)) (= (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex (tptp.aa_nat_nat tptp.suc M)) (tptp.plus_plus_complex tptp.one_one_complex (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex 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_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_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 ((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 ((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))))) (= (tptp.plus_plus_complex tptp.one_one_complex tptp.one_one_complex) _let_76) (= _let_163 _let_40) (= _let_162 _let_130) _let_159 (= _let_160 _let_63) (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_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 B)))) (not (= (not (tptp.pp (tptp.aa_Code_integer_bool _let_1 A))) (not (tptp.pp (tptp.aa_Code_integer_bool _let_1 B)))))))) (forall ((A tptp.nat) (B 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) B)))) (not (= (not (tptp.pp (tptp.aa_nat_bool _let_1 A))) (not (tptp.pp (tptp.aa_nat_bool _let_1 B)))))))) (forall ((A tptp.int) (B 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) B)))) (not (= (not (tptp.pp (tptp.aa_int_bool _let_1 A))) (not (tptp.pp (tptp.aa_int_bool _let_1 B)))))))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_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 B))) (= (tptp.pp (tptp.aa_Code_integer_bool _let_1 A)) (tptp.pp (tptp.aa_Code_integer_bool _let_1 B)))))) (forall ((A tptp.nat) (B 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) B))) (= (tptp.pp (tptp.aa_nat_bool _let_1 A)) (tptp.pp (tptp.aa_nat_bool _let_1 B)))))) (forall ((A tptp.int) (B 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) B))) (= (tptp.pp (tptp.aa_int_bool _let_1 A)) (tptp.pp (tptp.aa_int_bool _let_1 B)))))) (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 ((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 ((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)) (forall ((A tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_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 ((X tptp.rat) (Y4 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 Y4) _let_1)) tptp.zero_zero_rat) (and (= X tptp.zero_zero_rat) (= Y4 tptp.zero_zero_rat))))) (forall ((X tptp.int) (Y4 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 Y4) _let_1)) tptp.zero_zero_int) (and (= X tptp.zero_zero_int) (= Y4 tptp.zero_zero_int))))) (forall ((X tptp.real) (Y4 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 Y4) _let_1)) tptp.zero_zero_real) (and (= X tptp.zero_zero_real) (= Y4 tptp.zero_zero_real))))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_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 B))) (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.plus_p5714425477246183910nteger A B)))))) (forall ((A tptp.int) (B 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) B))) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) B)))))) (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) (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 ((A tptp.code_integer)) (let ((_let_1 (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.aa_int_fun_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.aa_int_fun_int_int tptp.divide_divide_int A) _let_1)) tptp.one_one_int))))) (forall ((A tptp.code_integer)) (let ((_let_1 (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.aa_int_fun_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.divide_divide_int A) _let_1))))) (forall ((A tptp.code_integer)) (let ((_let_1 (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.aa_int_fun_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.aa_int_fun_int_int tptp.divide_divide_int A) _let_1))))) (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.code_integer)) (let ((_let_1 (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.aa_int_fun_int_int tptp.divide_divide_int A) _let_1))) tptp.one_one_int) 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.aa_int_int (tptp.aa_nat_fun_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.aa_int_fun_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 ((A tptp.code_integer)) (let ((_let_1 (tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_nat6383147911832638789nteger tptp.bit_se2793503036327961859nteger tptp.zero_zero_nat) A) (tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger _let_1) (tptp.divide6298287555418463151nteger A _let_1)))))) (forall ((A tptp.code_integer) (N tptp.nat)) (let ((_let_1 (tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (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.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.aa_int_fun_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.aa_int_fun_int_int tptp.divide_divide_int A) _let_2))))))) (forall ((A2 tptp.set_complex) (B3 tptp.set_complex) (C tptp.complex)) (=> (tptp.ord_less_set_complex A2 B3) (=> (tptp.member_complex C A2) (tptp.member_complex C B3)))) (forall ((A2 tptp.set_real) (B3 tptp.set_real) (C tptp.real)) (=> (tptp.ord_less_set_real A2 B3) (=> (tptp.member_real C A2) (tptp.member_real C B3)))) (forall ((A2 tptp.set_set_nat) (B3 tptp.set_set_nat) (C tptp.set_nat)) (=> (tptp.ord_less_set_set_nat A2 B3) (=> (tptp.member_set_nat C A2) (tptp.member_set_nat C B3)))) (forall ((A2 tptp.set_nat) (B3 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 A2) B3)) (=> (tptp.pp (tptp.aa_set_nat_bool _let_1 A2)) (tptp.pp (tptp.aa_set_nat_bool _let_1 B3)))))) (forall ((A2 tptp.set_int) (B3 tptp.set_int) (C tptp.int)) (=> (tptp.ord_less_set_int A2 B3) (=> (tptp.member_int C A2) (tptp.member_int C B3)))) (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 ((A tptp.real) (B 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 B)) C) (tptp.aa_real_real _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real B) C))))) (forall ((A tptp.rat) (B 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 B)) C) (tptp.aa_rat_rat _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat B) C))))) (forall ((A tptp.nat) (B 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 B)) C) (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat B) C))))) (forall ((A tptp.int) (B 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 B)) C) (tptp.aa_int_int _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int B) 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 ((A2 tptp.real) (K tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real K))) (=> (= A2 (tptp.aa_real_real _let_1 A)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A2) B) (tptp.aa_real_real _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) B)))))) (forall ((A2 tptp.rat) (K tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat K))) (=> (= A2 (tptp.aa_rat_rat _let_1 A)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A2) B) (tptp.aa_rat_rat _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) B)))))) (forall ((A2 tptp.nat) (K tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat K))) (=> (= A2 (tptp.aa_nat_nat _let_1 A)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A2) B) (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) B)))))) (forall ((A2 tptp.int) (K tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.plus_plus_int K))) (=> (= A2 (tptp.aa_int_int _let_1 A)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A2) B) (tptp.aa_int_int _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) B)))))) (forall ((B3 tptp.real) (K tptp.real) (B 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))) (=> (= B3 (tptp.aa_real_real _let_2 B)) (= (tptp.aa_real_real _let_1 B3) (tptp.aa_real_real _let_2 (tptp.aa_real_real _let_1 B))))))) (forall ((B3 tptp.rat) (K tptp.rat) (B 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))) (=> (= B3 (tptp.aa_rat_rat _let_2 B)) (= (tptp.aa_rat_rat _let_1 B3) (tptp.aa_rat_rat _let_2 (tptp.aa_rat_rat _let_1 B))))))) (forall ((B3 tptp.nat) (K tptp.nat) (B 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))) (=> (= B3 (tptp.aa_nat_nat _let_2 B)) (= (tptp.aa_nat_nat _let_1 B3) (tptp.aa_nat_nat _let_2 (tptp.aa_nat_nat _let_1 B))))))) (forall ((B3 tptp.int) (K tptp.int) (B 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))) (=> (= B3 (tptp.aa_int_int _let_2 B)) (= (tptp.aa_int_int _let_1 B3) (tptp.aa_int_int _let_2 (tptp.aa_int_int _let_1 B))))))) (forall ((A tptp.real) (B 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 B)) C) (tptp.aa_real_real _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real B) C))))) (forall ((A tptp.rat) (B 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 B)) C) (tptp.aa_rat_rat _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat B) C))))) (forall ((A tptp.nat) (B 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 B)) C) (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat B) C))))) (forall ((A tptp.int) (B 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 B)) C) (tptp.aa_int_int _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int B) C))))) (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A))) (= (= (tptp.aa_real_real _let_1 B) (tptp.aa_real_real _let_1 C)) (= B C)))) (forall ((A tptp.rat) (B 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 B) (tptp.aa_rat_rat _let_1 C)) (= B C)))) (forall ((A tptp.int) (B 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 B) (tptp.aa_int_int _let_1 C)) (= B C)))) (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (= (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real B) A) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real C) A)) (= B C))) (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (= (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat B) A) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat C) A)) (= B C))) (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (= (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int B) A) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int C) A)) (= B C))) (forall ((A tptp.real) (B tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) B) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real B) A))) (forall ((A tptp.rat) (B tptp.rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) B) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat B) A))) (forall ((A tptp.nat) (B tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) B) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat B) A))) (forall ((A tptp.int) (B tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) B) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int B) A))) (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real B))) (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 ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat B))) (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 ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat B))) (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 ((B tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.plus_plus_int B))) (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) (B tptp.real) (C tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A))) (=> (= (tptp.aa_real_real _let_1 B) (tptp.aa_real_real _let_1 C)) (= B C)))) (forall ((A tptp.rat) (B 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 B) (tptp.aa_rat_rat _let_1 C)) (= B C)))) (forall ((A tptp.nat) (B 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 B) (tptp.aa_nat_nat _let_1 C)) (= B C)))) (forall ((A tptp.int) (B 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 B) (tptp.aa_int_int _let_1 C)) (= B C)))) (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (=> (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real B) A) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real C) A)) (= B C))) (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (=> (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat B) A) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat C) A)) (= B C))) (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat B) A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat C) A)) (= B C))) (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (=> (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int B) A) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int C) A)) (= B C))) (forall ((A tptp.real) (B 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 B)) C) (tptp.aa_real_real _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real B) C))))) (forall ((A tptp.rat) (B 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 B)) C) (tptp.aa_rat_rat _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat B) C))))) (forall ((A tptp.int) (B 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 B)) C) (tptp.aa_int_int _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int B) C))))) (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 (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 (= 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 (= 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 ((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 ((A tptp.rat) (B 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) B)) (=> (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 B) D)))))) (forall ((A tptp.nat) (B 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) B)) (=> (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 B) D)))))) (forall ((A tptp.int) (B 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) B)) (=> (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 B) D)))))) (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) B)) (=> (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 B) D)))))) (forall ((A tptp.rat) (B 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) B)) (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 B)))))) (forall ((A tptp.nat) (B 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) B)) (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 B)))))) (forall ((A tptp.int) (B 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) B)) (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 B)))))) (forall ((A tptp.real) (B 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) B)) (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 B)))))) (forall ((A tptp.nat) (B tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B)) (not (forall ((C3 tptp.nat)) (not (= B (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) C3))))))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B)) (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 B) C))))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B)) (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 B) C))))) (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B)) (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 B) C))))) (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) B)) (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 B) C))))) (forall ((A tptp.nat) (B tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B)) (exists ((C5 tptp.nat)) (= B (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) C5))))) (forall ((C tptp.rat) (A tptp.rat) (B 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 B))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B))))) (forall ((C tptp.nat) (A tptp.nat) (B 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 B))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B))))) (forall ((C tptp.int) (A tptp.int) (B 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 B))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B))))) (forall ((C tptp.real) (A tptp.real) (B 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 B))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) B))))) (forall ((A tptp.rat) (C tptp.rat) (B 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 B) C))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B)))) (forall ((A tptp.nat) (C tptp.nat) (B 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 B) C))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B)))) (forall ((A tptp.int) (C tptp.int) (B 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 B) C))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B)))) (forall ((A tptp.real) (C tptp.real) (B 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 B) C))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) B)))) (forall ((A tptp.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.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.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.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 ((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) (B tptp.real) (C tptp.real) (D tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B)) (=> (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 B) D)))))) (forall ((A tptp.rat) (B 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) B)) (=> (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 B) D)))))) (forall ((A tptp.nat) (B 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) B)) (=> (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 B) D)))))) (forall ((A tptp.int) (B 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) B)) (=> (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 B) D)))))) (forall ((A tptp.real) (B 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) B)) (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 B)))))) (forall ((A tptp.rat) (B 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) B)) (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 B)))))) (forall ((A tptp.nat) (B 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) B)) (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 B)))))) (forall ((A tptp.int) (B 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) B)) (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 B)))))) (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B)) (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 B) C))))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B)) (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 B) C))))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) B)) (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 B) C))))) (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B)) (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 B) C))))) (forall ((C tptp.real) (A tptp.real) (B 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 B))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B))))) (forall ((C tptp.rat) (A tptp.rat) (B 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 B))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B))))) (forall ((C tptp.nat) (A tptp.nat) (B 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 B))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) B))))) (forall ((C tptp.int) (A tptp.int) (B 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 B))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B))))) (forall ((A tptp.real) (C tptp.real) (B 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 B) C))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B)))) (forall ((A tptp.rat) (C tptp.rat) (B 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 B) C))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B)))) (forall ((A tptp.nat) (C tptp.nat) (B 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 B) C))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) B)))) (forall ((A tptp.int) (C tptp.int) (B 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 B) C))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B)))) (forall ((A tptp.real) (B 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) B)) 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 B) C)))) (forall ((A tptp.rat) (B 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) B)) 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 B) C)))) (forall ((A tptp.int) (B 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) B)) 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 B) C)))) (forall ((A tptp.real) (B 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 B) C)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real _let_1 B)) (tptp.aa_real_real _let_1 C))))) (forall ((A tptp.rat) (B 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 B) C)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat _let_1 B)) (tptp.aa_rat_rat _let_1 C))))) (forall ((A tptp.int) (B 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 B) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int _let_1 B)) (tptp.aa_int_int _let_1 C))))) (forall ((A tptp.real) (B 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) B)) 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 B) C)))) (forall ((A tptp.rat) (B 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) B)) 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 B) C)))) (forall ((A tptp.nat) (B 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) B)) 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 B) C)))) (forall ((A tptp.int) (B 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) B)) 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 B) C)))) (forall ((A tptp.real) (B 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 B) C)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real _let_1 B)) (tptp.aa_real_real _let_1 C))))) (forall ((A tptp.rat) (B 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 B) C)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat _let_1 B)) (tptp.aa_rat_rat _let_1 C))))) (forall ((A tptp.nat) (B 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 B) C)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat _let_1 B)) (tptp.aa_nat_nat _let_1 C))))) (forall ((A tptp.int) (B 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 B) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int _let_1 B)) (tptp.aa_int_int _let_1 C))))) (forall ((A tptp.real) (B 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) B)) 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 B) C)))) (forall ((A tptp.rat) (B 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) B)) 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 B) C)))) (forall ((A tptp.nat) (B 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) B)) 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 B) C)))) (forall ((A tptp.int) (B 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) B)) 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 B) C)))) (forall ((A tptp.real) (E2 tptp.real) (B 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) E2)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real B) E2)) 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) B)) E2)) C))) (forall ((A tptp.rat) (E2 tptp.rat) (B 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) E2)) (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 B) E2)) 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) B)) E2)) C))) (forall ((A tptp.nat) (E2 tptp.nat) (B 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) E2)) (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 B) E2)) 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) B)) E2)) C))) (forall ((A tptp.int) (E2 tptp.int) (B 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) E2)) (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) E2)) 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) B)) E2)) C))) (forall ((A tptp.real) (B 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 B)) C) (tptp.aa_real_real _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real B) C))))) (forall ((A tptp.rat) (B 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 B)) C) (tptp.aa_rat_rat _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat B) C))))) (forall ((A tptp.nat) (B 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 B)) C) (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat B) C))))) (forall ((A tptp.int) (B 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 B)) C) (tptp.aa_int_int _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int B) C))))) (forall ((C tptp.real) (B tptp.real) (A tptp.real)) (=> (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real C) B) A) (= C (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A) B)))) (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat C) B) A) (= C (tptp.aa_rat_rat (tptp.minus_minus_rat A) B)))) (forall ((C tptp.nat) (B tptp.nat) (A tptp.nat)) (=> (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat C) B) A) (= C (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat A) B)))) (forall ((C tptp.int) (B tptp.int) (A tptp.int)) (=> (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int C) B) A) (= C (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) B)))) (forall ((A tptp.real) (B 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 B) C)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real _let_1 C)) B)))) (forall ((A tptp.rat) (B 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 B) C)) (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_rat_rat _let_1 C)) B)))) (forall ((A tptp.int) (B 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 B) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_int_int _let_1 C)) B)))) (forall ((A tptp.real) (B 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) B)) 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)) B))) (forall ((A tptp.rat) (B 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) B)) 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)) B))) (forall ((A tptp.int) (B 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) B)) 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)) B))) (forall ((A tptp.real) (B 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 B) 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)) B))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (= (tptp.aa_rat_rat (tptp.minus_minus_rat A) (tptp.aa_rat_rat (tptp.minus_minus_rat B) 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)) B))) (forall ((A tptp.int) (B 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 B) 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)) B))) (forall ((A tptp.real) (B 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 B) C)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real _let_1 B)) C)))) (forall ((A tptp.rat) (B 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 B) C)) (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_rat_rat _let_1 B)) C)))) (forall ((A tptp.int) (B 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 B) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_int_int _let_1 B)) C)))) (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (= (= A (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real C) B)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) B) C))) (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (= (= A (tptp.aa_rat_rat (tptp.minus_minus_rat C) B)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) B) C))) (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (= A (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int C) B)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) B) C))) (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (= (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A) B) C) (= A (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real C) B)))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (= (= (tptp.aa_rat_rat (tptp.minus_minus_rat A) B) C) (= A (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat C) B)))) (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (= (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) B) C) (= A (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int C) B)))) (forall ((A2 tptp.real) (K tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real K))) (=> (= A2 (tptp.aa_real_real _let_1 A)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A2) B) (tptp.aa_real_real _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A) B)))))) (forall ((A2 tptp.rat) (K tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat K))) (=> (= A2 (tptp.aa_rat_rat _let_1 A)) (= (tptp.aa_rat_rat (tptp.minus_minus_rat A2) B) (tptp.aa_rat_rat _let_1 (tptp.aa_rat_rat (tptp.minus_minus_rat A) B)))))) (forall ((A2 tptp.int) (K tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.plus_plus_int K))) (=> (= A2 (tptp.aa_int_int _let_1 A)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A2) B) (tptp.aa_int_int _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) B)))))) (forall ((A tptp.real) (C tptp.real) (B 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 B) 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) B)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real C) D)))) (forall ((A tptp.rat) (C tptp.rat) (B 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 B) D)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.minus_minus_rat A) B)) (tptp.aa_rat_rat (tptp.minus_minus_rat C) D)))) (forall ((A tptp.int) (C tptp.int) (B 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 B) 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) B)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int C) D)))) (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (= (tptp.divide1717551699836669952omplex (tptp.plus_plus_complex A B) C) (tptp.plus_plus_complex (tptp.divide1717551699836669952omplex A C) (tptp.divide1717551699836669952omplex B C)))) (forall ((A tptp.real) (B 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) B)) 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 B) C)))) (forall ((A tptp.rat) (B 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) B)) 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 B) C)))) (forall ((A tptp.code_integer) (B 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 B)) (= (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.plus_p5714425477246183910nteger B C))) (tptp.pp (tptp.aa_Code_integer_bool _let_1 C)))))) (forall ((A tptp.real) (B 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 B)) (= (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real B) C))) (tptp.pp (tptp.aa_real_bool _let_1 C)))))) (forall ((A tptp.rat) (B 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 B)) (= (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat B) C))) (tptp.pp (tptp.aa_rat_bool _let_1 C)))))) (forall ((A tptp.nat) (B 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 B)) (= (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat B) C))) (tptp.pp (tptp.aa_nat_bool _let_1 C)))))) (forall ((A tptp.int) (B 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 B)) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int B) C))) (tptp.pp (tptp.aa_int_bool _let_1 C)))))) (forall ((A tptp.code_integer) (C tptp.code_integer) (B 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 B C))) (tptp.pp (tptp.aa_Code_integer_bool _let_1 B)))))) (forall ((A tptp.real) (C tptp.real) (B 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 B) C))) (tptp.pp (tptp.aa_real_bool _let_1 B)))))) (forall ((A tptp.rat) (C tptp.rat) (B 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 B) C))) (tptp.pp (tptp.aa_rat_bool _let_1 B)))))) (forall ((A tptp.nat) (C tptp.nat) (B 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 B) C))) (tptp.pp (tptp.aa_nat_bool _let_1 B)))))) (forall ((A tptp.int) (C tptp.int) (B 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 B) C))) (tptp.pp (tptp.aa_int_bool _let_1 B)))))) (forall ((A tptp.code_integer) (B 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 B)) (=> (tptp.pp (tptp.aa_Code_integer_bool _let_1 C)) (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.plus_p5714425477246183910nteger B C))))))) (forall ((A tptp.real) (B 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 B)) (=> (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 B) C))))))) (forall ((A tptp.rat) (B 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 B)) (=> (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 B) C))))))) (forall ((A tptp.nat) (B 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 B)) (=> (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 B) C))))))) (forall ((A tptp.int) (B 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 B)) (=> (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 B) C))))))) (forall ((A2 tptp.nat) (K tptp.nat) (A tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat K))) (=> (= A2 (tptp.aa_nat_nat _let_1 A)) (= (tptp.aa_nat_nat tptp.suc A2) (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_fun_nat_bool) (A tptp.nat) (B tptp.nat)) (=> (forall ((A3 tptp.nat) (B2 tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool P A3) B2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool P B2) 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) (B2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool P A3))) (=> (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 A3) B2)))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool P A) B)))))) (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.plus_plus_nat M) N) M) (= N tptp.zero_zero_nat))) (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) (N tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)) (exists ((K3 tptp.nat)) (= N (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) K3))))) (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 ((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) (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) (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 ((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 ((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 ((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 ((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 ((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 ((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 ((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.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 ((X tptp.rat) (Y4 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 Y4) tptp.zero_zero_rat)) (= (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat X) Y4) tptp.zero_zero_rat) (and (= X tptp.zero_zero_rat) (= Y4 tptp.zero_zero_rat)))))) (forall ((X tptp.nat) (Y4 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 Y4) tptp.zero_zero_nat)) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat X) Y4) tptp.zero_zero_nat) (and (= X tptp.zero_zero_nat) (= Y4 tptp.zero_zero_nat)))))) (forall ((X tptp.int) (Y4 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 Y4) tptp.zero_zero_int)) (= (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int X) Y4) tptp.zero_zero_int) (and (= X tptp.zero_zero_int) (= Y4 tptp.zero_zero_int)))))) (forall ((X tptp.real) (Y4 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 Y4) tptp.zero_zero_real)) (= (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) Y4) tptp.zero_zero_real) (and (= X tptp.zero_zero_real) (= Y4 tptp.zero_zero_real)))))) (forall ((X tptp.rat) (Y4 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 Y4)) (= (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat X) Y4) tptp.zero_zero_rat) (and (= X tptp.zero_zero_rat) (= Y4 tptp.zero_zero_rat))))))) (forall ((X tptp.nat) (Y4 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 Y4)) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat X) Y4) tptp.zero_zero_nat) (and (= X tptp.zero_zero_nat) (= Y4 tptp.zero_zero_nat))))))) (forall ((X tptp.int) (Y4 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 Y4)) (= (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int X) Y4) tptp.zero_zero_int) (and (= X tptp.zero_zero_int) (= Y4 tptp.zero_zero_int))))))) (forall ((X tptp.real) (Y4 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 Y4)) (= (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) Y4) tptp.zero_zero_real) (and (= X tptp.zero_zero_real) (= Y4 tptp.zero_zero_real))))))) (forall ((A tptp.rat) (B 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 B) 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) B)) tptp.zero_zero_rat))))) (forall ((A tptp.nat) (B 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 B) 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) B)) tptp.zero_zero_nat))))) (forall ((A tptp.int) (B 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 B) 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) B)) tptp.zero_zero_int))))) (forall ((A tptp.real) (B 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 B) 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) B)) tptp.zero_zero_real))))) (forall ((A tptp.rat) (B 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 B)) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) B))))))) (forall ((A tptp.nat) (B 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 B)) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) B))))))) (forall ((A tptp.int) (B 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 B)) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) B))))))) (forall ((A tptp.real) (B 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 B)) (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) B))))))) (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B))) (=> (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) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B))) (=> (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) (B tptp.int) (A tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B))) (=> (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 ((C tptp.real) (B tptp.real) (A tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real B))) (=> (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) (A tptp.rat) (B 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) B)) (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)) B))))) (forall ((C tptp.nat) (A tptp.nat) (B 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) B)) (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)) B))))) (forall ((C tptp.int) (A tptp.int) (B 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) B)) (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)) B))))) (forall ((C tptp.real) (A tptp.real) (B 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) B)) (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)) B))))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B))) (=> (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) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B))) (=> (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) (B tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B))) (=> (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) (B tptp.real) (C tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real B))) (=> (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) (C tptp.rat) (B 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) B)) (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)) B))))) (forall ((A tptp.nat) (C tptp.nat) (B 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) B)) (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)) B))))) (forall ((A tptp.int) (C tptp.int) (B 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) B)) (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)) B))))) (forall ((A tptp.real) (C tptp.real) (B 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) B)) (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)) B))))) (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_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_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 ((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 ((A tptp.rat) (B 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) B)) (=> (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 B) D)))))) (forall ((A tptp.nat) (B 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) B)) (=> (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 B) D)))))) (forall ((A tptp.int) (B 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) B)) (=> (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 B) D)))))) (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) B)) (=> (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 B) D)))))) (forall ((A tptp.rat) (B 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) B)) (=> (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 B) D)))))) (forall ((A tptp.nat) (B 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) B)) (=> (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 B) D)))))) (forall ((A tptp.int) (B 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) B)) (=> (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 B) D)))))) (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B)) (=> (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 B) D)))))) (forall ((X tptp.real) (Y4 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) Y4)) 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 Y4) tptp.zero_zero_real))))) (forall ((X tptp.rat) (Y4 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) Y4)) 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 Y4) tptp.zero_zero_rat))))) (forall ((X tptp.int) (Y4 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) Y4)) 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 Y4) tptp.zero_zero_int))))) (forall ((A tptp.real) (B 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 B) 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) B)) tptp.zero_zero_real))))) (forall ((A tptp.rat) (B 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 B) 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) B)) tptp.zero_zero_rat))))) (forall ((A tptp.nat) (B 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 B) 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) B)) tptp.zero_zero_nat))))) (forall ((A tptp.int) (B 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 B) 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) B)) tptp.zero_zero_int))))) (forall ((A tptp.real) (B 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 B)) (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) B))))))) (forall ((A tptp.rat) (B 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 B)) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) B))))))) (forall ((A tptp.nat) (B 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 B)) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) B))))))) (forall ((A tptp.int) (B 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 B)) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) B))))))) (forall ((A tptp.nat) (B tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) B)) (not (forall ((C3 tptp.nat)) (=> (= B (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) C3)) (= C3 tptp.zero_zero_nat)))))) (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B))) (=> (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) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B))) (=> (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) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat B))) (=> (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) (B tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_int B))) (=> (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 ((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 ((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) (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) (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 ((A tptp.rat) (B 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) B)) 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) B))))) (forall ((A tptp.int) (B 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) B)) 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) B))))) (forall ((A tptp.real) (B 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) B)) 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) B))))) (forall ((A tptp.rat) (C tptp.rat) (B 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) B))) (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) B)) C)))) (forall ((A tptp.int) (C tptp.int) (B 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) B))) (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) B)) C)))) (forall ((A tptp.real) (C tptp.real) (B 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) B))) (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) B)) C)))) (forall ((A tptp.nat) (B tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B)) (= (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 B) A)) A) B))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B)) (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 B) C)) A))))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B)) (= (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 B) 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)) B))))) (forall ((A tptp.nat) (B 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) B)) (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat B) A)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat _let_1 B)) A))))) (forall ((A tptp.nat) (B 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) B)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat _let_1 B)) A) (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat B) A)))))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B)) (= (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 B) 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 B) C)) A)))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B)) (= (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 B) 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 B) A)) C)))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B)) (= (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 B) 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)) B)))) (forall ((A tptp.nat) (B tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B)) (= (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 B) A)) B))) (forall ((A tptp.nat) (B 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) B)))) (=> _let_1 (=> _let_1 (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat B) A) C) (= B (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat C) A))))))) (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) (B tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B)) (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 B) tptp.one_one_real))))) (forall ((A tptp.rat) (B tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B)) (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 B) tptp.one_one_rat))))) (forall ((A tptp.nat) (B tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) B)) (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 B) tptp.one_one_nat))))) (forall ((A tptp.int) (B tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B)) (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 B) tptp.one_one_int))))) (forall ((N tptp.num)) (let ((_let_1 (tptp.numera6690914467698888265omplex N))) (= (tptp.numera6690914467698888265omplex (tptp.aa_num_num tptp.bit0 N)) (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 ((A tptp.real) (C tptp.real) (B 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) B))) (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) B)) C)))) (forall ((A tptp.rat) (C tptp.rat) (B 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) B))) (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) B)) C)))) (forall ((A tptp.int) (C tptp.int) (B 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) B))) (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) B)) C)))) (forall ((A tptp.real) (B 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) B)) 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) B))))) (forall ((A tptp.rat) (B 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) B)) 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) B))))) (forall ((A tptp.int) (B 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) B)) 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) B))))) (forall ((A tptp.real) (B tptp.real)) (=> (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B))) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real B) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A) B)) A))) (forall ((A tptp.rat) (B tptp.rat)) (=> (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B))) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat B) (tptp.aa_rat_rat (tptp.minus_minus_rat A) B)) A))) (forall ((A tptp.nat) (B tptp.nat)) (=> (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) B))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat B) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat A) B)) A))) (forall ((A tptp.int) (B tptp.int)) (=> (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B))) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int B) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) B)) A))) (forall ((X tptp.num)) (let ((_let_1 (tptp.numera6690914467698888265omplex X))) (= (tptp.plus_plus_complex tptp.one_one_complex _let_1) (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)))) (forall ((A tptp.real) (E2 tptp.real) (C tptp.real) (B 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) E2)) 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 B) E2)) 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) B)) E2)) C) D))) (forall ((A tptp.rat) (E2 tptp.rat) (C tptp.rat) (B 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) E2)) 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 B) E2)) 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) B)) E2)) C) D))) (forall ((A tptp.int) (E2 tptp.int) (C tptp.int) (B 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) E2)) 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 B) E2)) 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) B)) E2)) C) D))) (forall ((A tptp.real) (E2 tptp.real) (C tptp.real) (B 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) E2)) 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 B) E2)) 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 B) A)) E2)) D)))) (forall ((A tptp.rat) (E2 tptp.rat) (C tptp.rat) (B 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) E2)) 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 B) E2)) 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 B) A)) E2)) D)))) (forall ((A tptp.int) (E2 tptp.int) (C tptp.int) (B 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) E2)) 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 B) E2)) 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 B) A)) E2)) D)))) (forall ((X tptp.real) (Y4 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 Y4) Y4)) (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) Y4)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real X) Y4)))) (forall ((X tptp.rat) (Y4 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 Y4) Y4)) (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) Y4)) (tptp.aa_rat_rat (tptp.minus_minus_rat X) Y4)))) (forall ((X tptp.int) (Y4 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 Y4) Y4)) (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) Y4)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int X) Y4)))) (forall ((X tptp.real) (Y4 tptp.real) (A tptp.real) (B 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 Y4)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) B)) (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 Y4) B))) (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)) B))))) (forall ((X tptp.rat) (Y4 tptp.rat) (A tptp.rat) (B 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 Y4)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) B)) (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 Y4) B))) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat (tptp.minus_minus_rat X) A)) B))))) (forall ((X tptp.int) (Y4 tptp.int) (A tptp.int) (B 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 Y4)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) B)) (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 Y4) B))) (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)) B))))) (forall ((D tptp.code_integer) (S2 tptp.code_integer)) (exists ((Z2 tptp.code_integer)) (forall ((X4 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 X4 S2)))))) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger X4) Z2)) (= _let_1 _let_1)))))) (forall ((D tptp.real) (S2 tptp.real)) (exists ((Z2 tptp.real)) (forall ((X4 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 X4) S2)))))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X4) Z2)) (= _let_1 _let_1)))))) (forall ((D tptp.rat) (S2 tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X4 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 X4) S2)))))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X4) Z2)) (= _let_1 _let_1)))))) (forall ((D tptp.nat) (S2 tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X4 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 X4) S2)))))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X4) Z2)) (= _let_1 _let_1)))))) (forall ((D tptp.int) (S2 tptp.int)) (exists ((Z2 tptp.int)) (forall ((X4 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 X4) S2)))))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X4) Z2)) (= _let_1 _let_1)))))) (forall ((D tptp.code_integer) (S2 tptp.code_integer)) (exists ((Z2 tptp.code_integer)) (forall ((X4 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 X4 S2))))) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger X4) Z2)) (= _let_1 _let_1)))))) (forall ((D tptp.real) (S2 tptp.real)) (exists ((Z2 tptp.real)) (forall ((X4 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 X4) S2))))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X4) Z2)) (= _let_1 _let_1)))))) (forall ((D tptp.rat) (S2 tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X4 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 X4) S2))))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X4) Z2)) (= _let_1 _let_1)))))) (forall ((D tptp.nat) (S2 tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X4 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 X4) S2))))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X4) Z2)) (= _let_1 _let_1)))))) (forall ((D tptp.int) (S2 tptp.int)) (exists ((Z2 tptp.int)) (forall ((X4 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 X4) S2))))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X4) Z2)) (= _let_1 _let_1)))))) (forall ((D tptp.code_integer) (S2 tptp.code_integer)) (exists ((Z2 tptp.code_integer)) (forall ((X4 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 X4 S2)))))) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger Z2) X4)) (= _let_1 _let_1)))))) (forall ((D tptp.real) (S2 tptp.real)) (exists ((Z2 tptp.real)) (forall ((X4 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 X4) S2)))))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Z2) X4)) (= _let_1 _let_1)))))) (forall ((D tptp.rat) (S2 tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X4 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 X4) S2)))))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Z2) X4)) (= _let_1 _let_1)))))) (forall ((D tptp.nat) (S2 tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X4 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 X4) S2)))))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Z2) X4)) (= _let_1 _let_1)))))) (forall ((D tptp.int) (S2 tptp.int)) (exists ((Z2 tptp.int)) (forall ((X4 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 X4) S2)))))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Z2) X4)) (= _let_1 _let_1)))))) (forall ((D tptp.code_integer) (S2 tptp.code_integer)) (exists ((Z2 tptp.code_integer)) (forall ((X4 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 X4 S2))))) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger Z2) X4)) (= _let_1 _let_1)))))) (forall ((D tptp.real) (S2 tptp.real)) (exists ((Z2 tptp.real)) (forall ((X4 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 X4) S2))))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Z2) X4)) (= _let_1 _let_1)))))) (forall ((D tptp.rat) (S2 tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X4 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 X4) S2))))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Z2) X4)) (= _let_1 _let_1)))))) (forall ((D tptp.nat) (S2 tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X4 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 X4) S2))))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Z2) X4)) (= _let_1 _let_1)))))) (forall ((D tptp.int) (S2 tptp.int)) (exists ((Z2 tptp.int)) (forall ((X4 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 X4) S2))))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Z2) X4)) (= _let_1 _let_1)))))) (forall ((C tptp.code_integer) (A tptp.code_integer) (B 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 B) C) (tptp.plus_p5714425477246183910nteger (tptp.divide6298287555418463151nteger A C) (tptp.divide6298287555418463151nteger B C))))) (forall ((C tptp.nat) (A tptp.nat) (B 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) B)) 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 B) C))))) (forall ((C tptp.int) (A tptp.int) (B 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.aa_int_fun_int_int tptp.divide_divide_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) B)) 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.divide_divide_int A) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int B) C))))) (forall ((C tptp.code_integer) (B tptp.code_integer) (A tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer C) B)) (= (tptp.divide6298287555418463151nteger (tptp.plus_p5714425477246183910nteger A B) C) (tptp.plus_p5714425477246183910nteger (tptp.divide6298287555418463151nteger A C) (tptp.divide6298287555418463151nteger B C))))) (forall ((C tptp.nat) (B tptp.nat) (A tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat C) B)) (= (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) B)) 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 B) C))))) (forall ((C tptp.int) (B tptp.int) (A tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int C) B)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) B)) 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.divide_divide_int A) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int B) C))))) (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.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) (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 ((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)) (=> (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 ((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 ((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 ((Q4 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) Q4)))))))) (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 ((K2 tptp.nat)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) K2)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat I) K2) J))))) (forall ((F tptp.fun_nat_nat) (M tptp.nat) (K tptp.nat)) (=> (forall ((M4 tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M4) N2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat F M4)) (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 ((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 ((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 ((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 ((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 ((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_164 (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 ((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 ((D tptp.nat) (A tptp.nat) (B tptp.nat) (X 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 B))) (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 B)) (=> (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 Y4)) 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 Y4)) D))) (exists ((X3 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_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) B))) (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 X3) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat _let_3 Y)) D)) (= (tptp.aa_nat_nat _let_3 X3) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat _let_1 Y)) D)))))))))))))))) (forall ((A tptp.nat) (B tptp.nat)) (exists ((D2 tptp.nat) (X3 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 B))) (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 B)) (or (= (tptp.aa_nat_nat _let_1 X3) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat _let_2 Y)) D2)) (= (tptp.aa_nat_nat _let_2 X3) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat _let_1 Y)) D2))))))))) (forall ((X tptp.rat) (Y4 tptp.rat)) (=> (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)) (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 Y4) E))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) Y4)))) (forall ((X tptp.real) (Y4 tptp.real)) (=> (forall ((E tptp.real)) (=> (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 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real Y4) E))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) Y4)))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B))) (=> (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) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat B))) (=> (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) (B tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_int B))) (=> (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) (B tptp.real) (C tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B))) (=> (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) (B 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 B) C)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) C)))))) (forall ((A tptp.nat) (B 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 B) C)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat B) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) C)))))) (forall ((A tptp.int) (B 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 B) C)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) C)))))) (forall ((A tptp.real) (B 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 B) C)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) C)))))) (forall ((A tptp.rat) (B 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) B)) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) B))))))) (forall ((A tptp.nat) (B 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) B)) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) B))))))) (forall ((A tptp.int) (B 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) B)) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) B))))))) (forall ((A tptp.real) (B 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) B)) (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) B))))))) (forall ((A tptp.rat) (B 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 B) 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) B)) tptp.zero_zero_rat))))) (forall ((A tptp.nat) (B 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 B) 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) B)) tptp.zero_zero_nat))))) (forall ((A tptp.int) (B 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 B) 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) B)) tptp.zero_zero_int))))) (forall ((A tptp.real) (B 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 B) 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) B)) tptp.zero_zero_real))))) (forall ((A tptp.rat) (B 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 B)) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) B))))))) (forall ((A tptp.nat) (B 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 B)) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) B))))))) (forall ((A tptp.int) (B 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 B)) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) B))))))) (forall ((A tptp.real) (B 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 B)) (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) B))))))) (forall ((A tptp.rat) (B 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 B) 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) B)) tptp.zero_zero_rat))))) (forall ((A tptp.nat) (B 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 B) 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) B)) tptp.zero_zero_nat))))) (forall ((A tptp.int) (B 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 B) 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) B)) tptp.zero_zero_int))))) (forall ((A tptp.real) (B 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 B) 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) B)) tptp.zero_zero_real))))) (forall ((X tptp.rat) (Y4 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 Y4) Y4))))) (forall ((X tptp.int) (Y4 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 Y4) Y4))))) (forall ((X tptp.real) (Y4 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 Y4) Y4))))) (forall ((X tptp.rat) (Y4 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 Y4) Y4))) tptp.zero_zero_rat)) (and (= X tptp.zero_zero_rat) (= Y4 tptp.zero_zero_rat)))) (forall ((X tptp.int) (Y4 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 Y4) Y4))) tptp.zero_zero_int)) (and (= X tptp.zero_zero_int) (= Y4 tptp.zero_zero_int)))) (forall ((X tptp.real) (Y4 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 Y4) Y4))) tptp.zero_zero_real)) (and (= X tptp.zero_zero_real) (= Y4 tptp.zero_zero_real)))) (forall ((X tptp.real) (Y4 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 Y4) Y4))) tptp.zero_zero_real)))) (forall ((X tptp.rat) (Y4 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 Y4) Y4))) tptp.zero_zero_rat)))) (forall ((X tptp.int) (Y4 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 Y4) Y4))) tptp.zero_zero_int)))) (forall ((X tptp.real) (Y4 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 Y4) Y4)))) (or (not (= X tptp.zero_zero_real)) (not (= Y4 tptp.zero_zero_real))))) (forall ((X tptp.rat) (Y4 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 Y4) Y4)))) (or (not (= X tptp.zero_zero_rat)) (not (= Y4 tptp.zero_zero_rat))))) (forall ((X tptp.int) (Y4 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 Y4) Y4)))) (or (not (= X tptp.zero_zero_int)) (not (= Y4 tptp.zero_zero_int))))) (forall ((A tptp.nat) (B tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) B)) (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)) B)))) (forall ((A tptp.int) (B tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B)) (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)) B)))) (tptp.pp (tptp.aa_real_bool _let_96 _let_163)) (tptp.pp (tptp.aa_rat_bool _let_111 _let_162)) (tptp.pp (tptp.aa_nat_bool _let_161 _let_158)) (tptp.pp (tptp.aa_int_bool _let_112 _let_160)) (forall ((A tptp.rat) (E2 tptp.rat) (C tptp.rat) (B 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) E2)) 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 B) E2)) 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) B)) E2)) C)) D)))) (forall ((A tptp.int) (E2 tptp.int) (C tptp.int) (B 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) E2)) 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 B) E2)) 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) B)) E2)) C)) D)))) (forall ((A tptp.real) (E2 tptp.real) (C tptp.real) (B 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) E2)) 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 B) E2)) 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) B)) E2)) C)) D)))) (forall ((A tptp.rat) (E2 tptp.rat) (C tptp.rat) (B 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) E2)) 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 B) E2)) 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 B) A)) E2)) D))))) (forall ((A tptp.int) (E2 tptp.int) (C tptp.int) (B 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) E2)) 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 B) E2)) 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 B) A)) E2)) D))))) (forall ((A tptp.real) (E2 tptp.real) (C tptp.real) (B 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) E2)) 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 B) E2)) 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 B) A)) E2)) D))))) (forall ((Z tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (tptp.plus_plus_complex (tptp.divide1717551699836669952omplex A Z) B))) (let ((_let_2 (= Z tptp.zero_zero_complex))) (and (=> _let_2 (= _let_1 B)) (=> (not _let_2) (= _let_1 (tptp.divide1717551699836669952omplex (tptp.plus_plus_complex A (tptp.aa_complex_complex (tptp.times_times_complex B) Z)) Z))))))) (forall ((Z tptp.real) (A tptp.real) (B 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)) B))) (let ((_let_2 (= Z tptp.zero_zero_real))) (and (=> _let_2 (= _let_1 B)) (=> (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 B) Z))) Z))))))) (forall ((Z tptp.rat) (A tptp.rat) (B 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)) B))) (let ((_let_2 (= Z tptp.zero_zero_rat))) (and (=> _let_2 (= _let_1 B)) (=> (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 B) Z))) Z))))))) (forall ((Z tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (tptp.plus_plus_complex A (tptp.divide1717551699836669952omplex B Z)))) (let ((_let_2 (= Z tptp.zero_zero_complex))) (and (=> _let_2 (= _let_1 A)) (=> (not _let_2) (= _let_1 (tptp.divide1717551699836669952omplex (tptp.plus_plus_complex (tptp.aa_complex_complex (tptp.times_times_complex A) Z) B) Z))))))) (forall ((Z tptp.real) (A tptp.real) (B 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 B) 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)) B)) Z))))))) (forall ((Z tptp.rat) (A tptp.rat) (B 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 B) 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)) B)) Z))))))) (forall ((Y4 tptp.complex) (Z tptp.complex) (X tptp.complex) (W tptp.complex)) (=> (not (= Y4 tptp.zero_zero_complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (tptp.plus_plus_complex (tptp.divide1717551699836669952omplex X Y4) (tptp.divide1717551699836669952omplex W Z)) (tptp.divide1717551699836669952omplex (tptp.plus_plus_complex (tptp.aa_complex_complex (tptp.times_times_complex X) Z) (tptp.aa_complex_complex (tptp.times_times_complex W) Y4)) (tptp.aa_complex_complex (tptp.times_times_complex Y4) Z)))))) (forall ((Y4 tptp.real) (Z tptp.real) (X tptp.real) (W tptp.real)) (=> (not (= Y4 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) Y4)) (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) Y4))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real Y4) Z)))))) (forall ((Y4 tptp.rat) (Z tptp.rat) (X tptp.rat) (W tptp.rat)) (=> (not (= Y4 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) Y4)) (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) Y4))) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat Y4) Z)))))) (forall ((Y4 tptp.complex) (X tptp.complex) (Z tptp.complex)) (=> (not (= Y4 tptp.zero_zero_complex)) (= (tptp.plus_plus_complex (tptp.divide1717551699836669952omplex X Y4) Z) (tptp.divide1717551699836669952omplex (tptp.plus_plus_complex X (tptp.aa_complex_complex (tptp.times_times_complex Z) Y4)) Y4)))) (forall ((Y4 tptp.real) (X tptp.real) (Z tptp.real)) (=> (not (= Y4 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) Y4)) 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) Y4))) Y4)))) (forall ((Y4 tptp.rat) (X tptp.rat) (Z tptp.rat)) (=> (not (= Y4 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) Y4)) 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) Y4))) Y4)))) (forall ((Y4 tptp.complex) (Z tptp.complex) (X tptp.complex)) (=> (not (= Y4 tptp.zero_zero_complex)) (= (tptp.plus_plus_complex Z (tptp.divide1717551699836669952omplex X Y4)) (tptp.divide1717551699836669952omplex (tptp.plus_plus_complex X (tptp.aa_complex_complex (tptp.times_times_complex Z) Y4)) Y4)))) (forall ((Y4 tptp.real) (Z tptp.real) (X tptp.real)) (=> (not (= Y4 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) Y4)) (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) Y4))) Y4)))) (forall ((Y4 tptp.rat) (Z tptp.rat) (X tptp.rat)) (=> (not (= Y4 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) Y4)) (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) Y4))) Y4)))) (forall ((Z tptp.complex) (X tptp.complex) (Y4 tptp.complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (tptp.plus_plus_complex X (tptp.divide1717551699836669952omplex Y4 Z)) (tptp.divide1717551699836669952omplex (tptp.plus_plus_complex (tptp.aa_complex_complex (tptp.times_times_complex X) Z) Y4) Z)))) (forall ((Z tptp.real) (X tptp.real) (Y4 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 Y4) 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)) Y4)) Z)))) (forall ((Z tptp.rat) (X tptp.rat) (Y4 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 Y4) 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)) Y4)) Z)))) (forall ((Z tptp.complex) (X tptp.complex) (Y4 tptp.complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (tptp.plus_plus_complex (tptp.divide1717551699836669952omplex X Z) Y4) (tptp.divide1717551699836669952omplex (tptp.plus_plus_complex X (tptp.aa_complex_complex (tptp.times_times_complex Y4) Z)) Z)))) (forall ((Z tptp.real) (X tptp.real) (Y4 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)) Y4) (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 Y4) Z))) Z)))) (forall ((Z tptp.rat) (X tptp.rat) (Y4 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)) Y4) (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 Y4) Z))) Z)))) (forall ((A tptp.real) (E2 tptp.real) (C tptp.real) (B 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) E2)) 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 B) E2)) 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) B)) E2)) C)) D)))) (forall ((A tptp.rat) (E2 tptp.rat) (C tptp.rat) (B 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) E2)) 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 B) E2)) 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) B)) E2)) C)) D)))) (forall ((A tptp.int) (E2 tptp.int) (C tptp.int) (B 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) E2)) 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 B) E2)) 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) B)) E2)) C)) D)))) (forall ((A tptp.real) (E2 tptp.real) (C tptp.real) (B 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) E2)) 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 B) E2)) 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 B) A)) E2)) D))))) (forall ((A tptp.rat) (E2 tptp.rat) (C tptp.rat) (B 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) E2)) 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 B) E2)) 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 B) A)) E2)) D))))) (forall ((A tptp.int) (E2 tptp.int) (C tptp.int) (B 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) E2)) 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 B) E2)) 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 B) A)) E2)) D))))) (forall ((B tptp.nat) (A tptp.nat)) (=> (not (= B 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) B)) B) (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) B)) tptp.one_one_nat)))) (forall ((B tptp.int) (A tptp.int)) (=> (not (= B tptp.zero_zero_int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) B)) B) (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.divide_divide_int A) B)) tptp.one_one_int)))) (forall ((B tptp.nat) (A tptp.nat)) (=> (not (= B 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 B) A)) B) (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) B)) tptp.one_one_nat)))) (forall ((B tptp.int) (A tptp.int)) (=> (not (= B tptp.zero_zero_int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int B) A)) B) (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.divide_divide_int A) B)) tptp.one_one_int)))) (forall ((X tptp.nat) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (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.vEBT_VEBT_high X) N)) (tptp.aa_nat_nat _let_1 M))))))))) (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A))) (=> (tptp.pp (tptp.aa_real_bool _let_1 B)) (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) B)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real tptp.one_one_real) tptp.one_one_real))))))) (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 B)) (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) B)) (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) (B tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B)) (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) B)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real tptp.one_one_real) tptp.one_one_real))) B)))) (forall ((A tptp.rat) (B tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B)) (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) B)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat tptp.one_one_rat) tptp.one_one_rat))) B)))) (forall ((X tptp.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.plus_plus_complex X tptp.one_one_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 ((P tptp.fun_Co8822979462182099027r_bool) (L tptp.code_integer)) (= (exists ((X5 tptp.code_integer)) (tptp.pp (tptp.aa_Code_integer_bool P (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger L) X5)))) (exists ((X5 tptp.code_integer)) (and (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer L) (tptp.plus_p5714425477246183910nteger X5 tptp.zero_z3403309356797280102nteger))) (tptp.pp (tptp.aa_Code_integer_bool P X5)))))) (forall ((P tptp.fun_complex_bool) (L tptp.complex)) (= (exists ((X5 tptp.complex)) (tptp.pp (tptp.aa_complex_bool P (tptp.aa_complex_complex (tptp.times_times_complex L) X5)))) (exists ((X5 tptp.complex)) (and (tptp.pp (tptp.aa_complex_bool (tptp.dvd_dvd_complex L) (tptp.plus_plus_complex X5 tptp.zero_zero_complex))) (tptp.pp (tptp.aa_complex_bool P X5)))))) (forall ((P tptp.fun_real_bool) (L tptp.real)) (= (exists ((X5 tptp.real)) (tptp.pp (tptp.aa_real_bool P (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real L) X5)))) (exists ((X5 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 X5) tptp.zero_zero_real))) (tptp.pp (tptp.aa_real_bool P X5)))))) (forall ((P tptp.fun_rat_bool) (L tptp.rat)) (= (exists ((X5 tptp.rat)) (tptp.pp (tptp.aa_rat_bool P (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat L) X5)))) (exists ((X5 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 X5) tptp.zero_zero_rat))) (tptp.pp (tptp.aa_rat_bool P X5)))))) (forall ((P tptp.fun_nat_bool) (L tptp.nat)) (= (exists ((X5 tptp.nat)) (tptp.pp (tptp.aa_nat_bool P (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat L) X5)))) (exists ((X5 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 X5) tptp.zero_zero_nat))) (tptp.pp (tptp.aa_nat_bool P X5)))))) (forall ((P tptp.fun_int_bool) (L tptp.int)) (= (exists ((X5 tptp.int)) (tptp.pp (tptp.aa_int_bool P (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int L) X5)))) (exists ((X5 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 X5) tptp.zero_zero_int))) (tptp.pp (tptp.aa_int_bool P X5)))))) (forall ((D tptp.code_integer) (D3 tptp.code_integer) (T tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer D) D3)) (forall ((X4 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 X4 T))) (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.plus_p5714425477246183910nteger (tptp.minus_8373710615458151222nteger X4 (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger K4) D3)) T)))))))) (forall ((D tptp.real) (D3 tptp.real) (T tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.dvd_dvd_real D) D3)) (forall ((X4 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 X4) 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 X4) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real K4) D3))) T)))))))) (forall ((D tptp.rat) (D3 tptp.rat) (T tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.dvd_dvd_rat D) D3)) (forall ((X4 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 X4) 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 X4) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat K4) D3))) T)))))))) (forall ((D tptp.int) (D3 tptp.int) (T tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int D) D3)) (forall ((X4 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 X4) 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 X4) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int K4) D3))) T)))))))) (forall ((D tptp.code_integer) (D3 tptp.code_integer) (T tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer D) D3)) (forall ((X4 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 X4 T)))) (not (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.plus_p5714425477246183910nteger (tptp.minus_8373710615458151222nteger X4 (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger K4) D3)) T))))))))) (forall ((D tptp.real) (D3 tptp.real) (T tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.dvd_dvd_real D) D3)) (forall ((X4 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 X4) 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 X4) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real K4) D3))) T))))))))) (forall ((D tptp.rat) (D3 tptp.rat) (T tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.dvd_dvd_rat D) D3)) (forall ((X4 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 X4) 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 X4) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat K4) D3))) T))))))))) (forall ((D tptp.int) (D3 tptp.int) (T tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int D) D3)) (forall ((X4 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 X4) 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 X4) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int K4) D3))) T))))))))) (forall ((N tptp.num)) (let ((_let_1 (tptp.numera6690914467698888265omplex N))) (= (tptp.numera6690914467698888265omplex (tptp.aa_num_num tptp.bit1 N)) (tptp.plus_plus_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 ((P tptp.fun_nat_bool) (A tptp.nat) (B tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool P (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat A) B))) (not (or (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) B)) (not (tptp.pp (tptp.aa_nat_bool P tptp.zero_zero_nat)))) (exists ((D4 tptp.nat)) (and (= A (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat B) D4)) (not (tptp.pp (tptp.aa_nat_bool P D4))))))))) (forall ((P tptp.fun_nat_bool) (A tptp.nat) (B tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool P (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat A) B))) (and (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) B)) (tptp.pp (tptp.aa_nat_bool P tptp.zero_zero_nat))) (forall ((D4 tptp.nat)) (=> (= A (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat B) D4)) (tptp.pp (tptp.aa_nat_bool P D4))))))) (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 ((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 ((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.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.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.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.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 ((A tptp.nat) (B tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (exists ((D2 tptp.nat) (X3 tptp.nat) (Y 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 B)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) X3) (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 B) Y)) D2))))))) (forall ((X tptp.rat) (A tptp.rat) (Y4 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 Y4) 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) Y4))) A))))))))) (forall ((X tptp.int) (A tptp.int) (Y4 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 Y4) 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) Y4))) A))))))))) (forall ((X tptp.real) (A tptp.real) (Y4 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 Y4) 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) Y4))) A))))))))) (forall ((Z tptp.complex)) (= (tptp.aa_complex_complex (tptp.times_times_complex (tptp.numera6690914467698888265omplex (tptp.aa_num_num tptp.bit0 tptp.one))) Z) (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.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) (B tptp.complex)) (= (tptp.plus_plus_complex A (tptp.plus_plus_complex A B)) (tptp.plus_plus_complex (tptp.aa_complex_complex (tptp.times_times_complex (tptp.numera6690914467698888265omplex (tptp.aa_num_num tptp.bit0 tptp.one))) A) B))) (forall ((A tptp.real) (B 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 B)) (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)) B)))) (forall ((A tptp.rat) (B 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 B)) (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)) B)))) (forall ((A tptp.nat) (B 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 B)) (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)) B)))) (forall ((A tptp.int) (B 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 B)) (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)) B)))) (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 ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_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 B))) (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.plus_p5714425477246183910nteger A B))))))) (forall ((A tptp.nat) (B 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 B))) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) B))))))) (forall ((A tptp.int) (B 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 B))) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) B))))))) (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))) _let_159 (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 ((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 ((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 ((I2 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) I2)) J3)) (tptp.pp (tptp.aa_nat_bool P I2)))))))))) (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 ((Q2 tptp.nat) (N tptp.nat) (R2 tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat R2) 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 ((X tptp.rat) (A tptp.rat) (Y4 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 Y4) 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) Y4))) A))))))))) (forall ((X tptp.int) (A tptp.int) (Y4 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 Y4) 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) Y4))) A))))))))) (forall ((X tptp.real) (A tptp.real) (Y4 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 Y4) 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) Y4))) A))))))))) (forall ((U tptp.rat) (V tptp.rat) (R2 tptp.rat) (S2 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) R2)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat R2) S2)) (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 R2) (tptp.aa_rat_rat (tptp.minus_minus_rat V) U))) S2))) V)))))) (forall ((U tptp.real) (V tptp.real) (R2 tptp.real) (S2 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) R2)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real R2) S2)) (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 R2) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real V) U))) S2))) V)))))) (forall ((X tptp.real) (Y4 tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X))) (=> (tptp.pp (tptp.aa_real_bool _let_1 Y4)) (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) Y4)) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))))))) (forall ((X tptp.rat) (Y4 tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 Y4)) (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) Y4)) (tptp.aa_num_rat tptp.numeral_numeral_rat (tptp.aa_num_num tptp.bit0 tptp.one)))))))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (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.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 ((A tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (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.aa_int_fun_int_int tptp.divide_divide_int A))) (= (tptp.aa_int_int (tptp.aa_int_fun_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 ((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 ((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 ((X tptp.rat) (Y4 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 Y4) _let_1)))))) (forall ((X tptp.int) (Y4 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 Y4) _let_1)))))) (forall ((X tptp.real) (Y4 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 Y4) _let_1)))))) (forall ((X tptp.rat) (Y4 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 Y4) _let_1))) tptp.zero_zero_rat)) (and (= X tptp.zero_zero_rat) (= Y4 tptp.zero_zero_rat))))) (forall ((X tptp.int) (Y4 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 Y4) _let_1))) tptp.zero_zero_int)) (and (= X tptp.zero_zero_int) (= Y4 tptp.zero_zero_int))))) (forall ((X tptp.real) (Y4 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 Y4) _let_1))) tptp.zero_zero_real)) (and (= X tptp.zero_zero_real) (= Y4 tptp.zero_zero_real))))) (forall ((X tptp.real) (Y4 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 Y4) _let_1))) tptp.zero_zero_real))))) (forall ((X tptp.rat) (Y4 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 Y4) _let_1))) tptp.zero_zero_rat))))) (forall ((X tptp.int) (Y4 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 Y4) _let_1))) tptp.zero_zero_int))))) (forall ((X tptp.real) (Y4 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 Y4) _let_1)))) (or (not (= X tptp.zero_zero_real)) (not (= Y4 tptp.zero_zero_real)))))) (forall ((X tptp.rat) (Y4 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 Y4) _let_1)))) (or (not (= X tptp.zero_zero_rat)) (not (= Y4 tptp.zero_zero_rat)))))) (forall ((X tptp.int) (Y4 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 Y4) _let_1)))) (or (not (= X tptp.zero_zero_int)) (not (= Y4 tptp.zero_zero_int)))))) (forall ((A tptp.code_integer)) (=> (not (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))) A))) (not (forall ((B2 tptp.code_integer)) (not (= A (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))) B2) 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 ((B2 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))) B2)) 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 ((B2 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))) B2)) tptp.one_one_int))))))) (forall ((X tptp.complex) (Y4 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.plus_plus_complex X Y4)) _let_2) (tptp.plus_plus_complex (tptp.plus_plus_complex (tptp.aa_nat_complex (tptp.power_power_complex X) _let_2) (tptp.aa_nat_complex (tptp.power_power_complex Y4) _let_2)) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_complex_complex (tptp.times_times_complex (tptp.numera6690914467698888265omplex _let_1)) X)) Y4)))))) (forall ((X tptp.real) (Y4 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) Y4)) _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 Y4) _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)) Y4)))))) (forall ((X tptp.rat) (Y4 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) Y4)) _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 Y4) _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)) Y4)))))) (forall ((X tptp.nat) (Y4 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.power_power_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat X) Y4)) _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.power_power_nat X) _let_1)) (tptp.aa_nat_nat (tptp.power_power_nat Y4) _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)) Y4))))) (forall ((X tptp.int) (Y4 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) Y4)) _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 Y4) _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)) Y4)))))) (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.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.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.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 ((P tptp.fun_nat_bool)) (=> (not (tptp.pp (tptp.aa_nat_bool P tptp.zero_zero_nat))) (=> (exists ((X_13 tptp.nat)) (tptp.pp (tptp.aa_nat_bool P X_13))) (exists ((N2 tptp.nat)) (and (not (tptp.pp (tptp.aa_nat_bool P N2))) (tptp.pp (tptp.aa_nat_bool P (tptp.aa_nat_nat tptp.suc N2)))))))) (forall ((X tptp.rat) (Y4 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)) Y4)) (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 Y4) _let_2))))))) (forall ((X tptp.real) (Y4 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)) Y4)) (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 Y4) _let_2))))))) (forall ((X tptp.complex) (Y4 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.minus_minus_complex X Y4)) _let_2) (tptp.minus_minus_complex (tptp.plus_plus_complex (tptp.aa_nat_complex (tptp.power_power_complex X) _let_2) (tptp.aa_nat_complex (tptp.power_power_complex Y4) _let_2)) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_complex_complex (tptp.times_times_complex (tptp.numera6690914467698888265omplex _let_1)) X)) Y4)))))) (forall ((X tptp.real) (Y4 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) Y4)) _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 Y4) _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)) Y4)))))) (forall ((X tptp.rat) (Y4 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) Y4)) _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 Y4) _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)) Y4)))))) (forall ((X tptp.int) (Y4 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) Y4)) _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 Y4) _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)) Y4)))))) (forall ((B 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))) B)) (=> (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.power_power_nat B))) (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 ((B 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 B)) (=> (tptp.pp (tptp.aa_nat_bool _let_1 K)) (exists ((N2 tptp.nat)) (let ((_let_1 (tptp.power_power_nat B))) (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 ((U tptp.rat) (X tptp.rat) (Y4 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) Y4)) (=> (tptp.pp (tptp.aa_rat_bool _let_2 X)) (=> (tptp.pp (tptp.aa_rat_bool _let_2 Y4)) (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) Y4)) (tptp.aa_num_rat tptp.numeral_numeral_rat _let_1)))))))))) (forall ((U tptp.real) (X tptp.real) (Y4 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) Y4)) (=> (tptp.pp (tptp.aa_real_bool _let_2 X)) (=> (tptp.pp (tptp.aa_real_bool _let_2 Y4)) (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) Y4)) (tptp.aa_num_real tptp.numeral_numeral_real _let_1)))))))))) (forall ((X tptp.real) (Y4 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 Y4) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N2)) X)))))) (forall ((X tptp.rat) (Y4 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 Y4) (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.nat) (N tptp.nat) (Y4 tptp.nat)) (let ((_let_1 (tptp.aa_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.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 Y4) _let_1)) X)) N) X)))) (forall ((A tptp.real) (B tptp.real) (P tptp.fun_re1255401033344146673l_bool)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) B)) (=> (forall ((A3 tptp.real) (B2 tptp.real) (C3 tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool P A3))) (=> (tptp.pp (tptp.aa_real_bool _let_1 B2)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool P B2) C3)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A3) B2)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real B2) C3)) (tptp.pp (tptp.aa_real_bool _let_1 C3)))))))) (=> (forall ((X3 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) X3)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X3) B)) (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) (B2 tptp.real)) (=> (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A3) X3)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X3) 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 B2) A3)) D5))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool P A3) B2))))))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool P A) B)))))) (forall ((Z tptp.rat) (X tptp.rat) (Y4 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 Y4) Z))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) Y4))))) (forall ((Z tptp.int) (X tptp.int) (Y4 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 Y4) Z))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X) Y4))))) (forall ((Z tptp.real) (X tptp.real) (Y4 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 Y4) Z))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) Y4))))) (forall ((Z tptp.rat) (X tptp.rat) (Y4 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 Y4))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) Y4)))))) (forall ((Z tptp.int) (X tptp.int) (Y4 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 Y4))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X) Y4)))))) (forall ((Z tptp.real) (X tptp.real) (Y4 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 Y4))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) Y4)))))) (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.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.minus_minus_complex (tptp.divide1717551699836669952omplex (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)))))))))))) (= (tptp.neg_nu8557863876264182079omplex tptp.one_one_complex) _let_104) (= (tptp.aa_real_real tptp.neg_nu8295874005876285629c_real tptp.one_one_real) _let_81) (= (tptp.aa_rat_rat tptp.neg_nu5219082963157363817nc_rat tptp.one_one_rat) _let_103) (= (tptp.neg_nu5851722552734809277nc_int tptp.one_one_int) _let_105) (= (tptp.neg_nu7009210354673126013omplex tptp.one_one_complex) _let_76) (= (tptp.aa_real_real tptp.neg_numeral_dbl_real tptp.one_one_real) _let_40) (= (tptp.aa_rat_rat tptp.neg_numeral_dbl_rat tptp.one_one_rat) _let_130) (= (tptp.neg_numeral_dbl_int tptp.one_one_int) _let_63) (forall ((M tptp.num) (N tptp.num)) (= (tptp.aa_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.plus_plus_num M) N)))) (= (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.neg_numeral_dbl_int tptp.zero_zero_int) tptp.zero_zero_int) (= (tptp.aa_num_num (tptp.plus_plus_num tptp.one) tptp.one) _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) (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 ((M tptp.num) (N tptp.num)) (= (tptp.aa_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.plus_plus_num M) N)))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.aa_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.plus_plus_num M) N)))) (forall ((K tptp.num)) (= (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.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.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.neg_nu5851722552734809277nc_int tptp.zero_zero_int) tptp.one_one_int) (forall ((K tptp.num)) (= (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.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 ((A tptp.complex) (M tptp.num) (N tptp.num) (B 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))) B)) (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.plus_plus_num M) N)))) B)))) (forall ((A tptp.real) (M tptp.num) (N tptp.num) (B 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))) B)) (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.plus_plus_num M) N)))) B)))) (forall ((A tptp.rat) (M tptp.num) (N tptp.num) (B 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))) B)) (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.plus_plus_num M) N)))) B)))) (forall ((A tptp.nat) (M tptp.num) (N tptp.num) (B tptp.nat)) (let ((_let_1 (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))) B)) (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.plus_plus_num M) N)))) B)))) (forall ((A tptp.int) (M tptp.num) (N tptp.num) (B 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))) B)) (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.plus_plus_num M) N)))) B)))) (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.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.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.plus_plus_num M) N)))))) (forall ((A tptp.nat) (M tptp.num) (N tptp.num)) (let ((_let_1 (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.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.plus_plus_num M) N)))))) (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.plus_plus_num N) tptp.one)))) (forall ((N tptp.num)) (= (tptp.aa_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.plus_plus_num tptp.one) (tptp.aa_num_num tptp.bit1 N)) (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num (tptp.plus_plus_num N) tptp.one)))) (forall ((M tptp.num)) (= (tptp.aa_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.plus_plus_num (tptp.aa_num_num tptp.bit1 M)) tptp.one) (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num (tptp.plus_plus_num M) tptp.one)))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.aa_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.plus_plus_num (tptp.aa_num_num (tptp.plus_plus_num M) N)) tptp.one)))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.aa_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.plus_plus_num (tptp.aa_num_num (tptp.plus_plus_num M) N)) (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num (tptp.times_times_num M) N)))))) (forall ((N tptp.num)) (= (tptp.aa_num_num (tptp.plus_plus_num tptp.one) N) (tptp.aa_num_num (tptp.plus_plus_num N) tptp.one))) (forall ((K tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int K) tptp.zero_zero_int) K)) (forall ((L tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int tptp.zero_zero_int) L) L)) (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 ((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 ((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.neg_numeral_dbl_int X) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int X) X))) (forall ((Z tptp.int)) (not (= (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))) (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) (B tptp.nat)) (= (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) B)) (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 B)))) (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 ((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)) (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 ((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 ((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 ((N4 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 N4)))))) (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 ((Z tptp.extended_enat) (Y4 tptp.extended_enat) (X tptp.extended_enat)) (=> (tptp.pp (tptp.aa_Ext2772979874139974381t_bool (tptp.ord_le2932123472753598470d_enat Z) Y4)) (= (tptp.plus_p3455044024723400733d_enat X (tptp.minus_3235023915231533773d_enat Y4 Z)) (tptp.minus_3235023915231533773d_enat (tptp.plus_p3455044024723400733d_enat X Y4) Z)))) (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 ((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 ((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 ((N4 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 N4))))))) (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)) (= (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 ((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 ((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 ((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.plus_plus_num V) tptp.one))) N))) (forall ((X tptp.complex)) (= (tptp.neg_nu8557863876264182079omplex X) (tptp.plus_plus_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.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 ((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 ((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 ((B tptp.int) (Q5 tptp.int) (R4 tptp.int) (Q2 tptp.int) (R2 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_int B))) (let ((_let_2 (tptp.aa_int_fun_int_int tptp.times_times_int B))) (=> (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)) R2))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int R2) tptp.zero_zero_int)) (=> (tptp.pp (tptp.aa_int_bool _let_1 R2)) (=> (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 ((B tptp.int) (Q5 tptp.int) (R4 tptp.int) (Q2 tptp.int) (R2 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.times_times_int B))) (=> (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)) R2))) (=> (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) B)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int R2) B)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Q5) Q2)))))))) (forall ((B tptp.int) (Q2 tptp.int) (R2 tptp.int) (B4 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 B4) 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 B) Q2)) R2) _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 R2) B)) (=> (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) B4)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B4) B)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Q5) Q2)))))))))) (forall ((B tptp.int) (Q2 tptp.int) (R2 tptp.int) (B4 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 B4) 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 B) Q2)) R2) _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) B4)) (=> (tptp.pp (tptp.aa_int_bool _let_1 R2)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) B4)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B4) B)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Q2) Q5))))))))))) (forall ((B4 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 B4) Q5)) R4))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int R4) B4)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) B4)) (tptp.pp (tptp.aa_int_bool _let_1 Q5))))))) (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 ((X3 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool P X3)) (tptp.pp (tptp.aa_int_bool P (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int X3) D))))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) K)) (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) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int K) D)))))))))) (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 ((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.int) (B tptp.int) (Q2 tptp.int) (R2 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 B) Q2)) R2)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) R2)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int R2) B)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A) B) Q2))))) (forall ((A tptp.int) (B tptp.int) (Q2 tptp.int) (R2 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 B) Q2)) R2)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int R2) tptp.zero_zero_int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B) R2)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A) B) 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.aa_int_fun_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 ((I2 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) I2)) J3))) (tptp.pp (tptp.aa_int_bool P I2))))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int K) tptp.zero_zero_int)) (forall ((I2 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) I2)) J3))) (tptp.pp (tptp.aa_int_bool P I2)))))))) (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.aa_int_fun_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.aa_int_fun_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.real) (C tptp.real) (B 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 B) 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 B) _let_2)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real C) _let_2)))))))) (forall ((X tptp.nat) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (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.vEBT_VEBT_low X) N)) (tptp.aa_nat_nat _let_1 N))))))))) (forall ((A tptp.int) (B 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.aa_int_fun_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 B))) (tptp.aa_int_int _let_1 A)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int B) tptp.one_one_int)) A))))) (forall ((A tptp.int) (B 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.aa_int_fun_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 B))) (tptp.aa_int_int _let_1 A)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int B) A))))) (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 ((Z tptp.real) (X tptp.real) (Y4 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 Y4) Z))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Y4))))) (forall ((Z tptp.rat) (X tptp.rat) (Y4 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 Y4) Z))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) Y4))))) (forall ((Z tptp.int) (X tptp.int) (Y4 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 Y4) Z))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) Y4))))) (forall ((B 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 B) 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 B) A)) _let_1)))) (forall ((A tptp.real) (B 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) B)) _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 B) A)) _let_1)))) (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.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 ((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) (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 ((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 ((N tptp.nat)) (let ((_let_1 (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N))) (= (tptp.aa_real_real tptp.real_V7735802525324610683m_real _let_1) _let_1))) (forall ((N tptp.nat)) (= (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex N)) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N))) (forall ((X tptp.real)) (= (= (tptp.aa_real_real tptp.real_V7735802525324610683m_real X) tptp.zero_zero_real) (= X tptp.zero_zero_real))) (forall ((X tptp.complex)) (= (= (tptp.aa_complex_real tptp.real_V1022390504157884413omplex X) tptp.zero_zero_real) (= X tptp.zero_zero_complex))) (= (tptp.aa_real_real tptp.real_V7735802525324610683m_real tptp.zero_zero_real) tptp.zero_zero_real) (= (tptp.aa_complex_real tptp.real_V1022390504157884413omplex tptp.zero_zero_complex) tptp.zero_zero_real) (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) (B tptp.real)) (= (tptp.aa_real_real tptp.real_V7735802525324610683m_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A) B)) (tptp.aa_real_real tptp.real_V7735802525324610683m_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real B) A)))) (forall ((A tptp.complex) (B tptp.complex)) (= (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.minus_minus_complex A B)) (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.minus_minus_complex B A)))) (forall ((A tptp.real) (R2 tptp.real) (B tptp.real) (S2 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)) R2)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real B)) 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_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) B))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real R2) S2)))))) (forall ((A tptp.complex) (R2 tptp.real) (B tptp.complex) (S2 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)) R2)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex B)) S2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.plus_plus_complex A B))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real R2) S2)))))) (forall ((X tptp.real) (Y4 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) Y4))) (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 Y4))))) (forall ((X tptp.complex) (Y4 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.plus_plus_complex X Y4))) (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 Y4))))) (forall ((X tptp.real) (Y4 tptp.real) (E2 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 Y4))) E2)) (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) Y4))) E2)))) (forall ((X tptp.complex) (Y4 tptp.complex) (E2 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 Y4))) E2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.plus_plus_complex X Y4))) E2)))) (forall ((A tptp.real) (B 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) B))) C)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real B)) (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) (B 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.plus_plus_complex A B))) C)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex B)) (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) (Y4 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 Y4))) 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 Y4) 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) (Y4 tptp.complex) (E1 tptp.real) (Z tptp.complex) (E22 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.minus_minus_complex X Y4))) E1)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.minus_minus_complex Y4 Z))) E22)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.minus_minus_complex X Z))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real E1) E22)))))) (forall ((X tptp.real) (Y4 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 Y4)) (tptp.aa_real_real tptp.real_V7735802525324610683m_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real X) Y4)))))) (forall ((X tptp.complex) (Y4 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 Y4)) (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.minus_minus_complex X Y4)))))) (forall ((A tptp.real) (B 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) B))) (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 B))))) (forall ((A tptp.complex) (B 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.minus_minus_complex A B))) (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 B))))) (forall ((X tptp.real) (Y4 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 Y4))) 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 Y4) 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) (Y4 tptp.complex) (E1 tptp.real) (Z tptp.complex) (E22 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.minus_minus_complex X Y4))) E1)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.minus_minus_complex Y4 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.minus_minus_complex X Z))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real E1) E22)))))) (forall ((X tptp.real) (Y4 tptp.real) (E2 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 Y4))) E2)) (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) Y4))) E2)))) (forall ((X tptp.complex) (Y4 tptp.complex) (E2 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 Y4))) E2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.minus_minus_complex X Y4))) E2)))) (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) (Y4 tptp.real)) (= (tptp.aa_real_real tptp.real_V7735802525324610683m_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real X) Y4)) (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 Y4)))) (forall ((X tptp.complex) (Y4 tptp.complex)) (= (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.aa_complex_complex (tptp.times_times_complex X) Y4)) (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 Y4)))) (forall ((A tptp.real) (B tptp.real)) (= (tptp.aa_real_real tptp.real_V7735802525324610683m_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real A) B)) (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 B)))) (forall ((A tptp.complex) (B tptp.complex)) (= (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.divide1717551699836669952omplex A B)) (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 B)))) (forall ((A tptp.real) (B 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) B)) (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 B) D)))))) (forall ((A tptp.complex) (B 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.minus_minus_complex (tptp.plus_plus_complex A B) (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.minus_minus_complex A C))) (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.minus_minus_complex B D)))))) (forall ((B tptp.real) (A tptp.real)) (=> (not (= B 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) B)) (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 B))))) (forall ((B tptp.complex) (A tptp.complex)) (=> (not (= B tptp.zero_zero_complex)) (= (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.divide1717551699836669952omplex A B)) (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 B))))) (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) (R2 tptp.real) (Y4 tptp.real) (S2 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)) R2)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real Y4)) S2)) (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) Y4))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real R2) S2)))))) (forall ((X tptp.complex) (R2 tptp.real) (Y4 tptp.complex) (S2 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex X)) R2)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex Y4)) S2)) (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) Y4))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real R2) S2)))))) (forall ((X tptp.real) (Y4 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) Y4))) (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 Y4))))) (forall ((X tptp.complex) (Y4 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) Y4))) (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 Y4))))) (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) (B 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 B))) (tptp.aa_real_real tptp.real_V7735802525324610683m_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) B))))) (forall ((A tptp.complex) (B 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 B))) (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.plus_plus_complex A B))))) (forall ((A tptp.real) (B 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 B))) (tptp.aa_real_real tptp.real_V7735802525324610683m_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A) B))))) (forall ((A tptp.complex) (B 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 B))) (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.minus_minus_complex A B))))) (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 ((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.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.minus_minus_complex Z W)))))))) (= (tptp.aa_real_real tptp.arcosh_real tptp.one_one_real) tptp.zero_zero_real) (= (tptp.aa_real_real tptp.artanh_real tptp.zero_zero_real) tptp.zero_zero_real) (= (tptp.aa_real_real tptp.arsinh_real tptp.zero_zero_real) tptp.zero_zero_real) (forall ((X tptp.nat) (N tptp.nat)) (= (tptp.aa_nat_nat (tptp.vEBT_VEBT_low X) N) (tptp.aa_nat_nat (tptp.modulo_modulo_nat X) (tptp.aa_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.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.power_power_nat _let_3) _let_4))) (tptp.aa_nat_complex (tptp.comm_s2602460028002588243omplex Z) N))) (tptp.aa_nat_complex (tptp.comm_s2602460028002588243omplex (tptp.plus_plus_complex Z (tptp.divide1717551699836669952omplex tptp.one_one_complex _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.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 ((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.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 ((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.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 ((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.aa_nat_fun_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.aa_int_fun_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.aa_bool_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 ((A tptp.code_integer)) (let ((_let_1 (tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.bit_se1345352211410354436nteger tptp.zero_zero_nat A) (tptp.plus_p5714425477246183910nteger (tptp.aa_bool_Code_integer 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.nat) (B tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.modulo_modulo_nat A) B))) (= (tptp.aa_nat_nat (tptp.modulo_modulo_nat _let_1) B) _let_1))) (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (tptp.modulo_modulo_int A B))) (= (tptp.modulo_modulo_int _let_1 B) _let_1))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (tptp.modulo364778990260209775nteger A B))) (= (tptp.modulo364778990260209775nteger _let_1 B) _let_1))) (forall ((A tptp.nat)) (= (tptp.aa_nat_nat (tptp.modulo_modulo_nat A) A) tptp.zero_zero_nat)) (forall ((A tptp.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.modulo_modulo_nat A) tptp.zero_zero_nat) A)) (forall ((A tptp.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.modulo_modulo_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)) (forall ((A tptp.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.modulo_modulo_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)) (forall ((A tptp.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) (B tptp.nat)) (= (tptp.aa_nat_nat (tptp.modulo_modulo_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) B)) B) (tptp.aa_nat_nat (tptp.modulo_modulo_nat A) B))) (forall ((A tptp.int) (B tptp.int)) (= (tptp.modulo_modulo_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) B) B) (tptp.modulo_modulo_int A B))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (tptp.modulo364778990260209775nteger (tptp.plus_p5714425477246183910nteger A B) B) (tptp.modulo364778990260209775nteger A B))) (forall ((B tptp.nat) (A tptp.nat)) (= (tptp.aa_nat_nat (tptp.modulo_modulo_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat B) A)) B) (tptp.aa_nat_nat (tptp.modulo_modulo_nat A) B))) (forall ((B tptp.int) (A tptp.int)) (= (tptp.modulo_modulo_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int B) A) B) (tptp.modulo_modulo_int A B))) (forall ((B tptp.code_integer) (A tptp.code_integer)) (= (tptp.modulo364778990260209775nteger (tptp.plus_p5714425477246183910nteger B A) B) (tptp.modulo364778990260209775nteger A B))) (forall ((A tptp.int) (B tptp.int)) (= (tptp.modulo_modulo_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) B) B) (tptp.modulo_modulo_int A B))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (tptp.modulo364778990260209775nteger (tptp.minus_8373710615458151222nteger A B) B) (tptp.modulo364778990260209775nteger A B))) (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_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.zero_n3304061248610475627l_real P)) (tptp.zero_n3304061248610475627l_real 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.aa_bool_nat tptp.zero_n2687167440665602831ol_nat P)) (tptp.aa_bool_nat 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.aa_bool_Code_integer tptp.zero_n356916108424825756nteger P)) (tptp.aa_bool_Code_integer tptp.zero_n356916108424825756nteger Q))) (=> (tptp.pp P) (tptp.pp Q)))) (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.aa_bool_nat 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.aa_bool_Code_integer tptp.zero_n356916108424825756nteger P) tptp.zero_z3403309356797280102nteger) (not (tptp.pp P)))) (= (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.aa_bool_nat 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.aa_bool_Code_integer tptp.zero_n356916108424825756nteger tptp.fFalse) tptp.zero_z3403309356797280102nteger) (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.aa_bool_nat tptp.zero_n2687167440665602831ol_nat P)) (tptp.aa_bool_nat 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.aa_bool_Code_integer tptp.zero_n356916108424825756nteger P)) (tptp.aa_bool_Code_integer tptp.zero_n356916108424825756nteger Q))) (and (not (tptp.pp P)) (tptp.pp Q)))) (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.aa_bool_nat 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.aa_bool_Code_integer tptp.zero_n356916108424825756nteger P) tptp.one_one_Code_integer) (tptp.pp P))) (= (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.aa_bool_nat 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.aa_bool_Code_integer tptp.zero_n356916108424825756nteger tptp.fTrue) tptp.one_one_Code_integer) (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.modulo_modulo_nat M) N) M))) (forall ((P tptp.bool)) (= (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex (tptp.aa_bool_nat tptp.zero_n2687167440665602831ol_nat P)) (tptp.zero_n1201886186963655149omplex P))) (forall ((P tptp.bool)) (= (tptp.aa_nat_real tptp.semiri5074537144036343181t_real (tptp.aa_bool_nat tptp.zero_n2687167440665602831ol_nat P)) (tptp.zero_n3304061248610475627l_real P))) (forall ((P tptp.bool)) (= (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat (tptp.aa_bool_nat tptp.zero_n2687167440665602831ol_nat P)) (tptp.zero_n2052037380579107095ol_rat P))) (forall ((P tptp.bool)) (let ((_let_1 (tptp.aa_bool_nat 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.aa_bool_nat tptp.zero_n2687167440665602831ol_nat P)) (tptp.aa_bool_int tptp.zero_n2684676970156552555ol_int P))) (forall ((P tptp.bool)) (= (tptp.semiri4939895301339042750nteger (tptp.aa_bool_nat tptp.zero_n2687167440665602831ol_nat P)) (tptp.aa_bool_Code_integer tptp.zero_n356916108424825756nteger P))) (forall ((B tptp.nat) (A tptp.nat)) (= (tptp.aa_nat_nat (tptp.modulo_modulo_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B) A)) B) tptp.zero_zero_nat)) (forall ((B tptp.int) (A tptp.int)) (= (tptp.modulo_modulo_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B) A) B) tptp.zero_zero_int)) (forall ((B tptp.code_integer) (A tptp.code_integer)) (= (tptp.modulo364778990260209775nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B) A) B) tptp.zero_z3403309356797280102nteger)) (forall ((A tptp.nat) (B tptp.nat)) (= (tptp.aa_nat_nat (tptp.modulo_modulo_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) B)) B) tptp.zero_zero_nat)) (forall ((A tptp.int) (B tptp.int)) (= (tptp.modulo_modulo_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) B) B) tptp.zero_zero_int)) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (tptp.modulo364778990260209775nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) B) B) tptp.zero_z3403309356797280102nteger)) (forall ((A tptp.nat)) (= (tptp.aa_nat_nat (tptp.modulo_modulo_nat A) tptp.one_one_nat) tptp.zero_zero_nat)) (forall ((A tptp.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.modulo_modulo_nat A) tptp.one_one_nat) tptp.zero_zero_nat)) (forall ((A tptp.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) (B tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat (tptp.modulo_modulo_nat A) B)) B) tptp.zero_zero_nat)) (forall ((A tptp.int) (B tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int (tptp.modulo_modulo_int A B)) B) tptp.zero_zero_int)) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (tptp.divide6298287555418463151nteger (tptp.modulo364778990260209775nteger A B) B) tptp.zero_z3403309356797280102nteger)) (forall ((A tptp.nat) (B tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat (tptp.modulo_modulo_nat A) B)) B) tptp.zero_zero_nat)) (forall ((A tptp.int) (B tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int (tptp.modulo_modulo_int A B)) B) tptp.zero_zero_int)) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (tptp.divide6298287555418463151nteger (tptp.modulo364778990260209775nteger A B) B) tptp.zero_z3403309356797280102nteger)) (forall ((B tptp.nat) (C tptp.nat) (A tptp.nat)) (= (tptp.aa_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 B) C)) A)) B) (tptp.aa_nat_nat (tptp.modulo_modulo_nat A) B))) (forall ((B tptp.int) (C tptp.int) (A tptp.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 B) C)) A) B) (tptp.modulo_modulo_int A B))) (forall ((B 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 B) C) A) B) (tptp.modulo364778990260209775nteger A B))) (forall ((C tptp.nat) (B tptp.nat) (A tptp.nat)) (= (tptp.aa_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) B)) A)) B) (tptp.aa_nat_nat (tptp.modulo_modulo_nat A) B))) (forall ((C tptp.int) (B tptp.int) (A tptp.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) B)) A) B) (tptp.modulo_modulo_int A B))) (forall ((C tptp.code_integer) (B tptp.code_integer) (A tptp.code_integer)) (= (tptp.modulo364778990260209775nteger (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger C) B) A) B) (tptp.modulo364778990260209775nteger A B))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (= (tptp.aa_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 B) C))) B) (tptp.aa_nat_nat (tptp.modulo_modulo_nat A) B))) (forall ((A tptp.int) (B tptp.int) (C tptp.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 B) C)) B) (tptp.modulo_modulo_int A B))) (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (= (tptp.modulo364778990260209775nteger (tptp.plus_p5714425477246183910nteger A (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B) C)) B) (tptp.modulo364778990260209775nteger A B))) (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (= (tptp.aa_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) B))) B) (tptp.aa_nat_nat (tptp.modulo_modulo_nat A) B))) (forall ((A tptp.int) (C tptp.int) (B tptp.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) B)) B) (tptp.modulo_modulo_int A B))) (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (= (tptp.modulo364778990260209775nteger (tptp.plus_p5714425477246183910nteger A (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger C) B)) B) (tptp.modulo364778990260209775nteger A B))) (forall ((A tptp.nat) (B tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat A) B)) (= (tptp.aa_nat_nat (tptp.modulo_modulo_nat B) A) tptp.zero_zero_nat))) (forall ((A tptp.int) (B tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int A) B)) (= (tptp.modulo_modulo_int B A) tptp.zero_zero_int))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer A) B)) (= (tptp.modulo364778990260209775nteger B A) tptp.zero_z3403309356797280102nteger))) (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.aa_bool_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.aa_bool_Code_integer 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.aa_bool_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.aa_bool_Code_integer 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.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.aa_bool_Code_integer tptp.zero_n356916108424825756nteger (tptp.aa_bool_bool tptp.fNot P)) (tptp.minus_8373710615458151222nteger tptp.one_one_Code_integer (tptp.aa_bool_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.modulo_modulo_nat _let_1) N) (tptp.aa_bool_nat 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 ((M tptp.nat)) (= (tptp.aa_nat_nat (tptp.modulo_modulo_nat M) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)) tptp.zero_zero_nat)) (forall ((A tptp.complex)) (= (tptp.aa_nat_complex (tptp.comm_s2602460028002588243omplex A) tptp.zero_zero_nat) tptp.one_one_complex)) (forall ((A tptp.real)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.comm_s7457072308508201937r_real A) tptp.zero_zero_nat) tptp.one_one_real)) (forall ((A tptp.rat)) (= (tptp.aa_nat_rat (tptp.comm_s4028243227959126397er_rat A) tptp.zero_zero_nat) tptp.one_one_rat)) (forall ((A tptp.nat)) (= (tptp.aa_nat_nat (tptp.comm_s4663373288045622133er_nat A) tptp.zero_zero_nat) tptp.one_one_nat)) (forall ((A tptp.int)) (= (tptp.aa_nat_int (tptp.comm_s4660882817536571857er_int A) tptp.zero_zero_nat) tptp.one_one_int)) (forall ((M tptp.nat) (K tptp.nat) (N tptp.nat)) (= (tptp.aa_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.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.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.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.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.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.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.modulo_modulo_nat (tptp.aa_nat_nat tptp.suc M)) N))) _let_156 _let_154 _let_153 _let_156 _let_154 _let_153 (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.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.modulo_modulo_int A _let_1))) (tptp.pp (tptp.aa_int_bool _let_2 A)))))) (forall ((A tptp.code_integer)) (let ((_let_1 (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 ((P3 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.aa_bool_nat tptp.zero_n2687167440665602831ol_nat P3)))) (tptp.pp P3))) (forall ((P3 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 P3)))) (tptp.pp P3))) (forall ((P3 tptp.bool)) (= (not (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_bool_Code_integer tptp.zero_n356916108424825756nteger P3)))) (tptp.pp P3))) (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.modulo_modulo_nat (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat tptp.suc M))) _let_1) (tptp.aa_nat_nat (tptp.modulo_modulo_nat M) _let_1)))) (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.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)))) (forall ((A tptp.nat)) (let ((_let_1 (tptp.aa_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.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.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (not (= _let_1 tptp.one_one_Code_integer)) (= _let_1 tptp.zero_z3403309356797280102nteger)))) (forall ((A tptp.nat)) (let ((_let_1 (tptp.aa_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.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.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (not (= _let_1 tptp.zero_z3403309356797280102nteger)) (= _let_1 tptp.one_one_Code_integer)))) (forall ((B tptp.bool)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_bool_nat tptp.zero_n2687167440665602831ol_nat B)) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) tptp.zero_zero_nat)) (forall ((B tptp.bool)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int (tptp.aa_bool_int tptp.zero_n2684676970156552555ol_int B)) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) tptp.zero_zero_int)) (forall ((B tptp.bool)) (= (tptp.divide6298287555418463151nteger (tptp.aa_bool_Code_integer tptp.zero_n356916108424825756nteger B) (tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))) tptp.zero_z3403309356797280102nteger)) (forall ((N tptp.nat)) (let ((_let_1 (tptp.aa_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.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) (V tptp.num)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat V))) (= (tptp.aa_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.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 ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (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)) (let ((_let_1 (tptp.aa_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 ((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.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N)) (tptp.aa_bool_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)) (= (tptp.aa_int_int (tptp.aa_int_fun_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.power_8256067586552552935nteger (tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one)) N)) (tptp.aa_bool_Code_integer 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.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N)) (tptp.aa_bool_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)) (= (tptp.aa_int_int (tptp.aa_int_fun_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.power_8256067586552552935nteger (tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one)) N)) (tptp.aa_bool_Code_integer 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.modulo_modulo_nat tptp.one_one_nat) (tptp.aa_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_bool_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.nat)) (= (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.power_8256067586552552935nteger (tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one)) N)) (tptp.aa_bool_Code_integer tptp.zero_n356916108424825756nteger (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_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_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.modulo_modulo_nat (tptp.aa_nat_nat _let_3 A)) _let_2) (tptp.aa_nat_nat _let_3 (tptp.aa_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.modulo_modulo_int (tptp.aa_int_int _let_3 A) _let_2) (tptp.aa_int_int _let_3 (tptp.modulo_modulo_int A _let_2))))))))) (forall ((A tptp.code_integer) (N tptp.nat)) (let ((_let_1 (tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (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 ((P3 tptp.bool) (Q2 tptp.bool)) (= (= (tptp.aa_bool_nat tptp.zero_n2687167440665602831ol_nat P3) (tptp.aa_bool_nat tptp.zero_n2687167440665602831ol_nat Q2)) (= (tptp.pp P3) (tptp.pp Q2)))) (forall ((P3 tptp.bool) (Q2 tptp.bool)) (= (= (tptp.aa_bool_int tptp.zero_n2684676970156552555ol_int P3) (tptp.aa_bool_int tptp.zero_n2684676970156552555ol_int Q2)) (= (tptp.pp P3) (tptp.pp Q2)))) (forall ((P3 tptp.bool) (Q2 tptp.bool)) (= (= (tptp.aa_bool_Code_integer tptp.zero_n356916108424825756nteger P3) (tptp.aa_bool_Code_integer tptp.zero_n356916108424825756nteger Q2)) (= (tptp.pp P3) (tptp.pp Q2)))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.semiri4939895301339042750nteger (tptp.aa_nat_nat (tptp.modulo_modulo_nat M) N)) (tptp.modulo364778990260209775nteger (tptp.semiri4939895301339042750nteger M) (tptp.semiri4939895301339042750nteger N)))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat (tptp.aa_nat_nat (tptp.modulo_modulo_nat M) N)) (tptp.aa_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)) (= (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_nat (tptp.modulo_modulo_nat M) N)) (tptp.modulo_modulo_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int M) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N)))) (forall ((X tptp.nat) (N tptp.nat)) (= (tptp.aa_nat_complex (tptp.comm_s2602460028002588243omplex (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex X)) N) (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex (tptp.aa_nat_nat (tptp.comm_s4663373288045622133er_nat X) N)))) (forall ((X tptp.nat) (N tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.comm_s7457072308508201937r_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real X)) N) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real (tptp.aa_nat_nat (tptp.comm_s4663373288045622133er_nat X) N)))) (forall ((X tptp.nat) (N tptp.nat)) (= (tptp.aa_nat_rat (tptp.comm_s4028243227959126397er_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat X)) N) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat (tptp.aa_nat_nat (tptp.comm_s4663373288045622133er_nat X) N)))) (forall ((X tptp.nat) (N tptp.nat)) (= (tptp.aa_nat_nat (tptp.comm_s4663373288045622133er_nat (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat X)) N) (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat (tptp.aa_nat_nat (tptp.comm_s4663373288045622133er_nat X) N)))) (forall ((X tptp.nat) (N tptp.nat)) (= (tptp.aa_nat_int (tptp.comm_s4660882817536571857er_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int X)) N) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_nat (tptp.comm_s4663373288045622133er_nat X) N)))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A))) (= (tptp.aa_nat_nat (tptp.modulo_modulo_nat (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.modulo_modulo_nat B) C))) C) (tptp.aa_nat_nat (tptp.modulo_modulo_nat (tptp.aa_nat_nat _let_1 B)) C)))) (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.times_times_int A))) (= (tptp.modulo_modulo_int (tptp.aa_int_int _let_1 (tptp.modulo_modulo_int B C)) C) (tptp.modulo_modulo_int (tptp.aa_int_int _let_1 B) C)))) (forall ((A tptp.code_integer) (B 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 B C)) C) (tptp.modulo364778990260209775nteger (tptp.aa_Cod1783974652533396728nteger _let_1 B) C)))) (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (= (tptp.aa_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.modulo_modulo_nat A) C)) B)) C) (tptp.aa_nat_nat (tptp.modulo_modulo_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) B)) C))) (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (tptp.modulo_modulo_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.modulo_modulo_int A C)) B) C) (tptp.modulo_modulo_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) B) C))) (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (= (tptp.modulo364778990260209775nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.modulo364778990260209775nteger A C)) B) C) (tptp.modulo364778990260209775nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) B) C))) (forall ((C tptp.nat) (A tptp.nat) (B 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.modulo_modulo_nat A) B)) (tptp.aa_nat_nat (tptp.modulo_modulo_nat (tptp.aa_nat_nat _let_1 A)) (tptp.aa_nat_nat _let_1 B))))) (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.times_times_int C))) (= (tptp.aa_int_int _let_1 (tptp.modulo_modulo_int A B)) (tptp.modulo_modulo_int (tptp.aa_int_int _let_1 A) (tptp.aa_int_int _let_1 B))))) (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger C))) (= (tptp.aa_Cod1783974652533396728nteger _let_1 (tptp.modulo364778990260209775nteger A B)) (tptp.modulo364778990260209775nteger (tptp.aa_Cod1783974652533396728nteger _let_1 A) (tptp.aa_Cod1783974652533396728nteger _let_1 B))))) (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (= (tptp.aa_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 B) C)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.modulo_modulo_nat A) B)) C))) (forall ((A tptp.int) (C tptp.int) (B tptp.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 B) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.modulo_modulo_int A B)) C))) (forall ((A tptp.code_integer) (C tptp.code_integer) (B 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 B) C)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.modulo364778990260209775nteger A B)) C))) (forall ((A tptp.nat) (C tptp.nat) (A4 tptp.nat) (B tptp.nat) (B4 tptp.nat)) (=> (= (tptp.aa_nat_nat (tptp.modulo_modulo_nat A) C) (tptp.aa_nat_nat (tptp.modulo_modulo_nat A4) C)) (=> (= (tptp.aa_nat_nat (tptp.modulo_modulo_nat B) C) (tptp.aa_nat_nat (tptp.modulo_modulo_nat B4) C)) (= (tptp.aa_nat_nat (tptp.modulo_modulo_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) B)) C) (tptp.aa_nat_nat (tptp.modulo_modulo_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A4) B4)) C))))) (forall ((A tptp.int) (C tptp.int) (A4 tptp.int) (B tptp.int) (B4 tptp.int)) (=> (= (tptp.modulo_modulo_int A C) (tptp.modulo_modulo_int A4 C)) (=> (= (tptp.modulo_modulo_int B C) (tptp.modulo_modulo_int B4 C)) (= (tptp.modulo_modulo_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) B) C) (tptp.modulo_modulo_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A4) B4) C))))) (forall ((A tptp.code_integer) (C tptp.code_integer) (A4 tptp.code_integer) (B tptp.code_integer) (B4 tptp.code_integer)) (=> (= (tptp.modulo364778990260209775nteger A C) (tptp.modulo364778990260209775nteger A4 C)) (=> (= (tptp.modulo364778990260209775nteger B C) (tptp.modulo364778990260209775nteger B4 C)) (= (tptp.modulo364778990260209775nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) B) C) (tptp.modulo364778990260209775nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A4) B4) C))))) (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (= (tptp.aa_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.modulo_modulo_nat A) C)) (tptp.aa_nat_nat (tptp.modulo_modulo_nat B) C))) C) (tptp.aa_nat_nat (tptp.modulo_modulo_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) B)) C))) (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (tptp.modulo_modulo_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.modulo_modulo_int A C)) (tptp.modulo_modulo_int B C)) C) (tptp.modulo_modulo_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) B) C))) (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (= (tptp.modulo364778990260209775nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.modulo364778990260209775nteger A C)) (tptp.modulo364778990260209775nteger B C)) C) (tptp.modulo364778990260209775nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) B) C))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A))) (= (tptp.aa_nat_nat (tptp.modulo_modulo_nat (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.modulo_modulo_nat B) C))) C) (tptp.aa_nat_nat (tptp.modulo_modulo_nat (tptp.aa_nat_nat _let_1 B)) C)))) (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.plus_plus_int A))) (= (tptp.modulo_modulo_int (tptp.aa_int_int _let_1 (tptp.modulo_modulo_int B C)) C) (tptp.modulo_modulo_int (tptp.aa_int_int _let_1 B) C)))) (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (= (tptp.modulo364778990260209775nteger (tptp.plus_p5714425477246183910nteger A (tptp.modulo364778990260209775nteger B C)) C) (tptp.modulo364778990260209775nteger (tptp.plus_p5714425477246183910nteger A B) C))) (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (= (tptp.aa_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.modulo_modulo_nat A) C)) B)) C) (tptp.aa_nat_nat (tptp.modulo_modulo_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) B)) C))) (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (tptp.modulo_modulo_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.modulo_modulo_int A C)) B) C) (tptp.modulo_modulo_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) B) C))) (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (= (tptp.modulo364778990260209775nteger (tptp.plus_p5714425477246183910nteger (tptp.modulo364778990260209775nteger A C) B) C) (tptp.modulo364778990260209775nteger (tptp.plus_p5714425477246183910nteger A B) C))) (forall ((A tptp.nat) (C tptp.nat) (A4 tptp.nat) (B tptp.nat) (B4 tptp.nat)) (=> (= (tptp.aa_nat_nat (tptp.modulo_modulo_nat A) C) (tptp.aa_nat_nat (tptp.modulo_modulo_nat A4) C)) (=> (= (tptp.aa_nat_nat (tptp.modulo_modulo_nat B) C) (tptp.aa_nat_nat (tptp.modulo_modulo_nat B4) C)) (= (tptp.aa_nat_nat (tptp.modulo_modulo_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) B)) C) (tptp.aa_nat_nat (tptp.modulo_modulo_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A4) B4)) C))))) (forall ((A tptp.int) (C tptp.int) (A4 tptp.int) (B tptp.int) (B4 tptp.int)) (=> (= (tptp.modulo_modulo_int A C) (tptp.modulo_modulo_int A4 C)) (=> (= (tptp.modulo_modulo_int B C) (tptp.modulo_modulo_int B4 C)) (= (tptp.modulo_modulo_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) B) C) (tptp.modulo_modulo_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A4) B4) C))))) (forall ((A tptp.code_integer) (C tptp.code_integer) (A4 tptp.code_integer) (B tptp.code_integer) (B4 tptp.code_integer)) (=> (= (tptp.modulo364778990260209775nteger A C) (tptp.modulo364778990260209775nteger A4 C)) (=> (= (tptp.modulo364778990260209775nteger B C) (tptp.modulo364778990260209775nteger B4 C)) (= (tptp.modulo364778990260209775nteger (tptp.plus_p5714425477246183910nteger A B) C) (tptp.modulo364778990260209775nteger (tptp.plus_p5714425477246183910nteger A4 B4) C))))) (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (= (tptp.aa_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.modulo_modulo_nat A) C)) (tptp.aa_nat_nat (tptp.modulo_modulo_nat B) C))) C) (tptp.aa_nat_nat (tptp.modulo_modulo_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) B)) C))) (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (tptp.modulo_modulo_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.modulo_modulo_int A C)) (tptp.modulo_modulo_int B C)) C) (tptp.modulo_modulo_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) B) C))) (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (= (tptp.modulo364778990260209775nteger (tptp.plus_p5714425477246183910nteger (tptp.modulo364778990260209775nteger A C) (tptp.modulo364778990260209775nteger B C)) C) (tptp.modulo364778990260209775nteger (tptp.plus_p5714425477246183910nteger A B) C))) (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.minus_minus_int A))) (= (tptp.modulo_modulo_int (tptp.aa_int_int _let_1 (tptp.modulo_modulo_int B C)) C) (tptp.modulo_modulo_int (tptp.aa_int_int _let_1 B) C)))) (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (= (tptp.modulo364778990260209775nteger (tptp.minus_8373710615458151222nteger A (tptp.modulo364778990260209775nteger B C)) C) (tptp.modulo364778990260209775nteger (tptp.minus_8373710615458151222nteger A B) C))) (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (tptp.modulo_modulo_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.modulo_modulo_int A C)) B) C) (tptp.modulo_modulo_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) B) C))) (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (= (tptp.modulo364778990260209775nteger (tptp.minus_8373710615458151222nteger (tptp.modulo364778990260209775nteger A C) B) C) (tptp.modulo364778990260209775nteger (tptp.minus_8373710615458151222nteger A B) C))) (forall ((A tptp.int) (C tptp.int) (A4 tptp.int) (B tptp.int) (B4 tptp.int)) (=> (= (tptp.modulo_modulo_int A C) (tptp.modulo_modulo_int A4 C)) (=> (= (tptp.modulo_modulo_int B C) (tptp.modulo_modulo_int B4 C)) (= (tptp.modulo_modulo_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) B) C) (tptp.modulo_modulo_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A4) B4) C))))) (forall ((A tptp.code_integer) (C tptp.code_integer) (A4 tptp.code_integer) (B tptp.code_integer) (B4 tptp.code_integer)) (=> (= (tptp.modulo364778990260209775nteger A C) (tptp.modulo364778990260209775nteger A4 C)) (=> (= (tptp.modulo364778990260209775nteger B C) (tptp.modulo364778990260209775nteger B4 C)) (= (tptp.modulo364778990260209775nteger (tptp.minus_8373710615458151222nteger A B) C) (tptp.modulo364778990260209775nteger (tptp.minus_8373710615458151222nteger A4 B4) C))))) (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (tptp.modulo_modulo_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.modulo_modulo_int A C)) (tptp.modulo_modulo_int B C)) C) (tptp.modulo_modulo_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) B) C))) (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (= (tptp.modulo364778990260209775nteger (tptp.minus_8373710615458151222nteger (tptp.modulo364778990260209775nteger A C) (tptp.modulo364778990260209775nteger B C)) C) (tptp.modulo364778990260209775nteger (tptp.minus_8373710615458151222nteger A B) C))) (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.aa_bool_nat 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.aa_bool_nat tptp.zero_n2687167440665602831ol_nat P)) (tptp.aa_bool_nat 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.aa_bool_Code_integer tptp.zero_n356916108424825756nteger (tptp.aa_bool_bool (tptp.fconj P) Q)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_bool_Code_integer tptp.zero_n356916108424825756nteger P)) (tptp.aa_bool_Code_integer tptp.zero_n356916108424825756nteger Q)))) (forall ((A tptp.nat) (B tptp.nat) (N tptp.nat)) (= (tptp.aa_nat_nat (tptp.modulo_modulo_nat (tptp.aa_nat_nat (tptp.power_power_nat (tptp.aa_nat_nat (tptp.modulo_modulo_nat A) B)) N)) B) (tptp.aa_nat_nat (tptp.modulo_modulo_nat (tptp.aa_nat_nat (tptp.power_power_nat A) N)) B))) (forall ((A tptp.int) (B tptp.int) (N tptp.nat)) (= (tptp.modulo_modulo_int (tptp.aa_nat_int (tptp.power_power_int (tptp.modulo_modulo_int A B)) N) B) (tptp.modulo_modulo_int (tptp.aa_nat_int (tptp.power_power_int A) N) B))) (forall ((A tptp.code_integer) (B tptp.code_integer) (N tptp.nat)) (= (tptp.modulo364778990260209775nteger (tptp.power_8256067586552552935nteger (tptp.modulo364778990260209775nteger A B) N) B) (tptp.modulo364778990260209775nteger (tptp.power_8256067586552552935nteger A N) B))) (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.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.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) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (tptp.modulo_modulo_nat A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat C) B)) (= (tptp.aa_nat_nat (tptp.modulo_modulo_nat (tptp.aa_nat_nat _let_1 B)) C) (tptp.aa_nat_nat _let_1 C))))) (forall ((C tptp.int) (B tptp.int) (A tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int C) B)) (= (tptp.modulo_modulo_int (tptp.modulo_modulo_int A B) C) (tptp.modulo_modulo_int A C)))) (forall ((C tptp.code_integer) (B tptp.code_integer) (A tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer C) B)) (= (tptp.modulo364778990260209775nteger (tptp.modulo364778990260209775nteger A B) C) (tptp.modulo364778990260209775nteger A C)))) (forall ((C tptp.nat) (B 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 B)) (= (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.modulo_modulo_nat A) B))) (tptp.pp (tptp.aa_nat_bool _let_1 A)))))) (forall ((C tptp.int) (B 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 B)) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.modulo_modulo_int A B))) (tptp.pp (tptp.aa_int_bool _let_1 A)))))) (forall ((C tptp.code_integer) (B 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 B)) (= (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.modulo364778990260209775nteger A B))) (tptp.pp (tptp.aa_Code_integer_bool _let_1 A)))))) (forall ((C tptp.nat) (A tptp.nat) (B 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.modulo_modulo_nat A) B))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 B)) (tptp.pp (tptp.aa_nat_bool _let_1 A)))))) (forall ((C tptp.int) (A tptp.int) (B 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.modulo_modulo_int A B))) (=> (tptp.pp (tptp.aa_int_bool _let_1 B)) (tptp.pp (tptp.aa_int_bool _let_1 A)))))) (forall ((C tptp.code_integer) (A tptp.code_integer) (B 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 B))) (=> (tptp.pp (tptp.aa_Code_integer_bool _let_1 B)) (tptp.pp (tptp.aa_Code_integer_bool _let_1 A)))))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.aa_nat_nat (tptp.modulo_modulo_nat (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.modulo_modulo_nat M) N)))) N) (tptp.aa_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.aa_nat_nat (tptp.modulo_modulo_nat (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.modulo_modulo_nat M) N))) N) (tptp.aa_nat_nat (tptp.modulo_modulo_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.modulo_modulo_nat M) N)) M))) (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_bool_nat 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.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.modulo_modulo_int A _let_1)))) (forall ((A tptp.code_integer)) (let ((_let_1 (tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.aa_bool_Code_integer 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 ((A tptp.code_integer) (B 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 B)) A)))) (forall ((A tptp.nat) (B 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.modulo_modulo_nat A) B)) A)))) (forall ((A tptp.int) (B 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.modulo_modulo_int A B)) A)))) (forall ((B 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) B)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.modulo_modulo_nat A) B)) B)))) (forall ((B 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) B)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.modulo_modulo_int A B)) B)))) (forall ((B tptp.code_integer) (A tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) B)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.modulo364778990260209775nteger A B)) B)))) (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_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_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) (tptp.aa_bool_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.aa_bool_Code_integer tptp.zero_n356916108424825756nteger P)))) (forall ((A tptp.nat) (B tptp.nat)) (= (= (tptp.aa_nat_nat (tptp.modulo_modulo_nat A) B) A) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) B) tptp.zero_zero_nat))) (forall ((A tptp.int) (B tptp.int)) (= (= (tptp.modulo_modulo_int A B) A) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A) B) tptp.zero_zero_int))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= (tptp.modulo364778990260209775nteger A B) A) (= (tptp.divide6298287555418463151nteger A B) tptp.zero_z3403309356797280102nteger))) (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.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.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.modulo_modulo_nat (tptp.aa_num_nat tptp.numeral_numeral_nat M)) _let_1) (tptp.aa_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.modulo_modulo_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 M)) _let_2) (tptp.modulo_modulo_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 N)) _let_2)) (= (tptp.modulo_modulo_int (tptp.aa_num_int tptp.numeral_numeral_int M) _let_1) (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.numera6620942414471956472nteger Q2))) (let ((_let_2 (tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 Q2)))) (= (= (tptp.modulo364778990260209775nteger (tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 M)) _let_2) (tptp.modulo364778990260209775nteger (tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 N)) _let_2)) (= (tptp.modulo364778990260209775nteger (tptp.numera6620942414471956472nteger M) _let_1) (tptp.modulo364778990260209775nteger (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.modulo_modulo_nat (tptp.aa_num_nat tptp.numeral_numeral_nat M)) _let_1) (tptp.aa_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.modulo_modulo_int (tptp.aa_num_int tptp.numeral_numeral_int M) _let_1) (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.numera6620942414471956472nteger tptp.one))) (= (tptp.modulo364778990260209775nteger (tptp.numera6620942414471956472nteger M) _let_1) (tptp.modulo364778990260209775nteger (tptp.numera6620942414471956472nteger N) _let_1)))) (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (=> (= (tptp.modulo_modulo_int A C) (tptp.modulo_modulo_int B C)) (not (forall ((D2 tptp.int)) (not (= B (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) (B tptp.code_integer)) (=> (= (tptp.modulo364778990260209775nteger A C) (tptp.modulo364778990260209775nteger B C)) (not (forall ((D2 tptp.code_integer)) (not (= B (tptp.plus_p5714425477246183910nteger A (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger C) D2)))))))) (forall ((A tptp.nat) (B tptp.nat)) (= (= (tptp.aa_nat_nat (tptp.modulo_modulo_nat A) B) tptp.zero_zero_nat) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat B) A)))) (forall ((A tptp.int) (B tptp.int)) (= (= (tptp.modulo_modulo_int A B) tptp.zero_zero_int) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int B) A)))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= (tptp.modulo364778990260209775nteger A B) tptp.zero_z3403309356797280102nteger) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer B) A)))) (forall ((A tptp.nat) (B tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat A) B)) (= (tptp.aa_nat_nat (tptp.modulo_modulo_nat B) A) tptp.zero_zero_nat))) (forall ((A tptp.int) (B tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int A) B)) (= (tptp.modulo_modulo_int B A) tptp.zero_zero_int))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer A) B)) (= (tptp.modulo364778990260209775nteger B A) tptp.zero_z3403309356797280102nteger))) (forall ((A tptp.nat) (B tptp.nat)) (=> (= (tptp.aa_nat_nat (tptp.modulo_modulo_nat A) B) tptp.zero_zero_nat) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat B) A)))) (forall ((A tptp.int) (B tptp.int)) (=> (= (tptp.modulo_modulo_int A B) tptp.zero_zero_int) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int B) A)))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (= (tptp.modulo364778990260209775nteger A B) tptp.zero_z3403309356797280102nteger) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer B) A)))) (forall ((A tptp.nat) (B 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) B)) 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 B) 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.modulo_modulo_nat A) C)) (tptp.aa_nat_nat (tptp.modulo_modulo_nat B) C))) C)))) (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) B)) 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.aa_int_fun_int_int tptp.divide_divide_int A) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int B) C))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.modulo_modulo_int A C)) (tptp.modulo_modulo_int B C))) C)))) (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (= (tptp.divide6298287555418463151nteger (tptp.plus_p5714425477246183910nteger A B) C) (tptp.plus_p5714425477246183910nteger (tptp.plus_p5714425477246183910nteger (tptp.divide6298287555418463151nteger A C) (tptp.divide6298287555418463151nteger B C)) (tptp.divide6298287555418463151nteger (tptp.plus_p5714425477246183910nteger (tptp.modulo364778990260209775nteger A C) (tptp.modulo364778990260209775nteger B C)) C)))) (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_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_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_bool_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.aa_bool_Code_integer tptp.zero_n356916108424825756nteger P)) tptp.one_one_Code_integer))) (forall ((P tptp.fun_complex_bool) (P3 tptp.bool)) (let ((_let_1 (tptp.pp P3))) (= (tptp.pp (tptp.aa_complex_bool P (tptp.zero_n1201886186963655149omplex P3))) (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) (P3 tptp.bool)) (let ((_let_1 (tptp.pp P3))) (= (tptp.pp (tptp.aa_real_bool P (tptp.zero_n3304061248610475627l_real P3))) (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) (P3 tptp.bool)) (let ((_let_1 (tptp.pp P3))) (= (tptp.pp (tptp.aa_rat_bool P (tptp.zero_n2052037380579107095ol_rat P3))) (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) (P3 tptp.bool)) (let ((_let_1 (tptp.pp P3))) (= (tptp.pp (tptp.aa_nat_bool P (tptp.aa_bool_nat tptp.zero_n2687167440665602831ol_nat P3))) (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) (P3 tptp.bool)) (let ((_let_1 (tptp.pp P3))) (= (tptp.pp (tptp.aa_int_bool P (tptp.aa_bool_int tptp.zero_n2684676970156552555ol_int P3))) (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) (P3 tptp.bool)) (let ((_let_1 (tptp.pp P3))) (= (tptp.pp (tptp.aa_Code_integer_bool P (tptp.aa_bool_Code_integer tptp.zero_n356916108424825756nteger P3))) (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 ((P tptp.fun_complex_bool) (P3 tptp.bool)) (let ((_let_1 (tptp.pp P3))) (= (tptp.pp (tptp.aa_complex_bool P (tptp.zero_n1201886186963655149omplex P3))) (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) (P3 tptp.bool)) (let ((_let_1 (tptp.pp P3))) (= (tptp.pp (tptp.aa_real_bool P (tptp.zero_n3304061248610475627l_real P3))) (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) (P3 tptp.bool)) (let ((_let_1 (tptp.pp P3))) (= (tptp.pp (tptp.aa_rat_bool P (tptp.zero_n2052037380579107095ol_rat P3))) (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) (P3 tptp.bool)) (let ((_let_1 (tptp.pp P3))) (= (tptp.pp (tptp.aa_nat_bool P (tptp.aa_bool_nat tptp.zero_n2687167440665602831ol_nat P3))) (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) (P3 tptp.bool)) (let ((_let_1 (tptp.pp P3))) (= (tptp.pp (tptp.aa_int_bool P (tptp.aa_bool_int tptp.zero_n2684676970156552555ol_int P3))) (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) (P3 tptp.bool)) (let ((_let_1 (tptp.pp P3))) (= (tptp.pp (tptp.aa_Code_integer_bool P (tptp.aa_bool_Code_integer tptp.zero_n356916108424825756nteger P3))) (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 ((P3 tptp.bool)) (let ((_let_1 (tptp.zero_n1201886186963655149omplex P3))) (let ((_let_2 (tptp.pp P3))) (and (=> _let_2 (= _let_1 tptp.one_one_complex)) (=> (not _let_2) (= _let_1 tptp.zero_zero_complex)))))) (forall ((P3 tptp.bool)) (let ((_let_1 (tptp.zero_n3304061248610475627l_real P3))) (let ((_let_2 (tptp.pp P3))) (and (=> _let_2 (= _let_1 tptp.one_one_real)) (=> (not _let_2) (= _let_1 tptp.zero_zero_real)))))) (forall ((P3 tptp.bool)) (let ((_let_1 (tptp.zero_n2052037380579107095ol_rat P3))) (let ((_let_2 (tptp.pp P3))) (and (=> _let_2 (= _let_1 tptp.one_one_rat)) (=> (not _let_2) (= _let_1 tptp.zero_zero_rat)))))) (forall ((P3 tptp.bool)) (let ((_let_1 (tptp.aa_bool_nat tptp.zero_n2687167440665602831ol_nat P3))) (let ((_let_2 (tptp.pp P3))) (and (=> _let_2 (= _let_1 tptp.one_one_nat)) (=> (not _let_2) (= _let_1 tptp.zero_zero_nat)))))) (forall ((P3 tptp.bool)) (let ((_let_1 (tptp.aa_bool_int tptp.zero_n2684676970156552555ol_int P3))) (let ((_let_2 (tptp.pp P3))) (and (=> _let_2 (= _let_1 tptp.one_one_int)) (=> (not _let_2) (= _let_1 tptp.zero_zero_int)))))) (forall ((P3 tptp.bool)) (let ((_let_1 (tptp.aa_bool_Code_integer tptp.zero_n356916108424825756nteger P3))) (let ((_let_2 (tptp.pp P3))) (and (=> _let_2 (= _let_1 tptp.one_one_Code_integer)) (=> (not _let_2) (= _let_1 tptp.zero_z3403309356797280102nteger)))))) (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (= (tptp.modulo_modulo_int A C) (tptp.modulo_modulo_int B 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) B))))) (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (= (= (tptp.modulo364778990260209775nteger A C) (tptp.modulo364778990260209775nteger B C)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer C) (tptp.minus_8373710615458151222nteger A B))))) (forall ((B tptp.nat) (A tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat B) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat A) (tptp.aa_nat_nat (tptp.modulo_modulo_nat A) B))))) (forall ((B tptp.int) (A tptp.int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int B) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) (tptp.modulo_modulo_int A B))))) (forall ((B tptp.code_integer) (A tptp.code_integer)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer B) (tptp.minus_8373710615458151222nteger A (tptp.modulo364778990260209775nteger A B))))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.modulo_modulo_nat M) N)))) (let ((_let_2 (tptp.aa_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 ((P tptp.fun_nat_bool) (N tptp.nat) (P3 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) P3)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) P3)) (=> (forall ((N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) P3)) (=> (tptp.pp (tptp.aa_nat_bool P N2)) (tptp.pp (tptp.aa_nat_bool P (tptp.aa_nat_nat (tptp.modulo_modulo_nat (tptp.aa_nat_nat tptp.suc N2)) P3)))))) (tptp.pp (tptp.aa_nat_bool P 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.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.modulo_modulo_nat M) N)) N)))) (forall ((P tptp.fun_nat_fun_nat_bool) (M tptp.nat) (N tptp.nat)) (=> (forall ((M4 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool P M4) tptp.zero_zero_nat))) (=> (forall ((M4 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.modulo_modulo_nat M4) N2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool P M4) N2))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool P 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.modulo_modulo_nat M) (tptp.aa_nat_nat tptp.suc N))) N))) (forall ((M tptp.nat) (D tptp.nat)) (=> (= (tptp.aa_nat_nat (tptp.modulo_modulo_nat M) D) tptp.zero_zero_nat) (exists ((Q4 tptp.nat)) (= M (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat D) Q4))))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_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.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.modulo_modulo_nat M) N) (tptp.aa_nat_nat (tptp.modulo_modulo_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_eq_nat N) M)) (= (tptp.aa_nat_nat (tptp.modulo_modulo_nat M) N) (tptp.aa_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) (Y4 tptp.nat)) (= (= (tptp.aa_nat_nat (tptp.modulo_modulo_nat X) N) (tptp.aa_nat_nat (tptp.modulo_modulo_nat Y4) 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 Y4) (tptp.aa_nat_nat _let_1 Q22))))))) (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.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) (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 ((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 ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (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.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.aa_bool_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.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.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.power_8256067586552552935nteger _let_1 M))) (= (tptp.modulo364778990260209775nteger _let_2 (tptp.power_8256067586552552935nteger _let_1 N)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_bool_Code_integer tptp.zero_n356916108424825756nteger (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N))) _let_2))))) (forall ((B tptp.code_integer) (A tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) B)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (tptp.modulo364778990260209775nteger A B))))) (forall ((B 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) B)) (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.modulo_modulo_nat A) B))))) (forall ((B 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) B)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.modulo_modulo_int A B))))) (forall ((A tptp.code_integer) (B 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) B)) (= (tptp.modulo364778990260209775nteger A B) A)))) (forall ((A tptp.nat) (B 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) B)) (= (tptp.aa_nat_nat (tptp.modulo_modulo_nat A) B) A)))) (forall ((A tptp.int) (B 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) B)) (= (tptp.modulo_modulo_int A B) A)))) (forall ((N tptp.num) (Q2 tptp.num)) (= (= (tptp.aa_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.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.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.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.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 N)) (tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 Q2))) tptp.zero_z3403309356797280102nteger) (= (tptp.modulo364778990260209775nteger (tptp.numera6620942414471956472nteger N) (tptp.numera6620942414471956472nteger Q2)) tptp.zero_z3403309356797280102nteger))) (forall ((N tptp.num)) (= (tptp.aa_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.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.numera6620942414471956472nteger N) (tptp.numera6620942414471956472nteger tptp.one)) tptp.zero_z3403309356797280102nteger)) (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.modulo_modulo_nat (tptp.aa_num_nat tptp.numeral_numeral_nat tptp.one)) _let_1) (tptp.aa_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.modulo_modulo_int (tptp.aa_num_int tptp.numeral_numeral_int tptp.one) _let_1) (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.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 Q2)))) (not (= (tptp.modulo364778990260209775nteger (tptp.numera6620942414471956472nteger tptp.one) _let_1) (tptp.modulo364778990260209775nteger (tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 N)) _let_1))))) (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.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.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.modulo_modulo_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 M)) _let_1) (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.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 Q2)))) (not (= (tptp.modulo364778990260209775nteger (tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 M)) _let_1) (tptp.modulo364778990260209775nteger (tptp.numera6620942414471956472nteger tptp.one) _let_1))))) (forall ((A tptp.nat) (B 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 B)) 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 B) 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.modulo_modulo_nat B) C))) C))))) (forall ((A tptp.int) (B 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.divide_divide_int (tptp.aa_int_int _let_1 B)) 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.aa_int_fun_int_int tptp.divide_divide_int B) C))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int (tptp.aa_int_int _let_1 (tptp.modulo_modulo_int B C))) C))))) (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A))) (= (tptp.divide6298287555418463151nteger (tptp.aa_Cod1783974652533396728nteger _let_1 B) C) (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger _let_1 (tptp.divide6298287555418463151nteger B C)) (tptp.divide6298287555418463151nteger (tptp.aa_Cod1783974652533396728nteger _let_1 (tptp.modulo364778990260209775nteger B C)) C))))) (forall ((B 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 B) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) B))) (tptp.aa_nat_nat (tptp.modulo_modulo_nat A) B)) A)) (forall ((B 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 B) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A) B))) (tptp.modulo_modulo_int A B)) A)) (forall ((B tptp.code_integer) (A tptp.code_integer)) (= (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B) (tptp.divide6298287555418463151nteger A B)) (tptp.modulo364778990260209775nteger A B)) A)) (forall ((A tptp.nat) (B tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.modulo_modulo_nat A) B)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) B))) A)) (forall ((A tptp.int) (B tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.modulo_modulo_int A B)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A) B))) A)) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (tptp.plus_p5714425477246183910nteger (tptp.modulo364778990260209775nteger A B) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B) (tptp.divide6298287555418463151nteger A B))) A)) (forall ((A tptp.nat) (B tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.modulo_modulo_nat A) B)) (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) B)) B)) A)) (forall ((A tptp.int) (B tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.modulo_modulo_int A B)) (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.divide_divide_int A) B)) B)) A)) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (tptp.plus_p5714425477246183910nteger (tptp.modulo364778990260209775nteger A B) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.divide6298287555418463151nteger A B)) B)) A)) (forall ((A tptp.nat) (B 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) B)) B)) (tptp.aa_nat_nat (tptp.modulo_modulo_nat A) B)) A)) (forall ((A tptp.int) (B 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.aa_int_fun_int_int tptp.divide_divide_int A) B)) B)) (tptp.modulo_modulo_int A B)) A)) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.divide6298287555418463151nteger A B)) B) (tptp.modulo364778990260209775nteger A B)) A)) (forall ((A tptp.nat) (B 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) B)) B)) (tptp.aa_nat_nat (tptp.modulo_modulo_nat A) B)))) (forall ((A tptp.int) (B 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.aa_int_fun_int_int tptp.divide_divide_int A) B)) B)) (tptp.modulo_modulo_int A B)))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= A (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.divide6298287555418463151nteger A B)) B) (tptp.modulo364778990260209775nteger A B)))) (forall ((A tptp.nat) (B 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) B)) B)) (tptp.aa_nat_nat (tptp.modulo_modulo_nat A) B))) C) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) C))) (forall ((A tptp.int) (B 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.aa_int_fun_int_int tptp.divide_divide_int A) B)) B)) (tptp.modulo_modulo_int A B))) C) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) C))) (forall ((A tptp.code_integer) (B 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 B)) B) (tptp.modulo364778990260209775nteger A B)) C) (tptp.plus_p5714425477246183910nteger A C))) (forall ((B 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 B) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) B))) (tptp.aa_nat_nat (tptp.modulo_modulo_nat A) B))) C) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) C))) (forall ((B 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 B) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A) B))) (tptp.modulo_modulo_int A B))) C) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) C))) (forall ((B 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 B) (tptp.divide6298287555418463151nteger A B)) (tptp.modulo364778990260209775nteger A B)) C) (tptp.plus_p5714425477246183910nteger A C))) (forall ((B tptp.nat) (A tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat B) tptp.one_one_nat)) (= (tptp.aa_nat_nat (tptp.modulo_modulo_nat A) B) tptp.zero_zero_nat))) (forall ((B tptp.int) (A tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int B) tptp.one_one_int)) (= (tptp.modulo_modulo_int A B) tptp.zero_zero_int))) (forall ((B tptp.code_integer) (A tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer)) (= (tptp.modulo364778990260209775nteger A B) tptp.zero_z3403309356797280102nteger))) (forall ((A tptp.nat) (B 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 B) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) B))) (tptp.aa_nat_nat (tptp.modulo_modulo_nat A) B))) (forall ((A tptp.int) (B 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 B) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A) B))) (tptp.modulo_modulo_int A B))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (tptp.minus_8373710615458151222nteger A (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B) (tptp.divide6298287555418463151nteger A B))) (tptp.modulo364778990260209775nteger A B))) (forall ((A tptp.nat) (B tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat A) (tptp.aa_nat_nat (tptp.modulo_modulo_nat A) B)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) B)))) (forall ((A tptp.int) (B tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) (tptp.modulo_modulo_int A B)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A) B)))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (tptp.minus_8373710615458151222nteger A (tptp.modulo364778990260209775nteger A B)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B) (tptp.divide6298287555418463151nteger A B)))) (forall ((A tptp.nat) (B tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat A) (tptp.aa_nat_nat (tptp.modulo_modulo_nat A) B)) (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) B)) B))) (forall ((A tptp.int) (B tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) (tptp.modulo_modulo_int A B)) (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.divide_divide_int A) B)) B))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (tptp.minus_8373710615458151222nteger A (tptp.modulo364778990260209775nteger A B)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.divide6298287555418463151nteger A B)) B))) (forall ((A tptp.nat) (B 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) B)) B)) (tptp.aa_nat_nat (tptp.modulo_modulo_nat A) B))) (forall ((A tptp.int) (B 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.aa_int_fun_int_int tptp.divide_divide_int A) B)) B)) (tptp.modulo_modulo_int A B))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (tptp.minus_8373710615458151222nteger A (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.divide6298287555418463151nteger A B)) B)) (tptp.modulo364778990260209775nteger A B))) (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.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.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.modulo_modulo_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 M)) _let_1) (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.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 Q2)))) (not (= (tptp.modulo364778990260209775nteger (tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 M)) _let_1) (tptp.modulo364778990260209775nteger (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.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.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.modulo_modulo_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit1 M)) _let_1) (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.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 Q2)))) (not (= (tptp.modulo364778990260209775nteger (tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit1 M)) _let_1) (tptp.modulo364778990260209775nteger (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.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.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.modulo_modulo_nat (tptp.aa_num_nat tptp.numeral_numeral_nat M)) _let_1) (tptp.aa_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.modulo_modulo_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit1 M)) _let_2) (tptp.modulo_modulo_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit1 N)) _let_2)) (= (tptp.modulo_modulo_int (tptp.aa_num_int tptp.numeral_numeral_int M) _let_1) (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.numera6620942414471956472nteger Q2))) (let ((_let_2 (tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 Q2)))) (= (= (tptp.modulo364778990260209775nteger (tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit1 M)) _let_2) (tptp.modulo364778990260209775nteger (tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit1 N)) _let_2)) (= (tptp.modulo364778990260209775nteger (tptp.numera6620942414471956472nteger M) _let_1) (tptp.modulo364778990260209775nteger (tptp.numera6620942414471956472nteger 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) N)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.modulo_modulo_nat M) N)) 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.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 ((A2 tptp.nat) (B3 tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A2) B3)) (=> (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.modulo_modulo_nat A2) N) tptp.zero_zero_nat) (=> (= (tptp.aa_nat_nat (tptp.modulo_modulo_nat B3) 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 A2) N)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat B3) N)))))))) (forall ((M tptp.nat) (Q2 tptp.nat) (N tptp.nat)) (=> (= (tptp.aa_nat_nat (tptp.modulo_modulo_nat M) Q2) (tptp.aa_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.modulo_modulo_nat M) Q2) (tptp.aa_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) (Y4 tptp.nat)) (=> (= (tptp.aa_nat_nat (tptp.modulo_modulo_nat X) N) (tptp.aa_nat_nat (tptp.modulo_modulo_nat Y4) N)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Y4) X)) (exists ((Q4 tptp.nat)) (= X (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Y4) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat N) Q4))))))) (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.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))))) (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 ((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.modulo_modulo_nat M) Q2) (tptp.aa_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 ((M tptp.nat) (N tptp.nat) (Q2 tptp.nat)) (let ((_let_1 (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.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 ((A2 tptp.nat) (N tptp.nat)) (= A2 (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 A2) N)) N)) (tptp.aa_nat_nat (tptp.modulo_modulo_nat A2) N)))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.aa_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 ((N tptp.nat)) (let ((_let_1 (tptp.aa_nat_complex (tptp.comm_s2602460028002588243omplex 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)) (let ((_let_1 (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.comm_s7457072308508201937r_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_rat (tptp.comm_s4028243227959126397er_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.comm_s4663373288045622133er_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_int (tptp.comm_s4660882817536571857er_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.num) (Q2 tptp.num)) (not (= (tptp.aa_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.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.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit1 N)) (tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 Q2))) tptp.zero_z3403309356797280102nteger))) (forall ((A tptp.code_integer) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.semiri4939895301339042750nteger M))) (let ((_let_2 (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.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat M))) (let ((_let_2 (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.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 ((A tptp.int) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_int tptp.semiri1314217659103216013at_int M))) (let ((_let_2 (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N))) (let ((_let_3 (tptp.aa_int_fun_int_int tptp.times_times_int _let_1))) (= (tptp.modulo_modulo_int A (tptp.aa_int_int _let_3 _let_2)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int _let_3 (tptp.modulo_modulo_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A) _let_1) _let_2))) (tptp.modulo_modulo_int A _let_1))))))) (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.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.aa_nat_complex tptp.semiri8010041392384452111omplex (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat M) N)) (tptp.divide1717551699836669952omplex (tptp.minus_minus_complex (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex M) (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex (tptp.aa_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_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.modulo_modulo_nat M) N)))) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real 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.modulo_modulo_nat M) N)))) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat 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.modulo_modulo_nat M) N))) (and (=> _let_1 (tptp.pp (tptp.aa_nat_bool P M))) (=> (not _let_1) (forall ((I2 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) I2)) J3)) (tptp.pp (tptp.aa_nat_bool P J3)))))))))) (forall ((R2 tptp.nat) (N tptp.nat) (M tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat R2) N)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat R2) 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) R2))) (= (tptp.aa_nat_nat (tptp.modulo_modulo_nat M) N) R2))))) (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.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.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.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 ((Z tptp.complex) (N tptp.nat)) (let ((_let_1 (tptp.comm_s2602460028002588243omplex Z))) (= (tptp.aa_nat_complex _let_1 (tptp.aa_nat_nat tptp.suc N)) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.plus_plus_complex Z (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex N))) (tptp.aa_nat_complex _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.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.nat) (N tptp.nat)) (let ((_let_1 (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 ((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 ((A tptp.complex) (N tptp.nat)) (let ((_let_1 (tptp.comm_s2602460028002588243omplex 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)) (tptp.plus_plus_complex A (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex 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.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.nat) (N tptp.nat)) (let ((_let_1 (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 ((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 ((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.modulo_modulo_nat X) D))) _let_1))))) (forall ((Z tptp.complex) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.comm_s2602460028002588243omplex Z))) (= (tptp.aa_nat_complex _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N) M)) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_nat_complex _let_1 N)) (tptp.aa_nat_complex (tptp.comm_s2602460028002588243omplex (tptp.plus_plus_complex Z (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex 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.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.nat) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (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.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 ((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 ((N tptp.nat) (K tptp.nat)) (let ((_let_1 (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 ((K tptp.nat) (K6 tptp.nat) (N tptp.nat)) (let ((_let_1 (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 ((K tptp.nat) (K6 tptp.nat) (N tptp.nat)) (let ((_let_1 (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)) (let ((_let_1 (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 ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B))) (=> (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 B) C)) (tptp.modulo364778990260209775nteger A B)))))) (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (tptp.modulo_modulo_nat A))) (let ((_let_2 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B))) (=> (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.modulo_modulo_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) B)) C))) (tptp.aa_nat_nat _let_1 B))))))) (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.times_times_int B))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) C)) (= (tptp.modulo_modulo_int A (tptp.aa_int_int _let_1 C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int _let_1 (tptp.modulo_modulo_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A) B) C))) (tptp.modulo_modulo_int A B)))))) (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.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.modulo_modulo_int A _let_1) tptp.zero_zero_int)))) (forall ((A tptp.code_integer)) (let ((_let_1 (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 ((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.modulo_modulo_nat (tptp.aa_num_nat tptp.numeral_numeral_nat tptp.one)) _let_1) (tptp.aa_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.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.modulo_modulo_int (tptp.aa_num_int tptp.numeral_numeral_int tptp.one) _let_1) (tptp.modulo_modulo_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit1 N)) _let_1)) (= (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.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 Q2)))) (= (= (tptp.modulo364778990260209775nteger (tptp.numera6620942414471956472nteger tptp.one) _let_1) (tptp.modulo364778990260209775nteger (tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit1 N)) _let_1)) (= (tptp.modulo364778990260209775nteger (tptp.numera6620942414471956472nteger N) (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.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.modulo_modulo_nat (tptp.aa_num_nat tptp.numeral_numeral_nat tptp.one)) _let_1)) (= (tptp.aa_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.modulo_modulo_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit1 M)) _let_1) (tptp.modulo_modulo_int (tptp.aa_num_int tptp.numeral_numeral_int tptp.one) _let_1)) (= (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.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 Q2)))) (= (= (tptp.modulo364778990260209775nteger (tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit1 M)) _let_1) (tptp.modulo364778990260209775nteger (tptp.numera6620942414471956472nteger tptp.one) _let_1)) (= (tptp.modulo364778990260209775nteger (tptp.numera6620942414471956472nteger M) (tptp.numera6620942414471956472nteger Q2)) 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.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.modulo_modulo_int A _let_1) tptp.one_one_int)))) (forall ((A tptp.code_integer)) (let ((_let_1 (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 ((M tptp.nat) (N tptp.nat)) (= (tptp.aa_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.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 ((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.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 ((M tptp.nat) (N tptp.nat) (Z tptp.complex)) (let ((_let_1 (tptp.comm_s2602460028002588243omplex Z))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)) (= (tptp.aa_nat_complex _let_1 N) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_nat_complex _let_1 M)) (tptp.aa_nat_complex (tptp.comm_s2602460028002588243omplex (tptp.plus_plus_complex Z (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex 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.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.nat)) (let ((_let_1 (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.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 ((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 ((K tptp.nat) (K6 tptp.nat) (N tptp.nat)) (let ((_let_1 (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 ((K tptp.nat) (K6 tptp.nat) (N tptp.nat)) (let ((_let_1 (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) (N tptp.nat)) (let ((_let_1 (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 ((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.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 ((B tptp.nat) (A tptp.nat)) (let ((_let_1 (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))) B)))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) B)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_2) B)) (= _let_2 (tptp.aa_nat_nat _let_1 B))))))) (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (tptp.modulo_modulo_int 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))) 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 (tptp.aa_int_fun_int_bool tptp.ord_less_int _let_1) B)) (= _let_1 (tptp.modulo_modulo_int A B)))))) (forall ((B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (tptp.modulo364778990260209775nteger A (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))) B)))) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) B)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger _let_1) B)) (= _let_1 (tptp.modulo364778990260209775nteger A B)))))) (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.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.aa_int_fun_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.modulo_modulo_int A _let_1)) tptp.zero_zero_int)))) (forall ((A tptp.code_integer)) (let ((_let_1 (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 ((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.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.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.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.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.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.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 ((A tptp.nat) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (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.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.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.modulo_modulo_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A) _let_2) (tptp.aa_nat_int _let_1 M)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_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.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.power_8256067586552552935nteger _let_1 N))) (= (tptp.modulo364778990260209775nteger (tptp.divide6298287555418463151nteger A _let_2) (tptp.power_8256067586552552935nteger _let_1 M)) (tptp.divide6298287555418463151nteger (tptp.modulo364778990260209775nteger A (tptp.power_8256067586552552935nteger _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N) M))) _let_2))))) (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) (B2 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.aa_bool_nat tptp.zero_n2687167440665602831ol_nat B2)) (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.aa_int_fun_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) (B2 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 B2)) (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.aa_int_fun_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.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))) A3) (tptp.pp (tptp.aa_Code_integer_bool P A3)))) (=> (forall ((A3 tptp.code_integer) (B2 tptp.bool)) (let ((_let_1 (tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.plus_p5714425477246183910nteger (tptp.aa_bool_Code_integer tptp.zero_n356916108424825756nteger B2) (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 ((A2 tptp.nat) (B3 tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A2) B3)) (=> (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 A2) N)) (tptp.aa_nat_nat (tptp.if_nat (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.fequal_nat (tptp.aa_nat_nat (tptp.modulo_modulo_nat B3) 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 B3) N)))))) (forall ((B 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 B))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) B)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.modulo_modulo_nat A) _let_3)) B)) (= (tptp.aa_nat_nat _let_2 (tptp.aa_nat_nat _let_1 _let_3)) (tptp.aa_nat_nat _let_1 B)))))))) (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int 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 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 (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.modulo_modulo_int A _let_3)) B)) (= (tptp.aa_int_int _let_2 (tptp.aa_int_int _let_1 _let_3)) (tptp.aa_int_int _let_1 B)))))))) (forall ((B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_2 (tptp.aa_Cod1783974652533396728nteger _let_1 B))) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) B)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.modulo364778990260209775nteger A _let_2)) B)) (= (tptp.aa_Cod1783974652533396728nteger _let_1 (tptp.divide6298287555418463151nteger A _let_2)) (tptp.divide6298287555418463151nteger A B))))))) (forall ((M tptp.nat) (N tptp.nat) (A tptp.nat)) (let ((_let_1 (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.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.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.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.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.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.power_8256067586552552935nteger _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.power_8256067586552552935nteger _let_1 N)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.modulo364778990260209775nteger A (tptp.power_8256067586552552935nteger _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) M)))) _let_2)))))) (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.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.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 M))) (let ((_let_2 (tptp.modulo_modulo_int X (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_2 _let_1) (= _let_2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int _let_1) M)))))))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (tptp.modulo364778990260209775nteger A (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))) B)))) (=> (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) B)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger B) _let_1)) (= (tptp.minus_8373710615458151222nteger _let_1 B) (tptp.modulo364778990260209775nteger A B))))))) (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (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))) B)))) (=> (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) B)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B) _let_2)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat _let_2) B) (tptp.aa_nat_nat _let_1 B)))))))) (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (tptp.modulo_modulo_int 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))) B)))) (=> (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) _let_1)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int _let_1) B) (tptp.modulo_modulo_int A B))))))) (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.aa_nat_fun_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.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.aa_nat_fun_int_int tptp.bit_se4203085406695923979it_int N) (tptp.aa_int_int (tptp.aa_int_fun_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.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 ((N tptp.nat) (A tptp.code_integer)) (let ((_let_1 (tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_nat6383147911832638789nteger 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.aa_Cod1783974652533396728nteger (tptp.aa_nat6383147911832638789nteger 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.aa_nat_fun_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.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.aa_nat_fun_int_int tptp.bit_se7879613467334960850it_int N) (tptp.aa_int_int (tptp.aa_int_fun_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.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.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_nat6383147911832638789nteger 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.aa_Cod1783974652533396728nteger (tptp.aa_nat6383147911832638789nteger 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.aa_nat_fun_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.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.aa_nat_fun_int_int tptp.bit_se2159334234014336723it_int N) (tptp.aa_int_int (tptp.aa_int_fun_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.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 ((N tptp.nat) (A tptp.code_integer)) (let ((_let_1 (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)) (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.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.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.aa_bool_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.aa_int_fun_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.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.power_8256067586552552935nteger _let_1 M))) (= (tptp.divide6298287555418463151nteger _let_2 (tptp.power_8256067586552552935nteger _let_1 N)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_bool_Code_integer 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.power_8256067586552552935nteger _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) 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))) (=> (= (tptp.aa_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 ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_2 (tptp.aa_Cod1783974652533396728nteger _let_1 B))) (=> (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) B)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger B) (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 B)))))))) (forall ((A tptp.nat) (B 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 B))) (=> (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) B)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B) (tptp.aa_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 B))))))))) (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int 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 B))) (=> (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) (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 B))))))))) (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.binomial N) K))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) 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.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 ((N tptp.nat)) (= (tptp.aa_nat_nat (tptp.binomial N) tptp.zero_zero_nat) tptp.one_one_nat)) (forall ((N tptp.nat) (K tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc K))) (let ((_let_2 (tptp.binomial N))) (= (tptp.aa_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 ((N tptp.nat) (K tptp.nat)) (= (= (tptp.aa_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)) (= (tptp.aa_nat_nat (tptp.binomial N) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)) N)) (forall ((K tptp.nat)) (= (tptp.aa_nat_nat (tptp.binomial tptp.zero_zero_nat) (tptp.aa_nat_nat tptp.suc K)) tptp.zero_zero_nat)) (forall ((N tptp.nat) (K tptp.nat)) (let ((_let_1 (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.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 ((N tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N))) (= (tptp.aa_nat_nat (tptp.binomial _let_1) 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_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.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.modulo_modulo_int K L) K)))) (forall ((V tptp.num) (W tptp.num)) (= (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.modulo_modulo_int (tptp.aa_num_int tptp.numeral_numeral_int V) (tptp.aa_num_int tptp.numeral_numeral_int W))))) (forall ((V tptp.num) (W tptp.num)) (= (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.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 ((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.modulo_modulo_int M K)) M)))) (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.modulo_modulo_int K L)))))) (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.modulo_modulo_int K L)) L)))) (forall ((M tptp.int) (D tptp.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.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 ((A tptp.nat) (B tptp.nat)) (= (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_nat (tptp.modulo_modulo_nat A) B)) (tptp.modulo_modulo_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int A) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int B)))) (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.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.modulo_modulo_int K L))))) (forall ((I tptp.int) (K tptp.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 ((B tptp.int) (A tptp.int)) (let ((_let_1 (tptp.modulo_modulo_int A B))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) B)) (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) B)))))) (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (tptp.modulo_modulo_int A B))) (let ((_let_2 (tptp.aa_int_fun_int_bool tptp.ord_less_int B))) (=> (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 ((A2 tptp.int) (B3 tptp.int) (N tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A2) B3)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) N)) (=> (= (tptp.modulo_modulo_int A2 N) tptp.zero_zero_int) (=> (= (tptp.modulo_modulo_int B3 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.aa_int_fun_int_int tptp.divide_divide_int A2) N)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int B3) N)))))))) (forall ((A2 tptp.int) (N tptp.int)) (= A2 (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.divide_divide_int A2) N)) N)) (tptp.modulo_modulo_int A2 N)))) (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.modulo_modulo_int K L) _let_1))))) (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.modulo_modulo_int K L) (tptp.modulo_modulo_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int K) L) 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.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 ((P tptp.fun_int_bool) (N tptp.int) (K tptp.int)) (= (tptp.pp (tptp.aa_int_bool P (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 ((I2 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) I2)) 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 ((I2 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) I2)) J3))) (tptp.pp (tptp.aa_int_bool P J3)))))))) (forall ((A tptp.int) (B tptp.int) (Q2 tptp.int) (R2 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 B) Q2)) R2)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int R2) tptp.zero_zero_int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B) R2)) (= (tptp.modulo_modulo_int A B) R2))))) (forall ((A tptp.int) (B tptp.int) (Q2 tptp.int) (R2 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 B) Q2)) R2)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) R2)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int R2) B)) (= (tptp.modulo_modulo_int A B) R2))))) (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.times_times_int B))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) C)) (= (tptp.modulo_modulo_int A (tptp.aa_int_int _let_1 C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int _let_1 (tptp.modulo_modulo_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A) B) C))) (tptp.modulo_modulo_int A B)))))) (forall ((A2 tptp.int) (B3 tptp.int) (N tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A2) B3)) (=> (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.aa_int_fun_int_int tptp.divide_divide_int A2) N)) (tptp.if_int (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.fequal_int (tptp.modulo_modulo_int B3 N)) tptp.zero_zero_int) tptp.one_one_int tptp.zero_zero_int))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int B3) N)))))) (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.aa_int_fun_int_int tptp.divide_divide_int N) K)) (tptp.modulo_modulo_int N K))) (forall ((I2 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) I2)) J3))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool P I2) 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 tptp.zero_zero_int) K)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool P (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int N) K)) (tptp.modulo_modulo_int N K))) (forall ((I2 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) I2)) J3))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool P I2) J3))))))) (forall ((A tptp.int) (B 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.modulo_modulo_int (tptp.aa_int_int _let_2 (tptp.aa_int_int _let_1 B)) (tptp.aa_int_int _let_1 A)) (tptp.aa_int_int _let_2 (tptp.aa_int_int _let_1 (tptp.modulo_modulo_int B A)))))))) (forall ((A tptp.int) (B 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.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 B)) (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.modulo_modulo_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int B) tptp.one_one_int) A))) tptp.one_one_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_nat (tptp.binomial N) K) tptp.zero_zero_nat))) (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.binomial N) K)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.binomial _let_2) _let_1)) _let_1))))) (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.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.binomial N) K)))))) (forall ((K tptp.nat) (N tptp.nat)) (let ((_let_1 (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 ((M tptp.nat) (R2 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 R2))) (let ((_let_3 (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.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.binomial _let_2) M)))))))) (forall ((R2 tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat R2) N)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.binomial N) R2)) (tptp.aa_nat_nat (tptp.power_power_nat N) R2))))) (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.binomial N) K))))) (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (tptp.binomial (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) B))))) (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 B)) (tptp.aa_nat_nat _let_1 A)))))) (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (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.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.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 ((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.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.binomial N) K))) _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.binomial N) K)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat N) (tptp.aa_nat_nat (tptp.binomial (tptp.aa_nat_nat _let_1 tptp.one_one_nat)) K))))) (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.binomial N) _let_1)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat N) (tptp.aa_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.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.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_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.binomial N) 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.binomial N) K)) (tptp.aa_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) (K tptp.nat)) (let ((_let_1 (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.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 ((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.binomial N) K)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat N) (tptp.aa_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)))))) (forall ((M tptp.nat)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (let ((_let_2 (tptp.aa_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))))))) (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 ((N tptp.nat) (A tptp.code_integer)) (let ((_let_1 (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.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.aa_int_fun_int_int tptp.divide_divide_int A) _let_1))))))) (forall ((L tptp.nat)) (let ((_let_1 (tptp.aa_VEBT_VEBT_real tptp.vEBT_VEBT_cnt (tptp.vEBT_vebt_buildup (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.va))) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))))) (= (tptp.aa_real_real (tptp.foldr_real_real tptp.plus_plus_real (tptp.replicate_real L _let_1)) tptp.zero_zero_real) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real L)) _let_1)))) (forall ((R2 tptp.complex) (A tptp.complex) (B tptp.complex) (C tptp.complex) (D tptp.complex)) (let ((_let_1 (tptp.times_times_complex R2))) (=> (not (= R2 tptp.zero_zero_complex)) (=> (and (= A B) (not (= C D))) (not (= (tptp.plus_plus_complex A (tptp.aa_complex_complex _let_1 C)) (tptp.plus_plus_complex B (tptp.aa_complex_complex _let_1 D)))))))) (forall ((R2 tptp.real) (A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.times_times_real R2))) (=> (not (= R2 tptp.zero_zero_real)) (=> (and (= A B) (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 B) (tptp.aa_real_real _let_1 D)))))))) (forall ((R2 tptp.rat) (A tptp.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_rat tptp.times_times_rat R2))) (=> (not (= R2 tptp.zero_zero_rat)) (=> (and (= A B) (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 B) (tptp.aa_rat_rat _let_1 D)))))))) (forall ((R2 tptp.nat) (A tptp.nat) (B tptp.nat) (C tptp.nat) (D tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat R2))) (=> (not (= R2 tptp.zero_zero_nat)) (=> (and (= A B) (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 B) (tptp.aa_nat_nat _let_1 D)))))))) (forall ((R2 tptp.int) (A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.times_times_int R2))) (=> (not (= R2 tptp.zero_zero_int)) (=> (and (= A B) (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 B) (tptp.aa_int_int _let_1 D)))))))) (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))) (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.divide1717551699836669952omplex tptp.one_one_complex _let_2)) N))) (tptp.aa_nat_complex tptp.semiri5044797733671781792omplex N))))))) (forall ((X33 tptp.num)) (= (tptp.aa_num_nat tptp.size_num (tptp.aa_num_num tptp.bit1 X33)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_num_nat tptp.size_num X33)) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)))) (forall ((Xs tptp.list_real) (C tptp.real) (D tptp.real)) (let ((_let_1 (tptp.foldr_real_real tptp.plus_plus_real Xs))) (= (tptp.aa_real_real _let_1 (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 _let_1 D)) C)))) (forall ((X tptp.real) (Y4 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 Y4)) (= (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 Y4))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Y4))))))) (forall ((X tptp.real) (Y4 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 Y4)) (= (= (tptp.aa_real_real tptp.ln_ln_real X) (tptp.aa_real_real tptp.ln_ln_real Y4)) (= X Y4)))))) (forall ((N tptp.nat)) (= (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat N)) (tptp.aa_nat_rat tptp.semiri773545260158071498ct_rat N))) (forall ((N tptp.nat)) (= (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat N)) (tptp.aa_nat_int tptp.semiri1406184849735516958ct_int N))) (forall ((N tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat N))) (= (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat _let_1) _let_1))) (forall ((N tptp.nat)) (= (tptp.aa_nat_real tptp.semiri5074537144036343181t_real (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat N)) (tptp.aa_nat_real tptp.semiri2265585572941072030t_real N))) (forall ((N tptp.nat)) (= (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat N)) (tptp.aa_nat_complex tptp.semiri5044797733671781792omplex N))) (forall ((N tptp.nat)) (= (tptp.aa_int_int (tptp.bit_ri631733984087533419it_int N) tptp.zero_zero_int) tptp.zero_zero_int)) (forall ((M tptp.nat) (X tptp.real) (N tptp.nat) (Y4 tptp.real)) (= (= (tptp.replicate_real M X) (tptp.replicate_real N Y4)) (and (= M N) (=> (not (= M tptp.zero_zero_nat)) (= X Y4))))) (forall ((M tptp.nat) (X tptp.vEBT_VEBT) (N tptp.nat) (Y4 tptp.vEBT_VEBT)) (= (= (tptp.replicate_VEBT_VEBT M X) (tptp.replicate_VEBT_VEBT N Y4)) (and (= M N) (=> (not (= M tptp.zero_zero_nat)) (= X Y4))))) (forall ((X tptp.real) (Y4 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 Y4)) (= (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 Y4))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) Y4))))))) (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)))) (= (tptp.aa_real_real tptp.ln_ln_real tptp.one_one_real) tptp.zero_zero_real) (= (tptp.aa_nat_rat tptp.semiri773545260158071498ct_rat tptp.zero_zero_nat) tptp.one_one_rat) (= (tptp.aa_nat_int tptp.semiri1406184849735516958ct_int tptp.zero_zero_nat) tptp.one_one_int) (= (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat tptp.zero_zero_nat) tptp.one_one_nat) (= (tptp.aa_nat_real tptp.semiri2265585572941072030t_real tptp.zero_zero_nat) tptp.one_one_real) (= (tptp.aa_nat_complex tptp.semiri5044797733671781792omplex tptp.zero_zero_nat) tptp.one_one_complex) (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 ((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))))) (= (tptp.aa_nat_rat tptp.semiri773545260158071498ct_rat _let_58) tptp.one_one_rat) (= (tptp.aa_nat_int tptp.semiri1406184849735516958ct_int _let_58) tptp.one_one_int) (= (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat _let_58) tptp.one_one_nat) (= (tptp.aa_nat_real tptp.semiri2265585572941072030t_real _let_58) tptp.one_one_real) (= (tptp.aa_nat_complex tptp.semiri5044797733671781792omplex _let_58) tptp.one_one_complex) (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_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))))) (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_complex tptp.semiri5044797733671781792omplex _let_1) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex _let_1)) (tptp.aa_nat_complex tptp.semiri5044797733671781792omplex N))))) (= (tptp.aa_nat_rat tptp.semiri773545260158071498ct_rat _let_2) _let_130) (= (tptp.aa_nat_int tptp.semiri1406184849735516958ct_int _let_2) _let_63) (= (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat _let_2) _let_2) (= (tptp.aa_nat_real tptp.semiri2265585572941072030t_real _let_2) _let_40) (= (tptp.aa_nat_complex tptp.semiri5044797733671781792omplex _let_2) _let_76) (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 ((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 ((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)) (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 ((N tptp.nat)) (not (= (tptp.aa_nat_rat tptp.semiri773545260158071498ct_rat N) tptp.zero_zero_rat))) (forall ((N tptp.nat)) (not (= (tptp.aa_nat_int tptp.semiri1406184849735516958ct_int N) tptp.zero_zero_int))) (forall ((N tptp.nat)) (not (= (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat N) tptp.zero_zero_nat))) (forall ((N tptp.nat)) (not (= (tptp.aa_nat_real tptp.semiri2265585572941072030t_real N) tptp.zero_zero_real))) (forall ((N tptp.nat)) (not (= (tptp.aa_nat_complex tptp.semiri5044797733671781792omplex N) tptp.zero_zero_complex))) (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 ((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 ((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 ((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_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_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)) (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_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_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_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)) (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_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)) (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)) (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_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 ((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 ((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_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_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 ((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.semiri3624122377584611663nteger N)) (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_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 ((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)) (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 ((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)) (=> (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_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)) (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_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.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 ((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_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_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 ((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.semiri3624122377584611663nteger K)) (tptp.semiri3624122377584611663nteger N))) (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_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 ((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 ((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.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.semiri3624122377584611663nteger N) (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.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.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.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.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.power_power_nat N) N))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.ln_ln_real _let_40)) 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) (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 ((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) (Y4 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 Y4)) (= (tptp.aa_real_real tptp.ln_ln_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real X) Y4)) (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 Y4))))))) (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) (Y4 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 Y4)) (= (tptp.aa_real_real tptp.ln_ln_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real X) Y4)) (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 Y4))))))) (forall ((R2 tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat R2) 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) R2)))) (tptp.aa_nat_nat (tptp.power_power_nat N) R2))))) (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.binomial N) K)) (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat 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_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.semiri3624122377584611663nteger K)) (tptp.semiri3624122377584611663nteger (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) K)))) (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_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 ((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 ((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) (Y4 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 Y4)) (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 Y4))) (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) Y4)) Y4))))))) (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 ((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.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 ((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)))) (= (tptp.aa_num_nat tptp.size_num tptp.one) 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.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))))) (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_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_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 ((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_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 ((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_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 ((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_complex tptp.semiri5044797733671781792omplex N) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex N)) (tptp.aa_nat_complex tptp.semiri5044797733671781792omplex (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) tptp.one_one_nat)))))) (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 ((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 ((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.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.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 ((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.binomial N) K))) (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_nat_rat tptp.semiri681578069525770553at_rat (tptp.aa_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.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_nat_complex tptp.semiri8010041392384452111omplex (tptp.aa_nat_nat (tptp.binomial N) K)) (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 ((B tptp.complex) (A tptp.complex)) (= (= B (tptp.plus_plus_complex B A)) (= A tptp.zero_zero_complex))) (forall ((B tptp.real) (A tptp.real)) (= (= B (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real B) A)) (= A tptp.zero_zero_real))) (forall ((B tptp.rat) (A tptp.rat)) (= (= B (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat B) A)) (= A tptp.zero_zero_rat))) (forall ((B tptp.nat) (A tptp.nat)) (= (= B (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat B) A)) (= A tptp.zero_zero_nat))) (forall ((B tptp.int) (A tptp.int)) (= (= B (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int B) A)) (= A tptp.zero_zero_int))) (forall ((W tptp.real) (Y4 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 Y4)) (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 Y4))) (or (= W X) (= Y4 Z)))))) (forall ((W tptp.rat) (Y4 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 Y4)) (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 Y4))) (or (= W X) (= Y4 Z)))))) (forall ((W tptp.nat) (Y4 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 Y4)) (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 Y4))) (or (= W X) (= Y4 Z)))))) (forall ((W tptp.int) (Y4 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 Y4)) (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 Y4))) (or (= W X) (= Y4 Z)))))) (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.times_times_real B))) (let ((_let_2 (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A))) (= (and (not (= A B)) (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) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_rat tptp.times_times_rat B))) (let ((_let_2 (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A))) (= (and (not (= A B)) (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) (B tptp.nat) (C tptp.nat) (D tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B))) (let ((_let_2 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A))) (= (and (not (= A B)) (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) (B tptp.int) (C tptp.int) (D tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.times_times_int B))) (let ((_let_2 (tptp.aa_int_fun_int_int tptp.times_times_int A))) (= (and (not (= A B)) (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 ((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 ((X tptp.real) (Y4 tptp.real) (Z tptp.real)) (= (= X (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real Y4) Z)) (= Y4 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) Z)))) (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 ((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 ((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.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.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 ((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_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 ((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 ((N tptp.nat) (A tptp.code_integer)) (let ((_let_1 (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.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.aa_int_fun_int_int tptp.divide_divide_int A) _let_1)))))))))))) (= (tptp.aa_real_real (tptp.foldr_real_real tptp.plus_plus_real (tptp.map_VEBT_VEBT_real tptp.vEBT_VEBT_cnt (tptp.replicate_VEBT_VEBT (tptp.aa_nat_nat _let_52 _let_4) _let_152))) tptp.zero_zero_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_40) _let_4)) (tptp.aa_VEBT_VEBT_real tptp.vEBT_VEBT_cnt _let_152))) (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 ((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.uminus1482373934393186551omplex (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) (B tptp.real)) (= (= (tptp.aa_real_real tptp.uminus_uminus_real A) (tptp.aa_real_real tptp.uminus_uminus_real B)) (= A B))) (forall ((A tptp.int) (B tptp.int)) (= (= (tptp.aa_int_int tptp.uminus_uminus_int A) (tptp.aa_int_int tptp.uminus_uminus_int B)) (= A B))) (forall ((A tptp.complex) (B tptp.complex)) (= (= (tptp.uminus1482373934393186551omplex A) (tptp.uminus1482373934393186551omplex B)) (= A B))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger B)) (= A B))) (forall ((A tptp.rat) (B tptp.rat)) (= (= (tptp.aa_rat_rat tptp.uminus_uminus_rat A) (tptp.aa_rat_rat tptp.uminus_uminus_rat B)) (= A B))) (forall ((B tptp.real)) (= (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_real_real tptp.uminus_uminus_real B)) B)) (forall ((B tptp.int)) (= (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_int_int tptp.uminus_uminus_int B)) B)) (forall ((B tptp.complex)) (= (tptp.uminus1482373934393186551omplex (tptp.uminus1482373934393186551omplex B)) B)) (forall ((B tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger B)) B)) (forall ((B tptp.rat)) (= (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat B)) B)) (forall ((A2 tptp.set_int) (B3 tptp.set_int)) (= (tptp.ord_less_eq_set_int (tptp.uminus1532241313380277803et_int A2) (tptp.uminus1532241313380277803et_int B3)) (tptp.ord_less_eq_set_int B3 A2))) (forall ((A2 tptp.set_int) (B3 tptp.set_int)) (=> (tptp.ord_less_eq_set_int A2 B3) (tptp.ord_less_eq_set_int (tptp.uminus1532241313380277803et_int B3) (tptp.uminus1532241313380277803et_int A2)))) (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 ((B 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 B)) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A))) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger A) B)))) (forall ((B 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 B)) (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) B)))) (forall ((B 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 B)) (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) B)))) (forall ((B 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 B)) (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) B)))) (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 ((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) 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.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)) (= (= 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.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))) (= (tptp.aa_real_real tptp.uminus_uminus_real tptp.zero_zero_real) tptp.zero_zero_real) _let_125 (= (tptp.uminus1482373934393186551omplex tptp.zero_zero_complex) tptp.zero_zero_complex) _let_50 (= (tptp.aa_rat_rat tptp.uminus_uminus_rat tptp.zero_zero_rat) tptp.zero_zero_rat) (forall ((B 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 B)) (tptp.aa_real_real tptp.uminus_uminus_real A))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B)))) (forall ((B 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 B)) (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) B)))) (forall ((B 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 B)) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A))) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger A) B)))) (forall ((B 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 B)) (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) B)))) (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.uminus1482373934393186551omplex (tptp.numera6690914467698888265omplex M)) (tptp.uminus1482373934393186551omplex (tptp.numera6690914467698888265omplex N))) (= M N))) (forall ((M tptp.num) (N tptp.num)) (= (= (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.numera6620942414471956472nteger M)) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (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) (B tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real tptp.uminus_uminus_real A)) B) (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) B)))) (forall ((A tptp.int) (B 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)) B) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) B)))) (forall ((A tptp.complex) (B tptp.complex)) (= (tptp.aa_complex_complex (tptp.times_times_complex (tptp.uminus1482373934393186551omplex A)) B) (tptp.uminus1482373934393186551omplex (tptp.aa_complex_complex (tptp.times_times_complex A) B)))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A)) B) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) B)))) (forall ((A tptp.rat) (B 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)) B) (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) B)))) (forall ((A tptp.real) (B 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 B)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) B))) (forall ((A tptp.int) (B 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 B)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) B))) (forall ((A tptp.complex) (B tptp.complex)) (= (tptp.aa_complex_complex (tptp.times_times_complex (tptp.uminus1482373934393186551omplex A)) (tptp.uminus1482373934393186551omplex B)) (tptp.aa_complex_complex (tptp.times_times_complex A) B))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A)) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger B)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) B))) (forall ((A tptp.rat) (B 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 B)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) B))) (forall ((A tptp.real) (B 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 B)) (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_real_real _let_1 B))))) (forall ((A tptp.int) (B 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 B)) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_int_int _let_1 B))))) (forall ((A tptp.complex) (B tptp.complex)) (let ((_let_1 (tptp.times_times_complex A))) (= (tptp.aa_complex_complex _let_1 (tptp.uminus1482373934393186551omplex B)) (tptp.uminus1482373934393186551omplex (tptp.aa_complex_complex _let_1 B))))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A))) (= (tptp.aa_Cod1783974652533396728nteger _let_1 (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger B)) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_Cod1783974652533396728nteger _let_1 B))))) (forall ((A tptp.rat) (B 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 B)) (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_rat_rat _let_1 B))))) (forall ((A tptp.real) (B 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)) B)) B)) (forall ((A tptp.int) (B 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)) B)) B)) (forall ((A tptp.complex) (B tptp.complex)) (= (tptp.plus_plus_complex A (tptp.plus_plus_complex (tptp.uminus1482373934393186551omplex A) B)) B)) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (tptp.plus_p5714425477246183910nteger A (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A) B)) B)) (forall ((A tptp.rat) (B 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)) B)) B)) (forall ((A tptp.real) (B 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) B)) B)) (forall ((A tptp.int) (B 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) B)) B)) (forall ((A tptp.complex) (B tptp.complex)) (= (tptp.plus_plus_complex (tptp.uminus1482373934393186551omplex A) (tptp.plus_plus_complex A B)) B)) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A) (tptp.plus_p5714425477246183910nteger A B)) B)) (forall ((A tptp.rat) (B 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) B)) B)) (forall ((A tptp.real) (B tptp.real)) (= (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) B)) (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 B)))) (forall ((A tptp.int) (B 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) B)) (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 B)))) (forall ((A tptp.complex) (B tptp.complex)) (= (tptp.uminus1482373934393186551omplex (tptp.plus_plus_complex A B)) (tptp.plus_plus_complex (tptp.uminus1482373934393186551omplex A) (tptp.uminus1482373934393186551omplex B)))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.plus_p5714425477246183910nteger A B)) (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger B)))) (forall ((A tptp.rat) (B 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) B)) (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 B)))) (forall ((A tptp.real) (B tptp.real)) (= (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A) B)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real B) A))) (forall ((A tptp.int) (B 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) B)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int B) A))) (forall ((A tptp.complex) (B tptp.complex)) (= (tptp.uminus1482373934393186551omplex (tptp.minus_minus_complex A B)) (tptp.minus_minus_complex B A))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.minus_8373710615458151222nteger A B)) (tptp.minus_8373710615458151222nteger B A))) (forall ((A tptp.rat) (B tptp.rat)) (= (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_rat_rat (tptp.minus_minus_rat A) B)) (tptp.aa_rat_rat (tptp.minus_minus_rat B) A))) (forall ((A tptp.int) (B tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int (tptp.aa_int_int tptp.uminus_uminus_int A)) (tptp.aa_int_int tptp.uminus_uminus_int B)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A) B))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (tptp.divide6298287555418463151nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger B)) (tptp.divide6298287555418463151nteger A B))) _let_151 (= (tptp.abs_abs_complex tptp.zero_zero_complex) tptp.zero_zero_complex) _let_150 _let_149 _let_148 _let_151 _let_150 _let_149 _let_148 (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))) (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 ((X tptp.real) (Y4 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)) Y4)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.dvd_dvd_real X) Y4)))) (forall ((X tptp.int) (Y4 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)) Y4)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int X) Y4)))) (forall ((X tptp.complex) (Y4 tptp.complex)) (= (tptp.pp (tptp.aa_complex_bool (tptp.dvd_dvd_complex (tptp.uminus1482373934393186551omplex X)) Y4)) (tptp.pp (tptp.aa_complex_bool (tptp.dvd_dvd_complex X) Y4)))) (forall ((X tptp.code_integer) (Y4 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)) Y4)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer X) Y4)))) (forall ((X tptp.rat) (Y4 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)) Y4)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.dvd_dvd_rat X) Y4)))) (forall ((X tptp.real) (Y4 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 Y4))) (tptp.pp (tptp.aa_real_bool _let_1 Y4))))) (forall ((X tptp.int) (Y4 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 Y4))) (tptp.pp (tptp.aa_int_bool _let_1 Y4))))) (forall ((X tptp.complex) (Y4 tptp.complex)) (let ((_let_1 (tptp.dvd_dvd_complex X))) (= (tptp.pp (tptp.aa_complex_bool _let_1 (tptp.uminus1482373934393186551omplex Y4))) (tptp.pp (tptp.aa_complex_bool _let_1 Y4))))) (forall ((X tptp.code_integer) (Y4 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 Y4))) (tptp.pp (tptp.aa_Code_integer_bool _let_1 Y4))))) (forall ((X tptp.rat) (Y4 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 Y4))) (tptp.pp (tptp.aa_rat_bool _let_1 Y4))))) (forall ((N tptp.num)) (let ((_let_1 (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)))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (tptp.plus_p5714425477246183910nteger (tptp.abs_abs_Code_integer A) (tptp.abs_abs_Code_integer B)))) (= (tptp.abs_abs_Code_integer _let_1) _let_1))) (forall ((A tptp.real) (B 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 B)))) (= (tptp.aa_real_real tptp.abs_abs_real _let_1) _let_1))) (forall ((A tptp.rat) (B 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 B)))) (= (tptp.aa_rat_rat tptp.abs_abs_rat _let_1) _let_1))) (forall ((A tptp.int) (B 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 B)))) (= (tptp.aa_int_int tptp.abs_abs_int _let_1) _let_1))) _let_129 (= (tptp.abs_abs_complex tptp.one_one_complex) tptp.one_one_complex) _let_128 _let_127 _let_126 (forall ((A tptp.complex) (B tptp.complex)) (= (tptp.abs_abs_complex (tptp.divide1717551699836669952omplex A B)) (tptp.divide1717551699836669952omplex (tptp.abs_abs_complex A) (tptp.abs_abs_complex B)))) (forall ((A tptp.real) (B tptp.real)) (= (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real A) B)) (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 B)))) (forall ((A tptp.rat) (B tptp.rat)) (= (tptp.aa_rat_rat tptp.abs_abs_rat (tptp.aa_rat_rat (tptp.divide_divide_rat A) B)) (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 B)))) (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.abs_abs_complex (tptp.uminus1482373934393186551omplex A)) (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 ((A tptp.int) (B tptp.int)) (= (tptp.modulo_modulo_int (tptp.aa_int_int tptp.uminus_uminus_int A) (tptp.aa_int_int tptp.uminus_uminus_int B)) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.modulo_modulo_int A B)))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (tptp.modulo364778990260209775nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger B)) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.modulo364778990260209775nteger A B)))) (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 ((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 ((N tptp.nat)) (let ((_let_1 (tptp.semiri4939895301339042750nteger N))) (= (tptp.abs_abs_Code_integer _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)) (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 ((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.aa_bool_Code_integer tptp.zero_n356916108424825756nteger P))) (= (tptp.abs_abs_Code_integer _let_1) _let_1))) (= (tptp.tanh_complex tptp.zero_zero_complex) tptp.zero_zero_complex) (= (tptp.aa_real_real tptp.tanh_real tptp.zero_zero_real) tptp.zero_zero_real) (forall ((X tptp.real)) (= (= (tptp.aa_real_real tptp.tanh_real X) tptp.zero_zero_real) (= X tptp.zero_zero_real))) (forall ((X tptp.real) (Y4 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 Y4))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) Y4)))) (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)) (= (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)) (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)) (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)) (= (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.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.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_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.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.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)) (= (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)) 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.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.plus_plus_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.plus_plus_complex A (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 ((B tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real tptp.zero_zero_real) B) (tptp.aa_real_real tptp.uminus_uminus_real B))) (forall ((B tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int tptp.zero_zero_int) B) (tptp.aa_int_int tptp.uminus_uminus_int B))) (forall ((B tptp.complex)) (= (tptp.minus_minus_complex tptp.zero_zero_complex B) (tptp.uminus1482373934393186551omplex B))) (forall ((B tptp.code_integer)) (= (tptp.minus_8373710615458151222nteger tptp.zero_z3403309356797280102nteger B) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger B))) (forall ((B tptp.rat)) (= (tptp.aa_rat_rat (tptp.minus_minus_rat tptp.zero_zero_rat) B) (tptp.aa_rat_rat tptp.uminus_uminus_rat B))) (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.minus_minus_complex tptp.zero_zero_complex A) (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.plus_plus_complex (tptp.uminus1482373934393186551omplex _let_2) (tptp.uminus1482373934393186551omplex _let_1)) (tptp.uminus1482373934393186551omplex (tptp.plus_plus_complex _let_2 _let_1)))))) (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (tptp.numera6620942414471956472nteger N))) (let ((_let_2 (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 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.uminus1482373934393186551omplex tptp.one_one_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 ((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.uminus1482373934393186551omplex tptp.one_one_complex)) Z) (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 ((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.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.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.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.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.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.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.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.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.real) (B tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A) (tptp.aa_real_real tptp.uminus_uminus_real B)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) B))) (forall ((A tptp.int) (B 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 B)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) B))) (forall ((A tptp.complex) (B tptp.complex)) (= (tptp.minus_minus_complex A (tptp.uminus1482373934393186551omplex B)) (tptp.plus_plus_complex A B))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (tptp.minus_8373710615458151222nteger A (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger B)) (tptp.plus_p5714425477246183910nteger A B))) (forall ((A tptp.rat) (B tptp.rat)) (= (tptp.aa_rat_rat (tptp.minus_minus_rat A) (tptp.aa_rat_rat tptp.uminus_uminus_rat B)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) B))) (forall ((A tptp.real) (B tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real tptp.uminus_uminus_real A)) B) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real B) A))) (forall ((A tptp.int) (B 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)) B) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int B) A))) (forall ((A tptp.complex) (B tptp.complex)) (= (tptp.plus_plus_complex (tptp.uminus1482373934393186551omplex A) B) (tptp.minus_minus_complex B A))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A) B) (tptp.minus_8373710615458151222nteger B A))) (forall ((A tptp.rat) (B 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)) B) (tptp.aa_rat_rat (tptp.minus_minus_rat B) 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 ((A tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_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 ((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.divide1717551699836669952omplex X (tptp.uminus1482373934393186551omplex tptp.one_one_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 ((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.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_85) tptp.one_one_real) (= (tptp.aa_int_int tptp.abs_abs_int _let_59) tptp.one_one_int) (= (tptp.abs_abs_Code_integer _let_60) tptp.one_one_Code_integer) (= (tptp.aa_rat_rat tptp.abs_abs_rat _let_100) tptp.one_one_rat) (forall ((B tptp.int) (A tptp.int)) (= (tptp.modulo_modulo_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int B) A) B) (tptp.modulo_modulo_int (tptp.aa_int_int tptp.uminus_uminus_int A) B))) (forall ((B tptp.code_integer) (A tptp.code_integer)) (= (tptp.modulo364778990260209775nteger (tptp.minus_8373710615458151222nteger B A) B) (tptp.modulo364778990260209775nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A) B))) (forall ((N tptp.nat) (M tptp.nat)) (= (= (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N)) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int M)) (and (= N tptp.zero_zero_nat) (= M tptp.zero_zero_nat)))) (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 ((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) (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)) (= (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)) (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_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))))) (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.neg_numeral_dbl_int (tptp.aa_int_int tptp.uminus_uminus_int _let_1)) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.neg_numeral_dbl_int _let_1))))) (forall ((K tptp.num)) (let ((_let_1 (tptp.numera6690914467698888265omplex K))) (= (tptp.neg_nu7009210354673126013omplex (tptp.uminus1482373934393186551omplex _let_1)) (tptp.uminus1482373934393186551omplex (tptp.neg_nu7009210354673126013omplex _let_1))))) (forall ((K tptp.num)) (let ((_let_1 (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))))) (= (tptp.aa_real_real tptp.neg_nu8295874005876285629c_real _let_85) _let_85) (= (tptp.neg_nu5851722552734809277nc_int _let_59) _let_59) (= (tptp.neg_nu8557863876264182079omplex _let_75) _let_75) (= (tptp.neg_nu5831290666863070958nteger _let_60) _let_60) (= (tptp.aa_rat_rat tptp.neg_nu5219082963157363817nc_rat _let_100) _let_100) (= (tptp.aa_real_real _let_144 tptp.one_one_real) tptp.zero_zero_real) (= (tptp.aa_int_int _let_143 tptp.one_one_int) tptp.zero_zero_int) (= (tptp.plus_plus_complex _let_75 tptp.one_one_complex) tptp.zero_zero_complex) (= (tptp.plus_p5714425477246183910nteger _let_60 tptp.one_one_Code_integer) tptp.zero_z3403309356797280102nteger) (= (tptp.aa_rat_rat _let_142 tptp.one_one_rat) tptp.zero_zero_rat) (= (tptp.aa_real_real _let_147 _let_85) tptp.zero_zero_real) (= (tptp.aa_int_int _let_146 _let_59) tptp.zero_zero_int) (= (tptp.plus_plus_complex tptp.one_one_complex _let_75) tptp.zero_zero_complex) (= (tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer _let_60) tptp.zero_z3403309356797280102nteger) (= (tptp.aa_rat_rat _let_145 _let_100) tptp.zero_zero_rat) (= (tptp.aa_real_real _let_138 _let_85) tptp.zero_zero_real) (= (tptp.aa_int_int _let_137 _let_59) tptp.zero_zero_int) (= (tptp.minus_minus_complex _let_75 _let_75) tptp.zero_zero_complex) (= (tptp.minus_8373710615458151222nteger _let_60 _let_60) tptp.zero_z3403309356797280102nteger) (= (tptp.aa_rat_rat _let_136 _let_100) 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.uminus1482373934393186551omplex tptp.one_one_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.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.uminus1482373934393186551omplex (tptp.numera6690914467698888265omplex N)) (tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (= N tptp.one))) (forall ((N tptp.num)) (= (= (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (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 ((A tptp.rat) (B 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 B))) 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)) (= B tptp.zero_zero_rat)))) (forall ((A tptp.real) (B 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 B))) 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)) (= B tptp.zero_zero_real)))) (forall ((A tptp.rat) (B 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 B)))) (or (tptp.pp (tptp.aa_rat_bool _let_1 A)) (= B tptp.zero_zero_rat))))) (forall ((A tptp.real) (B 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 B)))) (or (tptp.pp (tptp.aa_real_bool _let_1 A)) (= B tptp.zero_zero_real))))) (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 ((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 ((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.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.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.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.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.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 ((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.uminus1482373934393186551omplex (tptp.numera6690914467698888265omplex W))) (tptp.aa_num_real tptp.numeral_numeral_real W))) (forall ((V tptp.num) (W tptp.num) (Y4 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))) Y4)) (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.plus_plus_num V) W)))) Y4))) (forall ((V tptp.num) (W tptp.num) (Y4 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))) Y4)) (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.plus_plus_num V) W)))) Y4))) (forall ((V tptp.num) (W tptp.num) (Y4 tptp.complex)) (= (tptp.plus_plus_complex (tptp.uminus1482373934393186551omplex (tptp.numera6690914467698888265omplex V)) (tptp.plus_plus_complex (tptp.uminus1482373934393186551omplex (tptp.numera6690914467698888265omplex W)) Y4)) (tptp.plus_plus_complex (tptp.uminus1482373934393186551omplex (tptp.numera6690914467698888265omplex (tptp.aa_num_num (tptp.plus_plus_num V) W))) Y4))) (forall ((V tptp.num) (W tptp.num) (Y4 tptp.code_integer)) (= (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.numera6620942414471956472nteger V)) (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.numera6620942414471956472nteger W)) Y4)) (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.numera6620942414471956472nteger (tptp.aa_num_num (tptp.plus_plus_num V) W))) Y4))) (forall ((V tptp.num) (W tptp.num) (Y4 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))) Y4)) (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.plus_plus_num V) W)))) Y4))) (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.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.plus_plus_num M) N))))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.minus_minus_complex (tptp.uminus1482373934393186551omplex (tptp.numera6690914467698888265omplex M)) (tptp.numera6690914467698888265omplex N)) (tptp.uminus1482373934393186551omplex (tptp.numera6690914467698888265omplex (tptp.aa_num_num (tptp.plus_plus_num M) N))))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.minus_8373710615458151222nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.numera6620942414471956472nteger M)) (tptp.numera6620942414471956472nteger N)) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.numera6620942414471956472nteger (tptp.aa_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.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.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.plus_plus_num M) N)))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.minus_minus_complex (tptp.numera6690914467698888265omplex M) (tptp.uminus1482373934393186551omplex (tptp.numera6690914467698888265omplex N))) (tptp.numera6690914467698888265omplex (tptp.aa_num_num (tptp.plus_plus_num M) N)))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.minus_8373710615458151222nteger (tptp.numera6620942414471956472nteger M) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.numera6620942414471956472nteger N))) (tptp.numera6620942414471956472nteger (tptp.aa_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.plus_plus_num M) N)))) (forall ((V tptp.num) (W tptp.num) (Y4 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))) Y4)) (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.times_times_num V) W))) Y4))) (forall ((V tptp.num) (W tptp.num) (Y4 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))) Y4)) (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.times_times_num V) W))) Y4))) (forall ((V tptp.num) (W tptp.num) (Y4 tptp.complex)) (= (tptp.aa_complex_complex (tptp.times_times_complex (tptp.uminus1482373934393186551omplex (tptp.numera6690914467698888265omplex V))) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.uminus1482373934393186551omplex (tptp.numera6690914467698888265omplex W))) Y4)) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.numera6690914467698888265omplex (tptp.aa_num_num (tptp.times_times_num V) W))) Y4))) (forall ((V tptp.num) (W tptp.num) (Y4 tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.numera6620942414471956472nteger V))) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.numera6620942414471956472nteger W))) Y4)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.numera6620942414471956472nteger (tptp.aa_num_num (tptp.times_times_num V) W))) Y4))) (forall ((V tptp.num) (W tptp.num) (Y4 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))) Y4)) (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.times_times_num V) W))) Y4))) (forall ((V tptp.num) (W tptp.num) (Y4 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))) Y4)) (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.times_times_num V) W)))) Y4))) (forall ((V tptp.num) (W tptp.num) (Y4 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))) Y4)) (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.times_times_num V) W)))) Y4))) (forall ((V tptp.num) (W tptp.num) (Y4 tptp.complex)) (= (tptp.aa_complex_complex (tptp.times_times_complex (tptp.numera6690914467698888265omplex V)) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.uminus1482373934393186551omplex (tptp.numera6690914467698888265omplex W))) Y4)) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.uminus1482373934393186551omplex (tptp.numera6690914467698888265omplex (tptp.aa_num_num (tptp.times_times_num V) W)))) Y4))) (forall ((V tptp.num) (W tptp.num) (Y4 tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.numera6620942414471956472nteger V)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.numera6620942414471956472nteger W))) Y4)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.numera6620942414471956472nteger (tptp.aa_num_num (tptp.times_times_num V) W)))) Y4))) (forall ((V tptp.num) (W tptp.num) (Y4 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))) Y4)) (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.times_times_num V) W)))) Y4))) (forall ((V tptp.num) (W tptp.num) (Y4 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)) Y4)) (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.times_times_num V) W)))) Y4))) (forall ((V tptp.num) (W tptp.num) (Y4 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)) Y4)) (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.times_times_num V) W)))) Y4))) (forall ((V tptp.num) (W tptp.num) (Y4 tptp.complex)) (= (tptp.aa_complex_complex (tptp.times_times_complex (tptp.uminus1482373934393186551omplex (tptp.numera6690914467698888265omplex V))) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.numera6690914467698888265omplex W)) Y4)) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.uminus1482373934393186551omplex (tptp.numera6690914467698888265omplex (tptp.aa_num_num (tptp.times_times_num V) W)))) Y4))) (forall ((V tptp.num) (W tptp.num) (Y4 tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.numera6620942414471956472nteger V))) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.numera6620942414471956472nteger W)) Y4)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.numera6620942414471956472nteger (tptp.aa_num_num (tptp.times_times_num V) W)))) Y4))) (forall ((V tptp.num) (W tptp.num) (Y4 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)) Y4)) (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.times_times_num V) W)))) Y4))) (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.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.times_times_num M) N))))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.aa_complex_complex (tptp.times_times_complex (tptp.numera6690914467698888265omplex M)) (tptp.uminus1482373934393186551omplex (tptp.numera6690914467698888265omplex N))) (tptp.uminus1482373934393186551omplex (tptp.numera6690914467698888265omplex (tptp.aa_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.numera6620942414471956472nteger M)) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.numera6620942414471956472nteger N))) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.numera6620942414471956472nteger (tptp.aa_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.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.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.times_times_num M) N))))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.aa_complex_complex (tptp.times_times_complex (tptp.uminus1482373934393186551omplex (tptp.numera6690914467698888265omplex M))) (tptp.numera6690914467698888265omplex N)) (tptp.uminus1482373934393186551omplex (tptp.numera6690914467698888265omplex (tptp.aa_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.numera6620942414471956472nteger M))) (tptp.numera6620942414471956472nteger N)) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.numera6620942414471956472nteger (tptp.aa_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.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.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.times_times_num M) N)))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.aa_complex_complex (tptp.times_times_complex (tptp.uminus1482373934393186551omplex (tptp.numera6690914467698888265omplex M))) (tptp.uminus1482373934393186551omplex (tptp.numera6690914467698888265omplex N))) (tptp.numera6690914467698888265omplex (tptp.aa_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.numera6620942414471956472nteger M))) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.numera6620942414471956472nteger N))) (tptp.numera6620942414471956472nteger (tptp.aa_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.times_times_num M) N)))) (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 ((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.numera6620942414471956472nteger M))) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (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_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_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.numera6620942414471956472nteger M))) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (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_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.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 ((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 ((B 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 B) _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)) B))))) (forall ((B 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 B) _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)) B))))) (forall ((A tptp.rat) (B 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 B) _let_1))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) _let_1)))))) (forall ((A tptp.real) (B 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 B) _let_1))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real B) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) _let_1)))))) (forall ((B 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 B) _let_1) A) (and (=> (not _let_2) (= B (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) _let_1))) (=> _let_2 (= A tptp.zero_zero_real))))))) (forall ((B tptp.complex) (W tptp.num) (A tptp.complex)) (let ((_let_1 (tptp.uminus1482373934393186551omplex (tptp.numera6690914467698888265omplex W)))) (let ((_let_2 (= _let_1 tptp.zero_zero_complex))) (= (= (tptp.divide1717551699836669952omplex B _let_1) A) (and (=> (not _let_2) (= B (tptp.aa_complex_complex (tptp.times_times_complex A) _let_1))) (=> _let_2 (= A tptp.zero_zero_complex))))))) (forall ((B 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 B) _let_1) A) (and (=> (not _let_2) (= B (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) (B 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 B) _let_1)) (and (=> (not _let_2) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) _let_1) B)) (=> _let_2 (= A tptp.zero_zero_real))))))) (forall ((A tptp.complex) (B tptp.complex) (W tptp.num)) (let ((_let_1 (tptp.uminus1482373934393186551omplex (tptp.numera6690914467698888265omplex W)))) (let ((_let_2 (= _let_1 tptp.zero_zero_complex))) (= (= A (tptp.divide1717551699836669952omplex B _let_1)) (and (=> (not _let_2) (= (tptp.aa_complex_complex (tptp.times_times_complex A) _let_1) B)) (=> _let_2 (= A tptp.zero_zero_complex))))))) (forall ((A tptp.rat) (B 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 B) _let_1)) (and (=> (not _let_2) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) _let_1) B)) (=> _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.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 ((B 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 B) _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)) B))))) (forall ((B 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 B) _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)) B))))) (forall ((A tptp.real) (B 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 B) _let_1))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) _let_1)))))) (forall ((A tptp.rat) (B 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 B) _let_1))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) (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.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.power_8256067586552552935nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A) _let_1) (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 ((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.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.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.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.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.code_integer)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.power_8256067586552552935nteger (tptp.abs_abs_Code_integer A) _let_1) (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.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 ((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)))) (= (tptp.aa_real_real _let_144 _let_85) _let_133) (= (tptp.aa_int_int _let_143 _let_59) _let_64) (= (tptp.plus_plus_complex _let_75 _let_75) _let_132) (= (tptp.plus_p5714425477246183910nteger _let_60 _let_60) _let_65) (= (tptp.aa_rat_rat _let_142 _let_100) _let_131) (= (tptp.aa_real_real _let_141 _let_85) _let_40) (= (tptp.aa_int_int _let_140 _let_59) _let_63) (= (tptp.minus_minus_complex tptp.one_one_complex _let_75) _let_76) (= (tptp.minus_8373710615458151222nteger tptp.one_one_Code_integer _let_60) _let_48) (= (tptp.aa_rat_rat _let_139 _let_100) _let_130) (= (tptp.aa_real_real _let_138 tptp.one_one_real) _let_133) (= (tptp.aa_int_int _let_137 tptp.one_one_int) _let_64) (= (tptp.minus_minus_complex _let_75 tptp.one_one_complex) _let_132) (= (tptp.minus_8373710615458151222nteger _let_60 tptp.one_one_Code_integer) _let_65) (= (tptp.aa_rat_rat _let_136 tptp.one_one_rat) _let_131) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int _let_59) _let_63) _let_59) (= (tptp.divide6298287555418463151nteger _let_60 _let_48) _let_60) _let_135 _let_134 _let_135 _let_134 (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.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.power_8256067586552552935nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A) _let_1) (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 ((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.uminus1482373934393186551omplex A)) N) (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.power_8256067586552552935nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A) N) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (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.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.power_8256067586552552935nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A) N) (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 ((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.power_8256067586552552935nteger (tptp.abs_abs_Code_integer A) _let_1) (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.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 ((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 ((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.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.plus_plus_num tptp.one) N)))) (forall ((N tptp.num)) (= (tptp.minus_minus_complex tptp.one_one_complex (tptp.uminus1482373934393186551omplex (tptp.numera6690914467698888265omplex N))) (tptp.numera6690914467698888265omplex (tptp.aa_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.numera6620942414471956472nteger N))) (tptp.numera6620942414471956472nteger (tptp.aa_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.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.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.plus_plus_num M) tptp.one))))) (forall ((M tptp.num)) (= (tptp.minus_minus_complex (tptp.uminus1482373934393186551omplex (tptp.numera6690914467698888265omplex M)) tptp.one_one_complex) (tptp.uminus1482373934393186551omplex (tptp.numera6690914467698888265omplex (tptp.aa_num_num (tptp.plus_plus_num M) tptp.one))))) (forall ((M tptp.num)) (= (tptp.minus_8373710615458151222nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.numera6620942414471956472nteger M)) tptp.one_one_Code_integer) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.numera6620942414471956472nteger (tptp.aa_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.plus_plus_num M) tptp.one))))) (= (tptp.aa_real_real tptp.neg_numeral_dbl_real _let_85) _let_133) (= (tptp.neg_numeral_dbl_int _let_59) _let_64) (= (tptp.neg_nu7009210354673126013omplex _let_75) _let_132) (= (tptp.neg_nu8804712462038260780nteger _let_60) _let_65) (= (tptp.aa_rat_rat tptp.neg_numeral_dbl_rat _let_100) _let_131) (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.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.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.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.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.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.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.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.modulo_modulo_int A (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 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 ((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 ((A tptp.real) (B tptp.real)) (= (= A (tptp.aa_real_real tptp.uminus_uminus_real B)) (= B (tptp.aa_real_real tptp.uminus_uminus_real A)))) (forall ((A tptp.int) (B tptp.int)) (= (= A (tptp.aa_int_int tptp.uminus_uminus_int B)) (= B (tptp.aa_int_int tptp.uminus_uminus_int A)))) (forall ((A tptp.complex) (B tptp.complex)) (= (= A (tptp.uminus1482373934393186551omplex B)) (= B (tptp.uminus1482373934393186551omplex A)))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= A (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger B)) (= B (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A)))) (forall ((A tptp.rat) (B tptp.rat)) (= (= A (tptp.aa_rat_rat tptp.uminus_uminus_rat B)) (= B (tptp.aa_rat_rat tptp.uminus_uminus_rat A)))) (forall ((A tptp.real) (B tptp.real)) (= (= (tptp.aa_real_real tptp.uminus_uminus_real A) B) (= (tptp.aa_real_real tptp.uminus_uminus_real B) A))) (forall ((A tptp.int) (B tptp.int)) (= (= (tptp.aa_int_int tptp.uminus_uminus_int A) B) (= (tptp.aa_int_int tptp.uminus_uminus_int B) A))) (forall ((A tptp.complex) (B tptp.complex)) (= (= (tptp.uminus1482373934393186551omplex A) B) (= (tptp.uminus1482373934393186551omplex B) A))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A) B) (= (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger B) A))) (forall ((A tptp.rat) (B tptp.rat)) (= (= (tptp.aa_rat_rat tptp.uminus_uminus_rat A) B) (= (tptp.aa_rat_rat tptp.uminus_uminus_rat B) A))) (forall ((X tptp.real) (Y4 tptp.real)) (= (= (tptp.aa_real_real tptp.abs_abs_real X) (tptp.aa_real_real tptp.abs_abs_real Y4)) (or (= X Y4) (= X (tptp.aa_real_real tptp.uminus_uminus_real Y4))))) (forall ((X tptp.int) (Y4 tptp.int)) (= (= (tptp.aa_int_int tptp.abs_abs_int X) (tptp.aa_int_int tptp.abs_abs_int Y4)) (or (= X Y4) (= X (tptp.aa_int_int tptp.uminus_uminus_int Y4))))) (forall ((X tptp.code_integer) (Y4 tptp.code_integer)) (= (= (tptp.abs_abs_Code_integer X) (tptp.abs_abs_Code_integer Y4)) (or (= X Y4) (= X (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger Y4))))) (forall ((X tptp.rat) (Y4 tptp.rat)) (= (= (tptp.aa_rat_rat tptp.abs_abs_rat X) (tptp.aa_rat_rat tptp.abs_abs_rat Y4)) (or (= X Y4) (= X (tptp.aa_rat_rat tptp.uminus_uminus_rat Y4))))) (forall ((A tptp.real) (B tptp.real)) (=> (= A B) (= (tptp.aa_real_real tptp.uminus_uminus_real A) (tptp.aa_real_real tptp.uminus_uminus_real B)))) (forall ((A tptp.int) (B tptp.int)) (=> (= A B) (= (tptp.aa_int_int tptp.uminus_uminus_int A) (tptp.aa_int_int tptp.uminus_uminus_int B)))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (= A B) (= (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger B)))) (forall ((A tptp.rat) (B tptp.rat)) (=> (= A B) (= (tptp.aa_rat_rat tptp.uminus_uminus_rat A) (tptp.aa_rat_rat tptp.uminus_uminus_rat B)))) (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)) (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) (B tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.abs_abs_Code_integer A)) B)) (and (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger A) B)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A)) B))))) (forall ((A tptp.rat) (B 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)) B)) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B)) (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)) B))))) (forall ((A tptp.int) (B 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)) B)) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B)) (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)) B))))) (forall ((A tptp.real) (B 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)) B)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) B)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real A)) B))))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.abs_abs_Code_integer A)) B)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A)) B)))) (forall ((A tptp.rat) (B 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)) B)) (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)) B)))) (forall ((A tptp.int) (B 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)) B)) (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)) B)))) (forall ((A tptp.real) (B 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)) B)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real A)) B)))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger A) B)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A)) B)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.abs_abs_Code_integer A)) B))))) (forall ((A tptp.rat) (B tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B)) (=> (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)) B)) (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)) B))))) (forall ((A tptp.int) (B tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B)) (=> (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)) B)) (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)) B))))) (forall ((A tptp.real) (B tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) B)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real A)) B)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real A)) B))))) (forall ((A tptp.real) (B 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)) B)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.uminus_uminus_real A)) B))))) (forall ((A tptp.int) (B 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)) B)) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B)) (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)) B))))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.abs_abs_Code_integer A)) B)) (and (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger A) B)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A)) B))))) (forall ((A tptp.rat) (B 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)) B)) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B)) (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)) B))))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= A (tptp.abs_abs_Code_integer B)) (and (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A)) (or (= B A) (= B (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A)))))) (forall ((A tptp.rat) (B tptp.rat)) (= (= A (tptp.aa_rat_rat tptp.abs_abs_rat B)) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) A)) (or (= B A) (= B (tptp.aa_rat_rat tptp.uminus_uminus_rat A)))))) (forall ((A tptp.int) (B tptp.int)) (= (= A (tptp.aa_int_int tptp.abs_abs_int B)) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) A)) (or (= B A) (= B (tptp.aa_int_int tptp.uminus_uminus_int A)))))) (forall ((A tptp.real) (B tptp.real)) (= (= A (tptp.aa_real_real tptp.abs_abs_real B)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) A)) (or (= B A) (= B (tptp.aa_real_real tptp.uminus_uminus_real A)))))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= (tptp.abs_abs_Code_integer A) B) (and (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) B)) (or (= A B) (= A (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger B)))))) (forall ((A tptp.rat) (B tptp.rat)) (= (= (tptp.aa_rat_rat tptp.abs_abs_rat A) B) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) B)) (or (= A B) (= A (tptp.aa_rat_rat tptp.uminus_uminus_rat B)))))) (forall ((A tptp.int) (B tptp.int)) (= (= (tptp.aa_int_int tptp.abs_abs_int A) B) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) B)) (or (= A B) (= A (tptp.aa_int_int tptp.uminus_uminus_int B)))))) (forall ((A tptp.real) (B tptp.real)) (= (= (tptp.aa_real_real tptp.abs_abs_real A) B) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) B)) (or (= A B) (= A (tptp.aa_real_real tptp.uminus_uminus_real B)))))) (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 ((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 ((X4 tptp.real)) (let ((_let_1 (tptp.aa_real_real tptp.abs_abs_real X4))) (let ((_let_2 (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X4) tptp.zero_zero_real)))) (and (=> _let_2 (= _let_1 (tptp.aa_real_real tptp.uminus_uminus_real X4))) (=> (not _let_2) (= _let_1 X4)))))) (forall ((X4 tptp.int)) (let ((_let_1 (tptp.aa_int_int tptp.abs_abs_int X4))) (let ((_let_2 (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X4) tptp.zero_zero_int)))) (and (=> _let_2 (= _let_1 (tptp.aa_int_int tptp.uminus_uminus_int X4))) (=> (not _let_2) (= _let_1 X4)))))) (forall ((X4 tptp.code_integer)) (let ((_let_1 (tptp.abs_abs_Code_integer X4))) (let ((_let_2 (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger X4) tptp.zero_z3403309356797280102nteger)))) (and (=> _let_2 (= _let_1 (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger X4))) (=> (not _let_2) (= _let_1 X4)))))) (forall ((X4 tptp.rat)) (let ((_let_1 (tptp.aa_rat_rat tptp.abs_abs_rat X4))) (let ((_let_2 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X4) tptp.zero_zero_rat)))) (and (=> _let_2 (= _let_1 (tptp.aa_rat_rat tptp.uminus_uminus_rat X4))) (=> (not _let_2) (= _let_1 X4)))))) (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 ((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 ((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.code_integer) (B tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.abs_abs_Code_integer A)) B)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger A) B)))) (forall ((A tptp.rat) (B 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)) B)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B)))) (forall ((A tptp.int) (B 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)) B)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B)))) (forall ((A tptp.real) (B 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)) B)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) B)))) (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)) (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.abs_abs_Code_integer A) tptp.zero_z3403309356797280102nteger) (= A tptp.zero_z3403309356797280102nteger))) (forall ((A tptp.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) (B tptp.code_integer)) (= (tptp.abs_abs_Code_integer (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) B)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.abs_abs_Code_integer A)) (tptp.abs_abs_Code_integer B)))) (forall ((A tptp.real) (B tptp.real)) (= (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) B)) (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 B)))) (forall ((A tptp.rat) (B 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) B)) (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 B)))) (forall ((A tptp.int) (B 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) B)) (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 B)))) _let_129 _let_128 _let_127 _let_126 (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (tptp.abs_abs_Code_integer (tptp.minus_8373710615458151222nteger A B)) (tptp.abs_abs_Code_integer (tptp.minus_8373710615458151222nteger B A)))) (forall ((A tptp.real) (B tptp.real)) (= (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A) B)) (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real B) A)))) (forall ((A tptp.rat) (B tptp.rat)) (= (tptp.aa_rat_rat tptp.abs_abs_rat (tptp.aa_rat_rat (tptp.minus_minus_rat A) B)) (tptp.aa_rat_rat tptp.abs_abs_rat (tptp.aa_rat_rat (tptp.minus_minus_rat B) A)))) (forall ((A tptp.int) (B 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) B)) (tptp.aa_int_int tptp.abs_abs_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int B) A)))) (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 ((A tptp.code_integer) (B tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger A) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger B))) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger B) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A))))) (forall ((A tptp.rat) (B 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 B))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) (tptp.aa_rat_rat tptp.uminus_uminus_rat A))))) (forall ((A tptp.int) (B 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 B))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B) (tptp.aa_int_int tptp.uminus_uminus_int A))))) (forall ((A tptp.real) (B 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 B))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real B) (tptp.aa_real_real tptp.uminus_uminus_real A))))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A)) B)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger B)) A)))) (forall ((A tptp.rat) (B 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)) B)) (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 B)) A)))) (forall ((A tptp.int) (B 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)) B)) (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 B)) A)))) (forall ((A tptp.real) (B 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)) B)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real B)) A)))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger A) B)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger B)) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A))))) (forall ((A tptp.rat) (B tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B)) (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 B)) (tptp.aa_rat_rat tptp.uminus_uminus_rat A))))) (forall ((A tptp.int) (B tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B)) (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 B)) (tptp.aa_int_int tptp.uminus_uminus_int A))))) (forall ((A tptp.real) (B tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) B)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real B)) (tptp.aa_real_real tptp.uminus_uminus_real A))))) (forall ((A tptp.real) (B 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 B))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B) (tptp.aa_real_real tptp.uminus_uminus_real A))))) (forall ((A tptp.int) (B 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 B))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B) (tptp.aa_int_int tptp.uminus_uminus_int A))))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger A) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger B))) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger B) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A))))) (forall ((A tptp.rat) (B 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 B))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) (tptp.aa_rat_rat tptp.uminus_uminus_rat A))))) (forall ((A tptp.real) (B 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)) B)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.uminus_uminus_real B)) A)))) (forall ((A tptp.int) (B 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)) B)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int tptp.uminus_uminus_int B)) A)))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A)) B)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger B)) A)))) (forall ((A tptp.rat) (B 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)) B)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat B)) A)))) (forall ((A tptp.real) (B tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.uminus_uminus_real B)) (tptp.aa_real_real tptp.uminus_uminus_real A))))) (forall ((A tptp.int) (B tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int tptp.uminus_uminus_int B)) (tptp.aa_int_int tptp.uminus_uminus_int A))))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger A) B)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger B)) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A))))) (forall ((A tptp.rat) (B tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat B)) (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.uminus1482373934393186551omplex (tptp.numera6690914467698888265omplex M)) (tptp.numera6690914467698888265omplex N)))) (forall ((M tptp.num) (N tptp.num)) (not (= (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.numera6620942414471956472nteger M)) (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.uminus1482373934393186551omplex (tptp.numera6690914467698888265omplex N))))) (forall ((M tptp.num) (N tptp.num)) (not (= (tptp.numera6620942414471956472nteger M) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (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) (B 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 B) B)) (or (= A B) (= A (tptp.aa_real_real tptp.uminus_uminus_real B))))) (forall ((A tptp.int) (B 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 B) B)) (or (= A B) (= A (tptp.aa_int_int tptp.uminus_uminus_int B))))) (forall ((A tptp.complex) (B tptp.complex)) (= (= (tptp.aa_complex_complex (tptp.times_times_complex A) A) (tptp.aa_complex_complex (tptp.times_times_complex B) B)) (or (= A B) (= A (tptp.uminus1482373934393186551omplex B))))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) A) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B) B)) (or (= A B) (= A (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger B))))) (forall ((A tptp.rat) (B 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 B) B)) (or (= A B) (= A (tptp.aa_rat_rat tptp.uminus_uminus_rat B))))) (forall ((A tptp.real) (B tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real tptp.uminus_uminus_real A)) B) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) (tptp.aa_real_real tptp.uminus_uminus_real B)))) (forall ((A tptp.int) (B 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)) B) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) (tptp.aa_int_int tptp.uminus_uminus_int B)))) (forall ((A tptp.complex) (B tptp.complex)) (= (tptp.aa_complex_complex (tptp.times_times_complex (tptp.uminus1482373934393186551omplex A)) B) (tptp.aa_complex_complex (tptp.times_times_complex A) (tptp.uminus1482373934393186551omplex B)))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A)) B) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger B)))) (forall ((A tptp.rat) (B 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)) B) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) (tptp.aa_rat_rat tptp.uminus_uminus_rat B)))) (forall ((A2 tptp.real) (K tptp.real) (A tptp.real)) (=> (= A2 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real K) A)) (= (tptp.aa_real_real tptp.uminus_uminus_real A2) (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 ((A2 tptp.int) (K tptp.int) (A tptp.int)) (=> (= A2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int K) A)) (= (tptp.aa_int_int tptp.uminus_uminus_int A2) (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 ((A2 tptp.complex) (K tptp.complex) (A tptp.complex)) (=> (= A2 (tptp.plus_plus_complex K A)) (= (tptp.uminus1482373934393186551omplex A2) (tptp.plus_plus_complex (tptp.uminus1482373934393186551omplex K) (tptp.uminus1482373934393186551omplex A))))) (forall ((A2 tptp.code_integer) (K tptp.code_integer) (A tptp.code_integer)) (=> (= A2 (tptp.plus_p5714425477246183910nteger K A)) (= (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A2) (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger K) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A))))) (forall ((A2 tptp.rat) (K tptp.rat) (A tptp.rat)) (=> (= A2 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat K) A)) (= (tptp.aa_rat_rat tptp.uminus_uminus_rat A2) (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) (B tptp.real)) (= (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) B)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real tptp.uminus_uminus_real B)) (tptp.aa_real_real tptp.uminus_uminus_real A)))) (forall ((A tptp.int) (B 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) B)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int tptp.uminus_uminus_int B)) (tptp.aa_int_int tptp.uminus_uminus_int A)))) (forall ((A tptp.complex) (B tptp.complex)) (= (tptp.uminus1482373934393186551omplex (tptp.plus_plus_complex A B)) (tptp.plus_plus_complex (tptp.uminus1482373934393186551omplex B) (tptp.uminus1482373934393186551omplex A)))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.plus_p5714425477246183910nteger A B)) (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger B) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A)))) (forall ((A tptp.rat) (B 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) B)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat B)) (tptp.aa_rat_rat tptp.uminus_uminus_rat A)))) (forall ((A tptp.real) (B tptp.real)) (= (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) B)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real tptp.uminus_uminus_real B)) (tptp.aa_real_real tptp.uminus_uminus_real A)))) (forall ((A tptp.int) (B 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) B)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int tptp.uminus_uminus_int B)) (tptp.aa_int_int tptp.uminus_uminus_int A)))) (forall ((A tptp.complex) (B tptp.complex)) (= (tptp.uminus1482373934393186551omplex (tptp.plus_plus_complex A B)) (tptp.plus_plus_complex (tptp.uminus1482373934393186551omplex B) (tptp.uminus1482373934393186551omplex A)))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.plus_p5714425477246183910nteger A B)) (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger B) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A)))) (forall ((A tptp.rat) (B 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) B)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat B)) (tptp.aa_rat_rat tptp.uminus_uminus_rat A)))) (not (= tptp.one_one_real _let_85)) (not (= tptp.one_one_int _let_59)) (not (= tptp.one_one_complex _let_75)) (not (= tptp.one_one_Code_integer _let_60)) (not (= tptp.one_one_rat _let_100)) (forall ((B 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 B)) A) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real tptp.uminus_uminus_real A)) B))) (forall ((B 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 B)) A) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_int_int tptp.uminus_uminus_int A)) B))) (forall ((B tptp.complex) (A tptp.complex)) (= (tptp.minus_minus_complex (tptp.uminus1482373934393186551omplex B) A) (tptp.minus_minus_complex (tptp.uminus1482373934393186551omplex A) B))) (forall ((B tptp.code_integer) (A tptp.code_integer)) (= (tptp.minus_8373710615458151222nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger B) A) (tptp.minus_8373710615458151222nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A) B))) (forall ((B tptp.rat) (A tptp.rat)) (= (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat B)) A) (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat A)) B))) (forall ((A tptp.real) (B 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 B)) (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A) B)))) (forall ((A tptp.int) (B 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 B)) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) B)))) (forall ((A tptp.complex) (B tptp.complex)) (= (tptp.minus_minus_complex (tptp.uminus1482373934393186551omplex A) (tptp.uminus1482373934393186551omplex B)) (tptp.uminus1482373934393186551omplex (tptp.minus_minus_complex A B)))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (tptp.minus_8373710615458151222nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger B)) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.minus_8373710615458151222nteger A B)))) (forall ((A tptp.rat) (B 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 B)) (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_rat_rat (tptp.minus_minus_rat A) B)))) (forall ((A tptp.int) (B tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A) (tptp.aa_int_int tptp.uminus_uminus_int B)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int (tptp.aa_int_int tptp.uminus_uminus_int A)) B))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (tptp.divide6298287555418463151nteger A (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger B)) (tptp.divide6298287555418463151nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A) B))) (forall ((A tptp.real) (B 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 B)) (tptp.aa_real_real _let_1 (tptp.aa_real_real tptp.uminus_uminus_real B))))) (forall ((A tptp.complex) (B tptp.complex)) (= (tptp.uminus1482373934393186551omplex (tptp.divide1717551699836669952omplex A B)) (tptp.divide1717551699836669952omplex A (tptp.uminus1482373934393186551omplex B)))) (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (tptp.divide_divide_rat A))) (= (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_rat_rat _let_1 B)) (tptp.aa_rat_rat _let_1 (tptp.aa_rat_rat tptp.uminus_uminus_rat B))))) (forall ((A tptp.real) (B 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 B)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real A) B))) (forall ((A tptp.complex) (B tptp.complex)) (= (tptp.divide1717551699836669952omplex (tptp.uminus1482373934393186551omplex A) (tptp.uminus1482373934393186551omplex B)) (tptp.divide1717551699836669952omplex A B))) (forall ((A tptp.rat) (B 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 B)) (tptp.aa_rat_rat (tptp.divide_divide_rat A) B))) (forall ((A tptp.real) (B tptp.real)) (= (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real A) B)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real tptp.uminus_uminus_real A)) B))) (forall ((A tptp.complex) (B tptp.complex)) (= (tptp.uminus1482373934393186551omplex (tptp.divide1717551699836669952omplex A B)) (tptp.divide1717551699836669952omplex (tptp.uminus1482373934393186551omplex A) B))) (forall ((A tptp.rat) (B tptp.rat)) (= (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_rat_rat (tptp.divide_divide_rat A) B)) (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat A)) B))) (forall ((A tptp.int) (B tptp.int)) (= (tptp.modulo_modulo_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.modulo_modulo_int A B)) B) (tptp.modulo_modulo_int (tptp.aa_int_int tptp.uminus_uminus_int A) B))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (tptp.modulo364778990260209775nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.modulo364778990260209775nteger A B)) B) (tptp.modulo364778990260209775nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A) B))) (forall ((A tptp.int) (B tptp.int) (A4 tptp.int)) (=> (= (tptp.modulo_modulo_int A B) (tptp.modulo_modulo_int A4 B)) (= (tptp.modulo_modulo_int (tptp.aa_int_int tptp.uminus_uminus_int A) B) (tptp.modulo_modulo_int (tptp.aa_int_int tptp.uminus_uminus_int A4) B)))) (forall ((A tptp.code_integer) (B tptp.code_integer) (A4 tptp.code_integer)) (=> (= (tptp.modulo364778990260209775nteger A B) (tptp.modulo364778990260209775nteger A4 B)) (= (tptp.modulo364778990260209775nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A) B) (tptp.modulo364778990260209775nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A4) B)))) (forall ((A tptp.int) (B tptp.int)) (= (tptp.modulo_modulo_int A (tptp.aa_int_int tptp.uminus_uminus_int B)) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.modulo_modulo_int (tptp.aa_int_int tptp.uminus_uminus_int A) B)))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (tptp.modulo364778990260209775nteger A (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger B)) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.modulo364778990260209775nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A) B)))) _let_125 (forall ((Z tptp.int)) (=> (forall ((N2 tptp.nat)) (not (= Z (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N2)))) (not (forall ((N2 tptp.nat)) (not (= Z (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N2)))))))) (forall ((D tptp.int) (T tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int D) T)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_int_int tptp.uminus_uminus_int D)) T)))) (forall ((D tptp.int) (T tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int D))) (= (tptp.pp (tptp.aa_int_bool _let_1 T)) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int tptp.uminus_uminus_int T)))))) (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.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.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.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)) (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) (B 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 B))) (tptp.plus_p5714425477246183910nteger (tptp.abs_abs_Code_integer A) (tptp.abs_abs_Code_integer B))))) (forall ((A tptp.rat) (B 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) B))) (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 B))))) (forall ((A tptp.int) (B 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) B))) (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 B))))) (forall ((A tptp.real) (B 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) B))) (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 B))))) (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer) (D tptp.code_integer)) (let ((_let_1 (tptp.abs_abs_Code_integer B))) (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) (B tptp.real) (D tptp.real)) (let ((_let_1 (tptp.aa_real_real tptp.abs_abs_real B))) (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) (B tptp.rat) (D tptp.rat)) (let ((_let_1 (tptp.aa_rat_rat tptp.abs_abs_rat B))) (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) (B tptp.int) (D tptp.int)) (let ((_let_1 (tptp.aa_int_int tptp.abs_abs_int B))) (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) (B 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 B))) (tptp.abs_abs_Code_integer (tptp.minus_8373710615458151222nteger A B))))) (forall ((A tptp.rat) (B 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 B))) (tptp.aa_rat_rat tptp.abs_abs_rat (tptp.aa_rat_rat (tptp.minus_minus_rat A) B))))) (forall ((A tptp.int) (B 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 B))) (tptp.aa_int_int tptp.abs_abs_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) B))))) (forall ((A tptp.real) (B 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 B))) (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A) B))))) (forall ((A tptp.code_integer) (B 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 B)))) (tptp.abs_abs_Code_integer (tptp.minus_8373710615458151222nteger A B))))) (forall ((A tptp.rat) (B 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 B)))) (tptp.aa_rat_rat tptp.abs_abs_rat (tptp.aa_rat_rat (tptp.minus_minus_rat A) B))))) (forall ((A tptp.int) (B 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 B)))) (tptp.aa_int_int tptp.abs_abs_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) B))))) (forall ((A tptp.real) (B 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 B)))) (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A) B))))) (forall ((A tptp.code_integer) (B 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 B))) (tptp.abs_abs_Code_integer (tptp.minus_8373710615458151222nteger B A))))) (forall ((A tptp.rat) (B 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 B))) (tptp.aa_rat_rat tptp.abs_abs_rat (tptp.aa_rat_rat (tptp.minus_minus_rat B) A))))) (forall ((A tptp.int) (B 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 B))) (tptp.aa_int_int tptp.abs_abs_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int B) A))))) (forall ((A tptp.real) (B 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 B))) (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real B) A))))) (forall ((B tptp.real) (A tptp.real)) (=> (not (= B 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) B)) (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 B))))) (forall ((B tptp.rat) (A tptp.rat)) (=> (not (= B tptp.zero_zero_rat)) (= (tptp.aa_rat_rat tptp.abs_abs_rat (tptp.aa_rat_rat (tptp.divide_divide_rat A) B)) (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 B))))) (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.numera6620942414471956472nteger M))) (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 ((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)) (not (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.numera6620942414471956472nteger M)) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (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)) (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 ((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.uminus1482373934393186551omplex (tptp.numera6690914467698888265omplex N))))) (forall ((N tptp.num)) (not (= tptp.zero_z3403309356797280102nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (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.numera6620942414471956472nteger M)) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (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.numera6620942414471956472nteger M))) (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_Code_integer_bool _let_118 tptp.one_one_Code_integer)) (tptp.pp (tptp.aa_rat_bool _let_117 tptp.one_one_rat)) (tptp.pp (tptp.aa_int_bool _let_116 tptp.one_one_int)) (tptp.pp (tptp.aa_real_bool _let_115 tptp.one_one_real)) (not (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) _let_60))) (not (tptp.pp (tptp.aa_rat_bool _let_124 _let_100))) (not (tptp.pp (tptp.aa_int_bool _let_123 _let_59))) (not (tptp.pp (tptp.aa_real_bool _let_122 _let_85))) (forall ((A tptp.real) (B tptp.real)) (= (= (tptp.aa_real_real tptp.uminus_uminus_real A) B) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) B) tptp.zero_zero_real))) (forall ((A tptp.int) (B tptp.int)) (= (= (tptp.aa_int_int tptp.uminus_uminus_int A) B) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) B) tptp.zero_zero_int))) (forall ((A tptp.complex) (B tptp.complex)) (= (= (tptp.uminus1482373934393186551omplex A) B) (= (tptp.plus_plus_complex A B) tptp.zero_zero_complex))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A) B) (= (tptp.plus_p5714425477246183910nteger A B) tptp.zero_z3403309356797280102nteger))) (forall ((A tptp.rat) (B tptp.rat)) (= (= (tptp.aa_rat_rat tptp.uminus_uminus_rat A) B) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) B) tptp.zero_zero_rat))) (forall ((A tptp.real) (B tptp.real)) (= (= A (tptp.aa_real_real tptp.uminus_uminus_real B)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) B) tptp.zero_zero_real))) (forall ((A tptp.int) (B tptp.int)) (= (= A (tptp.aa_int_int tptp.uminus_uminus_int B)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) B) tptp.zero_zero_int))) (forall ((A tptp.complex) (B tptp.complex)) (= (= A (tptp.uminus1482373934393186551omplex B)) (= (tptp.plus_plus_complex A B) tptp.zero_zero_complex))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= A (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger B)) (= (tptp.plus_p5714425477246183910nteger A B) tptp.zero_z3403309356797280102nteger))) (forall ((A tptp.rat) (B tptp.rat)) (= (= A (tptp.aa_rat_rat tptp.uminus_uminus_rat B)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) B) tptp.zero_zero_rat))) (forall ((A tptp.real) (B tptp.real)) (=> (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) B) tptp.zero_zero_real) (= (tptp.aa_real_real tptp.uminus_uminus_real A) B))) (forall ((A tptp.int) (B tptp.int)) (=> (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) B) tptp.zero_zero_int) (= (tptp.aa_int_int tptp.uminus_uminus_int A) B))) (forall ((A tptp.complex) (B tptp.complex)) (=> (= (tptp.plus_plus_complex A B) tptp.zero_zero_complex) (= (tptp.uminus1482373934393186551omplex A) B))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (= (tptp.plus_p5714425477246183910nteger A B) tptp.zero_z3403309356797280102nteger) (= (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A) B))) (forall ((A tptp.rat) (B tptp.rat)) (=> (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) B) tptp.zero_zero_rat) (= (tptp.aa_rat_rat tptp.uminus_uminus_rat A) B))) (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.plus_plus_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) (B tptp.real)) (= (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) B) tptp.zero_zero_real) (= B (tptp.aa_real_real tptp.uminus_uminus_real A)))) (forall ((A tptp.int) (B tptp.int)) (= (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) B) tptp.zero_zero_int) (= B (tptp.aa_int_int tptp.uminus_uminus_int A)))) (forall ((A tptp.complex) (B tptp.complex)) (= (= (tptp.plus_plus_complex A B) tptp.zero_zero_complex) (= B (tptp.uminus1482373934393186551omplex A)))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= (tptp.plus_p5714425477246183910nteger A B) tptp.zero_z3403309356797280102nteger) (= B (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A)))) (forall ((A tptp.rat) (B tptp.rat)) (= (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) B) tptp.zero_zero_rat) (= B (tptp.aa_rat_rat tptp.uminus_uminus_rat A)))) (not (= tptp.zero_zero_real _let_85)) (not (= tptp.zero_zero_int _let_59)) (not (= tptp.zero_zero_complex _let_75)) (not (= tptp.zero_z3403309356797280102nteger _let_60)) (not (= tptp.zero_zero_rat _let_100)) (not (tptp.pp (tptp.aa_real_bool _let_121 _let_85))) (not (tptp.pp (tptp.aa_int_bool _let_120 _let_59))) (not (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) _let_60))) (not (tptp.pp (tptp.aa_rat_bool _let_119 _let_100))) (tptp.pp (tptp.aa_real_bool _let_110 tptp.one_one_real)) (tptp.pp (tptp.aa_int_bool _let_109 tptp.one_one_int)) (tptp.pp (tptp.aa_Code_integer_bool _let_108 tptp.one_one_Code_integer)) (tptp.pp (tptp.aa_rat_bool _let_107 tptp.one_one_rat)) (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.uminus1482373934393186551omplex X)) (tptp.aa_complex_complex (tptp.times_times_complex X) (tptp.uminus1482373934393186551omplex _let_1))))) (forall ((W tptp.num) (X tptp.code_integer)) (let ((_let_1 (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 ((B tptp.real) (A tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real A))) (=> (not (= B tptp.zero_zero_real)) (= (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_real_real _let_1 B)) (tptp.aa_real_real _let_1 (tptp.aa_real_real tptp.uminus_uminus_real B)))))) (forall ((B tptp.complex) (A tptp.complex)) (=> (not (= B tptp.zero_zero_complex)) (= (tptp.uminus1482373934393186551omplex (tptp.divide1717551699836669952omplex A B)) (tptp.divide1717551699836669952omplex A (tptp.uminus1482373934393186551omplex B))))) (forall ((B tptp.rat) (A tptp.rat)) (let ((_let_1 (tptp.divide_divide_rat A))) (=> (not (= B tptp.zero_zero_rat)) (= (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_rat_rat _let_1 B)) (tptp.aa_rat_rat _let_1 (tptp.aa_rat_rat tptp.uminus_uminus_rat B)))))) (forall ((B tptp.real) (A tptp.real)) (=> (not (= B 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 B)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real A) B)))) (forall ((B tptp.complex) (A tptp.complex)) (=> (not (= B tptp.zero_zero_complex)) (= (tptp.divide1717551699836669952omplex (tptp.uminus1482373934393186551omplex A) (tptp.uminus1482373934393186551omplex B)) (tptp.divide1717551699836669952omplex A B)))) (forall ((B tptp.rat) (A tptp.rat)) (=> (not (= B 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 B)) (tptp.aa_rat_rat (tptp.divide_divide_rat A) B)))) (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.uminus1482373934393186551omplex (tptp.numera6690914467698888265omplex N))))) (forall ((N tptp.num)) (not (= tptp.one_one_Code_integer (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (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.uminus1482373934393186551omplex tptp.one_one_complex)))) (forall ((N tptp.num)) (not (= (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.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 ((B3 tptp.real) (K tptp.real) (B tptp.real) (A tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A))) (=> (= B3 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real K) B)) (= (tptp.aa_real_real _let_1 B3) (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 B)))))) (forall ((B3 tptp.int) (K tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.minus_minus_int A))) (=> (= B3 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int K) B)) (= (tptp.aa_int_int _let_1 B3) (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 B)))))) (forall ((B3 tptp.complex) (K tptp.complex) (B tptp.complex) (A tptp.complex)) (=> (= B3 (tptp.plus_plus_complex K B)) (= (tptp.minus_minus_complex A B3) (tptp.plus_plus_complex (tptp.uminus1482373934393186551omplex K) (tptp.minus_minus_complex A B))))) (forall ((B3 tptp.code_integer) (K tptp.code_integer) (B tptp.code_integer) (A tptp.code_integer)) (=> (= B3 (tptp.plus_p5714425477246183910nteger K B)) (= (tptp.minus_8373710615458151222nteger A B3) (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger K) (tptp.minus_8373710615458151222nteger A B))))) (forall ((B3 tptp.rat) (K tptp.rat) (B tptp.rat) (A tptp.rat)) (let ((_let_1 (tptp.minus_minus_rat A))) (=> (= B3 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat K) B)) (= (tptp.aa_rat_rat _let_1 B3) (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 B)))))) (forall ((A tptp.real) (B tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A) B) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) (tptp.aa_real_real tptp.uminus_uminus_real B)))) (forall ((A tptp.int) (B tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) B) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) (tptp.aa_int_int tptp.uminus_uminus_int B)))) (forall ((A tptp.complex) (B tptp.complex)) (= (tptp.minus_minus_complex A B) (tptp.plus_plus_complex A (tptp.uminus1482373934393186551omplex B)))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (tptp.minus_8373710615458151222nteger A B) (tptp.plus_p5714425477246183910nteger A (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger B)))) (forall ((A tptp.rat) (B tptp.rat)) (= (tptp.aa_rat_rat (tptp.minus_minus_rat A) B) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) (tptp.aa_rat_rat tptp.uminus_uminus_rat B)))) (forall ((A tptp.real) (B tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A) B) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) (tptp.aa_real_real tptp.uminus_uminus_real B)))) (forall ((A tptp.int) (B tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) B) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) (tptp.aa_int_int tptp.uminus_uminus_int B)))) (forall ((A tptp.complex) (B tptp.complex)) (= (tptp.minus_minus_complex A B) (tptp.plus_plus_complex A (tptp.uminus1482373934393186551omplex B)))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (tptp.minus_8373710615458151222nteger A B) (tptp.plus_p5714425477246183910nteger A (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger B)))) (forall ((A tptp.rat) (B tptp.rat)) (= (tptp.aa_rat_rat (tptp.minus_minus_rat A) B) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) (tptp.aa_rat_rat tptp.uminus_uminus_rat B)))) (forall ((B 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 B) A)) (= (tptp.aa_real_real _let_1 (tptp.aa_real_real tptp.uminus_uminus_real B)) (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_real_real _let_1 B)))))) (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.divide_divide_int A))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int B) A)) (= (tptp.aa_int_int _let_1 (tptp.aa_int_int tptp.uminus_uminus_int B)) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_int_int _let_1 B)))))) (forall ((B tptp.complex) (A tptp.complex)) (=> (tptp.pp (tptp.aa_complex_bool (tptp.dvd_dvd_complex B) A)) (= (tptp.divide1717551699836669952omplex A (tptp.uminus1482373934393186551omplex B)) (tptp.uminus1482373934393186551omplex (tptp.divide1717551699836669952omplex A B))))) (forall ((B tptp.code_integer) (A tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer B) A)) (= (tptp.divide6298287555418463151nteger A (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger B)) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.divide6298287555418463151nteger A B))))) (forall ((B 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 B) A)) (= (tptp.aa_rat_rat _let_1 (tptp.aa_rat_rat tptp.uminus_uminus_rat B)) (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_rat_rat _let_1 B)))))) (forall ((B tptp.real) (A tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.dvd_dvd_real B) A)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real tptp.uminus_uminus_real A)) B) (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real A) B))))) (forall ((B tptp.int) (A tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int B) A)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int (tptp.aa_int_int tptp.uminus_uminus_int A)) B) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A) B))))) (forall ((B tptp.complex) (A tptp.complex)) (=> (tptp.pp (tptp.aa_complex_bool (tptp.dvd_dvd_complex B) A)) (= (tptp.divide1717551699836669952omplex (tptp.uminus1482373934393186551omplex A) B) (tptp.uminus1482373934393186551omplex (tptp.divide1717551699836669952omplex A B))))) (forall ((B tptp.code_integer) (A tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer B) A)) (= (tptp.divide6298287555418463151nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A) B) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.divide6298287555418463151nteger A B))))) (forall ((B tptp.rat) (A tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.dvd_dvd_rat B) A)) (= (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat A)) B) (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_rat_rat (tptp.divide_divide_rat A) B))))) (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 ((P tptp.fun_int_bool) (Z tptp.int)) (=> (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_int_bool P (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N2)))) (=> (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_int_bool P (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_nat tptp.suc N2)))))) (tptp.pp (tptp.aa_int_bool P Z))))) (forall ((Z tptp.int)) (=> (forall ((N2 tptp.nat)) (not (= Z (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N2)))) (not (forall ((N2 tptp.nat)) (not (= Z (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_nat tptp.suc N2))))))))) (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 ((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 ((L tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int tptp.zero_zero_int) L) (tptp.aa_int_int tptp.uminus_uminus_int L))) (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 ((K tptp.int) (L tptp.int)) (=> (not (= (tptp.modulo_modulo_int (tptp.aa_int_int tptp.uminus_uminus_int K) L) tptp.zero_zero_int)) (not (= (tptp.modulo_modulo_int K L) tptp.zero_zero_int)))) (forall ((K tptp.int) (L tptp.int)) (=> (not (= (tptp.modulo_modulo_int K (tptp.aa_int_int tptp.uminus_uminus_int L)) tptp.zero_zero_int)) (not (= (tptp.modulo_modulo_int K L) tptp.zero_zero_int)))) (forall ((X tptp.real) (Y4 tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real X) Y4) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) (tptp.aa_real_real tptp.uminus_uminus_real Y4)))) (forall ((X tptp.rat)) (=> (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)) (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)) E)))) (= X tptp.zero_zero_rat))) (forall ((X tptp.real)) (=> (forall ((E tptp.real)) (=> (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 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real X)) E)))) (= X tptp.zero_zero_real))) (forall ((X tptp.code_integer) (Y4 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 Y4)) X) (tptp.abs_abs_Code_integer (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger Y4) X))))) (forall ((X tptp.rat) (Y4 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 Y4)) X) (tptp.aa_rat_rat tptp.abs_abs_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat Y4) X))))) (forall ((X tptp.int) (Y4 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 Y4)) X) (tptp.aa_int_int tptp.abs_abs_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int Y4) X))))) (forall ((X tptp.real) (Y4 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 Y4)) X) (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real Y4) X))))) (forall ((A tptp.code_integer) (B 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 B)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger B) tptp.zero_z3403309356797280102nteger)))) (= (tptp.abs_abs_Code_integer (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) B)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.abs_abs_Code_integer A)) (tptp.abs_abs_Code_integer B)))))) (forall ((A tptp.rat) (B 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 B)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) 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) B)) (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 B)))))) (forall ((A tptp.int) (B 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 B)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B) 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) B)) (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 B)))))) (forall ((A tptp.real) (B 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 B)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real B) 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) B)) (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 B)))))) (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.power_8256067586552552935nteger (tptp.abs_abs_Code_integer 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) (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 ((Y4 tptp.real) (X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) Y4)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real tptp.abs_abs_real X)) Y4) (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real X) Y4))))) (forall ((Y4 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) Y4)) (= (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_rat_rat tptp.abs_abs_rat X)) Y4) (tptp.aa_rat_rat tptp.abs_abs_rat (tptp.aa_rat_rat (tptp.divide_divide_rat X) Y4))))) (forall ((X tptp.code_integer) (A tptp.code_integer) (R2 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))) R2)) (and (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.minus_8373710615458151222nteger A R2)) X)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger X) (tptp.plus_p5714425477246183910nteger A R2)))))) (forall ((X tptp.rat) (A tptp.rat) (R2 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))) R2)) (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) R2)) 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) R2)))))) (forall ((X tptp.int) (A tptp.int) (R2 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))) R2)) (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) R2)) 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) R2)))))) (forall ((X tptp.real) (A tptp.real) (R2 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))) R2)) (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) R2)) 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) R2)))))) (forall ((A tptp.code_integer) (B 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 B))) (tptp.plus_p5714425477246183910nteger (tptp.abs_abs_Code_integer A) (tptp.abs_abs_Code_integer B))))) (forall ((A tptp.rat) (B 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) B))) (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 B))))) (forall ((A tptp.int) (B 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) B))) (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 B))))) (forall ((A tptp.real) (B 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) B))) (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 B))))) (forall ((A tptp.code_integer) (B 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 B) (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 B D)))))) (forall ((A tptp.rat) (B 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) B)) (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 B) D)))))) (forall ((A tptp.int) (B 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) B)) (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 B) D)))))) (forall ((A tptp.real) (B 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) B)) (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 B) D)))))) (forall ((X tptp.code_integer) (A tptp.code_integer) (R2 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))) R2)) (and (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.minus_8373710615458151222nteger A R2)) X)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger X) (tptp.plus_p5714425477246183910nteger A R2)))))) (forall ((X tptp.real) (A tptp.real) (R2 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))) R2)) (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) R2)) 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) R2)))))) (forall ((X tptp.rat) (A tptp.rat) (R2 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))) R2)) (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) R2)) 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) R2)))))) (forall ((X tptp.int) (A tptp.int) (R2 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))) R2)) (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) R2)) 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) R2)))))) (forall ((N tptp.num)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (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)) (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)) (not (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (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)) (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)) (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.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))) (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.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)))))) (tptp.pp (tptp.aa_Code_integer_bool _let_118 tptp.zero_z3403309356797280102nteger)) (tptp.pp (tptp.aa_rat_bool _let_117 tptp.zero_zero_rat)) (tptp.pp (tptp.aa_int_bool _let_116 tptp.zero_zero_int)) (tptp.pp (tptp.aa_real_bool _let_115 tptp.zero_zero_real)) (not (tptp.pp (tptp.aa_Code_integer_bool _let_51 _let_60))) (not (tptp.pp (tptp.aa_rat_bool _let_114 _let_100))) (not (tptp.pp (tptp.aa_int_bool _let_113 _let_59))) (not (tptp.pp (tptp.aa_real_bool _let_95 _let_85))) (not (tptp.pp (tptp.aa_real_bool _let_96 _let_85))) (not (tptp.pp (tptp.aa_int_bool _let_112 _let_59))) (not (tptp.pp (tptp.aa_Code_integer_bool _let_49 _let_60))) (not (tptp.pp (tptp.aa_rat_bool _let_111 _let_100))) (tptp.pp (tptp.aa_real_bool _let_110 tptp.zero_zero_real)) (tptp.pp (tptp.aa_int_bool _let_109 tptp.zero_zero_int)) (tptp.pp (tptp.aa_Code_integer_bool _let_108 tptp.zero_z3403309356797280102nteger)) (tptp.pp (tptp.aa_rat_bool _let_107 tptp.zero_zero_rat)) (forall ((M tptp.num)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (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)) (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.one_one_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.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.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.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.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)) (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.one_one_Code_integer) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (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.one_one_real) (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real 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.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 ((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.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)) (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.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)) (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.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_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.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 ((A tptp.real) (B 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 B) 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 B))) (=> _let_1 (= A tptp.zero_zero_real)))))) (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (= C tptp.zero_zero_complex))) (= (= A (tptp.uminus1482373934393186551omplex (tptp.divide1717551699836669952omplex B C))) (and (=> (not _let_1) (= (tptp.aa_complex_complex (tptp.times_times_complex A) C) (tptp.uminus1482373934393186551omplex B))) (=> _let_1 (= A tptp.zero_zero_complex)))))) (forall ((A tptp.rat) (B 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 B) 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 B))) (=> _let_1 (= A tptp.zero_zero_rat)))))) (forall ((B 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 B) C)) A) (and (=> (not _let_1) (= (tptp.aa_real_real tptp.uminus_uminus_real B) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) C))) (=> _let_1 (= A tptp.zero_zero_real)))))) (forall ((B tptp.complex) (C tptp.complex) (A tptp.complex)) (let ((_let_1 (= C tptp.zero_zero_complex))) (= (= (tptp.uminus1482373934393186551omplex (tptp.divide1717551699836669952omplex B C)) A) (and (=> (not _let_1) (= (tptp.uminus1482373934393186551omplex B) (tptp.aa_complex_complex (tptp.times_times_complex A) C))) (=> _let_1 (= A tptp.zero_zero_complex)))))) (forall ((B 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 B) C)) A) (and (=> (not _let_1) (= (tptp.aa_rat_rat tptp.uminus_uminus_rat B) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) C))) (=> _let_1 (= A tptp.zero_zero_rat)))))) (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (=> (not (= B 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) B)) C) (= (tptp.aa_real_real tptp.uminus_uminus_real A) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real C) B))))) (forall ((B tptp.complex) (A tptp.complex) (C tptp.complex)) (=> (not (= B tptp.zero_zero_complex)) (= (= (tptp.uminus1482373934393186551omplex (tptp.divide1717551699836669952omplex A B)) C) (= (tptp.uminus1482373934393186551omplex A) (tptp.aa_complex_complex (tptp.times_times_complex C) B))))) (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (=> (not (= B tptp.zero_zero_rat)) (= (= (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_rat_rat (tptp.divide_divide_rat A) B)) 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) B))))) (forall ((B tptp.real) (C tptp.real) (A tptp.real)) (=> (not (= B 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) B))) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real C) B) (tptp.aa_real_real tptp.uminus_uminus_real A))))) (forall ((B tptp.complex) (C tptp.complex) (A tptp.complex)) (=> (not (= B tptp.zero_zero_complex)) (= (= C (tptp.uminus1482373934393186551omplex (tptp.divide1717551699836669952omplex A B))) (= (tptp.aa_complex_complex (tptp.times_times_complex C) B) (tptp.uminus1482373934393186551omplex A))))) (forall ((B tptp.rat) (C tptp.rat) (A tptp.rat)) (=> (not (= B tptp.zero_zero_rat)) (= (= C (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_rat_rat (tptp.divide_divide_rat A) B))) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat C) B) (tptp.aa_rat_rat tptp.uminus_uminus_rat A))))) (forall ((B tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real B) (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 B))) (forall ((B tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B) (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 B))) (forall ((B tptp.complex)) (= (tptp.aa_complex_complex (tptp.times_times_complex B) (tptp.uminus1482373934393186551omplex (tptp.numera6690914467698888265omplex tptp.one))) (tptp.uminus1482373934393186551omplex B))) (forall ((B tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.numera6620942414471956472nteger tptp.one))) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger B))) (forall ((B tptp.rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat B) (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 B))) (forall ((B 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))) B) (tptp.aa_real_real tptp.uminus_uminus_real B))) (forall ((B 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))) B) (tptp.aa_int_int tptp.uminus_uminus_int B))) (forall ((B tptp.complex)) (= (tptp.aa_complex_complex (tptp.times_times_complex (tptp.uminus1482373934393186551omplex (tptp.numera6690914467698888265omplex tptp.one))) B) (tptp.uminus1482373934393186551omplex B))) (forall ((B tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.numera6620942414471956472nteger tptp.one))) B) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger B))) (forall ((B 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))) B) (tptp.aa_rat_rat tptp.uminus_uminus_rat B))) (forall ((A tptp.real) (B tptp.real)) (= (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real A) B) (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)) (and (not (= B tptp.zero_zero_real)) (= A (tptp.aa_real_real tptp.uminus_uminus_real B))))) (forall ((A tptp.complex) (B tptp.complex)) (= (= (tptp.divide1717551699836669952omplex A B) (tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (and (not (= B tptp.zero_zero_complex)) (= A (tptp.uminus1482373934393186551omplex B))))) (forall ((A tptp.rat) (B tptp.rat)) (= (= (tptp.aa_rat_rat (tptp.divide_divide_rat A) B) (tptp.aa_rat_rat tptp.uminus_uminus_rat tptp.one_one_rat)) (and (not (= B tptp.zero_zero_rat)) (= A (tptp.aa_rat_rat tptp.uminus_uminus_rat B))))) (= (tptp.aa_real_real tptp.uminus_uminus_real _let_68) _let_85) (= (tptp.aa_int_int tptp.uminus_uminus_int _let_106) _let_59) (= (tptp.uminus1482373934393186551omplex _let_67) _let_75) (= (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.numera6620942414471956472nteger tptp.one)) _let_60) (= (tptp.aa_rat_rat tptp.uminus_uminus_rat _let_66) _let_100) (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.uminus1482373934393186551omplex A)) N) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_nat_complex (tptp.power_power_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.power_8256067586552552935nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A) N) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.power_8256067586552552935nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer) N)) (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.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.power_8256067586552552935nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger X) _let_1) (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 ((A tptp.real) (X tptp.real) (B 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) B)) (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 ((Y3 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) Y3))) D2)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) Y3)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y3) B)))))))))) (forall ((X tptp.real) (Y4 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)) Y4)) (tptp.aa_real_real tptp.real_V7735802525324610683m_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) Y4)))) (forall ((X tptp.complex) (Y4 tptp.complex)) (= (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.minus_minus_complex (tptp.uminus1482373934393186551omplex X) Y4)) (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.plus_plus_complex X Y4)))) (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.uminus1482373934393186551omplex X)) _let_1) (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.power_8256067586552552935nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger X) _let_1) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (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 ((X tptp.real) (Y4 tptp.real) (U tptp.real) (V tptp.real)) (=> (= X Y4) (=> (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)) Y4))) V))))) (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 ((X tptp.real) (Y4 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) Y4))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.uminus_uminus_real X)) Y4)))) (forall ((X tptp.real) (Y4 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) Y4)) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y4) (tptp.aa_real_real tptp.uminus_uminus_real X))))) (forall ((X tptp.real) (Y4 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) Y4)) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y4) (tptp.aa_real_real tptp.uminus_uminus_real X))))) (forall ((X tptp.real) (Y4 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) Y4))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real X)) Y4)))) (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 ((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 ((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 ((A tptp.int) (B tptp.int)) (let ((_let_1 (tptp.modulo_modulo_int A B))) (let ((_let_2 (tptp.modulo_modulo_int (tptp.aa_int_int tptp.uminus_uminus_int A) B))) (let ((_let_3 (= _let_1 tptp.zero_zero_int))) (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.minus_minus_int B) _let_1)))))))) (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (tptp.modulo_modulo_int A B))) (let ((_let_2 (tptp.modulo_modulo_int A (tptp.aa_int_int tptp.uminus_uminus_int B)))) (let ((_let_3 (= _let_1 tptp.zero_zero_int))) (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.minus_minus_int _let_1) B)))))))) (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 ((A tptp.real) (B 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 B))) (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 B) 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) (B 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 B))) (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 B) 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 ((B 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 B))) (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 B) 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 ((B 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 B))) (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 B) 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 ((C tptp.real) (A tptp.real) (B 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 B) C)))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.uminus_uminus_real B)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) C)))))) (forall ((C tptp.rat) (A tptp.rat) (B 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 B) 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 B)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) C)))))) (forall ((C tptp.real) (B 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 B) 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 B)))))) (forall ((C tptp.rat) (B 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 B) 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 B)))))) (forall ((C tptp.real) (A tptp.real) (B 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 B) 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 B)))))) (forall ((C tptp.rat) (A tptp.rat) (B 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 B) 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 B)))))) (forall ((C tptp.real) (B 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 B) C))) A)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.uminus_uminus_real B)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) C)))))) (forall ((C tptp.rat) (B 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 B) 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 B)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) C)))))) (forall ((B 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 B) C) _let_1) (and (=> (not _let_2) (= B (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real _let_1) C))) (=> _let_2 (= _let_1 tptp.zero_zero_real))))))) (forall ((B tptp.complex) (C tptp.complex) (W tptp.num)) (let ((_let_1 (tptp.uminus1482373934393186551omplex (tptp.numera6690914467698888265omplex W)))) (let ((_let_2 (= C tptp.zero_zero_complex))) (= (= (tptp.divide1717551699836669952omplex B C) _let_1) (and (=> (not _let_2) (= B (tptp.aa_complex_complex (tptp.times_times_complex _let_1) C))) (=> _let_2 (= _let_1 tptp.zero_zero_complex))))))) (forall ((B 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 B) C) _let_1) (and (=> (not _let_2) (= B (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) (B 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 B) C)) (and (=> (not _let_2) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real _let_1) C) B)) (=> _let_2 (= _let_1 tptp.zero_zero_real))))))) (forall ((W tptp.num) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (tptp.uminus1482373934393186551omplex (tptp.numera6690914467698888265omplex W)))) (let ((_let_2 (= C tptp.zero_zero_complex))) (= (= _let_1 (tptp.divide1717551699836669952omplex B C)) (and (=> (not _let_2) (= (tptp.aa_complex_complex (tptp.times_times_complex _let_1) C) B)) (=> _let_2 (= _let_1 tptp.zero_zero_complex))))))) (forall ((W tptp.num) (B 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 B) C)) (and (=> (not _let_2) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat _let_1) C) B)) (=> _let_2 (= _let_1 tptp.zero_zero_rat))))))) (forall ((Z tptp.real) (A tptp.real) (B 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))) B))) (let ((_let_2 (= Z tptp.zero_zero_real))) (and (=> _let_2 (= _let_1 B)) (=> (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 B) Z))) Z))))))) (forall ((Z tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (tptp.plus_plus_complex (tptp.uminus1482373934393186551omplex (tptp.divide1717551699836669952omplex A Z)) B))) (let ((_let_2 (= Z tptp.zero_zero_complex))) (and (=> _let_2 (= _let_1 B)) (=> (not _let_2) (= _let_1 (tptp.divide1717551699836669952omplex (tptp.plus_plus_complex (tptp.uminus1482373934393186551omplex A) (tptp.aa_complex_complex (tptp.times_times_complex B) Z)) Z))))))) (forall ((Z tptp.rat) (A tptp.rat) (B 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))) B))) (let ((_let_2 (= Z tptp.zero_zero_rat))) (and (=> _let_2 (= _let_1 B)) (=> (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 B) Z))) Z))))))) (forall ((Z tptp.real) (X tptp.real) (Y4 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))) Y4) (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 Y4) Z))) Z)))) (forall ((Z tptp.complex) (X tptp.complex) (Y4 tptp.complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (tptp.plus_plus_complex (tptp.uminus1482373934393186551omplex (tptp.divide1717551699836669952omplex X Z)) Y4) (tptp.divide1717551699836669952omplex (tptp.plus_plus_complex (tptp.uminus1482373934393186551omplex X) (tptp.aa_complex_complex (tptp.times_times_complex Y4) Z)) Z)))) (forall ((Z tptp.rat) (X tptp.rat) (Y4 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))) Y4) (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 Y4) Z))) Z)))) (forall ((Z tptp.real) (A tptp.real) (B 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))) B))) (let ((_let_2 (= Z tptp.zero_zero_real))) (and (=> _let_2 (= _let_1 (tptp.aa_real_real tptp.uminus_uminus_real B))) (=> (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 B) Z))) Z))))))) (forall ((Z tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (tptp.minus_minus_complex (tptp.uminus1482373934393186551omplex (tptp.divide1717551699836669952omplex A Z)) B))) (let ((_let_2 (= Z tptp.zero_zero_complex))) (and (=> _let_2 (= _let_1 (tptp.uminus1482373934393186551omplex B))) (=> (not _let_2) (= _let_1 (tptp.divide1717551699836669952omplex (tptp.minus_minus_complex (tptp.uminus1482373934393186551omplex A) (tptp.aa_complex_complex (tptp.times_times_complex B) Z)) Z))))))) (forall ((Z tptp.rat) (A tptp.rat) (B 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))) B))) (let ((_let_2 (= Z tptp.zero_zero_rat))) (and (=> _let_2 (= _let_1 (tptp.aa_rat_rat tptp.uminus_uminus_rat B))) (=> (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 B) Z))) Z))))))) (forall ((Z tptp.real) (A tptp.real) (B 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)) B))) (let ((_let_2 (= Z tptp.zero_zero_real))) (and (=> _let_2 (= _let_1 (tptp.aa_real_real tptp.uminus_uminus_real B))) (=> (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 B) Z))) Z))))))) (forall ((Z tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (tptp.minus_minus_complex (tptp.divide1717551699836669952omplex A Z) B))) (let ((_let_2 (= Z tptp.zero_zero_complex))) (and (=> _let_2 (= _let_1 (tptp.uminus1482373934393186551omplex B))) (=> (not _let_2) (= _let_1 (tptp.divide1717551699836669952omplex (tptp.minus_minus_complex A (tptp.aa_complex_complex (tptp.times_times_complex B) Z)) Z))))))) (forall ((Z tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_rat_rat (tptp.divide_divide_rat A) Z)) B))) (let ((_let_2 (= Z tptp.zero_zero_rat))) (and (=> _let_2 (= _let_1 (tptp.aa_rat_rat tptp.uminus_uminus_rat B))) (=> (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 B) Z))) Z))))))) (forall ((Z tptp.real) (X tptp.real) (Y4 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))) Y4) (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 Y4) Z))) Z)))) (forall ((Z tptp.complex) (X tptp.complex) (Y4 tptp.complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (tptp.minus_minus_complex (tptp.uminus1482373934393186551omplex (tptp.divide1717551699836669952omplex X Z)) Y4) (tptp.divide1717551699836669952omplex (tptp.minus_minus_complex (tptp.uminus1482373934393186551omplex X) (tptp.aa_complex_complex (tptp.times_times_complex Y4) Z)) Z)))) (forall ((Z tptp.rat) (X tptp.rat) (Y4 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))) Y4) (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 Y4) 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.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 ((A tptp.real) (X tptp.real) (B 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) B)) (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 ((Y3 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) Y3))) D2)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) Y3)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y3) B)))))))))) (forall ((X tptp.real) (Y4 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 Y4) _let_1)) (or (= X Y4) (= X (tptp.aa_real_real tptp.uminus_uminus_real Y4)))))) (forall ((X tptp.int) (Y4 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 Y4) _let_1)) (or (= X Y4) (= X (tptp.aa_int_int tptp.uminus_uminus_int Y4)))))) (forall ((X tptp.complex) (Y4 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 Y4) _let_1)) (or (= X Y4) (= X (tptp.uminus1482373934393186551omplex Y4)))))) (forall ((X tptp.code_integer) (Y4 tptp.code_integer)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (= (tptp.power_8256067586552552935nteger X _let_1) (tptp.power_8256067586552552935nteger Y4 _let_1)) (or (= X Y4) (= X (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger Y4)))))) (forall ((X tptp.rat) (Y4 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 Y4) _let_1)) (or (= X Y4) (= X (tptp.aa_rat_rat tptp.uminus_uminus_rat Y4)))))) (forall ((A tptp.real) (B 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 B)))) (tptp.aa_real_real tptp.real_V7735802525324610683m_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A) B))))) (forall ((A tptp.complex) (B 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 B)))) (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.minus_minus_complex A B))))) (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 ((A tptp.complex) (N tptp.nat)) (= (= (tptp.aa_nat_complex (tptp.comm_s2602460028002588243omplex A) N) tptp.zero_zero_complex) (exists ((K3 tptp.nat)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat K3) N)) (= A (tptp.uminus1482373934393186551omplex (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex K3))))))) (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 ((K3 tptp.nat)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat K3) N)) (= A (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real K3))))))) (forall ((A tptp.rat) (N tptp.nat)) (= (= (tptp.aa_nat_rat (tptp.comm_s4028243227959126397er_rat A) N) tptp.zero_zero_rat) (exists ((K3 tptp.nat)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat K3) N)) (= A (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat K3))))))) (forall ((N tptp.nat) (K tptp.nat)) (= (= (tptp.comm_s8582702949713902594nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (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_complex (tptp.comm_s2602460028002588243omplex (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_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 ((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.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N) K)) (= (tptp.comm_s8582702949713902594nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (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_complex (tptp.comm_s2602460028002588243omplex (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_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.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 ((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 ((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.comm_s8582702949713902594nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (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_complex (tptp.comm_s2602460028002588243omplex (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_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 ((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 ((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 ((A2 tptp.int) (B3 tptp.int) (N tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A2) B3)) (=> (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.aa_int_fun_int_int tptp.divide_divide_int B3) N)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A2) N)))))) (forall ((B 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) B)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int _let_1) B) _let_1)))) (forall ((X tptp.code_integer) (Y4 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 Y4))) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.power_8256067586552552935nteger X _let_1)) (tptp.power_8256067586552552935nteger Y4 _let_1)))))) (forall ((X tptp.rat) (Y4 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 Y4))) (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 Y4) _let_1)))))) (forall ((X tptp.int) (Y4 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 Y4))) (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 Y4) _let_1)))))) (forall ((X tptp.real) (Y4 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 Y4))) (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 Y4) _let_1)))))) (forall ((X tptp.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.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 ((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 ((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.power_8256067586552552935nteger (tptp.abs_abs_Code_integer A) N) (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.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 ((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 ((A tptp.rat) (B 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 B))) (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 B) 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 ((A tptp.real) (B 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 B))) (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 B) 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 ((B 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 B))) (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 B) 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 ((B 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 B))) (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 B) 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 ((C tptp.rat) (A tptp.rat) (B 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 B) 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 B)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) C)))))) (forall ((C tptp.real) (A tptp.real) (B 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 B) C)))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real B)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) C)))))) (forall ((C tptp.rat) (B 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 B) 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 B)))))) (forall ((C tptp.real) (B 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 B) 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 B)))))) (forall ((C tptp.rat) (A tptp.rat) (B 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 B) 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 B)))))) (forall ((C tptp.real) (A tptp.real) (B 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 B) 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 B)))))) (forall ((C tptp.rat) (B 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 B) 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 B)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) C)))))) (forall ((C tptp.real) (B 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 B) 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 B)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) C)))))) (forall ((B 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 B) C)) _let_1)) (and (=> _let_5 (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B) _let_4))) (=> (not _let_5) (and (=> _let_3 (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real _let_4) B))) (=> (not _let_3) (tptp.pp (tptp.aa_real_bool _let_2 _let_1))))))))))))) (forall ((B 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 B) C)) _let_1)) (and (=> _let_5 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) _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) B))) (=> (not _let_3) (tptp.pp (tptp.aa_rat_bool _let_2 _let_1))))))))))))) (forall ((W tptp.num) (B 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 B) C))) (and (=> _let_5 (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real _let_4) B))) (=> (not _let_5) (and (=> _let_3 (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B) _let_4))) (=> (not _let_3) (tptp.pp (tptp.aa_real_bool _let_2 tptp.zero_zero_real))))))))))))) (forall ((W tptp.num) (B 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 B) C))) (and (=> _let_5 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat _let_4) B))) (=> (not _let_5) (and (=> _let_3 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) _let_4))) (=> (not _let_3) (tptp.pp (tptp.aa_rat_bool _let_2 tptp.zero_zero_rat))))))))))))) (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.uminus1482373934393186551omplex tptp.one_one_complex))))) (forall ((A tptp.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) (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.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.uminus1482373934393186551omplex _let_1)))))))) (forall ((N tptp.nat) (A tptp.code_integer)) (let ((_let_1 (tptp.power_8256067586552552935nteger A N))) (let ((_let_2 (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 ((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.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.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.power_8256067586552552935nteger _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N) K)) (tptp.power_8256067586552552935nteger _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 ((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 ((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 ((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.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.modulo_modulo_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int K) tptp.one_one_int) L))))) (forall ((B tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) B)) (= (tptp.modulo_modulo_int (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int) B) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int B) tptp.one_one_int)))) (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.divide_divide_int A))) (let ((_let_2 (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_int_int _let_1 B)))) (let ((_let_3 (tptp.aa_int_int _let_1 (tptp.aa_int_int tptp.uminus_uminus_int B)))) (let ((_let_4 (= (tptp.modulo_modulo_int A B) tptp.zero_zero_int))) (=> (not (= B tptp.zero_zero_int)) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int _let_2) tptp.one_one_int)))))))))) (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A) B)))) (let ((_let_2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int (tptp.aa_int_int tptp.uminus_uminus_int A)) B))) (let ((_let_3 (= (tptp.modulo_modulo_int A B) tptp.zero_zero_int))) (=> (not (= B tptp.zero_zero_int)) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int _let_1) tptp.one_one_int))))))))) (forall ((Y4 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) Y4)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.power_8256067586552552935nteger X _let_1)) (tptp.power_8256067586552552935nteger Y4 _let_1))) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.abs_abs_Code_integer X)) Y4)))))) (forall ((Y4 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) Y4)) (= (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 Y4) _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)) Y4)))))) (forall ((Y4 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) Y4)) (= (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 Y4) _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)) Y4)))))) (forall ((Y4 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) Y4)) (= (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 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 X)) Y4)))))) (forall ((X tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (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.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 ((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.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (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) (B 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 B))) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.power_8256067586552552935nteger A N)) (tptp.power_8256067586552552935nteger B N)))))) (forall ((N tptp.nat) (A tptp.rat) (B 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 B))) (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 B) N)))))) (forall ((N tptp.nat) (A tptp.int) (B 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 B))) (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 B) N)))))) (forall ((N tptp.nat) (A tptp.real) (B 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 B))) (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 B) N)))))) (forall ((B 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 B) C)) _let_1)) (and (=> _let_4 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) _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) B))) (=> (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 ((B 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 B) C)) _let_1)) (and (=> _let_4 (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real B) _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) B))) (=> (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 ((W tptp.num) (B 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 B) C))) (and (=> _let_5 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat _let_4) B))) (=> (not _let_5) (and (=> _let_3 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) _let_4))) (=> (not _let_3) (tptp.pp (tptp.aa_rat_bool _let_2 tptp.zero_zero_rat))))))))))))) (forall ((W tptp.num) (B 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 B) C))) (and (=> _let_5 (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real _let_4) B))) (=> (not _let_5) (and (=> _let_3 (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real B) _let_4))) (=> (not _let_3) (tptp.pp (tptp.aa_real_bool _let_2 tptp.zero_zero_real))))))))))))) (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 ((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.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 ((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 ((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.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.power_8256067586552552935nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A) N))) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger _let_1) _let_1) (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)) (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.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.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 ((R2 tptp.code_integer) (K tptp.nat)) (let ((_let_1 (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger R2))) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.minus_8373710615458151222nteger R2 (tptp.semiri4939895301339042750nteger K))) (tptp.comm_s8582702949713902594nteger _let_1 K)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger R2) (tptp.comm_s8582702949713902594nteger (tptp.plus_p5714425477246183910nteger _let_1 tptp.one_one_Code_integer) K))))) (forall ((R2 tptp.complex) (K tptp.nat)) (let ((_let_1 (tptp.uminus1482373934393186551omplex R2))) (= (tptp.aa_complex_complex (tptp.times_times_complex (tptp.minus_minus_complex R2 (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 R2) (tptp.aa_nat_complex (tptp.comm_s2602460028002588243omplex (tptp.plus_plus_complex _let_1 tptp.one_one_complex)) K))))) (forall ((R2 tptp.real) (K tptp.nat)) (let ((_let_1 (tptp.aa_real_real tptp.uminus_uminus_real R2))) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real R2) (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 R2) (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 ((R2 tptp.rat) (K tptp.nat)) (let ((_let_1 (tptp.aa_rat_rat tptp.uminus_uminus_rat R2))) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat (tptp.minus_minus_rat R2) (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 R2) (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 ((R2 tptp.int) (K tptp.nat)) (let ((_let_1 (tptp.aa_int_int tptp.uminus_uminus_int R2))) (= (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 R2) (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 R2) (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 ((N tptp.nat)) (= (tptp.comm_s8582702949713902594nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.semiri4939895301339042750nteger N)) N) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.power_8256067586552552935nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer) N)) (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)) (= (tptp.aa_nat_complex (tptp.comm_s2602460028002588243omplex (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.uminus1482373934393186551omplex tptp.one_one_complex)) N)) (tptp.aa_nat_complex tptp.semiri5044797733671781792omplex 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.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) (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 ((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 ((N tptp.nat)) (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.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.aa_int_fun_int_int tptp.divide_divide_int K) L) (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int))))) (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.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.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 ((B tptp.code_integer) (K tptp.nat)) (= (tptp.comm_s8582702949713902594nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger B) K) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.power_8256067586552552935nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer) K)) (tptp.comm_s8582702949713902594nteger (tptp.plus_p5714425477246183910nteger (tptp.minus_8373710615458151222nteger B (tptp.semiri4939895301339042750nteger K)) tptp.one_one_Code_integer) K)))) (forall ((B tptp.complex) (K tptp.nat)) (= (tptp.aa_nat_complex (tptp.comm_s2602460028002588243omplex (tptp.uminus1482373934393186551omplex B)) K) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_nat_complex (tptp.power_power_complex (tptp.uminus1482373934393186551omplex tptp.one_one_complex)) K)) (tptp.aa_nat_complex (tptp.comm_s2602460028002588243omplex (tptp.plus_plus_complex (tptp.minus_minus_complex B (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex K)) tptp.one_one_complex)) K)))) (forall ((B 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 B)) 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 B) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real K))) tptp.one_one_real)) K)))) (forall ((B tptp.rat) (K tptp.nat)) (= (tptp.aa_nat_rat (tptp.comm_s4028243227959126397er_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat B)) 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 B) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat K))) tptp.one_one_rat)) K)))) (forall ((B tptp.int) (K tptp.nat)) (= (tptp.aa_nat_int (tptp.comm_s4660882817536571857er_int (tptp.aa_int_int tptp.uminus_uminus_int B)) 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 B) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int K))) tptp.one_one_int)) K)))) (forall ((B tptp.code_integer) (K tptp.nat)) (= (tptp.comm_s8582702949713902594nteger (tptp.plus_p5714425477246183910nteger (tptp.minus_8373710615458151222nteger B (tptp.semiri4939895301339042750nteger K)) tptp.one_one_Code_integer) K) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.power_8256067586552552935nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer) K)) (tptp.comm_s8582702949713902594nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger B) K)))) (forall ((B tptp.complex) (K tptp.nat)) (= (tptp.aa_nat_complex (tptp.comm_s2602460028002588243omplex (tptp.plus_plus_complex (tptp.minus_minus_complex B (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.uminus1482373934393186551omplex tptp.one_one_complex)) K)) (tptp.aa_nat_complex (tptp.comm_s2602460028002588243omplex (tptp.uminus1482373934393186551omplex B)) K)))) (forall ((B 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 B) (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 B)) K)))) (forall ((B 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 B) (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 B)) K)))) (forall ((B 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 B) (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 B)) K)))) (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 ((K2 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool P K2)) (=> (not (= K2 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 K2) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one)))))))) (=> (forall ((K2 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool P K2)) (=> (not (= K2 (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 K2) (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.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 ((N tptp.nat)) (= (tptp.aa_nat_rat tptp.semiri773545260158071498ct_rat N) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat (tptp.aa_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_int tptp.semiri1406184849735516958ct_int N) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_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.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.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_complex tptp.semiri5044797733671781792omplex N) (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex (tptp.aa_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 ((P tptp.fun_Co8310303586393106575r_bool) (X tptp.code_integer)) (=> (forall ((X3 tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) X3)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool P X3) (tptp.power_8256067586552552935nteger X3 (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.power_8256067586552552935nteger 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 ((X3 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) X3)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool P X3) (tptp.aa_nat_rat (tptp.power_power_rat X3) (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 ((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_int_bool (tptp.aa_int_fun_int_bool P X3) (tptp.aa_nat_int (tptp.power_power_int X3) (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 ((P tptp.fun_re1255401033344146673l_bool) (X tptp.real)) (=> (forall ((X3 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) X3)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool P X3) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X3) (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 ((X4 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 X4))) (let ((_let_3 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat _let_1) X4)))) (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 X4) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat))) _let_1))) (tptp.aa_nat_real tptp.semiri2265585572941072030t_real X4))))))))) (forall ((X4 tptp.nat)) (let ((_let_1 (tptp.aa_nat_real tptp.cos_coeff X4))) (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) X4)))) (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 X4) _let_2))) (tptp.aa_nat_real tptp.semiri2265585572941072030t_real X4)))) (=> (not _let_3) (= _let_1 tptp.zero_zero_real))))))) (forall ((X tptp.set_int) (Y4 tptp.set_int)) (= (tptp.ord_less_eq_set_int (tptp.uminus1532241313380277803et_int X) (tptp.uminus1532241313380277803et_int Y4)) (tptp.ord_less_eq_set_int Y4 X))) (forall ((Xs tptp.list_complex) (F tptp.fun_complex_real) (Y4 tptp.real)) (=> (forall ((X3 tptp.complex)) (=> (tptp.member_complex X3 (tptp.set_complex2 Xs)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_complex_real F X3))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y4) (tptp.aa_real_real (tptp.foldr_real_real tptp.plus_plus_real (tptp.map_complex_real F Xs)) Y4))))) (forall ((Xs tptp.list_set_nat) (F tptp.fun_set_nat_real) (Y4 tptp.real)) (=> (forall ((X3 tptp.set_nat)) (=> (tptp.member_set_nat X3 (tptp.set_set_nat2 Xs)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_set_nat_real F X3))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y4) (tptp.aa_real_real (tptp.foldr_real_real tptp.plus_plus_real (tptp.map_set_nat_real F Xs)) Y4))))) (forall ((Xs tptp.list_VEBT_VEBT) (F tptp.fun_VEBT_VEBT_real) (Y4 tptp.real)) (=> (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_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_VEBT_VEBT_real F X3))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y4) (tptp.aa_real_real (tptp.foldr_real_real tptp.plus_plus_real (tptp.map_VEBT_VEBT_real F Xs)) Y4))))) (forall ((Xs tptp.list_nat) (F tptp.fun_nat_real) (Y4 tptp.real)) (=> (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) (tptp.set_nat2 Xs))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_nat_real F X3))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y4) (tptp.aa_real_real (tptp.foldr_real_real tptp.plus_plus_real (tptp.map_nat_real F Xs)) Y4))))) (forall ((Xs tptp.list_real) (F tptp.fun_real_real) (Y4 tptp.real)) (=> (forall ((X3 tptp.real)) (=> (tptp.member_real X3 (tptp.set_real2 Xs)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_real_real F X3))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y4) (tptp.aa_real_real (tptp.foldr_real_real tptp.plus_plus_real (tptp.map_real_real F Xs)) Y4))))) (forall ((Xs tptp.list_int) (F tptp.fun_int_real) (Y4 tptp.real)) (=> (forall ((X3 tptp.int)) (=> (tptp.member_int X3 (tptp.set_int2 Xs)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_int_real F X3))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y4) (tptp.aa_real_real (tptp.foldr_real_real tptp.plus_plus_real (tptp.map_int_real F Xs)) Y4))))) (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_85) (tptp.aa_real_real tptp.uminus_uminus_real _let_81)) (= (tptp.neg_nu3811975205180677377ec_int _let_59) (tptp.aa_int_int tptp.uminus_uminus_int _let_105)) (= (tptp.neg_nu6511756317524482435omplex _let_75) (tptp.uminus1482373934393186551omplex _let_104)) (= (tptp.neg_nu7757733837767384882nteger _let_60) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.numera6620942414471956472nteger _let_5))) (= (tptp.aa_rat_rat tptp.neg_nu3179335615603231917ec_rat _let_100) (tptp.aa_rat_rat tptp.uminus_uminus_rat _let_103)) (forall ((C tptp.complex) (A2 tptp.set_complex)) (=> (not (tptp.member_complex C A2)) (tptp.member_complex C (tptp.uminus8566677241136511917omplex A2)))) (forall ((C tptp.real) (A2 tptp.set_real)) (=> (not (tptp.member_real C A2)) (tptp.member_real C (tptp.uminus612125837232591019t_real A2)))) (forall ((C tptp.set_nat) (A2 tptp.set_set_nat)) (=> (not (tptp.member_set_nat C A2)) (tptp.member_set_nat C (tptp.uminus613421341184616069et_nat A2)))) (forall ((C tptp.nat) (A2 tptp.set_nat)) (let ((_let_1 (tptp.member_nat C))) (=> (not (tptp.pp (tptp.aa_set_nat_bool _let_1 A2))) (tptp.pp (tptp.aa_set_nat_bool _let_1 (tptp.uminus5710092332889474511et_nat A2)))))) (forall ((C tptp.int) (A2 tptp.set_int)) (=> (not (tptp.member_int C A2)) (tptp.member_int C (tptp.uminus1532241313380277803et_int A2)))) (forall ((C tptp.complex) (A2 tptp.set_complex)) (= (tptp.member_complex C (tptp.uminus8566677241136511917omplex A2)) (not (tptp.member_complex C A2)))) (forall ((C tptp.real) (A2 tptp.set_real)) (= (tptp.member_real C (tptp.uminus612125837232591019t_real A2)) (not (tptp.member_real C A2)))) (forall ((C tptp.set_nat) (A2 tptp.set_set_nat)) (= (tptp.member_set_nat C (tptp.uminus613421341184616069et_nat A2)) (not (tptp.member_set_nat C A2)))) (forall ((C tptp.nat) (A2 tptp.set_nat)) (let ((_let_1 (tptp.member_nat C))) (= (tptp.pp (tptp.aa_set_nat_bool _let_1 (tptp.uminus5710092332889474511et_nat A2))) (not (tptp.pp (tptp.aa_set_nat_bool _let_1 A2)))))) (forall ((C tptp.int) (A2 tptp.set_int)) (= (tptp.member_int C (tptp.uminus1532241313380277803et_int A2)) (not (tptp.member_int C A2)))) (forall ((X tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int X) tptp.one_one_int)) (= (tptp.aa_int_int tptp.abs_abs_int X) tptp.one_one_int))) (= (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.neg_nu3811975205180677377ec_int tptp.one_one_int) tptp.one_one_int) (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.complex) (N tptp.nat) (Y4 tptp.complex)) (= (tptp.member_complex X (tptp.set_complex2 (tptp.replicate_complex N Y4))) (and (= X Y4) (not (= N tptp.zero_zero_nat))))) (forall ((X tptp.set_nat) (N tptp.nat) (Y4 tptp.set_nat)) (= (tptp.member_set_nat X (tptp.set_set_nat2 (tptp.replicate_set_nat N Y4))) (and (= X Y4) (not (= N tptp.zero_zero_nat))))) (forall ((X tptp.nat) (N tptp.nat) (Y4 tptp.nat)) (= (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X) (tptp.set_nat2 (tptp.replicate_nat N Y4)))) (and (= X Y4) (not (= N tptp.zero_zero_nat))))) (forall ((X tptp.int) (N tptp.nat) (Y4 tptp.int)) (= (tptp.member_int X (tptp.set_int2 (tptp.replicate_int N Y4))) (and (= X Y4) (not (= N tptp.zero_zero_nat))))) (forall ((X tptp.real) (N tptp.nat) (Y4 tptp.real)) (= (tptp.member_real X (tptp.set_real2 (tptp.replicate_real N Y4))) (and (= X Y4) (not (= N tptp.zero_zero_nat))))) (forall ((X tptp.vEBT_VEBT) (N tptp.nat) (Y4 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 Y4)))) (and (= X Y4) (not (= N tptp.zero_zero_nat))))) (forall ((N tptp.nat) (A tptp.nat) (P tptp.fun_nat_bool)) (= (exists ((X5 tptp.nat)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X5) (tptp.set_nat2 (tptp.replicate_nat N A)))) (tptp.pp (tptp.aa_nat_bool P X5)))) (and (tptp.pp (tptp.aa_nat_bool P A)) (not (= N tptp.zero_zero_nat))))) (forall ((N tptp.nat) (A tptp.int) (P tptp.fun_int_bool)) (= (exists ((X5 tptp.int)) (and (tptp.member_int X5 (tptp.set_int2 (tptp.replicate_int N A))) (tptp.pp (tptp.aa_int_bool P X5)))) (and (tptp.pp (tptp.aa_int_bool P A)) (not (= N tptp.zero_zero_nat))))) (forall ((N tptp.nat) (A tptp.real) (P tptp.fun_real_bool)) (= (exists ((X5 tptp.real)) (and (tptp.member_real X5 (tptp.set_real2 (tptp.replicate_real N A))) (tptp.pp (tptp.aa_real_bool P X5)))) (and (tptp.pp (tptp.aa_real_bool P A)) (not (= N tptp.zero_zero_nat))))) (forall ((N tptp.nat) (A tptp.vEBT_VEBT) (P tptp.fun_VEBT_VEBT_bool)) (= (exists ((X5 tptp.vEBT_VEBT)) (and (tptp.pp (tptp.aa_set8260762808118238015T_bool (tptp.aa_VEB289770264548726718T_bool tptp.member_VEBT_VEBT X5) (tptp.set_VEBT_VEBT2 (tptp.replicate_VEBT_VEBT N A)))) (tptp.pp (tptp.aa_VEBT_VEBT_bool P X5)))) (and (tptp.pp (tptp.aa_VEBT_VEBT_bool P A)) (not (= N tptp.zero_zero_nat))))) (forall ((N tptp.nat) (A tptp.nat) (P tptp.fun_nat_bool)) (= (forall ((X5 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X5) (tptp.set_nat2 (tptp.replicate_nat N A)))) (tptp.pp (tptp.aa_nat_bool P X5)))) (or (tptp.pp (tptp.aa_nat_bool P A)) (= N tptp.zero_zero_nat)))) (forall ((N tptp.nat) (A tptp.int) (P tptp.fun_int_bool)) (= (forall ((X5 tptp.int)) (=> (tptp.member_int X5 (tptp.set_int2 (tptp.replicate_int N A))) (tptp.pp (tptp.aa_int_bool P X5)))) (or (tptp.pp (tptp.aa_int_bool P A)) (= N tptp.zero_zero_nat)))) (forall ((N tptp.nat) (A tptp.real) (P tptp.fun_real_bool)) (= (forall ((X5 tptp.real)) (=> (tptp.member_real X5 (tptp.set_real2 (tptp.replicate_real N A))) (tptp.pp (tptp.aa_real_bool P X5)))) (or (tptp.pp (tptp.aa_real_bool P A)) (= N tptp.zero_zero_nat)))) (forall ((N tptp.nat) (A tptp.vEBT_VEBT) (P tptp.fun_VEBT_VEBT_bool)) (= (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.replicate_VEBT_VEBT N A)))) (tptp.pp (tptp.aa_VEBT_VEBT_bool P X5)))) (or (tptp.pp (tptp.aa_VEBT_VEBT_bool P A)) (= N tptp.zero_zero_nat)))) (= (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)))) (= (tptp.aa_nat_real tptp.sin_coeff tptp.zero_zero_nat) tptp.zero_zero_real) (= (tptp.aa_nat_real tptp.cos_coeff tptp.zero_zero_nat) tptp.one_one_real) (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_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 ((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 ((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.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)))) (= (tptp.aa_real_real tptp.neg_nu6075765906172075777c_real tptp.zero_zero_real) _let_85) (= (tptp.neg_nu3811975205180677377ec_int tptp.zero_zero_int) _let_59) (= (tptp.neg_nu6511756317524482435omplex tptp.zero_zero_complex) _let_75) (= (tptp.neg_nu7757733837767384882nteger tptp.zero_z3403309356797280102nteger) _let_60) (= (tptp.aa_rat_rat tptp.neg_nu3179335615603231917ec_rat tptp.zero_zero_rat) _let_100) (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.neg_nu5851722552734809277nc_int (tptp.aa_int_int tptp.uminus_uminus_int _let_1)) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.neg_nu3811975205180677377ec_int _let_1))))) (forall ((K tptp.num)) (let ((_let_1 (tptp.numera6690914467698888265omplex K))) (= (tptp.neg_nu8557863876264182079omplex (tptp.uminus1482373934393186551omplex _let_1)) (tptp.uminus1482373934393186551omplex (tptp.neg_nu6511756317524482435omplex _let_1))))) (forall ((K tptp.num)) (let ((_let_1 (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.neg_nu3811975205180677377ec_int (tptp.aa_int_int tptp.uminus_uminus_int _let_1)) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.neg_nu5851722552734809277nc_int _let_1))))) (forall ((K tptp.num)) (let ((_let_1 (tptp.numera6690914467698888265omplex K))) (= (tptp.neg_nu6511756317524482435omplex (tptp.uminus1482373934393186551omplex _let_1)) (tptp.uminus1482373934393186551omplex (tptp.neg_nu8557863876264182079omplex _let_1))))) (forall ((K tptp.num)) (let ((_let_1 (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 ((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 ((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 ((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 ((C tptp.complex) (A2 tptp.set_complex)) (=> (tptp.member_complex C (tptp.uminus8566677241136511917omplex A2)) (not (tptp.member_complex C A2)))) (forall ((C tptp.real) (A2 tptp.set_real)) (=> (tptp.member_real C (tptp.uminus612125837232591019t_real A2)) (not (tptp.member_real C A2)))) (forall ((C tptp.set_nat) (A2 tptp.set_set_nat)) (=> (tptp.member_set_nat C (tptp.uminus613421341184616069et_nat A2)) (not (tptp.member_set_nat C A2)))) (forall ((C tptp.nat) (A2 tptp.set_nat)) (let ((_let_1 (tptp.member_nat C))) (=> (tptp.pp (tptp.aa_set_nat_bool _let_1 (tptp.uminus5710092332889474511et_nat A2))) (not (tptp.pp (tptp.aa_set_nat_bool _let_1 A2)))))) (forall ((C tptp.int) (A2 tptp.set_int)) (=> (tptp.member_int C (tptp.uminus1532241313380277803et_int A2)) (not (tptp.member_int C A2)))) (forall ((Xs tptp.list_complex) (B3 tptp.set_complex)) (= (tptp.ord_le211207098394363844omplex (tptp.set_complex2 Xs) B3) (forall ((X5 tptp.complex)) (=> (tptp.member_complex X5 (tptp.set_complex2 Xs)) (tptp.member_complex X5 B3))))) (forall ((Xs tptp.list_set_nat) (B3 tptp.set_set_nat)) (= (tptp.ord_le6893508408891458716et_nat (tptp.set_set_nat2 Xs) B3) (forall ((X5 tptp.set_nat)) (=> (tptp.member_set_nat X5 (tptp.set_set_nat2 Xs)) (tptp.member_set_nat X5 B3))))) (forall ((Xs tptp.list_VEBT_VEBT) (B3 tptp.set_VEBT_VEBT)) (= (tptp.ord_le4337996190870823476T_VEBT (tptp.set_VEBT_VEBT2 Xs) B3) (forall ((X5 tptp.vEBT_VEBT)) (let ((_let_1 (tptp.aa_VEB289770264548726718T_bool tptp.member_VEBT_VEBT X5))) (=> (tptp.pp (tptp.aa_set8260762808118238015T_bool _let_1 (tptp.set_VEBT_VEBT2 Xs))) (tptp.pp (tptp.aa_set8260762808118238015T_bool _let_1 B3))))))) (forall ((Xs tptp.list_nat) (B3 tptp.set_nat)) (= (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat (tptp.set_nat2 Xs)) B3)) (forall ((X5 tptp.nat)) (let ((_let_1 (tptp.member_nat X5))) (=> (tptp.pp (tptp.aa_set_nat_bool _let_1 (tptp.set_nat2 Xs))) (tptp.pp (tptp.aa_set_nat_bool _let_1 B3))))))) (forall ((Xs tptp.list_real) (B3 tptp.set_real)) (= (tptp.ord_less_eq_set_real (tptp.set_real2 Xs) B3) (forall ((X5 tptp.real)) (=> (tptp.member_real X5 (tptp.set_real2 Xs)) (tptp.member_real X5 B3))))) (forall ((Xs tptp.list_int) (B3 tptp.set_int)) (= (tptp.ord_less_eq_set_int (tptp.set_int2 Xs) B3) (forall ((X5 tptp.int)) (=> (tptp.member_int X5 (tptp.set_int2 Xs)) (tptp.member_int X5 B3))))) (forall ((A tptp.int) (B tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int A) B)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int B) A)) (= (tptp.aa_int_int tptp.abs_abs_int A) (tptp.aa_int_int tptp.abs_abs_int B))))) (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 ((Y4 tptp.int) (X tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int Y4) X)) (= (tptp.aa_int_int tptp.abs_abs_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int X) Y4)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int (tptp.aa_int_int tptp.abs_abs_int X)) (tptp.aa_int_int tptp.abs_abs_int Y4))))) (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 ((N tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N))) (= (tptp.aa_nat_real tptp.sin_coeff _let_1) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_nat_real tptp.cos_coeff N)) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real _let_1))))) (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 ((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 ((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.modulo_modulo_int K L))) (tptp.aa_int_int tptp.abs_abs_int L))))) (forall ((N tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N))) (= (tptp.aa_nat_real tptp.cos_coeff _let_1) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_nat_real tptp.sin_coeff N))) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real _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 ((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 ((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)) (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 ((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)) (= (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.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 ((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 ((X tptp.complex)) (= (tptp.neg_nu6511756317524482435omplex X) (tptp.minus_minus_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.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 ((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.set_int) (Y4 tptp.set_int)) (=> (tptp.ord_less_eq_set_int X Y4) (tptp.ord_less_eq_set_int (tptp.uminus1532241313380277803et_int Y4) (tptp.uminus1532241313380277803et_int X)))) (forall ((Y4 tptp.set_int) (X tptp.set_int)) (=> (tptp.ord_less_eq_set_int Y4 (tptp.uminus1532241313380277803et_int X)) (tptp.ord_less_eq_set_int X (tptp.uminus1532241313380277803et_int Y4)))) (forall ((Y4 tptp.set_int) (X tptp.set_int)) (=> (tptp.ord_less_eq_set_int (tptp.uminus1532241313380277803et_int Y4) X) (tptp.ord_less_eq_set_int (tptp.uminus1532241313380277803et_int X) Y4))) (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 ((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 ((B 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.plus_plus_complex B A))) (tptp.aa_complex_real tptp.real_V1022390504157884413omplex B))) (tptp.aa_complex_real tptp.real_V1022390504157884413omplex A)))) (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 ((TreeList tptp.list_VEBT_VEBT) (N tptp.nat) (M tptp.nat)) (=> (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_invar_vebt X3) N)))) (=> (= (tptp.size_s6755466524823107622T_VEBT TreeList) (tptp.aa_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 ((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)))))))))) (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.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.aa_int_fun_int_int tptp.divide_divide_int K) _let_1)) L)))))) (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.modulo_modulo_nat M) N)))) (let ((_let_2 (tptp.sgn_sgn_int L))) (let ((_let_3 (tptp.aa_int_fun_int_int tptp.times_times_int _let_2))) (let ((_let_4 (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.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.aa_bool_nat 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 ((N tptp.num)) (= (tptp.aa_nat_nat tptp.bit_se2002935070580805687sk_nat (tptp.aa_num_nat tptp.numeral_numeral_nat N)) (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 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_nat_nat tptp.bit_se2002935070580805687sk_nat (tptp.aa_num_nat tptp.pred_numeral N)))))) (forall ((N tptp.num)) (= (tptp.aa_nat_int tptp.bit_se2000444600071755411sk_int (tptp.aa_num_nat tptp.numeral_numeral_nat 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_nat_int tptp.bit_se2000444600071755411sk_int (tptp.aa_num_nat tptp.pred_numeral N)))))) (forall ((A tptp.int)) (let ((_let_1 (tptp.sgn_sgn_int A))) (= (tptp.sgn_sgn_int _let_1) _let_1))) (forall ((A tptp.real)) (let ((_let_1 (tptp.aa_real_real tptp.sgn_sgn_real A))) (= (tptp.aa_real_real tptp.sgn_sgn_real _let_1) _let_1))) (forall ((A tptp.complex)) (let ((_let_1 (tptp.sgn_sgn_complex A))) (= (tptp.sgn_sgn_complex _let_1) _let_1))) (forall ((A tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod1783974652533396728nteger tptp.sgn_sgn_Code_integer A))) (= (tptp.aa_Cod1783974652533396728nteger tptp.sgn_sgn_Code_integer _let_1) _let_1))) (forall ((A tptp.rat)) (let ((_let_1 (tptp.aa_rat_rat tptp.sgn_sgn_rat A))) (= (tptp.aa_rat_rat tptp.sgn_sgn_rat _let_1) _let_1))) (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))))) _let_102 _let_101 (= (tptp.aa_Cod1783974652533396728nteger tptp.sgn_sgn_Code_integer tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger) _let_102 _let_101 (= (tptp.aa_rat_rat tptp.sgn_sgn_rat tptp.zero_zero_rat) tptp.zero_zero_rat) (= (tptp.sgn_sgn_int tptp.zero_zero_int) tptp.zero_zero_int) (= (tptp.sgn_sgn_int tptp.one_one_int) tptp.one_one_int) (= (tptp.aa_real_real tptp.sgn_sgn_real tptp.one_one_real) tptp.one_one_real) (= (tptp.sgn_sgn_complex tptp.one_one_complex) tptp.one_one_complex) (= (tptp.aa_Cod1783974652533396728nteger tptp.sgn_sgn_Code_integer tptp.one_one_Code_integer) tptp.one_one_Code_integer) (= (tptp.aa_rat_rat tptp.sgn_sgn_rat tptp.one_one_rat) tptp.one_one_rat) (forall ((A tptp.complex) (B tptp.complex)) (= (tptp.sgn_sgn_complex (tptp.divide1717551699836669952omplex A B)) (tptp.divide1717551699836669952omplex (tptp.sgn_sgn_complex A) (tptp.sgn_sgn_complex B)))) (forall ((A tptp.real) (B tptp.real)) (= (tptp.aa_real_real tptp.sgn_sgn_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real A) B)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real tptp.sgn_sgn_real A)) (tptp.aa_real_real tptp.sgn_sgn_real B)))) (forall ((A tptp.rat) (B tptp.rat)) (= (tptp.aa_rat_rat tptp.sgn_sgn_rat (tptp.aa_rat_rat (tptp.divide_divide_rat A) B)) (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_rat_rat tptp.sgn_sgn_rat A)) (tptp.aa_rat_rat tptp.sgn_sgn_rat B)))) (forall ((A tptp.real)) (= (tptp.aa_real_real tptp.sgn_sgn_real (tptp.aa_real_real tptp.uminus_uminus_real A)) (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_real_real tptp.sgn_sgn_real A)))) (forall ((A tptp.int)) (= (tptp.sgn_sgn_int (tptp.aa_int_int tptp.uminus_uminus_int A)) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.sgn_sgn_int A)))) (forall ((A tptp.complex)) (= (tptp.sgn_sgn_complex (tptp.uminus1482373934393186551omplex A)) (tptp.uminus1482373934393186551omplex (tptp.sgn_sgn_complex A)))) (forall ((A tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger tptp.sgn_sgn_Code_integer (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A)) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_Cod1783974652533396728nteger tptp.sgn_sgn_Code_integer A)))) (forall ((A tptp.rat)) (= (tptp.aa_rat_rat tptp.sgn_sgn_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat A)) (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_rat_rat tptp.sgn_sgn_rat A)))) (forall ((X tptp.real)) (= (= (tptp.aa_real_real tptp.arctan X) tptp.zero_zero_real) (= X tptp.zero_zero_real))) (= (tptp.aa_real_real tptp.arctan tptp.zero_zero_real) tptp.zero_zero_real) (forall ((K tptp.int) (L tptp.int)) (= (tptp.aa_int_int (tptp.bit_concat_bit tptp.zero_zero_nat K) L) L)) (forall ((A tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_Cod1783974652533396728nteger tptp.sgn_sgn_Code_integer A)) tptp.zero_z3403309356797280102nteger)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger A) tptp.zero_z3403309356797280102nteger)))) (forall ((A tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.sgn_sgn_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.sgn_sgn_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.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.sgn_sgn_int 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.code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger))) (= (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.aa_Cod1783974652533396728nteger tptp.sgn_sgn_Code_integer A))) (tptp.pp (tptp.aa_Code_integer_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.sgn_sgn_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.sgn_sgn_rat 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.sgn_sgn_int A))) (tptp.pp (tptp.aa_int_bool _let_1 A))))) (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (tptp.aa_real_real tptp.sgn_sgn_real B))) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real A) _let_1) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) _let_1)))) (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (tptp.aa_rat_rat tptp.sgn_sgn_rat B))) (= (tptp.aa_rat_rat (tptp.divide_divide_rat A) _let_1) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) _let_1)))) (= (tptp.aa_nat_nat tptp.bit_se2002935070580805687sk_nat tptp.zero_zero_nat) tptp.zero_zero_nat) (= (tptp.aa_nat_int tptp.bit_se2000444600071755411sk_int tptp.zero_zero_nat) tptp.zero_zero_int) (forall ((N tptp.nat)) (= (= (tptp.aa_nat_nat tptp.bit_se2002935070580805687sk_nat N) tptp.zero_zero_nat) (= N tptp.zero_zero_nat))) (forall ((N tptp.nat)) (= (= (tptp.aa_nat_int tptp.bit_se2000444600071755411sk_int N) tptp.zero_zero_int) (= N tptp.zero_zero_nat))) (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_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)) (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 ((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 ((A tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A)) (= (tptp.aa_Cod1783974652533396728nteger tptp.sgn_sgn_Code_integer A) tptp.one_one_Code_integer))) (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.sgn_sgn_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 tptp.zero_zero_rat) A)) (= (tptp.aa_rat_rat tptp.sgn_sgn_rat A) tptp.one_one_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) A)) (= (tptp.sgn_sgn_int A) tptp.one_one_int))) (forall ((A tptp.code_integer)) (=> (not (= A tptp.zero_z3403309356797280102nteger)) (= (tptp.abs_abs_Code_integer (tptp.aa_Cod1783974652533396728nteger tptp.sgn_sgn_Code_integer A)) tptp.one_one_Code_integer))) (forall ((A tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_real_real tptp.sgn_sgn_real A)) tptp.one_one_real))) (forall ((A tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (= (tptp.aa_rat_rat tptp.abs_abs_rat (tptp.aa_rat_rat tptp.sgn_sgn_rat A)) tptp.one_one_rat))) (forall ((A tptp.int)) (=> (not (= A tptp.zero_zero_int)) (= (tptp.aa_int_int tptp.abs_abs_int (tptp.sgn_sgn_int A)) tptp.one_one_int))) (forall ((A tptp.real)) (let ((_let_1 (tptp.aa_real_real tptp.sgn_sgn_real A))) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real _let_1) _let_1) (tptp.zero_n3304061248610475627l_real (tptp.aa_bool_bool tptp.fNot (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.fequal_real A) tptp.zero_zero_real)))))) (forall ((A tptp.rat)) (let ((_let_1 (tptp.aa_rat_rat tptp.sgn_sgn_rat A))) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat _let_1) _let_1) (tptp.zero_n2052037380579107095ol_rat (tptp.aa_bool_bool tptp.fNot (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.fequal_rat A) tptp.zero_zero_rat)))))) (forall ((A tptp.int)) (let ((_let_1 (tptp.sgn_sgn_int A))) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int _let_1) _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.fequal_int A) tptp.zero_zero_int)))))) (forall ((A tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod1783974652533396728nteger tptp.sgn_sgn_Code_integer A))) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger _let_1) _let_1) (tptp.aa_bool_Code_integer tptp.zero_n356916108424825756nteger (tptp.aa_bool_bool tptp.fNot (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.fequal_Code_integer A) tptp.zero_z3403309356797280102nteger)))))) (= (tptp.aa_nat_nat tptp.bit_se2002935070580805687sk_nat _let_58) tptp.one_one_nat) (= (tptp.aa_nat_int tptp.bit_se2000444600071755411sk_int _let_58) tptp.one_one_int) (forall ((A tptp.complex)) (= (tptp.abs_abs_complex (tptp.sgn_sgn_complex A)) (tptp.zero_n1201886186963655149omplex (tptp.aa_bool_bool tptp.fNot (tptp.aa_complex_bool (tptp.fequal_complex A) tptp.zero_zero_complex))))) (forall ((A tptp.real)) (= (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_real_real tptp.sgn_sgn_real A)) (tptp.zero_n3304061248610475627l_real (tptp.aa_bool_bool tptp.fNot (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.fequal_real A) tptp.zero_zero_real))))) (forall ((A tptp.rat)) (= (tptp.aa_rat_rat tptp.abs_abs_rat (tptp.aa_rat_rat tptp.sgn_sgn_rat A)) (tptp.zero_n2052037380579107095ol_rat (tptp.aa_bool_bool tptp.fNot (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.fequal_rat A) tptp.zero_zero_rat))))) (forall ((A tptp.int)) (= (tptp.aa_int_int tptp.abs_abs_int (tptp.sgn_sgn_int A)) (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 A) tptp.zero_zero_int))))) (forall ((A tptp.code_integer)) (= (tptp.abs_abs_Code_integer (tptp.aa_Cod1783974652533396728nteger tptp.sgn_sgn_Code_integer A)) (tptp.aa_bool_Code_integer tptp.zero_n356916108424825756nteger (tptp.aa_bool_bool tptp.fNot (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.fequal_Code_integer A) tptp.zero_z3403309356797280102nteger))))) (forall ((A tptp.complex)) (= (tptp.sgn_sgn_complex (tptp.abs_abs_complex A)) (tptp.zero_n1201886186963655149omplex (tptp.aa_bool_bool tptp.fNot (tptp.aa_complex_bool (tptp.fequal_complex A) tptp.zero_zero_complex))))) (forall ((A tptp.real)) (= (tptp.aa_real_real tptp.sgn_sgn_real (tptp.aa_real_real tptp.abs_abs_real A)) (tptp.zero_n3304061248610475627l_real (tptp.aa_bool_bool tptp.fNot (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.fequal_real A) tptp.zero_zero_real))))) (forall ((A tptp.rat)) (= (tptp.aa_rat_rat tptp.sgn_sgn_rat (tptp.aa_rat_rat tptp.abs_abs_rat A)) (tptp.zero_n2052037380579107095ol_rat (tptp.aa_bool_bool tptp.fNot (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.fequal_rat A) tptp.zero_zero_rat))))) (forall ((A tptp.int)) (= (tptp.sgn_sgn_int (tptp.aa_int_int tptp.abs_abs_int A)) (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 A) tptp.zero_zero_int))))) (forall ((A tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger tptp.sgn_sgn_Code_integer (tptp.abs_abs_Code_integer A)) (tptp.aa_bool_Code_integer tptp.zero_n356916108424825756nteger (tptp.aa_bool_bool tptp.fNot (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.fequal_Code_integer A) tptp.zero_z3403309356797280102nteger))))) (forall ((R2 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.sgn_sgn_int R2)) L)) K)) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int L) K)) (=> (= R2 tptp.zero_zero_int) (= K tptp.zero_zero_int))))) (forall ((L tptp.int) (R2 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.sgn_sgn_int R2))) K)) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int L) K)) (=> (= R2 tptp.zero_zero_int) (= K tptp.zero_zero_int))))) (forall ((L tptp.int) (R2 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.sgn_sgn_int R2)) K))) (or (tptp.pp (tptp.aa_int_bool _let_1 K)) (= R2 tptp.zero_zero_int))))) (forall ((L tptp.int) (K tptp.int) (R2 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.sgn_sgn_int R2)))) (or (tptp.pp (tptp.aa_int_bool _let_1 K)) (= R2 tptp.zero_zero_int))))) (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.sgn_sgn_real A) (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)))) (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.sgn_sgn_int A) (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int)))) (forall ((A tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger A) tptp.zero_z3403309356797280102nteger)) (= (tptp.aa_Cod1783974652533396728nteger tptp.sgn_sgn_Code_integer A) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))) (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.sgn_sgn_rat A) (tptp.aa_rat_rat tptp.uminus_uminus_rat tptp.one_one_rat)))) (forall ((N tptp.nat)) (= (tptp.aa_real_real tptp.sgn_sgn_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N)) (tptp.zero_n3304061248610475627l_real (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_rat_rat tptp.sgn_sgn_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat N)) (tptp.zero_n2052037380579107095ol_rat (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)))) (forall ((N tptp.nat)) (= (tptp.sgn_sgn_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int 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.aa_Cod1783974652533396728nteger tptp.sgn_sgn_Code_integer (tptp.semiri4939895301339042750nteger N)) (tptp.aa_bool_Code_integer 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)) (let ((_let_1 (tptp.aa_nat_nat tptp.bit_se2002935070580805687sk_nat N))) (= (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat _let_1) _let_1))) (forall ((N tptp.nat)) (= (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_nat tptp.bit_se2002935070580805687sk_nat N)) (tptp.aa_nat_int tptp.bit_se2000444600071755411sk_int N))) (forall ((X tptp.list_real) (Y4 tptp.list_real)) (=> (not (= (tptp.size_size_list_real X) (tptp.size_size_list_real Y4))) (not (= X Y4)))) (forall ((X tptp.list_bool) (Y4 tptp.list_bool)) (=> (not (= (tptp.size_size_list_bool X) (tptp.size_size_list_bool Y4))) (not (= X Y4)))) (forall ((X tptp.list_nat) (Y4 tptp.list_nat)) (=> (not (= (tptp.size_size_list_nat X) (tptp.size_size_list_nat Y4))) (not (= X Y4)))) (forall ((X tptp.list_int) (Y4 tptp.list_int)) (=> (not (= (tptp.size_size_list_int X) (tptp.size_size_list_int Y4))) (not (= X Y4)))) (forall ((X tptp.num) (Y4 tptp.num)) (=> (not (= (tptp.aa_num_nat tptp.size_size_num X) (tptp.aa_num_nat tptp.size_size_num Y4))) (not (= X Y4)))) (forall ((X tptp.complex)) (= (= (tptp.sgn_sgn_complex X) tptp.zero_zero_complex) (= X tptp.zero_zero_complex))) (forall ((X tptp.real)) (= (= (tptp.aa_real_real tptp.sgn_sgn_real X) tptp.zero_zero_real) (= X tptp.zero_zero_real))) (forall ((A tptp.code_integer)) (= (= (tptp.aa_Cod1783974652533396728nteger tptp.sgn_sgn_Code_integer A) tptp.zero_z3403309356797280102nteger) (= A tptp.zero_z3403309356797280102nteger))) (forall ((A tptp.real)) (= (= (tptp.aa_real_real tptp.sgn_sgn_real A) tptp.zero_zero_real) (= A tptp.zero_zero_real))) (forall ((A tptp.rat)) (= (= (tptp.aa_rat_rat tptp.sgn_sgn_rat A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))) (forall ((A tptp.int)) (= (= (tptp.sgn_sgn_int A) tptp.zero_zero_int) (= A tptp.zero_zero_int))) (forall ((A tptp.code_integer)) (= (= (tptp.aa_Cod1783974652533396728nteger tptp.sgn_sgn_Code_integer A) tptp.zero_z3403309356797280102nteger) (= A tptp.zero_z3403309356797280102nteger))) (forall ((A tptp.complex)) (= (= (tptp.sgn_sgn_complex A) tptp.zero_zero_complex) (= A tptp.zero_zero_complex))) (forall ((A tptp.real)) (= (= (tptp.aa_real_real tptp.sgn_sgn_real A) tptp.zero_zero_real) (= A tptp.zero_zero_real))) (forall ((A tptp.rat)) (= (= (tptp.aa_rat_rat tptp.sgn_sgn_rat A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))) (forall ((A tptp.int)) (= (= (tptp.sgn_sgn_int A) tptp.zero_zero_int) (= A tptp.zero_zero_int))) (forall ((X tptp.complex) (Y4 tptp.complex)) (= (tptp.sgn_sgn_complex (tptp.aa_complex_complex (tptp.times_times_complex X) Y4)) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.sgn_sgn_complex X)) (tptp.sgn_sgn_complex Y4)))) (forall ((X tptp.real) (Y4 tptp.real)) (= (tptp.aa_real_real tptp.sgn_sgn_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real X) Y4)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real tptp.sgn_sgn_real X)) (tptp.aa_real_real tptp.sgn_sgn_real Y4)))) (forall ((A tptp.complex) (B tptp.complex)) (= (tptp.sgn_sgn_complex (tptp.aa_complex_complex (tptp.times_times_complex A) B)) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.sgn_sgn_complex A)) (tptp.sgn_sgn_complex B)))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger tptp.sgn_sgn_Code_integer (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) B)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger tptp.sgn_sgn_Code_integer A)) (tptp.aa_Cod1783974652533396728nteger tptp.sgn_sgn_Code_integer B)))) (forall ((A tptp.real) (B tptp.real)) (= (tptp.aa_real_real tptp.sgn_sgn_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) B)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real tptp.sgn_sgn_real A)) (tptp.aa_real_real tptp.sgn_sgn_real B)))) (forall ((A tptp.rat) (B tptp.rat)) (= (tptp.aa_rat_rat tptp.sgn_sgn_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) B)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat tptp.sgn_sgn_rat A)) (tptp.aa_rat_rat tptp.sgn_sgn_rat B)))) (forall ((A tptp.int) (B tptp.int)) (= (tptp.sgn_sgn_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) B)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.sgn_sgn_int A)) (tptp.sgn_sgn_int B)))) (forall ((B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod1783974652533396728nteger tptp.sgn_sgn_Code_integer A))) (=> (= (tptp.aa_Cod1783974652533396728nteger tptp.sgn_sgn_Code_integer B) _let_1) (= (tptp.aa_Cod1783974652533396728nteger tptp.sgn_sgn_Code_integer (tptp.plus_p5714425477246183910nteger A B)) _let_1)))) (forall ((B tptp.real) (A tptp.real)) (let ((_let_1 (tptp.aa_real_real tptp.sgn_sgn_real A))) (=> (= (tptp.aa_real_real tptp.sgn_sgn_real B) _let_1) (= (tptp.aa_real_real tptp.sgn_sgn_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) B)) _let_1)))) (forall ((B tptp.rat) (A tptp.rat)) (let ((_let_1 (tptp.aa_rat_rat tptp.sgn_sgn_rat A))) (=> (= (tptp.aa_rat_rat tptp.sgn_sgn_rat B) _let_1) (= (tptp.aa_rat_rat tptp.sgn_sgn_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) B)) _let_1)))) (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (tptp.sgn_sgn_int A))) (=> (= (tptp.sgn_sgn_int B) _let_1) (= (tptp.sgn_sgn_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) B)) _let_1)))) (forall ((K tptp.int) (L tptp.int)) (=> (= (tptp.sgn_sgn_int K) (tptp.sgn_sgn_int L)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int K) L) (tptp.aa_int_int (tptp.aa_int_fun_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 ((X tptp.real) (Y4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) Y4)) (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 Y4))))) (forall ((X tptp.real) (Y4 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 Y4))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) Y4)))) (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) (K tptp.int) (M tptp.nat) (L tptp.int) (R2 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) R2)) (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)) R2)))) (forall ((B tptp.real) (A tptp.real)) (let ((_let_1 (tptp.aa_real_real tptp.sgn_sgn_real B))) (let ((_let_2 (tptp.aa_real_real tptp.sgn_sgn_real A))) (=> (not (= _let_1 _let_2)) (=> (not (= _let_2 tptp.zero_zero_real)) (=> (not (= _let_1 tptp.zero_zero_real)) (= _let_2 (tptp.aa_real_real tptp.uminus_uminus_real _let_1)))))))) (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (tptp.sgn_sgn_int B))) (let ((_let_2 (tptp.sgn_sgn_int A))) (=> (not (= _let_1 _let_2)) (=> (not (= _let_2 tptp.zero_zero_int)) (=> (not (= _let_1 tptp.zero_zero_int)) (= _let_2 (tptp.aa_int_int tptp.uminus_uminus_int _let_1)))))))) (forall ((B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod1783974652533396728nteger tptp.sgn_sgn_Code_integer B))) (let ((_let_2 (tptp.aa_Cod1783974652533396728nteger tptp.sgn_sgn_Code_integer A))) (=> (not (= _let_1 _let_2)) (=> (not (= _let_2 tptp.zero_z3403309356797280102nteger)) (=> (not (= _let_1 tptp.zero_z3403309356797280102nteger)) (= _let_2 (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger _let_1)))))))) (forall ((B tptp.rat) (A tptp.rat)) (let ((_let_1 (tptp.aa_rat_rat tptp.sgn_sgn_rat B))) (let ((_let_2 (tptp.aa_rat_rat tptp.sgn_sgn_rat A))) (=> (not (= _let_1 _let_2)) (=> (not (= _let_2 tptp.zero_zero_rat)) (=> (not (= _let_1 tptp.zero_zero_rat)) (= _let_2 (tptp.aa_rat_rat tptp.uminus_uminus_rat _let_1)))))))) (= (tptp.aa_real_real tptp.sgn_sgn_real _let_85) _let_85) (= (tptp.sgn_sgn_int _let_59) _let_59) (= (tptp.sgn_sgn_complex _let_75) _let_75) (= (tptp.aa_Cod1783974652533396728nteger tptp.sgn_sgn_Code_integer _let_60) _let_60) (= (tptp.aa_rat_rat tptp.sgn_sgn_rat _let_100) _let_100) (forall ((K tptp.code_integer)) (= (tptp.abs_abs_Code_integer K) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger K) (tptp.aa_Cod1783974652533396728nteger tptp.sgn_sgn_Code_integer K)))) (forall ((K tptp.real)) (= (tptp.aa_real_real tptp.abs_abs_real K) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real K) (tptp.aa_real_real tptp.sgn_sgn_real K)))) (forall ((K tptp.rat)) (= (tptp.aa_rat_rat tptp.abs_abs_rat K) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat K) (tptp.aa_rat_rat tptp.sgn_sgn_rat K)))) (forall ((K tptp.int)) (= (tptp.aa_int_int tptp.abs_abs_int K) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int K) (tptp.sgn_sgn_int K)))) (forall ((A tptp.complex)) (= (tptp.aa_complex_complex (tptp.times_times_complex (tptp.abs_abs_complex A)) (tptp.sgn_sgn_complex A)) A)) (forall ((A tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.abs_abs_Code_integer A)) (tptp.aa_Cod1783974652533396728nteger tptp.sgn_sgn_Code_integer A)) A)) (forall ((A tptp.real)) (= (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.sgn_sgn_real A)) A)) (forall ((A tptp.rat)) (= (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.sgn_sgn_rat A)) A)) (forall ((A tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int tptp.abs_abs_int A)) (tptp.sgn_sgn_int A)) A)) (forall ((A tptp.complex)) (= (tptp.aa_complex_complex (tptp.times_times_complex (tptp.sgn_sgn_complex A)) (tptp.abs_abs_complex A)) A)) (forall ((A tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger tptp.sgn_sgn_Code_integer A)) (tptp.abs_abs_Code_integer A)) A)) (forall ((A 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_real_real tptp.abs_abs_real A)) A)) (forall ((A tptp.rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat tptp.sgn_sgn_rat A)) (tptp.aa_rat_rat tptp.abs_abs_rat A)) A)) (forall ((A tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.sgn_sgn_int A)) (tptp.aa_int_int tptp.abs_abs_int A)) A)) (forall ((X tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger tptp.sgn_sgn_Code_integer X)) (tptp.abs_abs_Code_integer X)) X)) (forall ((X tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real tptp.sgn_sgn_real X)) (tptp.aa_real_real tptp.abs_abs_real X)) X)) (forall ((X tptp.rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat tptp.sgn_sgn_rat X)) (tptp.aa_rat_rat tptp.abs_abs_rat X)) X)) (forall ((X tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.sgn_sgn_int X)) (tptp.aa_int_int tptp.abs_abs_int X)) X)) (forall ((K tptp.int)) (not (forall ((N2 tptp.nat) (L2 tptp.int)) (not (= K (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.sgn_sgn_int L2)) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N2))))))) (forall ((B tptp.code_integer) (A tptp.code_integer)) (=> (= (tptp.aa_Cod1783974652533396728nteger tptp.sgn_sgn_Code_integer B) (tptp.aa_Cod1783974652533396728nteger tptp.sgn_sgn_Code_integer A)) (= (tptp.abs_abs_Code_integer (tptp.plus_p5714425477246183910nteger A B)) (tptp.plus_p5714425477246183910nteger (tptp.abs_abs_Code_integer A) (tptp.abs_abs_Code_integer B))))) (forall ((B tptp.real) (A tptp.real)) (=> (= (tptp.aa_real_real tptp.sgn_sgn_real B) (tptp.aa_real_real tptp.sgn_sgn_real A)) (= (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) B)) (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 B))))) (forall ((B tptp.rat) (A tptp.rat)) (=> (= (tptp.aa_rat_rat tptp.sgn_sgn_rat B) (tptp.aa_rat_rat tptp.sgn_sgn_rat A)) (= (tptp.aa_rat_rat tptp.abs_abs_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) B)) (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 B))))) (forall ((B tptp.int) (A tptp.int)) (=> (= (tptp.sgn_sgn_int B) (tptp.sgn_sgn_int A)) (= (tptp.aa_int_int tptp.abs_abs_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) B)) (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 B))))) (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 ((A tptp.code_integer)) (= (= (tptp.aa_Cod1783974652533396728nteger tptp.sgn_sgn_Code_integer A) tptp.one_one_Code_integer) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A)))) (forall ((A tptp.real)) (= (= (tptp.aa_real_real tptp.sgn_sgn_real A) tptp.one_one_real) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) A)))) (forall ((A tptp.rat)) (= (= (tptp.aa_rat_rat tptp.sgn_sgn_rat A) tptp.one_one_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.int)) (= (= (tptp.sgn_sgn_int A) tptp.one_one_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)) (let ((_let_1 (tptp.abs_abs_Code_integer (tptp.aa_Cod1783974652533396728nteger tptp.sgn_sgn_Code_integer A)))) (let ((_let_2 (= A tptp.zero_z3403309356797280102nteger))) (and (=> _let_2 (= _let_1 tptp.zero_z3403309356797280102nteger)) (=> (not _let_2) (= _let_1 tptp.one_one_Code_integer)))))) (forall ((A tptp.real)) (let ((_let_1 (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_real_real tptp.sgn_sgn_real 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.abs_abs_rat (tptp.aa_rat_rat tptp.sgn_sgn_rat 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 ((A tptp.int)) (let ((_let_1 (tptp.aa_int_int tptp.abs_abs_int (tptp.sgn_sgn_int A)))) (let ((_let_2 (= A tptp.zero_zero_int))) (and (=> _let_2 (= _let_1 tptp.zero_zero_int)) (=> (not _let_2) (= _let_1 tptp.one_one_int)))))) (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.sgn_sgn_int V)))) (=> (not (= V tptp.zero_zero_int)) (= (tptp.aa_int_int (tptp.aa_int_fun_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.aa_int_fun_int_int tptp.divide_divide_int _let_2) _let_1))))))) (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.aa_int_fun_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.sgn_sgn_int K)) (tptp.sgn_sgn_int L))) (tptp.aa_int_int (tptp.aa_int_fun_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 ((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.sgn_sgn_int (tptp.modulo_modulo_int K L)) (tptp.sgn_sgn_int L))))) (forall ((X tptp.complex) (Xs tptp.list_complex)) (=> (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.set_nat) (Xs tptp.list_set_nat)) (=> (tptp.member_set_nat X (tptp.set_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_s3254054031482475050et_nat 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.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.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 ((X tptp.int) (Xs tptp.list_int)) (=> (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 ((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 ((X tptp.real)) (let ((_let_1 (tptp.aa_real_real tptp.sgn_sgn_real X))) (let ((_let_2 (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) X)))) (let ((_let_3 (= X tptp.zero_zero_real))) (and (=> _let_3 (= _let_1 tptp.zero_zero_real)) (=> (not _let_3) (and (=> _let_2 (= _let_1 tptp.one_one_real)) (=> (not _let_2) (= _let_1 (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)))))))))) (forall ((X tptp.int)) (let ((_let_1 (tptp.sgn_sgn_int X))) (let ((_let_2 (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) X)))) (let ((_let_3 (= X 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 ((X tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod1783974652533396728nteger tptp.sgn_sgn_Code_integer X))) (let ((_let_2 (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) X)))) (let ((_let_3 (= X tptp.zero_z3403309356797280102nteger))) (and (=> _let_3 (= _let_1 tptp.zero_z3403309356797280102nteger)) (=> (not _let_3) (and (=> _let_2 (= _let_1 tptp.one_one_Code_integer)) (=> (not _let_2) (= _let_1 (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))))))))) (forall ((X tptp.rat)) (let ((_let_1 (tptp.aa_rat_rat tptp.sgn_sgn_rat X))) (let ((_let_2 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) X)))) (let ((_let_3 (= X 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.real)) (= (= (tptp.aa_real_real tptp.sgn_sgn_real A) (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) tptp.zero_zero_real)))) (forall ((A tptp.int)) (= (= (tptp.sgn_sgn_int A) (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 A) tptp.zero_zero_int)))) (forall ((A tptp.code_integer)) (= (= (tptp.aa_Cod1783974652533396728nteger tptp.sgn_sgn_Code_integer A) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger A) tptp.zero_z3403309356797280102nteger)))) (forall ((A tptp.rat)) (= (= (tptp.aa_rat_rat tptp.sgn_sgn_rat A) (tptp.aa_rat_rat tptp.uminus_uminus_rat tptp.one_one_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) tptp.zero_zero_rat)))) (forall ((I tptp.int)) (let ((_let_1 (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 ((X tptp.real)) (let ((_let_1 (tptp.aa_real_real tptp.real_V7735802525324610683m_real (tptp.aa_real_real tptp.sgn_sgn_real X)))) (let ((_let_2 (= X tptp.zero_zero_real))) (and (=> _let_2 (= _let_1 tptp.zero_zero_real)) (=> (not _let_2) (= _let_1 tptp.one_one_real)))))) (forall ((X tptp.complex)) (let ((_let_1 (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.sgn_sgn_complex X)))) (let ((_let_2 (= X tptp.zero_zero_complex))) (and (=> _let_2 (= _let_1 tptp.zero_zero_real)) (=> (not _let_2) (= _let_1 tptp.one_one_real)))))) (forall ((L tptp.int) (K tptp.int)) (=> (not (= L tptp.zero_zero_int)) (=> (not (= (tptp.sgn_sgn_int K) (tptp.sgn_sgn_int L))) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int K) 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_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int (tptp.aa_int_int tptp.abs_abs_int K)) (tptp.aa_int_int tptp.abs_abs_int L)))) (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)))))))) (forall ((N tptp.nat)) (= (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat tptp.bit_se2002935070580805687sk_nat N)) (tptp.aa_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.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_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.bit_se2119862282449309892nteger N))) (= N tptp.zero_zero_nat))) (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))) (tptp.aa_nat_nat tptp.bit_se2002935070580805687sk_nat N))) (= N tptp.zero_zero_nat))) (forall ((N tptp.nat)) (= (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 tptp.bit_se2000444600071755411sk_int N))) (= N tptp.zero_zero_nat))) (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.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.aa_int_fun_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 ((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.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_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 ((X tptp.real) (Y4 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 Y4)) 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 Y4)) (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) Y4)) (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) Y4)))))))) (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.sgn_sgn_int L))) (let ((_let_3 (tptp.sgn_sgn_int K))) (let ((_let_4 (tptp.aa_int_int (tptp.aa_int_fun_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.aa_bool_nat 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 ((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.aa_int_fun_int_int tptp.divide_divide_int K) L))) (let ((_let_3 (= (tptp.sgn_sgn_int K) (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.aa_bool_nat 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 ((N tptp.nat) (A tptp.code_integer)) (let ((_let_1 (tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.bit_se1745604003318907178nteger N A))) (let ((_let_3 (= N tptp.zero_zero_nat))) (and (=> _let_3 (= _let_2 tptp.zero_z3403309356797280102nteger)) (=> (not _let_3) (= _let_2 (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.bit_se1745604003318907178nteger (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) tptp.one_one_nat) (tptp.divide6298287555418463151nteger A _let_1))) _let_1) (tptp.modulo364778990260209775nteger 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.bit_se2923211474154528505it_int N) A))) (let ((_let_3 (= N tptp.zero_zero_nat))) (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.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.bit_se2923211474154528505it_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.aa_int_fun_int_int tptp.divide_divide_int A) _let_1))) _let_1)) (tptp.modulo_modulo_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)))) (let ((_let_2 (tptp.aa_nat_nat (tptp.bit_se2925701944663578781it_nat N) A))) (let ((_let_3 (= 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.bit_se2925701944663578781it_nat (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.divide_divide_nat A) _let_1))) _let_1)) (tptp.aa_nat_nat (tptp.modulo_modulo_nat A) _let_1))))))))) (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 ((K tptp.num) (L tptp.num)) (= (tptp.aa_nat_complex (tptp.power_power_complex (tptp.numera6690914467698888265omplex K)) (tptp.aa_num_nat tptp.numeral_numeral_nat L)) (tptp.numera6690914467698888265omplex (tptp.aa_num_num (tptp.pow K) L)))) (forall ((K tptp.num) (L tptp.num)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_num_real tptp.numeral_numeral_real K)) (tptp.aa_num_nat tptp.numeral_numeral_nat L)) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num (tptp.pow K) L)))) (forall ((K tptp.num) (L tptp.num)) (= (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_num_rat tptp.numeral_numeral_rat K)) (tptp.aa_num_nat tptp.numeral_numeral_nat L)) (tptp.aa_num_rat tptp.numeral_numeral_rat (tptp.aa_num_num (tptp.pow K) L)))) (forall ((K tptp.num) (L tptp.num)) (= (tptp.aa_nat_nat (tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat K)) (tptp.aa_num_nat tptp.numeral_numeral_nat L)) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num (tptp.pow K) L)))) (forall ((K tptp.num) (L tptp.num)) (= (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int K)) (tptp.aa_num_nat tptp.numeral_numeral_nat L)) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num (tptp.pow K) L)))) (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.aa_int_fun_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.modulo_modulo_int K _let_1)) (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.aa_int_fun_int_int tptp.bit_se725231765392027082nd_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int K) _let_1)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int L) _let_1)))))))))))))))))) (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 ((A tptp.int) (B tptp.int)) (let ((_let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se725231765392027082nd_int A) B))) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se725231765392027082nd_int _let_1) B) _let_1))) (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.bit_se727722235901077358nd_nat A) B))) (= (tptp.aa_nat_nat (tptp.bit_se727722235901077358nd_nat _let_1) B) _let_1))) (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.bit_se725231765392027082nd_int A))) (let ((_let_2 (tptp.aa_int_int _let_1 B))) (= (tptp.aa_int_int _let_1 _let_2) _let_2)))) (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (tptp.bit_se727722235901077358nd_nat A))) (let ((_let_2 (tptp.aa_nat_nat _let_1 B))) (= (tptp.aa_nat_nat _let_1 _let_2) _let_2)))) (forall ((A tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se725231765392027082nd_int A) A) A)) (forall ((A tptp.nat)) (= (tptp.aa_nat_nat (tptp.bit_se727722235901077358nd_nat A) A) A)) (forall ((X tptp.real) (Y4 tptp.real)) (= (= (tptp.aa_real_real tptp.sqrt X) (tptp.aa_real_real tptp.sqrt Y4)) (= X Y4))) (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 ((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 ((N tptp.nat)) (= (tptp.aa_int_int (tptp.bit_se2923211474154528505it_int N) tptp.zero_zero_int) tptp.zero_zero_int)) (forall ((N tptp.nat)) (= (tptp.aa_nat_nat (tptp.bit_se2925701944663578781it_nat N) tptp.zero_zero_nat) tptp.zero_zero_nat)) (forall ((X tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se725231765392027082nd_int X) tptp.zero_zero_int) tptp.zero_zero_int)) (forall ((X tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se725231765392027082nd_int tptp.zero_zero_int) X) tptp.zero_zero_int)) (forall ((A tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se725231765392027082nd_int tptp.zero_zero_int) A) tptp.zero_zero_int)) (forall ((A tptp.nat)) (= (tptp.aa_nat_nat (tptp.bit_se727722235901077358nd_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.bit_se725231765392027082nd_int A) tptp.zero_zero_int) tptp.zero_zero_int)) (forall ((A tptp.nat)) (= (tptp.aa_nat_nat (tptp.bit_se727722235901077358nd_nat A) tptp.zero_zero_nat) tptp.zero_zero_nat)) (forall ((X tptp.real)) (= (= (tptp.aa_real_real tptp.sqrt X) tptp.zero_zero_real) (= X tptp.zero_zero_real))) (= (tptp.aa_real_real tptp.sqrt tptp.zero_zero_real) tptp.zero_zero_real) (forall ((X tptp.real) (Y4 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 Y4))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Y4)))) (forall ((X tptp.real) (Y4 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 Y4))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) Y4)))) (forall ((X tptp.real)) (= (= (tptp.aa_real_real tptp.sqrt X) tptp.one_one_real) (= X tptp.one_one_real))) (= (tptp.aa_real_real tptp.sqrt tptp.one_one_real) tptp.one_one_real) (forall ((N tptp.nat)) (= (tptp.aa_int_nat tptp.nat2 (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N)) N)) (forall ((N tptp.nat) (A tptp.int) (B 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.bit_se725231765392027082nd_int A) B)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se725231765392027082nd_int (tptp.aa_int_int _let_1 A)) (tptp.aa_int_int _let_1 B))))) (forall ((N tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (tptp.bit_se2925701944663578781it_nat N))) (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.bit_se727722235901077358nd_nat A) B)) (tptp.aa_nat_nat (tptp.bit_se727722235901077358nd_nat (tptp.aa_nat_nat _let_1 A)) (tptp.aa_nat_nat _let_1 B))))) (forall ((X tptp.real) (Y4 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 Y4))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) Y4)))) (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))) (= (tptp.exp_complex tptp.zero_zero_complex) tptp.one_one_complex) (= (tptp.aa_real_real tptp.exp_real tptp.zero_zero_real) tptp.one_one_real) (forall ((A tptp.int)) (= (tptp.aa_int_int (tptp.bit_se2923211474154528505it_int tptp.zero_zero_nat) A) tptp.zero_zero_int)) (forall ((A tptp.nat)) (= (tptp.aa_nat_nat (tptp.bit_se2925701944663578781it_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)) (forall ((N tptp.nat)) (= (tptp.aa_int_int (tptp.bit_se2923211474154528505it_int (tptp.aa_nat_nat tptp.suc N)) tptp.one_one_int) tptp.one_one_int)) (forall ((N tptp.nat)) (= (tptp.aa_nat_nat (tptp.bit_se2925701944663578781it_nat (tptp.aa_nat_nat tptp.suc N)) tptp.one_one_nat) tptp.one_one_nat)) (forall ((X tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.bit_se3949692690581998587nteger X) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) X)) (forall ((X tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se725231765392027082nd_int X) (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int)) X)) (forall ((A tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.bit_se3949692690581998587nteger A) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) A)) (forall ((A tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se725231765392027082nd_int A) (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int)) A)) (forall ((A tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.bit_se3949692690581998587nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) A) A)) (forall ((A tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se725231765392027082nd_int (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int)) A) A)) (forall ((L tptp.num)) (= (tptp.aa_int_int (tptp.bit_se2923211474154528505it_int (tptp.aa_num_nat tptp.numeral_numeral_nat L)) tptp.one_one_int) tptp.one_one_int)) (forall ((L tptp.num)) (= (tptp.aa_nat_nat (tptp.bit_se2925701944663578781it_nat (tptp.aa_num_nat tptp.numeral_numeral_nat L)) tptp.one_one_nat) tptp.one_one_nat)) (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 ((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 ((Y4 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 Y4))) (tptp.pp (tptp.aa_real_bool _let_1 Y4))))) (forall ((Y4 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 Y4))) (tptp.pp (tptp.aa_real_bool _let_1 Y4))))) (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 ((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 ((Y4 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 Y4))) (tptp.pp (tptp.aa_real_bool _let_1 Y4))))) (forall ((Y4 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 Y4))) (tptp.pp (tptp.aa_real_bool _let_1 Y4))))) (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 ((X tptp.real)) (= (= (tptp.aa_real_real tptp.exp_real X) tptp.one_one_real) (= X tptp.zero_zero_real))) (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.aa_int_fun_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.aa_int_fun_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 ((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))) (forall ((P tptp.bool)) (= (tptp.aa_int_nat tptp.nat2 (tptp.aa_bool_int tptp.zero_n2684676970156552555ol_int P)) (tptp.aa_bool_nat tptp.zero_n2687167440665602831ol_nat P))) (forall ((N tptp.nat)) (= (= (tptp.aa_int_int (tptp.bit_se2923211474154528505it_int N) tptp.one_one_int) tptp.zero_zero_int) (= N tptp.zero_zero_nat))) (forall ((N tptp.nat)) (= (= (tptp.aa_nat_nat (tptp.bit_se2925701944663578781it_nat N) tptp.one_one_nat) tptp.zero_zero_nat) (= N tptp.zero_zero_nat))) (forall ((Y4 tptp.num)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se725231765392027082nd_int tptp.one_one_int) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit1 Y4))) tptp.one_one_int)) (forall ((Y4 tptp.num)) (= (tptp.aa_nat_nat (tptp.bit_se727722235901077358nd_nat tptp.one_one_nat) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 Y4))) tptp.one_one_nat)) (forall ((X tptp.num)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se725231765392027082nd_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit1 X))) tptp.one_one_int) tptp.one_one_int)) (forall ((X tptp.num)) (= (tptp.aa_nat_nat (tptp.bit_se727722235901077358nd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 X))) tptp.one_one_nat) tptp.one_one_nat)) (= (tptp.aa_real_real tptp.sqrt _let_55) _let_40) (= _let_99 _let_58) (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 ((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.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)) (= (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 ((N tptp.nat)) (= (tptp.aa_int_nat tptp.nat2 (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N))) 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 ((N tptp.nat)) (= (tptp.bit_se1745604003318907178nteger N (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (tptp.bit_se2119862282449309892nteger N))) (forall ((N tptp.nat)) (= (tptp.aa_int_int (tptp.bit_se2923211474154528505it_int N) (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int)) (tptp.aa_nat_int tptp.bit_se2000444600071755411sk_int 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.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 ((N tptp.nat)) (= (tptp.aa_nat_nat (tptp.bit_se2925701944663578781it_nat N) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)) (tptp.aa_bool_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 ((Y4 tptp.num)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se725231765392027082nd_int tptp.one_one_int) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 Y4))) tptp.zero_zero_int)) (forall ((Y4 tptp.num)) (= (tptp.aa_nat_nat (tptp.bit_se727722235901077358nd_nat tptp.one_one_nat) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 Y4))) tptp.zero_zero_nat)) (forall ((X tptp.num)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se725231765392027082nd_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 X))) tptp.one_one_int) tptp.zero_zero_int)) (forall ((X tptp.num)) (= (tptp.aa_nat_nat (tptp.bit_se727722235901077358nd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 X))) tptp.one_one_nat) tptp.zero_zero_nat)) (forall ((X tptp.num) (Y4 tptp.num)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se725231765392027082nd_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 X))) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 Y4))) (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.aa_int_fun_int_int tptp.bit_se725231765392027082nd_int (tptp.aa_num_int tptp.numeral_numeral_int X)) (tptp.aa_num_int tptp.numeral_numeral_int Y4))))) (forall ((X tptp.num) (Y4 tptp.num)) (= (tptp.aa_nat_nat (tptp.bit_se727722235901077358nd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 X))) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 Y4))) (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.bit_se727722235901077358nd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat X)) (tptp.aa_num_nat tptp.numeral_numeral_nat Y4))))) (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 ((N tptp.nat)) (= (tptp.bit_se1745604003318907178nteger N tptp.one_one_Code_integer) (tptp.aa_bool_Code_integer 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)) (= (tptp.aa_int_int (tptp.bit_se2923211474154528505it_int N) tptp.one_one_int) (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.aa_nat_nat (tptp.bit_se2925701944663578781it_nat N) tptp.one_one_nat) (tptp.aa_bool_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 ((V tptp.num) (V2 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 V2)) (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 V2))))) (forall ((N tptp.num)) (= (tptp.aa_int_int (tptp.aa_int_fun_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.aa_int_fun_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 ((Y4 tptp.int) (X tptp.num) (N tptp.nat)) (= (= (tptp.aa_int_nat tptp.nat2 Y4) (tptp.aa_nat_nat (tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat X)) N)) (= Y4 (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) (Y4 tptp.int)) (= (= (tptp.aa_nat_nat (tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat X)) N) (tptp.aa_int_nat tptp.nat2 Y4)) (= (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int X)) N) Y4))) (forall ((N tptp.nat) (K tptp.int)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_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.dvd_dvd_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.dvd_dvd_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.dvd_dvd_int K) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N))))) (forall ((X tptp.num) (Y4 tptp.num)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se725231765392027082nd_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 X))) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit1 Y4))) (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.aa_int_fun_int_int tptp.bit_se725231765392027082nd_int (tptp.aa_num_int tptp.numeral_numeral_int X)) (tptp.aa_num_int tptp.numeral_numeral_int Y4))))) (forall ((X tptp.num) (Y4 tptp.num)) (= (tptp.aa_nat_nat (tptp.bit_se727722235901077358nd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 X))) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 Y4))) (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.bit_se727722235901077358nd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat X)) (tptp.aa_num_nat tptp.numeral_numeral_nat Y4))))) (forall ((X tptp.num) (Y4 tptp.num)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se725231765392027082nd_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit1 X))) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 Y4))) (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.aa_int_fun_int_int tptp.bit_se725231765392027082nd_int (tptp.aa_num_int tptp.numeral_numeral_int X)) (tptp.aa_num_int tptp.numeral_numeral_int Y4))))) (forall ((X tptp.num) (Y4 tptp.num)) (= (tptp.aa_nat_nat (tptp.bit_se727722235901077358nd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 X))) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 Y4))) (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.bit_se727722235901077358nd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat X)) (tptp.aa_num_nat tptp.numeral_numeral_nat Y4))))) (forall ((N tptp.nat) (A tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.bit_se1745604003318907178nteger N A))) (or (= N tptp.zero_zero_nat) (tptp.pp (tptp.aa_Code_integer_bool _let_1 A)))))) (forall ((N 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_se2923211474154528505it_int N) A))) (or (= N tptp.zero_zero_nat) (tptp.pp (tptp.aa_int_bool _let_1 A)))))) (forall ((N 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.bit_se2925701944663578781it_nat N) A))) (or (= N tptp.zero_zero_nat) (tptp.pp (tptp.aa_nat_bool _let_1 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 ((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 ((N tptp.num)) (= (tptp.aa_int_int (tptp.aa_int_fun_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.aa_int_fun_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 ((A tptp.code_integer)) (= (tptp.bit_se1745604003318907178nteger (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat) A) (tptp.modulo364778990260209775nteger A (tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))))) (forall ((A tptp.int)) (= (tptp.aa_int_int (tptp.bit_se2923211474154528505it_int (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)) A) (tptp.modulo_modulo_int A (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))))) (forall ((A tptp.nat)) (= (tptp.aa_nat_nat (tptp.bit_se2925701944663578781it_nat (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)) A) (tptp.aa_nat_nat (tptp.modulo_modulo_nat A) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (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)) (=> (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) (Y4 tptp.real) (Xa 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 Y4) _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 Xa) _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 ((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 ((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.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_nat (tptp.aa_int_nat tptp.nat2 A)) (tptp.aa_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 ((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.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.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 ((X tptp.num) (Y4 tptp.num)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se725231765392027082nd_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit1 X))) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit1 Y4))) (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.aa_int_fun_int_int tptp.bit_se725231765392027082nd_int (tptp.aa_num_int tptp.numeral_numeral_int X)) (tptp.aa_num_int tptp.numeral_numeral_int Y4)))))) (forall ((X tptp.num) (Y4 tptp.num)) (= (tptp.aa_nat_nat (tptp.bit_se727722235901077358nd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 X))) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 Y4))) (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 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_nat_nat (tptp.bit_se727722235901077358nd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat X)) (tptp.aa_num_nat tptp.numeral_numeral_nat Y4)))))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.power_8256067586552552935nteger (tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one)) N))) (= (tptp.bit_se1745604003318907178nteger M _let_1) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_bool_Code_integer tptp.zero_n356916108424825756nteger (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N) M))) _let_1)))) (forall ((M tptp.nat) (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.aa_int_int (tptp.bit_se2923211474154528505it_int M) _let_1) (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 N) M))) _let_1)))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_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.bit_se2925701944663578781it_nat M) _let_1) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_bool_nat tptp.zero_n2687167440665602831ol_nat (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N) M))) _let_1)))) (forall ((N tptp.nat)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (let ((_let_2 (tptp.numera6620942414471956472nteger _let_1))) (= (tptp.bit_se1745604003318907178nteger N _let_2) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_bool_Code_integer tptp.zero_n356916108424825756nteger (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1)) N))) _let_2))))) (forall ((N tptp.nat)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (let ((_let_2 (tptp.aa_num_int tptp.numeral_numeral_int _let_1))) (= (tptp.aa_int_int (tptp.bit_se2923211474154528505it_int N) _let_2) (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_eq_nat (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1)) N))) _let_2))))) (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.bit_se2925701944663578781it_nat N) _let_1) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_bool_nat tptp.zero_n2687167440665602831ol_nat (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat _let_1) N))) _let_1)))) (forall ((N tptp.nat) (A tptp.int)) (= (tptp.aa_int_int (tptp.bit_se2923211474154528505it_int N) A) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se725231765392027082nd_int A) (tptp.aa_nat_int tptp.bit_se2000444600071755411sk_int N)))) (forall ((N tptp.nat) (A tptp.nat)) (= (tptp.aa_nat_nat (tptp.bit_se2925701944663578781it_nat N) A) (tptp.aa_nat_nat (tptp.bit_se727722235901077358nd_nat A) (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))) (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.bit_se725231765392027082nd_int B))) (let ((_let_2 (tptp.aa_int_fun_int_int tptp.bit_se725231765392027082nd_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 ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (tptp.bit_se727722235901077358nd_nat B))) (let ((_let_2 (tptp.bit_se727722235901077358nd_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 ((A tptp.int) (B tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se725231765392027082nd_int A) B) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se725231765392027082nd_int B) A))) (forall ((A tptp.nat) (B tptp.nat)) (= (tptp.aa_nat_nat (tptp.bit_se727722235901077358nd_nat A) B) (tptp.aa_nat_nat (tptp.bit_se727722235901077358nd_nat B) A))) (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.bit_se725231765392027082nd_int A))) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se725231765392027082nd_int (tptp.aa_int_int _let_1 B)) C) (tptp.aa_int_int _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se725231765392027082nd_int B) C))))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (tptp.bit_se727722235901077358nd_nat A))) (= (tptp.aa_nat_nat (tptp.bit_se727722235901077358nd_nat (tptp.aa_nat_nat _let_1 B)) C) (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.bit_se727722235901077358nd_nat B) C))))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_nat (tptp.bit_se727722235901077358nd_nat M) N)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se725231765392027082nd_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.bit_se727722235901077358nd_nat M) N)) (tptp.aa_nat_nat (tptp.bit_se727722235901077358nd_nat (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat M)) (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat N)))) (forall ((N tptp.nat) (M tptp.nat)) (= (tptp.aa_int_int (tptp.bit_se2923211474154528505it_int N) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int M)) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_nat (tptp.bit_se2925701944663578781it_nat N) M)))) (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.bit_se2925701944663578781it_nat N))) (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat M)) (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat (tptp.aa_nat_nat _let_1 M))))) (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.bit_se2925701944663578781it_nat N) (tptp.aa_int_nat tptp.nat2 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_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 ((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.exp_complex X))) (tptp.aa_real_real tptp.exp_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex X))))) (forall ((N tptp.nat) (A tptp.int) (B 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.plus_plus_int (tptp.aa_int_int _let_1 A)) (tptp.aa_int_int _let_1 B))) (tptp.aa_int_int _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) B))))) (forall ((N tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (tptp.bit_se2925701944663578781it_nat N))) (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat _let_1 A)) (tptp.aa_nat_nat _let_1 B))) (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) B))))) (forall ((N tptp.nat) (A tptp.int) (B tptp.int) (M tptp.nat)) (let ((_let_1 (tptp.bit_se2923211474154528505it_int M))) (let ((_let_2 (tptp.bit_se2923211474154528505it_int N))) (=> (= (tptp.aa_int_int _let_2 A) (tptp.aa_int_int _let_2 B)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)) (= (tptp.aa_int_int _let_1 A) (tptp.aa_int_int _let_1 B))))))) (forall ((N tptp.nat) (A tptp.nat) (B tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.bit_se2925701944663578781it_nat M))) (let ((_let_2 (tptp.bit_se2925701944663578781it_nat N))) (=> (= (tptp.aa_nat_nat _let_2 A) (tptp.aa_nat_nat _let_2 B)) (=> (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 A) (tptp.aa_nat_nat _let_1 B))))))) (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.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.bit_se2925701944663578781it_nat M) Q2)) (tptp.aa_nat_nat (tptp.bit_se2925701944663578781it_nat N) Q2))))) (forall ((X tptp.real) (Y4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Y4)) (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 Y4))))) (forall ((X tptp.real) (Y4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) Y4)) (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 Y4))))) (forall ((X tptp.real) (Y4 tptp.real)) (= (tptp.aa_real_real tptp.sqrt (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real X) Y4)) (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 Y4)))) (forall ((X tptp.real) (Y4 tptp.real)) (= (tptp.aa_real_real tptp.sqrt (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real X) Y4)) (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 Y4)))) (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)) (= (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.complex)) (not (= (tptp.exp_complex X) tptp.zero_zero_complex))) (forall ((X tptp.real)) (not (= (tptp.aa_real_real tptp.exp_real X) tptp.zero_zero_real))) (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 ((A2 tptp.complex)) (let ((_let_1 (tptp.exp_complex A2))) (= (tptp.aa_complex_complex (tptp.times_times_complex _let_1) A2) (tptp.aa_complex_complex (tptp.times_times_complex A2) _let_1)))) (forall ((A2 tptp.real)) (let ((_let_1 (tptp.aa_real_real tptp.exp_real A2))) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real _let_1) A2) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A2) _let_1)))) (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) (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) (B tptp.int)) (= (tptp.bit_concat_bit N (tptp.aa_int_int (tptp.bit_se2923211474154528505it_int N) B)) (tptp.bit_concat_bit N B))) (forall ((N tptp.nat) (K tptp.int) (L tptp.int) (R2 tptp.int) (S2 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 R2) S2)) (and (= (tptp.aa_int_int _let_1 K) (tptp.aa_int_int _let_1 R2)) (= L S2))))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (= (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.bit_se3949692690581998587nteger A) B) _let_1) (and (= A _let_1) (= B _let_1))))) (forall ((A tptp.int) (B 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.bit_se725231765392027082nd_int A) B) _let_1) (and (= A _let_1) (= B _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 _let_1 (tptp.aa_real_real tptp.sqrt X)))))) (forall ((Y4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) Y4)) (exists ((X3 tptp.real)) (= (tptp.aa_real_real tptp.exp_real X3) Y4)))) (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)) (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 ((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)) (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.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)))))) (= tptp.zero_zero_nat (tptp.aa_int_nat tptp.nat2 tptp.zero_zero_int)) (forall ((Y4 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) Y4)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Y4) 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.bit_se725231765392027082nd_int X) Y4)) Z))))) (forall ((Y4 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) Y4)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Y4) 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.bit_se725231765392027082nd_int Y4) Ya)) Z))))) (forall ((Y4 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) Y4)) (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.bit_se725231765392027082nd_int X) Y4)) Y4)))) (forall ((X tptp.int) (Y4 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.aa_int_fun_int_int tptp.bit_se725231765392027082nd_int X) Y4)) X)))) (forall ((X tptp.int) (Y4 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.aa_int_fun_int_int tptp.bit_se725231765392027082nd_int X) Y4)))))) (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 ((X4 tptp.num)) (= (tptp.aa_num_nat tptp.numeral_numeral_nat X4) (tptp.aa_int_nat tptp.nat2 (tptp.aa_num_int tptp.numeral_numeral_int X4)))) (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)) (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 ((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 ((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 ((N tptp.nat) (A tptp.int) (B tptp.int)) (let ((_let_1 (tptp.bit_se2923211474154528505it_int (tptp.aa_nat_nat tptp.suc N)))) (let ((_let_2 (tptp.bit_ri631733984087533419it_int N))) (= (= (tptp.aa_int_int _let_2 A) (tptp.aa_int_int _let_2 B)) (= (tptp.aa_int_int _let_1 A) (tptp.aa_int_int _let_1 B)))))) (forall ((X tptp.real)) (= (tptp.aa_real_real tptp.sgn_sgn_real X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real X) (tptp.aa_real_real tptp.abs_abs_real X)))) (forall ((X tptp.int) (Y4 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X) Y4)) (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 Y4))))) (forall ((M tptp.nat) (N tptp.nat) (A tptp.int)) (let ((_let_1 (tptp.bit_ri631733984087533419it_int M))) (let ((_let_2 (tptp.bit_se2923211474154528505it_int N))) (= (tptp.aa_int_int _let_1 (tptp.aa_int_int _let_2 A)) (tptp.aa_int_int (tptp.if_fun_int_int (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N) M) _let_2 _let_1) A))))) (forall ((Z tptp.int) (Z4 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 Z4)) (= (= (tptp.aa_int_nat tptp.nat2 Z) (tptp.aa_int_nat tptp.nat2 Z4)) (= Z Z4)))))) (forall ((P tptp.fun_nat_bool)) (= (forall ((X_12 tptp.nat)) (tptp.pp (tptp.aa_nat_bool P X_12))) (forall ((X5 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) X5)) (tptp.pp (tptp.aa_nat_bool P (tptp.aa_int_nat tptp.nat2 X5))))))) (forall ((P tptp.fun_nat_bool)) (= (exists ((X_12 tptp.nat)) (tptp.pp (tptp.aa_nat_bool P X_12))) (exists ((X5 tptp.int)) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) X5)) (tptp.pp (tptp.aa_nat_bool P (tptp.aa_int_nat tptp.nat2 X5))))))) (forall ((X tptp.complex) (Y4 tptp.complex)) (= (tptp.aa_complex_complex (tptp.times_times_complex (tptp.exp_complex X)) (tptp.exp_complex Y4)) (tptp.exp_complex (tptp.plus_plus_complex X Y4)))) (forall ((X tptp.real) (Y4 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 Y4)) (tptp.aa_real_real tptp.exp_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) Y4)))) (forall ((X tptp.complex) (Y4 tptp.complex)) (=> (= (tptp.aa_complex_complex (tptp.times_times_complex X) Y4) (tptp.aa_complex_complex (tptp.times_times_complex Y4) X)) (= (tptp.exp_complex (tptp.plus_plus_complex X Y4)) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.exp_complex X)) (tptp.exp_complex Y4))))) (forall ((X tptp.real) (Y4 tptp.real)) (=> (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real X) Y4) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real Y4) X)) (= (tptp.aa_real_real tptp.exp_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) Y4)) (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 Y4))))) (forall ((X tptp.complex) (Y4 tptp.complex)) (= (tptp.exp_complex (tptp.minus_minus_complex X Y4)) (tptp.divide1717551699836669952omplex (tptp.exp_complex X) (tptp.exp_complex Y4)))) (forall ((X tptp.real) (Y4 tptp.real)) (= (tptp.aa_real_real tptp.exp_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real X) Y4)) (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 Y4)))) (= tptp.one_one_nat _let_99) (forall ((N tptp.nat) (M tptp.nat) (A tptp.int)) (let ((_let_1 (tptp.bit_se2923211474154528505it_int N))) (let ((_let_2 (tptp.aa_int_int _let_1 A))) (let ((_let_3 (tptp.aa_nat_fun_int_int tptp.bit_se4203085406695923979it_int M))) (let ((_let_4 (tptp.aa_int_int _let_1 (tptp.aa_int_int _let_3 A)))) (let ((_let_5 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N) M)))) (and (=> _let_5 (= _let_4 _let_2)) (=> (not _let_5) (= _let_4 (tptp.aa_int_int _let_3 _let_2)))))))))) (forall ((N tptp.nat) (M tptp.nat) (A tptp.nat)) (let ((_let_1 (tptp.bit_se2925701944663578781it_nat N))) (let ((_let_2 (tptp.aa_nat_nat _let_1 A))) (let ((_let_3 (tptp.aa_nat_fun_nat_nat tptp.bit_se4205575877204974255it_nat M))) (let ((_let_4 (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat _let_3 A)))) (let ((_let_5 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N) M)))) (and (=> _let_5 (= _let_4 _let_2)) (=> (not _let_5) (= _let_4 (tptp.aa_nat_nat _let_3 _let_2)))))))))) (forall ((N tptp.nat) (M tptp.nat) (A tptp.code_integer)) (let ((_let_1 (tptp.bit_se1745604003318907178nteger N A))) (let ((_let_2 (tptp.aa_nat6383147911832638789nteger tptp.bit_se8260200283734997820nteger M))) (let ((_let_3 (tptp.bit_se1745604003318907178nteger N (tptp.aa_Cod1783974652533396728nteger _let_2 A)))) (let ((_let_4 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N) M)))) (and (=> _let_4 (= _let_3 _let_1)) (=> (not _let_4) (= _let_3 (tptp.aa_Cod1783974652533396728nteger _let_2 _let_1))))))))) (forall ((N tptp.nat) (M tptp.nat) (A tptp.code_integer)) (let ((_let_1 (tptp.bit_se1745604003318907178nteger N A))) (let ((_let_2 (tptp.aa_nat6383147911832638789nteger tptp.bit_se2793503036327961859nteger M))) (let ((_let_3 (tptp.bit_se1745604003318907178nteger N (tptp.aa_Cod1783974652533396728nteger _let_2 A)))) (let ((_let_4 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N) M)))) (and (=> _let_4 (= _let_3 _let_1)) (=> (not _let_4) (= _let_3 (tptp.aa_Cod1783974652533396728nteger _let_2 _let_1))))))))) (forall ((N tptp.nat) (M tptp.nat) (A tptp.int)) (let ((_let_1 (tptp.bit_se2923211474154528505it_int N))) (let ((_let_2 (tptp.aa_int_int _let_1 A))) (let ((_let_3 (tptp.aa_nat_fun_int_int tptp.bit_se7879613467334960850it_int M))) (let ((_let_4 (tptp.aa_int_int _let_1 (tptp.aa_int_int _let_3 A)))) (let ((_let_5 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N) M)))) (and (=> _let_5 (= _let_4 _let_2)) (=> (not _let_5) (= _let_4 (tptp.aa_int_int _let_3 _let_2)))))))))) (forall ((N tptp.nat) (M tptp.nat) (A tptp.nat)) (let ((_let_1 (tptp.bit_se2925701944663578781it_nat N))) (let ((_let_2 (tptp.aa_nat_nat _let_1 A))) (let ((_let_3 (tptp.aa_nat_fun_nat_nat tptp.bit_se7882103937844011126it_nat M))) (let ((_let_4 (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat _let_3 A)))) (let ((_let_5 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N) M)))) (and (=> _let_5 (= _let_4 _let_2)) (=> (not _let_5) (= _let_4 (tptp.aa_nat_nat _let_3 _let_2)))))))))) (forall ((N tptp.nat) (M tptp.nat) (A tptp.code_integer)) (let ((_let_1 (tptp.bit_se1745604003318907178nteger N A))) (let ((_let_2 (tptp.bit_se1745604003318907178nteger N (tptp.bit_se1345352211410354436nteger M A)))) (let ((_let_3 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N) M)))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (tptp.bit_se1345352211410354436nteger M _let_1)))))))) (forall ((N tptp.nat) (M tptp.nat) (A tptp.int)) (let ((_let_1 (tptp.bit_se2923211474154528505it_int N))) (let ((_let_2 (tptp.aa_int_int _let_1 A))) (let ((_let_3 (tptp.aa_nat_fun_int_int tptp.bit_se2159334234014336723it_int M))) (let ((_let_4 (tptp.aa_int_int _let_1 (tptp.aa_int_int _let_3 A)))) (let ((_let_5 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N) M)))) (and (=> _let_5 (= _let_4 _let_2)) (=> (not _let_5) (= _let_4 (tptp.aa_int_int _let_3 _let_2)))))))))) (forall ((N tptp.nat) (M tptp.nat) (A tptp.nat)) (let ((_let_1 (tptp.bit_se2925701944663578781it_nat N))) (let ((_let_2 (tptp.aa_nat_nat _let_1 A))) (let ((_let_3 (tptp.aa_nat_fun_nat_nat tptp.bit_se2161824704523386999it_nat M))) (let ((_let_4 (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat _let_3 A)))) (let ((_let_5 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N) M)))) (and (=> _let_5 (= _let_4 _let_2)) (=> (not _let_5) (= _let_4 (tptp.aa_nat_nat _let_3 _let_2)))))))))) (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.aa_nat_fun_int_int tptp.bit_se4203085406695923979it_int M) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N))))) (forall ((X tptp.num)) (= (tptp.aa_num_num (tptp.pow X) tptp.one) 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 tptp.one_one_real) (tptp.aa_real_real tptp.exp_real X))))) (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 ((X tptp.real) (Y4 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 Y4)) (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) Y4))) (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 Y4)))))))) (forall ((M tptp.nat) (N tptp.nat) (A tptp.int)) (let ((_let_1 (tptp.bit_se2923211474154528505it_int M))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) (tptp.aa_nat_nat tptp.suc N))) (= (tptp.aa_int_int _let_1 (tptp.aa_int_int (tptp.bit_ri631733984087533419it_int N) A)) (tptp.aa_int_int _let_1 A))))) (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) (Y4 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 Y4) Y4)))))) (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.aa_int_fun_int_int tptp.bit_se725231765392027082nd_int K) L)) K)))) (forall ((Y4 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) Y4)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Y4) 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.bit_se725231765392027082nd_int Y4) Ya)) Z))))) (forall ((Y4 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) Y4)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Y4) 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.bit_se725231765392027082nd_int X) Y4)) Z))))) (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 ((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 ((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.exp_complex X)) (tptp.exp_complex (tptp.uminus1482373934393186551omplex X))) tptp.one_one_complex)) (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 ((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) (B 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 B))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) B))) (forall ((X tptp.complex) (N tptp.nat)) (= (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.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.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.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 ((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 ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_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.bit_se3949692690581998587nteger A) B))) (or (tptp.pp (tptp.aa_Code_integer_bool _let_1 A)) (tptp.pp (tptp.aa_Code_integer_bool _let_1 B)))))) (forall ((A tptp.int) (B 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.bit_se725231765392027082nd_int A) B))) (or (tptp.pp (tptp.aa_int_bool _let_1 A)) (tptp.pp (tptp.aa_int_bool _let_1 B)))))) (forall ((A tptp.nat) (B 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.bit_se727722235901077358nd_nat A) B))) (or (tptp.pp (tptp.aa_nat_bool _let_1 A)) (tptp.pp (tptp.aa_nat_bool _let_1 B)))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real _let_74) _let_40)) (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 ((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 ((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.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 ((Y4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.one_one_real) Y4)) (exists ((X3 tptp.real)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) X3)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X3) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real Y4) tptp.one_one_real))) (= (tptp.aa_real_real tptp.exp_real X3) Y4))))) (forall ((X tptp.real) (Y4 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 Y4) (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 Y4)) X))))) (forall ((X tptp.real) (Y4 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) Y4)) (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 Y4)) Y4)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real tptp.ln_ln_real X)) X)))))) (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 ((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 ((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 ((P tptp.fun_nat_bool) (I tptp.int)) (= (tptp.pp (tptp.aa_nat_bool P (tptp.aa_int_nat tptp.nat2 I))) (and (forall ((N4 tptp.nat)) (=> (= I (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N4)) (tptp.pp (tptp.aa_nat_bool P N4)))) (=> (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) (Z4 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 Z4)) (= (tptp.aa_int_nat tptp.nat2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int Z) Z4)) (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 Z4))))))) (forall ((Z tptp.int) (Z4 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) Z4)) (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 Z4))))) (forall ((X4 tptp.nat)) (= (tptp.aa_nat_nat tptp.suc X4) (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 X4)) tptp.one_one_int)))) (forall ((Z4 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) Z4)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Z4) Z)) (= (tptp.aa_int_nat tptp.nat2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int Z) Z4)) (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 Z4)))))) (forall ((X tptp.int) (Y4 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 Y4)) (= (tptp.aa_int_nat tptp.nat2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int X) Y4)) (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 Y4))))))) (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 ((X tptp.int) (Y4 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.aa_int_fun_int_int tptp.divide_divide_int X) Y4)) (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 Y4))))) (forall ((Y4 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) Y4)) (= (tptp.aa_int_nat tptp.nat2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int X) Y4)) (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 Y4))))) (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.power_power_nat (tptp.aa_int_nat tptp.nat2 Z)) N)))) (forall ((X tptp.int) (Y4 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 Y4)) (= (tptp.aa_int_nat tptp.nat2 (tptp.modulo_modulo_int X Y4)) (tptp.aa_nat_nat (tptp.modulo_modulo_nat (tptp.aa_int_nat tptp.nat2 X)) (tptp.aa_int_nat tptp.nat2 Y4))))))) (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.aa_int_fun_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))))))) (= (tptp.aa_num_nat tptp.size_size_num tptp.one) tptp.zero_zero_nat) (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.modulo_modulo_int _let_2 _let_1) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_nat (tptp.modulo_modulo_nat (tptp.aa_int_nat tptp.nat2 _let_2)) (tptp.aa_int_nat tptp.nat2 _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_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_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.num)) (= (tptp.aa_nat_nat (tptp.bit_se2925701944663578781it_nat (tptp.aa_nat_nat tptp.suc N)) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 K))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.bit_se2925701944663578781it_nat N) (tptp.aa_num_nat tptp.numeral_numeral_nat K))) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (forall ((N tptp.nat) (A tptp.code_integer)) (= (tptp.bit_se1745604003318907178nteger N A) (tptp.modulo364778990260209775nteger A (tptp.power_8256067586552552935nteger (tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one)) N)))) (forall ((N tptp.nat) (A tptp.int)) (= (tptp.aa_int_int (tptp.bit_se2923211474154528505it_int N) A) (tptp.modulo_modulo_int A (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) (A tptp.nat)) (= (tptp.aa_nat_nat (tptp.bit_se2925701944663578781it_nat N) A) (tptp.aa_nat_nat (tptp.modulo_modulo_nat A) (tptp.aa_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.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.bit_se3949692690581998587nteger tptp.one_one_Code_integer) A) (tptp.modulo364778990260209775nteger A (tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))))) (forall ((A tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se725231765392027082nd_int tptp.one_one_int) A) (tptp.modulo_modulo_int A (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))))) (forall ((A tptp.nat)) (= (tptp.aa_nat_nat (tptp.bit_se727722235901077358nd_nat tptp.one_one_nat) A) (tptp.aa_nat_nat (tptp.modulo_modulo_nat A) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (forall ((A tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.bit_se3949692690581998587nteger A) tptp.one_one_Code_integer) (tptp.modulo364778990260209775nteger A (tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))))) (forall ((A tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se725231765392027082nd_int A) tptp.one_one_int) (tptp.modulo_modulo_int A (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))))) (forall ((A tptp.nat)) (= (tptp.aa_nat_nat (tptp.bit_se727722235901077358nd_nat A) tptp.one_one_nat) (tptp.aa_nat_nat (tptp.modulo_modulo_nat A) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (forall ((N tptp.nat) (M tptp.nat)) (= (= (tptp.aa_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.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.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.bit_se2925701944663578781it_nat N) M)) (tptp.aa_nat_nat (tptp.power_power_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)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) (tptp.aa_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.bit_se2925701944663578781it_nat N) M) M))) (forall ((X tptp.real) (Y4 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)))) Y4)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) (tptp.aa_real_real tptp.sqrt Y4))))) (forall ((X tptp.real) (Y4 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)))) Y4)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) (tptp.aa_real_real tptp.sqrt Y4))))) (forall ((X tptp.real) (Y4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.sqrt X)) Y4)) (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 Y4) (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.exp_real tptp.one_one_real)) _let_81)) (forall ((N tptp.nat) (M tptp.nat)) (= (tptp.aa_nat_nat (tptp.bit_se2925701944663578781it_nat N) M) (tptp.aa_nat_nat (tptp.modulo_modulo_nat M) (tptp.aa_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_int_nat tptp.nat2 _let_63) _let_98) (forall ((A tptp.real) (N tptp.nat) (X tptp.real) (B 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 B)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real tptp.abs_abs_real B)) N))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (= A B))))) (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 ((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 ((N tptp.nat) (K tptp.int)) (= (tptp.aa_int_int (tptp.bit_se2923211474154528505it_int N) K) (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 ((Z tptp.int) (Z4 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) Z4)) (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 Z4)))))) (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.exp_complex (tptp.divide1717551699836669952omplex X (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex N)))) N) (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 ((A tptp.nat) (B 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 B)))))) (let ((_let_2 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B)))) (and (=> _let_2 (= _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat B) A))) (=> (not _let_2) (= _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat A) B))))))) (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.exp_complex (tptp.uminus1482373934393186551omplex X)))) (let ((_let_2 (tptp.exp_complex X))) (= (tptp.tanh_complex X) (tptp.divide1717551699836669952omplex (tptp.minus_minus_complex _let_2 _let_1) (tptp.plus_plus_complex _let_2 _let_1)))))) (forall ((N tptp.nat) (A tptp.code_integer)) (= (= (tptp.bit_se1745604003318907178nteger N A) tptp.zero_z3403309356797280102nteger) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.power_8256067586552552935nteger (tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one)) N)) A)))) (forall ((N tptp.nat) (A tptp.int)) (= (= (tptp.aa_int_int (tptp.bit_se2923211474154528505it_int N) A) tptp.zero_zero_int) (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)) A)))) (forall ((N tptp.nat) (A tptp.nat)) (= (= (tptp.aa_nat_nat (tptp.bit_se2925701944663578781it_nat N) 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.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N)) A)))) (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_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_num_int tptp.numeral_numeral_int K))) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))))) (forall ((L tptp.num) (K tptp.num)) (= (tptp.aa_nat_nat (tptp.bit_se2925701944663578781it_nat (tptp.aa_num_nat tptp.numeral_numeral_nat L)) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 K))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.bit_se2925701944663578781it_nat (tptp.aa_num_nat tptp.pred_numeral L)) (tptp.aa_num_nat tptp.numeral_numeral_nat K))) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (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.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.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N)) M)))) (forall ((Y4 tptp.real) (X tptp.real)) (=> (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Y4) (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) Y4)) (= (tptp.aa_real_real tptp.sqrt X) Y4)))) (forall ((X tptp.real) (Y4 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 Y4)) (=> (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 Y4) (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)) Y4))))))) (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) (Y4 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 Y4) _let_1))) Y4) (= X tptp.zero_zero_real)))) (forall ((X tptp.real) (Y4 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 Y4) _let_1))) X) (= Y4 tptp.zero_zero_real)))) (forall ((A tptp.real) (C tptp.real) (B 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 B) 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 B) _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 ((Y4 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 Y4) (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 Y4) _let_1))))))) (forall ((X tptp.real) (Y4 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 Y4) _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_88)) _let_40)) (forall ((X tptp.real) (Y4 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 Y4))) (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)))) Y4)))) (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 ((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 ((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 ((Z tptp.complex)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (= (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.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 ((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 ((X tptp.real) (Y4 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 Y4)) (=> (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 Y4) (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)) Y4))))))) (forall ((X tptp.real) (Y4 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 Y4)) (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 Y4) _let_1)))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) Y4)))))))) (forall ((X tptp.real) (Y4 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 Y4) _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 Y4)))))) (forall ((Y4 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 Y4)) (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 Y4) _let_1))))))) (forall ((X tptp.real) (Y4 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 Y4) _let_1))))))) (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)) (=> (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)))))) (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 ((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 ((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.aa_int_fun_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.aa_int_fun_int_int tptp.bit_se725231765392027082nd_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int K) _let_1)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int L) _let_1)))))))) (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.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.exp_complex Z))) _let_1))))) (forall ((N tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N))) (= (tptp.bit_se1745604003318907178nteger _let_1 (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (tptp.minus_8373710615458151222nteger (tptp.power_8256067586552552935nteger (tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one)) _let_1) tptp.one_one_Code_integer)))) (forall ((N tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N))) (= (tptp.aa_int_int (tptp.bit_se2923211474154528505it_int _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.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.one_one_int)))) (forall ((N tptp.nat) (K tptp.num)) (= (tptp.aa_int_int (tptp.bit_se2923211474154528505it_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_se2923211474154528505it_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 ((N tptp.nat) (K tptp.num)) (= (tptp.aa_nat_nat (tptp.bit_se2925701944663578781it_nat (tptp.aa_nat_nat tptp.suc N)) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 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.bit_se2925701944663578781it_nat N) (tptp.aa_num_nat tptp.numeral_numeral_nat K))) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) tptp.one_one_nat))) (forall ((K tptp.num)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat K))) (= (tptp.bit_se1745604003318907178nteger _let_1 (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (tptp.minus_8373710615458151222nteger (tptp.power_8256067586552552935nteger (tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one)) _let_1) tptp.one_one_Code_integer)))) (forall ((K tptp.num)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat K))) (= (tptp.aa_int_int (tptp.bit_se2923211474154528505it_int _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.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.one_one_int)))) (forall ((N tptp.nat) (A tptp.code_integer)) (let ((_let_1 (tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.bit_se1745604003318907178nteger (tptp.aa_nat_nat tptp.suc N) A) (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.bit_se1745604003318907178nteger N (tptp.divide6298287555418463151nteger A _let_1))) _let_1) (tptp.modulo364778990260209775nteger 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_se2923211474154528505it_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.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.bit_se2923211474154528505it_int N) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A) _let_1))) _let_1)) (tptp.modulo_modulo_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.bit_se2925701944663578781it_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.times_times_nat (tptp.aa_nat_nat (tptp.bit_se2925701944663578781it_nat N) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) _let_1))) _let_1)) (tptp.aa_nat_nat (tptp.modulo_modulo_nat A) _let_1))))) (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)) (=> (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) (Y4 tptp.real) (Xa 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 Y4) _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 Xa) _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) (Y4 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 Y4)) (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) Y4))) (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) Y4)) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))))))))) (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 ((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 ((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 ((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 ((A tptp.code_integer) (N tptp.nat)) (let ((_let_1 (tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.bit_se1745604003318907178nteger N A))) (let ((_let_3 (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer _let_1) A)))) (=> (= (tptp.divide6298287555418463151nteger A _let_1) A) (and (=> _let_3 (= _let_2 tptp.zero_z3403309356797280102nteger)) (=> (not _let_3) (= _let_2 (tptp.minus_8373710615458151222nteger (tptp.power_8256067586552552935nteger _let_1 N) tptp.one_one_Code_integer))))))))) (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_int_int (tptp.bit_se2923211474154528505it_int N) A))) (let ((_let_3 (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.divide_divide_int A) _let_1) A) (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.minus_minus_int (tptp.aa_nat_int (tptp.power_power_int _let_1) N)) tptp.one_one_int))))))))) (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.bit_se2925701944663578781it_nat N) A))) (let ((_let_3 (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 A) _let_1) A) (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.minus_minus_nat (tptp.aa_nat_nat (tptp.power_power_nat _let_1) N)) tptp.one_one_nat))))))))) (forall ((X33 tptp.num)) (= (tptp.aa_num_nat tptp.size_size_num (tptp.aa_num_num tptp.bit1 X33)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_num_nat tptp.size_size_num X33)) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)))) (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_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_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 ((L tptp.num) (K tptp.num)) (= (tptp.aa_nat_nat (tptp.bit_se2925701944663578781it_nat (tptp.aa_num_nat tptp.numeral_numeral_nat L)) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 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.bit_se2925701944663578781it_nat (tptp.aa_num_nat tptp.pred_numeral L)) (tptp.aa_num_nat tptp.numeral_numeral_nat K))) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) tptp.one_one_nat))) (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 ((X tptp.real) (Y4 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 Y4) _let_1)))))) tptp.one_one_real)))) (forall ((X tptp.real) (U tptp.real) (Y4 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 Y4)) _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 Y4) _let_2)))) U)))))))) (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 ((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 ((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 ((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.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 ((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.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.sgn_sgn_int L))) (let ((_let_4 (tptp.aa_int_fun_int_int tptp.times_times_int _let_3))) (let ((_let_5 (tptp.modulo_modulo_int K L))) (let ((_let_6 (= (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))))))))))))))) (forall ((X tptp.real) (U tptp.real) (Y4 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 Y4) _let_4)) (=> (tptp.pp (tptp.aa_real_bool _let_3 X)) (=> (tptp.pp (tptp.aa_real_bool _let_3 Y4)) (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 Y4) _let_2)))) U))))))))))) (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 ((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 ((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 ((Xs tptp.list_nat) (Y4 tptp.nat)) (=> (forall ((X3 tptp.nat) (Y tptp.nat)) (let ((_let_1 (tptp.set_nat2 Xs))) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) _let_1)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat Y) _let_1)) (= X3 Y))))) (=> (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) (tptp.set_nat2 Xs))) (= X3 Y4))) (= (tptp.aa_nat_nat (tptp.foldr_nat_nat tptp.plus_plus_nat Xs) tptp.zero_zero_nat) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.size_size_list_nat Xs)) Y4))))) (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 ((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)))))) (= _let_56 (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_55) (tptp.aa_real_real tptp.arctan (tptp.aa_real_real _let_83 _let_94)))) (tptp.aa_real_real tptp.arctan (tptp.aa_real_real _let_83 (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_93)))))))))) (forall ((D tptp.nat) (Ys tptp.list_nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat D) (tptp.aa_nat_nat (tptp.foldr_nat_nat tptp.plus_plus_nat Ys) D)))) (forall ((A tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.log A) tptp.one_one_real) tptp.zero_zero_real)) (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 ((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) (Y4 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 Y4)) (= (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 Y4))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Y4))))))))) (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) (Y4 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 Y4)) (= (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 Y4))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) Y4))))))))) (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)) (=> (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.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.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 ((M tptp.num)) (= (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 M))) (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 (tptp.aa_num_num tptp.inc M))))) (forall ((M tptp.num)) (= (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 M))) (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 (tptp.aa_num_num tptp.inc M))))) (forall ((M tptp.num)) (= (tptp.plus_plus_complex (tptp.uminus1482373934393186551omplex (tptp.numera6690914467698888265omplex M)) (tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (tptp.uminus1482373934393186551omplex (tptp.numera6690914467698888265omplex (tptp.aa_num_num tptp.inc M))))) (forall ((M tptp.num)) (= (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.numera6620942414471956472nteger M)) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.inc M))))) (forall ((M tptp.num)) (= (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 M))) (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 (tptp.aa_num_num tptp.inc M))))) (forall ((N tptp.num)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_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 N))) (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.inc N))))) (forall ((N tptp.num)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_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 N))) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.inc N))))) (forall ((N tptp.num)) (= (tptp.plus_plus_complex (tptp.uminus1482373934393186551omplex tptp.one_one_complex) (tptp.uminus1482373934393186551omplex (tptp.numera6690914467698888265omplex N))) (tptp.uminus1482373934393186551omplex (tptp.numera6690914467698888265omplex (tptp.aa_num_num tptp.inc N))))) (forall ((N tptp.num)) (= (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.numera6620942414471956472nteger N))) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.inc N))))) (forall ((N tptp.num)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_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 N))) (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat (tptp.aa_num_num tptp.inc N))))) (forall ((M 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.one_one_real)) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.inc M)))) (forall ((M 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.one_one_int)) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.inc M)))) (forall ((M tptp.num)) (= (tptp.minus_minus_complex (tptp.numera6690914467698888265omplex M) (tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (tptp.numera6690914467698888265omplex (tptp.aa_num_num tptp.inc M)))) (forall ((M tptp.num)) (= (tptp.minus_8373710615458151222nteger (tptp.numera6620942414471956472nteger M) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.inc M)))) (forall ((M 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.one_one_rat)) (tptp.aa_num_rat tptp.numeral_numeral_rat (tptp.aa_num_num tptp.inc M)))) (forall ((N tptp.num)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_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.inc N))))) (forall ((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.one_one_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.inc N))))) (forall ((N tptp.num)) (= (tptp.minus_minus_complex (tptp.uminus1482373934393186551omplex tptp.one_one_complex) (tptp.numera6690914467698888265omplex N)) (tptp.uminus1482373934393186551omplex (tptp.numera6690914467698888265omplex (tptp.aa_num_num tptp.inc N))))) (forall ((N tptp.num)) (= (tptp.minus_8373710615458151222nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer) (tptp.numera6620942414471956472nteger N)) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.inc N))))) (forall ((N tptp.num)) (= (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat tptp.one_one_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.inc N))))) (forall ((X tptp.num)) (= (tptp.aa_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 ((Y4 tptp.num)) (= (tptp.aa_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 Y4))) tptp.zero_zero_nat)) (forall ((A tptp.real) (B 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) B)) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real B))))) (forall ((X tptp.num)) (= (tptp.aa_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 ((Y4 tptp.num)) (= (tptp.aa_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 Y4))) tptp.one_one_nat)) (forall ((N tptp.nat)) (= (tptp.aa_nat_nat (tptp.bit_se727722235901077358nd_nat (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)) N) (tptp.aa_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.bit_se727722235901077358nd_nat N) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)) (tptp.aa_nat_nat (tptp.modulo_modulo_nat N) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (not (= tptp.pi tptp.zero_zero_real)) (forall ((P tptp.fun_num_bool) (X tptp.num)) (=> (tptp.pp (tptp.aa_num_bool P tptp.one)) (=> (forall ((X3 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool P X3)) (tptp.pp (tptp.aa_num_bool P (tptp.aa_num_num tptp.inc X3))))) (tptp.pp (tptp.aa_num_bool P X))))) (forall ((X tptp.num) (Y4 tptp.num)) (let ((_let_1 (tptp.plus_plus_num X))) (= (tptp.aa_num_num _let_1 (tptp.aa_num_num tptp.inc Y4)) (tptp.aa_num_num tptp.inc (tptp.aa_num_num _let_1 Y4))))) (forall ((A tptp.real) (X tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.log A) X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real tptp.ln_ln_real X)) (tptp.aa_real_real tptp.ln_ln_real A)))) (tptp.pp (tptp.aa_real_bool _let_96 tptp.pi)) (not (tptp.pp (tptp.aa_real_bool _let_97 tptp.zero_zero_real))) (tptp.pp (tptp.aa_real_bool _let_95 tptp.pi)) (= (tptp.aa_num_num tptp.inc tptp.one) _let_1) (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.inc (tptp.aa_num_num tptp.bit0 X)) (tptp.aa_num_num tptp.bit1 X))) (forall ((X tptp.num)) (= (tptp.aa_num_num (tptp.plus_plus_num X) tptp.one) (tptp.aa_num_num tptp.inc X))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.aa_nat_nat (tptp.bit_se727722235901077358nd_nat M) N) (tptp.aa_int_nat tptp.nat2 (tptp.aa_int_int (tptp.aa_int_fun_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) (Y4 tptp.num)) (let ((_let_1 (tptp.times_times_num X))) (= (tptp.aa_num_num _let_1 (tptp.aa_num_num tptp.inc Y4)) (tptp.aa_num_num (tptp.plus_plus_num (tptp.aa_num_num _let_1 Y4)) X)))) (forall ((A tptp.real) (B 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 B) 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 B))))))) (forall ((M tptp.nat) (B 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 B) N)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real) B)) (= (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.log B) _let_1)))))) (forall ((B 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 B) N)) M)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real) B)) (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 B) M)))))) (forall ((X tptp.num)) (= (tptp.numera6690914467698888265omplex (tptp.aa_num_num tptp.inc X)) (tptp.plus_plus_complex (tptp.numera6690914467698888265omplex X) tptp.one_one_complex))) (forall ((X tptp.num)) (= (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.inc X)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_num_real tptp.numeral_numeral_real X)) tptp.one_one_real))) (forall ((X tptp.num)) (= (tptp.aa_num_rat tptp.numeral_numeral_rat (tptp.aa_num_num tptp.inc X)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat X)) tptp.one_one_rat))) (forall ((X tptp.num)) (= (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.inc X)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_num_nat tptp.numeral_numeral_nat X)) tptp.one_one_nat))) (forall ((X tptp.num)) (= (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.inc X)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_num_int tptp.numeral_numeral_int X)) tptp.one_one_int))) (tptp.pp (tptp.aa_real_bool _let_97 _let_55)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real _let_40) tptp.pi)) (not (= _let_42 _let_40)) (forall ((A tptp.real) (X tptp.real) (Y4 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 Y4)) (= (tptp.aa_real_real _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real X) Y4)) (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 Y4)))))))))) (forall ((A tptp.real) (X tptp.real) (Y4 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 Y4)) (= (tptp.aa_real_real _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real X) Y4)) (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 Y4)))))))))) (forall ((B 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 B) N)) M)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real) B)) (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 B) 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) (B tptp.real) (N tptp.nat)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.log B))) (=> (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)))))) (not (= _let_42 tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real _let_42) _let_40)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real _let_42) _let_40)) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (=> (= M (tptp.aa_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) (B 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 B) N))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real) B)) (=> (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 B) _let_1)) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N)))))))) (forall ((A tptp.real) (B 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 B)) (=> (not (= B 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 B)) (tptp.aa_real_real tptp.ln_ln_real A))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.log B) X)))))))))) (tptp.pp (tptp.aa_real_bool _let_96 _let_42)) (tptp.pp (tptp.aa_real_bool _let_95 _let_42)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.uminus_uminus_real _let_72)) tptp.pi)) (forall ((Y4 tptp.real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.arctan Y4)) (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_56) (forall ((M tptp.nat) (B 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 B) N))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real) B)) (=> (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 B) _let_1)) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N)))))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real _let_45) tptp.zero_zero_real)) (forall ((Y4 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 Y4)))) (forall ((Y4 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 Y4))) (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 ((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.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.modulo_modulo_nat M) _let_1)) (tptp.aa_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.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 ((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.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.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_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.bit_se727722235901077358nd_nat M) N) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_bool_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.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_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.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.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))))))) (= (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_94) (tptp.aa_real_real tptp.arctan (tptp.aa_real_real _let_83 (tptp.aa_num_real tptp.numeral_numeral_real _let_93))))) (tptp.aa_real_real _let_54 (tptp.aa_real_real tptp.arctan (tptp.aa_real_real _let_91 (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_37))))))))) _let_56) (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 ((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 ((B tptp.nat) (K tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.power_power_nat B))) (=> (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))) B)) (=> (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 B)) (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 ((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 ((B tptp.nat) (N tptp.nat) (K tptp.nat)) (let ((_let_1 (tptp.power_power_nat B))) (=> (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))) B)) (= (tptp.aa_real_int tptp.archim7802044766580827645g_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.log (tptp.aa_nat_real tptp.semiri5074537144036343181t_real B)) (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 ((B tptp.nat) (K tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.power_power_nat B))) (=> (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))) B)) (=> (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 B)) (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)))))))))) (= (tptp.sin_complex tptp.zero_zero_complex) tptp.zero_zero_complex) (= (tptp.aa_real_real tptp.sin_real tptp.zero_zero_real) tptp.zero_zero_real) (= (tptp.cos_complex tptp.zero_zero_complex) tptp.one_one_complex) (= (tptp.aa_real_real tptp.cos_real tptp.zero_zero_real) tptp.one_one_real) (= (tptp.aa_real_int tptp.archim6058952711729229775r_real tptp.zero_zero_real) tptp.zero_zero_int) (= (tptp.aa_rat_int tptp.archim3151403230148437115or_rat tptp.zero_zero_rat) tptp.zero_zero_int) (forall ((V tptp.num)) (= (tptp.aa_real_int tptp.archim6058952711729229775r_real (tptp.aa_num_real tptp.numeral_numeral_real V)) (tptp.aa_num_int tptp.numeral_numeral_int V))) (forall ((V tptp.num)) (= (tptp.aa_rat_int tptp.archim3151403230148437115or_rat (tptp.aa_num_rat tptp.numeral_numeral_rat V)) (tptp.aa_num_int tptp.numeral_numeral_int V))) (= (tptp.aa_rat_int tptp.archim2889992004027027881ng_rat tptp.zero_zero_rat) tptp.zero_zero_int) (= (tptp.aa_real_int tptp.archim7802044766580827645g_real tptp.zero_zero_real) tptp.zero_zero_int) (forall ((V tptp.num)) (= (tptp.aa_real_int tptp.archim7802044766580827645g_real (tptp.aa_num_real tptp.numeral_numeral_real V)) (tptp.aa_num_int tptp.numeral_numeral_int V))) (forall ((V tptp.num)) (= (tptp.aa_rat_int tptp.archim2889992004027027881ng_rat (tptp.aa_num_rat tptp.numeral_numeral_rat V)) (tptp.aa_num_int tptp.numeral_numeral_int V))) (= (tptp.aa_real_real tptp.sin_real tptp.pi) tptp.zero_zero_real) (forall ((N tptp.nat)) (= (tptp.aa_real_int tptp.archim6058952711729229775r_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N)) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N))) (forall ((N tptp.nat)) (= (tptp.aa_rat_int tptp.archim3151403230148437115or_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat N)) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N))) (forall ((N tptp.nat)) (= (tptp.aa_real_int tptp.archim7802044766580827645g_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N)) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N))) (forall ((N tptp.nat)) (= (tptp.aa_rat_int tptp.archim2889992004027027881ng_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat N)) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N))) (forall ((X tptp.real)) (= (tptp.aa_real_real tptp.sin_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real tptp.pi) X)) (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 X) tptp.pi)) (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_real_real tptp.cos_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.pi) X)) (tptp.aa_real_real tptp.uminus_uminus_real (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.minus_minus_real X) tptp.pi)) (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_real_real tptp.sin_real X)))) (forall ((X tptp.real)) (= (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 tptp.archim6058952711729229775r_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.rat)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.aa_rat_int tptp.archim3151403230148437115or_rat X))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) X)))) (forall ((X tptp.complex)) (let ((_let_1 (tptp.sin_complex X))) (let ((_let_2 (tptp.cos_complex X))) (= (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 ((X tptp.real)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_real_int tptp.archim6058952711729229775r_real X)) tptp.zero_zero_int)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) tptp.zero_zero_real)))) (forall ((X tptp.rat)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_rat_int tptp.archim3151403230148437115or_rat X)) tptp.zero_zero_int)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) tptp.zero_zero_rat)))) (forall ((V tptp.num) (X tptp.real)) (= (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 V)) (tptp.aa_real_int tptp.archim6058952711729229775r_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 V)) X)))) (forall ((V tptp.num) (X tptp.rat)) (= (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 V)) (tptp.aa_rat_int tptp.archim3151403230148437115or_rat X))) (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 V)) X)))) (forall ((X tptp.real)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) (tptp.aa_real_int tptp.archim6058952711729229775r_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.rat)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) (tptp.aa_rat_int tptp.archim3151403230148437115or_rat X))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.one_one_rat) X)))) (forall ((X tptp.real)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_real_int tptp.archim6058952711729229775r_real X)) tptp.zero_zero_int)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) tptp.one_one_real)))) (forall ((X tptp.rat)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_rat_int tptp.archim3151403230148437115or_rat X)) tptp.zero_zero_int)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) tptp.one_one_rat)))) (forall ((X tptp.rat)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_rat_int tptp.archim2889992004027027881ng_rat X)) tptp.zero_zero_int)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) tptp.zero_zero_rat)))) (forall ((X tptp.real)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_real_int tptp.archim7802044766580827645g_real X)) tptp.zero_zero_int)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) tptp.zero_zero_real)))) (forall ((X tptp.real) (V tptp.num)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_real_int tptp.archim6058952711729229775r_real X)) (tptp.aa_num_int tptp.numeral_numeral_int V))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) (tptp.aa_num_real tptp.numeral_numeral_real V))))) (forall ((X tptp.rat) (V tptp.num)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_rat_int tptp.archim3151403230148437115or_rat X)) (tptp.aa_num_int tptp.numeral_numeral_int V))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) (tptp.aa_num_rat tptp.numeral_numeral_rat V))))) (forall ((X tptp.rat)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) (tptp.aa_rat_int tptp.archim2889992004027027881ng_rat X))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) X)))) (forall ((X tptp.real)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) (tptp.aa_real_int tptp.archim7802044766580827645g_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_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.one_one_int) (tptp.aa_real_int tptp.archim6058952711729229775r_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.rat)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.one_one_int) (tptp.aa_rat_int tptp.archim3151403230148437115or_rat X))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.one_one_rat) X)))) (forall ((X tptp.rat) (V tptp.num)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_rat_int tptp.archim2889992004027027881ng_rat X)) (tptp.aa_num_int tptp.numeral_numeral_int V))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) (tptp.aa_num_rat tptp.numeral_numeral_rat V))))) (forall ((X tptp.real) (V tptp.num)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_real_int tptp.archim7802044766580827645g_real X)) (tptp.aa_num_int tptp.numeral_numeral_int V))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) (tptp.aa_num_real tptp.numeral_numeral_real V))))) (forall ((X tptp.rat)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_rat_int tptp.archim2889992004027027881ng_rat X)) tptp.one_one_int)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) tptp.zero_zero_rat)))) (forall ((X tptp.real)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_real_int tptp.archim7802044766580827645g_real X)) tptp.one_one_int)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) tptp.zero_zero_real)))) (forall ((X tptp.rat)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.one_one_int) (tptp.aa_rat_int tptp.archim2889992004027027881ng_rat X))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) X)))) (forall ((X tptp.real)) (= (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 tptp.archim7802044766580827645g_real X))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) X)))) (forall ((V tptp.num) (X tptp.real)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_num_int tptp.numeral_numeral_int V)) (tptp.aa_real_int tptp.archim7802044766580827645g_real X))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_num_real tptp.numeral_numeral_real V)) X)))) (forall ((V tptp.num) (X tptp.rat)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_num_int tptp.numeral_numeral_int V)) (tptp.aa_rat_int tptp.archim2889992004027027881ng_rat X))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_num_rat tptp.numeral_numeral_rat V)) X)))) (forall ((V tptp.num)) (= (tptp.aa_real_int tptp.archim6058952711729229775r_real (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real V))) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int V)))) (forall ((V tptp.num)) (= (tptp.aa_rat_int tptp.archim3151403230148437115or_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat V))) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int V)))) (forall ((X tptp.rat)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_rat_int tptp.archim2889992004027027881ng_rat X)) tptp.one_one_int)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) tptp.one_one_rat)))) (forall ((X tptp.real)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_real_int tptp.archim7802044766580827645g_real X)) tptp.one_one_int)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) tptp.one_one_real)))) (forall ((X tptp.real) (V tptp.num)) (= (tptp.aa_real_int tptp.archim7802044766580827645g_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) (tptp.aa_num_real tptp.numeral_numeral_real V))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_real_int tptp.archim7802044766580827645g_real X)) (tptp.aa_num_int tptp.numeral_numeral_int V)))) (forall ((X tptp.rat) (V tptp.num)) (= (tptp.aa_rat_int tptp.archim2889992004027027881ng_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat X) (tptp.aa_num_rat tptp.numeral_numeral_rat V))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_rat_int tptp.archim2889992004027027881ng_rat X)) (tptp.aa_num_int tptp.numeral_numeral_int V)))) (forall ((X tptp.real) (V tptp.num)) (= (tptp.aa_real_int tptp.archim6058952711729229775r_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real X) (tptp.aa_num_real tptp.numeral_numeral_real V))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_real_int tptp.archim6058952711729229775r_real X)) (tptp.aa_num_int tptp.numeral_numeral_int V)))) (forall ((X tptp.rat) (V tptp.num)) (= (tptp.aa_rat_int tptp.archim3151403230148437115or_rat (tptp.aa_rat_rat (tptp.minus_minus_rat X) (tptp.aa_num_rat tptp.numeral_numeral_rat V))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_rat_int tptp.archim3151403230148437115or_rat X)) (tptp.aa_num_int tptp.numeral_numeral_int V)))) (forall ((V tptp.num)) (= (tptp.aa_real_int tptp.archim7802044766580827645g_real (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real V))) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int V)))) (forall ((V tptp.num)) (= (tptp.aa_rat_int tptp.archim2889992004027027881ng_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat V))) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int V)))) (forall ((X tptp.real)) (= (tptp.aa_real_int tptp.archim6058952711729229775r_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real X) tptp.one_one_real)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_real_int tptp.archim6058952711729229775r_real X)) tptp.one_one_int))) (forall ((X tptp.rat)) (= (tptp.aa_rat_int tptp.archim3151403230148437115or_rat (tptp.aa_rat_rat (tptp.minus_minus_rat X) tptp.one_one_rat)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_rat_int tptp.archim3151403230148437115or_rat X)) tptp.one_one_int))) (forall ((X tptp.real) (V tptp.num)) (= (tptp.aa_real_int tptp.archim7802044766580827645g_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real X) (tptp.aa_num_real tptp.numeral_numeral_real V))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_real_int tptp.archim7802044766580827645g_real X)) (tptp.aa_num_int tptp.numeral_numeral_int V)))) (forall ((X tptp.rat) (V tptp.num)) (= (tptp.aa_rat_int tptp.archim2889992004027027881ng_rat (tptp.aa_rat_rat (tptp.minus_minus_rat X) (tptp.aa_num_rat tptp.numeral_numeral_rat V))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_rat_int tptp.archim2889992004027027881ng_rat X)) (tptp.aa_num_int tptp.numeral_numeral_int V)))) (forall ((X tptp.rat)) (= (tptp.aa_rat_int tptp.archim2889992004027027881ng_rat (tptp.aa_rat_rat (tptp.minus_minus_rat X) tptp.one_one_rat)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_rat_int tptp.archim2889992004027027881ng_rat X)) tptp.one_one_int))) (forall ((X tptp.real)) (= (tptp.aa_real_int tptp.archim7802044766580827645g_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real X) tptp.one_one_real)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_real_int tptp.archim7802044766580827645g_real X)) tptp.one_one_int))) (forall ((X tptp.num) (N tptp.nat)) (= (tptp.aa_real_int tptp.archim6058952711729229775r_real (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_int (tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int X)) N))) (forall ((X tptp.num) (N tptp.nat)) (= (tptp.aa_rat_int tptp.archim3151403230148437115or_rat (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_num_rat tptp.numeral_numeral_rat X)) N)) (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)) (= (tptp.aa_real_int tptp.archim7802044766580827645g_real (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_int (tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int X)) N))) (forall ((X tptp.num) (N tptp.nat)) (= (tptp.aa_rat_int tptp.archim2889992004027027881ng_rat (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_num_rat tptp.numeral_numeral_rat X)) N)) (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int X)) N))) (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.num) (B 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 B))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int (tptp.aa_num_int tptp.numeral_numeral_int A)) (tptp.aa_num_int tptp.numeral_numeral_int B)))) (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 ((X tptp.rat)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_rat_int tptp.archim2889992004027027881ng_rat X)) tptp.zero_zero_int)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) (tptp.aa_rat_rat tptp.uminus_uminus_rat tptp.one_one_rat))))) (forall ((X tptp.real)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_real_int tptp.archim7802044766580827645g_real X)) tptp.zero_zero_int)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real))))) (forall ((X tptp.real)) (= (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 tptp.archim7802044766580827645g_real X))) (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)))) (forall ((X tptp.rat)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.aa_rat_int tptp.archim2889992004027027881ng_rat X))) (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)) X)))) (forall ((A tptp.num) (B 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 B))) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_int_int (tptp.aa_int_fun_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 B))))) (forall ((V tptp.num) (X tptp.real)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_num_int tptp.numeral_numeral_int V)) (tptp.aa_real_int tptp.archim6058952711729229775r_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_num_real tptp.numeral_numeral_real V)) tptp.one_one_real)) X)))) (forall ((V tptp.num) (X tptp.rat)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_num_int tptp.numeral_numeral_int V)) (tptp.aa_rat_int tptp.archim3151403230148437115or_rat X))) (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_num_rat tptp.numeral_numeral_rat V)) tptp.one_one_rat)) X)))) (forall ((X tptp.real) (V tptp.num)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_real_int tptp.archim6058952711729229775r_real X)) (tptp.aa_num_int tptp.numeral_numeral_int V))) (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 (tptp.aa_num_real tptp.numeral_numeral_real V)) tptp.one_one_real))))) (forall ((X tptp.rat) (V tptp.num)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_rat_int tptp.archim3151403230148437115or_rat X)) (tptp.aa_num_int tptp.numeral_numeral_int V))) (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 (tptp.aa_num_rat tptp.numeral_numeral_rat V)) tptp.one_one_rat))))) (forall ((X tptp.real)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.one_one_int) (tptp.aa_real_int tptp.archim6058952711729229775r_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))) X)))) (forall ((X tptp.rat)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.one_one_int) (tptp.aa_rat_int tptp.archim3151403230148437115or_rat X))) (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 (tptp.aa_num_num tptp.bit0 tptp.one))) X)))) (forall ((X tptp.real)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_real_int tptp.archim6058952711729229775r_real X)) tptp.one_one_int)) (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)))))) (forall ((X tptp.rat)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_rat_int tptp.archim3151403230148437115or_rat X)) tptp.one_one_int)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) (tptp.aa_num_rat tptp.numeral_numeral_rat (tptp.aa_num_num tptp.bit0 tptp.one)))))) (forall ((X tptp.rat) (V tptp.num)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_rat_int tptp.archim2889992004027027881ng_rat X)) (tptp.aa_num_int tptp.numeral_numeral_int V))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat V)) tptp.one_one_rat))))) (forall ((X tptp.real) (V tptp.num)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_real_int tptp.archim7802044766580827645g_real X)) (tptp.aa_num_int tptp.numeral_numeral_int V))) (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.minus_minus_real (tptp.aa_num_real tptp.numeral_numeral_real V)) tptp.one_one_real))))) (forall ((V tptp.num) (X tptp.real)) (= (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 V)) (tptp.aa_real_int tptp.archim7802044766580827645g_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.minus_minus_real (tptp.aa_num_real tptp.numeral_numeral_real V)) tptp.one_one_real)) X)))) (forall ((V tptp.num) (X tptp.rat)) (= (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 V)) (tptp.aa_rat_int tptp.archim2889992004027027881ng_rat X))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat V)) tptp.one_one_rat)) X)))) (forall ((V tptp.num) (X tptp.real)) (= (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 V))) (tptp.aa_real_int tptp.archim6058952711729229775r_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 (tptp.aa_num_real tptp.numeral_numeral_real V))) X)))) (forall ((V tptp.num) (X tptp.rat)) (= (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 V))) (tptp.aa_rat_int tptp.archim3151403230148437115or_rat X))) (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 V))) X)))) (forall ((X tptp.real) (V tptp.num)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_real_int tptp.archim6058952711729229775r_real X)) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int V)))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real V)))))) (forall ((X tptp.rat) (V tptp.num)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_rat_int tptp.archim3151403230148437115or_rat X)) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int V)))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat V)))))) (forall ((X tptp.rat) (V tptp.num)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_rat_int tptp.archim2889992004027027881ng_rat X)) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int V)))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat V)))))) (forall ((X tptp.real) (V tptp.num)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_real_int tptp.archim7802044766580827645g_real X)) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int V)))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real V)))))) (forall ((V tptp.num) (X tptp.real)) (= (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 V))) (tptp.aa_real_int tptp.archim7802044766580827645g_real X))) (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 V))) X)))) (forall ((V tptp.num) (X tptp.rat)) (= (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 V))) (tptp.aa_rat_int tptp.archim2889992004027027881ng_rat X))) (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 V))) X)))) (= (tptp.aa_real_real tptp.cos_real _let_42) tptp.zero_zero_real) (= (tptp.aa_real_real tptp.sin_real _let_72) tptp.zero_zero_real) (= (tptp.aa_real_real tptp.sin_real _let_42) tptp.one_one_real) (= (tptp.aa_real_real tptp.cos_real _let_72) 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 ((B 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 B))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int tptp.one_one_int) (tptp.aa_num_int tptp.numeral_numeral_int B)))) (forall ((A tptp.num) (B 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 B)))) (tptp.aa_int_int (tptp.aa_int_fun_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 B)))) (forall ((A tptp.num) (B 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 B)))) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int (tptp.aa_num_int tptp.numeral_numeral_int A)) (tptp.aa_num_int tptp.numeral_numeral_int B))))) (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.plus_plus_complex (tptp.aa_nat_complex (tptp.power_power_complex (tptp.cos_complex X)) _let_1) (tptp.aa_nat_complex (tptp.power_power_complex (tptp.sin_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.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.plus_plus_complex (tptp.aa_nat_complex (tptp.power_power_complex (tptp.sin_complex X)) _let_1) (tptp.aa_nat_complex (tptp.power_power_complex (tptp.cos_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)))) (forall ((V tptp.num) (X tptp.real)) (= (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 V))) (tptp.aa_real_int tptp.archim6058952711729229775r_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.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real V))) tptp.one_one_real)) X)))) (forall ((V tptp.num) (X tptp.rat)) (= (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 V))) (tptp.aa_rat_int tptp.archim3151403230148437115or_rat X))) (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.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat V))) tptp.one_one_rat)) X)))) (forall ((X tptp.real) (V tptp.num)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_real_int tptp.archim6058952711729229775r_real X)) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int V)))) (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 (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real V))) tptp.one_one_real))))) (forall ((X tptp.rat) (V tptp.num)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_rat_int tptp.archim3151403230148437115or_rat X)) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int V)))) (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 (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat V))) tptp.one_one_rat))))) (forall ((X tptp.rat) (V tptp.num)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_rat_int tptp.archim2889992004027027881ng_rat X)) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int V)))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat V))) tptp.one_one_rat))))) (forall ((X tptp.real) (V tptp.num)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_real_int tptp.archim7802044766580827645g_real X)) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int V)))) (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.minus_minus_real (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real V))) tptp.one_one_real))))) (forall ((V tptp.num) (X tptp.real)) (= (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 V))) (tptp.aa_real_int tptp.archim7802044766580827645g_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.minus_minus_real (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real V))) tptp.one_one_real)) X)))) (forall ((V tptp.num) (X tptp.rat)) (= (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 V))) (tptp.aa_rat_int tptp.archim2889992004027027881ng_rat X))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat V))) tptp.one_one_rat)) X)))) (= (tptp.aa_real_real tptp.cos_real _let_92) tptp.zero_zero_real) (forall ((B 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 B)))) (tptp.aa_int_int (tptp.aa_int_fun_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 B)))) (= (tptp.aa_real_real tptp.sin_real _let_92) _let_85) (forall ((X tptp.real) (Y4 tptp.real)) (= (tptp.aa_real_real tptp.sin_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) Y4)) (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 Y4))) (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 Y4))))) (forall ((X tptp.real)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_real_int tptp.archim6058952711729229775r_real X)) (tptp.aa_real_int tptp.archim7802044766580827645g_real X)))) (forall ((X tptp.rat)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_rat_int tptp.archim3151403230148437115or_rat X)) (tptp.aa_rat_int tptp.archim2889992004027027881ng_rat X)))) (forall ((X tptp.real) (Y4 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))) (= Y4 (tptp.aa_real_real _let_1 (tptp.aa_real_real tptp.sin_real A3))))))) (forall ((X tptp.real) (Y4 tptp.real)) (= (tptp.aa_real_real tptp.sin_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real X) Y4)) (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 Y4))) (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 Y4))))) (forall ((X tptp.complex)) (=> (= (tptp.cos_complex X) tptp.one_one_complex) (= (tptp.sin_complex X) tptp.zero_zero_complex))) (forall ((X tptp.real)) (=> (= (tptp.aa_real_real tptp.cos_real X) tptp.one_one_real) (= (tptp.aa_real_real tptp.sin_real X) tptp.zero_zero_real))) (forall ((X tptp.real) (Y4 tptp.real)) (= (tptp.aa_real_real tptp.cos_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) Y4)) (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 Y4))) (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 Y4))))) (forall ((X tptp.real) (Y4 tptp.real)) (= (tptp.aa_real_real tptp.cos_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real X) Y4)) (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 Y4))) (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 Y4))))) (forall ((X tptp.real)) (=> (= (tptp.aa_real_real tptp.sin_real X) tptp.zero_zero_real) (= (tptp.aa_real_real tptp.real_V7735802525324610683m_real (tptp.aa_real_real tptp.cos_real X)) tptp.one_one_real))) (forall ((X tptp.complex)) (=> (= (tptp.sin_complex X) tptp.zero_zero_complex) (= (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.cos_complex X)) tptp.one_one_real))) (forall ((X tptp.real)) (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_real_int tptp.archim7802044766580827645g_real X)) (tptp.aa_real_int tptp.archim6058952711729229775r_real X))) tptp.one_one_int))) (forall ((X tptp.rat)) (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_rat_int tptp.archim2889992004027027881ng_rat X)) (tptp.aa_rat_int tptp.archim3151403230148437115or_rat X))) tptp.one_one_int))) (forall ((X tptp.real)) (=> (= (tptp.aa_real_real tptp.sin_real X) tptp.zero_zero_real) (= (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_real_real tptp.cos_real X)) tptp.one_one_real))) (forall ((X tptp.complex)) (let ((_let_1 (tptp.times_times_complex (tptp.numera6690914467698888265omplex (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (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.sin_complex X))) (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 ((Y 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)) Y)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y) tptp.pi)) (= (tptp.aa_real_real tptp.sin_real Y) (tptp.aa_real_real tptp.sin_real X)) (= (tptp.aa_real_real tptp.cos_real Y) (tptp.aa_real_real tptp.cos_real X))))) (forall ((X tptp.real) (Y4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) Y4)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_real_int tptp.archim6058952711729229775r_real X)) (tptp.aa_real_int tptp.archim6058952711729229775r_real Y4))))) (forall ((X tptp.rat) (Y4 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) Y4)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_rat_int tptp.archim3151403230148437115or_rat X)) (tptp.aa_rat_int tptp.archim3151403230148437115or_rat Y4))))) (forall ((Y4 tptp.rat) (X tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat Y4) X)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_rat_int tptp.archim2889992004027027881ng_rat Y4)) (tptp.aa_rat_int tptp.archim2889992004027027881ng_rat X))))) (forall ((Y4 tptp.real) (X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y4) X)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_real_int tptp.archim7802044766580827645g_real Y4)) (tptp.aa_real_int tptp.archim7802044766580827645g_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 ((X tptp.real)) (not (= (tptp.aa_real_real tptp.cos_real (tptp.aa_real_real tptp.arctan X)) tptp.zero_zero_real))) (forall ((X tptp.real) (Y4 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 Y4))) (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 Y4))))) 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.sin_complex X)) _let_1) (tptp.minus_minus_complex tptp.one_one_complex (tptp.aa_nat_complex (tptp.power_power_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 ((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.cos_complex X)) _let_1) (tptp.minus_minus_complex tptp.one_one_complex (tptp.aa_nat_complex (tptp.power_power_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.real) (Y4 tptp.real)) (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_real_int tptp.archim6058952711729229775r_real X)) (tptp.aa_real_int tptp.archim6058952711729229775r_real Y4))) (tptp.aa_real_int tptp.archim6058952711729229775r_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) Y4))))) (forall ((X tptp.rat) (Y4 tptp.rat)) (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_rat_int tptp.archim3151403230148437115or_rat X)) (tptp.aa_rat_int tptp.archim3151403230148437115or_rat Y4))) (tptp.aa_rat_int tptp.archim3151403230148437115or_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat X) Y4))))) (forall ((R2 tptp.rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat R2) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat (tptp.aa_int_nat tptp.nat2 (tptp.aa_rat_int tptp.archim2889992004027027881ng_rat R2)))))) (forall ((R2 tptp.real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real R2) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real (tptp.aa_int_nat tptp.nat2 (tptp.aa_real_int tptp.archim7802044766580827645g_real R2)))))) (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 ((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 ((X tptp.rat) (Y4 tptp.rat)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_rat_int tptp.archim2889992004027027881ng_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat X) Y4))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_rat_int tptp.archim2889992004027027881ng_rat X)) (tptp.aa_rat_int tptp.archim2889992004027027881ng_rat Y4))))) (forall ((X tptp.real) (Y4 tptp.real)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_real_int tptp.archim7802044766580827645g_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) Y4))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_real_int tptp.archim7802044766580827645g_real X)) (tptp.aa_real_int tptp.archim7802044766580827645g_real Y4))))) (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 ((Y4 tptp.real) (X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) Y4)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y4) 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 Y4))))))) (forall ((X tptp.real) (Y4 tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y4))) (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 Y4)) (=> (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 Y4))) (tptp.pp (tptp.aa_real_bool _let_1 X)))))))))) (forall ((X tptp.real) (Y4 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 Y4)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y4) tptp.pi)) (=> (= (tptp.aa_real_real tptp.cos_real X) (tptp.aa_real_real tptp.cos_real Y4)) (= X Y4)))))))) (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.sin_complex W)) (tptp.sin_complex Z)) (tptp.divide1717551699836669952omplex (tptp.minus_minus_complex (tptp.cos_complex (tptp.minus_minus_complex W Z)) (tptp.cos_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.sin_complex W)) (tptp.cos_complex Z)) (tptp.divide1717551699836669952omplex (tptp.plus_plus_complex (tptp.sin_complex (tptp.plus_plus_complex W Z)) (tptp.sin_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.cos_complex W)) (tptp.sin_complex Z)) (tptp.divide1717551699836669952omplex (tptp.minus_minus_complex (tptp.sin_complex (tptp.plus_plus_complex W Z)) (tptp.sin_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.plus_plus_complex (tptp.sin_complex W) (tptp.sin_complex Z)) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_complex_complex (tptp.times_times_complex _let_1) (tptp.sin_complex (tptp.divide1717551699836669952omplex (tptp.plus_plus_complex W Z) _let_1)))) (tptp.cos_complex (tptp.divide1717551699836669952omplex (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.minus_minus_complex (tptp.sin_complex W) (tptp.sin_complex Z)) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_complex_complex (tptp.times_times_complex _let_1) (tptp.sin_complex (tptp.divide1717551699836669952omplex (tptp.minus_minus_complex W Z) _let_1)))) (tptp.cos_complex (tptp.divide1717551699836669952omplex (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.minus_minus_complex (tptp.cos_complex W) (tptp.cos_complex Z)) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_complex_complex (tptp.times_times_complex _let_1) (tptp.sin_complex (tptp.divide1717551699836669952omplex (tptp.plus_plus_complex W Z) _let_1)))) (tptp.sin_complex (tptp.divide1717551699836669952omplex (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.cos_complex (tptp.aa_complex_complex (tptp.times_times_complex (tptp.numera6690914467698888265omplex _let_1)) X)) (tptp.minus_minus_complex (tptp.aa_nat_complex (tptp.power_power_complex (tptp.cos_complex X)) _let_2) (tptp.aa_nat_complex (tptp.power_power_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.cos_complex (tptp.aa_complex_complex _let_2 W)) (tptp.minus_minus_complex tptp.one_one_complex (tptp.aa_complex_complex _let_2 (tptp.aa_nat_complex (tptp.power_power_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 ((R2 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) R2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real (tptp.aa_int_nat tptp.nat2 (tptp.aa_real_int tptp.archim6058952711729229775r_real R2)))) R2)))) (forall ((R2 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) R2)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat (tptp.aa_int_nat tptp.nat2 (tptp.aa_rat_int tptp.archim3151403230148437115or_rat R2)))) R2)))) (forall ((A tptp.real) (B tptp.real)) (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_int_nat tptp.nat2 (tptp.aa_real_int tptp.archim6058952711729229775r_real A))) (tptp.aa_int_nat tptp.nat2 (tptp.aa_real_int tptp.archim6058952711729229775r_real B)))) (tptp.aa_int_nat tptp.nat2 (tptp.aa_real_int tptp.archim6058952711729229775r_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) B)))))) (forall ((A tptp.rat) (B tptp.rat)) (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_int_nat tptp.nat2 (tptp.aa_rat_int tptp.archim3151403230148437115or_rat A))) (tptp.aa_int_nat tptp.nat2 (tptp.aa_rat_int tptp.archim3151403230148437115or_rat B)))) (tptp.aa_int_nat tptp.nat2 (tptp.aa_rat_int tptp.archim3151403230148437115or_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) B)))))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.aa_real_int tptp.archim6058952711729229775r_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real M)) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N))) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat M) N)))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.aa_rat_int tptp.archim3151403230148437115or_rat (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat M)) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat N))) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat M) 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))) (not (= _let_90 tptp.zero_zero_real)) (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 ((Y4 tptp.real) (X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) Y4)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y4) 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 Y4))))))) (forall ((X tptp.real) (Y4 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 Y4)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y4) 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 Y4))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y4) 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.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 ((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 ((Y4 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)) Y4)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y4) 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 Y4)) (tptp.aa_real_real tptp.cos_real X))))))) (forall ((Y4 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) Y4)) (=> (= (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 Y4) _let_1)) tptp.one_one_real) (exists ((T3 tptp.real)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) T3)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real T3) tptp.pi)) (= X (tptp.aa_real_real tptp.cos_real T3)) (= Y4 (tptp.aa_real_real tptp.sin_real T3)))))))) (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) (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 ((A tptp.real) (B 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 B)) (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_real_int tptp.archim6058952711729229775r_real A)) (tptp.aa_real_int tptp.archim6058952711729229775r_real B))) (tptp.aa_real_int tptp.archim6058952711729229775r_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) B)))))))) (forall ((A tptp.rat) (B 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 B)) (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_rat_int tptp.archim3151403230148437115or_rat A)) (tptp.aa_rat_int tptp.archim3151403230148437115or_rat B))) (tptp.aa_rat_int tptp.archim3151403230148437115or_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) B)))))))) (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))))))) (forall ((A tptp.rat) (B 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 B)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_rat_int tptp.archim2889992004027027881ng_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) B))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_rat_int tptp.archim2889992004027027881ng_rat A)) (tptp.aa_rat_int tptp.archim2889992004027027881ng_rat B)))))))) (forall ((A tptp.real) (B 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 B)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_real_int tptp.archim7802044766580827645g_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) B))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_real_int tptp.archim7802044766580827645g_real A)) (tptp.aa_real_int tptp.archim7802044766580827645g_real B)))))))) (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.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real _let_90) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real _let_90) tptp.zero_zero_real)) (exists ((X3 tptp.real)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) X3)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X3) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.aa_real_real tptp.cos_real X3) tptp.zero_zero_real) (forall ((Y3 tptp.real)) (=> (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) Y3)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y3) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.aa_real_real tptp.cos_real Y3) tptp.zero_zero_real)) (= Y3 X3))))) (forall ((Y4 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)) Y4)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y4) 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 Y4)) (tptp.aa_real_real tptp.cos_real X))))))) (forall ((Y4 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)) Y4)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y4) tptp.one_one_real)) (exists ((X3 tptp.real)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) X3)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X3) tptp.pi)) (= (tptp.aa_real_real tptp.cos_real X3) Y4) (forall ((Y3 tptp.real)) (=> (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) Y3)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y3) tptp.pi)) (= (tptp.aa_real_real tptp.cos_real Y3) Y4)) (= Y3 X3)))))))) (forall ((X tptp.real) (Y4 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 Y4)) (=> (= (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 Y4) _let_1)) tptp.one_one_real) (exists ((T3 tptp.real)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) T3)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real T3) (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 T3)) (= Y4 (tptp.aa_real_real tptp.sin_real T3)))))))))) (forall ((X tptp.real) (Y4 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 Y4) _let_1)) tptp.one_one_real) (exists ((T3 tptp.real)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) T3)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real T3) (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 T3)) (= Y4 (tptp.aa_real_real tptp.sin_real T3))))))) (forall ((X tptp.real) (Y4 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 Y4) _let_1)) tptp.one_one_real) (not (forall ((T3 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) T3)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real T3) (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 T3)) (not (= Y4 (tptp.aa_real_real tptp.sin_real T3))))))))))) (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))))))) (= (tptp.aa_real_real tptp.sin_real _let_56) _let_89) (= (tptp.aa_real_real tptp.cos_real _let_56) _let_89) (forall ((W tptp.complex) (Z tptp.complex)) (= (tptp.aa_complex_complex (tptp.times_times_complex (tptp.cos_complex W)) (tptp.cos_complex Z)) (tptp.divide1717551699836669952omplex (tptp.plus_plus_complex (tptp.cos_complex (tptp.minus_minus_complex W Z)) (tptp.cos_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.plus_plus_complex (tptp.cos_complex W) (tptp.cos_complex Z)) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_complex_complex (tptp.times_times_complex _let_1) (tptp.cos_complex (tptp.divide1717551699836669952omplex (tptp.plus_plus_complex W Z) _let_1)))) (tptp.cos_complex (tptp.divide1717551699836669952omplex (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 ((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_84) _let_88) (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 ((Y4 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)) Y4)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y4) 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 Y4)) (tptp.aa_real_real tptp.sin_real X)))))))) (forall ((X tptp.real) (Y4 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 Y4)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y4) _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 Y4))) (tptp.pp (tptp.aa_real_bool _let_1 Y4))))))))))) (forall ((X tptp.real) (Y4 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 Y4)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y4) _let_1)) (=> (= (tptp.aa_real_real tptp.sin_real X) (tptp.aa_real_real tptp.sin_real Y4)) (= X Y4))))))))) (= (tptp.aa_real_real tptp.cos_real _let_86) _let_88) (= (tptp.aa_real_real tptp.sin_real _let_86) _let_87) (= (tptp.aa_real_real tptp.cos_real _let_84) _let_87) (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.cos_complex (tptp.aa_complex_complex _let_2 W)) (tptp.minus_minus_complex (tptp.aa_complex_complex _let_2 (tptp.aa_nat_complex (tptp.power_power_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.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.cos_complex (tptp.aa_complex_complex _let_3 X)) (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 ((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 ((Y4 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)) Y4)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y4) 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 Y4)) (tptp.aa_real_real tptp.sin_real X)))))))) (forall ((X tptp.real) (Y4 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 Y4)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y4) _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 Y4))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Y4)))))))))) (forall ((Y4 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)) Y4)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y4) tptp.one_one_real)) (exists ((X3 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)) X3)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X3) _let_1)) (= (tptp.aa_real_real tptp.sin_real X3) Y4) (forall ((Y3 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)) Y3)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y3) _let_1)) (= (tptp.aa_real_real tptp.sin_real Y3) Y4)) (= Y3 X3)))))))))) (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 ((X5 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 X5)) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))) tptp.pi))) (exists ((X5 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 X5)) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))) tptp.pi))))))) (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.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 ((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 ((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 ((B tptp.nat) (N tptp.nat) (K tptp.nat)) (let ((_let_1 (tptp.power_power_nat B))) (=> (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))) B)) (= (tptp.aa_real_int tptp.archim6058952711729229775r_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.log (tptp.aa_nat_real tptp.semiri5074537144036343181t_real B)) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real K))) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int 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 ((N4 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)) N4)) (= X (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N4)) (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 ((N4 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)) N4)) (= 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 N4)) (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 ((N4 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)) N4))) (= X (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N4)) (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 ((N4 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)) N4))) (= 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 N4)) (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.complex)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (let ((_let_2 (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.cos_complex X) tptp.zero_zero_complex)) (=> (not (= (tptp.cos_complex _let_4) tptp.zero_zero_complex)) (= (tptp.tan_complex _let_4) (tptp.divide1717551699836669952omplex (tptp.aa_complex_complex _let_3 _let_2) (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.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)) (=> (= (tptp.aa_complex_real tptp.real_V1022390504157884413omplex Z) tptp.one_one_real) (not (forall ((T3 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) T3)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real T3) (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.complex2 (tptp.aa_real_real tptp.cos_real T3) (tptp.aa_real_real tptp.sin_real T3)))))))))) (forall ((X tptp.real) (B tptp.real) (K tptp.nat)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.powr_real B))) (=> (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) B)) (= (= (tptp.aa_real_int tptp.archim7802044766580827645g_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.log B) 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 ((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 ((W tptp.real) (Z tptp.real)) (= (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.powr_real W) Z) tptp.zero_zero_real) (= W tptp.zero_zero_real))) (forall ((Z tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.powr_real tptp.zero_zero_real) Z) tptp.zero_zero_real)) (= (tptp.tan_complex tptp.zero_zero_complex) tptp.zero_zero_complex) (= (tptp.aa_real_real tptp.tan_real tptp.zero_zero_real) tptp.zero_zero_real) (= (tptp.aa_real_real tptp.arcsin tptp.zero_zero_real) tptp.zero_zero_real) (forall ((X tptp.real)) (let ((_let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.powr_real X) tptp.zero_zero_real))) (let ((_let_2 (= X tptp.zero_zero_real))) (and (=> _let_2 (= _let_1 tptp.zero_zero_real)) (=> (not _let_2) (= _let_1 tptp.one_one_real)))))) (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))) (= (tptp.aa_real_real tptp.tan_real tptp.pi) tptp.zero_zero_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.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.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)) (=> (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) (A tptp.real) (B 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 B))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) B)))))) (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) (Y4 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) Y4)) Y4)))) (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) (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 ((Y4 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)) Y4)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y4) tptp.one_one_real)) (= (tptp.aa_real_real tptp.sin_real (tptp.aa_real_real tptp.arcsin Y4)) Y4)))) (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))))) (= (tptp.aa_real_real tptp.arcsin tptp.one_one_real) _let_42) (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))) (= (tptp.aa_real_real tptp.arcsin _let_85) _let_45) (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 ((X tptp.real) (A tptp.real) (B 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)) B) (tptp.aa_real_real _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) B))))) (forall ((A tptp.real) (B tptp.real)) (= (= (tptp.complex2 A B) tptp.zero_zero_complex) (and (= A tptp.zero_zero_real) (= B tptp.zero_zero_real)))) (= tptp.zero_zero_complex (tptp.complex2 tptp.zero_zero_real tptp.zero_zero_real)) (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (= (tptp.minus_minus_complex (tptp.complex2 A B) (tptp.complex2 C D)) (tptp.complex2 (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 B) D)))) (forall ((A tptp.real) (X tptp.real) (Y4 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) Y4)) (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 Y4) 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) (Y4 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) Y4)))) (forall ((A tptp.real) (X tptp.real) (Y4 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) Y4)) (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 Y4) A)))))))) (forall ((A tptp.real) (B 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) B)) (=> (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 B))))))) (forall ((A tptp.real) (B tptp.real)) (= (= (tptp.complex2 A B) tptp.one_one_complex) (and (= A tptp.one_one_real) (= B tptp.zero_zero_real)))) (= tptp.one_one_complex (tptp.complex2 tptp.one_one_real tptp.zero_zero_real)) (forall ((A tptp.real) (B tptp.real) (W tptp.num)) (= (= (tptp.complex2 A B) (tptp.numera6690914467698888265omplex W)) (and (= A (tptp.aa_num_real tptp.numeral_numeral_real W)) (= B tptp.zero_zero_real)))) (forall ((A tptp.real) (X tptp.real) (Y4 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) Y4)) (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 Y4) A))))))) (forall ((A tptp.real) (X tptp.real) (Y4 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) Y4)) (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 Y4) A)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.powr_real X) A))))))) (forall ((X tptp.real) (Y4 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) Y4)) (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.powr_real X) Y4))))))) (forall ((A tptp.real) (X tptp.real) (Y4 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 Y4)) (= X Y4)))))) (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 ((A tptp.real) (B tptp.real) (X tptp.real) (Y4 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) B)) (=> (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) Y4)) (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 Y4) B)))))))) (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 ((X tptp.real) (Y4 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 Y4)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.powr_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real X) Y4)) 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 Y4) A))))))) (forall ((X tptp.real) (Y4 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 Y4)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.powr_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real X) Y4)) 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 Y4) A))))))) (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.powr_real B))) (= (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) (Y4 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) Y4)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real Y4) (tptp.aa_real_real tptp.ln_ln_real X))))) (forall ((A tptp.real) (B tptp.real) (X tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.log (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.powr_real A) B)) 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)) B)))) (forall ((X tptp.real) (B tptp.real) (Y4 tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.log B))) (=> (not (= X tptp.zero_zero_real)) (= (tptp.aa_real_real _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.powr_real X) Y4)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real Y4) (tptp.aa_real_real _let_1 X)))))) (forall ((A tptp.real) (B tptp.real)) (= (= (tptp.complex2 A B) (tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (and (= A (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)) (= B tptp.zero_zero_real)))) (forall ((A tptp.real) (B tptp.real) (W tptp.num)) (= (= (tptp.complex2 A B) (tptp.uminus1482373934393186551omplex (tptp.numera6690914467698888265omplex W))) (and (= A (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real W))) (= B tptp.zero_zero_real)))) (forall ((X tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.powr_real X))) (= (tptp.aa_real_real _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) B)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real _let_1 A)) (tptp.aa_real_real _let_1 B))))) (forall ((W tptp.real) (Z1 tptp.real) (Z22 tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.powr_real W))) (= (tptp.aa_real_real _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real Z1) Z22)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real _let_1 Z1)) (tptp.aa_real_real _let_1 Z22))))) (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.times_times_real B))) (let ((_let_2 (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A))) (= (tptp.aa_complex_complex (tptp.times_times_complex (tptp.complex2 A B)) (tptp.complex2 C D)) (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 ((X tptp.real) (Y4 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) Y4)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y4) 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 Y4))))))) (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) (Y4 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 Y4)) 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 Y4))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) Y4)))))) (forall ((X tptp.real) (Y4 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 Y4)) tptp.one_one_real)) (= (= (tptp.aa_real_real tptp.arcsin X) (tptp.aa_real_real tptp.arcsin Y4)) (= X Y4))))) (forall ((X4 tptp.complex)) (= (tptp.tan_complex X4) (tptp.divide1717551699836669952omplex (tptp.sin_complex X4) (tptp.cos_complex X4)))) (forall ((X4 tptp.real)) (= (tptp.aa_real_real tptp.tan_real X4) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real tptp.sin_real X4)) (tptp.aa_real_real tptp.cos_real X4)))) (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 ((B tptp.real) (X tptp.real) (Y4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real) B)) (=> (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 B) Y4)) X)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y4) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.log B) X))))))) (forall ((B tptp.real) (X tptp.real) (Y4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real) B)) (=> (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 B) Y4))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.log B) X)) Y4)))))) (forall ((B tptp.real) (X tptp.real) (Y4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real) B)) (=> (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 B) X)) Y4)) (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 B) Y4))))))) (forall ((B tptp.real) (X tptp.real) (Y4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real) B)) (=> (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 Y4) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.log B) 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 B) Y4)) X)))))) (forall ((X tptp.real) (A tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.powr_real X))) (= (tptp.aa_real_real _let_1 (tptp.aa_real_real tptp.uminus_uminus_real A)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.one_one_real) (tptp.aa_real_real _let_1 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.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) (Y4 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) Y4)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y4) 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 Y4))))))) (forall ((X tptp.real) (Y4 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 Y4)) (tptp.aa_real_real _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real tptp.one_one_real) Y4)))))) (forall ((X tptp.real) (Y4 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 Y4)) 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 Y4))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Y4)))))) (forall ((B tptp.real) (X tptp.real) (Y4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real) B)) (=> (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 Y4) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.log B) 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 B) Y4)) X)))))) (forall ((B tptp.real) (X tptp.real) (Y4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real) B)) (=> (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 B) X)) Y4)) (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 B) Y4))))))) (forall ((B tptp.real) (X tptp.real) (Y4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real) B)) (=> (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 B) Y4))) (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 B) X)) Y4)))))) (forall ((B tptp.real) (X tptp.real) (Y4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real) B)) (=> (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 B) Y4)) X)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y4) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.log B) X))))))) (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)))))) (= (tptp.aa_real_real tptp.tan_real _let_56) tptp.one_one_real) (forall ((B tptp.real) (X tptp.real) (Y4 tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.log B))) (let ((_let_2 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool _let_2 B)) (=> (not (= B 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)) Y4) (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 B) Y4)))))))))) (forall ((B tptp.real) (X tptp.real) (Y4 tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.log B))) (let ((_let_2 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool _let_2 B)) (=> (not (= B 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 Y4) (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 B) Y4)) X))))))))) (forall ((B tptp.real) (X tptp.real) (Y4 tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.log B))) (let ((_let_2 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool _let_2 B)) (=> (not (= B 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 Y4) (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 B) Y4)) X))))))))) (= (tptp.aa_real_real tptp.tan_real _let_86) _let_82) (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 ((X tptp.real) (A tptp.real)) (let ((_let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.powr_real X) A))) (let ((_let_2 (= X tptp.zero_zero_real))) (and (=> _let_2 (= _let_1 tptp.zero_zero_real)) (=> (not _let_2) (= _let_1 (tptp.aa_real_real tptp.exp_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) (tptp.aa_real_real tptp.ln_ln_real X))))))))) (forall ((Y4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) Y4)) (exists ((X3 tptp.real)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) X3)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X3) (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 Y4) (tptp.aa_real_real tptp.tan_real X3))))))) (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 ((Y4 tptp.real)) (exists ((X3 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)) X3)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X3) _let_1)) (= (tptp.aa_real_real tptp.tan_real X3) Y4))))) (forall ((X tptp.real) (Y4 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 Y4)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y4) _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 Y4))) (tptp.pp (tptp.aa_real_bool _let_1 Y4))))))))))) (forall ((Y4 tptp.real) (X tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y4))) (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 Y4)) (=> (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 Y4)) (tptp.aa_real_real tptp.tan_real X)))))))))))) (forall ((Y4 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)) Y4)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y4) 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 Y4)) (tptp.aa_real_real tptp.tan_real X)))))))) (forall ((Y4 tptp.real)) (exists ((X3 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)) X3)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X3) _let_1)) (= (tptp.aa_real_real tptp.tan_real X3) Y4) (forall ((Y3 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)) Y3)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y3) _let_1)) (= (tptp.aa_real_real tptp.tan_real Y3) Y4)) (= Y3 X3)))))))) (= (tptp.aa_real_real tptp.tan_real (tptp.aa_real_real tptp.uminus_uminus_real _let_56)) _let_85) (forall ((Y4 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 Y4)) (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)))) Y4)))) (forall ((B tptp.real) (X tptp.real) (Y4 tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.log B))) (let ((_let_2 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool _let_2 B)) (=> (not (= B 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)) Y4) (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 B) (tptp.aa_real_real tptp.uminus_uminus_real Y4))))))))))) (forall ((X tptp.real) (Y4 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.complex2 X Y4)) (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 Y4) _let_1)))))) (forall ((X tptp.complex) (Y4 tptp.complex)) (let ((_let_1 (tptp.cos_complex Y4))) (let ((_let_2 (tptp.cos_complex X))) (=> (not (= _let_2 tptp.zero_zero_complex)) (=> (not (= _let_1 tptp.zero_zero_complex)) (= (tptp.plus_plus_complex (tptp.tan_complex X) (tptp.tan_complex Y4)) (tptp.divide1717551699836669952omplex (tptp.sin_complex (tptp.plus_plus_complex X Y4)) (tptp.aa_complex_complex (tptp.times_times_complex _let_2) _let_1)))))))) (forall ((X tptp.real) (Y4 tptp.real)) (let ((_let_1 (tptp.aa_real_real tptp.cos_real Y4))) (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 Y4)) (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) Y4))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real _let_2) _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.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 ((Y4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) Y4)) (exists ((X3 tptp.real)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) X3)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X3) (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 X3) Y4))))) (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 ((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) (Y4 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) Y4)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y4) _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 Y4)))))))) (forall ((X tptp.real) (Y4 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 Y4)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y4) _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 Y4))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) Y4)))))))))) (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)))) (= (tptp.aa_real_real tptp.tan_real _let_84) (tptp.aa_real_real _let_83 _let_82)) (forall ((X tptp.real) (Y4 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) Y4) (= (tptp.aa_real_real tptp.arctan Y4) 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 ((Y4 tptp.real)) (let ((_let_1 (tptp.aa_real_real tptp.arctan Y4))) (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) Y4))))) (forall ((X tptp.complex) (Y4 tptp.complex)) (let ((_let_1 (tptp.cos_complex Y4))) (let ((_let_2 (tptp.cos_complex X))) (=> (not (= _let_2 tptp.zero_zero_complex)) (=> (not (= _let_1 tptp.zero_zero_complex)) (= (tptp.minus_minus_complex tptp.one_one_complex (tptp.aa_complex_complex (tptp.times_times_complex (tptp.tan_complex X)) (tptp.tan_complex Y4))) (tptp.divide1717551699836669952omplex (tptp.cos_complex (tptp.plus_plus_complex X Y4)) (tptp.aa_complex_complex (tptp.times_times_complex _let_2) _let_1)))))))) (forall ((X tptp.real) (Y4 tptp.real)) (let ((_let_1 (tptp.aa_real_real tptp.cos_real Y4))) (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 Y4))) (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) Y4))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real _let_2) _let_1)))))))) (forall ((X tptp.complex) (Y4 tptp.complex)) (let ((_let_1 (tptp.tan_complex Y4))) (let ((_let_2 (tptp.tan_complex X))) (let ((_let_3 (tptp.minus_minus_complex X Y4))) (=> (not (= (tptp.cos_complex X) tptp.zero_zero_complex)) (=> (not (= (tptp.cos_complex Y4) tptp.zero_zero_complex)) (=> (not (= (tptp.cos_complex _let_3) tptp.zero_zero_complex)) (= (tptp.tan_complex _let_3) (tptp.divide1717551699836669952omplex (tptp.minus_minus_complex _let_2 _let_1) (tptp.plus_plus_complex tptp.one_one_complex (tptp.aa_complex_complex (tptp.times_times_complex _let_2) _let_1))))))))))) (forall ((X tptp.real) (Y4 tptp.real)) (let ((_let_1 (tptp.aa_real_real tptp.tan_real Y4))) (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) Y4))) (=> (not (= (tptp.aa_real_real tptp.cos_real X) tptp.zero_zero_real)) (=> (not (= (tptp.aa_real_real tptp.cos_real Y4) 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) (Y4 tptp.complex)) (let ((_let_1 (tptp.tan_complex Y4))) (let ((_let_2 (tptp.tan_complex X))) (let ((_let_3 (tptp.plus_plus_complex X Y4))) (=> (not (= (tptp.cos_complex X) tptp.zero_zero_complex)) (=> (not (= (tptp.cos_complex Y4) tptp.zero_zero_complex)) (=> (not (= (tptp.cos_complex _let_3) tptp.zero_zero_complex)) (= (tptp.tan_complex _let_3) (tptp.divide1717551699836669952omplex (tptp.plus_plus_complex _let_2 _let_1) (tptp.minus_minus_complex tptp.one_one_complex (tptp.aa_complex_complex (tptp.times_times_complex _let_2) _let_1))))))))))) (forall ((X tptp.real) (Y4 tptp.real)) (let ((_let_1 (tptp.aa_real_real tptp.tan_real Y4))) (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) Y4))) (=> (not (= (tptp.aa_real_real tptp.cos_real X) tptp.zero_zero_real)) (=> (not (= (tptp.aa_real_real tptp.cos_real Y4) 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)) (=> (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 ((Z2 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)) Z2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Z2) _let_1)) (= (tptp.aa_real_real tptp.tan_real Z2) X)))))) (forall ((Y4 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 Y4))) (=> (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)) Y4)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y4) 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 ((Y4 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)) Y4)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y4) 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 Y4)))))) (forall ((Y4 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)) Y4)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y4) 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 Y4)) (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 ((Y4 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 Y4))) (=> (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)) Y4)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y4) 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 ((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.tan_complex X) (tptp.divide1717551699836669952omplex (tptp.sin_complex _let_1) (tptp.plus_plus_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 ((Y4 tptp.real)) (let ((_let_1 (tptp.aa_real_real tptp.arcsin Y4))) (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)) Y4)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y4) 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) Y4))))))) (forall ((Y4 tptp.real)) (let ((_let_1 (tptp.aa_real_real tptp.arcsin Y4))) (=> (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)) Y4)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y4) 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) Y4)))))) (forall ((X tptp.real) (Y4 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)) Y4)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y4) (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)) Y4)) (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real tptp.sin_real Y4))))))))))) (forall ((X tptp.real) (Y4 tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y4))) (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)) Y4)) (=> (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 Y4)) X)))))))))) (forall ((X tptp.real)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (= (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.aa_rea7340605660300375871l_real tptp.powr_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) (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1))) tptp.one_one_real)) (tptp.aa_real_real tptp.real_V1803761363581548252l_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 _let_1))))))))) (forall ((Y4 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 Y4)) tptp.one_one_real)) (= (tptp.aa_real_real tptp.sin_real (tptp.aa_real_real tptp.arccos Y4)) (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 Y4) (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 ((X tptp.real)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (= (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.aa_rea7340605660300375871l_real tptp.powr_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) (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1))) tptp.one_one_real)) (tptp.aa_real_real tptp.real_V1803761363581548252l_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 _let_1))))))))) (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 ((W tptp.int) (Z tptp.int)) (= (= (tptp.aa_int_real tptp.ring_1_of_int_real W) (tptp.aa_int_real tptp.ring_1_of_int_real Z)) (= W Z))) (forall ((W tptp.int) (Z tptp.int)) (= (= (tptp.ring_17405671764205052669omplex W) (tptp.ring_17405671764205052669omplex Z)) (= W Z))) (forall ((W tptp.int) (Z tptp.int)) (= (= (tptp.aa_int_rat tptp.ring_1_of_int_rat W) (tptp.aa_int_rat tptp.ring_1_of_int_rat Z)) (= W Z))) (forall ((X tptp.real)) (= (= (tptp.aa_int_real tptp.ring_1_of_int_real (tptp.aa_real_int tptp.archim6058952711729229775r_real X)) X) (exists ((N4 tptp.int)) (= X (tptp.aa_int_real tptp.ring_1_of_int_real N4))))) (forall ((X tptp.rat)) (= (= (tptp.aa_int_rat tptp.ring_1_of_int_rat (tptp.aa_rat_int tptp.archim3151403230148437115or_rat X)) X) (exists ((N4 tptp.int)) (= X (tptp.aa_int_rat tptp.ring_1_of_int_rat N4))))) (forall ((X tptp.rat)) (= (= (tptp.aa_int_rat tptp.ring_1_of_int_rat (tptp.aa_rat_int tptp.archim2889992004027027881ng_rat X)) X) (exists ((N4 tptp.int)) (= X (tptp.aa_int_rat tptp.ring_1_of_int_rat N4))))) (forall ((X tptp.real)) (= (= (tptp.aa_int_real tptp.ring_1_of_int_real (tptp.aa_real_int tptp.archim7802044766580827645g_real X)) X) (exists ((N4 tptp.int)) (= X (tptp.aa_int_real tptp.ring_1_of_int_real N4))))) (forall ((Z tptp.int)) (= (= (tptp.ring_1_of_int_int Z) tptp.zero_zero_int) (= Z tptp.zero_zero_int))) (forall ((Z tptp.int)) (= (= (tptp.aa_int_real tptp.ring_1_of_int_real Z) tptp.zero_zero_real) (= Z tptp.zero_zero_int))) (forall ((Z tptp.int)) (= (= (tptp.ring_17405671764205052669omplex Z) tptp.zero_zero_complex) (= Z tptp.zero_zero_int))) (forall ((Z tptp.int)) (= (= (tptp.aa_int_rat tptp.ring_1_of_int_rat Z) tptp.zero_zero_rat) (= Z tptp.zero_zero_int))) (forall ((Z tptp.int)) (= (= tptp.zero_zero_int (tptp.ring_1_of_int_int Z)) (= Z tptp.zero_zero_int))) (forall ((Z tptp.int)) (= (= tptp.zero_zero_real (tptp.aa_int_real tptp.ring_1_of_int_real Z)) (= Z tptp.zero_zero_int))) (forall ((Z tptp.int)) (= (= tptp.zero_zero_complex (tptp.ring_17405671764205052669omplex Z)) (= Z tptp.zero_zero_int))) (forall ((Z tptp.int)) (= (= tptp.zero_zero_rat (tptp.aa_int_rat tptp.ring_1_of_int_rat Z)) (= Z tptp.zero_zero_int))) (= (tptp.ring_1_of_int_int tptp.zero_zero_int) tptp.zero_zero_int) (= (tptp.aa_int_real tptp.ring_1_of_int_real tptp.zero_zero_int) tptp.zero_zero_real) (= (tptp.ring_17405671764205052669omplex tptp.zero_zero_int) tptp.zero_zero_complex) (= (tptp.aa_int_rat tptp.ring_1_of_int_rat tptp.zero_zero_int) tptp.zero_zero_rat) (= (tptp.aa_real_real tptp.real_V1803761363581548252l_real tptp.zero_zero_real) tptp.zero_zero_real) (= (tptp.real_V4546457046886955230omplex tptp.zero_zero_real) tptp.zero_zero_complex) (forall ((X tptp.real)) (= (= (tptp.aa_real_real tptp.real_V1803761363581548252l_real X) tptp.zero_zero_real) (= X tptp.zero_zero_real))) (forall ((X tptp.real)) (= (= (tptp.real_V4546457046886955230omplex X) tptp.zero_zero_complex) (= X tptp.zero_zero_real))) (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.ring_1_of_int_int W)) (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 ((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 ((Z tptp.int) (N tptp.num)) (= (= (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.ring_1_of_int_int Z) _let_1) (= Z _let_1)))) (forall ((K tptp.num)) (= (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.ring_1_of_int_int _let_1) _let_1))) (forall ((W tptp.int) (Z tptp.int)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_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_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_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_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_int (tptp.ring_1_of_int_int W)) (tptp.ring_1_of_int_int Z))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int W) Z)))) (forall ((Z tptp.int)) (= (= (tptp.ring_1_of_int_int Z) tptp.one_one_int) (= Z tptp.one_one_int))) (forall ((Z tptp.int)) (= (= (tptp.aa_int_real tptp.ring_1_of_int_real Z) tptp.one_one_real) (= Z tptp.one_one_int))) (forall ((Z tptp.int)) (= (= (tptp.ring_17405671764205052669omplex Z) tptp.one_one_complex) (= Z tptp.one_one_int))) (forall ((Z tptp.int)) (= (= (tptp.aa_int_rat tptp.ring_1_of_int_rat Z) tptp.one_one_rat) (= Z tptp.one_one_int))) (= (tptp.ring_1_of_int_int tptp.one_one_int) tptp.one_one_int) (= (tptp.aa_int_real tptp.ring_1_of_int_real tptp.one_one_int) tptp.one_one_real) (= (tptp.ring_17405671764205052669omplex tptp.one_one_int) tptp.one_one_complex) (= (tptp.aa_int_rat tptp.ring_1_of_int_rat tptp.one_one_int) tptp.one_one_rat) (forall ((W tptp.int) (Z tptp.int)) (= (tptp.ring_17405671764205052669omplex (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int W) Z)) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.ring_17405671764205052669omplex W)) (tptp.ring_17405671764205052669omplex Z)))) (forall ((W tptp.int) (Z tptp.int)) (= (tptp.aa_int_real tptp.ring_1_of_int_real (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int W) Z)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_int_real tptp.ring_1_of_int_real W)) (tptp.aa_int_real tptp.ring_1_of_int_real Z)))) (forall ((W tptp.int) (Z tptp.int)) (= (tptp.aa_int_rat tptp.ring_1_of_int_rat (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int W) Z)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_int_rat tptp.ring_1_of_int_rat W)) (tptp.aa_int_rat tptp.ring_1_of_int_rat Z)))) (forall ((W tptp.int) (Z tptp.int)) (= (tptp.ring_1_of_int_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int W) Z)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.ring_1_of_int_int W)) (tptp.ring_1_of_int_int Z)))) (forall ((W tptp.int) (Z tptp.int)) (= (tptp.ring_1_of_int_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int W) Z)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.ring_1_of_int_int W)) (tptp.ring_1_of_int_int Z)))) (forall ((W tptp.int) (Z tptp.int)) (= (tptp.aa_int_real tptp.ring_1_of_int_real (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int W) Z)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_int_real tptp.ring_1_of_int_real W)) (tptp.aa_int_real tptp.ring_1_of_int_real Z)))) (forall ((W tptp.int) (Z tptp.int)) (= (tptp.ring_17405671764205052669omplex (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int W) Z)) (tptp.plus_plus_complex (tptp.ring_17405671764205052669omplex W) (tptp.ring_17405671764205052669omplex Z)))) (forall ((W tptp.int) (Z tptp.int)) (= (tptp.aa_int_rat tptp.ring_1_of_int_rat (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int W) Z)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_int_rat tptp.ring_1_of_int_rat W)) (tptp.aa_int_rat tptp.ring_1_of_int_rat Z)))) (forall ((Z tptp.int)) (= (tptp.aa_int_real tptp.ring_1_of_int_real (tptp.aa_int_int tptp.uminus_uminus_int Z)) (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_int_real tptp.ring_1_of_int_real Z)))) (forall ((Z tptp.int)) (= (tptp.ring_1_of_int_int (tptp.aa_int_int tptp.uminus_uminus_int Z)) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.ring_1_of_int_int Z)))) (forall ((Z tptp.int)) (= (tptp.ring_17405671764205052669omplex (tptp.aa_int_int tptp.uminus_uminus_int Z)) (tptp.uminus1482373934393186551omplex (tptp.ring_17405671764205052669omplex Z)))) (forall ((Z tptp.int)) (= (tptp.ring_18347121197199848620nteger (tptp.aa_int_int tptp.uminus_uminus_int Z)) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.ring_18347121197199848620nteger Z)))) (forall ((Z tptp.int)) (= (tptp.aa_int_rat tptp.ring_1_of_int_rat (tptp.aa_int_int tptp.uminus_uminus_int Z)) (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_int_rat tptp.ring_1_of_int_rat Z)))) (forall ((X tptp.real) (Y4 tptp.real)) (= (tptp.aa_real_real tptp.real_V1803761363581548252l_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real X) Y4)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real tptp.real_V1803761363581548252l_real X)) (tptp.aa_real_real tptp.real_V1803761363581548252l_real Y4)))) (forall ((X tptp.real) (Y4 tptp.real)) (= (tptp.real_V4546457046886955230omplex (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real X) Y4)) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.real_V4546457046886955230omplex X)) (tptp.real_V4546457046886955230omplex Y4)))) (forall ((W tptp.num)) (let ((_let_1 (tptp.aa_num_real tptp.numeral_numeral_real W))) (= (tptp.aa_real_real tptp.real_V1803761363581548252l_real _let_1) _let_1))) (forall ((W tptp.num)) (= (tptp.real_V4546457046886955230omplex (tptp.aa_num_real tptp.numeral_numeral_real W)) (tptp.numera6690914467698888265omplex W))) (forall ((X tptp.real) (Y4 tptp.real)) (= (tptp.aa_real_real tptp.real_V1803761363581548252l_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real X) Y4)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real tptp.real_V1803761363581548252l_real X)) (tptp.aa_real_real tptp.real_V1803761363581548252l_real Y4)))) (forall ((X tptp.real) (Y4 tptp.real)) (= (tptp.real_V4546457046886955230omplex (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real X) Y4)) (tptp.divide1717551699836669952omplex (tptp.real_V4546457046886955230omplex X) (tptp.real_V4546457046886955230omplex Y4)))) (forall ((W tptp.int) (Z tptp.int)) (= (tptp.ring_17405671764205052669omplex (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int W) Z)) (tptp.minus_minus_complex (tptp.ring_17405671764205052669omplex W) (tptp.ring_17405671764205052669omplex Z)))) (forall ((W tptp.int) (Z tptp.int)) (= (tptp.aa_int_real tptp.ring_1_of_int_real (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int W) Z)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_int_real tptp.ring_1_of_int_real W)) (tptp.aa_int_real tptp.ring_1_of_int_real Z)))) (forall ((W tptp.int) (Z tptp.int)) (= (tptp.aa_int_rat tptp.ring_1_of_int_rat (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int W) Z)) (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_int_rat tptp.ring_1_of_int_rat W)) (tptp.aa_int_rat tptp.ring_1_of_int_rat Z)))) (forall ((W tptp.int) (Z tptp.int)) (= (tptp.ring_1_of_int_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int W) Z)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.ring_1_of_int_int W)) (tptp.ring_1_of_int_int Z)))) (forall ((N tptp.nat)) (= (tptp.ring_17405671764205052669omplex (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N)) (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex N))) (forall ((N tptp.nat)) (= (tptp.aa_int_real tptp.ring_1_of_int_real (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N)) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N))) (forall ((N tptp.nat)) (= (tptp.aa_int_rat tptp.ring_1_of_int_rat (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N)) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat N))) (forall ((N tptp.nat)) (let ((_let_1 (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N))) (= (tptp.ring_1_of_int_int _let_1) _let_1))) (forall ((X tptp.real) (Y4 tptp.real)) (= (tptp.aa_real_real tptp.real_V1803761363581548252l_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real X) Y4)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real tptp.real_V1803761363581548252l_real X)) (tptp.aa_real_real tptp.real_V1803761363581548252l_real Y4)))) (forall ((X tptp.real) (Y4 tptp.real)) (= (tptp.real_V4546457046886955230omplex (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real X) Y4)) (tptp.minus_minus_complex (tptp.real_V4546457046886955230omplex X) (tptp.real_V4546457046886955230omplex Y4)))) (forall ((N tptp.nat)) (= (tptp.real_V4546457046886955230omplex (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N)) (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex N))) (forall ((N tptp.nat)) (let ((_let_1 (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N))) (= (tptp.aa_real_real tptp.real_V1803761363581548252l_real _let_1) _let_1))) (forall ((X tptp.int)) (= (tptp.ring_1_of_int_int (tptp.aa_int_int tptp.abs_abs_int X)) (tptp.aa_int_int tptp.abs_abs_int (tptp.ring_1_of_int_int X)))) (forall ((X tptp.int)) (= (tptp.ring_18347121197199848620nteger (tptp.aa_int_int tptp.abs_abs_int X)) (tptp.abs_abs_Code_integer (tptp.ring_18347121197199848620nteger X)))) (forall ((X tptp.int)) (= (tptp.aa_int_real tptp.ring_1_of_int_real (tptp.aa_int_int tptp.abs_abs_int X)) (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_int_real tptp.ring_1_of_int_real X)))) (forall ((X tptp.int)) (= (tptp.aa_int_rat tptp.ring_1_of_int_rat (tptp.aa_int_int tptp.abs_abs_int X)) (tptp.aa_rat_rat tptp.abs_abs_rat (tptp.aa_int_rat tptp.ring_1_of_int_rat X)))) (forall ((X tptp.int) (B tptp.int) (W tptp.nat)) (= (= (tptp.aa_int_rat tptp.ring_1_of_int_rat X) (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_int_rat tptp.ring_1_of_int_rat B)) W)) (= X (tptp.aa_nat_int (tptp.power_power_int B) W)))) (forall ((X tptp.int) (B tptp.int) (W tptp.nat)) (= (= (tptp.ring_1_of_int_int X) (tptp.aa_nat_int (tptp.power_power_int (tptp.ring_1_of_int_int B)) W)) (= X (tptp.aa_nat_int (tptp.power_power_int B) W)))) (forall ((X tptp.int) (B tptp.int) (W tptp.nat)) (= (= (tptp.aa_int_real tptp.ring_1_of_int_real X) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_int_real tptp.ring_1_of_int_real B)) W)) (= X (tptp.aa_nat_int (tptp.power_power_int B) W)))) (forall ((X tptp.int) (B tptp.int) (W tptp.nat)) (= (= (tptp.ring_17405671764205052669omplex X) (tptp.aa_nat_complex (tptp.power_power_complex (tptp.ring_17405671764205052669omplex B)) W)) (= X (tptp.aa_nat_int (tptp.power_power_int B) W)))) (forall ((B tptp.int) (W tptp.nat) (X tptp.int)) (= (= (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_int_rat tptp.ring_1_of_int_rat B)) W) (tptp.aa_int_rat tptp.ring_1_of_int_rat X)) (= (tptp.aa_nat_int (tptp.power_power_int B) W) X))) (forall ((B tptp.int) (W tptp.nat) (X tptp.int)) (= (= (tptp.aa_nat_int (tptp.power_power_int (tptp.ring_1_of_int_int B)) W) (tptp.ring_1_of_int_int X)) (= (tptp.aa_nat_int (tptp.power_power_int B) W) X))) (forall ((B tptp.int) (W tptp.nat) (X tptp.int)) (= (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_int_real tptp.ring_1_of_int_real B)) W) (tptp.aa_int_real tptp.ring_1_of_int_real X)) (= (tptp.aa_nat_int (tptp.power_power_int B) W) X))) (forall ((B tptp.int) (W tptp.nat) (X tptp.int)) (= (= (tptp.aa_nat_complex (tptp.power_power_complex (tptp.ring_17405671764205052669omplex B)) W) (tptp.ring_17405671764205052669omplex X)) (= (tptp.aa_nat_int (tptp.power_power_int B) W) X))) (forall ((Z tptp.int) (N tptp.nat)) (= (tptp.aa_int_rat tptp.ring_1_of_int_rat (tptp.aa_nat_int (tptp.power_power_int Z) N)) (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_int_rat tptp.ring_1_of_int_rat Z)) N))) (forall ((Z tptp.int) (N tptp.nat)) (= (tptp.ring_1_of_int_int (tptp.aa_nat_int (tptp.power_power_int Z) N)) (tptp.aa_nat_int (tptp.power_power_int (tptp.ring_1_of_int_int Z)) N))) (forall ((Z tptp.int) (N tptp.nat)) (= (tptp.aa_int_real tptp.ring_1_of_int_real (tptp.aa_nat_int (tptp.power_power_int Z) N)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_int_real tptp.ring_1_of_int_real Z)) N))) (forall ((Z tptp.int) (N tptp.nat)) (= (tptp.ring_17405671764205052669omplex (tptp.aa_nat_int (tptp.power_power_int Z) N)) (tptp.aa_nat_complex (tptp.power_power_complex (tptp.ring_17405671764205052669omplex Z)) N))) (= (tptp.aa_real_real tptp.arccos tptp.one_one_real) tptp.zero_zero_real) (forall ((P tptp.bool)) (= (tptp.aa_int_real tptp.ring_1_of_int_real (tptp.aa_bool_int tptp.zero_n2684676970156552555ol_int P)) (tptp.zero_n3304061248610475627l_real P))) (forall ((P tptp.bool)) (= (tptp.ring_17405671764205052669omplex (tptp.aa_bool_int tptp.zero_n2684676970156552555ol_int P)) (tptp.zero_n1201886186963655149omplex P))) (forall ((P tptp.bool)) (= (tptp.aa_int_rat tptp.ring_1_of_int_rat (tptp.aa_bool_int tptp.zero_n2684676970156552555ol_int P)) (tptp.zero_n2052037380579107095ol_rat P))) (forall ((P tptp.bool)) (let ((_let_1 (tptp.aa_bool_int tptp.zero_n2684676970156552555ol_int P))) (= (tptp.ring_1_of_int_int _let_1) _let_1))) (forall ((P tptp.bool)) (= (tptp.ring_18347121197199848620nteger (tptp.aa_bool_int tptp.zero_n2684676970156552555ol_int P)) (tptp.aa_bool_Code_integer tptp.zero_n356916108424825756nteger P))) (= (tptp.aa_real_real tptp.sin_real _let_79) tptp.zero_zero_real) (= (tptp.sin_complex _let_77) tptp.zero_zero_complex) (forall ((X tptp.real) (Z tptp.int)) (= (tptp.aa_real_int tptp.archim6058952711729229775r_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real X) (tptp.aa_int_real tptp.ring_1_of_int_real Z))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_real_int tptp.archim6058952711729229775r_real X)) Z))) (forall ((X tptp.rat) (Z tptp.int)) (= (tptp.aa_rat_int tptp.archim3151403230148437115or_rat (tptp.aa_rat_rat (tptp.minus_minus_rat X) (tptp.aa_int_rat tptp.ring_1_of_int_rat Z))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_rat_int tptp.archim3151403230148437115or_rat X)) Z))) (forall ((X tptp.rat) (Z tptp.int)) (= (tptp.aa_rat_int tptp.archim2889992004027027881ng_rat (tptp.aa_rat_rat (tptp.minus_minus_rat X) (tptp.aa_int_rat tptp.ring_1_of_int_rat Z))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_rat_int tptp.archim2889992004027027881ng_rat X)) Z))) (forall ((X tptp.real) (Z tptp.int)) (= (tptp.aa_real_int tptp.archim7802044766580827645g_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real X) (tptp.aa_int_real tptp.ring_1_of_int_real Z))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_real_int tptp.archim7802044766580827645g_real X)) Z))) (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (tptp.aa_int_int (tptp.bit_se2923211474154528505it_int N) K))) (= (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex (tptp.aa_int_nat tptp.nat2 _let_1)) (tptp.ring_17405671764205052669omplex _let_1)))) (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (tptp.aa_int_int (tptp.bit_se2923211474154528505it_int N) K))) (= (tptp.aa_nat_real tptp.semiri5074537144036343181t_real (tptp.aa_int_nat tptp.nat2 _let_1)) (tptp.aa_int_real tptp.ring_1_of_int_real _let_1)))) (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (tptp.aa_int_int (tptp.bit_se2923211474154528505it_int N) K))) (= (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat (tptp.aa_int_nat tptp.nat2 _let_1)) (tptp.aa_int_rat tptp.ring_1_of_int_rat _let_1)))) (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (tptp.aa_int_int (tptp.bit_se2923211474154528505it_int N) K))) (= (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_int_nat tptp.nat2 _let_1)) (tptp.ring_1_of_int_int _let_1)))) (forall ((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 Z)) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Z) 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 (tptp.ring_1_of_int_int Z)) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Z) tptp.zero_zero_int)))) (forall ((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 Z)) tptp.zero_zero_real)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Z) tptp.zero_zero_int)))) (forall ((Z tptp.int)) (= (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.ring_1_of_int_rat Z))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) Z)))) (forall ((Z 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.ring_1_of_int_int Z))) (tptp.pp (tptp.aa_int_bool _let_1 Z))))) (forall ((Z tptp.int)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (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 tptp.zero_zero_int) Z)))) (forall ((Z tptp.int)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_int_real tptp.ring_1_of_int_real Z)) tptp.zero_zero_real)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Z) tptp.zero_zero_int)))) (forall ((Z tptp.int)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_int_rat tptp.ring_1_of_int_rat Z)) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Z) tptp.zero_zero_int)))) (forall ((Z tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.ring_1_of_int_int 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 ((Z tptp.int)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) (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_int tptp.zero_zero_int) Z)))) (forall ((Z tptp.int)) (= (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.ring_1_of_int_rat Z))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) Z)))) (forall ((Z 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.ring_1_of_int_int Z))) (tptp.pp (tptp.aa_int_bool _let_1 Z))))) (forall ((N tptp.num) (Z tptp.int)) (= (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.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 (tptp.aa_num_int tptp.numeral_numeral_int N)) Z)))) (forall ((N tptp.num) (Z tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_num_int tptp.numeral_numeral_int N)))) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.ring_1_of_int_int Z))) (tptp.pp (tptp.aa_int_bool _let_1 Z))))) (forall ((N tptp.num) (Z tptp.int)) (= (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_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 (tptp.aa_num_int tptp.numeral_numeral_int N)) Z)))) (forall ((Z tptp.int) (N tptp.num)) (= (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 Z)) (tptp.aa_num_rat tptp.numeral_numeral_rat N))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int 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.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.ring_1_of_int_int Z)) _let_1)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Z) _let_1))))) (forall ((Z tptp.int) (N tptp.num)) (= (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 Z)) (tptp.aa_num_real tptp.numeral_numeral_real N))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Z) (tptp.aa_num_int tptp.numeral_numeral_int N))))) (forall ((Z tptp.int) (N tptp.num)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_int_real tptp.ring_1_of_int_real Z)) (tptp.aa_num_real tptp.numeral_numeral_real N))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Z) (tptp.aa_num_int tptp.numeral_numeral_int N))))) (forall ((Z tptp.int) (N tptp.num)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_int_rat tptp.ring_1_of_int_rat Z)) (tptp.aa_num_rat tptp.numeral_numeral_rat N))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int 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.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.ring_1_of_int_int Z)) _let_1)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Z) _let_1))))) (forall ((N tptp.num) (Z tptp.int)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_num_real tptp.numeral_numeral_real N)) (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_int (tptp.aa_num_int tptp.numeral_numeral_int N)) Z)))) (forall ((N tptp.num) (Z tptp.int)) (= (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.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_int (tptp.aa_num_int tptp.numeral_numeral_int N)) Z)))) (forall ((N tptp.num) (Z tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_num_int tptp.numeral_numeral_int N)))) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.ring_1_of_int_int Z))) (tptp.pp (tptp.aa_int_bool _let_1 Z))))) (forall ((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 Z)) tptp.one_one_rat)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Z) tptp.one_one_int)))) (forall ((Z tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.ring_1_of_int_int Z)) tptp.one_one_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Z) tptp.one_one_int)))) (forall ((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 Z)) tptp.one_one_real)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Z) tptp.one_one_int)))) (forall ((Z tptp.int)) (= (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.ring_1_of_int_rat Z))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.one_one_int) Z)))) (forall ((Z tptp.int)) (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 (tptp.ring_1_of_int_int Z))) (tptp.pp (tptp.aa_int_bool _let_1 Z))))) (forall ((Z tptp.int)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.one_one_real) (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 tptp.one_one_int) Z)))) (forall ((Z tptp.int)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_int_real tptp.ring_1_of_int_real Z)) tptp.one_one_real)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Z) tptp.one_one_int)))) (forall ((Z tptp.int)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_int_rat tptp.ring_1_of_int_rat Z)) tptp.one_one_rat)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Z) tptp.one_one_int)))) (forall ((Z tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.ring_1_of_int_int Z)) tptp.one_one_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Z) tptp.one_one_int)))) (forall ((Z tptp.int)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real) (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_int tptp.one_one_int) Z)))) (forall ((Z tptp.int)) (= (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.ring_1_of_int_rat Z))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.one_one_int) Z)))) (forall ((Z 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 (tptp.ring_1_of_int_int Z))) (tptp.pp (tptp.aa_int_bool _let_1 Z))))) (forall ((W tptp.num)) (let ((_let_1 (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real W)))) (= (tptp.aa_real_real tptp.real_V1803761363581548252l_real _let_1) _let_1))) (forall ((W tptp.num)) (= (tptp.real_V4546457046886955230omplex (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real W))) (tptp.uminus1482373934393186551omplex (tptp.numera6690914467698888265omplex W)))) (forall ((X tptp.int) (B tptp.int) (W tptp.nat)) (= (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 X)) (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_int_rat tptp.ring_1_of_int_rat B)) W))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X) (tptp.aa_nat_int (tptp.power_power_int B) W))))) (forall ((X tptp.int) (B tptp.int) (W tptp.nat)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.ring_1_of_int_int X)) (tptp.aa_nat_int (tptp.power_power_int (tptp.ring_1_of_int_int B)) W))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X) (tptp.aa_nat_int (tptp.power_power_int B) W))))) (forall ((X tptp.int) (B tptp.int) (W tptp.nat)) (= (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 X)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_int_real tptp.ring_1_of_int_real B)) W))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X) (tptp.aa_nat_int (tptp.power_power_int B) W))))) (forall ((B tptp.int) (W tptp.nat) (X tptp.int)) (= (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_int_rat tptp.ring_1_of_int_rat B)) W)) (tptp.aa_int_rat tptp.ring_1_of_int_rat X))) (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 B) W)) X)))) (forall ((B tptp.int) (W tptp.nat) (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 (tptp.ring_1_of_int_int B)) W)) (tptp.ring_1_of_int_int X))) (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 B) W)) X)))) (forall ((B tptp.int) (W tptp.nat) (X tptp.int)) (= (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_int_real tptp.ring_1_of_int_real B)) W)) (tptp.aa_int_real tptp.ring_1_of_int_real X))) (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 B) W)) X)))) (forall ((X tptp.num) (N tptp.nat) (Y4 tptp.int)) (= (= (tptp.aa_nat_complex (tptp.power_power_complex (tptp.numera6690914467698888265omplex X)) N) (tptp.ring_17405671764205052669omplex Y4)) (= (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int X)) N) Y4))) (forall ((X tptp.num) (N tptp.nat) (Y4 tptp.int)) (= (= (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_int_real tptp.ring_1_of_int_real Y4)) (= (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int X)) N) Y4))) (forall ((X tptp.num) (N tptp.nat) (Y4 tptp.int)) (= (= (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_num_rat tptp.numeral_numeral_rat X)) N) (tptp.aa_int_rat tptp.ring_1_of_int_rat Y4)) (= (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int X)) N) Y4))) (forall ((X tptp.num) (N tptp.nat) (Y4 tptp.int)) (let ((_let_1 (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int X)) N))) (= (= _let_1 (tptp.ring_1_of_int_int Y4)) (= _let_1 Y4)))) (forall ((Y4 tptp.int) (X tptp.num) (N tptp.nat)) (= (= (tptp.ring_17405671764205052669omplex Y4) (tptp.aa_nat_complex (tptp.power_power_complex (tptp.numera6690914467698888265omplex X)) N)) (= Y4 (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int X)) N)))) (forall ((Y4 tptp.int) (X tptp.num) (N tptp.nat)) (= (= (tptp.aa_int_real tptp.ring_1_of_int_real Y4) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_num_real tptp.numeral_numeral_real X)) N)) (= Y4 (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int X)) N)))) (forall ((Y4 tptp.int) (X tptp.num) (N tptp.nat)) (= (= (tptp.aa_int_rat tptp.ring_1_of_int_rat Y4) (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_num_rat tptp.numeral_numeral_rat X)) N)) (= Y4 (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int X)) N)))) (forall ((Y4 tptp.int) (X tptp.num) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int X)) N))) (= (= (tptp.ring_1_of_int_int Y4) _let_1) (= Y4 _let_1)))) (forall ((X tptp.int) (B tptp.int) (W tptp.nat)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_int_real tptp.ring_1_of_int_real X)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_int_real tptp.ring_1_of_int_real B)) W))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) (tptp.aa_nat_int (tptp.power_power_int B) W))))) (forall ((X tptp.int) (B tptp.int) (W tptp.nat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_int_rat tptp.ring_1_of_int_rat X)) (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_int_rat tptp.ring_1_of_int_rat B)) W))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) (tptp.aa_nat_int (tptp.power_power_int B) W))))) (forall ((X tptp.int) (B tptp.int) (W tptp.nat)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.ring_1_of_int_int X)) (tptp.aa_nat_int (tptp.power_power_int (tptp.ring_1_of_int_int B)) W))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) (tptp.aa_nat_int (tptp.power_power_int B) W))))) (forall ((B tptp.int) (W tptp.nat) (X tptp.int)) (= (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_int_real tptp.ring_1_of_int_real B)) W)) (tptp.aa_int_real tptp.ring_1_of_int_real X))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_nat_int (tptp.power_power_int B) W)) X)))) (forall ((B tptp.int) (W tptp.nat) (X tptp.int)) (= (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_int_rat tptp.ring_1_of_int_rat B)) W)) (tptp.aa_int_rat tptp.ring_1_of_int_rat X))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_nat_int (tptp.power_power_int B) W)) X)))) (forall ((B tptp.int) (W tptp.nat) (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 (tptp.ring_1_of_int_int B)) W)) (tptp.ring_1_of_int_int X))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_nat_int (tptp.power_power_int B) W)) X)))) (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_complex tptp.semiri8010041392384452111omplex (tptp.aa_int_nat tptp.nat2 Z)) (tptp.ring_17405671764205052669omplex 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.aa_nat_real tptp.semiri5074537144036343181t_real (tptp.aa_int_nat tptp.nat2 Z)) (tptp.aa_int_real tptp.ring_1_of_int_real 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.aa_nat_rat tptp.semiri681578069525770553at_rat (tptp.aa_int_nat tptp.nat2 Z)) (tptp.aa_int_rat tptp.ring_1_of_int_rat 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.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_int_nat tptp.nat2 Z)) (tptp.ring_1_of_int_int Z)))) (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 ((Y4 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)) Y4)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y4) tptp.one_one_real)) (= (tptp.aa_real_real tptp.cos_real (tptp.aa_real_real tptp.arccos Y4)) Y4)))) (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 ((A tptp.int) (X tptp.num) (N tptp.nat)) (= (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 A)) (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_num_rat tptp.numeral_numeral_rat 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 ((A tptp.int) (X tptp.num) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int X)) N))) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.ring_1_of_int_int A)) _let_1)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) _let_1))))) (forall ((A tptp.int) (X tptp.num) (N tptp.nat)) (= (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 A)) (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.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_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 X)) N)) (tptp.aa_int_rat tptp.ring_1_of_int_rat 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 ((X tptp.num) (N tptp.nat) (A tptp.int)) (let ((_let_1 (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)))) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.ring_1_of_int_int A))) (tptp.pp (tptp.aa_int_bool _let_1 A))))) (forall ((X tptp.num) (N tptp.nat) (A tptp.int)) (= (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 X)) N)) (tptp.aa_int_real tptp.ring_1_of_int_real 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 ((A tptp.int) (X tptp.num) (N tptp.nat)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_int_real tptp.ring_1_of_int_real A)) (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.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 ((A tptp.int) (X tptp.num) (N tptp.nat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_int_rat tptp.ring_1_of_int_rat A)) (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_num_rat tptp.numeral_numeral_rat 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 ((A tptp.int) (X tptp.num) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int X)) N))) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.ring_1_of_int_int A)) _let_1)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) _let_1))))) (forall ((X tptp.num) (N tptp.nat) (A tptp.int)) (= (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 X)) N)) (tptp.aa_int_real tptp.ring_1_of_int_real 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 ((X tptp.num) (N tptp.nat) (A tptp.int)) (= (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 X)) N)) (tptp.aa_int_rat tptp.ring_1_of_int_rat 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 ((X tptp.num) (N tptp.nat) (A tptp.int)) (let ((_let_1 (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)))) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.ring_1_of_int_int A))) (tptp.pp (tptp.aa_int_bool _let_1 A))))) (forall ((Y4 tptp.int) (X tptp.num) (N tptp.nat)) (= (= (tptp.aa_int_real tptp.ring_1_of_int_real Y4) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real X))) N)) (= Y4 (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int X))) N)))) (forall ((Y4 tptp.int) (X tptp.num) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int X))) N))) (= (= (tptp.ring_1_of_int_int Y4) _let_1) (= Y4 _let_1)))) (forall ((Y4 tptp.int) (X tptp.num) (N tptp.nat)) (= (= (tptp.ring_17405671764205052669omplex Y4) (tptp.aa_nat_complex (tptp.power_power_complex (tptp.uminus1482373934393186551omplex (tptp.numera6690914467698888265omplex X))) N)) (= Y4 (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int X))) N)))) (forall ((Y4 tptp.int) (X tptp.num) (N tptp.nat)) (= (= (tptp.ring_18347121197199848620nteger Y4) (tptp.power_8256067586552552935nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.numera6620942414471956472nteger X)) N)) (= Y4 (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int X))) N)))) (forall ((Y4 tptp.int) (X tptp.num) (N tptp.nat)) (= (= (tptp.aa_int_rat tptp.ring_1_of_int_rat Y4) (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat X))) N)) (= Y4 (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int X))) N)))) (forall ((X tptp.num) (N tptp.nat) (Y4 tptp.int)) (= (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real X))) N) (tptp.aa_int_real tptp.ring_1_of_int_real Y4)) (= (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int X))) N) Y4))) (forall ((X tptp.num) (N tptp.nat) (Y4 tptp.int)) (let ((_let_1 (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int X))) N))) (= (= _let_1 (tptp.ring_1_of_int_int Y4)) (= _let_1 Y4)))) (forall ((X tptp.num) (N tptp.nat) (Y4 tptp.int)) (= (= (tptp.aa_nat_complex (tptp.power_power_complex (tptp.uminus1482373934393186551omplex (tptp.numera6690914467698888265omplex X))) N) (tptp.ring_17405671764205052669omplex Y4)) (= (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int X))) N) Y4))) (forall ((X tptp.num) (N tptp.nat) (Y4 tptp.int)) (= (= (tptp.power_8256067586552552935nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.numera6620942414471956472nteger X)) N) (tptp.ring_18347121197199848620nteger Y4)) (= (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int X))) N) Y4))) (forall ((X tptp.num) (N tptp.nat) (Y4 tptp.int)) (= (= (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat X))) N) (tptp.aa_int_rat tptp.ring_1_of_int_rat Y4)) (= (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int X))) N) Y4))) (forall ((X tptp.real) (B tptp.num)) (let ((_let_1 (tptp.aa_num_real tptp.numeral_numeral_real B))) (= (tptp.aa_real_real tptp.real_V7735802525324610683m_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real tptp.real_V1803761363581548252l_real X)) _let_1)) (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) _let_1))))) (forall ((X tptp.real) (B tptp.num)) (= (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.plus_plus_complex (tptp.real_V4546457046886955230omplex X) (tptp.numera6690914467698888265omplex B))) (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) (tptp.aa_num_real tptp.numeral_numeral_real B))))) (= (tptp.aa_real_real tptp.arccos tptp.zero_zero_real) _let_42) (= (tptp.aa_real_real tptp.cos_real _let_80) tptp.zero_zero_real) (= (tptp.cos_complex _let_78) tptp.zero_zero_complex) (= (tptp.aa_real_real tptp.sin_real _let_80) tptp.one_one_real) (= (tptp.sin_complex _let_78) tptp.one_one_complex) (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 ((X tptp.num) (N tptp.nat) (A tptp.int)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.power_8256067586552552935nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.numera6620942414471956472nteger X)) N)) (tptp.ring_18347121197199848620nteger 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_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int X))) N)) A)))) (forall ((X tptp.num) (N tptp.nat) (A tptp.int)) (= (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.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat X))) N)) (tptp.aa_int_rat tptp.ring_1_of_int_rat 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_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int X))) N)) A)))) (forall ((X tptp.num) (N tptp.nat) (A tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int X))) N)))) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.ring_1_of_int_int A))) (tptp.pp (tptp.aa_int_bool _let_1 A))))) (forall ((X tptp.num) (N tptp.nat) (A tptp.int)) (= (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.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real X))) N)) (tptp.aa_int_real tptp.ring_1_of_int_real 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_int_int tptp.uminus_uminus_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_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.ring_18347121197199848620nteger A)) (tptp.power_8256067586552552935nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.numera6620942414471956472nteger 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_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int X))) N))))) (forall ((A tptp.int) (X tptp.num) (N tptp.nat)) (= (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 A)) (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat 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_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int X))) N))))) (forall ((A tptp.int) (X tptp.num) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int X))) N))) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.ring_1_of_int_int A)) _let_1)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) _let_1))))) (forall ((A tptp.int) (X tptp.num) (N tptp.nat)) (= (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 A)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real 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_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int X))) N))))) (forall ((A tptp.int) (X tptp.num) (N tptp.nat)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_int_real tptp.ring_1_of_int_real A)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real 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_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int X))) N))))) (forall ((A tptp.int) (X tptp.num) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int X))) N))) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.ring_1_of_int_int A)) _let_1)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) _let_1))))) (forall ((A tptp.int) (X tptp.num) (N tptp.nat)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.ring_18347121197199848620nteger A)) (tptp.power_8256067586552552935nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.numera6620942414471956472nteger 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_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int X))) N))))) (forall ((A tptp.int) (X tptp.num) (N tptp.nat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_int_rat tptp.ring_1_of_int_rat A)) (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat 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_int_int tptp.uminus_uminus_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_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_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real X))) N)) (tptp.aa_int_real tptp.ring_1_of_int_real 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_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int X))) N)) A)))) (forall ((X tptp.num) (N tptp.nat) (A tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int X))) N)))) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.ring_1_of_int_int A))) (tptp.pp (tptp.aa_int_bool _let_1 A))))) (forall ((X tptp.num) (N tptp.nat) (A tptp.int)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.power_8256067586552552935nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.numera6620942414471956472nteger X)) N)) (tptp.ring_18347121197199848620nteger 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_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int X))) N)) A)))) (forall ((X tptp.num) (N tptp.nat) (A tptp.int)) (= (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_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat X))) N)) (tptp.aa_int_rat tptp.ring_1_of_int_rat 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_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int X))) N)) A)))) (forall ((X tptp.rat)) (exists ((Z2 tptp.int)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) (tptp.aa_int_rat tptp.ring_1_of_int_rat Z2))))) (forall ((X tptp.real)) (exists ((Z2 tptp.int)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) (tptp.aa_int_real tptp.ring_1_of_int_real Z2))))) (forall ((X tptp.int) (Y4 tptp.complex)) (let ((_let_1 (tptp.ring_17405671764205052669omplex X))) (= (tptp.aa_complex_complex (tptp.times_times_complex _let_1) Y4) (tptp.aa_complex_complex (tptp.times_times_complex Y4) _let_1)))) (forall ((X tptp.int) (Y4 tptp.real)) (let ((_let_1 (tptp.aa_int_real tptp.ring_1_of_int_real X))) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real _let_1) Y4) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real Y4) _let_1)))) (forall ((X tptp.int) (Y4 tptp.rat)) (let ((_let_1 (tptp.aa_int_rat tptp.ring_1_of_int_rat X))) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat _let_1) Y4) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat Y4) _let_1)))) (forall ((X tptp.int) (Y4 tptp.int)) (let ((_let_1 (tptp.ring_1_of_int_int X))) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int _let_1) Y4) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int Y4) _let_1)))) (forall ((M tptp.int) (X tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_int_real tptp.ring_1_of_int_real M)))) (= (tptp.aa_real_real tptp.cos_real (tptp.aa_real_real _let_1 (tptp.aa_real_real tptp.real_V1803761363581548252l_real X))) (tptp.aa_real_real tptp.real_V1803761363581548252l_real (tptp.aa_real_real tptp.cos_real (tptp.aa_real_real _let_1 X)))))) (forall ((M tptp.int) (X tptp.real)) (= (tptp.cos_complex (tptp.aa_complex_complex (tptp.times_times_complex (tptp.ring_17405671764205052669omplex M)) (tptp.real_V4546457046886955230omplex X))) (tptp.real_V4546457046886955230omplex (tptp.aa_real_real tptp.cos_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_int_real tptp.ring_1_of_int_real M)) X))))) (forall ((M tptp.int) (X tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_int_real tptp.ring_1_of_int_real M)))) (= (tptp.aa_real_real tptp.sin_real (tptp.aa_real_real _let_1 (tptp.aa_real_real tptp.real_V1803761363581548252l_real X))) (tptp.aa_real_real tptp.real_V1803761363581548252l_real (tptp.aa_real_real tptp.sin_real (tptp.aa_real_real _let_1 X)))))) (forall ((M tptp.int) (X tptp.real)) (= (tptp.sin_complex (tptp.aa_complex_complex (tptp.times_times_complex (tptp.ring_17405671764205052669omplex M)) (tptp.real_V4546457046886955230omplex X))) (tptp.real_V4546457046886955230omplex (tptp.aa_real_real tptp.sin_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_int_real tptp.ring_1_of_int_real M)) X))))) (forall ((X tptp.real)) (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_real_int tptp.archim6058952711729229775r_real X))) X))) (forall ((X tptp.rat)) (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 (tptp.aa_rat_int tptp.archim3151403230148437115or_rat X))) X))) (forall ((X tptp.rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) (tptp.aa_int_rat tptp.ring_1_of_int_rat (tptp.aa_rat_int tptp.archim2889992004027027881ng_rat X))))) (forall ((X tptp.real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) (tptp.aa_int_real tptp.ring_1_of_int_real (tptp.aa_real_int tptp.archim7802044766580827645g_real X))))) (forall ((R2 tptp.real)) (= (tptp.real_V4546457046886955230omplex R2) (tptp.complex2 R2 tptp.zero_zero_real))) (forall ((X4 tptp.real)) (= (tptp.real_V4546457046886955230omplex X4) (tptp.complex2 X4 tptp.zero_zero_real))) (forall ((X tptp.real) (Y4 tptp.real) (Xa tptp.real)) (= (= (tptp.complex2 X Y4) (tptp.real_V4546457046886955230omplex Xa)) (and (= X Xa) (= Y4 tptp.zero_zero_real)))) (forall ((R2 tptp.real) (X tptp.real) (Y4 tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.times_times_real R2))) (= (tptp.aa_complex_complex (tptp.times_times_complex (tptp.real_V4546457046886955230omplex R2)) (tptp.complex2 X Y4)) (tptp.complex2 (tptp.aa_real_real _let_1 X) (tptp.aa_real_real _let_1 Y4))))) (forall ((X tptp.real) (Y4 tptp.real) (R2 tptp.real)) (= (tptp.aa_complex_complex (tptp.times_times_complex (tptp.complex2 X Y4)) (tptp.real_V4546457046886955230omplex R2)) (tptp.complex2 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real X) R2) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real Y4) R2)))) (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (tptp.bit_se2923211474154528505it_int N))) (= (tptp.aa_int_int _let_1 (tptp.ring_1_of_int_int K)) (tptp.ring_1_of_int_int (tptp.aa_int_int _let_1 K))))) (forall ((K tptp.int) (L tptp.int)) (= (tptp.ring_1_of_int_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se725231765392027082nd_int K) L)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se725231765392027082nd_int (tptp.ring_1_of_int_int K)) (tptp.ring_1_of_int_int L)))) (forall ((N tptp.nat)) (let ((_let_1 (tptp.aa_nat_int tptp.bit_se2000444600071755411sk_int N))) (= (tptp.ring_1_of_int_int _let_1) _let_1))) (forall ((Y4 tptp.real) (X tptp.real)) (=> (not (= Y4 tptp.zero_zero_real)) (= (tptp.aa_real_real tptp.real_V1803761363581548252l_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real X) Y4)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real tptp.real_V1803761363581548252l_real X)) (tptp.aa_real_real tptp.real_V1803761363581548252l_real Y4))))) (forall ((Y4 tptp.real) (X tptp.real)) (=> (not (= Y4 tptp.zero_zero_real)) (= (tptp.real_V4546457046886955230omplex (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real X) Y4)) (tptp.divide1717551699836669952omplex (tptp.real_V4546457046886955230omplex X) (tptp.real_V4546457046886955230omplex Y4))))) (forall ((Z tptp.int) (X tptp.real)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Z) (tptp.aa_real_int tptp.archim6058952711729229775r_real X))) (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 Z)) X)))) (forall ((Z tptp.int) (X tptp.rat)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Z) (tptp.aa_rat_int tptp.archim3151403230148437115or_rat X))) (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 Z)) X)))) (forall ((X tptp.rat) (Z tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_rat_int tptp.archim2889992004027027881ng_rat X)) Z)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) (tptp.aa_int_rat tptp.ring_1_of_int_rat Z))))) (forall ((X tptp.real) (Z tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_real_int tptp.archim7802044766580827645g_real X)) Z)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) (tptp.aa_int_real tptp.ring_1_of_int_real Z))))) (forall ((X tptp.rat) (A tptp.int)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) (tptp.aa_int_rat tptp.ring_1_of_int_rat A))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_rat_int tptp.archim2889992004027027881ng_rat X)) A)))) (forall ((X tptp.real) (A tptp.int)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) (tptp.aa_int_real tptp.ring_1_of_int_real A))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_real_int tptp.archim7802044766580827645g_real X)) A)))) (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.aa_int_fun_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 ((K tptp.int) (L tptp.int)) (= (tptp.aa_real_int tptp.archim6058952711729229775r_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_int_real tptp.ring_1_of_int_real K)) (tptp.aa_int_real tptp.ring_1_of_int_real L))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int K) L))) (forall ((K tptp.int) (L tptp.int)) (= (tptp.aa_rat_int tptp.archim3151403230148437115or_rat (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_int_rat tptp.ring_1_of_int_rat K)) (tptp.aa_int_rat tptp.ring_1_of_int_rat L))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int K) L))) (forall ((X tptp.real) (N tptp.nat)) (let ((_let_1 (tptp.aa_real_int tptp.archim6058952711729229775r_real X))) (=> (= X (tptp.aa_int_real tptp.ring_1_of_int_real _let_1)) (= (tptp.aa_real_int tptp.archim6058952711729229775r_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) N)) (tptp.aa_nat_int (tptp.power_power_int _let_1) N))))) (forall ((X tptp.rat) (N tptp.nat)) (let ((_let_1 (tptp.aa_rat_int tptp.archim3151403230148437115or_rat X))) (=> (= X (tptp.aa_int_rat tptp.ring_1_of_int_rat _let_1)) (= (tptp.aa_rat_int tptp.archim3151403230148437115or_rat (tptp.aa_nat_rat (tptp.power_power_rat X) N)) (tptp.aa_nat_int (tptp.power_power_int _let_1) N))))) (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.aa_int_fun_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 ((X tptp.real) (Y4 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) Y4)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y4) 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 Y4)) (tptp.aa_real_real tptp.arccos X))))))) (forall ((X tptp.real) (Y4 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 Y4)) tptp.one_one_real))) (= (= (tptp.aa_real_real tptp.arccos X) (tptp.aa_real_real tptp.arccos Y4)) (= X Y4)))) (forall ((X tptp.real) (Y4 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 Y4)) 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 Y4))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y4) X)))))) (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_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_int_rat tptp.ring_1_of_int_rat Z))))) (forall ((Z 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 (tptp.ring_1_of_int_int 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_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_int_real tptp.ring_1_of_int_real Z))))) (forall ((N tptp.int) (X tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.abs_abs_Code_integer (tptp.ring_18347121197199848620nteger N))) X)) (or (= N tptp.zero_zero_int) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) X))))) (forall ((N tptp.int) (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.abs_abs_rat (tptp.aa_int_rat tptp.ring_1_of_int_rat N))) X)) (or (= N tptp.zero_zero_int) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.one_one_rat) X))))) (forall ((N tptp.int) (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.abs_abs_int (tptp.ring_1_of_int_int N))) X)) (or (= N 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) X))))) (forall ((N tptp.int) (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_int_real tptp.ring_1_of_int_real N))) X)) (or (= N tptp.zero_zero_int) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.one_one_real) X))))) (forall ((Z 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_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) (tptp.aa_int_real tptp.ring_1_of_int_real Z))))) (forall ((Z 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_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) (tptp.aa_int_rat tptp.ring_1_of_int_rat Z))))) (forall ((Z 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 Z)) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.ring_1_of_int_int Z)))))) (forall ((N tptp.int) (X tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.abs_abs_Code_integer (tptp.ring_18347121197199848620nteger N))) X)) (or (= N tptp.zero_zero_int) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) X))))) (forall ((N tptp.int) (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 (tptp.aa_int_real tptp.ring_1_of_int_real N))) X)) (or (= N tptp.zero_zero_int) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real) X))))) (forall ((N tptp.int) (X 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_int_rat tptp.ring_1_of_int_rat N))) X)) (or (= N tptp.zero_zero_int) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.one_one_rat) X))))) (forall ((N tptp.int) (X 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.ring_1_of_int_int N))) X)) (or (= N tptp.zero_zero_int) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.one_one_int) X))))) (forall ((X tptp.rat)) (exists ((X3 tptp.int)) (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 X3)) X)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) (tptp.aa_int_rat tptp.ring_1_of_int_rat (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int X3) tptp.one_one_int)))) (forall ((Y3 tptp.int)) (=> (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 Y3)) X)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) (tptp.aa_int_rat tptp.ring_1_of_int_rat (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int Y3) tptp.one_one_int))))) (= Y3 X3)))))) (forall ((X tptp.real)) (exists ((X3 tptp.int)) (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 X3)) X)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) (tptp.aa_int_real tptp.ring_1_of_int_real (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int X3) tptp.one_one_int)))) (forall ((Y3 tptp.int)) (=> (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 Y3)) X)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) (tptp.aa_int_real tptp.ring_1_of_int_real (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int Y3) tptp.one_one_int))))) (= Y3 X3)))))) (forall ((X tptp.rat)) (exists ((Z2 tptp.int)) (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 Z2)) X)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) (tptp.aa_int_rat tptp.ring_1_of_int_rat (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int Z2) tptp.one_one_int))))))) (forall ((X tptp.real)) (exists ((Z2 tptp.int)) (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 Z2)) X)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) (tptp.aa_int_real tptp.ring_1_of_int_real (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int Z2) tptp.one_one_int))))))) (forall ((R2 tptp.rat)) (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 (tptp.aa_rat_int tptp.archim2889992004027027881ng_rat R2))) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat R2) tptp.one_one_rat)))) (forall ((R2 tptp.real)) (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_real_int tptp.archim7802044766580827645g_real R2))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real R2) tptp.one_one_real)))) (forall ((K tptp.num)) (= (tptp.aa_int_real tptp.ring_1_of_int_real (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int K))) (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real K)))) (forall ((K tptp.num)) (let ((_let_1 (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int K)))) (= (tptp.ring_1_of_int_int _let_1) _let_1))) (forall ((K tptp.num)) (= (tptp.ring_17405671764205052669omplex (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int K))) (tptp.uminus1482373934393186551omplex (tptp.numera6690914467698888265omplex K)))) (forall ((K tptp.num)) (= (tptp.ring_18347121197199848620nteger (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int K))) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.numera6620942414471956472nteger K)))) (forall ((K tptp.num)) (= (tptp.aa_int_rat tptp.ring_1_of_int_rat (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int K))) (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat K)))) (forall ((R2 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_int_rat tptp.ring_1_of_int_rat (tptp.aa_rat_int tptp.archim2889992004027027881ng_rat R2))) tptp.one_one_rat)) R2))) (forall ((R2 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_int_real tptp.ring_1_of_int_real (tptp.aa_real_int tptp.archim7802044766580827645g_real R2))) tptp.one_one_real)) R2))) (forall ((N tptp.nat) (X tptp.int)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N)) (tptp.aa_int_real tptp.ring_1_of_int_real X))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N)) X)))) (forall ((N tptp.nat) (X tptp.int)) (= (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_int_rat tptp.ring_1_of_int_rat X))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N)) X)))) (forall ((N tptp.nat) (X tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N)))) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.ring_1_of_int_int X))) (tptp.pp (tptp.aa_int_bool _let_1 X))))) (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 ((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 ((A tptp.int) (B tptp.int)) (= (tptp.aa_real_int tptp.archim7802044766580827645g_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_int_real tptp.ring_1_of_int_real A)) (tptp.aa_int_real tptp.ring_1_of_int_real B))) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int (tptp.aa_int_int tptp.uminus_uminus_int A)) B)))) (forall ((A tptp.int) (B tptp.int)) (= (tptp.aa_rat_int tptp.archim2889992004027027881ng_rat (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_int_rat tptp.ring_1_of_int_rat A)) (tptp.aa_int_rat tptp.ring_1_of_int_rat B))) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int (tptp.aa_int_int tptp.uminus_uminus_int A)) B)))) (forall ((X tptp.real)) (= (= (tptp.aa_real_real tptp.sin_real X) tptp.zero_zero_real) (exists ((I2 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 I2)) tptp.pi))))) (forall ((Theta tptp.real)) (not (forall ((K2 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 K2)) (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.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.aa_int_fun_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.modulo_modulo_int X D))) _let_1))))) (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 ((R2 tptp.real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real R2) (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 R2))) tptp.one_one_real)))) (forall ((R2 tptp.real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real R2) (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 R2))) tptp.one_one_real)))) (forall ((R2 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 R2) tptp.one_one_real)) (tptp.aa_int_real tptp.ring_1_of_int_real (tptp.aa_real_int tptp.archim6058952711729229775r_real R2))))) (forall ((R2 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 R2) tptp.one_one_real)) (tptp.aa_int_real tptp.ring_1_of_int_real (tptp.aa_real_int tptp.archim6058952711729229775r_real R2))))) (forall ((Y4 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)) Y4)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y4) 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 Y4)))))) (forall ((X tptp.real) (Y4 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) Y4)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y4) tptp.one_one_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.arccos Y4)) (tptp.aa_real_real tptp.arccos X))))))) (forall ((X tptp.real) (Y4 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 Y4)) 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 Y4))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y4) X)))))) (forall ((Y4 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)) Y4)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y4) 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 Y4)) 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 ((P tptp.fun_int_bool) (T tptp.real)) (= (tptp.pp (tptp.aa_int_bool P (tptp.aa_real_int tptp.archim6058952711729229775r_real T))) (forall ((I2 tptp.int)) (let ((_let_1 (tptp.aa_int_real tptp.ring_1_of_int_real I2))) (=> (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real _let_1) T)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real T) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real _let_1) tptp.one_one_real)))) (tptp.pp (tptp.aa_int_bool P I2))))))) (forall ((P tptp.fun_int_bool) (T tptp.rat)) (= (tptp.pp (tptp.aa_int_bool P (tptp.aa_rat_int tptp.archim3151403230148437115or_rat T))) (forall ((I2 tptp.int)) (let ((_let_1 (tptp.aa_int_rat tptp.ring_1_of_int_rat I2))) (=> (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat _let_1) T)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat T) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat _let_1) tptp.one_one_rat)))) (tptp.pp (tptp.aa_int_bool P I2))))))) (forall ((X tptp.real) (A tptp.int)) (let ((_let_1 (tptp.aa_int_real tptp.ring_1_of_int_real A))) (= (= (tptp.aa_real_int tptp.archim6058952711729229775r_real X) A) (and (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))))))) (forall ((X tptp.rat) (A tptp.int)) (let ((_let_1 (tptp.aa_int_rat tptp.ring_1_of_int_rat A))) (= (= (tptp.aa_rat_int tptp.archim3151403230148437115or_rat X) A) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat _let_1) 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 _let_1) tptp.one_one_rat))))))) (forall ((Z tptp.int) (X tptp.real)) (let ((_let_1 (tptp.aa_int_real tptp.ring_1_of_int_real Z))) (=> (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) Z))))) (forall ((Z tptp.int) (X tptp.rat)) (let ((_let_1 (tptp.aa_int_rat tptp.ring_1_of_int_rat Z))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat _let_1) 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 _let_1) tptp.one_one_rat))) (= (tptp.aa_rat_int tptp.archim3151403230148437115or_rat X) Z))))) (forall ((Y4 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 Y4)) tptp.one_one_real)) (= (tptp.aa_real_real tptp.cos_real (tptp.aa_real_real tptp.arccos Y4)) Y4))) (forall ((B 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.real_V7735802525324610683m_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real tptp.real_V1803761363581548252l_real B)) (tptp.aa_real_real tptp.real_V1803761363581548252l_real A)))) (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real B) A))))) (forall ((B tptp.real) (A 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.minus_minus_complex (tptp.real_V4546457046886955230omplex B) (tptp.real_V4546457046886955230omplex A)))) (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real B) A))))) (forall ((P tptp.fun_int_bool) (T tptp.rat)) (= (tptp.pp (tptp.aa_int_bool P (tptp.aa_rat_int tptp.archim2889992004027027881ng_rat T))) (forall ((I2 tptp.int)) (let ((_let_1 (tptp.aa_int_rat tptp.ring_1_of_int_rat I2))) (=> (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 _let_1) tptp.one_one_rat)) T)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat T) _let_1))) (tptp.pp (tptp.aa_int_bool P I2))))))) (forall ((P tptp.fun_int_bool) (T tptp.real)) (= (tptp.pp (tptp.aa_int_bool P (tptp.aa_real_int tptp.archim7802044766580827645g_real T))) (forall ((I2 tptp.int)) (let ((_let_1 (tptp.aa_int_real tptp.ring_1_of_int_real I2))) (=> (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 _let_1) tptp.one_one_real)) T)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real T) _let_1))) (tptp.pp (tptp.aa_int_bool P I2))))))) (forall ((X tptp.rat) (A tptp.int)) (let ((_let_1 (tptp.aa_int_rat tptp.ring_1_of_int_rat A))) (= (= (tptp.aa_rat_int tptp.archim2889992004027027881ng_rat X) A) (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 _let_1) tptp.one_one_rat)) X)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) _let_1)))))) (forall ((X tptp.real) (A tptp.int)) (let ((_let_1 (tptp.aa_int_real tptp.ring_1_of_int_real A))) (= (= (tptp.aa_real_int tptp.archim7802044766580827645g_real X) A) (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 _let_1) tptp.one_one_real)) X)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) _let_1)))))) (forall ((Z tptp.int) (X tptp.rat)) (let ((_let_1 (tptp.aa_int_rat tptp.ring_1_of_int_rat Z))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.minus_minus_rat _let_1) tptp.one_one_rat)) X)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) _let_1)) (= (tptp.aa_rat_int tptp.archim2889992004027027881ng_rat X) Z))))) (forall ((Z tptp.int) (X tptp.real)) (let ((_let_1 (tptp.aa_int_real tptp.ring_1_of_int_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.minus_minus_real _let_1) tptp.one_one_real)) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) _let_1)) (= (tptp.aa_real_int tptp.archim7802044766580827645g_real X) Z))))) (forall ((X tptp.rat)) (let ((_let_1 (tptp.aa_int_rat tptp.ring_1_of_int_rat (tptp.aa_rat_int tptp.archim2889992004027027881ng_rat X)))) (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 _let_1) tptp.one_one_rat)) X)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) _let_1))))) (forall ((X tptp.real)) (let ((_let_1 (tptp.aa_int_real tptp.ring_1_of_int_real (tptp.aa_real_int tptp.archim7802044766580827645g_real X)))) (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 _let_1) tptp.one_one_real)) X)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) _let_1))))) (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 ((Z tptp.int) (X tptp.real)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Z) (tptp.aa_real_int tptp.archim6058952711729229775r_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_int_real tptp.ring_1_of_int_real Z)) tptp.one_one_real)) X)))) (forall ((Z tptp.int) (X tptp.rat)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Z) (tptp.aa_rat_int tptp.archim3151403230148437115or_rat X))) (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_int_rat tptp.ring_1_of_int_rat Z)) tptp.one_one_rat)) X)))) (forall ((X tptp.real) (Z tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_real_int tptp.archim6058952711729229775r_real X)) Z)) (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 (tptp.aa_int_real tptp.ring_1_of_int_real Z)) tptp.one_one_real))))) (forall ((X tptp.rat) (Z tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_rat_int tptp.archim3151403230148437115or_rat X)) Z)) (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 (tptp.aa_int_rat tptp.ring_1_of_int_rat Z)) tptp.one_one_rat))))) (forall ((X tptp.rat) (Z tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_rat_int tptp.archim2889992004027027881ng_rat X)) Z)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_int_rat tptp.ring_1_of_int_rat Z)) tptp.one_one_rat))))) (forall ((X tptp.real) (Z tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_real_int tptp.archim7802044766580827645g_real X)) Z)) (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.minus_minus_real (tptp.aa_int_real tptp.ring_1_of_int_real Z)) tptp.one_one_real))))) (forall ((Z tptp.int) (X tptp.rat)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Z) (tptp.aa_rat_int tptp.archim2889992004027027881ng_rat X))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_int_rat tptp.ring_1_of_int_rat Z)) tptp.one_one_rat)) X)))) (forall ((Z tptp.int) (X tptp.real)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Z) (tptp.aa_real_int tptp.archim7802044766580827645g_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.minus_minus_real (tptp.aa_int_real tptp.ring_1_of_int_real Z)) tptp.one_one_real)) X)))) (forall ((X tptp.real)) (let ((_let_1 (tptp.aa_real_int tptp.archim6058952711729229775r_real X))) (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 _let_1)) X)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) (tptp.aa_int_real tptp.ring_1_of_int_real (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int _let_1) tptp.one_one_int))))))) (forall ((X tptp.rat)) (let ((_let_1 (tptp.aa_rat_int tptp.archim3151403230148437115or_rat X))) (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)) X)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) (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 ((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.aa_int_fun_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.aa_int_fun_int_int tptp.divide_divide_int N) X)))) tptp.one_one_real))) (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 ((B 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) B)) (= (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 B))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int (tptp.aa_real_int tptp.archim6058952711729229775r_real A)) B)))) (forall ((Q2 tptp.real) (P3 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) Q2)) (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_int_real tptp.ring_1_of_int_real (tptp.aa_real_int tptp.archim6058952711729229775r_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real P3) Q2)))) Q2)) P3)))) (forall ((Q2 tptp.rat) (P3 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) Q2)) (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_int_rat tptp.ring_1_of_int_rat (tptp.aa_rat_int tptp.archim3151403230148437115or_rat (tptp.aa_rat_rat (tptp.divide_divide_rat P3) Q2)))) Q2)) P3)))) (forall ((Q2 tptp.rat) (P3 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) Q2)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat P3) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_int_rat tptp.ring_1_of_int_rat (tptp.aa_rat_int tptp.archim2889992004027027881ng_rat (tptp.aa_rat_rat (tptp.divide_divide_rat P3) Q2)))) Q2))))) (forall ((Q2 tptp.real) (P3 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) Q2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real P3) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_int_real tptp.ring_1_of_int_real (tptp.aa_real_int tptp.archim7802044766580827645g_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real P3) Q2)))) Q2))))) (forall ((Y4 tptp.real)) (let ((_let_1 (tptp.aa_real_real tptp.arccos Y4))) (=> (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)) Y4)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y4) 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 ((K tptp.int)) (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.numera6620942414471956472nteger _let_1)) (tptp.ring_18347121197199848620nteger 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 ((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.ring_1_of_int_int K))) (tptp.pp (tptp.aa_int_bool _let_1 K))))) (forall ((Y4 tptp.real)) (let ((_let_1 (tptp.aa_real_real tptp.arccos Y4))) (=> (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)) Y4)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y4) 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 ((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 ((K tptp.int)) (let ((_let_1 (tptp.ring_18347121197199848620nteger K))) (let ((_let_2 (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int K) tptp.zero_zero_int)))) (and (=> _let_2 (= _let_1 (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.semiri4939895301339042750nteger (tptp.aa_int_nat tptp.nat2 (tptp.aa_int_int tptp.uminus_uminus_int K)))))) (=> (not _let_2) (= _let_1 (tptp.semiri4939895301339042750nteger (tptp.aa_int_nat tptp.nat2 K)))))))) (forall ((K tptp.int)) (let ((_let_1 (tptp.ring_17405671764205052669omplex K))) (let ((_let_2 (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int K) tptp.zero_zero_int)))) (and (=> _let_2 (= _let_1 (tptp.uminus1482373934393186551omplex (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex (tptp.aa_int_nat tptp.nat2 (tptp.aa_int_int tptp.uminus_uminus_int K)))))) (=> (not _let_2) (= _let_1 (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex (tptp.aa_int_nat tptp.nat2 K)))))))) (forall ((K tptp.int)) (let ((_let_1 (tptp.aa_int_real tptp.ring_1_of_int_real K))) (let ((_let_2 (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int K) tptp.zero_zero_int)))) (and (=> _let_2 (= _let_1 (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real (tptp.aa_int_nat tptp.nat2 (tptp.aa_int_int tptp.uminus_uminus_int K)))))) (=> (not _let_2) (= _let_1 (tptp.aa_nat_real tptp.semiri5074537144036343181t_real (tptp.aa_int_nat tptp.nat2 K)))))))) (forall ((K tptp.int)) (let ((_let_1 (tptp.aa_int_rat tptp.ring_1_of_int_rat K))) (let ((_let_2 (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int K) tptp.zero_zero_int)))) (and (=> _let_2 (= _let_1 (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat (tptp.aa_int_nat tptp.nat2 (tptp.aa_int_int tptp.uminus_uminus_int K)))))) (=> (not _let_2) (= _let_1 (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat (tptp.aa_int_nat tptp.nat2 K)))))))) (forall ((K tptp.int)) (let ((_let_1 (tptp.ring_1_of_int_int K))) (let ((_let_2 (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int K) tptp.zero_zero_int)))) (and (=> _let_2 (= _let_1 (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_int_nat tptp.nat2 (tptp.aa_int_int tptp.uminus_uminus_int K)))))) (=> (not _let_2) (= _let_1 (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_int_nat tptp.nat2 K)))))))) (forall ((Q2 tptp.real) (P3 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) Q2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real P3) (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_int_real tptp.ring_1_of_int_real (tptp.aa_real_int tptp.archim6058952711729229775r_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real P3) Q2)))) tptp.one_one_real)) Q2))))) (forall ((Q2 tptp.rat) (P3 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) Q2)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat P3) (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 (tptp.aa_int_rat tptp.ring_1_of_int_rat (tptp.aa_rat_int tptp.archim3151403230148437115or_rat (tptp.aa_rat_rat (tptp.divide_divide_rat P3) Q2)))) tptp.one_one_rat)) Q2))))) (forall ((Q2 tptp.real) (P3 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) Q2)) (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 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_int_real tptp.ring_1_of_int_real (tptp.aa_real_int tptp.archim7802044766580827645g_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real P3) Q2)))) tptp.one_one_real)) Q2)) P3)))) (forall ((Q2 tptp.rat) (P3 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) Q2)) (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 (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_int_rat tptp.ring_1_of_int_rat (tptp.aa_rat_int tptp.archim2889992004027027881ng_rat (tptp.aa_rat_rat (tptp.divide_divide_rat P3) Q2)))) tptp.one_one_rat)) Q2)) P3)))) (forall ((N tptp.int) (X tptp.rat)) (let ((_let_1 (tptp.aa_int_rat tptp.ring_1_of_int_rat N))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat _let_1) 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 _let_1) tptp.one_one_rat))) (= (tptp.aa_rat_int tptp.archim2889992004027027881ng_rat X) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int N) tptp.one_one_int)))))) (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_eq_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.archim7802044766580827645g_real X) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int N) tptp.one_one_int)))))) (forall ((X tptp.real)) (= (= (tptp.aa_real_real tptp.cos_real X) tptp.one_one_real) (exists ((X5 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 X5)) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))) tptp.pi))))) (forall ((Y4 tptp.real)) (let ((_let_1 (tptp.aa_real_real tptp.arccos Y4))) (=> (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)) Y4)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y4) 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) Y4)))))) (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 ((X tptp.real)) (= (tptp.aa_real_real tptp.sin_real X) (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.divide_divide_real (tptp.aa_real_real tptp.real_V1803761363581548252l_real tptp.pi)) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))) X)))) (forall ((X tptp.complex)) (= (tptp.sin_complex X) (tptp.cos_complex (tptp.minus_minus_complex (tptp.divide1717551699836669952omplex (tptp.real_V4546457046886955230omplex tptp.pi) (tptp.numera6690914467698888265omplex (tptp.aa_num_num tptp.bit0 tptp.one))) X)))) (forall ((X tptp.real)) (= (tptp.aa_real_real tptp.cos_real X) (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.divide_divide_real (tptp.aa_real_real tptp.real_V1803761363581548252l_real tptp.pi)) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))) X)))) (forall ((X tptp.complex)) (= (tptp.cos_complex X) (tptp.sin_complex (tptp.minus_minus_complex (tptp.divide1717551699836669952omplex (tptp.real_V4546457046886955230omplex tptp.pi) (tptp.numera6690914467698888265omplex (tptp.aa_num_num tptp.bit0 tptp.one))) X)))) (forall ((X tptp.real)) (= (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_real_real tptp.sin_real X)) (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.divide_divide_real (tptp.aa_real_real tptp.real_V1803761363581548252l_real tptp.pi)) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))))))) (forall ((X tptp.complex)) (= (tptp.uminus1482373934393186551omplex (tptp.sin_complex X)) (tptp.cos_complex (tptp.plus_plus_complex X (tptp.divide1717551699836669952omplex (tptp.real_V4546457046886955230omplex tptp.pi) (tptp.numera6690914467698888265omplex (tptp.aa_num_num tptp.bit0 tptp.one))))))) (forall ((Y4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) Y4)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y4) 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 Y4)) (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 ((X tptp.real) (B tptp.real) (K tptp.int)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.powr_real B))) (=> (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) B)) (= (= (tptp.aa_real_int tptp.archim6058952711729229775r_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.log B) 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)) (= (= (tptp.aa_real_real tptp.cos_real X) tptp.zero_zero_real) (exists ((I2 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)) I2))) (= X (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_int_real tptp.ring_1_of_int_real I2)) (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 ((I2 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)) I2)) (= X (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_int_real tptp.ring_1_of_int_real I2)) (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) (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 ((X tptp.rat) (Y4 tptp.int)) (let ((_let_1 (tptp.aa_rat_rat (tptp.divide_divide_rat tptp.one_one_rat) (tptp.aa_num_rat tptp.numeral_numeral_rat (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_2 (tptp.aa_int_rat tptp.ring_1_of_int_rat Y4))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.minus_minus_rat X) _let_1)) _let_2)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat _let_2) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat X) _let_1))) (= (tptp.aa_rat_int tptp.archim7778729529865785530nd_rat X) Y4)))))) (forall ((X tptp.real) (Y4 tptp.int)) (let ((_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 (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_2 (tptp.aa_int_real tptp.ring_1_of_int_real Y4))) (=> (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 X) _let_1)) _let_2)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real _let_2) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) _let_1))) (= (tptp.aa_real_int tptp.archim8280529875227126926d_real X) Y4)))))) (forall ((X tptp.real) (N tptp.int)) (=> (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) (tptp.aa_int_real tptp.ring_1_of_int_real N)))) (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_int tptp.archim8280529875227126926d_real X) N))) (forall ((X tptp.rat) (N tptp.int)) (=> (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) (tptp.aa_int_rat tptp.ring_1_of_int_rat N)))) (tptp.aa_rat_rat (tptp.divide_divide_rat tptp.one_one_rat) (tptp.aa_num_rat tptp.numeral_numeral_rat (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.aa_rat_int tptp.archim7778729529865785530nd_rat X) N))) (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.abs_abs_rat (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_int_rat tptp.ring_1_of_int_rat (tptp.aa_rat_int tptp.archim7778729529865785530nd_rat X))) X))) (tptp.aa_rat_rat (tptp.divide_divide_rat tptp.one_one_rat) (tptp.aa_num_rat tptp.numeral_numeral_rat (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.abs_abs_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_int_real tptp.ring_1_of_int_real (tptp.aa_real_int tptp.archim8280529875227126926d_real X))) 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)))))) (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.minus_minus_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_int_real tptp.ring_1_of_int_real (tptp.aa_real_int tptp.archim8280529875227126926d_real X))))) (forall ((X 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 X) (tptp.aa_rat_rat (tptp.divide_divide_rat tptp.one_one_rat) (tptp.aa_num_rat tptp.numeral_numeral_rat (tptp.aa_num_num tptp.bit0 tptp.one))))) (tptp.aa_int_rat tptp.ring_1_of_int_rat (tptp.aa_rat_int tptp.archim7778729529865785530nd_rat X))))) (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.minus_minus_rat X) (tptp.aa_rat_rat (tptp.divide_divide_rat tptp.one_one_rat) (tptp.aa_num_rat tptp.numeral_numeral_rat (tptp.aa_num_num tptp.bit0 tptp.one))))) (tptp.aa_int_rat tptp.ring_1_of_int_rat (tptp.aa_rat_int tptp.archim7778729529865785530nd_rat 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.minus_minus_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_int_real tptp.ring_1_of_int_real (tptp.aa_real_int tptp.archim8280529875227126926d_real X))))) (= (tptp.aa_real_int tptp.archim8280529875227126926d_real tptp.zero_zero_real) tptp.zero_zero_int) (= (tptp.aa_rat_int tptp.archim7778729529865785530nd_rat tptp.zero_zero_rat) tptp.zero_zero_int) (forall ((N tptp.num)) (= (tptp.aa_real_int tptp.archim8280529875227126926d_real (tptp.aa_num_real tptp.numeral_numeral_real N)) (tptp.aa_num_int tptp.numeral_numeral_int N))) (forall ((N tptp.num)) (= (tptp.aa_rat_int tptp.archim7778729529865785530nd_rat (tptp.aa_num_rat tptp.numeral_numeral_rat N)) (tptp.aa_num_int tptp.numeral_numeral_int N))) (forall ((N tptp.nat)) (= (tptp.aa_real_int tptp.archim8280529875227126926d_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N)) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N))) (forall ((N tptp.nat)) (= (tptp.aa_rat_int tptp.archim7778729529865785530nd_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat N)) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N))) (forall ((N tptp.num)) (= (tptp.aa_real_int tptp.archim8280529875227126926d_real (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real N))) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int N)))) (forall ((N tptp.num)) (= (tptp.aa_rat_int tptp.archim7778729529865785530nd_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat N))) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int N)))) (forall ((X tptp.rat) (Y4 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) Y4)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_rat_int tptp.archim7778729529865785530nd_rat X)) (tptp.aa_rat_int tptp.archim7778729529865785530nd_rat Y4))))) (forall ((X tptp.real) (Y4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) Y4)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_real_int tptp.archim8280529875227126926d_real X)) (tptp.aa_real_int tptp.archim8280529875227126926d_real Y4))))) (forall ((X tptp.real)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_real_int tptp.archim6058952711729229775r_real X)) (tptp.aa_real_int tptp.archim8280529875227126926d_real X)))) (forall ((X tptp.rat)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_rat_int tptp.archim3151403230148437115or_rat X)) (tptp.aa_rat_int tptp.archim7778729529865785530nd_rat X)))) (forall ((X tptp.real)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_real_int tptp.archim8280529875227126926d_real X)) (tptp.aa_real_int tptp.archim7802044766580827645g_real X)))) (forall ((Z tptp.rat) (M tptp.int)) (let ((_let_1 (tptp.minus_minus_rat Z))) (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 _let_1 (tptp.aa_int_rat tptp.ring_1_of_int_rat (tptp.aa_rat_int tptp.archim7778729529865785530nd_rat Z))))) (tptp.aa_rat_rat tptp.abs_abs_rat (tptp.aa_rat_rat _let_1 (tptp.aa_int_rat tptp.ring_1_of_int_rat M))))))) (forall ((Z tptp.real) (M tptp.int)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real Z))) (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 _let_1 (tptp.aa_int_real tptp.ring_1_of_int_real (tptp.aa_real_int tptp.archim8280529875227126926d_real Z))))) (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_real_real _let_1 (tptp.aa_int_real tptp.ring_1_of_int_real M))))))) (forall ((X tptp.real)) (= (tptp.aa_real_int tptp.archim8280529875227126926d_real X) (tptp.aa_real_int tptp.archim6058952711729229775r_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 tptp.one_one_real) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))))))) (forall ((X tptp.rat)) (= (tptp.aa_rat_int tptp.archim7778729529865785530nd_rat X) (tptp.aa_rat_int tptp.archim3151403230148437115or_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat X) (tptp.aa_rat_rat (tptp.divide_divide_rat tptp.one_one_rat) (tptp.aa_num_rat tptp.numeral_numeral_rat (tptp.aa_num_num tptp.bit0 tptp.one))))))) (forall ((X tptp.rat)) (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 (tptp.aa_rat_int tptp.archim7778729529865785530nd_rat X))) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat X) (tptp.aa_rat_rat (tptp.divide_divide_rat tptp.one_one_rat) (tptp.aa_num_rat tptp.numeral_numeral_rat (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_int_real tptp.ring_1_of_int_real (tptp.aa_real_int tptp.archim8280529875227126926d_real X))) (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 tptp.one_one_real) (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_int tptp.archim8280529875227126926d_real X))) (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.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.archim2898591450579166408c_real X))))) (and (=> _let_2 (= _let_1 (tptp.aa_real_int tptp.archim7802044766580827645g_real X))) (=> (not _let_2) (= _let_1 (tptp.aa_real_int tptp.archim6058952711729229775r_real X))))))) (forall ((X tptp.rat)) (let ((_let_1 (tptp.aa_rat_int tptp.archim7778729529865785530nd_rat X))) (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.divide_divide_rat tptp.one_one_rat) (tptp.aa_num_rat tptp.numeral_numeral_rat (tptp.aa_num_num tptp.bit0 tptp.one)))) (tptp.aa_rat_rat tptp.archimedean_frac_rat X))))) (and (=> _let_2 (= _let_1 (tptp.aa_rat_int tptp.archim2889992004027027881ng_rat X))) (=> (not _let_2) (= _let_1 (tptp.aa_rat_int tptp.archim3151403230148437115or_rat X))))))) (= (tptp.exp_complex (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_complex_complex (tptp.times_times_complex _let_76) _let_77)) tptp.imaginary_unit)) tptp.one_one_complex) (= (tptp.exp_complex (tptp.aa_complex_complex (tptp.times_times_complex tptp.imaginary_unit) (tptp.aa_complex_complex (tptp.times_times_complex _let_77) _let_76))) tptp.one_one_complex) (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 ((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.cot_complex tptp.zero_zero_complex) tptp.zero_zero_complex) (= (tptp.aa_real_real tptp.cot_real tptp.zero_zero_real) tptp.zero_zero_real) (forall ((Z tptp.int)) (= (tptp.aa_real_real tptp.archim2898591450579166408c_real (tptp.aa_int_real tptp.ring_1_of_int_real Z)) tptp.zero_zero_real)) (forall ((Z tptp.int)) (= (tptp.aa_rat_rat tptp.archimedean_frac_rat (tptp.aa_int_rat tptp.ring_1_of_int_rat Z)) tptp.zero_zero_rat)) (= (tptp.aa_real_real tptp.cot_real tptp.pi) tptp.zero_zero_real) (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)) (= (tptp.aa_nat_complex (tptp.power_power_complex tptp.imaginary_unit) _let_2) _let_75) (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.uminus1482373934393186551omplex tptp.one_one_complex)) N))) (not (= tptp.imaginary_unit tptp.zero_zero_complex)) (forall ((X 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.archimedean_frac_rat 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.archim2898591450579166408c_real X)))) (= tptp.imaginary_unit (tptp.complex2 tptp.zero_zero_real tptp.one_one_real)) (forall ((X tptp.real) (Y4 tptp.real)) (= (= (tptp.complex2 X Y4) tptp.imaginary_unit) (and (= X tptp.zero_zero_real) (= Y4 tptp.one_one_real)))) (forall ((X tptp.real)) (= (tptp.aa_real_real tptp.archim2898591450579166408c_real X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real X) (tptp.aa_int_real tptp.ring_1_of_int_real (tptp.aa_real_int tptp.archim6058952711729229775r_real X))))) (forall ((X tptp.rat)) (= (tptp.aa_rat_rat tptp.archimedean_frac_rat X) (tptp.aa_rat_rat (tptp.minus_minus_rat X) (tptp.aa_int_rat tptp.ring_1_of_int_rat (tptp.aa_rat_int tptp.archim3151403230148437115or_rat X))))) (forall ((X4 tptp.complex)) (= (tptp.cot_complex X4) (tptp.divide1717551699836669952omplex (tptp.cos_complex X4) (tptp.sin_complex X4)))) (forall ((X4 tptp.real)) (= (tptp.aa_real_real tptp.cot_real X4) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real tptp.cos_real X4)) (tptp.aa_real_real tptp.sin_real X4)))) (forall ((R2 tptp.real)) (= (tptp.aa_complex_complex (tptp.times_times_complex (tptp.real_V4546457046886955230omplex R2)) tptp.imaginary_unit) (tptp.complex2 tptp.zero_zero_real R2))) (forall ((R2 tptp.real)) (= (tptp.aa_complex_complex (tptp.times_times_complex tptp.imaginary_unit) (tptp.real_V4546457046886955230omplex R2)) (tptp.complex2 tptp.zero_zero_real R2))) (forall ((X tptp.rat)) (= (= (tptp.aa_rat_rat tptp.archimedean_frac_rat X) X) (and (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) tptp.one_one_rat))))) (forall ((X tptp.real)) (= (= (tptp.aa_real_real tptp.archim2898591450579166408c_real X) X) (and (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))))) (forall ((X tptp.real) (Y4 tptp.real)) (let ((_let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real tptp.archim2898591450579166408c_real X)) (tptp.aa_real_real tptp.archim2898591450579166408c_real Y4)))) (let ((_let_2 (tptp.aa_real_real tptp.archim2898591450579166408c_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) Y4)))) (let ((_let_3 (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real _let_1) tptp.one_one_real)))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real _let_1) tptp.one_one_real)))))))) (forall ((X tptp.rat) (Y4 tptp.rat)) (let ((_let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat tptp.archimedean_frac_rat X)) (tptp.aa_rat_rat tptp.archimedean_frac_rat Y4)))) (let ((_let_2 (tptp.aa_rat_rat tptp.archimedean_frac_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat X) Y4)))) (let ((_let_3 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat _let_1) tptp.one_one_rat)))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (tptp.aa_rat_rat (tptp.minus_minus_rat _let_1) tptp.one_one_rat)))))))) (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_73) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.pi)) _let_40)) (= (tptp.csqrt tptp.imaginary_unit) (tptp.divide1717551699836669952omplex (tptp.plus_plus_complex tptp.one_one_complex tptp.imaginary_unit) (tptp.real_V4546457046886955230omplex _let_74))) (= (tptp.aa_complex_real tptp.arg tptp.imaginary_unit) _let_42) (= (tptp.cis _let_45) _let_73) (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.bit_se1146084159140164899it_int K) N))))))) (forall ((Z tptp.complex)) (= (= (tptp.csqrt Z) tptp.zero_zero_complex) (= Z tptp.zero_zero_complex))) (= (tptp.csqrt tptp.zero_zero_complex) tptp.zero_zero_complex) (= (tptp.cis tptp.zero_zero_real) tptp.one_one_complex) (forall ((M tptp.num) (N tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.bit_se1146084159140164899it_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 M))) (tptp.aa_nat_nat tptp.suc N))) (tptp.pp (tptp.aa_nat_bool (tptp.bit_se1146084159140164899it_int (tptp.aa_num_int tptp.numeral_numeral_int M)) N)))) (forall ((M tptp.num) (N tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.bit_se1148574629649215175it_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 M))) (tptp.aa_nat_nat tptp.suc N))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.bit_se1148574629649215175it_nat (tptp.aa_num_nat tptp.numeral_numeral_nat M)) N)))) (forall ((M tptp.num) (N tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.bit_se1146084159140164899it_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit1 M))) (tptp.aa_nat_nat tptp.suc N))) (tptp.pp (tptp.aa_nat_bool (tptp.bit_se1146084159140164899it_int (tptp.aa_num_int tptp.numeral_numeral_int M)) N)))) (forall ((M tptp.num) (N tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.bit_se1148574629649215175it_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 M))) (tptp.aa_nat_nat tptp.suc N))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.bit_se1148574629649215175it_nat (tptp.aa_num_nat tptp.numeral_numeral_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_eq_int tptp.zero_zero_int) (tptp.aa_int_int (tptp.bit_ri631733984087533419it_int N) K))) (not (tptp.pp (tptp.aa_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.bit_se1146084159140164899it_int K) N)))) (forall ((W tptp.num) (N tptp.num)) (= (tptp.pp (tptp.aa_nat_bool (tptp.bit_se1146084159140164899it_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.bit_se1146084159140164899it_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_nat_fun_nat_bool tptp.bit_se1148574629649215175it_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 W))) (tptp.aa_num_nat tptp.numeral_numeral_nat N))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.bit_se1148574629649215175it_nat (tptp.aa_num_nat tptp.numeral_numeral_nat W)) (tptp.aa_num_nat tptp.pred_numeral N))))) (forall ((W tptp.num) (N tptp.nat)) (= (tptp.pp (tptp.aa_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.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.num)) (= (tptp.pp (tptp.aa_nat_bool (tptp.bit_se1146084159140164899it_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))) (tptp.pp (tptp.aa_nat_bool (tptp.bit_se1146084159140164899it_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_nat_fun_nat_bool tptp.bit_se1148574629649215175it_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 W))) (tptp.aa_num_nat tptp.numeral_numeral_nat N))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.bit_se1148574629649215175it_nat (tptp.aa_num_nat tptp.numeral_numeral_nat W)) (tptp.aa_num_nat tptp.pred_numeral N))))) (forall ((W tptp.num) (N tptp.nat)) (= (tptp.pp (tptp.aa_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.bit_se1146084159140164899it_int (tptp.aa_num_int tptp.numeral_numeral_int W)) N))))) (forall ((Z tptp.complex)) (= (tptp.aa_nat_complex (tptp.power_power_complex (tptp.csqrt Z)) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) Z)) (forall ((A tptp.code_integer)) (= (tptp.pp (tptp.aa_nat_bool (tptp.bit_se9216721137139052372nteger A) tptp.zero_zero_nat)) (not (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))) A))))) (forall ((A tptp.int)) (= (tptp.pp (tptp.aa_nat_bool (tptp.bit_se1146084159140164899it_int A) tptp.zero_zero_nat)) (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))))) (forall ((A tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.bit_se1148574629649215175it_nat A) tptp.zero_zero_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))))) (forall ((W tptp.num) (N tptp.num)) (= (tptp.pp (tptp.aa_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.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.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.bit_se1146084159140164899it_int (tptp.aa_num_int tptp.numeral_numeral_int W)) (tptp.aa_num_nat tptp.pred_numeral N)))))) (forall ((A tptp.code_integer) (N tptp.nat)) (let ((_let_1 (tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.pp (tptp.aa_nat_bool (tptp.bit_se9216721137139052372nteger (tptp.modulo364778990260209775nteger A _let_1)) N)) (and (= N tptp.zero_zero_nat) (not (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer _let_1) A))))))) (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)))) (= (tptp.pp (tptp.aa_nat_bool (tptp.bit_se1146084159140164899it_int (tptp.modulo_modulo_int A _let_1)) N)) (and (= N tptp.zero_zero_nat) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int _let_1) 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)))) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.bit_se1148574629649215175it_nat (tptp.aa_nat_nat (tptp.modulo_modulo_nat A) _let_1)) N)) (and (= N tptp.zero_zero_nat) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat _let_1) A))))))) (= (tptp.cis _let_42) tptp.imaginary_unit) (= (tptp.cis _let_72) tptp.one_one_complex) (forall ((Z tptp.complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (tptp.cis (tptp.aa_complex_real tptp.arg Z)) (tptp.sgn_sgn_complex Z)))) (forall ((M tptp.num) (N tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.bit_se1146084159140164899it_int (tptp.aa_num_int tptp.numeral_numeral_int M)) N)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.bit_se1148574629649215175it_nat (tptp.aa_num_nat tptp.numeral_numeral_nat M)) N)))) (forall ((M tptp.num) (N tptp.nat)) (let ((_let_1 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.bit_se1148574629649215175it_nat (tptp.aa_num_nat tptp.numeral_numeral_nat M)) N)))) (= _let_1 _let_1))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.bit_se1146084159140164899it_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int M)) N)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.bit_se1148574629649215175it_nat M) N)))) (forall ((M 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.semiri1316708129612266289at_nat M)) N)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.bit_se1148574629649215175it_nat M) N)))) (forall ((A tptp.int) (B tptp.int) (N tptp.nat)) (=> (forall ((N2 tptp.nat)) (or (not (tptp.pp (tptp.aa_nat_bool (tptp.bit_se1146084159140164899it_int A) N2))) (not (tptp.pp (tptp.aa_nat_bool (tptp.bit_se1146084159140164899it_int B) N2))))) (= (tptp.pp (tptp.aa_nat_bool (tptp.bit_se1146084159140164899it_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) B)) N)) (or (tptp.pp (tptp.aa_nat_bool (tptp.bit_se1146084159140164899it_int A) N)) (tptp.pp (tptp.aa_nat_bool (tptp.bit_se1146084159140164899it_int B) N)))))) (forall ((A tptp.nat) (B tptp.nat) (N tptp.nat)) (=> (forall ((N2 tptp.nat)) (or (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.bit_se1148574629649215175it_nat A) N2))) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.bit_se1148574629649215175it_nat B) N2))))) (= (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.plus_plus_nat A) B)) N)) (or (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.bit_se1148574629649215175it_nat A) N)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.bit_se1148574629649215175it_nat B) N)))))) (forall ((A tptp.int) (B tptp.int) (N tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.bit_se1146084159140164899it_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se725231765392027082nd_int A) B)) N)) (and (tptp.pp (tptp.aa_nat_bool (tptp.bit_se1146084159140164899it_int A) N)) (tptp.pp (tptp.aa_nat_bool (tptp.bit_se1146084159140164899it_int B) N))))) (forall ((A tptp.nat) (B 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.bit_se727722235901077358nd_nat A) B)) N)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.bit_se1148574629649215175it_nat A) N)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.bit_se1148574629649215175it_nat B) N))))) (forall ((K tptp.int) (L tptp.int) (N tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.bit_se1146084159140164899it_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se725231765392027082nd_int K) L)) N)) (and (tptp.pp (tptp.aa_nat_bool (tptp.bit_se1146084159140164899it_int K) N)) (tptp.pp (tptp.aa_nat_bool (tptp.bit_se1146084159140164899it_int L) N))))) (forall ((M tptp.nat) (A tptp.int) (N tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.bit_se1146084159140164899it_int (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_se4203085406695923979it_int M) A)) N)) (and (tptp.pp (tptp.aa_nat_bool (tptp.bit_se1146084159140164899it_int A) N)) (not (= M N))))) (forall ((M tptp.nat) (A 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_se4205575877204974255it_nat M) A)) N)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.bit_se1148574629649215175it_nat A) N)) (not (= M N))))) (forall ((M tptp.nat) (A tptp.code_integer) (N tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.bit_se9216721137139052372nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_nat6383147911832638789nteger tptp.bit_se8260200283734997820nteger M) A)) N)) (and (tptp.pp (tptp.aa_nat_bool (tptp.bit_se9216721137139052372nteger A) N)) (not (= M N))))) (forall ((A tptp.real) (B tptp.real)) (= (tptp.divide1717551699836669952omplex (tptp.cis A) (tptp.cis B)) (tptp.cis (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A) B)))) (forall ((A tptp.real)) (not (= (tptp.cis A) tptp.zero_zero_complex))) (forall ((N tptp.nat)) (not (tptp.pp (tptp.aa_nat_bool (tptp.bit_se1146084159140164899it_int tptp.one_one_int) (tptp.aa_nat_nat tptp.suc N))))) (forall ((N tptp.nat)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.bit_se1148574629649215175it_nat tptp.one_one_nat) (tptp.aa_nat_nat tptp.suc N))))) (forall ((N tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.bit_se1146084159140164899it_int tptp.one_one_int) N)) (= N tptp.zero_zero_nat))) (forall ((N tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.bit_se1148574629649215175it_nat tptp.one_one_nat) N)) (= N tptp.zero_zero_nat))) (forall ((N tptp.num)) (not (tptp.pp (tptp.aa_nat_bool (tptp.bit_se1146084159140164899it_int tptp.one_one_int) (tptp.aa_num_nat tptp.numeral_numeral_nat N))))) (forall ((N tptp.num)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.bit_se1148574629649215175it_nat tptp.one_one_nat) (tptp.aa_num_nat tptp.numeral_numeral_nat N))))) (forall ((M tptp.nat) (A tptp.int) (N tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.bit_se1146084159140164899it_int (tptp.aa_int_int (tptp.bit_se2923211474154528505it_int M) A)) N)) (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.bit_se1146084159140164899it_int A) N))))) (forall ((M tptp.nat) (A 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.bit_se2925701944663578781it_nat M) A)) N)) (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_nat_fun_nat_bool tptp.bit_se1148574629649215175it_nat A) N))))) (forall ((B tptp.bool) (N tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.bit_se9216721137139052372nteger (tptp.aa_bool_Code_integer tptp.zero_n356916108424825756nteger B)) N)) (and (tptp.pp B) (= N tptp.zero_zero_nat)))) (forall ((B tptp.bool) (N tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.bit_se1146084159140164899it_int (tptp.aa_bool_int tptp.zero_n2684676970156552555ol_int B)) N)) (and (tptp.pp B) (= N tptp.zero_zero_nat)))) (forall ((B tptp.bool) (N tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.bit_se1148574629649215175it_nat (tptp.aa_bool_nat tptp.zero_n2687167440665602831ol_nat B)) N)) (and (tptp.pp B) (= N tptp.zero_zero_nat)))) (forall ((A tptp.int) (N tptp.nat)) (=> (not (tptp.pp (tptp.aa_nat_bool (tptp.bit_se1146084159140164899it_int A) N))) (= (tptp.aa_int_int (tptp.bit_ri631733984087533419it_int N) A) (tptp.aa_int_int (tptp.bit_se2923211474154528505it_int N) A)))) (forall ((A tptp.real) (N tptp.nat)) (= (tptp.aa_nat_complex (tptp.power_power_complex (tptp.cis A)) N) (tptp.cis (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N)) A)))) (forall ((Z tptp.complex) (X tptp.real)) (=> (= (tptp.sgn_sgn_complex Z) (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_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.bit_se1146084159140164899it_int K) N))))) (forall ((N tptp.nat) (A tptp.int)) (= (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_se2159334234014336723it_int N) A) (tptp.aa_int_int (tptp.aa_nat_fun_int_int (tptp.if_fun5757141600869472092nt_int (tptp.aa_nat_bool (tptp.bit_se1146084159140164899it_int A) N) tptp.bit_se4203085406695923979it_int tptp.bit_se7879613467334960850it_int) N) A))) (forall ((N tptp.nat) (A tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se2161824704523386999it_nat N) A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.if_fun6060303171108177060at_nat (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.bit_se1148574629649215175it_nat A) N) tptp.bit_se4205575877204974255it_nat tptp.bit_se7882103937844011126it_nat) N) A))) (forall ((N tptp.nat) (A tptp.code_integer)) (= (tptp.bit_se1345352211410354436nteger N A) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_nat6383147911832638789nteger (tptp.if_fun4784160582202652222nteger (tptp.aa_nat_bool (tptp.bit_se9216721137139052372nteger A) N) tptp.bit_se8260200283734997820nteger tptp.bit_se2793503036327961859nteger) N) A))) (forall ((Z tptp.complex)) (let ((_let_1 (tptp.aa_complex_real tptp.arg Z))) (=> (not (= Z tptp.zero_zero_complex)) (and (= (tptp.sgn_sgn_complex Z) (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)))))) (= (tptp.aa_complex_real tptp.arg tptp.zero_zero_complex) tptp.zero_zero_real) (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.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.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.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.bit_se1146084159140164899it_int L) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) M))))))) (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.bit_se1146084159140164899it_int K) N)))))) (forall ((N tptp.nat) (A tptp.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) (not (tptp.pp (tptp.aa_nat_bool (tptp.bit_se1146084159140164899it_int A) N))))) (forall ((N tptp.nat) (A tptp.nat)) (=> (= (tptp.aa_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_zero_nat) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.bit_se1148574629649215175it_nat A) N))))) (forall ((A tptp.int) (N tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.bit_se1146084159140164899it_int A) (tptp.aa_nat_nat tptp.suc N))) (tptp.pp (tptp.aa_nat_bool (tptp.bit_se1146084159140164899it_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one)))) N)))) (forall ((A tptp.nat) (N tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.bit_se1148574629649215175it_nat A) (tptp.aa_nat_nat tptp.suc N))) (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.divide_divide_nat A) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) N)))) (forall ((A tptp.code_integer)) (=> (forall ((N2 tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.bit_se9216721137139052372nteger A) N2)) (not (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))) A))))) (= (tptp.divide6298287555418463151nteger A (tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))) A))) (forall ((A tptp.int)) (=> (forall ((N2 tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.bit_se1146084159140164899it_int A) N2)) (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))))) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) A))) (forall ((A tptp.nat)) (=> (forall ((N2 tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.bit_se1148574629649215175it_nat A) N2)) (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))))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) A))) (forall ((A tptp.code_integer) (N tptp.nat)) (let ((_let_1 (tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (= (tptp.divide6298287555418463151nteger A _let_1) A) (= (tptp.pp (tptp.aa_nat_bool (tptp.bit_se9216721137139052372nteger A) N)) (not (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer _let_1) A))))))) (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)))) (=> (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A) _let_1) A) (= (tptp.pp (tptp.aa_nat_bool (tptp.bit_se1146084159140164899it_int A) N)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int _let_1) 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)))) (=> (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) _let_1) A) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.bit_se1148574629649215175it_nat A) N)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat _let_1) A))))))) (forall ((K tptp.int)) (not (forall ((N2 tptp.nat)) (let ((_let_1 (tptp.bit_se1146084159140164899it_int K))) (=> (forall ((M2 tptp.nat)) (let ((_let_1 (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 ((A tptp.code_integer) (N tptp.nat)) (let ((_let_1 (tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.pp (tptp.aa_nat_bool (tptp.bit_se9216721137139052372nteger A) N)) (not (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer _let_1) (tptp.divide6298287555418463151nteger A (tptp.power_8256067586552552935nteger _let_1 N)))))))) (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)))) (= (tptp.pp (tptp.aa_nat_bool (tptp.bit_se1146084159140164899it_int A) 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.aa_int_fun_int_int tptp.divide_divide_int A) (tptp.aa_nat_int (tptp.power_power_int _let_1) N)))))))) (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)))) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.bit_se1148574629649215175it_nat A) 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 A) (tptp.aa_nat_nat (tptp.power_power_nat _let_1) N)))))))) (forall ((A tptp.int) (N tptp.nat)) (= (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se725231765392027082nd_int A) (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) (not (tptp.pp (tptp.aa_nat_bool (tptp.bit_se1146084159140164899it_int A) N))))) (forall ((A tptp.nat) (N tptp.nat)) (= (= (tptp.aa_nat_nat (tptp.bit_se727722235901077358nd_nat A) (tptp.aa_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_zero_nat) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.bit_se1148574629649215175it_nat A) N))))) (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.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.aa_int_fun_int_int tptp.divide_divide_int K) (tptp.aa_nat_int (tptp.power_power_int _let_1) 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.real_V4546457046886955230omplex (tptp.aa_real_real tptp.sqrt X)) (tptp.csqrt (tptp.real_V4546457046886955230omplex X))))) (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.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))) A)) (= (tptp.pp (tptp.aa_nat_bool (tptp.bit_se9216721137139052372nteger (tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer A)) N)) (or (tptp.pp (tptp.aa_nat_bool (tptp.bit_se9216721137139052372nteger A) N)) (= 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_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) A)) (= (tptp.pp (tptp.aa_nat_bool (tptp.bit_se1146084159140164899it_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int tptp.one_one_int) A)) N)) (or (tptp.pp (tptp.aa_nat_bool (tptp.bit_se1146084159140164899it_int A) N)) (= 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_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) A)) (= (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.plus_plus_nat tptp.one_one_nat) A)) N)) (or (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.bit_se1148574629649215175it_nat A) N)) (= N tptp.zero_zero_nat))))) (forall ((A tptp.code_integer) (N tptp.nat)) (=> (not (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))) A))) (= (tptp.pp (tptp.aa_nat_bool (tptp.bit_se9216721137139052372nteger A) N)) (or (tptp.pp (tptp.aa_nat_bool (tptp.bit_se9216721137139052372nteger (tptp.minus_8373710615458151222nteger A tptp.one_one_Code_integer)) N)) (= N tptp.zero_zero_nat))))) (forall ((A tptp.int) (N tptp.nat)) (=> (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))) (= (tptp.pp (tptp.aa_nat_bool (tptp.bit_se1146084159140164899it_int A) N)) (or (tptp.pp (tptp.aa_nat_bool (tptp.bit_se1146084159140164899it_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) tptp.one_one_int)) N)) (= N tptp.zero_zero_nat))))) (forall ((A tptp.nat) (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))) A))) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.bit_se1148574629649215175it_nat A) N)) (or (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.minus_minus_nat A) tptp.one_one_nat)) N)) (= N tptp.zero_zero_nat))))) (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 ((A tptp.code_integer) (B tptp.code_integer) (N tptp.nat)) (let ((_let_1 (tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger _let_1) B))) (let ((_let_3 (= N tptp.zero_zero_nat))) (=> (forall ((J2 tptp.nat)) (not (tptp.pp (tptp.aa_nat_bool (tptp.bit_se9216721137139052372nteger A) (tptp.aa_nat_nat tptp.suc J2))))) (= (tptp.pp (tptp.aa_nat_bool (tptp.bit_se9216721137139052372nteger (tptp.plus_p5714425477246183910nteger A _let_2)) N)) (and (=> _let_3 (not (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer _let_1) A)))) (=> (not _let_3) (tptp.pp (tptp.aa_nat_bool (tptp.bit_se9216721137139052372nteger _let_2) N)))))))))) (forall ((A tptp.int) (B 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_int_int (tptp.aa_int_fun_int_int tptp.times_times_int _let_1) B))) (let ((_let_3 (= N tptp.zero_zero_nat))) (=> (forall ((J2 tptp.nat)) (not (tptp.pp (tptp.aa_nat_bool (tptp.bit_se1146084159140164899it_int A) (tptp.aa_nat_nat tptp.suc J2))))) (= (tptp.pp (tptp.aa_nat_bool (tptp.bit_se1146084159140164899it_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) _let_2)) N)) (and (=> _let_3 (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int _let_1) A)))) (=> (not _let_3) (tptp.pp (tptp.aa_nat_bool (tptp.bit_se1146084159140164899it_int _let_2) N)))))))))) (forall ((A tptp.nat) (B 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.times_times_nat _let_1) B))) (let ((_let_3 (= N tptp.zero_zero_nat))) (=> (forall ((J2 tptp.nat)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.bit_se1148574629649215175it_nat A) (tptp.aa_nat_nat tptp.suc J2))))) (= (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.plus_plus_nat A) _let_2)) N)) (and (=> _let_3 (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat _let_1) A)))) (=> (not _let_3) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.bit_se1148574629649215175it_nat _let_2) N)))))))))) (forall ((A tptp.code_integer) (N tptp.nat)) (let ((_let_1 (tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (= N tptp.zero_zero_nat))) (= (tptp.pp (tptp.aa_nat_bool (tptp.bit_se9216721137139052372nteger A) N)) (and (=> _let_2 (not (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer _let_1) A)))) (=> (not _let_2) (tptp.pp (tptp.aa_nat_bool (tptp.bit_se9216721137139052372nteger (tptp.divide6298287555418463151nteger A _let_1)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) tptp.one_one_nat))))))))) (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 (= N tptp.zero_zero_nat))) (= (tptp.pp (tptp.aa_nat_bool (tptp.bit_se1146084159140164899it_int A) N)) (and (=> _let_2 (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int _let_1) A)))) (=> (not _let_2) (tptp.pp (tptp.aa_nat_bool (tptp.bit_se1146084159140164899it_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A) _let_1)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) tptp.one_one_nat))))))))) (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 (= N tptp.zero_zero_nat))) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.bit_se1148574629649215175it_nat A) N)) (and (=> _let_2 (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat _let_1) A)))) (=> (not _let_2) (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.divide_divide_nat A) _let_1)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) tptp.one_one_nat))))))))) (forall ((N tptp.nat) (K tptp.int)) (= (tptp.aa_int_int (tptp.aa_nat_fun_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.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.aa_nat_fun_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.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_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.bit_se1146084159140164899it_int K) N)))) (tptp.aa_int_int (tptp.bit_se2923211474154528505it_int N) K)))) (forall ((N tptp.real)) (=> (tptp.member_real N tptp.ring_1_Ints_real) (= (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 ((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 ((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.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.aa_bool_nat tptp.zero_n2687167440665602831ol_nat _let_1))) (tptp.aa_bool_nat tptp.zero_n2687167440665602831ol_nat (tptp.aa_bool_bool tptp.fNot _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.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.aa_bool_nat tptp.zero_n2687167440665602831ol_nat _let_1))) (tptp.aa_bool_nat tptp.zero_n2687167440665602831ol_nat (tptp.aa_bool_bool tptp.fNot _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.divide1717551699836669952omplex A (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex K))) (tptp.aa_nat_complex (tptp.gbinomial_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.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 ((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 ((A tptp.real)) (= (tptp.aa_real_real tptp.inverse_inverse_real (tptp.aa_real_real tptp.inverse_inverse_real A)) A)) (forall ((A tptp.complex)) (= (tptp.invers8013647133539491842omplex (tptp.invers8013647133539491842omplex A)) A)) (forall ((A tptp.rat)) (= (tptp.aa_rat_rat tptp.inverse_inverse_rat (tptp.aa_rat_rat tptp.inverse_inverse_rat A)) A)) (forall ((A tptp.real) (B tptp.real)) (= (= (tptp.aa_real_real tptp.inverse_inverse_real A) (tptp.aa_real_real tptp.inverse_inverse_real B)) (= A B))) (forall ((A tptp.complex) (B tptp.complex)) (= (= (tptp.invers8013647133539491842omplex A) (tptp.invers8013647133539491842omplex B)) (= A B))) (forall ((A tptp.rat) (B tptp.rat)) (= (= (tptp.aa_rat_rat tptp.inverse_inverse_rat A) (tptp.aa_rat_rat tptp.inverse_inverse_rat B)) (= A B))) (forall ((X tptp.int) (Y4 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.bit_se6526347334894502574or_int X))) (= (tptp.aa_int_int _let_1 (tptp.aa_int_int _let_1 Y4)) Y4))) (forall ((A tptp.real)) (= (= (tptp.aa_real_real tptp.inverse_inverse_real A) tptp.zero_zero_real) (= A tptp.zero_zero_real))) (forall ((A tptp.complex)) (= (= (tptp.invers8013647133539491842omplex A) tptp.zero_zero_complex) (= A tptp.zero_zero_complex))) (forall ((A tptp.rat)) (= (= (tptp.aa_rat_rat tptp.inverse_inverse_rat A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))) _let_71 _let_70 _let_69 (forall ((A tptp.real) (B tptp.real)) (= (tptp.aa_real_real tptp.inverse_inverse_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) B)) (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 B)))) (forall ((A tptp.complex) (B tptp.complex)) (= (tptp.invers8013647133539491842omplex (tptp.aa_complex_complex (tptp.times_times_complex A) B)) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.invers8013647133539491842omplex A)) (tptp.invers8013647133539491842omplex B)))) (forall ((A tptp.rat) (B 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) B)) (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 B)))) (= (tptp.aa_real_real tptp.inverse_inverse_real tptp.one_one_real) tptp.one_one_real) (= (tptp.invers8013647133539491842omplex tptp.one_one_complex) tptp.one_one_complex) (= (tptp.aa_rat_rat tptp.inverse_inverse_rat tptp.one_one_rat) tptp.one_one_rat) (forall ((X tptp.real)) (= (= (tptp.aa_real_real tptp.inverse_inverse_real X) tptp.one_one_real) (= X tptp.one_one_real))) (forall ((X tptp.complex)) (= (= (tptp.invers8013647133539491842omplex X) tptp.one_one_complex) (= X tptp.one_one_complex))) (forall ((X tptp.rat)) (= (= (tptp.aa_rat_rat tptp.inverse_inverse_rat X) tptp.one_one_rat) (= X tptp.one_one_rat))) (forall ((A tptp.real) (B tptp.real)) (= (tptp.aa_real_real tptp.inverse_inverse_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real A) B)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real B) A))) (forall ((A tptp.complex) (B tptp.complex)) (= (tptp.invers8013647133539491842omplex (tptp.divide1717551699836669952omplex A B)) (tptp.divide1717551699836669952omplex B A))) (forall ((A tptp.rat) (B tptp.rat)) (= (tptp.aa_rat_rat tptp.inverse_inverse_rat (tptp.aa_rat_rat (tptp.divide_divide_rat A) B)) (tptp.aa_rat_rat (tptp.divide_divide_rat B) A))) (forall ((A tptp.real)) (= (tptp.aa_real_real tptp.inverse_inverse_real (tptp.aa_real_real tptp.uminus_uminus_real A)) (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_real_real tptp.inverse_inverse_real A)))) (forall ((A tptp.complex)) (= (tptp.invers8013647133539491842omplex (tptp.uminus1482373934393186551omplex A)) (tptp.uminus1482373934393186551omplex (tptp.invers8013647133539491842omplex A)))) (forall ((A tptp.rat)) (= (tptp.aa_rat_rat tptp.inverse_inverse_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat A)) (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_rat_rat tptp.inverse_inverse_rat A)))) (forall ((A tptp.nat)) (= (tptp.aa_nat_nat (tptp.bit_se6528837805403552850or_nat A) tptp.zero_zero_nat) A)) (forall ((A tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se6526347334894502574or_int A) tptp.zero_zero_int) A)) (forall ((A tptp.nat)) (= (tptp.aa_nat_nat (tptp.bit_se6528837805403552850or_nat tptp.zero_zero_nat) A) A)) (forall ((A tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se6526347334894502574or_int tptp.zero_zero_int) A) A)) (forall ((A tptp.nat)) (= (tptp.aa_nat_nat (tptp.bit_se6528837805403552850or_nat A) A) tptp.zero_zero_nat)) (forall ((A tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se6526347334894502574or_int A) A) tptp.zero_zero_int)) (forall ((X tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se6526347334894502574or_int X) X) tptp.zero_zero_int)) (forall ((A tptp.real)) (= (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_real_real tptp.inverse_inverse_real A)) (tptp.aa_real_real tptp.inverse_inverse_real (tptp.aa_real_real tptp.abs_abs_real A)))) (forall ((A tptp.complex)) (= (tptp.abs_abs_complex (tptp.invers8013647133539491842omplex A)) (tptp.invers8013647133539491842omplex (tptp.abs_abs_complex A)))) (forall ((A tptp.rat)) (= (tptp.aa_rat_rat tptp.abs_abs_rat (tptp.aa_rat_rat tptp.inverse_inverse_rat A)) (tptp.aa_rat_rat tptp.inverse_inverse_rat (tptp.aa_rat_rat tptp.abs_abs_rat A)))) (forall ((A tptp.real)) (let ((_let_1 (tptp.aa_real_real tptp.sgn_sgn_real A))) (= (tptp.aa_real_real tptp.inverse_inverse_real _let_1) _let_1))) (forall ((A tptp.rat)) (let ((_let_1 (tptp.aa_rat_rat tptp.sgn_sgn_rat A))) (= (tptp.aa_rat_rat tptp.inverse_inverse_rat _let_1) _let_1))) (forall ((A tptp.real)) (= (tptp.aa_real_real tptp.sgn_sgn_real (tptp.aa_real_real tptp.inverse_inverse_real A)) (tptp.aa_real_real tptp.inverse_inverse_real (tptp.aa_real_real tptp.sgn_sgn_real A)))) (forall ((A tptp.complex)) (= (tptp.sgn_sgn_complex (tptp.invers8013647133539491842omplex A)) (tptp.invers8013647133539491842omplex (tptp.sgn_sgn_complex A)))) (forall ((A tptp.rat)) (= (tptp.aa_rat_rat tptp.sgn_sgn_rat (tptp.aa_rat_rat tptp.inverse_inverse_rat A)) (tptp.aa_rat_rat tptp.inverse_inverse_rat (tptp.aa_rat_rat tptp.sgn_sgn_rat A)))) (forall ((N tptp.nat) (A tptp.int) (B 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.bit_se6526347334894502574or_int A) B)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se6526347334894502574or_int (tptp.aa_int_int _let_1 A)) (tptp.aa_int_int _let_1 B))))) (forall ((N tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (tptp.bit_se2925701944663578781it_nat N))) (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.bit_se6528837805403552850or_nat A) B)) (tptp.aa_nat_nat (tptp.bit_se6528837805403552850or_nat (tptp.aa_nat_nat _let_1 A)) (tptp.aa_nat_nat _let_1 B))))) (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)) (= (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_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) (B tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B))) (=> (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 B))) (tptp.pp (tptp.aa_real_bool _let_1 A))))))) (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B))) (=> (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 B))) (tptp.pp (tptp.aa_rat_bool _let_1 A))))))) (forall ((A tptp.real) (B 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 B)) (= (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 B))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B) A))))))) (forall ((A tptp.rat) (B 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 B)) (= (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 B))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) A))))))) (forall ((K tptp.nat)) (= (tptp.aa_nat_complex (tptp.gbinomial_complex tptp.zero_zero_complex) (tptp.aa_nat_nat tptp.suc K)) tptp.zero_zero_complex)) (forall ((K tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.gbinomial_real tptp.zero_zero_real) (tptp.aa_nat_nat tptp.suc K)) tptp.zero_zero_real)) (forall ((K tptp.nat)) (= (tptp.aa_nat_rat (tptp.gbinomial_rat tptp.zero_zero_rat) (tptp.aa_nat_nat tptp.suc K)) tptp.zero_zero_rat)) (forall ((K tptp.nat)) (= (tptp.aa_nat_nat (tptp.gbinomial_nat tptp.zero_zero_nat) (tptp.aa_nat_nat tptp.suc K)) tptp.zero_zero_nat)) (forall ((K tptp.nat)) (= (tptp.aa_nat_int (tptp.gbinomial_int tptp.zero_zero_int) (tptp.aa_nat_nat tptp.suc K)) tptp.zero_zero_int)) (forall ((A tptp.complex)) (= (tptp.aa_nat_complex (tptp.gbinomial_complex A) tptp.zero_zero_nat) tptp.one_one_complex)) (forall ((A tptp.real)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.gbinomial_real A) tptp.zero_zero_nat) tptp.one_one_real)) (forall ((A tptp.rat)) (= (tptp.aa_nat_rat (tptp.gbinomial_rat A) tptp.zero_zero_nat) tptp.one_one_rat)) (forall ((A tptp.nat)) (= (tptp.aa_nat_nat (tptp.gbinomial_nat A) tptp.zero_zero_nat) tptp.one_one_nat)) (forall ((A tptp.int)) (= (tptp.aa_nat_int (tptp.gbinomial_int A) tptp.zero_zero_nat) tptp.one_one_int)) (forall ((X tptp.real)) (= (= (tptp.aa_real_real tptp.archim2898591450579166408c_real X) tptp.zero_zero_real) (tptp.member_real X tptp.ring_1_Ints_real))) (forall ((X tptp.rat)) (= (= (tptp.aa_rat_rat tptp.archimedean_frac_rat X) tptp.zero_zero_rat) (tptp.member_rat X tptp.ring_1_Ints_rat))) (forall ((A tptp.real) (B 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 B) tptp.zero_zero_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.aa_real_real tptp.inverse_inverse_real B))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real B) A)))))) (forall ((A tptp.rat) (B 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 B) 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.inverse_inverse_rat A)) (tptp.aa_rat_rat tptp.inverse_inverse_rat B))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) A)))))) (forall ((A tptp.real) (B 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 B)) (= (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.aa_real_real tptp.inverse_inverse_real B))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real B) A))))))) (forall ((A tptp.rat) (B 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 B)) (= (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.aa_rat_rat tptp.inverse_inverse_rat B))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) A))))))) (forall ((A tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) (tptp.aa_real_real tptp.inverse_inverse_real A)) tptp.one_one_real))) (forall ((A tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (tptp.aa_complex_complex (tptp.times_times_complex A) (tptp.invers8013647133539491842omplex A)) tptp.one_one_complex))) (forall ((A tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) (tptp.aa_rat_rat tptp.inverse_inverse_rat A)) tptp.one_one_rat))) (forall ((A tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real tptp.inverse_inverse_real A)) A) tptp.one_one_real))) (forall ((A tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (tptp.aa_complex_complex (tptp.times_times_complex (tptp.invers8013647133539491842omplex A)) A) tptp.one_one_complex))) (forall ((A tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat tptp.inverse_inverse_rat A)) A) tptp.one_one_rat))) (forall ((W tptp.num)) (let ((_let_1 (tptp.aa_num_real tptp.numeral_numeral_real W))) (= (tptp.aa_real_real tptp.inverse_inverse_real _let_1) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.one_one_real) _let_1)))) (forall ((W tptp.num)) (let ((_let_1 (tptp.numera6690914467698888265omplex W))) (= (tptp.invers8013647133539491842omplex _let_1) (tptp.divide1717551699836669952omplex tptp.one_one_complex _let_1)))) (forall ((W tptp.num)) (let ((_let_1 (tptp.aa_num_rat tptp.numeral_numeral_rat W))) (= (tptp.aa_rat_rat tptp.inverse_inverse_rat _let_1) (tptp.aa_rat_rat (tptp.divide_divide_rat tptp.one_one_rat) _let_1)))) (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.archim2898591450579166408c_real X))) (not (tptp.member_real X tptp.ring_1_Ints_real)))) (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.archimedean_frac_rat X))) (not (tptp.member_rat X tptp.ring_1_Ints_rat)))) (forall ((W tptp.num)) (let ((_let_1 (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real W)))) (= (tptp.aa_real_real tptp.inverse_inverse_real _let_1) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.one_one_real) _let_1)))) (forall ((W tptp.num)) (let ((_let_1 (tptp.uminus1482373934393186551omplex (tptp.numera6690914467698888265omplex W)))) (= (tptp.invers8013647133539491842omplex _let_1) (tptp.divide1717551699836669952omplex tptp.one_one_complex _let_1)))) (forall ((W tptp.num)) (let ((_let_1 (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat W)))) (= (tptp.aa_rat_rat tptp.inverse_inverse_rat _let_1) (tptp.aa_rat_rat (tptp.divide_divide_rat tptp.one_one_rat) _let_1)))) (forall ((X tptp.num) (Y4 tptp.num)) (= (tptp.aa_nat_nat (tptp.bit_se6528837805403552850or_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 X))) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 Y4))) (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.bit_se6528837805403552850or_nat (tptp.aa_num_nat tptp.numeral_numeral_nat X)) (tptp.aa_num_nat tptp.numeral_numeral_nat Y4))))) (forall ((X tptp.num) (Y4 tptp.num)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se6526347334894502574or_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 X))) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 Y4))) (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.aa_int_fun_int_int tptp.bit_se6526347334894502574or_int (tptp.aa_num_int tptp.numeral_numeral_int X)) (tptp.aa_num_int tptp.numeral_numeral_int Y4))))) (forall ((Y4 tptp.num)) (= (tptp.aa_nat_nat (tptp.bit_se6528837805403552850or_nat tptp.one_one_nat) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 Y4))) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 Y4)))) (forall ((Y4 tptp.num)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se6526347334894502574or_int tptp.one_one_int) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 Y4))) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit1 Y4)))) (forall ((Y4 tptp.num)) (= (tptp.aa_nat_nat (tptp.bit_se6528837805403552850or_nat tptp.one_one_nat) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 Y4))) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 Y4)))) (forall ((Y4 tptp.num)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se6526347334894502574or_int tptp.one_one_int) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit1 Y4))) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 Y4)))) (forall ((X tptp.num)) (= (tptp.aa_nat_nat (tptp.bit_se6528837805403552850or_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 X))) tptp.one_one_nat) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 X)))) (forall ((X tptp.num)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se6526347334894502574or_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 X))) tptp.one_one_int) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit1 X)))) (forall ((X tptp.num)) (= (tptp.aa_nat_nat (tptp.bit_se6528837805403552850or_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 X))) tptp.one_one_nat) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 X)))) (forall ((X tptp.num)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se6526347334894502574or_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit1 X))) tptp.one_one_int) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 X)))) (forall ((X tptp.num) (Y4 tptp.num)) (= (tptp.aa_nat_nat (tptp.bit_se6528837805403552850or_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 X))) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 Y4))) (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.bit_se6528837805403552850or_nat (tptp.aa_num_nat tptp.numeral_numeral_nat X)) (tptp.aa_num_nat tptp.numeral_numeral_nat Y4))))) (forall ((X tptp.num) (Y4 tptp.num)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se6526347334894502574or_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit1 X))) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit1 Y4))) (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.aa_int_fun_int_int tptp.bit_se6526347334894502574or_int (tptp.aa_num_int tptp.numeral_numeral_int X)) (tptp.aa_num_int tptp.numeral_numeral_int Y4))))) (forall ((Y4 tptp.num)) (= (tptp.aa_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 Y4))) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 Y4)))) (forall ((Y4 tptp.num)) (= (tptp.aa_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 Y4))) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 Y4)))) (forall ((X tptp.num)) (= (tptp.aa_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 ((X tptp.num)) (= (tptp.aa_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) (Y4 tptp.num)) (= (tptp.aa_nat_nat (tptp.bit_se6528837805403552850or_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 X))) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 Y4))) (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 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_nat_nat (tptp.bit_se6528837805403552850or_nat (tptp.aa_num_nat tptp.numeral_numeral_nat X)) (tptp.aa_num_nat tptp.numeral_numeral_nat Y4)))))) (forall ((X tptp.num) (Y4 tptp.num)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se6526347334894502574or_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 X))) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit1 Y4))) (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.aa_int_fun_int_int tptp.bit_se6526347334894502574or_int (tptp.aa_num_int tptp.numeral_numeral_int X)) (tptp.aa_num_int tptp.numeral_numeral_int Y4)))))) (forall ((X tptp.num) (Y4 tptp.num)) (= (tptp.aa_nat_nat (tptp.bit_se6528837805403552850or_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 X))) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 Y4))) (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 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_nat_nat (tptp.bit_se6528837805403552850or_nat (tptp.aa_num_nat tptp.numeral_numeral_nat X)) (tptp.aa_num_nat tptp.numeral_numeral_nat Y4)))))) (forall ((X tptp.num) (Y4 tptp.num)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se6526347334894502574or_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit1 X))) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 Y4))) (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.aa_int_fun_int_int tptp.bit_se6526347334894502574or_int (tptp.aa_num_int tptp.numeral_numeral_int X)) (tptp.aa_num_int tptp.numeral_numeral_int Y4)))))) (forall ((A tptp.int) (N tptp.nat)) (=> (tptp.member_int A tptp.ring_1_Ints_int) (tptp.member_int (tptp.aa_nat_int (tptp.power_power_int A) N) tptp.ring_1_Ints_int))) (forall ((A tptp.real) (N tptp.nat)) (=> (tptp.member_real A tptp.ring_1_Ints_real) (tptp.member_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real A) N) tptp.ring_1_Ints_real))) (forall ((A tptp.complex) (N tptp.nat)) (=> (tptp.member_complex A tptp.ring_1_Ints_complex) (tptp.member_complex (tptp.aa_nat_complex (tptp.power_power_complex A) N) tptp.ring_1_Ints_complex))) (forall ((X tptp.real)) (=> (not (= X tptp.zero_zero_real)) (= (tptp.aa_real_real tptp.real_V1803761363581548252l_real (tptp.aa_real_real tptp.inverse_inverse_real X)) (tptp.aa_real_real tptp.inverse_inverse_real (tptp.aa_real_real tptp.real_V1803761363581548252l_real X))))) (forall ((X tptp.real)) (=> (not (= X tptp.zero_zero_real)) (= (tptp.real_V4546457046886955230omplex (tptp.aa_real_real tptp.inverse_inverse_real X)) (tptp.invers8013647133539491842omplex (tptp.real_V4546457046886955230omplex X))))) (forall ((K tptp.int) (L tptp.int)) (= (tptp.ring_1_of_int_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se6526347334894502574or_int K) L)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se6526347334894502574or_int (tptp.ring_1_of_int_int K)) (tptp.ring_1_of_int_int L)))) (tptp.member_complex tptp.zero_zero_complex tptp.ring_1_Ints_complex) (tptp.member_real tptp.zero_zero_real tptp.ring_1_Ints_real) (tptp.member_rat tptp.zero_zero_rat tptp.ring_1_Ints_rat) (tptp.member_int tptp.zero_zero_int tptp.ring_1_Ints_int) (forall ((N tptp.num)) (tptp.member_complex (tptp.numera6690914467698888265omplex N) tptp.ring_1_Ints_complex)) (forall ((N tptp.num)) (tptp.member_real (tptp.aa_num_real tptp.numeral_numeral_real N) tptp.ring_1_Ints_real)) (forall ((N tptp.num)) (tptp.member_rat (tptp.aa_num_rat tptp.numeral_numeral_rat N) tptp.ring_1_Ints_rat)) (forall ((N tptp.num)) (tptp.member_int (tptp.aa_num_int tptp.numeral_numeral_int N) tptp.ring_1_Ints_int)) (forall ((A tptp.complex) (B tptp.complex)) (=> (tptp.member_complex A tptp.ring_1_Ints_complex) (=> (tptp.member_complex B tptp.ring_1_Ints_complex) (tptp.member_complex (tptp.aa_complex_complex (tptp.times_times_complex A) B) tptp.ring_1_Ints_complex)))) (forall ((A tptp.real) (B tptp.real)) (=> (tptp.member_real A tptp.ring_1_Ints_real) (=> (tptp.member_real B tptp.ring_1_Ints_real) (tptp.member_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) B) tptp.ring_1_Ints_real)))) (forall ((A tptp.rat) (B tptp.rat)) (=> (tptp.member_rat A tptp.ring_1_Ints_rat) (=> (tptp.member_rat B tptp.ring_1_Ints_rat) (tptp.member_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) B) tptp.ring_1_Ints_rat)))) (forall ((A tptp.int) (B tptp.int)) (=> (tptp.member_int A tptp.ring_1_Ints_int) (=> (tptp.member_int B tptp.ring_1_Ints_int) (tptp.member_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) B) tptp.ring_1_Ints_int)))) (forall ((A tptp.complex) (B tptp.complex)) (=> (tptp.member_complex A tptp.ring_1_Ints_complex) (=> (tptp.member_complex B tptp.ring_1_Ints_complex) (tptp.member_complex (tptp.plus_plus_complex A B) tptp.ring_1_Ints_complex)))) (forall ((A tptp.real) (B tptp.real)) (=> (tptp.member_real A tptp.ring_1_Ints_real) (=> (tptp.member_real B tptp.ring_1_Ints_real) (tptp.member_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) B) tptp.ring_1_Ints_real)))) (forall ((A tptp.rat) (B tptp.rat)) (=> (tptp.member_rat A tptp.ring_1_Ints_rat) (=> (tptp.member_rat B tptp.ring_1_Ints_rat) (tptp.member_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) B) tptp.ring_1_Ints_rat)))) (forall ((A tptp.int) (B tptp.int)) (=> (tptp.member_int A tptp.ring_1_Ints_int) (=> (tptp.member_int B tptp.ring_1_Ints_int) (tptp.member_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) B) tptp.ring_1_Ints_int)))) (tptp.member_rat tptp.one_one_rat tptp.ring_1_Ints_rat) (tptp.member_int tptp.one_one_int tptp.ring_1_Ints_int) (tptp.member_real tptp.one_one_real tptp.ring_1_Ints_real) (tptp.member_complex tptp.one_one_complex tptp.ring_1_Ints_complex) (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 ((A tptp.complex) (B tptp.complex)) (=> (tptp.member_complex A tptp.ring_1_Ints_complex) (=> (tptp.member_complex B tptp.ring_1_Ints_complex) (tptp.member_complex (tptp.minus_minus_complex A B) tptp.ring_1_Ints_complex)))) (forall ((A tptp.real) (B tptp.real)) (=> (tptp.member_real A tptp.ring_1_Ints_real) (=> (tptp.member_real B tptp.ring_1_Ints_real) (tptp.member_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A) B) tptp.ring_1_Ints_real)))) (forall ((A tptp.rat) (B tptp.rat)) (=> (tptp.member_rat A tptp.ring_1_Ints_rat) (=> (tptp.member_rat B tptp.ring_1_Ints_rat) (tptp.member_rat (tptp.aa_rat_rat (tptp.minus_minus_rat A) B) tptp.ring_1_Ints_rat)))) (forall ((A tptp.int) (B tptp.int)) (=> (tptp.member_int A tptp.ring_1_Ints_int) (=> (tptp.member_int B tptp.ring_1_Ints_int) (tptp.member_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) B) tptp.ring_1_Ints_int)))) (forall ((A tptp.real)) (=> (tptp.member_real A tptp.ring_1_Ints_real) (tptp.member_real (tptp.aa_real_real tptp.uminus_uminus_real A) tptp.ring_1_Ints_real))) (forall ((A tptp.int)) (=> (tptp.member_int A tptp.ring_1_Ints_int) (tptp.member_int (tptp.aa_int_int tptp.uminus_uminus_int A) tptp.ring_1_Ints_int))) (forall ((A tptp.complex)) (=> (tptp.member_complex A tptp.ring_1_Ints_complex) (tptp.member_complex (tptp.uminus1482373934393186551omplex A) tptp.ring_1_Ints_complex))) (forall ((A tptp.code_integer)) (=> (tptp.member_Code_integer A tptp.ring_11222124179247155820nteger) (tptp.member_Code_integer (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A) tptp.ring_11222124179247155820nteger))) (forall ((A tptp.rat)) (=> (tptp.member_rat A tptp.ring_1_Ints_rat) (tptp.member_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat A) tptp.ring_1_Ints_rat))) (forall ((X tptp.real)) (= (tptp.member_real (tptp.aa_real_real tptp.uminus_uminus_real X) tptp.ring_1_Ints_real) (tptp.member_real X tptp.ring_1_Ints_real))) (forall ((X tptp.int)) (= (tptp.member_int (tptp.aa_int_int tptp.uminus_uminus_int X) tptp.ring_1_Ints_int) (tptp.member_int X tptp.ring_1_Ints_int))) (forall ((X tptp.complex)) (= (tptp.member_complex (tptp.uminus1482373934393186551omplex X) tptp.ring_1_Ints_complex) (tptp.member_complex X tptp.ring_1_Ints_complex))) (forall ((X tptp.code_integer)) (= (tptp.member_Code_integer (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger X) tptp.ring_11222124179247155820nteger) (tptp.member_Code_integer X tptp.ring_11222124179247155820nteger))) (forall ((X tptp.rat)) (= (tptp.member_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat X) tptp.ring_1_Ints_rat) (tptp.member_rat X tptp.ring_1_Ints_rat))) (forall ((N tptp.nat) (K tptp.nat)) (= (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex (tptp.aa_nat_nat (tptp.gbinomial_nat N) K)) (tptp.aa_nat_complex (tptp.gbinomial_complex (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex N)) K))) (forall ((N tptp.nat) (K tptp.nat)) (= (tptp.aa_nat_real tptp.semiri5074537144036343181t_real (tptp.aa_nat_nat (tptp.gbinomial_nat N) K)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.gbinomial_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N)) K))) (forall ((N tptp.nat) (K tptp.nat)) (= (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat (tptp.aa_nat_nat (tptp.gbinomial_nat N) K)) (tptp.aa_nat_rat (tptp.gbinomial_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat N)) K))) (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (tptp.bit_se6528837805403552850or_nat B))) (let ((_let_2 (tptp.bit_se6528837805403552850or_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 ((B tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.bit_se6526347334894502574or_int B))) (let ((_let_2 (tptp.aa_int_fun_int_int tptp.bit_se6526347334894502574or_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.nat) (B tptp.nat)) (= (tptp.aa_nat_nat (tptp.bit_se6528837805403552850or_nat A) B) (tptp.aa_nat_nat (tptp.bit_se6528837805403552850or_nat B) A))) (forall ((A tptp.int) (B tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se6526347334894502574or_int A) B) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se6526347334894502574or_int B) A))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (tptp.bit_se6528837805403552850or_nat A))) (= (tptp.aa_nat_nat (tptp.bit_se6528837805403552850or_nat (tptp.aa_nat_nat _let_1 B)) C) (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.bit_se6528837805403552850or_nat B) C))))) (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.bit_se6526347334894502574or_int A))) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se6526347334894502574or_int (tptp.aa_int_int _let_1 B)) C) (tptp.aa_int_int _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se6526347334894502574or_int B) C))))) (forall ((A tptp.real) (B tptp.real)) (=> (= (tptp.aa_real_real tptp.inverse_inverse_real A) (tptp.aa_real_real tptp.inverse_inverse_real B)) (= A B))) (forall ((A tptp.complex) (B tptp.complex)) (=> (= (tptp.invers8013647133539491842omplex A) (tptp.invers8013647133539491842omplex B)) (= A B))) (forall ((A tptp.rat) (B tptp.rat)) (=> (= (tptp.aa_rat_rat tptp.inverse_inverse_rat A) (tptp.aa_rat_rat tptp.inverse_inverse_rat B)) (= A B))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat (tptp.aa_nat_nat (tptp.bit_se6528837805403552850or_nat M) N)) (tptp.aa_nat_nat (tptp.bit_se6528837805403552850or_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_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_nat (tptp.bit_se6528837805403552850or_nat M) N)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se6526347334894502574or_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int M)) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N)))) (forall ((A tptp.real)) (=> (not (= A tptp.zero_zero_real)) (not (= (tptp.aa_real_real tptp.inverse_inverse_real A) tptp.zero_zero_real)))) (forall ((A tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (not (= (tptp.invers8013647133539491842omplex A) tptp.zero_zero_complex)))) (forall ((A tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (not (= (tptp.aa_rat_rat tptp.inverse_inverse_rat A) tptp.zero_zero_rat)))) (forall ((A tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (tptp.aa_real_real tptp.inverse_inverse_real (tptp.aa_real_real tptp.inverse_inverse_real A)) A))) (forall ((A tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (tptp.invers8013647133539491842omplex (tptp.invers8013647133539491842omplex A)) A))) (forall ((A tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (= (tptp.aa_rat_rat tptp.inverse_inverse_rat (tptp.aa_rat_rat tptp.inverse_inverse_rat A)) A))) (forall ((A tptp.real) (B tptp.real)) (=> (= (tptp.aa_real_real tptp.inverse_inverse_real A) (tptp.aa_real_real tptp.inverse_inverse_real B)) (=> (not (= A tptp.zero_zero_real)) (=> (not (= B tptp.zero_zero_real)) (= A B))))) (forall ((A tptp.complex) (B tptp.complex)) (=> (= (tptp.invers8013647133539491842omplex A) (tptp.invers8013647133539491842omplex B)) (=> (not (= A tptp.zero_zero_complex)) (=> (not (= B tptp.zero_zero_complex)) (= A B))))) (forall ((A tptp.rat) (B tptp.rat)) (=> (= (tptp.aa_rat_rat tptp.inverse_inverse_rat A) (tptp.aa_rat_rat tptp.inverse_inverse_rat B)) (=> (not (= A tptp.zero_zero_rat)) (=> (not (= B tptp.zero_zero_rat)) (= A B))))) (forall ((A tptp.real)) (=> (= (tptp.aa_real_real tptp.inverse_inverse_real A) tptp.zero_zero_real) (= A tptp.zero_zero_real))) (forall ((A tptp.complex)) (=> (= (tptp.invers8013647133539491842omplex A) tptp.zero_zero_complex) (= A tptp.zero_zero_complex))) (forall ((A tptp.rat)) (=> (= (tptp.aa_rat_rat tptp.inverse_inverse_rat A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))) _let_71 _let_70 _let_69 (forall ((Y4 tptp.real) (X tptp.real)) (let ((_let_1 (tptp.aa_real_real tptp.inverse_inverse_real Y4))) (let ((_let_2 (tptp.aa_rea7340605660300375871l_real tptp.times_times_real X))) (=> (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real Y4) X) (tptp.aa_real_real _let_2 Y4)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real _let_1) X) (tptp.aa_real_real _let_2 _let_1)))))) (forall ((Y4 tptp.complex) (X tptp.complex)) (let ((_let_1 (tptp.invers8013647133539491842omplex Y4))) (let ((_let_2 (tptp.times_times_complex X))) (=> (= (tptp.aa_complex_complex (tptp.times_times_complex Y4) X) (tptp.aa_complex_complex _let_2 Y4)) (= (tptp.aa_complex_complex (tptp.times_times_complex _let_1) X) (tptp.aa_complex_complex _let_2 _let_1)))))) (forall ((Y4 tptp.rat) (X tptp.rat)) (let ((_let_1 (tptp.aa_rat_rat tptp.inverse_inverse_rat Y4))) (let ((_let_2 (tptp.aa_rat_fun_rat_rat tptp.times_times_rat X))) (=> (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat Y4) X) (tptp.aa_rat_rat _let_2 Y4)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat _let_1) X) (tptp.aa_rat_rat _let_2 _let_1)))))) (forall ((A tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (tptp.aa_real_real tptp.real_V7735802525324610683m_real (tptp.aa_real_real tptp.inverse_inverse_real A)) (tptp.aa_real_real tptp.inverse_inverse_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real A))))) (forall ((A tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.invers8013647133539491842omplex A)) (tptp.aa_real_real tptp.inverse_inverse_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex A))))) (forall ((N tptp.nat)) (tptp.member_complex (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex N) tptp.ring_1_Ints_complex)) (forall ((N tptp.nat)) (tptp.member_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N) tptp.ring_1_Ints_real)) (forall ((N tptp.nat)) (tptp.member_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat N) tptp.ring_1_Ints_rat)) (forall ((N tptp.nat)) (tptp.member_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N) tptp.ring_1_Ints_int)) (forall ((Y4 tptp.int) (Z tptp.int) (X tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se725231765392027082nd_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se6526347334894502574or_int Y4) Z)) X) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se6526347334894502574or_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se725231765392027082nd_int Y4) X)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se725231765392027082nd_int Z) X)))) (forall ((X tptp.int) (Y4 tptp.int) (Z tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.bit_se725231765392027082nd_int X))) (= (tptp.aa_int_int _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se6526347334894502574or_int Y4) Z)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se6526347334894502574or_int (tptp.aa_int_int _let_1 Y4)) (tptp.aa_int_int _let_1 Z))))) (forall ((A tptp.nat) (B 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.bit_se6528837805403552850or_nat A) B)) N)) (not (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.bit_se1148574629649215175it_nat A) N)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.bit_se1148574629649215175it_nat B) N)))))) (forall ((A tptp.int) (B tptp.int) (N tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.bit_se1146084159140164899it_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se6526347334894502574or_int A) B)) N)) (not (= (tptp.pp (tptp.aa_nat_bool (tptp.bit_se1146084159140164899it_int A) N)) (tptp.pp (tptp.aa_nat_bool (tptp.bit_se1146084159140164899it_int B) N)))))) (forall ((A tptp.int)) (=> (tptp.member_int A tptp.ring_1_Ints_int) (tptp.member_int (tptp.aa_int_int tptp.abs_abs_int A) tptp.ring_1_Ints_int))) (forall ((A tptp.code_integer)) (=> (tptp.member_Code_integer A tptp.ring_11222124179247155820nteger) (tptp.member_Code_integer (tptp.abs_abs_Code_integer A) tptp.ring_11222124179247155820nteger))) (forall ((A tptp.rat)) (=> (tptp.member_rat A tptp.ring_1_Ints_rat) (tptp.member_rat (tptp.aa_rat_rat tptp.abs_abs_rat A) tptp.ring_1_Ints_rat))) (forall ((A tptp.real)) (=> (tptp.member_real A tptp.ring_1_Ints_real) (tptp.member_real (tptp.aa_real_real tptp.abs_abs_real A) tptp.ring_1_Ints_real))) (forall ((Z tptp.int)) (tptp.member_int (tptp.ring_1_of_int_int Z) tptp.ring_1_Ints_int)) (forall ((Z tptp.int)) (tptp.member_real (tptp.aa_int_real tptp.ring_1_of_int_real Z) tptp.ring_1_Ints_real)) (forall ((Z tptp.int)) (tptp.member_complex (tptp.ring_17405671764205052669omplex Z) tptp.ring_1_Ints_complex)) (forall ((Z tptp.int)) (tptp.member_rat (tptp.aa_int_rat tptp.ring_1_of_int_rat Z) tptp.ring_1_Ints_rat)) (forall ((Q2 tptp.int) (P tptp.fun_int_bool)) (=> (tptp.member_int Q2 tptp.ring_1_Ints_int) (=> (forall ((Z2 tptp.int)) (tptp.pp (tptp.aa_int_bool P (tptp.ring_1_of_int_int Z2)))) (tptp.pp (tptp.aa_int_bool P Q2))))) (forall ((Q2 tptp.real) (P tptp.fun_real_bool)) (=> (tptp.member_real Q2 tptp.ring_1_Ints_real) (=> (forall ((Z2 tptp.int)) (tptp.pp (tptp.aa_real_bool P (tptp.aa_int_real tptp.ring_1_of_int_real Z2)))) (tptp.pp (tptp.aa_real_bool P Q2))))) (forall ((Q2 tptp.complex) (P tptp.fun_complex_bool)) (=> (tptp.member_complex Q2 tptp.ring_1_Ints_complex) (=> (forall ((Z2 tptp.int)) (tptp.pp (tptp.aa_complex_bool P (tptp.ring_17405671764205052669omplex Z2)))) (tptp.pp (tptp.aa_complex_bool P Q2))))) (forall ((Q2 tptp.rat) (P tptp.fun_rat_bool)) (=> (tptp.member_rat Q2 tptp.ring_1_Ints_rat) (=> (forall ((Z2 tptp.int)) (tptp.pp (tptp.aa_rat_bool P (tptp.aa_int_rat tptp.ring_1_of_int_rat Z2)))) (tptp.pp (tptp.aa_rat_bool P Q2))))) (forall ((Q2 tptp.int)) (=> (tptp.member_int Q2 tptp.ring_1_Ints_int) (not (forall ((Z2 tptp.int)) (not (= Q2 (tptp.ring_1_of_int_int Z2))))))) (forall ((Q2 tptp.real)) (=> (tptp.member_real Q2 tptp.ring_1_Ints_real) (not (forall ((Z2 tptp.int)) (not (= Q2 (tptp.aa_int_real tptp.ring_1_of_int_real Z2))))))) (forall ((Q2 tptp.complex)) (=> (tptp.member_complex Q2 tptp.ring_1_Ints_complex) (not (forall ((Z2 tptp.int)) (not (= Q2 (tptp.ring_17405671764205052669omplex Z2))))))) (forall ((Q2 tptp.rat)) (=> (tptp.member_rat Q2 tptp.ring_1_Ints_rat) (not (forall ((Z2 tptp.int)) (not (= Q2 (tptp.aa_int_rat tptp.ring_1_of_int_rat Z2))))))) (forall ((R2 tptp.real) (X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real R2) (tptp.aa_real_real tptp.real_V7735802525324610683m_real X))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) R2)) (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.inverse_inverse_real X))) (tptp.aa_real_real tptp.inverse_inverse_real R2)))))) (forall ((R2 tptp.real) (X tptp.complex)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real R2) (tptp.aa_complex_real tptp.real_V1022390504157884413omplex X))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) R2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.invers8013647133539491842omplex X))) (tptp.aa_real_real tptp.inverse_inverse_real R2)))))) (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.inverse_inverse_real 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 A)) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat tptp.inverse_inverse_rat A)))))) (forall ((A 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.aa_real_real tptp.inverse_inverse_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 A) 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.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.inverse_inverse_real A))) (=> (not (= A tptp.zero_zero_real)) (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))) (=> (not (= A tptp.zero_zero_rat)) (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)) (=> (not (= 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)) (=> (not (= 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) (B tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B) 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 B)) (tptp.aa_real_real tptp.inverse_inverse_real A)))))) (forall ((A tptp.rat) (B tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) 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 B)) (tptp.aa_rat_rat tptp.inverse_inverse_rat A)))))) (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B))) (=> (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 B))) (=> (tptp.pp (tptp.aa_real_bool _let_1 tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool _let_1 A)))))) (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B))) (=> (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 B))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool _let_1 A)))))) (forall ((A tptp.real) (B tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B)) (=> (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.inverse_inverse_real B)) (tptp.aa_real_real tptp.inverse_inverse_real A)))))) (forall ((A tptp.rat) (B tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B)) (=> (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.inverse_inverse_rat B)) (tptp.aa_rat_rat tptp.inverse_inverse_rat A)))))) (forall ((A tptp.real) (B 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.aa_real_real tptp.inverse_inverse_real B))) (=> (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 B) A))))) (forall ((A tptp.rat) (B 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.aa_rat_rat tptp.inverse_inverse_rat B))) (=> (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 B) A))))) (forall ((A tptp.real) (B tptp.real)) (=> (not (= A tptp.zero_zero_real)) (=> (not (= B tptp.zero_zero_real)) (= (tptp.aa_real_real tptp.inverse_inverse_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) B)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real tptp.inverse_inverse_real B)) (tptp.aa_real_real tptp.inverse_inverse_real A)))))) (forall ((A tptp.complex) (B tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (=> (not (= B tptp.zero_zero_complex)) (= (tptp.invers8013647133539491842omplex (tptp.aa_complex_complex (tptp.times_times_complex A) B)) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.invers8013647133539491842omplex B)) (tptp.invers8013647133539491842omplex A)))))) (forall ((A tptp.rat) (B tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (=> (not (= B tptp.zero_zero_rat)) (= (tptp.aa_rat_rat tptp.inverse_inverse_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) B)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat tptp.inverse_inverse_rat B)) (tptp.aa_rat_rat tptp.inverse_inverse_rat A)))))) (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 ((A tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (tptp.aa_real_real tptp.inverse_inverse_real (tptp.aa_real_real tptp.uminus_uminus_real A)) (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_real_real tptp.inverse_inverse_real A))))) (forall ((A tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (tptp.invers8013647133539491842omplex (tptp.uminus1482373934393186551omplex A)) (tptp.uminus1482373934393186551omplex (tptp.invers8013647133539491842omplex A))))) (forall ((A tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (= (tptp.aa_rat_rat tptp.inverse_inverse_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat A)) (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_rat_rat tptp.inverse_inverse_rat A))))) (= (tptp.aa_real_real tptp.inverse_inverse_real _let_68) _let_68) (= (tptp.invers8013647133539491842omplex _let_67) _let_67) (= (tptp.aa_rat_rat tptp.inverse_inverse_rat _let_66) _let_66) (forall ((A tptp.real) (B tptp.real)) (=> (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) B) tptp.one_one_real) (= (tptp.aa_real_real tptp.inverse_inverse_real A) B))) (forall ((A tptp.complex) (B tptp.complex)) (=> (= (tptp.aa_complex_complex (tptp.times_times_complex A) B) tptp.one_one_complex) (= (tptp.invers8013647133539491842omplex A) B))) (forall ((A tptp.rat) (B tptp.rat)) (=> (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) B) tptp.one_one_rat) (= (tptp.aa_rat_rat tptp.inverse_inverse_rat A) B))) (forall ((A tptp.real) (B tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real A) B) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real tptp.inverse_inverse_real B)) A))) (forall ((A tptp.complex) (B tptp.complex)) (= (tptp.divide1717551699836669952omplex A B) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.invers8013647133539491842omplex B)) A))) (forall ((A tptp.rat) (B tptp.rat)) (= (tptp.aa_rat_rat (tptp.divide_divide_rat A) B) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat tptp.inverse_inverse_rat B)) A))) (forall ((A tptp.real) (B tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real A) B) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) (tptp.aa_real_real tptp.inverse_inverse_real B)))) (forall ((A tptp.complex) (B tptp.complex)) (= (tptp.divide1717551699836669952omplex A B) (tptp.aa_complex_complex (tptp.times_times_complex A) (tptp.invers8013647133539491842omplex B)))) (forall ((A tptp.rat) (B tptp.rat)) (= (tptp.aa_rat_rat (tptp.divide_divide_rat A) B) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) (tptp.aa_rat_rat tptp.inverse_inverse_rat B)))) (forall ((A tptp.real) (B tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real A) B) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) (tptp.aa_real_real tptp.inverse_inverse_real B)))) (forall ((A tptp.complex) (B tptp.complex)) (= (tptp.divide1717551699836669952omplex A B) (tptp.aa_complex_complex (tptp.times_times_complex A) (tptp.invers8013647133539491842omplex B)))) (forall ((A tptp.rat) (B tptp.rat)) (= (tptp.aa_rat_rat (tptp.divide_divide_rat A) B) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) (tptp.aa_rat_rat tptp.inverse_inverse_rat B)))) (forall ((A tptp.real)) (= (tptp.aa_real_real tptp.inverse_inverse_real A) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.one_one_real) A))) (forall ((A tptp.complex)) (= (tptp.invers8013647133539491842omplex A) (tptp.divide1717551699836669952omplex tptp.one_one_complex A))) (forall ((A tptp.rat)) (= (tptp.aa_rat_rat tptp.inverse_inverse_rat A) (tptp.aa_rat_rat (tptp.divide_divide_rat tptp.one_one_rat) A))) (forall ((X tptp.real) (M tptp.nat)) (let ((_let_1 (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) M))) (let ((_let_2 (tptp.aa_real_real tptp.inverse_inverse_real X))) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real _let_1) _let_2) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real _let_2) _let_1))))) (forall ((X tptp.complex) (M tptp.nat)) (let ((_let_1 (tptp.aa_nat_complex (tptp.power_power_complex X) M))) (let ((_let_2 (tptp.invers8013647133539491842omplex X))) (= (tptp.aa_complex_complex (tptp.times_times_complex _let_1) _let_2) (tptp.aa_complex_complex (tptp.times_times_complex _let_2) _let_1))))) (forall ((X tptp.rat) (M tptp.nat)) (let ((_let_1 (tptp.aa_nat_rat (tptp.power_power_rat X) M))) (let ((_let_2 (tptp.aa_rat_rat tptp.inverse_inverse_rat X))) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat _let_1) _let_2) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat _let_2) _let_1))))) (forall ((X tptp.real) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) M))) (let ((_let_2 (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real tptp.inverse_inverse_real X)) N))) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real _let_1) _let_2) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real _let_2) _let_1))))) (forall ((X tptp.complex) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_complex (tptp.power_power_complex X) M))) (let ((_let_2 (tptp.aa_nat_complex (tptp.power_power_complex (tptp.invers8013647133539491842omplex X)) N))) (= (tptp.aa_complex_complex (tptp.times_times_complex _let_1) _let_2) (tptp.aa_complex_complex (tptp.times_times_complex _let_2) _let_1))))) (forall ((X tptp.rat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_rat (tptp.power_power_rat X) M))) (let ((_let_2 (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_rat_rat tptp.inverse_inverse_rat X)) N))) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat _let_1) _let_2) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat _let_2) _let_1))))) (forall ((Xa tptp.nat) (X tptp.real)) (let ((_let_1 (tptp.aa_real_real tptp.inverse_inverse_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real Xa)))) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real _let_1) X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real X) _let_1)))) (forall ((Xa tptp.nat) (X tptp.complex)) (let ((_let_1 (tptp.invers8013647133539491842omplex (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex Xa)))) (= (tptp.aa_complex_complex (tptp.times_times_complex _let_1) X) (tptp.aa_complex_complex (tptp.times_times_complex X) _let_1)))) (forall ((Xa tptp.nat) (X tptp.rat)) (let ((_let_1 (tptp.aa_rat_rat tptp.inverse_inverse_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat Xa)))) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat _let_1) X) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat X) _let_1)))) (forall ((A tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_real_real tptp.inverse_inverse_real A)) (tptp.aa_real_real tptp.inverse_inverse_real (tptp.aa_real_real tptp.abs_abs_real A))))) (forall ((A tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (= (tptp.aa_rat_rat tptp.abs_abs_rat (tptp.aa_rat_rat tptp.inverse_inverse_rat A)) (tptp.aa_rat_rat tptp.inverse_inverse_rat (tptp.aa_rat_rat tptp.abs_abs_rat A))))) (forall ((Xa tptp.int) (X tptp.real)) (let ((_let_1 (tptp.aa_real_real tptp.inverse_inverse_real (tptp.aa_int_real tptp.ring_1_of_int_real Xa)))) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real _let_1) X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real X) _let_1)))) (forall ((Xa tptp.int) (X tptp.complex)) (let ((_let_1 (tptp.invers8013647133539491842omplex (tptp.ring_17405671764205052669omplex Xa)))) (= (tptp.aa_complex_complex (tptp.times_times_complex _let_1) X) (tptp.aa_complex_complex (tptp.times_times_complex X) _let_1)))) (forall ((Xa tptp.int) (X tptp.rat)) (let ((_let_1 (tptp.aa_rat_rat tptp.inverse_inverse_rat (tptp.aa_int_rat tptp.ring_1_of_int_rat Xa)))) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat _let_1) X) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat X) _let_1)))) (forall ((X tptp.real) (Y4 tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real X) Y4) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real X) (tptp.aa_real_real tptp.inverse_inverse_real Y4)))) (forall ((A tptp.complex)) (=> (tptp.member_complex A tptp.ring_1_Ints_complex) (= (= (tptp.plus_plus_complex A A) tptp.zero_zero_complex) (= A tptp.zero_zero_complex)))) (forall ((A tptp.real)) (=> (tptp.member_real A tptp.ring_1_Ints_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.member_rat A tptp.ring_1_Ints_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.member_int A tptp.ring_1_Ints_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 ((N tptp.nat) (K tptp.nat)) (= (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex (tptp.aa_nat_nat (tptp.binomial N) K)) (tptp.aa_nat_complex (tptp.gbinomial_complex (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex N)) K))) (forall ((N tptp.nat) (K tptp.nat)) (= (tptp.aa_nat_real tptp.semiri5074537144036343181t_real (tptp.aa_nat_nat (tptp.binomial N) K)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.gbinomial_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N)) K))) (forall ((N tptp.nat) (K tptp.nat)) (= (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat (tptp.aa_nat_nat (tptp.binomial N) K)) (tptp.aa_nat_rat (tptp.gbinomial_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat N)) K))) (forall ((A tptp.real) (B tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) B)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.inverse_inverse_real B)) (tptp.aa_real_real tptp.inverse_inverse_real A)))))) (forall ((A tptp.rat) (B tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) 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.inverse_inverse_rat B)) (tptp.aa_rat_rat tptp.inverse_inverse_rat A)))))) (forall ((A tptp.real) (B 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.aa_real_real tptp.inverse_inverse_real B))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real B) A))))) (forall ((A tptp.rat) (B 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.aa_rat_rat tptp.inverse_inverse_rat B))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) A))))) (forall ((A tptp.real) (B tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) B)) (=> (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.inverse_inverse_real B)) (tptp.aa_real_real tptp.inverse_inverse_real A)))))) (forall ((A tptp.rat) (B tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B)) (=> (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.inverse_inverse_rat B)) (tptp.aa_rat_rat tptp.inverse_inverse_rat A)))))) (forall ((A tptp.real) (B 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.aa_real_real tptp.inverse_inverse_real B))) (=> (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 B) A))))) (forall ((A tptp.rat) (B 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.aa_rat_rat tptp.inverse_inverse_rat B))) (=> (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 B) A))))) (forall ((X 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 X)) tptp.one_one_real)) (or (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.one_one_real) X))))) (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.inverse_inverse_rat X)) tptp.one_one_rat)) (or (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.one_one_rat) X))))) (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.inverse_inverse_real X))) (and (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))))) (forall ((X tptp.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.inverse_inverse_rat X))) (and (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 X) tptp.one_one_rat))))) (forall ((A 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 A) tptp.one_one_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real) (tptp.aa_real_real tptp.inverse_inverse_real 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.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.one_one_rat) (tptp.aa_rat_rat tptp.inverse_inverse_rat A)))))) (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (tptp.aa_real_real tptp.inverse_inverse_real B))) (let ((_let_2 (tptp.aa_real_real tptp.inverse_inverse_real A))) (=> (not (= A tptp.zero_zero_real)) (=> (not (= B tptp.zero_zero_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.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real _let_2) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) B))) _let_1))))))) (forall ((A tptp.complex) (B tptp.complex)) (let ((_let_1 (tptp.invers8013647133539491842omplex B))) (let ((_let_2 (tptp.invers8013647133539491842omplex A))) (=> (not (= A tptp.zero_zero_complex)) (=> (not (= B tptp.zero_zero_complex)) (= (tptp.plus_plus_complex _let_2 _let_1) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_complex_complex (tptp.times_times_complex _let_2) (tptp.plus_plus_complex A B))) _let_1))))))) (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (tptp.aa_rat_rat tptp.inverse_inverse_rat B))) (let ((_let_2 (tptp.aa_rat_rat tptp.inverse_inverse_rat A))) (=> (not (= A tptp.zero_zero_rat)) (=> (not (= B tptp.zero_zero_rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat _let_2) _let_1) (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 _let_2) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) B))) _let_1))))))) (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (tptp.aa_real_real tptp.inverse_inverse_real B))) (let ((_let_2 (tptp.aa_real_real tptp.inverse_inverse_real A))) (=> (not (= A tptp.zero_zero_real)) (=> (not (= B tptp.zero_zero_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.times_times_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) B)) _let_2)) _let_1))))))) (forall ((A tptp.complex) (B tptp.complex)) (let ((_let_1 (tptp.invers8013647133539491842omplex B))) (let ((_let_2 (tptp.invers8013647133539491842omplex A))) (=> (not (= A tptp.zero_zero_complex)) (=> (not (= B tptp.zero_zero_complex)) (= (tptp.plus_plus_complex _let_2 _let_1) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_complex_complex (tptp.times_times_complex (tptp.plus_plus_complex A B)) _let_2)) _let_1))))))) (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (tptp.aa_rat_rat tptp.inverse_inverse_rat B))) (let ((_let_2 (tptp.aa_rat_rat tptp.inverse_inverse_rat A))) (=> (not (= A tptp.zero_zero_rat)) (=> (not (= B tptp.zero_zero_rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat _let_2) _let_1) (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.plus_plus_rat A) B)) _let_2)) _let_1))))))) (forall ((A tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real tptp.inverse_inverse_real A)) A) tptp.one_one_real))) (forall ((A tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (tptp.aa_complex_complex (tptp.times_times_complex (tptp.invers8013647133539491842omplex A)) A) tptp.one_one_complex))) (forall ((A tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat tptp.inverse_inverse_rat A)) A) tptp.one_one_rat))) (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (tptp.aa_real_real tptp.inverse_inverse_real B))) (let ((_let_2 (tptp.aa_real_real tptp.inverse_inverse_real A))) (=> (not (= A tptp.zero_zero_real)) (=> (not (= B tptp.zero_zero_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.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real _let_2) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real B) A))) _let_1))))))) (forall ((A tptp.complex) (B tptp.complex)) (let ((_let_1 (tptp.invers8013647133539491842omplex B))) (let ((_let_2 (tptp.invers8013647133539491842omplex A))) (=> (not (= A tptp.zero_zero_complex)) (=> (not (= B tptp.zero_zero_complex)) (= (tptp.minus_minus_complex _let_2 _let_1) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_complex_complex (tptp.times_times_complex _let_2) (tptp.minus_minus_complex B A))) _let_1))))))) (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (tptp.aa_rat_rat tptp.inverse_inverse_rat B))) (let ((_let_2 (tptp.aa_rat_rat tptp.inverse_inverse_rat A))) (=> (not (= A tptp.zero_zero_rat)) (=> (not (= B tptp.zero_zero_rat)) (= (tptp.aa_rat_rat (tptp.minus_minus_rat _let_2) _let_1) (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 _let_2) (tptp.aa_rat_rat (tptp.minus_minus_rat B) A))) _let_1))))))) (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 ((A tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (tptp.aa_real_real tptp.inverse_inverse_real A) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.one_one_real) A)))) (forall ((A tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (tptp.invers8013647133539491842omplex A) (tptp.divide1717551699836669952omplex tptp.one_one_complex A)))) (forall ((A tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (= (tptp.aa_rat_rat tptp.inverse_inverse_rat A) (tptp.aa_rat_rat (tptp.divide_divide_rat tptp.one_one_rat) A)))) (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.plus_plus_complex A tptp.one_one_complex)) _let_1) (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.gbinomial_complex (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex N)))) (=> (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 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.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 ((K tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.gbinomial_rat (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 K) N)) (= (tptp.aa_nat_rat _let_1 K) (tptp.aa_nat_rat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) K)))))) (forall ((Y4 tptp.real) (A tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) Y4)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.powr_real (tptp.aa_real_real tptp.inverse_inverse_real Y4)) A) (tptp.aa_real_real tptp.inverse_inverse_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.powr_real Y4) A))))) (forall ((A tptp.complex)) (=> (tptp.member_complex A tptp.ring_1_Ints_complex) (not (= (tptp.plus_plus_complex (tptp.plus_plus_complex tptp.one_one_complex A) A) tptp.zero_zero_complex)))) (forall ((A tptp.real)) (=> (tptp.member_real A tptp.ring_1_Ints_real) (not (= (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) A)) A) tptp.zero_zero_real)))) (forall ((A tptp.rat)) (=> (tptp.member_rat A tptp.ring_1_Ints_rat) (not (= (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.one_one_rat) A)) A) tptp.zero_zero_rat)))) (forall ((A tptp.int)) (=> (tptp.member_int A tptp.ring_1_Ints_int) (not (= (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) A)) A) tptp.zero_zero_int)))) (forall ((B tptp.int) (A tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int B) A)) (tptp.member_complex (tptp.divide1717551699836669952omplex (tptp.ring_17405671764205052669omplex A) (tptp.ring_17405671764205052669omplex B)) tptp.ring_1_Ints_complex))) (forall ((B tptp.int) (A tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int B) A)) (tptp.member_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_int_real tptp.ring_1_of_int_real A)) (tptp.aa_int_real tptp.ring_1_of_int_real B)) tptp.ring_1_Ints_real))) (forall ((B tptp.int) (A tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int B) A)) (tptp.member_rat (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_int_rat tptp.ring_1_of_int_rat A)) (tptp.aa_int_rat tptp.ring_1_of_int_rat B)) tptp.ring_1_Ints_rat))) (forall ((B tptp.int) (A tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int B) A)) (tptp.member_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int (tptp.ring_1_of_int_int A)) (tptp.ring_1_of_int_int B)) tptp.ring_1_Ints_int))) (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) B))) (= (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.aa_real_real tptp.inverse_inverse_real B))) (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_eq_real B) A))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real _let_1) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) B))))))) (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) B))) (= (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.aa_rat_rat tptp.inverse_inverse_rat B))) (and (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) _let_1)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) A))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat _let_1) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B))))))) (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) B))) (= (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 B))) (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 B) A))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real _let_1) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B))))))) (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) B))) (= (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 B))) (and (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) _let_1)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) A))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat _let_1) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B))))))) (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.inverse_inverse_real X))) (and (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.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.one_one_rat) (tptp.aa_rat_rat tptp.inverse_inverse_rat X))) (and (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 X) tptp.one_one_rat))))) (forall ((X tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.inverse_inverse_real X)) tptp.one_one_real)) (or (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.one_one_real) X))))) (forall ((X 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 X)) tptp.one_one_rat)) (or (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.one_one_rat) X))))) (forall ((A 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 A) tptp.one_one_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.inverse_inverse_real 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.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.one_one_rat) (tptp.aa_rat_rat tptp.inverse_inverse_rat A)))))) (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (tptp.aa_real_real tptp.inverse_inverse_real B))) (let ((_let_2 (tptp.aa_real_real tptp.inverse_inverse_real A))) (=> (not (= A tptp.zero_zero_real)) (=> (not (= B tptp.zero_zero_real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real _let_2) _let_1) (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 _let_2) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A) B))) _let_1)))))))) (forall ((A tptp.complex) (B tptp.complex)) (let ((_let_1 (tptp.invers8013647133539491842omplex B))) (let ((_let_2 (tptp.invers8013647133539491842omplex A))) (=> (not (= A tptp.zero_zero_complex)) (=> (not (= B tptp.zero_zero_complex)) (= (tptp.minus_minus_complex _let_2 _let_1) (tptp.uminus1482373934393186551omplex (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_complex_complex (tptp.times_times_complex _let_2) (tptp.minus_minus_complex A B))) _let_1)))))))) (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (tptp.aa_rat_rat tptp.inverse_inverse_rat B))) (let ((_let_2 (tptp.aa_rat_rat tptp.inverse_inverse_rat A))) (=> (not (= A tptp.zero_zero_rat)) (=> (not (= B tptp.zero_zero_rat)) (= (tptp.aa_rat_rat (tptp.minus_minus_rat _let_2) _let_1) (tptp.aa_rat_rat tptp.uminus_uminus_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 _let_2) (tptp.aa_rat_rat (tptp.minus_minus_rat A) B))) _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)) (exists ((N2 tptp.nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.inverse_inverse_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real (tptp.aa_nat_nat tptp.suc N2)))) 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) X)) (exists ((N2 tptp.nat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat tptp.inverse_inverse_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat (tptp.aa_nat_nat tptp.suc N2)))) X))))) (forall ((A tptp.complex) (K tptp.nat)) (let ((_let_1 (tptp.gbinomial_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.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)) (= (tptp.aa_complex_complex (tptp.times_times_complex (tptp.minus_minus_complex A (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.minus_minus_complex A tptp.one_one_complex)) 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 ((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 ((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 ((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 ((A tptp.complex) (K tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc K))) (let ((_let_2 (tptp.gbinomial_complex A))) (let ((_let_3 (tptp.aa_nat_complex _let_2 K))) (= (tptp.aa_complex_complex (tptp.times_times_complex _let_3) A) (tptp.plus_plus_complex (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex K)) _let_3) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex _let_1)) (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))) (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 ((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.complex) (K tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc K))) (let ((_let_2 (tptp.gbinomial_complex A))) (let ((_let_3 (tptp.aa_nat_complex _let_2 K))) (= (tptp.aa_complex_complex (tptp.times_times_complex A) _let_3) (tptp.plus_plus_complex (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex K)) _let_3) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex _let_1)) (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))) (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 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 ((P tptp.fun_real_bool) (E2 tptp.real)) (=> (forall ((D2 tptp.real) (E tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real D2) E)) (=> (tptp.pp (tptp.aa_real_bool P D2)) (tptp.pp (tptp.aa_real_bool P E))))) (=> (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) E2)) (tptp.pp (tptp.aa_real_bool P E2)))))) (forall ((E2 tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) E2)) (exists ((N4 tptp.nat)) (let ((_let_1 (tptp.aa_real_real tptp.inverse_inverse_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N4)))) (and (not (= N4 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) E2))))))) (forall ((P tptp.fun_real_bool) (E2 tptp.real)) (=> (forall ((D2 tptp.real) (E tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real D2) E)) (=> (tptp.pp (tptp.aa_real_bool P D2)) (tptp.pp (tptp.aa_real_bool P E))))) (=> (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) E2)) (tptp.pp (tptp.aa_real_bool P E2)))))) (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.bit_se1146084159140164899it_int K) N))))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_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.bit_se3222712562003087583nteger A) B))) (= (tptp.pp (tptp.aa_Code_integer_bool _let_1 A)) (tptp.pp (tptp.aa_Code_integer_bool _let_1 B)))))) (forall ((A tptp.nat) (B 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.bit_se6528837805403552850or_nat A) B))) (= (tptp.pp (tptp.aa_nat_bool _let_1 A)) (tptp.pp (tptp.aa_nat_bool _let_1 B)))))) (forall ((A tptp.int) (B 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.bit_se6526347334894502574or_int A) B))) (= (tptp.pp (tptp.aa_int_bool _let_1 A)) (tptp.pp (tptp.aa_int_bool _let_1 B)))))) (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 ((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 ((A tptp.real)) (=> (tptp.member_real A tptp.ring_1_Ints_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.plus_plus_real tptp.one_one_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.member_rat A tptp.ring_1_Ints_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.plus_plus_rat tptp.one_one_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.member_int A tptp.ring_1_Ints_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) 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 ((X tptp.code_integer)) (=> (tptp.member_Code_integer X tptp.ring_11222124179247155820nteger) (=> (not (= X tptp.zero_z3403309356797280102nteger)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (tptp.abs_abs_Code_integer X)))))) (forall ((X tptp.rat)) (=> (tptp.member_rat X tptp.ring_1_Ints_rat) (=> (not (= X 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.abs_abs_rat X)))))) (forall ((X tptp.int)) (=> (tptp.member_int X tptp.ring_1_Ints_int) (=> (not (= X 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) (tptp.aa_int_int tptp.abs_abs_int X)))))) (forall ((X tptp.real)) (=> (tptp.member_real X tptp.ring_1_Ints_real) (=> (not (= X 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.abs_abs_real X)))))) (forall ((X tptp.code_integer)) (=> (tptp.member_Code_integer X tptp.ring_11222124179247155820nteger) (=> (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)) (= X tptp.zero_z3403309356797280102nteger)))) (forall ((X tptp.real)) (=> (tptp.member_real X tptp.ring_1_Ints_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)) (= X tptp.zero_zero_real)))) (forall ((X tptp.rat)) (=> (tptp.member_rat X tptp.ring_1_Ints_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)) (= X tptp.zero_zero_rat)))) (forall ((X tptp.int)) (=> (tptp.member_int X tptp.ring_1_Ints_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)) (= X tptp.zero_zero_int)))) (forall ((X tptp.code_integer) (Y4 tptp.code_integer)) (=> (tptp.member_Code_integer X tptp.ring_11222124179247155820nteger) (=> (tptp.member_Code_integer Y4 tptp.ring_11222124179247155820nteger) (= (= X Y4) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.abs_abs_Code_integer (tptp.minus_8373710615458151222nteger X Y4))) tptp.one_one_Code_integer)))))) (forall ((X tptp.real) (Y4 tptp.real)) (=> (tptp.member_real X tptp.ring_1_Ints_real) (=> (tptp.member_real Y4 tptp.ring_1_Ints_real) (= (= X Y4) (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))) tptp.one_one_real)))))) (forall ((X tptp.rat) (Y4 tptp.rat)) (=> (tptp.member_rat X tptp.ring_1_Ints_rat) (=> (tptp.member_rat Y4 tptp.ring_1_Ints_rat) (= (= X Y4) (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) Y4))) tptp.one_one_rat)))))) (forall ((X tptp.int) (Y4 tptp.int)) (=> (tptp.member_int X tptp.ring_1_Ints_int) (=> (tptp.member_int Y4 tptp.ring_1_Ints_int) (= (= X Y4) (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) Y4))) tptp.one_one_int)))))) (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 ((X 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)) (and (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_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.inverse_inverse_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N2))) 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) X)) (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)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat tptp.inverse_inverse_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat N2))) X)))))) (forall ((X tptp.real) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_real_fun_nat_real tptp.power_power_real X))) (=> (not (= X tptp.zero_zero_real)) (=> (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 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_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.power_power_real (tptp.aa_real_real tptp.inverse_inverse_real X)) M))))))) (forall ((X tptp.complex) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.power_power_complex X))) (=> (not (= X tptp.zero_zero_complex)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)) (= (tptp.aa_nat_complex _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) M)) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_nat_complex _let_1 N)) (tptp.aa_nat_complex (tptp.power_power_complex (tptp.invers8013647133539491842omplex X)) M))))))) (forall ((X tptp.rat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.power_power_rat X))) (=> (not (= X tptp.zero_zero_rat)) (=> (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 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_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.power_power_rat (tptp.aa_rat_rat tptp.inverse_inverse_rat X)) M))))))) (forall ((K tptp.nat) (A tptp.complex)) (let ((_let_1 (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.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.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.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.minus_minus_complex A tptp.one_one_complex)) 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) (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) (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.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.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 ((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 ((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 ((X tptp.real)) (let ((_let_1 (tptp.aa_real_real tptp.archim2898591450579166408c_real (tptp.aa_real_real tptp.uminus_uminus_real X)))) (let ((_let_2 (tptp.member_real X tptp.ring_1_Ints_real))) (and (=> _let_2 (= _let_1 tptp.zero_zero_real)) (=> (not _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.archim2898591450579166408c_real X)))))))) (forall ((X tptp.rat)) (let ((_let_1 (tptp.aa_rat_rat tptp.archimedean_frac_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat X)))) (let ((_let_2 (tptp.member_rat X tptp.ring_1_Ints_rat))) (and (=> _let_2 (= _let_1 tptp.zero_zero_rat)) (=> (not _let_2) (= _let_1 (tptp.aa_rat_rat (tptp.minus_minus_rat tptp.one_one_rat) (tptp.aa_rat_rat tptp.archimedean_frac_rat X)))))))) (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.power_power_nat _let_1) N)))))))) (forall ((A tptp.complex) (K tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc K))) (let ((_let_2 (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.divide1717551699836669952omplex _let_2 (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex _let_1))) (tptp.aa_nat_complex (tptp.gbinomial_complex 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 ((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.complex) (K tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc K))) (let ((_let_2 (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.divide1717551699836669952omplex _let_2 (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex _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.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 ((K tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.power_power_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.minus_minus_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.minus_minus_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.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 ((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 ((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.uminus1482373934393186551omplex tptp.one_one_complex)) K)) (tptp.aa_nat_complex (tptp.gbinomial_complex (tptp.minus_minus_complex (tptp.minus_minus_complex (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex K) A) tptp.one_one_complex)) 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 ((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 ((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 ((A tptp.real) (B tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) A)) (=> (tptp.member_real A tptp.ring_1_Ints_real) (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 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_real_int tptp.archim6058952711729229775r_real A)) (tptp.aa_real_int tptp.archim6058952711729229775r_real B)))) (tptp.aa_int_rat tptp.ring_1_of_int_rat (tptp.aa_real_int tptp.archim6058952711729229775r_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) B)))))))) (forall ((A tptp.real) (B tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) A)) (=> (tptp.member_real A tptp.ring_1_Ints_real) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.ring_1_of_int_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_real_int tptp.archim6058952711729229775r_real A)) (tptp.aa_real_int tptp.archim6058952711729229775r_real B)))) (tptp.ring_1_of_int_int (tptp.aa_real_int tptp.archim6058952711729229775r_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) B)))))))) (forall ((A tptp.real) (B tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) A)) (=> (tptp.member_real A tptp.ring_1_Ints_real) (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.aa_int_fun_int_int tptp.times_times_int (tptp.aa_real_int tptp.archim6058952711729229775r_real A)) (tptp.aa_real_int tptp.archim6058952711729229775r_real B)))) (tptp.aa_int_real tptp.ring_1_of_int_real (tptp.aa_real_int tptp.archim6058952711729229775r_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) B)))))))) (forall ((A tptp.rat) (B 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.member_rat A tptp.ring_1_Ints_rat) (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 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_rat_int tptp.archim3151403230148437115or_rat A)) (tptp.aa_rat_int tptp.archim3151403230148437115or_rat B)))) (tptp.aa_int_rat tptp.ring_1_of_int_rat (tptp.aa_rat_int tptp.archim3151403230148437115or_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) B)))))))) (forall ((A tptp.rat) (B 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.member_rat A tptp.ring_1_Ints_rat) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.ring_1_of_int_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_rat_int tptp.archim3151403230148437115or_rat A)) (tptp.aa_rat_int tptp.archim3151403230148437115or_rat B)))) (tptp.ring_1_of_int_int (tptp.aa_rat_int tptp.archim3151403230148437115or_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) B)))))))) (forall ((A tptp.rat) (B 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.member_rat A tptp.ring_1_Ints_rat) (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.aa_int_fun_int_int tptp.times_times_int (tptp.aa_rat_int tptp.archim3151403230148437115or_rat A)) (tptp.aa_rat_int tptp.archim3151403230148437115or_rat B)))) (tptp.aa_int_real tptp.ring_1_of_int_real (tptp.aa_rat_int tptp.archim3151403230148437115or_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) B)))))))) (forall ((X tptp.rat) (A tptp.rat)) (= (= (tptp.aa_rat_rat tptp.archimedean_frac_rat X) A) (and (tptp.member_rat (tptp.aa_rat_rat (tptp.minus_minus_rat X) A) tptp.ring_1_Ints_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_rat A) tptp.one_one_rat))))) (forall ((X tptp.real) (A tptp.real)) (= (= (tptp.aa_real_real tptp.archim2898591450579166408c_real X) A) (and (tptp.member_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real X) A) tptp.ring_1_Ints_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_real A) tptp.one_one_real))))) (forall ((A tptp.rat) (B 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.member_rat A tptp.ring_1_Ints_rat) (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 (tptp.aa_rat_int tptp.archim2889992004027027881ng_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) B)))) (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_rat_int tptp.archim2889992004027027881ng_rat A)) (tptp.aa_rat_int tptp.archim2889992004027027881ng_rat B)))))))) (forall ((A tptp.rat) (B 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.member_rat A tptp.ring_1_Ints_rat) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.ring_1_of_int_int (tptp.aa_rat_int tptp.archim2889992004027027881ng_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) B)))) (tptp.ring_1_of_int_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_rat_int tptp.archim2889992004027027881ng_rat A)) (tptp.aa_rat_int tptp.archim2889992004027027881ng_rat B)))))))) (forall ((A tptp.rat) (B 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.member_rat A tptp.ring_1_Ints_rat) (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_rat_int tptp.archim2889992004027027881ng_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) B)))) (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_rat_int tptp.archim2889992004027027881ng_rat A)) (tptp.aa_rat_int tptp.archim2889992004027027881ng_rat B)))))))) (forall ((A tptp.real) (B tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) A)) (=> (tptp.member_real A tptp.ring_1_Ints_real) (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 (tptp.aa_real_int tptp.archim7802044766580827645g_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) B)))) (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_real_int tptp.archim7802044766580827645g_real A)) (tptp.aa_real_int tptp.archim7802044766580827645g_real B)))))))) (forall ((A tptp.real) (B tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) A)) (=> (tptp.member_real A tptp.ring_1_Ints_real) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.ring_1_of_int_int (tptp.aa_real_int tptp.archim7802044766580827645g_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) B)))) (tptp.ring_1_of_int_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_real_int tptp.archim7802044766580827645g_real A)) (tptp.aa_real_int tptp.archim7802044766580827645g_real B)))))))) (forall ((A tptp.real) (B tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) A)) (=> (tptp.member_real A tptp.ring_1_Ints_real) (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_real_int tptp.archim7802044766580827645g_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) B)))) (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_real_int tptp.archim7802044766580827645g_real A)) (tptp.aa_real_int tptp.archim7802044766580827645g_real B)))))))) (forall ((A tptp.complex) (K tptp.nat)) (= (tptp.aa_nat_complex (tptp.gbinomial_complex (tptp.uminus1482373934393186551omplex A)) K) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_nat_complex (tptp.power_power_complex (tptp.uminus1482373934393186551omplex tptp.one_one_complex)) K)) (tptp.aa_nat_complex (tptp.gbinomial_complex (tptp.minus_minus_complex (tptp.plus_plus_complex A (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex K)) tptp.one_one_complex)) 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 ((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 ((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 ((K tptp.nat) (A tptp.complex)) (let ((_let_1 (tptp.gbinomial_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.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 ((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.divide1717551699836669952omplex (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_nat_complex (tptp.power_power_complex (tptp.uminus1482373934393186551omplex tptp.one_one_complex)) K)) (tptp.aa_nat_complex (tptp.comm_s2602460028002588243omplex (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_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 ((A tptp.complex) (K tptp.nat)) (= (tptp.aa_nat_complex (tptp.gbinomial_complex A) K) (tptp.divide1717551699836669952omplex (tptp.aa_nat_complex (tptp.comm_s2602460028002588243omplex (tptp.plus_plus_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 ((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 ((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 ((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.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.modulo_modulo_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.modulo_modulo_nat M) _let_1)) (tptp.aa_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.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 ((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 ((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.bit_se6528837805403552850or_nat M) N) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_bool_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.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 ((A tptp.code_integer)) (let ((_let_1 (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))) A))) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.bit_se3222712562003087583nteger tptp.one_one_Code_integer) A) (tptp.minus_8373710615458151222nteger (tptp.plus_p5714425477246183910nteger A (tptp.aa_bool_Code_integer tptp.zero_n356916108424825756nteger _let_1)) (tptp.aa_bool_Code_integer tptp.zero_n356916108424825756nteger (tptp.aa_bool_bool tptp.fNot _let_1)))))) (forall ((A 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))) A))) (= (tptp.aa_nat_nat (tptp.bit_se6528837805403552850or_nat tptp.one_one_nat) 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 A) (tptp.aa_bool_nat tptp.zero_n2687167440665602831ol_nat _let_1))) (tptp.aa_bool_nat tptp.zero_n2687167440665602831ol_nat (tptp.aa_bool_bool tptp.fNot _let_1)))))) (forall ((A tptp.int)) (let ((_let_1 (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))) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se6526347334894502574or_int tptp.one_one_int) 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.plus_plus_int A) (tptp.aa_bool_int tptp.zero_n2684676970156552555ol_int _let_1))) (tptp.aa_bool_int tptp.zero_n2684676970156552555ol_int (tptp.aa_bool_bool tptp.fNot _let_1)))))) (forall ((A tptp.code_integer)) (let ((_let_1 (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))) A))) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.bit_se3222712562003087583nteger A) tptp.one_one_Code_integer) (tptp.minus_8373710615458151222nteger (tptp.plus_p5714425477246183910nteger A (tptp.aa_bool_Code_integer tptp.zero_n356916108424825756nteger _let_1)) (tptp.aa_bool_Code_integer tptp.zero_n356916108424825756nteger (tptp.aa_bool_bool tptp.fNot _let_1)))))) (forall ((A 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))) A))) (= (tptp.aa_nat_nat (tptp.bit_se6528837805403552850or_nat A) tptp.one_one_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) (tptp.aa_bool_nat tptp.zero_n2687167440665602831ol_nat _let_1))) (tptp.aa_bool_nat tptp.zero_n2687167440665602831ol_nat (tptp.aa_bool_bool tptp.fNot _let_1)))))) (forall ((A tptp.int)) (let ((_let_1 (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))) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se6526347334894502574or_int A) tptp.one_one_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) (tptp.aa_bool_int tptp.zero_n2684676970156552555ol_int _let_1))) (tptp.aa_bool_int tptp.zero_n2684676970156552555ol_int (tptp.aa_bool_bool tptp.fNot _let_1)))))) (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 ((X 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.cos_real X))) (=> (not (= _let_2 tptp.zero_zero_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 (tptp.aa_real_real tptp.tan_real X)) _let_1)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real tptp.inverse_inverse_real _let_2)) _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.cos_complex X))) (=> (not (= _let_2 tptp.zero_zero_complex)) (= (tptp.plus_plus_complex tptp.one_one_complex (tptp.aa_nat_complex (tptp.power_power_complex (tptp.tan_complex X)) _let_1)) (tptp.aa_nat_complex (tptp.power_power_complex (tptp.invers8013647133539491842omplex _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.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 ((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 ((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 ((X tptp.real)) (= (= (tptp.aa_real_real tptp.cosh_real X) tptp.zero_zero_real) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real tptp.exp_real X)) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)))) (forall ((X tptp.complex)) (= (= (tptp.cosh_complex X) tptp.zero_zero_complex) (= (tptp.aa_nat_complex (tptp.power_power_complex (tptp.exp_complex X)) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.uminus1482373934393186551omplex tptp.one_one_complex)))) (forall ((N tptp.num)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat N))) (= (tptp.bit_se7788150548672797655nteger _let_1 (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.power_8256067586552552935nteger (tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one)) _let_1))))) (forall ((N tptp.num)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat N))) (= (tptp.bit_se545348938243370406it_int _let_1 (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))) _let_1))))) (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.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.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)) (= (tptp.bit_se545348938243370406it_int N tptp.zero_zero_int) tptp.zero_zero_int)) (forall ((N tptp.nat)) (= (tptp.aa_nat_nat (tptp.bit_se547839408752420682it_nat N) tptp.zero_zero_nat) tptp.zero_zero_nat)) (forall ((N tptp.nat) (A tptp.int)) (= (= (tptp.bit_se545348938243370406it_int N A) tptp.zero_zero_int) (= A tptp.zero_zero_int))) (forall ((N tptp.nat) (A tptp.nat)) (= (= (tptp.aa_nat_nat (tptp.bit_se547839408752420682it_nat N) A) tptp.zero_zero_nat) (= A tptp.zero_zero_nat))) (= (tptp.sinh_complex tptp.zero_zero_complex) tptp.zero_zero_complex) (= (tptp.aa_real_real tptp.sinh_real tptp.zero_zero_real) tptp.zero_zero_real) (forall ((M tptp.nat) (N tptp.nat) (A tptp.int)) (= (tptp.bit_se545348938243370406it_int M (tptp.bit_se545348938243370406it_int N A)) (tptp.bit_se545348938243370406it_int (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) N) A))) (forall ((M tptp.nat) (N tptp.nat) (A tptp.nat)) (= (tptp.aa_nat_nat (tptp.bit_se547839408752420682it_nat M) (tptp.aa_nat_nat (tptp.bit_se547839408752420682it_nat N) A)) (tptp.aa_nat_nat (tptp.bit_se547839408752420682it_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) N)) A))) (forall ((N tptp.nat) (A tptp.int) (B tptp.int)) (= (tptp.bit_se545348938243370406it_int N (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se725231765392027082nd_int A) B)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se725231765392027082nd_int (tptp.bit_se545348938243370406it_int N A)) (tptp.bit_se545348938243370406it_int N B)))) (forall ((N tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (tptp.bit_se547839408752420682it_nat N))) (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.bit_se727722235901077358nd_nat A) B)) (tptp.aa_nat_nat (tptp.bit_se727722235901077358nd_nat (tptp.aa_nat_nat _let_1 A)) (tptp.aa_nat_nat _let_1 B))))) (forall ((N tptp.nat) (A tptp.int) (B tptp.int)) (= (tptp.bit_se545348938243370406it_int N (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se6526347334894502574or_int A) B)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se6526347334894502574or_int (tptp.bit_se545348938243370406it_int N A)) (tptp.bit_se545348938243370406it_int N B)))) (forall ((N tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (tptp.bit_se547839408752420682it_nat N))) (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.bit_se6528837805403552850or_nat A) B)) (tptp.aa_nat_nat (tptp.bit_se6528837805403552850or_nat (tptp.aa_nat_nat _let_1 A)) (tptp.aa_nat_nat _let_1 B))))) (forall ((N tptp.nat) (L tptp.int)) (= (tptp.aa_int_int (tptp.bit_concat_bit N tptp.zero_zero_int) L) (tptp.bit_se545348938243370406it_int N L))) (forall ((X tptp.real)) (= (= (tptp.aa_real_real tptp.sinh_real X) tptp.zero_zero_real) (= X tptp.zero_zero_real))) (forall ((X tptp.real) (Y4 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 Y4))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) Y4)))) (= (tptp.cosh_complex tptp.zero_zero_complex) tptp.one_one_complex) (= (tptp.aa_real_real tptp.cosh_real tptp.zero_zero_real) tptp.one_one_real) (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)) (= (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.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 ((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.aa_int_fun_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.aa_int_fun_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) (K tptp.num)) (= (tptp.bit_se545348938243370406it_int (tptp.aa_nat_nat tptp.suc N) (tptp.aa_num_int tptp.numeral_numeral_int K)) (tptp.bit_se545348938243370406it_int N (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 K))))) (forall ((N tptp.nat) (K tptp.num)) (= (tptp.aa_nat_nat (tptp.bit_se547839408752420682it_nat (tptp.aa_nat_nat tptp.suc N)) (tptp.aa_num_nat tptp.numeral_numeral_nat K)) (tptp.aa_nat_nat (tptp.bit_se547839408752420682it_nat N) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 K))))) (forall ((N tptp.nat) (K tptp.num)) (= (tptp.bit_se7788150548672797655nteger (tptp.aa_nat_nat tptp.suc N) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.numera6620942414471956472nteger K))) (tptp.bit_se7788150548672797655nteger N (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 K)))))) (forall ((N tptp.nat) (K tptp.num)) (= (tptp.bit_se545348938243370406it_int (tptp.aa_nat_nat tptp.suc N) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int K))) (tptp.bit_se545348938243370406it_int N (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 K)))))) (forall ((L tptp.num) (K tptp.num)) (= (tptp.bit_se545348938243370406it_int (tptp.aa_num_nat tptp.numeral_numeral_nat L) (tptp.aa_num_int tptp.numeral_numeral_int K)) (tptp.bit_se545348938243370406it_int (tptp.aa_num_nat tptp.pred_numeral L) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 K))))) (forall ((L tptp.num) (K tptp.num)) (= (tptp.aa_nat_nat (tptp.bit_se547839408752420682it_nat (tptp.aa_num_nat tptp.numeral_numeral_nat L)) (tptp.aa_num_nat tptp.numeral_numeral_nat K)) (tptp.aa_nat_nat (tptp.bit_se547839408752420682it_nat (tptp.aa_num_nat tptp.pred_numeral L)) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 K))))) (forall ((N tptp.nat) (A tptp.int)) (= (tptp.bit_se545348938243370406it_int (tptp.aa_nat_nat tptp.suc N) A) (tptp.bit_se545348938243370406it_int N (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one)))))) (forall ((N tptp.nat) (A tptp.nat)) (= (tptp.aa_nat_nat (tptp.bit_se547839408752420682it_nat (tptp.aa_nat_nat tptp.suc N)) A) (tptp.aa_nat_nat (tptp.bit_se547839408752420682it_nat N) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) (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.bit_se547839408752420682it_nat N) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)) (tptp.aa_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.bit_se545348938243370406it_int N 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))) (forall ((N tptp.nat)) (= (tptp.aa_nat_nat (tptp.bit_se547839408752420682it_nat N) tptp.one_one_nat) (tptp.aa_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) (A tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.bit_se7788150548672797655nteger N A))) (or (not (= N tptp.zero_zero_nat)) (tptp.pp (tptp.aa_Code_integer_bool _let_1 A)))))) (forall ((N 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.bit_se545348938243370406it_int N A))) (or (not (= N tptp.zero_zero_nat)) (tptp.pp (tptp.aa_int_bool _let_1 A)))))) (forall ((N 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.bit_se547839408752420682it_nat N) A))) (or (not (= N tptp.zero_zero_nat)) (tptp.pp (tptp.aa_nat_bool _let_1 A)))))) (forall ((L tptp.num) (K tptp.num)) (= (tptp.bit_se7788150548672797655nteger (tptp.aa_num_nat tptp.numeral_numeral_nat L) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.numera6620942414471956472nteger K))) (tptp.bit_se7788150548672797655nteger (tptp.aa_num_nat tptp.pred_numeral L) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 K)))))) (forall ((L tptp.num) (K tptp.num)) (= (tptp.bit_se545348938243370406it_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 K))) (tptp.bit_se545348938243370406it_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.bit0 K)))))) (forall ((N tptp.nat) (K tptp.int)) (= (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_se2159334234014336723it_int N) K) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se6526347334894502574or_int K) (tptp.bit_se545348938243370406it_int N tptp.one_one_int)))) (forall ((K tptp.int) (L tptp.int) (N tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.bit_se1146084159140164899it_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se6526347334894502574or_int K) L)) N)) (not (= (tptp.pp (tptp.aa_nat_bool (tptp.bit_se1146084159140164899it_int K) N)) (tptp.pp (tptp.aa_nat_bool (tptp.bit_se1146084159140164899it_int L) N)))))) (forall ((X tptp.real) (Y4 tptp.real)) (= (tptp.aa_real_real tptp.sinh_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) Y4)) (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.sinh_real X)) (tptp.aa_real_real tptp.cosh_real Y4))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real tptp.cosh_real X)) (tptp.aa_real_real tptp.sinh_real Y4))))) (forall ((X tptp.real) (Y4 tptp.real)) (= (tptp.aa_real_real tptp.cosh_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) Y4)) (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.cosh_real X)) (tptp.aa_real_real tptp.cosh_real Y4))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real tptp.sinh_real X)) (tptp.aa_real_real tptp.sinh_real Y4))))) (forall ((X tptp.real) (Y4 tptp.real)) (= (tptp.aa_real_real tptp.cosh_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real X) Y4)) (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.cosh_real X)) (tptp.aa_real_real tptp.cosh_real Y4))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real tptp.sinh_real X)) (tptp.aa_real_real tptp.sinh_real Y4))))) (forall ((X tptp.real) (Y4 tptp.real)) (= (tptp.aa_real_real tptp.sinh_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real X) Y4)) (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.sinh_real X)) (tptp.aa_real_real tptp.cosh_real Y4))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real tptp.cosh_real X)) (tptp.aa_real_real tptp.sinh_real Y4))))) (forall ((X tptp.real)) (not (= (tptp.aa_real_real tptp.cosh_real X) tptp.zero_zero_real))) (forall ((N tptp.nat) (K tptp.int)) (= (tptp.aa_nat_nat (tptp.bit_se547839408752420682it_nat N) (tptp.aa_int_nat tptp.nat2 K)) (tptp.aa_int_nat tptp.nat2 (tptp.bit_se545348938243370406it_int N 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.sinh_real X)) (tptp.aa_real_real tptp.cosh_real X)))) (forall ((N tptp.nat) (M tptp.nat)) (= (tptp.bit_se545348938243370406it_int N (tptp.aa_nat_int tptp.semiri1314217659103216013at_int M)) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_nat (tptp.bit_se547839408752420682it_nat N) M)))) (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.bit_se547839408752420682it_nat N))) (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat M)) (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat (tptp.aa_nat_nat _let_1 M))))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_nat (tptp.bit_se547839408752420682it_nat M) N)) (tptp.bit_se545348938243370406it_int M (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N)))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.bit_se547839408752420682it_nat M))) (= (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat (tptp.aa_nat_nat _let_1 N)) (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat N))))) (forall ((N tptp.nat) (A tptp.code_integer)) (= (tptp.bit_se7788150548672797655nteger N (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A)) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.bit_se7788150548672797655nteger N A)))) (forall ((N tptp.nat) (A tptp.int)) (= (tptp.bit_se545348938243370406it_int N (tptp.aa_int_int tptp.uminus_uminus_int A)) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.bit_se545348938243370406it_int N A)))) (forall ((N tptp.nat) (A tptp.int) (B tptp.int)) (= (tptp.bit_se545348938243370406it_int N (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) B)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.bit_se545348938243370406it_int N A)) (tptp.bit_se545348938243370406it_int N B)))) (forall ((N tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (tptp.bit_se547839408752420682it_nat N))) (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) B)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat _let_1 A)) (tptp.aa_nat_nat _let_1 B))))) (forall ((N tptp.nat) (K tptp.int)) (= (tptp.bit_se545348938243370406it_int N (tptp.ring_1_of_int_int K)) (tptp.ring_1_of_int_int (tptp.bit_se545348938243370406it_int N K)))) (forall ((X tptp.complex)) (= (tptp.tanh_complex X) (tptp.divide1717551699836669952omplex (tptp.sinh_complex X) (tptp.cosh_complex X)))) (forall ((X tptp.real)) (= (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.sinh_real X)) (tptp.aa_real_real tptp.cosh_real X)))) (forall ((X tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real tptp.sinh_real X)) (tptp.aa_real_real tptp.cosh_real X)) (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_real_real tptp.exp_real (tptp.aa_real_real tptp.uminus_uminus_real X))))) (forall ((X tptp.complex)) (= (tptp.minus_minus_complex (tptp.sinh_complex X) (tptp.cosh_complex X)) (tptp.uminus1482373934393186551omplex (tptp.exp_complex (tptp.uminus1482373934393186551omplex X))))) (forall ((X tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real tptp.cosh_real X)) (tptp.aa_real_real tptp.sinh_real X)) (tptp.aa_real_real tptp.exp_real (tptp.aa_real_real tptp.uminus_uminus_real X)))) (forall ((X tptp.complex)) (= (tptp.minus_minus_complex (tptp.cosh_complex X) (tptp.sinh_complex X)) (tptp.exp_complex (tptp.uminus1482373934393186551omplex X)))) (forall ((X tptp.int) (Y4 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 Y4)) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se6526347334894502574or_int X) Y4))))))) (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) (Y4 tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y4))) (=> (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 Y4))) (tptp.pp (tptp.aa_real_bool _let_1 X))))))) (forall ((X tptp.real) (Y4 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 Y4)) (= (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 Y4))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) Y4))))))) (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)) (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 ((X tptp.complex)) (let ((_let_1 (tptp.times_times_complex (tptp.numera6690914467698888265omplex (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.sinh_complex (tptp.aa_complex_complex _let_1 X)) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_complex_complex _let_1 (tptp.sinh_complex X))) (tptp.cosh_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.sinh_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.sinh_real X))) (tptp.aa_real_real tptp.cosh_real X))))) (forall ((M tptp.nat) (N tptp.nat) (A tptp.int)) (= (tptp.bit_se545348938243370406it_int M (tptp.aa_int_int (tptp.bit_se2923211474154528505it_int N) A)) (tptp.aa_int_int (tptp.bit_se2923211474154528505it_int (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) N)) (tptp.bit_se545348938243370406it_int M A)))) (forall ((M tptp.nat) (N tptp.nat) (A tptp.nat)) (let ((_let_1 (tptp.bit_se547839408752420682it_nat M))) (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.bit_se2925701944663578781it_nat N) A)) (tptp.aa_nat_nat (tptp.bit_se2925701944663578781it_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) N)) (tptp.aa_nat_nat _let_1 A))))) (forall ((M tptp.nat) (N tptp.nat) (A tptp.int)) (= (tptp.aa_int_int (tptp.bit_se2923211474154528505it_int M) (tptp.bit_se545348938243370406it_int N A)) (tptp.bit_se545348938243370406it_int N (tptp.aa_int_int (tptp.bit_se2923211474154528505it_int (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) N)) A)))) (forall ((M tptp.nat) (N tptp.nat) (A tptp.nat)) (let ((_let_1 (tptp.bit_se547839408752420682it_nat N))) (= (tptp.aa_nat_nat (tptp.bit_se2925701944663578781it_nat M) (tptp.aa_nat_nat _let_1 A)) (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.bit_se2925701944663578781it_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) N)) A))))) (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.bit_se6528837805403552850or_nat N) (tptp.aa_nat_nat (tptp.bit_se547839408752420682it_nat M) tptp.one_one_nat)))) (forall ((X tptp.real) (Y4 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 Y4) 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 Y4))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y4) X)))))) (forall ((X tptp.real) (Y4 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 Y4)) (= (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 Y4))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Y4))))))) (forall ((X tptp.real) (Y4 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) Y4)) (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 Y4)))))) (forall ((M tptp.nat) (K tptp.int) (N tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.bit_se1146084159140164899it_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.bit_se1146084159140164899it_int K) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) M)))))) (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.cosh_real X)) _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_real_real tptp.sinh_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_nat_complex (tptp.power_power_complex (tptp.cosh_complex X)) _let_1) (tptp.plus_plus_complex (tptp.aa_nat_complex (tptp.power_power_complex (tptp.sinh_complex X)) _let_1) tptp.one_one_complex)))) (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.sinh_complex X)) _let_1) (tptp.minus_minus_complex (tptp.aa_nat_complex (tptp.power_power_complex (tptp.cosh_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_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real tptp.sinh_real 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_real_real tptp.cosh_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.minus_minus_complex (tptp.aa_nat_complex (tptp.power_power_complex (tptp.cosh_complex X)) _let_1) (tptp.aa_nat_complex (tptp.power_power_complex (tptp.sinh_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.minus_minus_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real tptp.cosh_real X)) _let_1)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real tptp.sinh_real X)) _let_1)) tptp.one_one_real))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.aa_nat_nat (tptp.bit_se6528837805403552850or_nat M) N) (tptp.aa_int_nat tptp.nat2 (tptp.aa_int_int (tptp.aa_int_fun_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.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 ((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.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.bit_se545348938243370406it_int N L)))) (forall ((N tptp.nat) (A tptp.code_integer)) (= (tptp.bit_se1345352211410354436nteger N A) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.bit_se3222712562003087583nteger A) (tptp.bit_se7788150548672797655nteger N tptp.one_one_Code_integer)))) (forall ((N tptp.nat) (A tptp.int)) (= (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_se2159334234014336723it_int N) A) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se6526347334894502574or_int A) (tptp.bit_se545348938243370406it_int N tptp.one_one_int)))) (forall ((N tptp.nat) (A tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se2161824704523386999it_nat N) A) (tptp.aa_nat_nat (tptp.bit_se6528837805403552850or_nat A) (tptp.aa_nat_nat (tptp.bit_se547839408752420682it_nat N) tptp.one_one_nat)))) (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.cosh_complex (tptp.aa_complex_complex (tptp.times_times_complex (tptp.numera6690914467698888265omplex _let_1)) X)) (tptp.plus_plus_complex (tptp.aa_nat_complex (tptp.power_power_complex (tptp.cosh_complex X)) _let_2) (tptp.aa_nat_complex (tptp.power_power_complex (tptp.sinh_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.cosh_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.plus_plus_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real tptp.cosh_real X)) _let_2)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real tptp.sinh_real X)) _let_2)))))) (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.bit_se545348938243370406it_int N (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 (tptp.bit_se545348938243370406it_int N 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)))) (let ((_let_2 (tptp.bit_se547839408752420682it_nat N))) (= (tptp.aa_nat_nat _let_2 (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 (tptp.aa_nat_nat _let_2 A)) _let_1))))) (forall ((A tptp.int) (N tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.bit_se1146084159140164899it_int A) N)) (not (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se725231765392027082nd_int A) (tptp.bit_se545348938243370406it_int N tptp.one_one_int)) tptp.zero_zero_int)))) (forall ((A tptp.nat) (N tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.bit_se1148574629649215175it_nat A) N)) (not (= (tptp.aa_nat_nat (tptp.bit_se727722235901077358nd_nat A) (tptp.aa_nat_nat (tptp.bit_se547839408752420682it_nat N) tptp.one_one_nat)) tptp.zero_zero_nat)))) (forall ((N tptp.nat) (K tptp.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.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.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N)))) (forall ((N tptp.nat) (A tptp.int)) (= (tptp.bit_se545348938243370406it_int N A) (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_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) N)))) (forall ((N tptp.nat) (A tptp.nat)) (= (tptp.aa_nat_nat (tptp.bit_se547839408752420682it_nat N) A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) (tptp.aa_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) (A tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.power_8256067586552552935nteger (tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one)) N)) A)) (not (forall ((B2 tptp.code_integer)) (not (= A (tptp.bit_se7788150548672797655nteger N B2))))))) (forall ((N tptp.nat) (A tptp.int)) (=> (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)) A)) (not (forall ((B2 tptp.int)) (not (= A (tptp.bit_se545348938243370406it_int N B2))))))) (forall ((N tptp.nat) (A tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_nat_nat (tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N)) A)) (not (forall ((B2 tptp.nat)) (not (= A (tptp.aa_nat_nat (tptp.bit_se547839408752420682it_nat N) B2))))))) (forall ((N tptp.nat)) (= (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.complex) (Y4 tptp.complex)) (let ((_let_1 (tptp.tanh_complex Y4))) (let ((_let_2 (tptp.tanh_complex X))) (=> (not (= (tptp.cosh_complex X) tptp.zero_zero_complex)) (=> (not (= (tptp.cosh_complex Y4) tptp.zero_zero_complex)) (= (tptp.tanh_complex (tptp.plus_plus_complex X Y4)) (tptp.divide1717551699836669952omplex (tptp.plus_plus_complex _let_2 _let_1) (tptp.plus_plus_complex tptp.one_one_complex (tptp.aa_complex_complex (tptp.times_times_complex _let_2) _let_1))))))))) (forall ((X tptp.real) (Y4 tptp.real)) (let ((_let_1 (tptp.aa_real_real tptp.tanh_real Y4))) (let ((_let_2 (tptp.aa_real_real tptp.tanh_real X))) (=> (not (= (tptp.aa_real_real tptp.cosh_real X) tptp.zero_zero_real)) (=> (not (= (tptp.aa_real_real tptp.cosh_real Y4) tptp.zero_zero_real)) (= (tptp.aa_real_real tptp.tanh_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) Y4)) (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.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.int) (N tptp.nat) (Y4 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 Y4) _let_1)) (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.bit_se6526347334894502574or_int X) Y4)) _let_1))))))) (forall ((Z tptp.real)) (= (tptp.aa_real_real tptp.cosh_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.exp_real Z)) (tptp.aa_real_real tptp.exp_real (tptp.aa_real_real tptp.uminus_uminus_real Z)))) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))))) (forall ((Z tptp.complex)) (= (tptp.cosh_complex Z) (tptp.divide1717551699836669952omplex (tptp.plus_plus_complex (tptp.exp_complex Z) (tptp.exp_complex (tptp.uminus1482373934393186551omplex Z))) (tptp.numera6690914467698888265omplex (tptp.aa_num_num tptp.bit0 tptp.one))))) (forall ((A tptp.real) (B 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 B) _let_1)))) (= (tptp.invers8013647133539491842omplex (tptp.complex2 A B)) (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 B)) _let_2)))))) (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.aa_int_fun_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.aa_int_fun_int_int tptp.bit_se6526347334894502574or_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int K) _let_1)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int L) _let_1)))))))) (forall ((Z tptp.real)) (= (tptp.aa_real_real tptp.sinh_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.exp_real Z)) (tptp.aa_real_real tptp.exp_real (tptp.aa_real_real tptp.uminus_uminus_real Z)))) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))))) (forall ((Z tptp.complex)) (= (tptp.sinh_complex Z) (tptp.divide1717551699836669952omplex (tptp.minus_minus_complex (tptp.exp_complex Z) (tptp.exp_complex (tptp.uminus1482373934393186551omplex Z))) (tptp.numera6690914467698888265omplex (tptp.aa_num_num tptp.bit0 tptp.one))))) (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.aa_int_fun_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.modulo_modulo_int K _let_1)) (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.aa_int_fun_int_int tptp.bit_se6526347334894502574or_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int K) _let_1)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int L) _let_1))))))))))))))))))))) (forall ((Bs tptp.list_bool) (N tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.bit_se9216721137139052372nteger (tptp.groups7755797274146815065nteger tptp.zero_n356916108424825756nteger (tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one)) Bs)) N)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N) (tptp.size_size_list_bool Bs))) (tptp.pp (tptp.aa_nat_bool (tptp.nth_bool Bs) N))))) (forall ((Bs tptp.list_bool) (N tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.bit_se1148574629649215175it_nat (tptp.groups4051137065250181068ol_nat tptp.zero_n2687167440665602831ol_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)) Bs)) N)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N) (tptp.size_size_list_bool Bs))) (tptp.pp (tptp.aa_nat_bool (tptp.nth_bool Bs) N))))) (forall ((Bs tptp.list_bool) (N tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.bit_se1146084159140164899it_int (tptp.groups4048646594741130792ol_int tptp.zero_n2684676970156552555ol_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one)) Bs)) N)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N) (tptp.size_size_list_bool Bs))) (tptp.pp (tptp.aa_nat_bool (tptp.nth_bool Bs) N))))) (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)))) (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_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_real_bool) (X tptp.real)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I) N)) (=> (tptp.pp (tptp.aa_real_bool P X)) (tptp.pp (tptp.aa_real_bool P (tptp.aa_nat_real (tptp.nth_real (tptp.replicate_real 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 ((Xs tptp.list_complex) (P tptp.fun_complex_bool) (N tptp.nat)) (=> (forall ((X3 tptp.complex)) (=> (tptp.member_complex X3 (tptp.set_complex2 Xs)) (tptp.pp (tptp.aa_complex_bool P X3)))) (=> (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_set_nat) (P tptp.fun_set_nat_bool) (N tptp.nat)) (=> (forall ((X3 tptp.set_nat)) (=> (tptp.member_set_nat X3 (tptp.set_set_nat2 Xs)) (tptp.pp (tptp.aa_set_nat_bool P X3)))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N) (tptp.size_s3254054031482475050et_nat Xs))) (tptp.pp (tptp.aa_set_nat_bool P (tptp.nth_set_nat Xs N)))))) (forall ((Xs tptp.list_VEBT_VEBT) (P tptp.fun_VEBT_VEBT_bool) (N tptp.nat)) (=> (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)))) (=> (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_real) (P tptp.fun_real_bool) (N tptp.nat)) (=> (forall ((X3 tptp.real)) (=> (tptp.member_real X3 (tptp.set_real2 Xs)) (tptp.pp (tptp.aa_real_bool P X3)))) (=> (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_bool) (P tptp.fun_bool_bool) (N tptp.nat)) (=> (forall ((X3 tptp.bool)) (=> (tptp.member_bool X3 (tptp.set_bool2 Xs)) (tptp.pp (tptp.aa_bool_bool P X3)))) (=> (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 ((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)))) (=> (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 ((Xs tptp.list_int) (P tptp.fun_int_bool) (N tptp.nat)) (=> (forall ((X3 tptp.int)) (=> (tptp.member_int X3 (tptp.set_int2 Xs)) (tptp.pp (tptp.aa_int_bool P X3)))) (=> (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 ((X tptp.int) (Y4 tptp.int)) (= (= (tptp.aa_int_int tptp.bit_ri7919022796975470100ot_int X) (tptp.aa_int_int tptp.bit_ri7919022796975470100ot_int Y4)) (= X Y4))) (forall ((X tptp.int)) (= (tptp.aa_int_int tptp.bit_ri7919022796975470100ot_int (tptp.aa_int_int tptp.bit_ri7919022796975470100ot_int X)) X)) (forall ((X tptp.int) (Y4 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.bit_se6526347334894502574or_int X))) (= (tptp.aa_int_int _let_1 (tptp.aa_int_int tptp.bit_ri7919022796975470100ot_int Y4)) (tptp.aa_int_int tptp.bit_ri7919022796975470100ot_int (tptp.aa_int_int _let_1 Y4))))) (forall ((X tptp.int) (Y4 tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se6526347334894502574or_int (tptp.aa_int_int tptp.bit_ri7919022796975470100ot_int X)) Y4) (tptp.aa_int_int tptp.bit_ri7919022796975470100ot_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se6526347334894502574or_int X) Y4)))) (forall ((X tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se725231765392027082nd_int (tptp.aa_int_int tptp.bit_ri7919022796975470100ot_int X)) X) tptp.zero_zero_int)) (forall ((X tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se725231765392027082nd_int X) (tptp.aa_int_int tptp.bit_ri7919022796975470100ot_int X)) tptp.zero_zero_int)) (= (tptp.aa_Cod1783974652533396728nteger tptp.bit_ri7632146776885996613nteger tptp.zero_z3403309356797280102nteger) _let_60) (= _let_61 _let_59) (= (tptp.aa_Cod1783974652533396728nteger tptp.bit_ri7632146776885996613nteger _let_60) tptp.zero_z3403309356797280102nteger) (= (tptp.aa_int_int tptp.bit_ri7919022796975470100ot_int _let_59) tptp.zero_zero_int) (forall ((X tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.bit_se3222712562003087583nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) X) (tptp.aa_Cod1783974652533396728nteger tptp.bit_ri7632146776885996613nteger X))) (forall ((X tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se6526347334894502574or_int (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int)) X) (tptp.aa_int_int tptp.bit_ri7919022796975470100ot_int X))) (forall ((X tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.bit_se3222712562003087583nteger X) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (tptp.aa_Cod1783974652533396728nteger tptp.bit_ri7632146776885996613nteger X))) (forall ((X tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se6526347334894502574or_int X) (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int)) (tptp.aa_int_int tptp.bit_ri7919022796975470100ot_int X))) (forall ((X tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.bit_se3222712562003087583nteger (tptp.aa_Cod1783974652533396728nteger tptp.bit_ri7632146776885996613nteger X)) X) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (forall ((X tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se6526347334894502574or_int (tptp.aa_int_int tptp.bit_ri7919022796975470100ot_int X)) X) (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int))) (forall ((X tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.bit_se3222712562003087583nteger X) (tptp.aa_Cod1783974652533396728nteger tptp.bit_ri7632146776885996613nteger X)) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (forall ((X tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se6526347334894502574or_int X) (tptp.aa_int_int tptp.bit_ri7919022796975470100ot_int X)) (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_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 ((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 ((N tptp.num)) (= (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_Cod1783974652533396728nteger tptp.bit_ri7632146776885996613nteger (tptp.numera6620942414471956472nteger N))) (tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.inc N)))) (forall ((N tptp.num)) (= (tptp.aa_int_int tptp.uminus_uminus_int (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 (tptp.aa_num_num tptp.inc N)))) (forall ((A tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_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.bit_ri7632146776885996613nteger A))) (not (tptp.pp (tptp.aa_Code_integer_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.bit_ri7919022796975470100ot_int A))) (not (tptp.pp (tptp.aa_int_bool _let_1 A)))))) (forall ((N tptp.nat)) (= (tptp.bit_se7788150548672797655nteger N (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (tptp.aa_Cod1783974652533396728nteger tptp.bit_ri7632146776885996613nteger (tptp.bit_se2119862282449309892nteger N)))) (forall ((N tptp.nat)) (= (tptp.bit_se545348938243370406it_int N (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int)) (tptp.aa_int_int tptp.bit_ri7919022796975470100ot_int (tptp.aa_nat_int tptp.bit_se2000444600071755411sk_int N)))) (= (tptp.aa_Cod1783974652533396728nteger tptp.bit_ri7632146776885996613nteger tptp.one_one_Code_integer) _let_65) (= _let_62 _let_64) (forall ((K tptp.int)) (= (tptp.ring_1_of_int_int (tptp.aa_int_int tptp.bit_ri7919022796975470100ot_int K)) (tptp.aa_int_int tptp.bit_ri7919022796975470100ot_int (tptp.ring_1_of_int_int K)))) (forall ((N tptp.nat) (A tptp.int) (B tptp.int)) (let ((_let_1 (tptp.bit_se2923211474154528505it_int N))) (= (= (tptp.aa_int_int _let_1 (tptp.aa_int_int tptp.bit_ri7919022796975470100ot_int A)) (tptp.aa_int_int _let_1 (tptp.aa_int_int tptp.bit_ri7919022796975470100ot_int B))) (= (tptp.aa_int_int _let_1 A) (tptp.aa_int_int _let_1 B))))) (forall ((N tptp.nat) (A tptp.int)) (let ((_let_1 (tptp.bit_se2923211474154528505it_int N))) (= (tptp.aa_int_int _let_1 (tptp.aa_int_int tptp.bit_ri7919022796975470100ot_int (tptp.aa_int_int _let_1 A))) (tptp.aa_int_int _let_1 (tptp.aa_int_int tptp.bit_ri7919022796975470100ot_int A))))) (forall ((K tptp.int) (N tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.bit_se1146084159140164899it_int (tptp.aa_int_int tptp.bit_ri7919022796975470100ot_int K)) N)) (not (tptp.pp (tptp.aa_nat_bool (tptp.bit_se1146084159140164899it_int K) N))))) (forall ((K tptp.num)) (let ((_let_1 (tptp.aa_int_int tptp.bit_ri7919022796975470100ot_int (tptp.aa_num_int tptp.numeral_numeral_int K)))) (= (tptp.ring_1_of_int_int _let_1) _let_1))) (forall ((A tptp.int) (B tptp.int)) (= (tptp.aa_int_int tptp.bit_ri7919022796975470100ot_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) B)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_int_int tptp.bit_ri7919022796975470100ot_int A)) B))) (forall ((A tptp.int) (B tptp.int)) (= (tptp.aa_int_int tptp.bit_ri7919022796975470100ot_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) B)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int tptp.bit_ri7919022796975470100ot_int A)) B))) (forall ((A tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A) (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger tptp.bit_ri7632146776885996613nteger A) tptp.one_one_Code_integer))) (forall ((A tptp.int)) (= (tptp.aa_int_int tptp.uminus_uminus_int A) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int tptp.bit_ri7919022796975470100ot_int A)) tptp.one_one_int))) (forall ((A tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger tptp.bit_ri7632146776885996613nteger A) (tptp.minus_8373710615458151222nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A) tptp.one_one_Code_integer))) (forall ((A tptp.int)) (= (tptp.aa_int_int tptp.bit_ri7919022796975470100ot_int A) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_int_int tptp.uminus_uminus_int A)) tptp.one_one_int))) (forall ((A tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A) (tptp.aa_Cod1783974652533396728nteger tptp.bit_ri7632146776885996613nteger (tptp.minus_8373710615458151222nteger A tptp.one_one_Code_integer)))) (forall ((A tptp.int)) (= (tptp.aa_int_int tptp.uminus_uminus_int A) (tptp.aa_int_int tptp.bit_ri7919022796975470100ot_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) tptp.one_one_int)))) (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.aa_int_fun_int_int tptp.bit_se725231765392027082nd_int tptp.one_one_int) _let_62) tptp.zero_zero_int) (forall ((B tptp.int) (A tptp.int)) (=> (forall ((N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.bit_se1146084159140164899it_int B) N2)) (tptp.pp (tptp.aa_nat_bool (tptp.bit_se1146084159140164899it_int A) N2)))) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) B) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se725231765392027082nd_int A) (tptp.aa_int_int tptp.bit_ri7919022796975470100ot_int B))))) (forall ((N tptp.nat) (A tptp.int)) (let ((_let_1 (tptp.bit_se2923211474154528505it_int N))) (= (tptp.aa_int_int _let_1 (tptp.aa_int_int tptp.bit_ri7919022796975470100ot_int A)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_nat_int tptp.bit_se2000444600071755411sk_int N)) (tptp.aa_int_int _let_1 A))))) (forall ((N tptp.num)) (= (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.inc N))) (tptp.aa_Cod1783974652533396728nteger tptp.bit_ri7632146776885996613nteger (tptp.numera6620942414471956472nteger N)))) (forall ((N tptp.num)) (= (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.inc N))) (tptp.aa_int_int tptp.bit_ri7919022796975470100ot_int (tptp.aa_num_int tptp.numeral_numeral_int N)))) (forall ((N tptp.nat) (K tptp.int)) (= (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_se4203085406695923979it_int N) K) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se725231765392027082nd_int K) (tptp.aa_int_int tptp.bit_ri7919022796975470100ot_int (tptp.bit_se545348938243370406it_int N tptp.one_one_int))))) (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.aa_int_fun_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.aa_int_fun_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_Cod1783974652533396728nteger tptp.bit_ri7632146776885996613nteger (tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 N))) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit1 N))))) (forall ((N tptp.num)) (= (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.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit1 N))))) (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.aa_int_fun_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)) (= (tptp.aa_int_int (tptp.aa_int_fun_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 ((K tptp.int) (N tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.bit_se1146084159140164899it_int (tptp.aa_int_int tptp.uminus_uminus_int K)) N)) (tptp.pp (tptp.aa_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.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.bit_se2923211474154528505it_int M) (tptp.aa_int_int tptp.bit_ri7919022796975470100ot_int (tptp.aa_nat_int tptp.bit_se2000444600071755411sk_int N))) tptp.zero_zero_int))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.bit_se545348938243370406it_int M (tptp.aa_nat_int tptp.bit_se2000444600071755411sk_int N)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se725231765392027082nd_int (tptp.aa_nat_int tptp.bit_se2000444600071755411sk_int (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N) M))) (tptp.aa_int_int tptp.bit_ri7919022796975470100ot_int (tptp.aa_nat_int tptp.bit_se2000444600071755411sk_int M))))) (forall ((N tptp.nat) (A tptp.int)) (= (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_se4203085406695923979it_int N) A) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se725231765392027082nd_int A) (tptp.aa_int_int tptp.bit_ri7919022796975470100ot_int (tptp.bit_se545348938243370406it_int N tptp.one_one_int))))) (forall ((N tptp.nat) (A tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_nat6383147911832638789nteger tptp.bit_se8260200283734997820nteger N) A) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.bit_se3949692690581998587nteger A) (tptp.aa_Cod1783974652533396728nteger tptp.bit_ri7632146776885996613nteger (tptp.bit_se7788150548672797655nteger N tptp.one_one_Code_integer))))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.aa_int_int (tptp.aa_int_fun_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.aa_int_fun_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.aa_int_fun_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.aa_int_fun_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) (N tptp.num)) (= (tptp.aa_int_int (tptp.aa_int_fun_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.aa_int_fun_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.aa_int_fun_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.aa_int_fun_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 ((A tptp.int) (N tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.bit_se1146084159140164899it_int (tptp.aa_int_int tptp.bit_ri7919022796975470100ot_int A)) N)) (and (not (= (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)) (not (tptp.pp (tptp.aa_nat_bool (tptp.bit_se1146084159140164899it_int A) N)))))) (forall ((N tptp.nat)) (= (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.power_8256067586552552935nteger (tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one)) N)) (tptp.aa_Cod1783974652533396728nteger tptp.bit_ri7632146776885996613nteger (tptp.bit_se2119862282449309892nteger N)))) (forall ((N tptp.nat)) (= (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_ri7919022796975470100ot_int (tptp.aa_nat_int tptp.bit_se2000444600071755411sk_int N)))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.aa_int_int (tptp.aa_int_fun_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.aa_int_fun_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 ((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.aa_int_fun_int_int tptp.divide_divide_int K) _let_1))))))) (forall ((X7 tptp.fun_nat_real)) (= (tptp.topolo4055970368930404560y_real X7) (forall ((J3 tptp.nat)) (exists ((M7 tptp.nat)) (forall ((M5 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M7) M5)) (forall ((N4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M7) N4)) (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 M5)) (tptp.aa_nat_real X7 N4)))) (tptp.aa_real_real tptp.inverse_inverse_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real (tptp.aa_nat_nat tptp.suc J3))))))))))))) (forall ((Xs tptp.list_real)) (= (tptp.size_s6660260683639930848t_real (tptp.subseqs_real Xs)) (tptp.aa_nat_nat (tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.size_size_list_real Xs)))) (forall ((Xs tptp.list_bool)) (= (tptp.size_s9193230429364170767t_bool (tptp.subseqs_bool Xs)) (tptp.aa_nat_nat (tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.size_size_list_bool Xs)))) (forall ((Xs tptp.list_nat)) (= (tptp.size_s3023201423986296836st_nat (tptp.subseqs_nat Xs)) (tptp.aa_nat_nat (tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.size_size_list_nat Xs)))) (forall ((Xs tptp.list_int)) (= (tptp.size_s533118279054570080st_int (tptp.subseqs_int Xs)) (tptp.aa_nat_nat (tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.size_size_list_int Xs)))) (forall ((Z tptp.complex)) (= (tptp.aa_complex_real tptp.re (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 ((X tptp.complex)) (= (tptp.sinh_complex X) (tptp.real_V2046097035970521341omplex (tptp.aa_real_real tptp.inverse_inverse_real (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.minus_minus_complex (tptp.exp_complex X) (tptp.exp_complex (tptp.uminus1482373934393186551omplex X)))))) (forall ((X tptp.real)) (= (tptp.aa_real_real tptp.sinh_real X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.real_V1485227260804924795R_real (tptp.aa_real_real tptp.inverse_inverse_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.minus_minus_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)))))) (forall ((A tptp.real) (X tptp.complex) (B tptp.real)) (= (= (tptp.real_V2046097035970521341omplex A X) (tptp.real_V2046097035970521341omplex B X)) (or (= A B) (= X tptp.zero_zero_complex)))) (forall ((A tptp.real) (X tptp.real) (B 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.real_V1485227260804924795R_real B) X)) (or (= A B) (= X tptp.zero_zero_real)))) (forall ((A tptp.real)) (= (tptp.real_V2046097035970521341omplex A tptp.zero_zero_complex) tptp.zero_zero_complex)) (forall ((A tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.real_V1485227260804924795R_real A) tptp.zero_zero_real) tptp.zero_zero_real)) (forall ((X tptp.complex) (A tptp.real) (Y4 tptp.complex)) (let ((_let_1 (tptp.times_times_complex X))) (= (tptp.aa_complex_complex _let_1 (tptp.real_V2046097035970521341omplex A Y4)) (tptp.real_V2046097035970521341omplex A (tptp.aa_complex_complex _let_1 Y4))))) (forall ((X tptp.real) (A tptp.real) (Y4 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 Y4)) (tptp.aa_real_real _let_2 (tptp.aa_real_real _let_1 Y4)))))) (forall ((A tptp.real) (X tptp.complex) (Y4 tptp.complex)) (= (tptp.aa_complex_complex (tptp.times_times_complex (tptp.real_V2046097035970521341omplex A X)) Y4) (tptp.real_V2046097035970521341omplex A (tptp.aa_complex_complex (tptp.times_times_complex X) Y4)))) (forall ((A tptp.real) (X tptp.real) (Y4 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)) Y4) (tptp.aa_real_real _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real X) Y4))))) (forall ((A tptp.real) (X tptp.complex) (Y4 tptp.complex)) (= (= (tptp.real_V2046097035970521341omplex A X) (tptp.real_V2046097035970521341omplex A Y4)) (or (= X Y4) (= A tptp.zero_zero_real)))) (forall ((A tptp.real) (X tptp.real) (Y4 tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.real_V1485227260804924795R_real A))) (= (= (tptp.aa_real_real _let_1 X) (tptp.aa_real_real _let_1 Y4)) (or (= X Y4) (= A tptp.zero_zero_real))))) (forall ((A tptp.real) (B tptp.real) (X tptp.complex)) (= (tptp.real_V2046097035970521341omplex A (tptp.real_V2046097035970521341omplex B X)) (tptp.real_V2046097035970521341omplex (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) B) X))) (forall ((A tptp.real) (B 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 B) 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) B)) X))) (forall ((N tptp.nat)) (= (tptp.aa_complex_real tptp.re (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex N)) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N))) (forall ((X tptp.complex)) (= (tptp.real_V2046097035970521341omplex tptp.zero_zero_real X) tptp.zero_zero_complex)) (forall ((X tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.real_V1485227260804924795R_real tptp.zero_zero_real) X) tptp.zero_zero_real)) (forall ((A tptp.real) (X tptp.complex)) (= (= (tptp.real_V2046097035970521341omplex A X) tptp.zero_zero_complex) (or (= A tptp.zero_zero_real) (= X tptp.zero_zero_complex)))) (forall ((A tptp.real) (X tptp.real)) (= (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.real_V1485227260804924795R_real A) X) tptp.zero_zero_real) (or (= A tptp.zero_zero_real) (= X tptp.zero_zero_real)))) (forall ((V tptp.num)) (= (tptp.aa_complex_real tptp.re (tptp.numera6690914467698888265omplex V)) (tptp.aa_num_real tptp.numeral_numeral_real V))) (forall ((U tptp.real) (A tptp.complex)) (= (tptp.plus_plus_complex (tptp.real_V2046097035970521341omplex (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real tptp.one_one_real) U) A) (tptp.real_V2046097035970521341omplex U A)) A)) (forall ((U tptp.real) (A tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.real_V1485227260804924795R_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real tptp.one_one_real) U)) A)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.real_V1485227260804924795R_real U) A)) A)) (forall ((A tptp.real) (X tptp.complex)) (= (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.real_V2046097035970521341omplex A X)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real tptp.abs_abs_real A)) (tptp.aa_complex_real tptp.real_V1022390504157884413omplex X)))) (forall ((A tptp.real) (X tptp.real)) (= (tptp.aa_real_real tptp.real_V7735802525324610683m_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 (tptp.aa_real_real tptp.abs_abs_real A)) (tptp.aa_real_real tptp.real_V7735802525324610683m_real X)))) (forall ((Z tptp.complex) (N tptp.nat)) (= (tptp.aa_complex_real tptp.re (tptp.divide1717551699836669952omplex Z (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex N))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_complex_real tptp.re Z)) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N)))) (forall ((Z tptp.complex) (R2 tptp.real)) (= (tptp.aa_complex_real tptp.re (tptp.divide1717551699836669952omplex Z (tptp.real_V4546457046886955230omplex R2))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_complex_real tptp.re Z)) R2))) (forall ((Z tptp.complex)) (= (tptp.aa_complex_real tptp.re (tptp.sgn_sgn_complex Z)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_complex_real tptp.re Z)) (tptp.aa_complex_real tptp.real_V1022390504157884413omplex Z)))) (forall ((U tptp.num) (W tptp.num) (A tptp.complex)) (let ((_let_1 (tptp.aa_num_real tptp.numeral_numeral_real U))) (= (tptp.real_V2046097035970521341omplex _let_1 (tptp.aa_complex_complex (tptp.times_times_complex (tptp.numera6690914467698888265omplex W)) A)) (tptp.real_V2046097035970521341omplex (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real _let_1) (tptp.aa_num_real tptp.numeral_numeral_real W)) A)))) (forall ((U tptp.num) (W tptp.num) (A tptp.real)) (let ((_let_1 (tptp.aa_num_real tptp.numeral_numeral_real W))) (let ((_let_2 (tptp.aa_num_real tptp.numeral_numeral_real U))) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.real_V1485227260804924795R_real _let_2) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real _let_1) A)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.real_V1485227260804924795R_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real _let_2) _let_1)) A))))) (forall ((Z tptp.complex) (W tptp.num)) (= (tptp.aa_complex_real tptp.re (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 ((Y4 tptp.complex)) (=> (not (= Y4 tptp.zero_zero_complex)) (=> (= (tptp.aa_complex_real tptp.re Y4) tptp.zero_zero_real) (= (tptp.aa_real_real tptp.cos_real (tptp.aa_complex_real tptp.arg Y4)) tptp.zero_zero_real)))) (forall ((V tptp.num) (W tptp.num) (A tptp.complex)) (let ((_let_1 (tptp.aa_num_real tptp.numeral_numeral_real V))) (= (tptp.real_V2046097035970521341omplex (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.one_one_real) _let_1) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.numera6690914467698888265omplex W)) A)) (tptp.real_V2046097035970521341omplex (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_num_real tptp.numeral_numeral_real W)) _let_1) A)))) (forall ((V tptp.num) (W tptp.num) (A tptp.real)) (let ((_let_1 (tptp.aa_num_real tptp.numeral_numeral_real V))) (let ((_let_2 (tptp.aa_num_real tptp.numeral_numeral_real W))) (= (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.one_one_real) _let_1)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real _let_2) A)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.real_V1485227260804924795R_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real _let_2) _let_1)) A))))) (forall ((U tptp.num) (V tptp.num) (W tptp.num) (A tptp.complex)) (let ((_let_1 (tptp.aa_num_real tptp.numeral_numeral_real V))) (let ((_let_2 (tptp.aa_num_real tptp.numeral_numeral_real U))) (= (tptp.real_V2046097035970521341omplex (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real _let_2) _let_1) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.numera6690914467698888265omplex W)) A)) (tptp.real_V2046097035970521341omplex (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real _let_2) (tptp.aa_num_real tptp.numeral_numeral_real W))) _let_1) A))))) (forall ((U tptp.num) (V tptp.num) (W tptp.num) (A tptp.real)) (let ((_let_1 (tptp.aa_num_real tptp.numeral_numeral_real V))) (let ((_let_2 (tptp.aa_num_real tptp.numeral_numeral_real W))) (let ((_let_3 (tptp.aa_num_real tptp.numeral_numeral_real U))) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.real_V1485227260804924795R_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real _let_3) _let_1)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real _let_2) A)) (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_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real _let_3) _let_2)) _let_1)) A)))))) (forall ((A tptp.complex)) (= (tptp.real_V2046097035970521341omplex (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.plus_plus_complex A A)) A)) (forall ((A tptp.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.one_one_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 A) A)) A)) (forall ((X tptp.complex) (A tptp.real) (B tptp.real)) (=> (not (= X tptp.zero_zero_complex)) (=> (= (tptp.real_V2046097035970521341omplex A X) (tptp.real_V2046097035970521341omplex B X)) (= A B)))) (forall ((X tptp.real) (A tptp.real) (B tptp.real)) (=> (not (= X tptp.zero_zero_real)) (=> (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.real_V1485227260804924795R_real A) X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.real_V1485227260804924795R_real B) X)) (= A B)))) (forall ((A tptp.real) (X tptp.complex) (Y4 tptp.complex)) (= (tptp.real_V2046097035970521341omplex A (tptp.minus_minus_complex X Y4)) (tptp.minus_minus_complex (tptp.real_V2046097035970521341omplex A X) (tptp.real_V2046097035970521341omplex A Y4)))) (forall ((A tptp.real) (X tptp.real) (Y4 tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.real_V1485227260804924795R_real A))) (= (tptp.aa_real_real _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real X) Y4)) (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 Y4))))) (forall ((R2 tptp.real) (X tptp.complex)) (= (tptp.aa_complex_real tptp.re (tptp.real_V2046097035970521341omplex R2 X)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real R2) (tptp.aa_complex_real tptp.re X)))) (forall ((A tptp.real) (X tptp.complex) (Y4 tptp.complex)) (=> (not (= A tptp.zero_zero_real)) (=> (= (tptp.real_V2046097035970521341omplex A X) (tptp.real_V2046097035970521341omplex A Y4)) (= X Y4)))) (forall ((A tptp.real) (X tptp.real) (Y4 tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.real_V1485227260804924795R_real A))) (=> (not (= A tptp.zero_zero_real)) (=> (= (tptp.aa_real_real _let_1 X) (tptp.aa_real_real _let_1 Y4)) (= X Y4))))) (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 ((R2 tptp.real) (X tptp.complex)) (= (tptp.real_V2046097035970521341omplex R2 X) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.real_V4546457046886955230omplex R2)) X))) (forall ((R2 tptp.real) (X tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.real_V1485227260804924795R_real R2) X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real tptp.real_V1803761363581548252l_real R2)) X))) (forall ((A tptp.real) (B tptp.real) (X tptp.complex)) (= (tptp.real_V2046097035970521341omplex (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A) B) X) (tptp.minus_minus_complex (tptp.real_V2046097035970521341omplex A X) (tptp.real_V2046097035970521341omplex B X)))) (forall ((A tptp.real) (B tptp.real) (X tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.real_V1485227260804924795R_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A) B)) X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.real_V1485227260804924795R_real A) X)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.real_V1485227260804924795R_real B) X)))) (forall ((X tptp.real) (Y4 tptp.real) (Xa tptp.complex)) (= (tptp.real_V2046097035970521341omplex (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real X) Y4) Xa) (tptp.minus_minus_complex (tptp.real_V2046097035970521341omplex X Xa) (tptp.real_V2046097035970521341omplex Y4 Xa)))) (forall ((X tptp.real) (Y4 tptp.real) (Xa tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.real_V1485227260804924795R_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real X) Y4)) Xa) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.real_V1485227260804924795R_real X) Xa)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.real_V1485227260804924795R_real Y4) Xa)))) (= (tptp.aa_complex_real tptp.re tptp.imaginary_unit) 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.re X)) (tptp.aa_complex_real tptp.real_V1022390504157884413omplex X)))) (= (tptp.aa_complex_real tptp.re tptp.zero_zero_complex) tptp.zero_zero_real) (forall ((R2 tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.times_times_real R2))) (= (tptp.real_V2046097035970521341omplex R2 (tptp.complex2 A B)) (tptp.complex2 (tptp.aa_real_real _let_1 A) (tptp.aa_real_real _let_1 B))))) (forall ((X tptp.complex) (Y4 tptp.complex)) (= (tptp.aa_complex_real tptp.re (tptp.minus_minus_complex X Y4)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_complex_real tptp.re X)) (tptp.aa_complex_real tptp.re Y4)))) (forall ((A tptp.real) (B tptp.real) (X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) B)) (=> (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.real_V1485227260804924795R_real A) X)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.real_V1485227260804924795R_real B) X)))))) (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real B) 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.real_V1485227260804924795R_real A) C)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.real_V1485227260804924795R_real B) C)))))) (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.real_V1485227260804924795R_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 B))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) B)))))) (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.real_V1485227260804924795R_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 B))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real B) A)))))) (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.real_V1485227260804924795R_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 B))) (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) B))) (=> (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 B) A))))))) (forall ((X tptp.real) (Y4 tptp.real) (A tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.real_V1485227260804924795R_real A))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) Y4)) (=> (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 _let_1 X)) (tptp.aa_real_real _let_1 Y4))))))) (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.real_V1485227260804924795R_real C))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real B) 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 B))))))) (forall ((U tptp.real) (V tptp.real) (A tptp.complex) (X tptp.complex)) (let ((_let_1 (= V tptp.zero_zero_real))) (= (= (tptp.real_V2046097035970521341omplex (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real U) V) A) X) (and (=> _let_1 (= X tptp.zero_zero_complex)) (=> (not _let_1) (= (tptp.real_V2046097035970521341omplex U A) (tptp.real_V2046097035970521341omplex V X))))))) (forall ((U tptp.real) (V tptp.real) (A tptp.real) (X tptp.real)) (let ((_let_1 (= V tptp.zero_zero_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 U) V)) A) X) (and (=> _let_1 (= X tptp.zero_zero_real)) (=> (not _let_1) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.real_V1485227260804924795R_real U) A) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.real_V1485227260804924795R_real V) X))))))) (forall ((X tptp.complex) (U tptp.real) (V tptp.real) (A tptp.complex)) (let ((_let_1 (= V tptp.zero_zero_real))) (= (= X (tptp.real_V2046097035970521341omplex (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real U) V) A)) (and (=> _let_1 (= X tptp.zero_zero_complex)) (=> (not _let_1) (= (tptp.real_V2046097035970521341omplex V X) (tptp.real_V2046097035970521341omplex U A))))))) (forall ((X tptp.real) (U tptp.real) (V tptp.real) (A tptp.real)) (let ((_let_1 (= V tptp.zero_zero_real))) (= (= X (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.real_V1485227260804924795R_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real U) V)) A)) (and (=> _let_1 (= X tptp.zero_zero_real)) (=> (not _let_1) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.real_V1485227260804924795R_real V) X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.real_V1485227260804924795R_real U) A))))))) (forall ((A tptp.real) (E2 tptp.real) (C tptp.real) (B 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.real_V1485227260804924795R_real A) E2)) C)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.real_V1485227260804924795R_real B) E2)) 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.real_V1485227260804924795R_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A) B)) E2)) C)) D)))) (forall ((A tptp.real) (E2 tptp.real) (C tptp.real) (B 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.real_V1485227260804924795R_real A) E2)) C)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.real_V1485227260804924795R_real B) E2)) 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.real_V1485227260804924795R_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real B) A)) E2)) D))))) (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.csqrt Z))))) (forall ((A tptp.real) (B 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.real_V1485227260804924795R_real A) B))) (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 B))) (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 B) tptp.zero_zero_real))) (= A tptp.zero_zero_real))))) (forall ((A tptp.real) (B 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.real_V1485227260804924795R_real A) B)) tptp.zero_zero_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 B) 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 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) B))) (= A tptp.zero_zero_real)))) (forall ((A tptp.real) (B tptp.real) (X tptp.real) (Y4 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) B)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) Y4)) (=> (tptp.pp (tptp.aa_real_bool _let_1 B)) (=> (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.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.real_V1485227260804924795R_real A) X)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.real_V1485227260804924795R_real B) Y4))))))))) (forall ((A tptp.real) (B 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) B)) (=> (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.real_V1485227260804924795R_real A) C)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.real_V1485227260804924795R_real B) D))))))))) (forall ((A tptp.real) (X 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 X) 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 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.real_V1485227260804924795R_real A) X)) tptp.zero_zero_real))))) (forall ((A tptp.real) (B 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 B))) (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 B) tptp.zero_zero_real)))) (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.real_V1485227260804924795R_real A) B)))))) (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 _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.real_V1485227260804924795R_real A) X))))))) (forall ((A tptp.real) (X 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 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.aa_rea7340605660300375871l_real tptp.real_V1485227260804924795R_real A) 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 A) tptp.zero_zero_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.real_V1485227260804924795R_real A) X)) tptp.zero_zero_real))))) (forall ((A tptp.real) (B 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 B) 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.real_V1485227260804924795R_real A) B)))))) (forall ((X tptp.real) (A 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 A) 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.real_V1485227260804924795R_real A) X)) X))))) (forall ((X tptp.complex)) (= (tptp.real_V2046097035970521341omplex (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)) X) (tptp.plus_plus_complex X X))) (forall ((X tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.real_V1485227260804924795R_real (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))) X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) X))) (forall ((M tptp.real) (Y4 tptp.complex) (X tptp.complex) (C tptp.complex)) (let ((_let_1 (tptp.aa_real_real tptp.inverse_inverse_real M))) (=> (not (= M tptp.zero_zero_real)) (= (= Y4 (tptp.plus_plus_complex (tptp.real_V2046097035970521341omplex M X) C)) (= (tptp.minus_minus_complex (tptp.real_V2046097035970521341omplex _let_1 Y4) (tptp.real_V2046097035970521341omplex _let_1 C)) X))))) (forall ((M tptp.real) (Y4 tptp.real) (X tptp.real) (C tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.real_V1485227260804924795R_real (tptp.aa_real_real tptp.inverse_inverse_real M)))) (=> (not (= M tptp.zero_zero_real)) (= (= Y4 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.real_V1485227260804924795R_real M) X)) C)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real _let_1 Y4)) (tptp.aa_real_real _let_1 C)) X))))) (forall ((M tptp.real) (X tptp.complex) (C tptp.complex) (Y4 tptp.complex)) (let ((_let_1 (tptp.aa_real_real tptp.inverse_inverse_real M))) (=> (not (= M tptp.zero_zero_real)) (= (= (tptp.plus_plus_complex (tptp.real_V2046097035970521341omplex M X) C) Y4) (= X (tptp.minus_minus_complex (tptp.real_V2046097035970521341omplex _let_1 Y4) (tptp.real_V2046097035970521341omplex _let_1 C))))))) (forall ((M tptp.real) (X tptp.real) (C tptp.real) (Y4 tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.real_V1485227260804924795R_real (tptp.aa_real_real tptp.inverse_inverse_real M)))) (=> (not (= M 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.real_V1485227260804924795R_real M) X)) C) Y4) (= X (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real _let_1 Y4)) (tptp.aa_real_real _let_1 C))))))) (forall ((C tptp.real) (B 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.real_V1485227260804924795R_real (tptp.aa_real_real tptp.inverse_inverse_real C)) B)) A)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real B) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.real_V1485227260804924795R_real C) A)))))) (forall ((C tptp.real) (A tptp.real) (B 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.real_V1485227260804924795R_real (tptp.aa_real_real tptp.inverse_inverse_real C)) B))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.real_V1485227260804924795R_real C) A)) B))))) (forall ((C tptp.real) (B 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.real_V1485227260804924795R_real (tptp.aa_real_real tptp.inverse_inverse_real C)) B)) 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.real_V1485227260804924795R_real C) A)) B))))) (forall ((C tptp.real) (A tptp.real) (B 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.real_V1485227260804924795R_real (tptp.aa_real_real tptp.inverse_inverse_real C)) B))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real B) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.real_V1485227260804924795R_real C) A)))))) (forall ((C tptp.real) (A tptp.real) (B 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.real_V1485227260804924795R_real (tptp.aa_real_real tptp.inverse_inverse_real C)) B))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.real_V1485227260804924795R_real C) A)))))) (forall ((C tptp.real) (B 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.real_V1485227260804924795R_real (tptp.aa_real_real tptp.inverse_inverse_real C)) B)) A)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.real_V1485227260804924795R_real C) A)) B))))) (forall ((C tptp.real) (A tptp.real) (B 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.real_V1485227260804924795R_real (tptp.aa_real_real tptp.inverse_inverse_real C)) B))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.real_V1485227260804924795R_real C) A)) B))))) (forall ((C tptp.real) (B 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.real_V1485227260804924795R_real (tptp.aa_real_real tptp.inverse_inverse_real C)) B)) A)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.real_V1485227260804924795R_real C) A)))))) (forall ((A tptp.real) (X tptp.complex)) (=> (not (= A tptp.zero_zero_real)) (=> (not (= X tptp.zero_zero_complex)) (= (tptp.invers8013647133539491842omplex (tptp.real_V2046097035970521341omplex A X)) (tptp.real_V2046097035970521341omplex (tptp.aa_real_real tptp.inverse_inverse_real A) (tptp.invers8013647133539491842omplex X)))))) (forall ((A tptp.real) (X tptp.real)) (=> (not (= A tptp.zero_zero_real)) (=> (not (= X tptp.zero_zero_real)) (= (tptp.aa_real_real tptp.inverse_inverse_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.real_V1485227260804924795R_real A) X)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.real_V1485227260804924795R_real (tptp.aa_real_real tptp.inverse_inverse_real A)) (tptp.aa_real_real tptp.inverse_inverse_real X)))))) (forall ((C tptp.real) (A tptp.real) (B 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.real_V1485227260804924795R_real (tptp.aa_real_real tptp.inverse_inverse_real C)) B)))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.real_V1485227260804924795R_real C) A)) (tptp.aa_real_real tptp.uminus_uminus_real B)))))) (forall ((C tptp.real) (B 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.real_V1485227260804924795R_real (tptp.aa_real_real tptp.inverse_inverse_real C)) B))) A)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real B)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.real_V1485227260804924795R_real C) A)))))) (forall ((C tptp.real) (A tptp.real) (B 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.real_V1485227260804924795R_real (tptp.aa_real_real tptp.inverse_inverse_real C)) B)))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real B)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.real_V1485227260804924795R_real C) A)))))) (forall ((C tptp.real) (B 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.real_V1485227260804924795R_real (tptp.aa_real_real tptp.inverse_inverse_real C)) B))) 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.real_V1485227260804924795R_real C) A)) (tptp.aa_real_real tptp.uminus_uminus_real B)))))) (forall ((C tptp.real) (A tptp.real) (B 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.real_V1485227260804924795R_real (tptp.aa_real_real tptp.inverse_inverse_real C)) B)))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.real_V1485227260804924795R_real C) A)) (tptp.aa_real_real tptp.uminus_uminus_real B)))))) (forall ((C tptp.real) (B 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.real_V1485227260804924795R_real (tptp.aa_real_real tptp.inverse_inverse_real C)) B))) A)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.uminus_uminus_real B)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.real_V1485227260804924795R_real C) A)))))) (forall ((C tptp.real) (A tptp.real) (B 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.real_V1485227260804924795R_real (tptp.aa_real_real tptp.inverse_inverse_real C)) B)))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.uminus_uminus_real B)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.real_V1485227260804924795R_real C) A)))))) (forall ((C tptp.real) (B 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.real_V1485227260804924795R_real (tptp.aa_real_real tptp.inverse_inverse_real C)) B))) A)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.real_V1485227260804924795R_real C) A)) (tptp.aa_real_real tptp.uminus_uminus_real B)))))) (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.cis A)) N)))) (forall ((X7 tptp.fun_nat_complex) (E2 tptp.real)) (=> (tptp.topolo6517432010174082258omplex X7) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) E2)) (exists ((M8 tptp.nat)) (forall ((M2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M8) M2)) (forall ((N6 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M8) N6)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.minus_minus_complex (tptp.aa_nat_complex X7 M2) (tptp.aa_nat_complex X7 N6)))) E2)))))))))) (forall ((X7 tptp.fun_nat_real) (E2 tptp.real)) (=> (tptp.topolo4055970368930404560y_real X7) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) E2)) (exists ((M8 tptp.nat)) (forall ((M2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M8) M2)) (forall ((N6 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M8) N6)) (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 (tptp.aa_nat_real X7 M2)) (tptp.aa_nat_real X7 N6)))) E2)))))))))) (forall ((X7 tptp.fun_nat_complex)) (=> (forall ((E tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) E)) (exists ((M9 tptp.nat)) (forall ((M4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M9) M4)) (forall ((N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M9) N2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.minus_minus_complex (tptp.aa_nat_complex X7 M4) (tptp.aa_nat_complex X7 N2)))) E))))))))) (tptp.topolo6517432010174082258omplex X7))) (forall ((X7 tptp.fun_nat_real)) (=> (forall ((E tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) E)) (exists ((M9 tptp.nat)) (forall ((M4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M9) M4)) (forall ((N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M9) N2)) (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 (tptp.aa_nat_real X7 M4)) (tptp.aa_nat_real X7 N2)))) E))))))))) (tptp.topolo4055970368930404560y_real X7))) (forall ((X7 tptp.fun_nat_complex)) (= (tptp.topolo6517432010174082258omplex X7) (forall ((E3 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) E3)) (exists ((M7 tptp.nat)) (forall ((M5 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M7) M5)) (forall ((N4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M7) N4)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.minus_minus_complex (tptp.aa_nat_complex X7 M5) (tptp.aa_nat_complex X7 N4)))) E3))))))))))) (forall ((X7 tptp.fun_nat_real)) (= (tptp.topolo4055970368930404560y_real X7) (forall ((E3 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) E3)) (exists ((M7 tptp.nat)) (forall ((M5 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M7) M5)) (forall ((N4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M7) N4)) (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 (tptp.aa_nat_real X7 M5)) (tptp.aa_nat_real X7 N4)))) E3))))))))))) (forall ((X tptp.complex)) (= (tptp.cosh_complex X) (tptp.real_V2046097035970521341omplex (tptp.aa_real_real tptp.inverse_inverse_real (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.plus_plus_complex (tptp.exp_complex X) (tptp.exp_complex (tptp.uminus1482373934393186551omplex X)))))) (forall ((X tptp.real)) (= (tptp.aa_real_real tptp.cosh_real X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.real_V1485227260804924795R_real (tptp.aa_real_real tptp.inverse_inverse_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 (tptp.aa_real_real tptp.exp_real X)) (tptp.aa_real_real tptp.exp_real (tptp.aa_real_real tptp.uminus_uminus_real X)))))) (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.csqrt Z) (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.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.csqrt X) (tptp.aa_complex_complex (tptp.times_times_complex tptp.imaginary_unit) (tptp.real_V4546457046886955230omplex (tptp.aa_real_real tptp.sqrt (tptp.aa_real_real tptp.abs_abs_real _let_1))))))))) (forall ((X tptp.complex) (Y4 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 Y4))) (let ((_let_3 (tptp.aa_complex_real tptp.re Y4))) (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.divide1717551699836669952omplex X Y4) (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 ((Z tptp.int)) (= (tptp.aa_complex_real tptp.im (tptp.ring_17405671764205052669omplex Z)) tptp.zero_zero_real)) (forall ((N tptp.nat)) (= (tptp.aa_complex_real tptp.im (tptp.aa_nat_complex tptp.semiri5044797733671781792omplex N)) tptp.zero_zero_real)) (forall ((Z tptp.real)) (= (tptp.aa_complex_real tptp.im (tptp.real_V4546457046886955230omplex Z)) tptp.zero_zero_real)) (forall ((X tptp.complex) (N tptp.nat)) (=> (= (tptp.aa_complex_real tptp.im X) tptp.zero_zero_real) (= (tptp.aa_complex_real tptp.im (tptp.aa_nat_complex (tptp.power_power_complex X) N)) tptp.zero_zero_real))) (forall ((V tptp.num)) (= (tptp.aa_complex_real tptp.im (tptp.numera6690914467698888265omplex V)) tptp.zero_zero_real)) (forall ((N tptp.nat)) (= (tptp.aa_complex_real tptp.im (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex N)) tptp.zero_zero_real)) (forall ((Z tptp.complex) (R2 tptp.real)) (= (tptp.aa_complex_real tptp.im (tptp.divide1717551699836669952omplex Z (tptp.real_V4546457046886955230omplex R2))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_complex_real tptp.im Z)) R2))) (forall ((Z tptp.complex)) (= (tptp.aa_complex_real tptp.im (tptp.sgn_sgn_complex Z)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_complex_real tptp.im Z)) (tptp.aa_complex_real tptp.real_V1022390504157884413omplex Z)))) (forall ((X tptp.complex) (N tptp.nat)) (=> (= (tptp.aa_complex_real tptp.im X) tptp.zero_zero_real) (= (tptp.aa_complex_real tptp.re (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.re X)) N)))) (forall ((Z tptp.complex) (W tptp.num)) (= (tptp.aa_complex_real tptp.im (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 ((Z tptp.complex) (N tptp.nat)) (= (tptp.aa_complex_real tptp.im (tptp.divide1717551699836669952omplex Z (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex N))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_complex_real tptp.im Z)) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N)))) (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.csqrt X) (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.csqrt (tptp.uminus1482373934393186551omplex X)) (tptp.aa_complex_complex (tptp.times_times_complex tptp.imaginary_unit) (tptp.csqrt X)))))) (forall ((R2 tptp.real) (X tptp.complex)) (= (tptp.aa_complex_real tptp.im (tptp.real_V2046097035970521341omplex R2 X)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real R2) (tptp.aa_complex_real tptp.im X)))) (= (tptp.aa_complex_real tptp.im tptp.zero_zero_complex) tptp.zero_zero_real) (= (tptp.aa_complex_real tptp.im tptp.one_one_complex) tptp.zero_zero_real) (forall ((X tptp.complex) (Y4 tptp.complex)) (= (tptp.aa_complex_real tptp.im (tptp.minus_minus_complex X Y4)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_complex_real tptp.im X)) (tptp.aa_complex_real tptp.im Y4)))) (forall ((Z tptp.complex)) (= (tptp.member_complex Z tptp.ring_1_Ints_complex) (and (= (tptp.aa_complex_real tptp.im Z) tptp.zero_zero_real) (exists ((I2 tptp.int)) (= (tptp.aa_complex_real tptp.re Z) (tptp.aa_int_real tptp.ring_1_of_int_real I2)))))) (forall ((R2 tptp.real) (X tptp.complex)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.times_times_real R2))) (= (tptp.real_V2046097035970521341omplex R2 X) (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 ((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) (Y4 tptp.complex)) (= (tptp.aa_complex_real tptp.im (tptp.aa_complex_complex (tptp.times_times_complex X) Y4)) (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 Y4))) (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 Y4))))) (forall ((Z tptp.complex)) (=> (= (tptp.aa_complex_real tptp.im Z) tptp.zero_zero_real) (= (tptp.aa_complex_real tptp.real_V1022390504157884413omplex Z) (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_complex_real tptp.re Z))))) (forall ((Z tptp.complex)) (=> (= (tptp.aa_complex_real tptp.re Z) tptp.zero_zero_real) (= (tptp.aa_complex_real tptp.real_V1022390504157884413omplex Z) (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_complex_real tptp.im Z))))) (forall ((Z tptp.complex)) (=> (= (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_complex_real tptp.re Z)) (tptp.aa_complex_real tptp.real_V1022390504157884413omplex Z)) (= (tptp.aa_complex_real tptp.im Z) tptp.zero_zero_real))) (forall ((X tptp.complex) (Y4 tptp.complex)) (=> (= (tptp.aa_complex_real tptp.re X) (tptp.aa_complex_real tptp.re Y4)) (= (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 Y4))) (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 Y4))))))) (forall ((X tptp.complex) (Y4 tptp.complex)) (=> (= (tptp.aa_complex_real tptp.im X) (tptp.aa_complex_real tptp.im Y4)) (= (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 Y4))) (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 Y4))))))) (forall ((X tptp.complex) (Y4 tptp.complex)) (= (tptp.aa_complex_real tptp.re (tptp.aa_complex_complex (tptp.times_times_complex X) Y4)) (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 Y4))) (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 Y4))))) (forall ((X tptp.complex) (Y4 tptp.complex)) (= (tptp.minus_minus_complex X Y4) (tptp.complex2 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_complex_real tptp.re X)) (tptp.aa_complex_real tptp.re Y4)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_complex_real tptp.im X)) (tptp.aa_complex_real tptp.im Y4))))) (forall ((Z tptp.complex)) (let ((_let_1 (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.cis A)) N)))) (forall ((Z tptp.complex)) (= (tptp.aa_complex_real tptp.re (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.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 ((X tptp.complex) (Y4 tptp.complex)) (let ((_let_1 (tptp.aa_complex_real tptp.re Y4))) (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 Y4))) (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) Y4) (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)) (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.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) (Y4 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 Y4))) (let ((_let_3 (tptp.aa_complex_real tptp.re Y4))) (= (tptp.aa_complex_real tptp.re (tptp.divide1717551699836669952omplex X Y4)) (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.csqrt Z) W))))) (forall ((B tptp.complex)) (let ((_let_1 (tptp.aa_complex_real tptp.re B))) (=> (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 B))))) (= (tptp.csqrt (tptp.aa_nat_complex (tptp.power_power_complex B) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) B)))) (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.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) (Y4 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 Y4))) (let ((_let_3 (tptp.aa_complex_real tptp.re Y4))) (= (tptp.aa_complex_real tptp.im (tptp.divide1717551699836669952omplex X Y4)) (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.invers8013647133539491842omplex X) (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 ((R2 tptp.complex) (Z tptp.complex)) (=> (tptp.member_complex R2 tptp.real_V2521375963428798218omplex) (= (tptp.aa_complex_real tptp.im (tptp.divide1717551699836669952omplex R2 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 R2))) (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 ((Xs tptp.list_list_real) (N tptp.nat)) (=> (forall ((X3 tptp.list_real)) (=> (tptp.member_list_real X3 (tptp.set_list_real2 Xs)) (= (tptp.size_size_list_real X3) N))) (= (tptp.size_size_list_real (tptp.concat_real Xs)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.size_s6660260683639930848t_real Xs)) N)))) (forall ((Xs tptp.list_list_bool) (N tptp.nat)) (=> (forall ((X3 tptp.list_bool)) (=> (tptp.member_list_bool X3 (tptp.set_list_bool2 Xs)) (= (tptp.size_size_list_bool X3) N))) (= (tptp.size_size_list_bool (tptp.concat_bool Xs)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.size_s9193230429364170767t_bool Xs)) N)))) (forall ((Xs tptp.list_list_nat) (N tptp.nat)) (=> (forall ((X3 tptp.list_nat)) (=> (tptp.member_list_nat X3 (tptp.set_list_nat2 Xs)) (= (tptp.size_size_list_nat X3) N))) (= (tptp.size_size_list_nat (tptp.concat_nat Xs)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.size_s3023201423986296836st_nat Xs)) N)))) (forall ((Xs tptp.list_list_int) (N tptp.nat)) (=> (forall ((X3 tptp.list_int)) (=> (tptp.member_list_int X3 (tptp.set_list_int2 Xs)) (= (tptp.size_size_list_int X3) N))) (= (tptp.size_size_list_int (tptp.concat_int Xs)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.size_s533118279054570080st_int Xs)) N)))) (forall ((R2 tptp.complex) (Z tptp.complex)) (=> (tptp.member_complex R2 tptp.real_V2521375963428798218omplex) (= (tptp.aa_complex_real tptp.re (tptp.divide1717551699836669952omplex R2 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 R2)) (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)) (= (tptp.minus_minus_complex Z (tptp.cnj Z)) (tptp.aa_complex_complex (tptp.times_times_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 ((Z tptp.complex)) (= (= (tptp.cnj Z) tptp.zero_zero_complex) (= Z tptp.zero_zero_complex))) (= (tptp.cnj tptp.zero_zero_complex) tptp.zero_zero_complex) (forall ((X tptp.complex) (Y4 tptp.complex)) (= (tptp.cnj (tptp.minus_minus_complex X Y4)) (tptp.minus_minus_complex (tptp.cnj X) (tptp.cnj Y4)))) (forall ((Z tptp.complex)) (= (tptp.aa_complex_real tptp.im (tptp.aa_complex_complex (tptp.times_times_complex Z) (tptp.cnj Z))) tptp.zero_zero_real)) (forall ((R2 tptp.complex) (Z tptp.complex)) (=> (tptp.member_complex R2 tptp.real_V2521375963428798218omplex) (= (tptp.aa_complex_real tptp.re (tptp.divide1717551699836669952omplex Z R2)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_complex_real tptp.re Z)) (tptp.aa_complex_real tptp.re R2))))) (forall ((Y4 tptp.complex) (X tptp.complex)) (=> (tptp.member_complex Y4 tptp.real_V2521375963428798218omplex) (=> (tptp.member_complex X tptp.real_V2521375963428798218omplex) (= (= (tptp.aa_complex_complex (tptp.times_times_complex tptp.imaginary_unit) Y4) X) (and (= X tptp.zero_zero_complex) (= Y4 tptp.zero_zero_complex)))))) (forall ((Y4 tptp.complex) (X tptp.complex)) (=> (tptp.member_complex Y4 tptp.real_V2521375963428798218omplex) (=> (tptp.member_complex X tptp.real_V2521375963428798218omplex) (= (= X (tptp.aa_complex_complex (tptp.times_times_complex tptp.imaginary_unit) Y4)) (and (= X tptp.zero_zero_complex) (= Y4 tptp.zero_zero_complex)))))) (forall ((R2 tptp.complex) (Z tptp.complex)) (=> (tptp.member_complex R2 tptp.real_V2521375963428798218omplex) (= (tptp.aa_complex_real tptp.im (tptp.divide1717551699836669952omplex Z R2)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_complex_real tptp.im Z)) (tptp.aa_complex_real tptp.re R2))))) (forall ((N tptp.nat)) (tptp.member_complex (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex N) tptp.real_V2521375963428798218omplex)) (forall ((N tptp.nat)) (tptp.member_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N) tptp.real_V470468836141973256s_real)) (forall ((A tptp.complex) (B tptp.complex)) (=> (tptp.member_complex A tptp.real_V2521375963428798218omplex) (=> (tptp.member_complex B tptp.real_V2521375963428798218omplex) (tptp.member_complex (tptp.divide1717551699836669952omplex A B) tptp.real_V2521375963428798218omplex)))) (forall ((A tptp.real) (B tptp.real)) (=> (tptp.member_real A tptp.real_V470468836141973256s_real) (=> (tptp.member_real B tptp.real_V470468836141973256s_real) (tptp.member_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real A) B) tptp.real_V470468836141973256s_real)))) (forall ((A tptp.real) (B tptp.real)) (=> (tptp.member_real A tptp.real_V470468836141973256s_real) (=> (tptp.member_real B tptp.real_V470468836141973256s_real) (tptp.member_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A) B) tptp.real_V470468836141973256s_real)))) (forall ((A tptp.complex) (B tptp.complex)) (=> (tptp.member_complex A tptp.real_V2521375963428798218omplex) (=> (tptp.member_complex B tptp.real_V2521375963428798218omplex) (tptp.member_complex (tptp.minus_minus_complex A B) tptp.real_V2521375963428798218omplex)))) (forall ((A tptp.real) (B tptp.real)) (=> (tptp.member_real A tptp.real_V470468836141973256s_real) (=> (tptp.member_real B tptp.real_V470468836141973256s_real) (tptp.member_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) B) tptp.real_V470468836141973256s_real)))) (forall ((A tptp.complex) (B tptp.complex)) (=> (tptp.member_complex A tptp.real_V2521375963428798218omplex) (=> (tptp.member_complex B tptp.real_V2521375963428798218omplex) (tptp.member_complex (tptp.aa_complex_complex (tptp.times_times_complex A) B) tptp.real_V2521375963428798218omplex)))) (forall ((W tptp.num)) (tptp.member_complex (tptp.numera6690914467698888265omplex W) tptp.real_V2521375963428798218omplex)) (forall ((W tptp.num)) (tptp.member_real (tptp.aa_num_real tptp.numeral_numeral_real W) tptp.real_V470468836141973256s_real)) (tptp.member_real tptp.zero_zero_real tptp.real_V470468836141973256s_real) (tptp.member_complex tptp.zero_zero_complex tptp.real_V2521375963428798218omplex) (forall ((Z tptp.complex)) (= (tptp.member_complex Z tptp.real_V2521375963428798218omplex) (= (tptp.aa_complex_real tptp.im Z) tptp.zero_zero_real))) (forall ((A tptp.complex) (B tptp.complex)) (=> (tptp.member_complex A tptp.real_V2521375963428798218omplex) (=> (tptp.member_complex B tptp.real_V2521375963428798218omplex) (=> (not (= B tptp.zero_zero_complex)) (tptp.member_complex (tptp.divide1717551699836669952omplex A B) tptp.real_V2521375963428798218omplex))))) (forall ((A tptp.real) (B tptp.real)) (=> (tptp.member_real A tptp.real_V470468836141973256s_real) (=> (tptp.member_real B tptp.real_V470468836141973256s_real) (=> (not (= B tptp.zero_zero_real)) (tptp.member_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real A) B) tptp.real_V470468836141973256s_real))))) (forall ((X tptp.real)) (tptp.member_complex (tptp.complex2 X tptp.zero_zero_real) tptp.real_V2521375963428798218omplex)) (forall ((A tptp.real)) (=> (tptp.member_real A tptp.real_V470468836141973256s_real) (=> (not (= A tptp.zero_zero_real)) (tptp.member_real (tptp.aa_real_real tptp.inverse_inverse_real A) tptp.real_V470468836141973256s_real)))) (forall ((A tptp.complex)) (=> (tptp.member_complex A tptp.real_V2521375963428798218omplex) (=> (not (= A tptp.zero_zero_complex)) (tptp.member_complex (tptp.invers8013647133539491842omplex A) tptp.real_V2521375963428798218omplex)))) (forall ((A tptp.complex) (B tptp.complex)) (= (= (tptp.aa_complex_real tptp.re (tptp.divide1717551699836669952omplex A B)) tptp.zero_zero_real) (= (tptp.aa_complex_real tptp.re (tptp.aa_complex_complex (tptp.times_times_complex A) (tptp.cnj B))) tptp.zero_zero_real))) (forall ((A tptp.complex) (B tptp.complex)) (= (= (tptp.aa_complex_real tptp.im (tptp.divide1717551699836669952omplex A B)) tptp.zero_zero_real) (= (tptp.aa_complex_real tptp.im (tptp.aa_complex_complex (tptp.times_times_complex A) (tptp.cnj B))) tptp.zero_zero_real))) (forall ((A tptp.complex) (B 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.divide1717551699836669952omplex A B)))) (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_complex_real tptp.re (tptp.aa_complex_complex (tptp.times_times_complex A) (tptp.cnj B)))))))) (forall ((A tptp.complex) (B tptp.complex)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_complex_real tptp.re (tptp.divide1717551699836669952omplex A B))) 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.cnj B)))) tptp.zero_zero_real)))) (forall ((A tptp.complex) (B 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.divide1717551699836669952omplex A B)))) (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_complex_real tptp.re (tptp.aa_complex_complex (tptp.times_times_complex A) (tptp.cnj B)))))))) (forall ((A tptp.complex) (B tptp.complex)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_complex_real tptp.re (tptp.divide1717551699836669952omplex A B))) 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.cnj B)))) tptp.zero_zero_real)))) (forall ((A tptp.complex) (B 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.divide1717551699836669952omplex A B)))) (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_complex_real tptp.im (tptp.aa_complex_complex (tptp.times_times_complex A) (tptp.cnj B)))))))) (forall ((A tptp.complex) (B tptp.complex)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_complex_real tptp.im (tptp.divide1717551699836669952omplex A B))) 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.cnj B)))) tptp.zero_zero_real)))) (forall ((A tptp.complex) (B 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.divide1717551699836669952omplex A B)))) (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_complex_real tptp.im (tptp.aa_complex_complex (tptp.times_times_complex A) (tptp.cnj B)))))))) (forall ((A tptp.complex) (B tptp.complex)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_complex_real tptp.im (tptp.divide1717551699836669952omplex A B))) 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.cnj B)))) tptp.zero_zero_real)))) (forall ((Z tptp.complex)) (= (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.aa_complex_complex (tptp.times_times_complex Z) (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) (B tptp.complex)) (let ((_let_1 (tptp.aa_complex_complex (tptp.times_times_complex A) (tptp.cnj B)))) (let ((_let_2 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real))) (let ((_let_3 (tptp.divide1717551699836669952omplex A B))) (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.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.cnj Z)))) (forall ((Z tptp.complex)) (= (tptp.plus_plus_complex Z (tptp.cnj Z)) (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 ((A tptp.complex) (B tptp.complex)) (= (tptp.divide1717551699836669952omplex A B) (tptp.divide1717551699836669952omplex (tptp.aa_complex_complex (tptp.times_times_complex A) (tptp.cnj B)) (tptp.real_V4546457046886955230omplex (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex B)) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))))) (forall ((Z tptp.complex) (W tptp.complex)) (let ((_let_1 (tptp.aa_complex_complex (tptp.times_times_complex Z) (tptp.cnj W)))) (= (tptp.plus_plus_complex _let_1 (tptp.aa_complex_complex (tptp.times_times_complex (tptp.cnj Z)) W)) (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 ((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.cnj Z)) (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 ((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.aa_int_fun_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.aa_int_fun_int_int tptp.bit_se1409905431419307370or_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int K) _let_1)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int L) _let_1)))))))) (forall ((L tptp.num) (K tptp.num)) (= (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.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 ((X tptp.num) (Y4 tptp.num)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se1409905431419307370or_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit1 X))) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit1 Y4))) (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.aa_int_fun_int_int tptp.bit_se1409905431419307370or_int (tptp.aa_num_int tptp.numeral_numeral_int X)) (tptp.aa_num_int tptp.numeral_numeral_int Y4)))))) (forall ((X tptp.num) (Y4 tptp.num)) (= (tptp.aa_nat_nat (tptp.bit_se1412395901928357646or_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 X))) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 Y4))) (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 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_nat_nat (tptp.bit_se1412395901928357646or_nat (tptp.aa_num_nat tptp.numeral_numeral_nat X)) (tptp.aa_num_nat tptp.numeral_numeral_nat Y4)))))) (forall ((X tptp.num) (Y4 tptp.num)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se1409905431419307370or_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit1 X))) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 Y4))) (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.aa_int_fun_int_int tptp.bit_se1409905431419307370or_int (tptp.aa_num_int tptp.numeral_numeral_int X)) (tptp.aa_num_int tptp.numeral_numeral_int Y4)))))) (forall ((X tptp.num) (Y4 tptp.num)) (= (tptp.aa_nat_nat (tptp.bit_se1412395901928357646or_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 X))) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 Y4))) (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 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_nat_nat (tptp.bit_se1412395901928357646or_nat (tptp.aa_num_nat tptp.numeral_numeral_nat X)) (tptp.aa_num_nat tptp.numeral_numeral_nat Y4)))))) (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se1409905431419307370or_int A) B))) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se1409905431419307370or_int _let_1) B) _let_1))) (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.bit_se1412395901928357646or_nat A) B))) (= (tptp.aa_nat_nat (tptp.bit_se1412395901928357646or_nat _let_1) B) _let_1))) (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.bit_se1409905431419307370or_int A))) (let ((_let_2 (tptp.aa_int_int _let_1 B))) (= (tptp.aa_int_int _let_1 _let_2) _let_2)))) (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (tptp.bit_se1412395901928357646or_nat A))) (let ((_let_2 (tptp.aa_nat_nat _let_1 B))) (= (tptp.aa_nat_nat _let_1 _let_2) _let_2)))) (forall ((A tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se1409905431419307370or_int A) A) A)) (forall ((A tptp.nat)) (= (tptp.aa_nat_nat (tptp.bit_se1412395901928357646or_nat A) A) A)) (forall ((A tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se1409905431419307370or_int tptp.zero_zero_int) A) A)) (forall ((A tptp.nat)) (= (tptp.aa_nat_nat (tptp.bit_se1412395901928357646or_nat tptp.zero_zero_nat) A) A)) (forall ((A tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se1409905431419307370or_int A) tptp.zero_zero_int) A)) (forall ((A tptp.nat)) (= (tptp.aa_nat_nat (tptp.bit_se1412395901928357646or_nat A) tptp.zero_zero_nat) A)) (forall ((N tptp.nat)) (= (tptp.bit_se8568078237143864401it_int N tptp.zero_zero_int) tptp.zero_zero_int)) (forall ((N tptp.nat)) (= (tptp.aa_nat_nat (tptp.bit_se8570568707652914677it_nat N) tptp.zero_zero_nat) tptp.zero_zero_nat)) (forall ((M tptp.nat) (N tptp.nat) (A tptp.int)) (= (tptp.bit_se8568078237143864401it_int M (tptp.bit_se8568078237143864401it_int N A)) (tptp.bit_se8568078237143864401it_int (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) N) A))) (forall ((M tptp.nat) (N tptp.nat) (A tptp.nat)) (= (tptp.aa_nat_nat (tptp.bit_se8570568707652914677it_nat M) (tptp.aa_nat_nat (tptp.bit_se8570568707652914677it_nat N) A)) (tptp.aa_nat_nat (tptp.bit_se8570568707652914677it_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) N)) A))) (forall ((N tptp.nat) (A tptp.int) (B 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.bit_se1409905431419307370or_int A) B)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se1409905431419307370or_int (tptp.aa_int_int _let_1 A)) (tptp.aa_int_int _let_1 B))))) (forall ((N tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (tptp.bit_se2925701944663578781it_nat N))) (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.bit_se1412395901928357646or_nat A) B)) (tptp.aa_nat_nat (tptp.bit_se1412395901928357646or_nat (tptp.aa_nat_nat _let_1 A)) (tptp.aa_nat_nat _let_1 B))))) (forall ((N tptp.nat) (A tptp.int) (B tptp.int)) (= (tptp.bit_se545348938243370406it_int N (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se1409905431419307370or_int A) B)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se1409905431419307370or_int (tptp.bit_se545348938243370406it_int N A)) (tptp.bit_se545348938243370406it_int N B)))) (forall ((N tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (tptp.bit_se547839408752420682it_nat N))) (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.bit_se1412395901928357646or_nat A) B)) (tptp.aa_nat_nat (tptp.bit_se1412395901928357646or_nat (tptp.aa_nat_nat _let_1 A)) (tptp.aa_nat_nat _let_1 B))))) (forall ((N tptp.nat) (A tptp.int) (B tptp.int)) (= (tptp.bit_se8568078237143864401it_int N (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se725231765392027082nd_int A) B)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se725231765392027082nd_int (tptp.bit_se8568078237143864401it_int N A)) (tptp.bit_se8568078237143864401it_int N B)))) (forall ((N tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (tptp.bit_se8570568707652914677it_nat N))) (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.bit_se727722235901077358nd_nat A) B)) (tptp.aa_nat_nat (tptp.bit_se727722235901077358nd_nat (tptp.aa_nat_nat _let_1 A)) (tptp.aa_nat_nat _let_1 B))))) (forall ((N tptp.nat) (A tptp.int) (B tptp.int)) (= (tptp.bit_se8568078237143864401it_int N (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se1409905431419307370or_int A) B)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se1409905431419307370or_int (tptp.bit_se8568078237143864401it_int N A)) (tptp.bit_se8568078237143864401it_int N B)))) (forall ((N tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (tptp.bit_se8570568707652914677it_nat N))) (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.bit_se1412395901928357646or_nat A) B)) (tptp.aa_nat_nat (tptp.bit_se1412395901928357646or_nat (tptp.aa_nat_nat _let_1 A)) (tptp.aa_nat_nat _let_1 B))))) (forall ((N tptp.nat) (A tptp.int) (B tptp.int)) (= (tptp.bit_se8568078237143864401it_int N (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se6526347334894502574or_int A) B)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se6526347334894502574or_int (tptp.bit_se8568078237143864401it_int N A)) (tptp.bit_se8568078237143864401it_int N B)))) (forall ((N tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (tptp.bit_se8570568707652914677it_nat N))) (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.bit_se6528837805403552850or_nat A) B)) (tptp.aa_nat_nat (tptp.bit_se6528837805403552850or_nat (tptp.aa_nat_nat _let_1 A)) (tptp.aa_nat_nat _let_1 B))))) (forall ((X tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.bit_se1080825931792720795nteger X) _let_1) _let_1))) (forall ((X 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.bit_se1409905431419307370or_int X) _let_1) _let_1))) (forall ((X tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.bit_se1080825931792720795nteger _let_1) X) _let_1))) (forall ((X 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.bit_se1409905431419307370or_int _let_1) X) _let_1))) (forall ((N tptp.nat) (B tptp.bool)) (= (tptp.bit_se3928097537394005634nteger N (tptp.aa_bool_Code_integer tptp.zero_n356916108424825756nteger B)) (tptp.aa_bool_Code_integer tptp.zero_n356916108424825756nteger (tptp.aa_bool_bool (tptp.fconj (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.fequal_nat N) tptp.zero_zero_nat)) B)))) (forall ((N tptp.nat) (B tptp.bool)) (= (tptp.bit_se8568078237143864401it_int N (tptp.aa_bool_int tptp.zero_n2684676970156552555ol_int B)) (tptp.aa_bool_int tptp.zero_n2684676970156552555ol_int (tptp.aa_bool_bool (tptp.fconj (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.fequal_nat N) tptp.zero_zero_nat)) B)))) (forall ((N tptp.nat) (B tptp.bool)) (= (tptp.aa_nat_nat (tptp.bit_se8570568707652914677it_nat N) (tptp.aa_bool_nat tptp.zero_n2687167440665602831ol_nat B)) (tptp.aa_bool_nat tptp.zero_n2687167440665602831ol_nat (tptp.aa_bool_bool (tptp.fconj (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.fequal_nat N) tptp.zero_zero_nat)) B)))) (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.aa_int_fun_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.aa_int_fun_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 ((X tptp.int) (Y4 tptp.int)) (= (tptp.aa_int_int tptp.bit_ri7919022796975470100ot_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se1409905431419307370or_int X) Y4)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se725231765392027082nd_int (tptp.aa_int_int tptp.bit_ri7919022796975470100ot_int X)) (tptp.aa_int_int tptp.bit_ri7919022796975470100ot_int Y4)))) (forall ((X tptp.int) (Y4 tptp.int)) (= (tptp.aa_int_int tptp.bit_ri7919022796975470100ot_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se725231765392027082nd_int X) Y4)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se1409905431419307370or_int (tptp.aa_int_int tptp.bit_ri7919022796975470100ot_int X)) (tptp.aa_int_int tptp.bit_ri7919022796975470100ot_int Y4)))) (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.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.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.bit_se8568078237143864401it_int N _let_1) _let_1))) (forall ((Y4 tptp.num)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 Y4)))) (= (tptp.aa_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.bit_se1412395901928357646or_nat _let_1) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)) _let_1))) (forall ((Y4 tptp.num)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit1 Y4)))) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se1409905431419307370or_int tptp.one_one_int) _let_1) _let_1))) (forall ((Y4 tptp.num)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 Y4)))) (= (tptp.aa_nat_nat (tptp.bit_se1412395901928357646or_nat tptp.one_one_nat) _let_1) _let_1))) (forall ((X tptp.num)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit1 X)))) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se1409905431419307370or_int _let_1) tptp.one_one_int) _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.bit_se1412395901928357646or_nat _let_1) tptp.one_one_nat) _let_1))) (forall ((N tptp.nat) (K tptp.num)) (= (tptp.bit_se8568078237143864401it_int (tptp.aa_nat_nat tptp.suc N) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 K))) (tptp.bit_se8568078237143864401it_int N (tptp.aa_num_int tptp.numeral_numeral_int K)))) (forall ((N tptp.nat) (K tptp.num)) (= (tptp.aa_nat_nat (tptp.bit_se8570568707652914677it_nat (tptp.aa_nat_nat tptp.suc N)) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 K))) (tptp.aa_nat_nat (tptp.bit_se8570568707652914677it_nat N) (tptp.aa_num_nat tptp.numeral_numeral_nat K)))) (forall ((N tptp.nat) (K tptp.num)) (= (tptp.bit_se8568078237143864401it_int (tptp.aa_nat_nat tptp.suc N) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit1 K))) (tptp.bit_se8568078237143864401it_int N (tptp.aa_num_int tptp.numeral_numeral_int K)))) (forall ((N tptp.nat) (K tptp.num)) (= (tptp.aa_nat_nat (tptp.bit_se8570568707652914677it_nat (tptp.aa_nat_nat tptp.suc N)) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 K))) (tptp.aa_nat_nat (tptp.bit_se8570568707652914677it_nat N) (tptp.aa_num_nat tptp.numeral_numeral_nat K)))) (forall ((X tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.bit_se1080825931792720795nteger (tptp.aa_Cod1783974652533396728nteger tptp.bit_ri7632146776885996613nteger X)) X) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (forall ((X tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se1409905431419307370or_int (tptp.aa_int_int tptp.bit_ri7919022796975470100ot_int X)) X) (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int))) (forall ((X tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.bit_se1080825931792720795nteger X) (tptp.aa_Cod1783974652533396728nteger tptp.bit_ri7632146776885996613nteger X)) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (forall ((X tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se1409905431419307370or_int X) (tptp.aa_int_int tptp.bit_ri7919022796975470100ot_int X)) (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int))) (forall ((N tptp.nat)) (= (tptp.bit_se3928097537394005634nteger N tptp.one_one_Code_integer) (tptp.aa_bool_Code_integer 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.bit_se8568078237143864401it_int N tptp.one_one_int) (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.aa_nat_nat (tptp.bit_se8570568707652914677it_nat N) tptp.one_one_nat) (tptp.aa_bool_nat tptp.zero_n2687167440665602831ol_nat (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.fequal_nat N) tptp.zero_zero_nat)))) (forall ((Y4 tptp.num)) (= (tptp.aa_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 Y4))) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 Y4)))) (forall ((X tptp.num)) (= (tptp.aa_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 ((X tptp.num) (Y4 tptp.num)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se1409905431419307370or_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 X))) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 Y4))) (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.aa_int_fun_int_int tptp.bit_se1409905431419307370or_int (tptp.aa_num_int tptp.numeral_numeral_int X)) (tptp.aa_num_int tptp.numeral_numeral_int Y4))))) (forall ((X tptp.num) (Y4 tptp.num)) (= (tptp.aa_nat_nat (tptp.bit_se1412395901928357646or_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 X))) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 Y4))) (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.bit_se1412395901928357646or_nat (tptp.aa_num_nat tptp.numeral_numeral_nat X)) (tptp.aa_num_nat tptp.numeral_numeral_nat Y4))))) (forall ((Y4 tptp.num)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se1409905431419307370or_int tptp.one_one_int) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 Y4))) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit1 Y4)))) (forall ((Y4 tptp.num)) (= (tptp.aa_nat_nat (tptp.bit_se1412395901928357646or_nat tptp.one_one_nat) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 Y4))) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 Y4)))) (forall ((X tptp.num)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se1409905431419307370or_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 X))) tptp.one_one_int) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit1 X)))) (forall ((X tptp.num)) (= (tptp.aa_nat_nat (tptp.bit_se1412395901928357646or_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 X))) tptp.one_one_nat) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 X)))) (forall ((L tptp.num) (K tptp.num)) (= (tptp.bit_se8568078237143864401it_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.bit_se8568078237143864401it_int (tptp.aa_num_nat tptp.pred_numeral L) (tptp.aa_num_int tptp.numeral_numeral_int K)))) (forall ((L tptp.num) (K tptp.num)) (= (tptp.aa_nat_nat (tptp.bit_se8570568707652914677it_nat (tptp.aa_num_nat tptp.numeral_numeral_nat L)) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 K))) (tptp.aa_nat_nat (tptp.bit_se8570568707652914677it_nat (tptp.aa_num_nat tptp.pred_numeral L)) (tptp.aa_num_nat tptp.numeral_numeral_nat K)))) (forall ((L tptp.num) (K tptp.num)) (= (tptp.bit_se8568078237143864401it_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.bit_se8568078237143864401it_int (tptp.aa_num_nat tptp.pred_numeral L) (tptp.aa_num_int tptp.numeral_numeral_int K)))) (forall ((L tptp.num) (K tptp.num)) (= (tptp.aa_nat_nat (tptp.bit_se8570568707652914677it_nat (tptp.aa_num_nat tptp.numeral_numeral_nat L)) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 K))) (tptp.aa_nat_nat (tptp.bit_se8570568707652914677it_nat (tptp.aa_num_nat tptp.pred_numeral L)) (tptp.aa_num_nat tptp.numeral_numeral_nat K)))) (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.aa_int_fun_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.aa_int_fun_int_int tptp.bit_se1409905431419307370or_int tptp.one_one_int) _let_1) _let_1))) (forall ((N tptp.nat) (K tptp.num)) (= (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.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.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.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.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.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.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.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.aa_int_fun_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.aa_int_fun_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.aa_int_fun_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 ((X tptp.num) (Y4 tptp.num)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se1409905431419307370or_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 X))) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit1 Y4))) (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.aa_int_fun_int_int tptp.bit_se1409905431419307370or_int (tptp.aa_num_int tptp.numeral_numeral_int X)) (tptp.aa_num_int tptp.numeral_numeral_int Y4)))))) (forall ((X tptp.num) (Y4 tptp.num)) (= (tptp.aa_nat_nat (tptp.bit_se1412395901928357646or_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 X))) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 Y4))) (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 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_nat_nat (tptp.bit_se1412395901928357646or_nat (tptp.aa_num_nat tptp.numeral_numeral_nat X)) (tptp.aa_num_nat tptp.numeral_numeral_nat Y4)))))) (forall ((K tptp.int) (L tptp.int)) (= (tptp.ring_1_of_int_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se1409905431419307370or_int K) L)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se1409905431419307370or_int (tptp.ring_1_of_int_int K)) (tptp.ring_1_of_int_int L)))) (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.bit_se1409905431419307370or_int B))) (let ((_let_2 (tptp.aa_int_fun_int_int tptp.bit_se1409905431419307370or_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 ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (tptp.bit_se1412395901928357646or_nat B))) (let ((_let_2 (tptp.bit_se1412395901928357646or_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 ((A tptp.int) (B tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se1409905431419307370or_int A) B) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se1409905431419307370or_int B) A))) (forall ((A tptp.nat) (B tptp.nat)) (= (tptp.aa_nat_nat (tptp.bit_se1412395901928357646or_nat A) B) (tptp.aa_nat_nat (tptp.bit_se1412395901928357646or_nat B) A))) (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.bit_se1409905431419307370or_int A))) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se1409905431419307370or_int (tptp.aa_int_int _let_1 B)) C) (tptp.aa_int_int _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se1409905431419307370or_int B) C))))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (tptp.bit_se1412395901928357646or_nat A))) (= (tptp.aa_nat_nat (tptp.bit_se1412395901928357646or_nat (tptp.aa_nat_nat _let_1 B)) C) (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.bit_se1412395901928357646or_nat B) C))))) (forall ((X tptp.int) (Y4 tptp.int) (Z tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.bit_se725231765392027082nd_int X))) (= (tptp.aa_int_int _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se1409905431419307370or_int Y4) Z)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se1409905431419307370or_int (tptp.aa_int_int _let_1 Y4)) (tptp.aa_int_int _let_1 Z))))) (forall ((X tptp.int) (Y4 tptp.int) (Z tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.bit_se1409905431419307370or_int X))) (= (tptp.aa_int_int _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se725231765392027082nd_int Y4) Z)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se725231765392027082nd_int (tptp.aa_int_int _let_1 Y4)) (tptp.aa_int_int _let_1 Z))))) (forall ((Y4 tptp.int) (Z tptp.int) (X tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se725231765392027082nd_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se1409905431419307370or_int Y4) Z)) X) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se1409905431419307370or_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se725231765392027082nd_int Y4) X)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se725231765392027082nd_int Z) X)))) (forall ((Y4 tptp.int) (Z tptp.int) (X tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se1409905431419307370or_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se725231765392027082nd_int Y4) Z)) X) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se725231765392027082nd_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se1409905431419307370or_int Y4) X)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se1409905431419307370or_int Z) X)))) (forall ((X tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se1409905431419307370or_int X) tptp.zero_zero_int) X)) (forall ((A tptp.int) (B tptp.int)) (= (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se1409905431419307370or_int A) B) tptp.zero_zero_int) (and (= A tptp.zero_zero_int) (= B tptp.zero_zero_int)))) (forall ((A tptp.nat) (B tptp.nat)) (= (= (tptp.aa_nat_nat (tptp.bit_se1412395901928357646or_nat A) B) tptp.zero_zero_nat) (and (= A tptp.zero_zero_nat) (= B tptp.zero_zero_nat)))) (forall ((K tptp.int) (L tptp.int) (N tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.bit_se1146084159140164899it_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se1409905431419307370or_int K) L)) N)) (or (tptp.pp (tptp.aa_nat_bool (tptp.bit_se1146084159140164899it_int K) N)) (tptp.pp (tptp.aa_nat_bool (tptp.bit_se1146084159140164899it_int L) N))))) (forall ((A tptp.int) (B tptp.int) (N tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.bit_se1146084159140164899it_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se1409905431419307370or_int A) B)) N)) (or (tptp.pp (tptp.aa_nat_bool (tptp.bit_se1146084159140164899it_int A) N)) (tptp.pp (tptp.aa_nat_bool (tptp.bit_se1146084159140164899it_int B) N))))) (forall ((A tptp.nat) (B 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.bit_se1412395901928357646or_nat A) B)) N)) (or (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.bit_se1148574629649215175it_nat A) N)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.bit_se1148574629649215175it_nat B) N))))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.aa_nat_nat (tptp.bit_se1412395901928357646or_nat M) N) (tptp.aa_int_nat tptp.nat2 (tptp.aa_int_int (tptp.aa_int_fun_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.nat) (N tptp.nat)) (= (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_nat (tptp.bit_se8570568707652914677it_nat M) N)) (tptp.bit_se8568078237143864401it_int M (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N)))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.bit_se8570568707652914677it_nat M))) (= (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat (tptp.aa_nat_nat _let_1 N)) (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat N))))) (forall ((N tptp.nat) (M tptp.nat)) (= (tptp.bit_se8568078237143864401it_int N (tptp.aa_nat_int tptp.semiri1314217659103216013at_int M)) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_nat (tptp.bit_se8570568707652914677it_nat N) M)))) (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.bit_se8570568707652914677it_nat N))) (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat M)) (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat (tptp.aa_nat_nat _let_1 M))))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_nat (tptp.bit_se1412395901928357646or_nat M) N)) (tptp.aa_int_int (tptp.aa_int_fun_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.nat) (N tptp.nat)) (= (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat (tptp.aa_nat_nat (tptp.bit_se1412395901928357646or_nat M) N)) (tptp.aa_nat_nat (tptp.bit_se1412395901928357646or_nat (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat M)) (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat 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.aa_int_fun_int_int tptp.bit_se1409905431419307370or_int K) L))))) (forall ((X tptp.int) (Y4 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 Y4)) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se1409905431419307370or_int X) Y4))))))) (forall ((A tptp.int) (B tptp.int)) (=> (forall ((N2 tptp.nat)) (or (not (tptp.pp (tptp.aa_nat_bool (tptp.bit_se1146084159140164899it_int A) N2))) (not (tptp.pp (tptp.aa_nat_bool (tptp.bit_se1146084159140164899it_int B) N2))))) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) B) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se1409905431419307370or_int A) B)))) (forall ((A tptp.nat) (B tptp.nat)) (=> (forall ((N2 tptp.nat)) (or (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.bit_se1148574629649215175it_nat A) N2))) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.bit_se1148574629649215175it_nat B) N2))))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) B) (tptp.aa_nat_nat (tptp.bit_se1412395901928357646or_nat A) B)))) (forall ((X tptp.int) (Y4 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.bit_se725231765392027082nd_int X) Y4)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se1409905431419307370or_int X) Y4)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int X) Y4))) (forall ((A tptp.int) (B tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se1409905431419307370or_int A) B) (tptp.aa_int_int tptp.bit_ri7919022796975470100ot_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se725231765392027082nd_int (tptp.aa_int_int tptp.bit_ri7919022796975470100ot_int A)) (tptp.aa_int_int tptp.bit_ri7919022796975470100ot_int B))))) (forall ((A tptp.int) (B tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se725231765392027082nd_int A) B) (tptp.aa_int_int tptp.bit_ri7919022796975470100ot_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se1409905431419307370or_int (tptp.aa_int_int tptp.bit_ri7919022796975470100ot_int A)) (tptp.aa_int_int tptp.bit_ri7919022796975470100ot_int B))))) (forall ((K tptp.int) (L tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se1409905431419307370or_int K) L) (tptp.aa_int_int tptp.bit_ri7919022796975470100ot_int (tptp.aa_int_int (tptp.aa_int_fun_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 ((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.bit_se1412395901928357646or_nat N) (tptp.aa_nat_nat (tptp.bit_se547839408752420682it_nat M) tptp.one_one_nat)))) (forall ((N tptp.nat) (A tptp.int)) (= (= (tptp.aa_int_int (tptp.bit_se2923211474154528505it_int N) A) A) (= (tptp.bit_se8568078237143864401it_int N A) tptp.zero_zero_int))) (forall ((N tptp.nat) (A tptp.nat)) (= (= (tptp.aa_nat_nat (tptp.bit_se2925701944663578781it_nat N) A) A) (= (tptp.aa_nat_nat (tptp.bit_se8570568707652914677it_nat N) A) tptp.zero_zero_nat))) (forall ((M tptp.nat) (N tptp.nat) (K tptp.int)) (= (tptp.bit_se8568078237143864401it_int M (tptp.bit_se545348938243370406it_int N K)) (tptp.bit_se8568078237143864401it_int (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) N) (tptp.bit_se545348938243370406it_int (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) M) K)))) (forall ((M tptp.nat) (N tptp.nat) (A tptp.int)) (= (tptp.aa_int_int (tptp.bit_se2923211474154528505it_int M) (tptp.bit_se8568078237143864401it_int N A)) (tptp.bit_se8568078237143864401it_int N (tptp.aa_int_int (tptp.bit_se2923211474154528505it_int (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) N)) A)))) (forall ((M tptp.nat) (N tptp.nat) (A tptp.nat)) (let ((_let_1 (tptp.bit_se8570568707652914677it_nat N))) (= (tptp.aa_nat_nat (tptp.bit_se2925701944663578781it_nat M) (tptp.aa_nat_nat _let_1 A)) (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.bit_se2925701944663578781it_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) N)) A))))) (forall ((M tptp.nat) (N tptp.nat) (A tptp.int)) (= (tptp.bit_se8568078237143864401it_int M (tptp.aa_int_int (tptp.bit_se2923211474154528505it_int N) A)) (tptp.aa_int_int (tptp.bit_se2923211474154528505it_int (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) M)) (tptp.bit_se8568078237143864401it_int M A)))) (forall ((M tptp.nat) (N tptp.nat) (A tptp.nat)) (let ((_let_1 (tptp.bit_se8570568707652914677it_nat M))) (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.bit_se2925701944663578781it_nat N) A)) (tptp.aa_nat_nat (tptp.bit_se2925701944663578781it_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) M)) (tptp.aa_nat_nat _let_1 A))))) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se1409905431419307370or_int tptp.one_one_int) _let_62) _let_61) (forall ((X tptp.int) (Y4 tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se6526347334894502574or_int X) Y4) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se725231765392027082nd_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se1409905431419307370or_int X) Y4)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se1409905431419307370or_int (tptp.aa_int_int tptp.bit_ri7919022796975470100ot_int X)) (tptp.aa_int_int tptp.bit_ri7919022796975470100ot_int Y4))))) (forall ((X tptp.int) (Y4 tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se6526347334894502574or_int X) Y4) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se1409905431419307370or_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se725231765392027082nd_int X) (tptp.aa_int_int tptp.bit_ri7919022796975470100ot_int Y4))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se725231765392027082nd_int (tptp.aa_int_int tptp.bit_ri7919022796975470100ot_int X)) Y4)))) (forall ((N tptp.nat) (A tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_nat6383147911832638789nteger tptp.bit_se2793503036327961859nteger N) A) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.bit_se1080825931792720795nteger A) (tptp.bit_se7788150548672797655nteger N tptp.one_one_Code_integer)))) (forall ((N tptp.nat) (A tptp.int)) (= (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_se7879613467334960850it_int N) A) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se1409905431419307370or_int A) (tptp.bit_se545348938243370406it_int N tptp.one_one_int)))) (forall ((N tptp.nat) (A tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se7882103937844011126it_nat N) A) (tptp.aa_nat_nat (tptp.bit_se1412395901928357646or_nat A) (tptp.aa_nat_nat (tptp.bit_se547839408752420682it_nat N) tptp.one_one_nat)))) (forall ((K tptp.int) (L tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se6526347334894502574or_int K) L) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se1409905431419307370or_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se725231765392027082nd_int K) (tptp.aa_int_int tptp.bit_ri7919022796975470100ot_int L))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se725231765392027082nd_int (tptp.aa_int_int tptp.bit_ri7919022796975470100ot_int K)) L)))) (forall ((A tptp.int) (N tptp.nat)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A) (tptp.bit_se545348938243370406it_int N tptp.one_one_int)) (tptp.bit_se8568078237143864401it_int N A))) (forall ((A tptp.nat) (N tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) (tptp.aa_nat_nat (tptp.bit_se547839408752420682it_nat N) tptp.one_one_nat)) (tptp.aa_nat_nat (tptp.bit_se8570568707652914677it_nat N) A))) (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.bit_se1409905431419307370or_int (tptp.aa_int_int (tptp.bit_se2923211474154528505it_int N) K)) (tptp.bit_se545348938243370406it_int N L)))) (forall ((A tptp.int) (N tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.bit_se1146084159140164899it_int A) N)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se725231765392027082nd_int (tptp.bit_se8568078237143864401it_int N A)) tptp.one_one_int) tptp.one_one_int))) (forall ((A tptp.nat) (N tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.bit_se1148574629649215175it_nat A) N)) (= (tptp.aa_nat_nat (tptp.bit_se727722235901077358nd_nat (tptp.aa_nat_nat (tptp.bit_se8570568707652914677it_nat N) A)) tptp.one_one_nat) tptp.one_one_nat))) (forall ((N tptp.nat) (K tptp.int)) (= (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_se7879613467334960850it_int N) K) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se1409905431419307370or_int K) (tptp.bit_se545348938243370406it_int N tptp.one_one_int)))) (forall ((N tptp.nat) (A tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.bit_se545348938243370406it_int N (tptp.bit_se8568078237143864401it_int N A))) (tptp.aa_int_int (tptp.bit_se2923211474154528505it_int N) A)) A)) (forall ((N tptp.nat) (A tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.bit_se547839408752420682it_nat N) (tptp.aa_nat_nat (tptp.bit_se8570568707652914677it_nat N) A))) (tptp.aa_nat_nat (tptp.bit_se2925701944663578781it_nat N) A)) A)) (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_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.bit_se1080825931792720795nteger A) B))) (and (tptp.pp (tptp.aa_Code_integer_bool _let_1 A)) (tptp.pp (tptp.aa_Code_integer_bool _let_1 B)))))) (forall ((A tptp.int) (B 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.bit_se1409905431419307370or_int A) B))) (and (tptp.pp (tptp.aa_int_bool _let_1 A)) (tptp.pp (tptp.aa_int_bool _let_1 B)))))) (forall ((A tptp.nat) (B 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.bit_se1412395901928357646or_nat A) B))) (and (tptp.pp (tptp.aa_nat_bool _let_1 A)) (tptp.pp (tptp.aa_nat_bool _let_1 B)))))) (forall ((A tptp.code_integer) (X tptp.code_integer) (Y4 tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (let ((_let_2 (tptp.aa_Cod4161879620478718930nteger tptp.bit_se1080825931792720795nteger A))) (let ((_let_3 (tptp.aa_Cod4161879620478718930nteger tptp.bit_se3949692690581998587nteger A))) (=> (= (tptp.aa_Cod1783974652533396728nteger _let_3 X) tptp.zero_z3403309356797280102nteger) (=> (= (tptp.aa_Cod1783974652533396728nteger _let_2 X) _let_1) (=> (= (tptp.aa_Cod1783974652533396728nteger _let_3 Y4) tptp.zero_z3403309356797280102nteger) (=> (= (tptp.aa_Cod1783974652533396728nteger _let_2 Y4) _let_1) (= X Y4))))))))) (forall ((A tptp.int) (X tptp.int) (Y4 tptp.int)) (let ((_let_1 (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int))) (let ((_let_2 (tptp.aa_int_fun_int_int tptp.bit_se1409905431419307370or_int A))) (let ((_let_3 (tptp.aa_int_fun_int_int tptp.bit_se725231765392027082nd_int A))) (=> (= (tptp.aa_int_int _let_3 X) tptp.zero_zero_int) (=> (= (tptp.aa_int_int _let_2 X) _let_1) (=> (= (tptp.aa_int_int _let_3 Y4) tptp.zero_zero_int) (=> (= (tptp.aa_int_int _let_2 Y4) _let_1) (= X Y4))))))))) (forall ((M tptp.num)) (let ((_let_1 (tptp.aa_int_int tptp.bit_ri7919022796975470100ot_int tptp.one_one_int))) (= (tptp.aa_int_int (tptp.aa_int_fun_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 ((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.aa_int_fun_int_int tptp.bit_se1409905431419307370or_int tptp.one_one_int) _let_1) _let_1))) (forall ((A tptp.int) (N tptp.nat)) (=> (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) A) (= (tptp.bit_se8568078237143864401it_int N A) A))) (forall ((A tptp.nat) (N tptp.nat)) (=> (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) A) (= (tptp.aa_nat_nat (tptp.bit_se8570568707652914677it_nat N) A) A))) (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.bit_se8568078237143864401it_int N (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A) _let_1)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int (tptp.bit_se8568078237143864401it_int N 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)))) (let ((_let_2 (tptp.bit_se8570568707652914677it_nat N))) (= (tptp.aa_nat_nat _let_2 (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 (tptp.aa_nat_nat _let_2 A)) _let_1))))) (forall ((X tptp.code_integer) (Y4 tptp.code_integer)) (=> (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.bit_se3949692690581998587nteger X) Y4) tptp.zero_z3403309356797280102nteger) (=> (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.bit_se1080825931792720795nteger X) Y4) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (= (tptp.aa_Cod1783974652533396728nteger tptp.bit_ri7632146776885996613nteger X) Y4)))) (forall ((X tptp.int) (Y4 tptp.int)) (=> (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se725231765392027082nd_int X) Y4) tptp.zero_zero_int) (=> (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se1409905431419307370or_int X) Y4) (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int)) (= (tptp.aa_int_int tptp.bit_ri7919022796975470100ot_int X) Y4)))) (forall ((N tptp.num)) (= (tptp.aa_int_int (tptp.aa_int_fun_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 ((M tptp.num)) (= (tptp.aa_int_int (tptp.aa_int_fun_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 ((N tptp.nat) (K tptp.int)) (= (tptp.bit_se8568078237143864401it_int N K) (tptp.aa_int_int (tptp.aa_int_fun_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 ((A tptp.int) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.bit_se1146084159140164899it_int A) N)) (= (tptp.aa_int_int (tptp.bit_ri631733984087533419it_int N) A) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se1409905431419307370or_int (tptp.aa_int_int (tptp.bit_se2923211474154528505it_int N) A)) (tptp.aa_int_int tptp.bit_ri7919022796975470100ot_int (tptp.aa_nat_int tptp.bit_se2000444600071755411sk_int N)))))) (forall ((N tptp.nat) (A tptp.int)) (= (tptp.bit_se8568078237143864401it_int (tptp.aa_nat_nat tptp.suc N) A) (tptp.bit_se8568078237143864401it_int N (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one)))))) (forall ((N tptp.nat) (A tptp.nat)) (= (tptp.aa_nat_nat (tptp.bit_se8570568707652914677it_nat (tptp.aa_nat_nat tptp.suc N)) A) (tptp.aa_nat_nat (tptp.bit_se8570568707652914677it_nat N) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))))) (forall ((N tptp.nat) (A tptp.int)) (= (tptp.bit_se8568078237143864401it_int N A) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A) (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) (A tptp.nat)) (= (tptp.aa_nat_nat (tptp.bit_se8570568707652914677it_nat N) A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) (tptp.aa_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) (A tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.bit_se3928097537394005634nteger N A))) (not (tptp.pp (tptp.aa_nat_bool (tptp.bit_se9216721137139052372nteger A) N))))) (forall ((N tptp.nat) (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))) (tptp.bit_se8568078237143864401it_int N A))) (not (tptp.pp (tptp.aa_nat_bool (tptp.bit_se1146084159140164899it_int A) N))))) (forall ((N tptp.nat) (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))) (tptp.aa_nat_nat (tptp.bit_se8570568707652914677it_nat N) A))) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.bit_se1148574629649215175it_nat A) N))))) (forall ((A tptp.code_integer) (N tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.bit_se9216721137139052372nteger A) N)) (not (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.bit_se3928097537394005634nteger N A)))))) (forall ((A tptp.int) (N tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.bit_se1146084159140164899it_int A) N)) (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.bit_se8568078237143864401it_int N A)))))) (forall ((A tptp.nat) (N tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.bit_se1148574629649215175it_nat A) 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))) (tptp.aa_nat_nat (tptp.bit_se8570568707652914677it_nat N) A)))))) (forall ((N tptp.nat)) (= (tptp.aa_nat_nat tptp.bit_se2002935070580805687sk_nat (tptp.aa_nat_nat tptp.suc N)) (tptp.aa_nat_nat (tptp.bit_se1412395901928357646or_nat (tptp.aa_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.bit_se2002935070580805687sk_nat N)))) (forall ((N tptp.nat)) (= (tptp.aa_nat_int tptp.bit_se2000444600071755411sk_int (tptp.aa_nat_nat tptp.suc N)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se1409905431419307370or_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_nat_int tptp.bit_se2000444600071755411sk_int N)))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.aa_int_int (tptp.aa_int_fun_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.aa_int_fun_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 ((A tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.bit_se1080825931792720795nteger A) tptp.one_one_Code_integer) (tptp.plus_p5714425477246183910nteger A (tptp.aa_bool_Code_integer tptp.zero_n356916108424825756nteger (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))) A))))) (forall ((A tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se1409905431419307370or_int A) tptp.one_one_int) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) (tptp.aa_bool_int tptp.zero_n2684676970156552555ol_int (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))))) (forall ((A tptp.nat)) (= (tptp.aa_nat_nat (tptp.bit_se1412395901928357646or_nat A) tptp.one_one_nat) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) (tptp.aa_bool_nat 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))) A))))) (forall ((A tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.bit_se1080825931792720795nteger tptp.one_one_Code_integer) A) (tptp.plus_p5714425477246183910nteger A (tptp.aa_bool_Code_integer tptp.zero_n356916108424825756nteger (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))) A))))) (forall ((A tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se1409905431419307370or_int tptp.one_one_int) A) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) (tptp.aa_bool_int tptp.zero_n2684676970156552555ol_int (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))))) (forall ((A tptp.nat)) (= (tptp.aa_nat_nat (tptp.bit_se1412395901928357646or_nat tptp.one_one_nat) A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) (tptp.aa_bool_nat 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))) A))))) (forall ((N tptp.nat)) (= (tptp.aa_nat_nat tptp.bit_se2002935070580805687sk_nat (tptp.aa_nat_nat tptp.suc N)) (tptp.aa_nat_nat (tptp.bit_se1412395901928357646or_nat tptp.one_one_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))) (tptp.aa_nat_nat tptp.bit_se2002935070580805687sk_nat N))))) (forall ((N tptp.nat)) (= (tptp.aa_nat_int tptp.bit_se2000444600071755411sk_int (tptp.aa_nat_nat tptp.suc N)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se1409905431419307370or_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_nat_int tptp.bit_se2000444600071755411sk_int N))))) (forall ((X tptp.int) (N tptp.nat) (Y4 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 Y4) _let_1)) (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.bit_se1409905431419307370or_int X) Y4)) _let_1))))))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.aa_int_int (tptp.aa_int_fun_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.aa_int_fun_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 ((N tptp.nat) (M tptp.nat) (A tptp.int)) (= (tptp.bit_se545348938243370406it_int N (tptp.aa_int_int (tptp.bit_se2923211474154528505it_int M) (tptp.bit_se8568078237143864401it_int N A))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se725231765392027082nd_int A) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se725231765392027082nd_int (tptp.aa_nat_int tptp.bit_se2000444600071755411sk_int (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) N))) (tptp.aa_int_int tptp.bit_ri7919022796975470100ot_int (tptp.aa_nat_int tptp.bit_se2000444600071755411sk_int N)))))) (forall ((N tptp.nat) (A tptp.code_integer)) (= (tptp.bit_ri6519982836138164636nteger N A) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.bit_se1080825931792720795nteger (tptp.bit_se1745604003318907178nteger N A)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_bool_Code_integer tptp.zero_n356916108424825756nteger (tptp.aa_nat_bool (tptp.bit_se9216721137139052372nteger A) N))) (tptp.aa_Cod1783974652533396728nteger tptp.bit_ri7632146776885996613nteger (tptp.bit_se2119862282449309892nteger N)))))) (forall ((N tptp.nat) (A tptp.int)) (= (tptp.aa_int_int (tptp.bit_ri631733984087533419it_int N) A) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se1409905431419307370or_int (tptp.aa_int_int (tptp.bit_se2923211474154528505it_int N) A)) (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.bit_se1146084159140164899it_int A) N))) (tptp.aa_int_int tptp.bit_ri7919022796975470100ot_int (tptp.aa_nat_int tptp.bit_se2000444600071755411sk_int N)))))) (forall ((N tptp.nat)) (= (tptp.aa_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.aa_bool_nat 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.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.aa_bool_nat 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) (A tptp.int)) (let ((_let_1 (tptp.bit_se8568078237143864401it_int N A))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 A)) (=> (not _let_2) (= _let_1 (tptp.bit_se8568078237143864401it_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.aa_int_fun_int_int tptp.divide_divide_int A) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one)))))))))) (forall ((N tptp.nat) (A tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.bit_se8570568707652914677it_nat N) A))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 A)) (=> (not _let_2) (= _let_1 (tptp.aa_nat_nat (tptp.bit_se8570568707652914677it_nat (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.divide_divide_nat A) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))))))))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.aa_int_int (tptp.aa_int_fun_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.aa_int_fun_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.aa_int_fun_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.aa_int_fun_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.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.bit_se1412395901928357646or_nat M) N) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_bool_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.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 ((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.aa_int_fun_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.aa_int_fun_int_int tptp.ord_max_int (tptp.modulo_modulo_int K _let_1)) (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.aa_int_fun_int_int tptp.bit_se1409905431419307370or_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int K) _let_1)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int L) _let_1)))))))))))))))))) (tptp.boolea2445317508997433345nteger tptp.bit_se3949692690581998587nteger tptp.bit_se1080825931792720795nteger tptp.bit_ri7632146776885996613nteger tptp.zero_z3403309356797280102nteger _let_60 tptp.bit_se3222712562003087583nteger) (tptp.boolea8527374999097803216ff_int tptp.bit_se725231765392027082nd_int tptp.bit_se1409905431419307370or_int tptp.bit_ri7919022796975470100ot_int tptp.zero_zero_int _let_59 tptp.bit_se6526347334894502574or_int) (forall ((N tptp.num) (M tptp.num)) (= (tptp.aa_int_int (tptp.aa_int_fun_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.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.aa_int_fun_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.bit_or_not_num_neg M) (tptp.aa_num_num tptp.bit0 N)))))) (forall ((B 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 B) C)) A)) (and (tptp.pp (tptp.aa_Ext2772979874139974381t_bool (tptp.ord_le2932123472753598470d_enat B) A)) (tptp.pp (tptp.aa_Ext2772979874139974381t_bool (tptp.ord_le2932123472753598470d_enat C) A))))) (forall ((B tptp.code_integer) (C tptp.code_integer) (A tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.ord_max_Code_integer B C)) A)) (and (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger B) A)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger C) A))))) (forall ((B 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 B) C)) A)) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) A)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat C) A))))) (forall ((B 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.ord_max_num B) C)) A)) (and (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num B) A)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num C) A))))) (forall ((B 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 B) C)) A)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B) A)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat C) A))))) (forall ((B 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.aa_int_fun_int_int tptp.ord_max_int B) C)) A)) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B) A)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int C) A))))) (forall ((B tptp.real) (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.ord_max_real B) C)) A)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real B) A)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real C) A))))) (forall ((A tptp.extended_enat) (B tptp.extended_enat)) (=> (tptp.pp (tptp.aa_Ext2772979874139974381t_bool (tptp.ord_le2932123472753598470d_enat A) B)) (= (tptp.aa_Ext7969882492699152700d_enat (tptp.aa_Ext3475206891998675565d_enat tptp.ord_ma741700101516333627d_enat A) B) B))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger A) B)) (= (tptp.ord_max_Code_integer A B) B))) (forall ((A tptp.rat) (B tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B)) (= (tptp.aa_rat_rat (tptp.ord_max_rat A) B) B))) (forall ((A tptp.num) (B tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A) B)) (= (tptp.aa_num_num (tptp.ord_max_num A) B) B))) (forall ((A tptp.nat) (B tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat A) B) B))) (forall ((A tptp.int) (B tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.ord_max_int A) B) B))) (forall ((A tptp.real) (B tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) B)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.ord_max_real A) B) B))) (forall ((B tptp.extended_enat) (A tptp.extended_enat)) (=> (tptp.pp (tptp.aa_Ext2772979874139974381t_bool (tptp.ord_le2932123472753598470d_enat B) A)) (= (tptp.aa_Ext7969882492699152700d_enat (tptp.aa_Ext3475206891998675565d_enat tptp.ord_ma741700101516333627d_enat A) B) A))) (forall ((B tptp.code_integer) (A tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger B) A)) (= (tptp.ord_max_Code_integer A B) A))) (forall ((B tptp.rat) (A tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) A)) (= (tptp.aa_rat_rat (tptp.ord_max_rat A) B) A))) (forall ((B tptp.num) (A tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num B) A)) (= (tptp.aa_num_num (tptp.ord_max_num A) B) A))) (forall ((B tptp.nat) (A tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B) A)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat A) B) A))) (forall ((B tptp.int) (A tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B) A)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.ord_max_int A) B) A))) (forall ((B tptp.real) (A tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real B) A)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.ord_max_real A) B) A))) (forall ((P tptp.bool) (Q tptp.bool)) (= (tptp.aa_bool_nat 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.aa_bool_nat tptp.zero_n2687167440665602831ol_nat P)) (tptp.aa_bool_nat 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.aa_int_fun_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.aa_bool_Code_integer tptp.zero_n356916108424825756nteger (tptp.aa_bool_bool (tptp.fdisj P) Q)) (tptp.ord_max_Code_integer (tptp.aa_bool_Code_integer tptp.zero_n356916108424825756nteger P) (tptp.aa_bool_Code_integer tptp.zero_n356916108424825756nteger Q)))) (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.numera6620942414471956472nteger U))) (let ((_let_2 (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_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.aa_int_fun_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_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 ((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.numera6620942414471956472nteger X))) (= (tptp.ord_max_Code_integer tptp.zero_z3403309356797280102nteger _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.aa_int_fun_int_int tptp.ord_max_int tptp.zero_zero_int) _let_1) _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.numera6620942414471956472nteger X))) (= (tptp.ord_max_Code_integer _let_1 tptp.zero_z3403309356797280102nteger) _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.aa_int_fun_int_int tptp.ord_max_int _let_1) tptp.zero_zero_int) _let_1))) (= (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_int_int (tptp.aa_int_fun_int_int tptp.ord_max_int tptp.one_one_int) tptp.zero_zero_int) tptp.one_one_int) (= (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.ord_max_Code_integer tptp.one_one_Code_integer tptp.zero_z3403309356797280102nteger) tptp.one_one_Code_integer) (= (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_int_int (tptp.aa_int_fun_int_int tptp.ord_max_int tptp.zero_zero_int) tptp.one_one_int) tptp.one_one_int) (= (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.ord_max_Code_integer tptp.zero_z3403309356797280102nteger tptp.one_one_Code_integer) tptp.one_one_Code_integer) (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.numera6620942414471956472nteger X))) (= (tptp.ord_max_Code_integer tptp.one_one_Code_integer _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.aa_int_fun_int_int tptp.ord_max_int tptp.one_one_int) _let_1) _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.one_on7984719198319812577d_enat) _let_1))) (forall ((X tptp.num)) (let ((_let_1 (tptp.numera6620942414471956472nteger X))) (= (tptp.ord_max_Code_integer _let_1 tptp.one_one_Code_integer) _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.aa_int_fun_int_int tptp.ord_max_int _let_1) tptp.one_one_int) _let_1))) (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.numera6620942414471956472nteger U)))) (let ((_let_2 (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (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.aa_int_fun_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.numera6620942414471956472nteger U)))) (let ((_let_2 (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.aa_int_fun_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.numera6620942414471956472nteger U))) (let ((_let_2 (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (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.aa_int_fun_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_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 ((N tptp.nat)) (= (tptp.aa_nat_nat (tptp.bit_se8570568707652914677it_nat N) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)) (tptp.aa_bool_nat tptp.zero_n2687167440665602831ol_nat (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.fequal_nat N) tptp.zero_zero_nat)))) (forall ((X tptp.nat) (Y4 tptp.nat)) (= (tptp.semiri4216267220026989637d_enat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat X) Y4)) (tptp.aa_Ext7969882492699152700d_enat (tptp.aa_Ext3475206891998675565d_enat tptp.ord_ma741700101516333627d_enat (tptp.semiri4216267220026989637d_enat X)) (tptp.semiri4216267220026989637d_enat Y4)))) (forall ((X tptp.nat) (Y4 tptp.nat)) (= (tptp.semiri4939895301339042750nteger (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat X) Y4)) (tptp.ord_max_Code_integer (tptp.semiri4939895301339042750nteger X) (tptp.semiri4939895301339042750nteger Y4)))) (forall ((X tptp.nat) (Y4 tptp.nat)) (= (tptp.aa_nat_real tptp.semiri5074537144036343181t_real (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat X) Y4)) (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 Y4)))) (forall ((X tptp.nat) (Y4 tptp.nat)) (= (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat X) Y4)) (tptp.aa_rat_rat (tptp.ord_max_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat X)) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat Y4)))) (forall ((X tptp.nat) (Y4 tptp.nat)) (= (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat X) Y4)) (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 Y4)))) (forall ((X tptp.nat) (Y4 tptp.nat)) (= (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat X) Y4)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.ord_max_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int X)) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int Y4)))) (forall ((X tptp.code_integer) (Y4 tptp.code_integer) (Z tptp.code_integer)) (= (tptp.minus_8373710615458151222nteger (tptp.ord_max_Code_integer X Y4) Z) (tptp.ord_max_Code_integer (tptp.minus_8373710615458151222nteger X Z) (tptp.minus_8373710615458151222nteger Y4 Z)))) (forall ((X tptp.real) (Y4 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) Y4)) 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 Y4) Z)))) (forall ((X tptp.rat) (Y4 tptp.rat) (Z tptp.rat)) (= (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_rat_rat (tptp.ord_max_rat X) Y4)) 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 Y4) Z)))) (forall ((X tptp.int) (Y4 tptp.int) (Z 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.ord_max_int X) Y4)) Z) (tptp.aa_int_int (tptp.aa_int_fun_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 Y4) Z)))) (forall ((X tptp.real) (Y4 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 Y4) Z)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.ord_max_real (tptp.aa_real_real _let_1 Y4)) (tptp.aa_real_real _let_1 Z))))) (forall ((X tptp.rat) (Y4 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 Y4) Z)) (tptp.aa_rat_rat (tptp.ord_max_rat (tptp.aa_rat_rat _let_1 Y4)) (tptp.aa_rat_rat _let_1 Z))))) (forall ((X tptp.int) (Y4 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.aa_int_fun_int_int tptp.ord_max_int Y4) Z)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.ord_max_int (tptp.aa_int_int _let_1 Y4)) (tptp.aa_int_int _let_1 Z))))) (forall ((X tptp.nat) (Y4 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 Y4) Z)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat (tptp.aa_nat_nat _let_1 Y4)) (tptp.aa_nat_nat _let_1 Z))))) (forall ((X tptp.code_integer) (Y4 tptp.code_integer) (Z tptp.code_integer)) (= (tptp.plus_p5714425477246183910nteger X (tptp.ord_max_Code_integer Y4 Z)) (tptp.ord_max_Code_integer (tptp.plus_p5714425477246183910nteger X Y4) (tptp.plus_p5714425477246183910nteger X Z)))) (forall ((X tptp.real) (Y4 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) Y4)) 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 Y4) Z)))) (forall ((X tptp.rat) (Y4 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) Y4)) 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 Y4) Z)))) (forall ((X tptp.int) (Y4 tptp.int) (Z 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.ord_max_int X) Y4)) Z) (tptp.aa_int_int (tptp.aa_int_fun_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 Y4) Z)))) (forall ((X tptp.nat) (Y4 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) Y4)) 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 Y4) Z)))) (forall ((X tptp.code_integer) (Y4 tptp.code_integer) (Z tptp.code_integer)) (= (tptp.plus_p5714425477246183910nteger (tptp.ord_max_Code_integer X Y4) Z) (tptp.ord_max_Code_integer (tptp.plus_p5714425477246183910nteger X Z) (tptp.plus_p5714425477246183910nteger Y4 Z)))) (forall ((X tptp.extended_enat) (Y4 tptp.extended_enat)) (=> (tptp.pp (tptp.aa_Ext2772979874139974381t_bool (tptp.ord_le2932123472753598470d_enat X) Y4)) (= (tptp.aa_Ext7969882492699152700d_enat (tptp.aa_Ext3475206891998675565d_enat tptp.ord_ma741700101516333627d_enat X) Y4) Y4))) (forall ((X tptp.code_integer) (Y4 tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger X) Y4)) (= (tptp.ord_max_Code_integer X Y4) Y4))) (forall ((X tptp.set_int) (Y4 tptp.set_int)) (=> (tptp.ord_less_eq_set_int X Y4) (= (tptp.ord_max_set_int X Y4) Y4))) (forall ((X tptp.rat) (Y4 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) Y4)) (= (tptp.aa_rat_rat (tptp.ord_max_rat X) Y4) Y4))) (forall ((X tptp.num) (Y4 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X) Y4)) (= (tptp.aa_num_num (tptp.ord_max_num X) Y4) Y4))) (forall ((X tptp.nat) (Y4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X) Y4)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat X) Y4) Y4))) (forall ((X tptp.int) (Y4 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X) Y4)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.ord_max_int X) Y4) Y4))) (forall ((X tptp.real) (Y4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) Y4)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.ord_max_real X) Y4) Y4))) (forall ((Y4 tptp.extended_enat) (X tptp.extended_enat)) (=> (tptp.pp (tptp.aa_Ext2772979874139974381t_bool (tptp.ord_le2932123472753598470d_enat Y4) X)) (= (tptp.aa_Ext7969882492699152700d_enat (tptp.aa_Ext3475206891998675565d_enat tptp.ord_ma741700101516333627d_enat X) Y4) X))) (forall ((Y4 tptp.code_integer) (X tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger Y4) X)) (= (tptp.ord_max_Code_integer X Y4) X))) (forall ((Y4 tptp.set_int) (X tptp.set_int)) (=> (tptp.ord_less_eq_set_int Y4 X) (= (tptp.ord_max_set_int X Y4) X))) (forall ((Y4 tptp.rat) (X tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat Y4) X)) (= (tptp.aa_rat_rat (tptp.ord_max_rat X) Y4) X))) (forall ((Y4 tptp.num) (X tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num Y4) X)) (= (tptp.aa_num_num (tptp.ord_max_num X) Y4) X))) (forall ((Y4 tptp.nat) (X tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Y4) X)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat X) Y4) X))) (forall ((Y4 tptp.int) (X tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Y4) X)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.ord_max_int X) Y4) X))) (forall ((Y4 tptp.real) (X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y4) X)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.ord_max_real X) Y4) X))) (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat A) B))) (let ((_let_2 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B)))) (and (=> _let_2 (= _let_1 B)) (=> (not _let_2) (= _let_1 A)))))) (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.ord_max_int A) B))) (let ((_let_2 (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B)))) (and (=> _let_2 (= _let_1 B)) (=> (not _let_2) (= _let_1 A)))))) (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.ord_max_real A) B))) (let ((_let_2 (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) B)))) (and (=> _let_2 (= _let_1 B)) (=> (not _let_2) (= _let_1 A)))))) (= (tptp.aa_num_num (tptp.bit_or_not_num_neg tptp.one) tptp.one) tptp.one) (forall ((N tptp.num)) (= (tptp.aa_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.nat) (K tptp.int)) (= (tptp.aa_nat_nat (tptp.bit_se8570568707652914677it_nat N) (tptp.aa_int_nat tptp.nat2 K)) (tptp.aa_int_nat tptp.nat2 (tptp.bit_se8568078237143864401it_int N K)))) (forall ((N tptp.num) (M tptp.num)) (= (tptp.aa_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.bit_or_not_num_neg N) M)))) (forall ((N tptp.num)) (= (tptp.aa_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.bit_or_not_num_neg tptp.one) _let_1) _let_1))) (forall ((M tptp.num)) (= (tptp.aa_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.nat) (M tptp.nat)) (= (tptp.aa_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.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N)))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.aa_int_int (tptp.aa_int_fun_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.bit_or_not_num_neg M) N))))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.aa_int_int (tptp.aa_int_fun_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.bit_or_not_num_neg N) M))))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num (tptp.bit_or_not_num_neg M) N)) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_int_int (tptp.aa_int_fun_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 ((N tptp.num)) (= (tptp.aa_int_int (tptp.aa_int_fun_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.bit_or_not_num_neg tptp.one) (tptp.aa_num_num tptp.bitM N)))))) (forall ((N tptp.num)) (= (tptp.aa_int_int (tptp.aa_int_fun_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.bit_or_not_num_neg tptp.one) (tptp.aa_num_num tptp.bitM 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_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.modulo_modulo_nat M) _let_1)) (tptp.aa_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.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.num) (M tptp.num)) (= (tptp.aa_int_int (tptp.aa_int_fun_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.bit_or_not_num_neg M) (tptp.aa_num_num tptp.bitM N)))))) (forall ((Q2 tptp.extended_enat)) (= (tptp.aa_Ext7969882492699152700d_enat (tptp.aa_Ext3475206891998675565d_enat tptp.ord_ma741700101516333627d_enat Q2) tptp.zero_z5237406670263579293d_enat) Q2)) (forall ((Q2 tptp.extended_enat)) (= (tptp.aa_Ext7969882492699152700d_enat (tptp.aa_Ext3475206891998675565d_enat tptp.ord_ma741700101516333627d_enat tptp.zero_z5237406670263579293d_enat) Q2) Q2)) (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) (B tptp.nat)) (= (= tptp.zero_zero_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat A) B)) (and (= A tptp.zero_zero_nat) (= B 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) (B tptp.nat)) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat A) B) tptp.zero_zero_nat) (and (= A tptp.zero_zero_nat) (= B tptp.zero_zero_nat)))) (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 ((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 ((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 ((M tptp.num) (N tptp.num)) (= (tptp.aa_int_int (tptp.aa_int_fun_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.bit_or_not_num_neg M) (tptp.aa_num_num tptp.bitM N)))))) (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 ((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)) (= (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)))) (= (tptp.aa_num_num tptp.bitM tptp.one) tptp.one) (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 ((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 ((N tptp.num) (M tptp.num)) (= (tptp.aa_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.bit_or_not_num_neg N) M)))) (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) (M tptp.num)) (= (tptp.aa_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.bit_or_not_num_neg N) M)))) (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 ((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.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.plus_plus_num (tptp.aa_num_num tptp.bitM N)) tptp.one) (tptp.aa_num_num tptp.bit0 N))) (forall ((N tptp.num) (M tptp.num)) (= (tptp.aa_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.bit_or_not_num_neg N) M)))) (forall ((X tptp.num) (Xa tptp.num) (Y4 tptp.num)) (let ((_let_1 (= Xa tptp.one))) (let ((_let_2 (=> _let_1 (not (= Y4 tptp.one))))) (let ((_let_3 (= X tptp.one))) (=> (= (tptp.aa_num_num (tptp.bit_or_not_num_neg X) Xa) Y4) (=> (=> _let_3 _let_2) (=> (=> _let_3 (forall ((M4 tptp.num)) (=> (= Xa (tptp.aa_num_num tptp.bit0 M4)) (not (= Y4 (tptp.aa_num_num tptp.bit1 M4)))))) (=> (=> _let_3 (forall ((M4 tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit1 M4))) (=> (= Xa _let_1) (not (= Y4 _let_1)))))) (=> (=> (exists ((N2 tptp.num)) (= X (tptp.aa_num_num tptp.bit0 N2))) (=> _let_1 (not (= Y4 (tptp.aa_num_num tptp.bit0 tptp.one))))) (=> (forall ((N2 tptp.num)) (=> (= X (tptp.aa_num_num tptp.bit0 N2)) (forall ((M4 tptp.num)) (=> (= Xa (tptp.aa_num_num tptp.bit0 M4)) (not (= Y4 (tptp.aa_num_num tptp.bitM (tptp.aa_num_num (tptp.bit_or_not_num_neg N2) M4)))))))) (=> (forall ((N2 tptp.num)) (=> (= X (tptp.aa_num_num tptp.bit0 N2)) (forall ((M4 tptp.num)) (=> (= Xa (tptp.aa_num_num tptp.bit1 M4)) (not (= Y4 (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num (tptp.bit_or_not_num_neg N2) M4)))))))) (=> (=> (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 ((M4 tptp.num)) (=> (= Xa (tptp.aa_num_num tptp.bit0 M4)) (not (= Y4 (tptp.aa_num_num tptp.bitM (tptp.aa_num_num (tptp.bit_or_not_num_neg N2) M4)))))))) (not (forall ((N2 tptp.num)) (=> (= X (tptp.aa_num_num tptp.bit1 N2)) (forall ((M4 tptp.num)) (=> (= Xa (tptp.aa_num_num tptp.bit1 M4)) (not (= Y4 (tptp.aa_num_num tptp.bitM (tptp.aa_num_num (tptp.bit_or_not_num_neg N2) M4)))))))))))))))))))))) (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 ((K tptp.int) (N tptp.num)) (let ((_let_1 (tptp.aa_int_fun_int_int 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.aa_int_fun_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.aa_int_fun_int_int tptp.bit_se6526347334894502574or_int (tptp.aa_num_int (tptp.neg_numeral_sub_int N) tptp.one)) K)))) (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) (Y4 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 Y4)) (= X Y4))))) (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) (Y4 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 Y4))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Y4)))))) (forall ((N tptp.nat) (X tptp.real) (Y4 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 Y4))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) Y4)))))) (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) (Y4 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) Y4))) (tptp.pp (tptp.aa_real_bool _let_1 Y4)))))) (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) (Y4 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) Y4))) (tptp.pp (tptp.aa_real_bool _let_1 Y4)))))) (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) (Y4 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) Y4))) (tptp.pp (tptp.aa_real_bool _let_1 Y4)))))) (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) (Y4 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) Y4))) (tptp.pp (tptp.aa_real_bool _let_1 Y4)))))) (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) (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 ((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) (Y4 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) Y4)) (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 Y4))))) (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) (Y4 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) Y4)) (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 Y4))))) (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) (Y4 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) Y4)) (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 Y4))))))) (forall ((N tptp.nat) (X tptp.real) (Y4 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) Y4)) (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 Y4))))))) (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) (N5 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) N5)) (=> (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 N5) 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_2)) (forall ((N tptp.nat) (Y4 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 Y4) N))) (tptp.aa_real_real tptp.abs_abs_real Y4)))) (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) (N5 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) N5)) (=> (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 N5) X)))))))) (forall ((N tptp.nat) (N5 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) N5)) (=> (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 N5) 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) (Y4 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) Y4)) (=> (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Y4) N) X) (= (tptp.aa_real_real (tptp.aa_nat_fun_real_real tptp.root N) X) Y4))))) (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_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) (Y4 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 Y4) N) X) (= (tptp.aa_real_real (tptp.aa_nat_fun_real_real tptp.root N) X) Y4)))) (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) (N5 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) N5)) (=> (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 N5) X)))))))) (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) (Y4 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 Y4)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real tptp.abs_abs_real Y4)) N))) Y4))) (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) (B 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) B)) (= (tptp.aa_real_real tptp.ln_ln_real (tptp.aa_real_real (tptp.aa_nat_fun_real_real tptp.root N) B)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real tptp.ln_ln_real B)) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N)))))) (forall ((N tptp.nat) (A tptp.real) (B tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.log B))) (=> (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) (B 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) B)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.log (tptp.aa_real_real (tptp.aa_nat_fun_real_real tptp.root N) B)) 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 B) 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 ((Y5 tptp.real)) (=> (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real tptp.sgn_sgn_real Y5)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real tptp.abs_abs_real Y5)) N)) X) (tptp.pp (tptp.aa_real_bool P Y5)))))))) (forall ((Info tptp.option4927543243414619207at_nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (= (tptp.aa_VEBT_VEBT_real tptp.vEBT_VEBT_cnt (tptp.vEBT_Node Info Deg TreeList Summary)) (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) (tptp.aa_VEBT_VEBT_real tptp.vEBT_VEBT_cnt Summary))) (tptp.aa_real_real (tptp.foldr_real_real tptp.plus_plus_real (tptp.map_VEBT_VEBT_real tptp.vEBT_VEBT_cnt TreeList)) tptp.zero_zero_real)))) (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 ((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)))) (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.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.vEBT_VEBT_high X) _let_3))) (tptp.aa_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 ((Info tptp.option4927543243414619207at_nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (= (tptp.aa_VEBT_VEBT_nat tptp.vEBT_VEBT_space (tptp.vEBT_Node Info Deg TreeList Summary)) (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.plus_plus_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit0 tptp.one)))) (tptp.aa_VEBT_VEBT_nat tptp.vEBT_VEBT_space Summary))) (tptp.size_s6755466524823107622T_VEBT TreeList))) (tptp.aa_nat_nat (tptp.foldr_nat_nat tptp.plus_plus_nat (tptp.map_VEBT_VEBT_nat tptp.vEBT_VEBT_space TreeList)) tptp.zero_zero_nat)))) (forall ((Info tptp.option4927543243414619207at_nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (= (tptp.aa_VEBT_VEBT_nat tptp.vEBT_VEBT_space2 (tptp.vEBT_Node Info Deg TreeList Summary)) (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_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit1 tptp.one)))) (tptp.aa_VEBT_VEBT_nat tptp.vEBT_VEBT_space2 Summary))) (tptp.aa_nat_nat (tptp.foldr_nat_nat tptp.plus_plus_nat (tptp.map_VEBT_VEBT_nat tptp.vEBT_VEBT_space2 TreeList)) tptp.zero_zero_nat)))) (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 ((X21 tptp.bool) (X222 tptp.bool) (Y21 tptp.bool) (Y22 tptp.bool)) (= (= (tptp.vEBT_Leaf X21 X222) (tptp.vEBT_Leaf Y21 Y22)) (and (= (tptp.pp X21) (tptp.pp Y21)) (= (tptp.pp X222) (tptp.pp Y22))))) (forall ((X tptp.vEBT_VEBT)) (=> (forall ((A3 tptp.bool) (B2 tptp.bool)) (not (= X (tptp.vEBT_Leaf A3 B2)))) (not (forall ((Info2 tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (not (= X (tptp.vEBT_Node Info2 Deg2 TreeList2 Summary2))))))) (forall ((Y4 tptp.vEBT_VEBT)) (=> (forall ((X112 tptp.option4927543243414619207at_nat) (X122 tptp.nat) (X132 tptp.list_VEBT_VEBT) (X142 tptp.vEBT_VEBT)) (not (= Y4 (tptp.vEBT_Node X112 X122 X132 X142)))) (not (forall ((X212 tptp.bool) (X223 tptp.bool)) (not (= Y4 (tptp.vEBT_Leaf X212 X223))))))) (forall ((X11 tptp.option4927543243414619207at_nat) (X12 tptp.nat) (X13 tptp.list_VEBT_VEBT) (X14 tptp.vEBT_VEBT) (X21 tptp.bool) (X222 tptp.bool)) (not (= (tptp.vEBT_Node X11 X12 X13 X14) (tptp.vEBT_Leaf X21 X222)))) (forall ((Uu tptp.bool) (Uv tptp.bool) (Uw tptp.nat)) (not (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_VEBT_membermima (tptp.vEBT_Leaf Uu Uv)) Uw)))) (forall ((X21 tptp.bool) (X222 tptp.bool)) (= (tptp.aa_VEBT_VEBT_nat tptp.size_size_VEBT_VEBT (tptp.vEBT_Leaf X21 X222)) tptp.zero_zero_nat)) (= (tptp.vEBT_vebt_buildup tptp.zero_zero_nat) _let_57) (forall ((Uu tptp.bool) (Uv tptp.bool) (D tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_VEBT_valid (tptp.vEBT_Leaf Uu Uv)) D)) (= D tptp.one_one_nat))) (forall ((A tptp.bool) (B tptp.bool)) (= (tptp.aa_VEBT_VEBT_real tptp.vEBT_VEBT_cnt (tptp.vEBT_Leaf A B)) tptp.one_one_real)) (forall ((A tptp.bool) (B tptp.bool)) (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt (tptp.vEBT_Leaf A B)) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)))) (= (tptp.vEBT_vebt_buildup _let_58) _let_57) (forall ((A tptp.bool) (B 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_V5719532721284313246member (tptp.vEBT_Leaf A B)) X)) (and (=> _let_2 (tptp.pp A)) (=> (not _let_2) (and (=> _let_1 (tptp.pp B)) _let_1))))))) (forall ((A tptp.bool) (B tptp.bool)) (= (tptp.aa_VEBT_VEBT_nat tptp.vEBT_VEBT_space2 (tptp.vEBT_Leaf A B)) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit0 tptp.one))))) (forall ((A tptp.bool) (B tptp.bool)) (= (tptp.aa_VEBT_VEBT_nat tptp.vEBT_VEBT_space (tptp.vEBT_Leaf A B)) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 tptp.one)))) (forall ((X tptp.vEBT_VEBT) (Y4 tptp.nat)) (=> (= (tptp.aa_VEBT_VEBT_nat tptp.vEBT_VEBT_space2 X) Y4) (=> (=> (exists ((A3 tptp.bool) (B2 tptp.bool)) (= X (tptp.vEBT_Leaf A3 B2))) (not (= Y4 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit0 tptp.one)))))) (not (forall ((Info2 tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (=> (= X (tptp.vEBT_Node Info2 Deg2 TreeList2 Summary2)) (not (= Y4 (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_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit1 tptp.one)))) (tptp.aa_VEBT_VEBT_nat tptp.vEBT_VEBT_space2 Summary2))) (tptp.aa_nat_nat (tptp.foldr_nat_nat tptp.plus_plus_nat (tptp.map_VEBT_VEBT_nat tptp.vEBT_VEBT_space2 TreeList2)) tptp.zero_zero_nat)))))))))) (forall ((X tptp.vEBT_VEBT) (Y4 tptp.nat)) (=> (= (tptp.aa_VEBT_VEBT_nat tptp.vEBT_VEBT_space X) Y4) (=> (=> (exists ((A3 tptp.bool) (B2 tptp.bool)) (= X (tptp.vEBT_Leaf A3 B2))) (not (= Y4 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 tptp.one))))) (not (forall ((Info2 tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (=> (= X (tptp.vEBT_Node Info2 Deg2 TreeList2 Summary2)) (not (= Y4 (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.plus_plus_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit0 tptp.one)))) (tptp.aa_VEBT_VEBT_nat tptp.vEBT_VEBT_space Summary2))) (tptp.size_s6755466524823107622T_VEBT TreeList2))) (tptp.aa_nat_nat (tptp.foldr_nat_nat tptp.plus_plus_nat (tptp.map_VEBT_VEBT_nat tptp.vEBT_VEBT_space TreeList2)) tptp.zero_zero_nat)))))))))) (forall ((X tptp.vEBT_VEBT) (Y4 tptp.real)) (=> (= (tptp.aa_VEBT_VEBT_real tptp.vEBT_VEBT_cnt X) Y4) (=> (=> (exists ((A3 tptp.bool) (B2 tptp.bool)) (= X (tptp.vEBT_Leaf A3 B2))) (not (= Y4 tptp.one_one_real))) (not (forall ((Info2 tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (=> (= X (tptp.vEBT_Node Info2 Deg2 TreeList2 Summary2)) (not (= Y4 (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) (tptp.aa_VEBT_VEBT_real tptp.vEBT_VEBT_cnt Summary2))) (tptp.aa_real_real (tptp.foldr_real_real tptp.plus_plus_real (tptp.map_VEBT_VEBT_real tptp.vEBT_VEBT_cnt TreeList2)) tptp.zero_zero_real)))))))))) (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.vEBT_VEBT_high X) N))) (tptp.aa_nat_nat (tptp.vEBT_VEBT_low X) N))))) (forall ((TreeList tptp.list_VEBT_VEBT) (N tptp.nat) (Summary tptp.vEBT_VEBT) (M tptp.nat) (Deg tptp.nat)) (=> (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_invar_vebt X3) N)))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt Summary) M)) (=> (= (tptp.size_s6755466524823107622T_VEBT TreeList) (tptp.aa_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_1 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions Summary) 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 TreeList))) (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.vEBT_invar_vebt (tptp.vEBT_Node tptp.none_P5556105721700978146at_nat Deg TreeList Summary)) Deg)))))))))) (forall ((X tptp.vEBT_VEBT) (Y4 tptp.nat)) (=> (= (tptp.aa_VEBT_VEBT_nat tptp.vEBT_VEBT_space X) Y4) (=> (tptp.pp (tptp.aa_VEBT_VEBT_bool (tptp.accp_VEBT_VEBT tptp.vEBT_VEBT_space_rel2) X)) (=> (forall ((A3 tptp.bool) (B2 tptp.bool)) (let ((_let_1 (tptp.vEBT_Leaf A3 B2))) (=> (= X _let_1) (=> (= Y4 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 tptp.one))) (not (tptp.pp (tptp.aa_VEBT_VEBT_bool (tptp.accp_VEBT_VEBT tptp.vEBT_VEBT_space_rel2) _let_1))))))) (not (forall ((Info2 tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (tptp.vEBT_Node Info2 Deg2 TreeList2 Summary2))) (=> (= X _let_1) (=> (= Y4 (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.plus_plus_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit0 tptp.one)))) (tptp.aa_VEBT_VEBT_nat tptp.vEBT_VEBT_space Summary2))) (tptp.size_s6755466524823107622T_VEBT TreeList2))) (tptp.aa_nat_nat (tptp.foldr_nat_nat tptp.plus_plus_nat (tptp.map_VEBT_VEBT_nat tptp.vEBT_VEBT_space TreeList2)) tptp.zero_zero_nat))) (not (tptp.pp (tptp.aa_VEBT_VEBT_bool (tptp.accp_VEBT_VEBT tptp.vEBT_VEBT_space_rel2) _let_1)))))))))))) (forall ((TreeList tptp.list_VEBT_VEBT) (N tptp.nat) (Summary tptp.vEBT_VEBT) (M tptp.nat) (Deg tptp.nat)) (=> (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_invar_vebt X3) N)))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt Summary) M)) (=> (= (tptp.size_s6755466524823107622T_VEBT TreeList) (tptp.aa_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_1 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions Summary) 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 TreeList))) (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.vEBT_invar_vebt (tptp.vEBT_Node tptp.none_P5556105721700978146at_nat Deg TreeList Summary)) Deg)))))))))) (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)))) (forall ((X tptp.vEBT_VEBT) (Y4 tptp.nat)) (=> (= (tptp.aa_VEBT_VEBT_nat tptp.vEBT_VEBT_space2 X) Y4) (=> (tptp.pp (tptp.aa_VEBT_VEBT_bool (tptp.accp_VEBT_VEBT tptp.vEBT_VEBT_space_rel) X)) (=> (forall ((A3 tptp.bool) (B2 tptp.bool)) (let ((_let_1 (tptp.vEBT_Leaf A3 B2))) (=> (= X _let_1) (=> (= Y4 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit0 tptp.one)))) (not (tptp.pp (tptp.aa_VEBT_VEBT_bool (tptp.accp_VEBT_VEBT tptp.vEBT_VEBT_space_rel) _let_1))))))) (not (forall ((Info2 tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (tptp.vEBT_Node Info2 Deg2 TreeList2 Summary2))) (=> (= X _let_1) (=> (= Y4 (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_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit1 tptp.one)))) (tptp.aa_VEBT_VEBT_nat tptp.vEBT_VEBT_space2 Summary2))) (tptp.aa_nat_nat (tptp.foldr_nat_nat tptp.plus_plus_nat (tptp.map_VEBT_VEBT_nat tptp.vEBT_VEBT_space2 TreeList2)) tptp.zero_zero_nat))) (not (tptp.pp (tptp.aa_VEBT_VEBT_bool (tptp.accp_VEBT_VEBT tptp.vEBT_VEBT_space_rel) _let_1)))))))))))) (forall ((X tptp.vEBT_VEBT) (Y4 tptp.real)) (=> (= (tptp.aa_VEBT_VEBT_real tptp.vEBT_VEBT_cnt X) Y4) (=> (tptp.pp (tptp.aa_VEBT_VEBT_bool (tptp.accp_VEBT_VEBT tptp.vEBT_VEBT_cnt_rel) X)) (=> (forall ((A3 tptp.bool) (B2 tptp.bool)) (let ((_let_1 (tptp.vEBT_Leaf A3 B2))) (=> (= X _let_1) (=> (= Y4 tptp.one_one_real) (not (tptp.pp (tptp.aa_VEBT_VEBT_bool (tptp.accp_VEBT_VEBT tptp.vEBT_VEBT_cnt_rel) _let_1))))))) (not (forall ((Info2 tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (tptp.vEBT_Node Info2 Deg2 TreeList2 Summary2))) (=> (= X _let_1) (=> (= Y4 (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) (tptp.aa_VEBT_VEBT_real tptp.vEBT_VEBT_cnt Summary2))) (tptp.aa_real_real (tptp.foldr_real_real tptp.plus_plus_real (tptp.map_VEBT_VEBT_real tptp.vEBT_VEBT_cnt TreeList2)) tptp.zero_zero_real))) (not (tptp.pp (tptp.aa_VEBT_VEBT_bool (tptp.accp_VEBT_VEBT tptp.vEBT_VEBT_cnt_rel) _let_1)))))))))))) (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.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) Deg)))))) (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.vEBT_VEBT_high X) _let_1))) (tptp.aa_nat_nat (tptp.vEBT_VEBT_low X) _let_1))) (= X Mi) (= X Ma)))))) (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.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.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 ((X tptp.product_prod_nat_nat)) (not (forall ((K2 tptp.nat) (M4 tptp.nat)) (not (= X (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat K2) M4)))))) (forall ((Mi tptp.nat) (Ma tptp.nat) (Va2 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 Va2 Vb)) X)) (or (= X Mi) (= X Ma)))) (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.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (=> (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_invar_vebt X3) 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.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) M))) (= (exists ((X_12 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions (tptp.nth_VEBT_VEBT TreeList I3)) X_12))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions Summary) I3))))) (=> (=> _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 TreeList))) (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 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.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.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.vEBT_VEBT_low Ma) N)))) (forall ((X3 tptp.nat)) (=> (and (= (tptp.aa_nat_nat (tptp.vEBT_VEBT_high X3) 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.vEBT_VEBT_low X3) N)))) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Mi) X3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X3) 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 ((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.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (=> (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_invar_vebt X3) 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.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) M))) (= (exists ((X_12 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions (tptp.nth_VEBT_VEBT TreeList I3)) X_12))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions Summary) I3))))) (=> (=> _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 TreeList))) (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 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.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.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.vEBT_VEBT_low Ma) N)))) (forall ((X3 tptp.nat)) (=> (and (= (tptp.aa_nat_nat (tptp.vEBT_VEBT_high X3) 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.vEBT_VEBT_low X3) N)))) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Mi) X3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X3) 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 ((A1 tptp.vEBT_VEBT) (A22 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt A1) A22)) (=> (=> (exists ((A3 tptp.bool) (B2 tptp.bool)) (= A1 (tptp.vEBT_Leaf A3 B2))) (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) (M4 tptp.nat) (Deg2 tptp.nat)) (=> (= A1 (tptp.vEBT_Node tptp.none_P5556105721700978146at_nat Deg2 TreeList2 Summary2)) (=> (= A22 Deg2) (=> (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_invar_vebt X4) N2)))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt Summary2) M4)) (=> (= (tptp.size_s6755466524823107622T_VEBT TreeList2) (tptp.aa_nat_nat (tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) M4)) (=> (= M4 N2) (=> (= Deg2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N2) M4)) (=> (not (exists ((X_13 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions Summary2) X_13)))) (not (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))) (not (exists ((X_13 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions X4) X_13)))))))))))))))) (=> (forall ((TreeList2 tptp.list_VEBT_VEBT) (N2 tptp.nat) (Summary2 tptp.vEBT_VEBT) (M4 tptp.nat) (Deg2 tptp.nat)) (=> (= A1 (tptp.vEBT_Node tptp.none_P5556105721700978146at_nat Deg2 TreeList2 Summary2)) (=> (= A22 Deg2) (=> (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_invar_vebt X4) N2)))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt Summary2) M4)) (=> (= (tptp.size_s6755466524823107622T_VEBT TreeList2) (tptp.aa_nat_nat (tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) M4)) (=> (= M4 (tptp.aa_nat_nat tptp.suc N2)) (=> (= Deg2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N2) M4)) (=> (not (exists ((X_13 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions Summary2) X_13)))) (not (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))) (not (exists ((X_13 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions X4) X_13)))))))))))))))) (=> (forall ((TreeList2 tptp.list_VEBT_VEBT) (N2 tptp.nat) (Summary2 tptp.vEBT_VEBT) (M4 tptp.nat) (Deg2 tptp.nat) (Mi2 tptp.nat) (Ma2 tptp.nat)) (let ((_let_1 (= Mi2 Ma2))) (let ((_let_2 (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 ((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_invar_vebt X4) N2)))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt Summary2) M4)) (=> (= (tptp.size_s6755466524823107622T_VEBT TreeList2) (tptp.aa_nat_nat _let_2 M4)) (=> (= M4 N2) (=> (= Deg2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N2) M4)) (=> (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.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) M4))) (= (exists ((X_12 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions (tptp.nth_VEBT_VEBT TreeList2 I4)) X_12))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions Summary2) I4))))) (=> (=> _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 TreeList2))) (not (exists ((X_13 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions X4) 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 ((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.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) M4))) (and (=> (= (tptp.aa_nat_nat (tptp.vEBT_VEBT_high Ma2) N2) I4) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions (tptp.nth_VEBT_VEBT TreeList2 I4)) (tptp.aa_nat_nat (tptp.vEBT_VEBT_low Ma2) N2)))) (forall ((X4 tptp.nat)) (=> (and (= (tptp.aa_nat_nat (tptp.vEBT_VEBT_high X4) N2) I4) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions (tptp.nth_VEBT_VEBT TreeList2 I4)) (tptp.aa_nat_nat (tptp.vEBT_VEBT_low X4) N2)))) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Mi2) X4)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X4) Ma2)))))))))))))))))))))))) (not (forall ((TreeList2 tptp.list_VEBT_VEBT) (N2 tptp.nat) (Summary2 tptp.vEBT_VEBT) (M4 tptp.nat) (Deg2 tptp.nat) (Mi2 tptp.nat) (Ma2 tptp.nat)) (let ((_let_1 (= Mi2 Ma2))) (let ((_let_2 (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 ((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_invar_vebt X4) N2)))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt Summary2) M4)) (=> (= (tptp.size_s6755466524823107622T_VEBT TreeList2) (tptp.aa_nat_nat _let_2 M4)) (=> (= M4 (tptp.aa_nat_nat tptp.suc N2)) (=> (= Deg2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N2) M4)) (=> (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.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) M4))) (= (exists ((X_12 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions (tptp.nth_VEBT_VEBT TreeList2 I4)) X_12))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions Summary2) I4))))) (=> (=> _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 TreeList2))) (not (exists ((X_13 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions X4) 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 ((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.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) M4))) (and (=> (= (tptp.aa_nat_nat (tptp.vEBT_VEBT_high Ma2) N2) I4) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions (tptp.nth_VEBT_VEBT TreeList2 I4)) (tptp.aa_nat_nat (tptp.vEBT_VEBT_low Ma2) N2)))) (forall ((X4 tptp.nat)) (=> (and (= (tptp.aa_nat_nat (tptp.vEBT_VEBT_high X4) N2) I4) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions (tptp.nth_VEBT_VEBT TreeList2 I4)) (tptp.aa_nat_nat (tptp.vEBT_VEBT_low X4) N2)))) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Mi2) X4)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X4) Ma2))))))))))))))))))))))))))))))) (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) (B6 tptp.bool)) (= A1 (tptp.vEBT_Leaf A5 B6))) (= A22 (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat))) (exists ((TreeList3 tptp.list_VEBT_VEBT) (N4 tptp.nat) (Summary3 tptp.vEBT_VEBT)) (and (= A1 (tptp.vEBT_Node tptp.none_P5556105721700978146at_nat A22 TreeList3 Summary3)) (forall ((X5 tptp.vEBT_VEBT)) (=> (tptp.pp (tptp.aa_set8260762808118238015T_bool (tptp.aa_VEB289770264548726718T_bool tptp.member_VEBT_VEBT X5) (tptp.set_VEBT_VEBT2 TreeList3))) (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt X5) N4)))) (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt Summary3) N4)) (= (tptp.size_s6755466524823107622T_VEBT TreeList3) (tptp.aa_nat_nat (tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N4)) (= A22 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N4) N4)) (not (exists ((X_12 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions Summary3) X_12)))) (forall ((X5 tptp.vEBT_VEBT)) (=> (tptp.pp (tptp.aa_set8260762808118238015T_bool (tptp.aa_VEB289770264548726718T_bool tptp.member_VEBT_VEBT X5) (tptp.set_VEBT_VEBT2 TreeList3))) (not (exists ((X_12 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions X5) X_12)))))))) (exists ((TreeList3 tptp.list_VEBT_VEBT) (N4 tptp.nat) (Summary3 tptp.vEBT_VEBT)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N4))) (and (= A1 (tptp.vEBT_Node tptp.none_P5556105721700978146at_nat A22 TreeList3 Summary3)) (forall ((X5 tptp.vEBT_VEBT)) (=> (tptp.pp (tptp.aa_set8260762808118238015T_bool (tptp.aa_VEB289770264548726718T_bool tptp.member_VEBT_VEBT X5) (tptp.set_VEBT_VEBT2 TreeList3))) (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt X5) N4)))) (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt Summary3) _let_1)) (= (tptp.size_s6755466524823107622T_VEBT TreeList3) (tptp.aa_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 N4) _let_1)) (not (exists ((X_12 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions Summary3) X_12)))) (forall ((X5 tptp.vEBT_VEBT)) (=> (tptp.pp (tptp.aa_set8260762808118238015T_bool (tptp.aa_VEB289770264548726718T_bool tptp.member_VEBT_VEBT X5) (tptp.set_VEBT_VEBT2 TreeList3))) (not (exists ((X_12 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions X5) X_12))))))))) (exists ((TreeList3 tptp.list_VEBT_VEBT) (N4 tptp.nat) (Summary3 tptp.vEBT_VEBT) (Mi3 tptp.nat) (Ma3 tptp.nat)) (let ((_let_1 (= Mi3 Ma3))) (let ((_let_2 (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 ((X5 tptp.vEBT_VEBT)) (=> (tptp.pp (tptp.aa_set8260762808118238015T_bool (tptp.aa_VEB289770264548726718T_bool tptp.member_VEBT_VEBT X5) (tptp.set_VEBT_VEBT2 TreeList3))) (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt X5) N4)))) (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt Summary3) N4)) (= (tptp.size_s6755466524823107622T_VEBT TreeList3) (tptp.aa_nat_nat _let_2 N4)) (= A22 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N4) N4)) (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.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N4))) (= (exists ((X_12 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions (tptp.nth_VEBT_VEBT TreeList3 I2)) X_12))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions Summary3) 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 TreeList3))) (not (exists ((X_12 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions X5) X_12))))))) (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 ((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.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N4))) (and (=> (= (tptp.aa_nat_nat (tptp.vEBT_VEBT_high Ma3) N4) I2) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions (tptp.nth_VEBT_VEBT TreeList3 I2)) (tptp.aa_nat_nat (tptp.vEBT_VEBT_low Ma3) N4)))) (forall ((X5 tptp.nat)) (=> (and (= (tptp.aa_nat_nat (tptp.vEBT_VEBT_high X5) N4) I2) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions (tptp.nth_VEBT_VEBT TreeList3 I2)) (tptp.aa_nat_nat (tptp.vEBT_VEBT_low X5) N4)))) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Mi3) X5)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X5) Ma3))))))))))))) (exists ((TreeList3 tptp.list_VEBT_VEBT) (N4 tptp.nat) (Summary3 tptp.vEBT_VEBT) (Mi3 tptp.nat) (Ma3 tptp.nat)) (let ((_let_1 (= Mi3 Ma3))) (let ((_let_2 (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 N4))) (and (= A1 (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Mi3) Ma3)) A22 TreeList3 Summary3)) (forall ((X5 tptp.vEBT_VEBT)) (=> (tptp.pp (tptp.aa_set8260762808118238015T_bool (tptp.aa_VEB289770264548726718T_bool tptp.member_VEBT_VEBT X5) (tptp.set_VEBT_VEBT2 TreeList3))) (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt X5) N4)))) (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 N4) _let_3)) (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.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 N4)))) (= (exists ((X_12 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions (tptp.nth_VEBT_VEBT TreeList3 I2)) X_12))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions Summary3) 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 TreeList3))) (not (exists ((X_12 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions X5) X_12))))))) (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 ((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.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 N4)))) (and (=> (= (tptp.aa_nat_nat (tptp.vEBT_VEBT_high Ma3) N4) I2) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions (tptp.nth_VEBT_VEBT TreeList3 I2)) (tptp.aa_nat_nat (tptp.vEBT_VEBT_low Ma3) N4)))) (forall ((X5 tptp.nat)) (=> (and (= (tptp.aa_nat_nat (tptp.vEBT_VEBT_high X5) N4) I2) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions (tptp.nth_VEBT_VEBT TreeList3 I2)) (tptp.aa_nat_nat (tptp.vEBT_VEBT_low X5) N4)))) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Mi3) X5)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X5) Ma3))))))))))))))))) (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 ((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 ((M4 tptp.num)) (not (= X (tptp.product_Pair_num_num (tptp.aa_num_num tptp.bit0 M4) tptp.one)))) (=> (forall ((M4 tptp.num) (N2 tptp.num)) (not (= X (tptp.product_Pair_num_num (tptp.aa_num_num tptp.bit0 M4) (tptp.aa_num_num tptp.bit0 N2))))) (=> (forall ((M4 tptp.num) (N2 tptp.num)) (not (= X (tptp.product_Pair_num_num (tptp.aa_num_num tptp.bit0 M4) (tptp.aa_num_num tptp.bit1 N2))))) (=> (forall ((M4 tptp.num)) (not (= X (tptp.product_Pair_num_num (tptp.aa_num_num tptp.bit1 M4) tptp.one)))) (=> (forall ((M4 tptp.num) (N2 tptp.num)) (not (= X (tptp.product_Pair_num_num (tptp.aa_num_num tptp.bit1 M4) (tptp.aa_num_num tptp.bit0 N2))))) (not (forall ((M4 tptp.num) (N2 tptp.num)) (not (= X (tptp.product_Pair_num_num (tptp.aa_num_num tptp.bit1 M4) (tptp.aa_num_num tptp.bit1 N2))))))))))))))) (forall ((X tptp.produc9072475918466114483BT_nat)) (=> (forall ((A3 tptp.bool) (B2 tptp.bool) (X3 tptp.nat)) (not (= X (tptp.produc738532404422230701BT_nat (tptp.vEBT_Leaf A3 B2) X3)))) (=> (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) (V3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (S3 tptp.vEBT_VEBT) (X3 tptp.nat)) (not (= X (tptp.produc738532404422230701BT_nat (tptp.vEBT_Node Uy2 (tptp.aa_nat_nat tptp.suc V3) TreeList2 S3) X3)))))))) (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) (X3 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) X3)))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (V3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Vc tptp.vEBT_VEBT) (X3 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 V3) TreeList2 Vc) X3)))) (not (forall ((V3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Vd tptp.vEBT_VEBT) (X3 tptp.nat)) (not (= X (tptp.produc738532404422230701BT_nat (tptp.vEBT_Node tptp.none_P5556105721700978146at_nat (tptp.aa_nat_nat tptp.suc V3) TreeList2 Vd) X3)))))))))) (forall ((B tptp.int) (A tptp.int) (Q2 tptp.int) (R2 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 B) tptp.zero_zero_int)) (=> (tptp.eucl_rel_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) tptp.one_one_int) B (tptp.product_Pair_int_int Q2 R2)) (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 B) (tptp.product_Pair_int_int Q2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_int_int _let_1 R2)) tptp.one_one_int))))))) (forall ((Q2 tptp.int) (R2 tptp.int)) (= (tptp.adjust_div (tptp.product_Pair_int_int Q2 R2)) (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 R2) tptp.zero_zero_int)))))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.aa_int_int (tptp.aa_int_fun_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.aa_int_fun_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 ((N tptp.num)) (= (tptp.aa_int_int (tptp.aa_int_fun_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.aa_int_fun_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 ((M tptp.num)) (= (tptp.unique5052692396658037445od_int (tptp.aa_num_num tptp.bitM M) (tptp.aa_num_num tptp.bit0 tptp.one)) (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 ((A tptp.int) (B tptp.int) (Q2 tptp.int) (R2 tptp.int) (Q5 tptp.int) (R4 tptp.int)) (=> (tptp.eucl_rel_int A B (tptp.product_Pair_int_int Q2 R2)) (=> (tptp.eucl_rel_int A B (tptp.product_Pair_int_int Q5 R4)) (= Q2 Q5)))) (forall ((A tptp.int) (B tptp.int) (Q2 tptp.int) (R2 tptp.int) (Q5 tptp.int) (R4 tptp.int)) (=> (tptp.eucl_rel_int A B (tptp.product_Pair_int_int Q2 R2)) (=> (tptp.eucl_rel_int A B (tptp.product_Pair_int_int Q5 R4)) (= R2 R4)))) (forall ((K tptp.int)) (tptp.eucl_rel_int K tptp.zero_zero_int (tptp.product_Pair_int_int tptp.zero_zero_int K))) (forall ((K tptp.int) (L tptp.int) (Q2 tptp.int) (R2 tptp.int)) (=> (tptp.eucl_rel_int K L (tptp.product_Pair_int_int Q2 R2)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int K) L) Q2))) (forall ((K tptp.int) (L tptp.int) (Q2 tptp.int) (R2 tptp.int)) (=> (tptp.eucl_rel_int K L (tptp.product_Pair_int_int Q2 R2)) (= (tptp.modulo_modulo_int K L) R2))) (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.eucl_rel_int K L (tptp.product_Pair_int_int Q2 tptp.zero_zero_int))))) (forall ((K tptp.int) (L tptp.int)) (tptp.eucl_rel_int K L (tptp.product_Pair_int_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int K) L) (tptp.modulo_modulo_int K L)))) (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.product_Pair_int_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int _let_2) _let_1) (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.modulo_modulo_nat _let_2) _let_1)))))) (forall ((A tptp.int) (B tptp.int) (Q2 tptp.int) (R2 tptp.int)) (let ((_let_1 (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.fequal_int R2) tptp.zero_zero_int))) (let ((_let_2 (tptp.aa_int_int tptp.uminus_uminus_int Q2))) (=> (tptp.eucl_rel_int A B (tptp.product_Pair_int_int Q2 R2)) (=> (not (= B tptp.zero_zero_int)) (tptp.eucl_rel_int (tptp.aa_int_int tptp.uminus_uminus_int A) B (tptp.product_Pair_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.if_int _let_1 tptp.zero_zero_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int B) R2))))))))) (forall ((K tptp.int) (L tptp.int) (Q2 tptp.int) (R2 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.eucl_rel_int K L (tptp.product_Pair_int_int Q2 R2)) (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)) R2)) (=> _let_3 (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) R2)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int R2) L)))) (=> (not _let_3) (and (=> _let_2 (and (tptp.pp (tptp.aa_int_bool _let_1 R2)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int R2) tptp.zero_zero_int)))) (=> (not _let_2) (= Q2 tptp.zero_zero_int)))))))))) (forall ((R2 tptp.int) (L tptp.int) (K tptp.int) (Q2 tptp.int)) (=> (= (tptp.sgn_sgn_int R2) (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 R2)) (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)) R2)) (tptp.eucl_rel_int K L (tptp.product_Pair_int_int Q2 R2)))))) (forall ((A1 tptp.int) (A22 tptp.int) (A32 tptp.product_prod_int_int)) (= (tptp.eucl_rel_int A1 A22 A32) (or (exists ((K3 tptp.int)) (and (= A1 K3) (= A22 tptp.zero_zero_int) (= A32 (tptp.product_Pair_int_int tptp.zero_zero_int K3)))) (exists ((L3 tptp.int) (K3 tptp.int) (Q3 tptp.int)) (and (= A1 K3) (= A22 L3) (= A32 (tptp.product_Pair_int_int Q3 tptp.zero_zero_int)) (not (= L3 tptp.zero_zero_int)) (= K3 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int Q3) L3)))) (exists ((R5 tptp.int) (L3 tptp.int) (K3 tptp.int) (Q3 tptp.int)) (and (= A1 K3) (= A22 L3) (= A32 (tptp.product_Pair_int_int Q3 R5)) (= (tptp.sgn_sgn_int R5) (tptp.sgn_sgn_int L3)) (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 L3))) (= K3 (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) L3)) R5))))))) (forall ((A1 tptp.int) (A22 tptp.int) (A32 tptp.product_prod_int_int)) (=> (tptp.eucl_rel_int A1 A22 A32) (=> (=> (= A22 tptp.zero_zero_int) (not (= A32 (tptp.product_Pair_int_int tptp.zero_zero_int A1)))) (=> (forall ((Q4 tptp.int)) (=> (= A32 (tptp.product_Pair_int_int Q4 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 Q4) A22)))))) (not (forall ((R3 tptp.int) (Q4 tptp.int)) (=> (= A32 (tptp.product_Pair_int_int Q4 R3)) (=> (= (tptp.sgn_sgn_int R3) (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 Q4) A22)) R3)))))))))))) (forall ((B tptp.int) (A tptp.int) (Q2 tptp.int) (R2 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) B)) (=> (tptp.eucl_rel_int A B (tptp.product_Pair_int_int Q2 R2)) (tptp.eucl_rel_int (tptp.aa_int_int _let_2 (tptp.aa_int_int _let_1 A)) (tptp.aa_int_int _let_1 B) (tptp.product_Pair_int_int Q2 (tptp.aa_int_int _let_2 (tptp.aa_int_int _let_1 R2))))))))) (forall ((X tptp.vEBT_VEBT) (Xa tptp.nat)) (=> (not (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_VEBT_membermima X) Xa))) (=> (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 (= Xa Mi2) (= Xa Ma2)))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (V3 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 V3)) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_2 (tptp.aa_nat_nat (tptp.vEBT_VEBT_high Xa) _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 ((Vc 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 V3) TreeList2 Vc))) (or (= Xa Mi2) (= Xa 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.vEBT_VEBT_low Xa) _let_1)))) _let_3))))))) (not (forall ((V3 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 V3)) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_2 (tptp.aa_nat_nat (tptp.vEBT_VEBT_high Xa) _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 ((Vd tptp.vEBT_VEBT)) (= X (tptp.vEBT_Node tptp.none_P5556105721700978146at_nat (tptp.aa_nat_nat tptp.suc V3) TreeList2 Vd))) (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.vEBT_VEBT_low Xa) _let_1)))) _let_3))))))))))))) (forall ((X tptp.vEBT_VEBT) (Xa tptp.nat) (Y4 tptp.bool)) (let ((_let_1 (tptp.pp Y4))) (=> (= (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_VEBT_membermima X) Xa)) _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 Y4) (not (or (= Xa Mi2) (= Xa Ma2)))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (V3 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 V3)) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_2 (tptp.aa_nat_nat (tptp.vEBT_VEBT_high Xa) _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 ((Vc 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 V3) TreeList2 Vc))) (= (tptp.pp Y4) (not (or (= Xa Mi2) (= Xa 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.vEBT_VEBT_low Xa) _let_1)))) _let_3))))))))) (not (forall ((V3 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 V3)) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_2 (tptp.aa_nat_nat (tptp.vEBT_VEBT_high Xa) _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 ((Vd tptp.vEBT_VEBT)) (= X (tptp.vEBT_Node tptp.none_P5556105721700978146at_nat (tptp.aa_nat_nat tptp.suc V3) TreeList2 Vd))) (= (tptp.pp Y4) (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.vEBT_VEBT_low Xa) _let_1)))) _let_3)))))))))))))))) (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) (Xa tptp.nat) (Y4 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 Xa) X)))) (=> (= (tptp.nat_prod_decode_aux X Xa) Y4) (and (=> _let_2 (= Y4 (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Xa) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat X) Xa)))) (=> (not _let_2) (= Y4 (tptp.nat_prod_decode_aux _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Xa) _let_1))))))))) (forall ((Xs tptp.list_real) (Y4 tptp.real)) (=> (forall ((X3 tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.set_real2 Xs))) (=> (tptp.member_real X3 _let_1) (=> (tptp.member_real Y _let_1) (= X3 Y))))) (=> (forall ((X3 tptp.real)) (=> (tptp.member_real X3 (tptp.set_real2 Xs)) (= X3 Y4))) (= (tptp.aa_real_real (tptp.foldr_real_real tptp.plus_plus_real Xs) tptp.zero_zero_real) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real (tptp.size_size_list_real Xs))) Y4))))) (forall ((Xs tptp.list_nat) (Ys tptp.list_nat) (C tptp.nat) (D tptp.nat)) (let ((_let_1 (tptp.size_size_list_nat Ys))) (=> (= (tptp.size_size_list_nat Xs) _let_1) (=> (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 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.nth_nat Xs) I3)) (tptp.aa_nat_nat (tptp.nth_nat Ys) I3))))) (=> (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 (tptp.aa_nat_nat (tptp.foldr_nat_nat tptp.plus_plus_nat Xs) C)) _let_1)) (tptp.aa_nat_nat (tptp.foldr_nat_nat tptp.plus_plus_nat Ys) D)))))))) (forall ((Xs tptp.list_nat) (D 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 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.aa_nat_nat (tptp.nth_nat Xs) I3))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.size_size_list_nat Xs)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat (tptp.foldr_nat_nat tptp.plus_plus_nat Xs) D)) D))))) (forall ((X4 tptp.nat) (Xa2 tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X4) Xa2)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int X4)) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int Xa2))))) (forall ((X4 tptp.nat) (Xa2 tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X4) Xa2)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int X4)) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int Xa2))))) (forall ((X4 tptp.nat) (Xa2 tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat X4) Xa2) (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 X4)) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int Xa2))))) (forall ((X4 tptp.nat) (Xa2 tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat X4) Xa2) (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 X4)) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int Xa2))))) (forall ((X4 tptp.nat) (Xa2 tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat X4) Xa2) (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 X4)) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int Xa2))))) (forall ((X4 tptp.nat) (Xa2 tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat X4) Xa2) (tptp.aa_int_nat tptp.nat2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int X4)) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int Xa2))))) (forall ((X4 tptp.nat) (Xa2 tptp.nat)) (= (tptp.aa_nat_nat (tptp.modulo_modulo_nat X4) Xa2) (tptp.aa_int_nat tptp.nat2 (tptp.modulo_modulo_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int X4) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int Xa2))))) (forall ((Z4 tptp.int) (Z tptp.int)) (let ((_let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int Z) Z4))) (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 Z4)))) (let ((_let_4 (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Z4) tptp.zero_zero_int)))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (tptp.aa_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 ((X tptp.nat)) (= (tptp.nat_set_decode X) (tptp.collect_nat (tptp.aa_nat_fun_nat_bool tptp.aTP_Lamm_af X)))) (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.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 ((Va2 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.aa_nat_nat tptp.suc Va2)))) (let ((_let_4 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat _let_3) _let_2))) (let ((_let_5 (tptp.aa_nat_nat tptp.vEBT_V8646137997579335489_i_l_d _let_4))) (let ((_let_6 (tptp.aa_nat_nat tptp.suc _let_4))) (let ((_let_7 (tptp.power_power_nat _let_2))) (let ((_let_8 (tptp.aa_nat_nat tptp.vEBT_V8646137997579335489_i_l_d _let_3))) (let ((_let_9 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat _let_2) _let_3)))) (and (=> _let_9 (= _let_8 (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.plus_plus_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.aa_num_num tptp.bit1 _let_1)))) _let_5)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat _let_7 _let_4)) _let_5))))) (=> (not _let_9) (= _let_8 (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_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit1 tptp.one))))) (tptp.aa_nat_nat tptp.vEBT_V8646137997579335489_i_l_d _let_6))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat _let_7 _let_6)) _let_5))))))))))))))) (forall ((Va2 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.aa_nat_nat tptp.suc Va2)))) (let ((_let_4 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat _let_3) _let_2))) (let ((_let_5 (tptp.aa_nat_nat tptp.vEBT_V8346862874174094_d_u_p _let_4))) (let ((_let_6 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat _let_5) tptp.one_one_nat))) (let ((_let_7 (tptp.aa_nat_nat tptp.suc _let_4))) (let ((_let_8 (tptp.power_power_nat _let_2))) (let ((_let_9 (tptp.aa_nat_nat tptp.vEBT_V8346862874174094_d_u_p _let_3))) (let ((_let_10 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat _let_2) _let_3)))) (and (=> _let_10 (= _let_9 (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.plus_plus_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.aa_num_num tptp.bit0 _let_1)))) _let_5)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat _let_8 _let_4)) _let_6))))) (=> (not _let_10) (= _let_9 (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_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit1 _let_1)))) (tptp.aa_nat_nat tptp.vEBT_V8346862874174094_d_u_p _let_7))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat _let_8 _let_7)) _let_6)))))))))))))))) (forall ((Uy tptp.option4927543243414619207at_nat) (V tptp.nat) (TreeList tptp.list_VEBT_VEBT) (S2 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.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 S2)) 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.vEBT_VEBT_low X) _let_2)))) _let_4))))))) (forall ((X tptp.nat) (Y4 tptp.nat)) (let ((_let_1 (not (= Y4 (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.vEBT_V8646137997579335489_i_l_d X) Y4) (=> (=> (= X tptp.zero_zero_nat) _let_1) (=> (=> (= X (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)) _let_1) (not (forall ((Va 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.aa_nat_nat tptp.suc Va)))) (let ((_let_4 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat _let_3) _let_2))) (let ((_let_5 (tptp.aa_nat_nat tptp.vEBT_V8646137997579335489_i_l_d _let_4))) (let ((_let_6 (tptp.aa_nat_nat tptp.suc _let_4))) (let ((_let_7 (tptp.power_power_nat _let_2))) (let ((_let_8 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat _let_2) _let_3)))) (=> (= X _let_3) (not (and (=> _let_8 (= Y4 (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.plus_plus_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.aa_num_num tptp.bit1 _let_1)))) _let_5)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat _let_7 _let_4)) _let_5))))) (=> (not _let_8) (= Y4 (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_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit1 tptp.one))))) (tptp.aa_nat_nat tptp.vEBT_V8646137997579335489_i_l_d _let_6))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat _let_7 _let_6)) _let_5)))))))))))))))))))))) (forall ((X tptp.nat) (Y4 tptp.nat)) (let ((_let_1 (not (= Y4 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 tptp.one)))))) (=> (= (tptp.aa_nat_nat tptp.vEBT_V8346862874174094_d_u_p X) Y4) (=> (=> (= X tptp.zero_zero_nat) _let_1) (=> (=> (= X (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)) _let_1) (not (forall ((Va 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.aa_nat_nat tptp.suc Va)))) (let ((_let_4 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat _let_3) _let_2))) (let ((_let_5 (tptp.aa_nat_nat tptp.vEBT_V8346862874174094_d_u_p _let_4))) (let ((_let_6 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat _let_5) tptp.one_one_nat))) (let ((_let_7 (tptp.aa_nat_nat tptp.suc _let_4))) (let ((_let_8 (tptp.power_power_nat _let_2))) (let ((_let_9 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat _let_2) _let_3)))) (=> (= X _let_3) (not (and (=> _let_9 (= Y4 (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.plus_plus_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.aa_num_num tptp.bit0 _let_1)))) _let_5)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat _let_8 _let_4)) _let_6))))) (=> (not _let_9) (= Y4 (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_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit1 _let_1)))) (tptp.aa_nat_nat tptp.vEBT_V8346862874174094_d_u_p _let_7))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat _let_8 _let_7)) _let_6))))))))))))))))))))))) (forall ((V tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Vd2 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.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 Vd2)) 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.vEBT_VEBT_low X) _let_2)))) _let_4))))))) (forall ((X tptp.nat) (Y4 tptp.vEBT_VEBT)) (let ((_let_1 (not (= Y4 (tptp.vEBT_Leaf tptp.fFalse tptp.fFalse))))) (=> (= (tptp.vEBT_vebt_buildup X) Y4) (=> (=> (= X tptp.zero_zero_nat) _let_1) (=> (=> (= X (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)) _let_1) (not (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.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 (= Y4 (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) (= Y4 (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 ((Mi tptp.nat) (Ma tptp.nat) (V tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Vc2 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.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 Vc2)) 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.vEBT_VEBT_low X) _let_2)))) _let_4)))))))) (forall ((X tptp.vEBT_VEBT) (Xa tptp.nat) (Y4 tptp.bool)) (let ((_let_1 (tptp.pp Y4))) (=> (= (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_V5719532721284313246member X) Xa)) _let_1) (=> (forall ((A3 tptp.bool) (B2 tptp.bool)) (let ((_let_1 (= Xa tptp.one_one_nat))) (let ((_let_2 (= Xa tptp.zero_zero_nat))) (=> (= X (tptp.vEBT_Leaf A3 B2)) (= (tptp.pp Y4) (not (and (=> _let_2 (tptp.pp A3)) (=> (not _let_2) (and (=> _let_1 (tptp.pp B2)) _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) (V3 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 V3)) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_2 (tptp.aa_nat_nat (tptp.vEBT_VEBT_high Xa) _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 V3) TreeList2 S3))) (= (tptp.pp Y4) (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.vEBT_VEBT_low Xa) _let_1)))) _let_3)))))))))))))) (forall ((X tptp.vEBT_VEBT) (Xa tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_V5719532721284313246member X) Xa)) (=> (forall ((A3 tptp.bool) (B2 tptp.bool)) (let ((_let_1 (= Xa tptp.one_one_nat))) (let ((_let_2 (= Xa tptp.zero_zero_nat))) (=> (= X (tptp.vEBT_Leaf A3 B2)) (not (and (=> _let_2 (tptp.pp A3)) (=> (not _let_2) (and (=> _let_1 (tptp.pp B2)) _let_1)))))))) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V3 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 V3)) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_2 (tptp.aa_nat_nat (tptp.vEBT_VEBT_high Xa) _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 V3) 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.vEBT_VEBT_low Xa) _let_1)))) _let_3))))))))))) (forall ((X tptp.vEBT_VEBT) (Xa tptp.nat)) (=> (not (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_V5719532721284313246member X) Xa))) (=> (forall ((A3 tptp.bool) (B2 tptp.bool)) (let ((_let_1 (= Xa tptp.one_one_nat))) (let ((_let_2 (= Xa tptp.zero_zero_nat))) (=> (= X (tptp.vEBT_Leaf A3 B2)) (and (=> _let_2 (tptp.pp A3)) (=> (not _let_2) (and (=> _let_1 (tptp.pp B2)) _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) (V3 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 V3)) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_2 (tptp.aa_nat_nat (tptp.vEBT_VEBT_high Xa) _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 V3) 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.vEBT_VEBT_low Xa) _let_1)))) _let_3))))))))))) (forall ((X tptp.vEBT_VEBT) (Xa tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_VEBT_membermima X) Xa)) (=> (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 (= Xa Mi2) (= Xa Ma2))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (V3 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 V3)) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_2 (tptp.aa_nat_nat (tptp.vEBT_VEBT_high Xa) _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 ((Vc 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 V3) TreeList2 Vc))) (not (or (= Xa Mi2) (= Xa 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.vEBT_VEBT_low Xa) _let_1)))) _let_3)))))))) (not (forall ((V3 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 V3)) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_2 (tptp.aa_nat_nat (tptp.vEBT_VEBT_high Xa) _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 ((Vd tptp.vEBT_VEBT)) (= X (tptp.vEBT_Node tptp.none_P5556105721700978146at_nat (tptp.aa_nat_nat tptp.suc V3) TreeList2 Vd))) (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.vEBT_VEBT_low Xa) _let_1)))) _let_3)))))))))))) (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_ag 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_ah 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 X) tptp.one_one_real)) (tptp.topolo6980174941875973593q_real (tptp.aa_real_fun_nat_real tptp.power_power_real X))))) (= _let_56 (tptp.suminf_real tptp.aTP_Lamm_ai)) (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_aj X))))) (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.bij_be1856998921033663316omplex (tptp.times_times_complex (tptp.aa_complex_complex (tptp.times_times_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.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_ak N)) (tptp.collect_complex (tptp.aa_nat5545486172511849908x_bool (tptp.aTP_Lamm_al C) N)))))) (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_aj X)))) (forall ((F tptp.fun_nat_real) (G tptp.fun_nat_real)) (=> (exists ((N7 tptp.nat)) (forall ((N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N7) 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_am F))))) (forall ((F tptp.fun_nat_real)) (let ((_let_1 (tptp.aTP_Lamm_am 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) (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_an F) Z))))))) (forall ((X tptp.real)) (tptp.pp (tptp.aa_real_bool (tptp.sums_real (tptp.aa_real_fun_nat_real tptp.aTP_Lamm_ao X)) (tptp.aa_real_real tptp.sin_real X)))) (forall ((X tptp.vEBT_VEBT) (Xa tptp.nat)) (=> (not (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_VEBT_membermima X) Xa))) (=> (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel (tptp.produc738532404422230701BT_nat X Xa)) (=> (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 Xa)))))) (=> (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 Xa)))))) (=> (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 Xa)) (or (= Xa Mi2) (= Xa Ma2)))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (V3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Vc tptp.vEBT_VEBT)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc V3))) (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.vEBT_VEBT_high Xa) _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 Vc))) (=> (= X _let_5) (=> (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel (tptp.produc738532404422230701BT_nat _let_5 Xa)) (or (= Xa Mi2) (= Xa 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.vEBT_VEBT_low Xa) _let_2)))) _let_4)))))))))) (not (forall ((V3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Vd tptp.vEBT_VEBT)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc V3))) (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.vEBT_VEBT_high Xa) _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 Vd))) (=> (= X _let_5) (=> (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel (tptp.produc738532404422230701BT_nat _let_5 Xa)) (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.vEBT_VEBT_low Xa) _let_2)))) _let_4))))))))))))))))) (forall ((X tptp.vEBT_VEBT) (Xa tptp.nat) (Y4 tptp.bool)) (=> (= (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_VEBT_membermima X) Xa)) (tptp.pp Y4)) (=> (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel (tptp.produc738532404422230701BT_nat X Xa)) (=> (forall ((Uu2 tptp.bool) (Uv2 tptp.bool)) (let ((_let_1 (tptp.vEBT_Leaf Uu2 Uv2))) (=> (= X _let_1) (=> (not (tptp.pp Y4)) (not (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel (tptp.produc738532404422230701BT_nat _let_1 Xa))))))) (=> (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 Y4)) (not (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel (tptp.produc738532404422230701BT_nat _let_1 Xa))))))) (=> (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 Y4) (or (= Xa Mi2) (= Xa Ma2))) (not (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel (tptp.produc738532404422230701BT_nat _let_1 Xa))))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (V3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Vc tptp.vEBT_VEBT)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc V3))) (let ((_let_2 (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Mi2) Ma2)) _let_1 TreeList2 Vc))) (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.vEBT_VEBT_high Xa) _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 Y4) (or (= Xa Mi2) (= Xa 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.vEBT_VEBT_low Xa) _let_3)))) _let_5))) (not (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel (tptp.produc738532404422230701BT_nat _let_2 Xa))))))))))) (not (forall ((V3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Vd tptp.vEBT_VEBT)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc V3))) (let ((_let_2 (tptp.vEBT_Node tptp.none_P5556105721700978146at_nat _let_1 TreeList2 Vd))) (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.vEBT_VEBT_high Xa) _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 Y4) (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.vEBT_VEBT_low Xa) _let_3)))) _let_5)) (not (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel (tptp.produc738532404422230701BT_nat _let_2 Xa))))))))))))))))))) (tptp.pp (tptp.aa_real_bool (tptp.sums_real tptp.aTP_Lamm_ap) tptp.one_one_real)) (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_aq G)) X)))) (forall ((G tptp.fun_nat_real) (X tptp.real) (F tptp.fun_nat_real) (Y4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.sums_real G) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.sums_real F) Y4)) (tptp.pp (tptp.aa_real_bool (tptp.sums_real (tptp.aa_fun1839206346889086768t_real (tptp.aTP_Lamm_ar G) F)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) Y4)))))) (forall ((X tptp.real)) (tptp.pp (tptp.aa_real_bool (tptp.sums_real (tptp.aa_real_fun_nat_real tptp.aTP_Lamm_as X)) (tptp.aa_real_real tptp.cos_real X)))) (forall ((X tptp.vEBT_VEBT) (Xa tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_VEBT_membermima X) Xa)) (=> (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel (tptp.produc738532404422230701BT_nat X Xa)) (=> (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 Xa)) (not (or (= Xa Mi2) (= Xa Ma2))))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (V3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Vc tptp.vEBT_VEBT)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc V3))) (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.vEBT_VEBT_high Xa) _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 Vc))) (=> (= X _let_5) (=> (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel (tptp.produc738532404422230701BT_nat _let_5 Xa)) (not (or (= Xa Mi2) (= Xa 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.vEBT_VEBT_low Xa) _let_2)))) _let_4))))))))))) (not (forall ((V3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Vd tptp.vEBT_VEBT)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc V3))) (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.vEBT_VEBT_high Xa) _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 Vd))) (=> (= X _let_5) (=> (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel (tptp.produc738532404422230701BT_nat _let_5 Xa)) (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.vEBT_VEBT_low Xa) _let_2)))) _let_4)))))))))))))))) (forall ((X tptp.vEBT_VEBT) (Xa tptp.nat)) (=> (not (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_V5719532721284313246member X) Xa))) (=> (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel (tptp.produc738532404422230701BT_nat X Xa)) (=> (forall ((A3 tptp.bool) (B2 tptp.bool)) (let ((_let_1 (= Xa tptp.one_one_nat))) (let ((_let_2 (= Xa tptp.zero_zero_nat))) (let ((_let_3 (tptp.vEBT_Leaf A3 B2))) (=> (= X _let_3) (=> (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel (tptp.produc738532404422230701BT_nat _let_3 Xa)) (and (=> _let_2 (tptp.pp A3)) (=> (not _let_2) (and (=> _let_1 (tptp.pp B2)) _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 Xa)))))) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (S3 tptp.vEBT_VEBT)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc V3))) (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.vEBT_VEBT_high Xa) _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 Xa)) (and (=> _let_4 (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_V5719532721284313246member (tptp.nth_VEBT_VEBT TreeList2 _let_3)) (tptp.aa_nat_nat (tptp.vEBT_VEBT_low Xa) _let_2)))) _let_4))))))))))))))) (forall ((X tptp.vEBT_VEBT) (Xa tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_V5719532721284313246member X) Xa)) (=> (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel (tptp.produc738532404422230701BT_nat X Xa)) (=> (forall ((A3 tptp.bool) (B2 tptp.bool)) (let ((_let_1 (= Xa tptp.one_one_nat))) (let ((_let_2 (= Xa tptp.zero_zero_nat))) (let ((_let_3 (tptp.vEBT_Leaf A3 B2))) (=> (= X _let_3) (=> (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel (tptp.produc738532404422230701BT_nat _let_3 Xa)) (not (and (=> _let_2 (tptp.pp A3)) (=> (not _let_2) (and (=> _let_1 (tptp.pp B2)) _let_1)))))))))) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (S3 tptp.vEBT_VEBT)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc V3))) (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.vEBT_VEBT_high Xa) _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 Xa)) (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.vEBT_VEBT_low Xa) _let_2)))) _let_4))))))))))))))) (forall ((X tptp.vEBT_VEBT) (Xa tptp.nat) (Y4 tptp.bool)) (=> (= (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_V5719532721284313246member X) Xa)) (tptp.pp Y4)) (=> (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel (tptp.produc738532404422230701BT_nat X Xa)) (=> (forall ((A3 tptp.bool) (B2 tptp.bool)) (let ((_let_1 (tptp.vEBT_Leaf A3 B2))) (let ((_let_2 (= Xa tptp.one_one_nat))) (let ((_let_3 (= Xa tptp.zero_zero_nat))) (=> (= X _let_1) (=> (= (tptp.pp Y4) (and (=> _let_3 (tptp.pp A3)) (=> (not _let_3) (and (=> _let_2 (tptp.pp B2)) _let_2)))) (not (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel (tptp.produc738532404422230701BT_nat _let_1 Xa))))))))) (=> (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 Y4)) (not (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel (tptp.produc738532404422230701BT_nat _let_1 Xa))))))) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (S3 tptp.vEBT_VEBT)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc V3))) (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.vEBT_VEBT_high Xa) _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 Y4) (and (=> _let_5 (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_V5719532721284313246member (tptp.nth_VEBT_VEBT TreeList2 _let_4)) (tptp.aa_nat_nat (tptp.vEBT_VEBT_low Xa) _let_3)))) _let_5)) (not (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel (tptp.produc738532404422230701BT_nat _let_2 Xa))))))))))))))))) (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.aTP_Lamm_at Z)))))))) (forall ((T tptp.vEBT_VEBT)) (= (tptp.vEBT_set_vebt T) (tptp.collect_nat (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions T)))) (forall ((R2 tptp.nat) (N tptp.nat)) (= (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aTP_Lamm_au R2)) (tptp.set_ord_atMost_nat N)) (tptp.aa_nat_nat (tptp.binomial (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat R2) N))) N))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aTP_Lamm_av M)) (tptp.set_ord_atMost_nat N)) (tptp.aa_nat_nat (tptp.binomial (tptp.aa_nat_nat tptp.suc N)) (tptp.aa_nat_nat tptp.suc 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.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_nat_fun_nat_nat (tptp.aTP_Lamm_aw M) N)) (tptp.set_ord_atMost_nat M)) (tptp.aa_nat_nat (tptp.binomial (tptp.aa_nat_nat tptp.suc N)) M)))) (forall ((M tptp.nat) (N tptp.nat) (R2 tptp.nat)) (= (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_nat_fun_nat_nat (tptp.aa_nat3783148529270815480at_nat (tptp.aTP_Lamm_ax M) N) R2)) (tptp.set_ord_atMost_nat R2)) (tptp.aa_nat_nat (tptp.binomial (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) N)) R2))) (forall ((N tptp.nat)) (= (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.binomial N)) (tptp.set_ord_atMost_nat N)) (tptp.aa_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) (B tptp.nat) (N tptp.nat)) (= (tptp.aa_nat_nat (tptp.power_power_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) B)) N) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_nat_fun_nat_nat (tptp.aa_nat3783148529270815480at_nat (tptp.aTP_Lamm_ay A) B) N)) (tptp.set_ord_atMost_nat N)))) (forall ((M tptp.nat) (A tptp.fun_nat_nat) (N tptp.nat) (B 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 B 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_az 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_az B) 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_bb A) B) 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.aTP_Lamm_bc N)) (tptp.set_ord_atMost_nat N)) (tptp.aa_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 ((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.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.power_power_nat _let_1) _let_2))))) (forall ((N tptp.nat)) (= (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aTP_Lamm_bd 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.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)) (let ((_let_1 (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_be N)))))) (forall ((P tptp.fun_nat_bool) (X tptp.nat) (M10 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool P X)) (=> (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool P X3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X3) M10)))) (not (forall ((M4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool P M4)) (not (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) M4))))))))))) (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_bf (tptp.collect_complex (tptp.aa_com1553036987509291606x_bool (tptp.aTP_Lamm_bg 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_bf (tptp.collect_complex (tptp.aTP_Lamm_ak N))) tptp.zero_zero_complex))) (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 ((T3 tptp.real)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) T3)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real T3) 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.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real tptp.aTP_Lamm_bh 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 T3) (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)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (exists ((T3 tptp.real)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) T3)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real T3) X)) (= (tptp.aa_real_real tptp.cos_real X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real tptp.aTP_Lamm_bh 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 T3) (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 ((T3 tptp.real)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) T3)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real T3) X)) (= (tptp.aa_real_real tptp.sin_real X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real tptp.aTP_Lamm_bi 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 T3) (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 ((T3 tptp.real)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) T3)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real T3) X)) (= (tptp.aa_real_real tptp.sin_real X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real tptp.aTP_Lamm_bi 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 T3) (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)) (= (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real tptp.aTP_Lamm_bj) (tptp.set_ord_lessThan_nat (tptp.aa_nat_nat tptp.suc N))) tptp.one_one_real)) (forall ((K tptp.nat)) (= (tptp.set_ord_lessThan_nat (tptp.aa_nat_nat tptp.suc K)) (tptp.set_ord_atMost_nat K))) (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 ((B7 tptp.real)) (= (tptp.aa_real_real F H) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aa_fun1839206346889086768t_real (tptp.aTP_Lamm_bk H) J)) (tptp.set_ord_lessThan_nat N))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real B7) (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 ((F tptp.fun_nat_real) (G tptp.fun_nat_real) (N tptp.nat)) (let ((_let_1 (tptp.set_ord_lessThan_nat N))) (= (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aa_fun1839206346889086768t_real (tptp.aTP_Lamm_bl 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.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aTP_Lamm_bm F)) _let_1)) (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aTP_Lamm_bn G)) _let_1))))) (forall ((X tptp.real) (N tptp.nat)) (exists ((T3 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 T3)) (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.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real tptp.aTP_Lamm_bo 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 T3)) (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_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.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real tptp.aTP_Lamm_bi 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 ((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.aa_set_nat_real (tptp.groups6591440286371151544t_real F) (tptp.set_ord_lessThan_nat K))) (tptp.suminf_real F)))))) (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 ((T3 tptp.real)) (let ((_let_1 (tptp.aa_real_real tptp.abs_abs_real T3))) (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.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real tptp.aTP_Lamm_bo 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 T3)) (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 ((T3 tptp.real)) (= (tptp.aa_real_real tptp.sin_real X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real tptp.aTP_Lamm_bi 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 T3) (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 ((T3 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 T3)) (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.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real tptp.aTP_Lamm_bi 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 T3) (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 ((T3 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 T3)) (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.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real tptp.aTP_Lamm_bh 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 T3) (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)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (tptp.bij_betw_nat_complex (tptp.aTP_Lamm_bp N) (tptp.set_ord_lessThan_nat N) (tptp.collect_complex (tptp.aTP_Lamm_ak N))))) (forall ((N tptp.nat) (P tptp.fun_nat_bool)) (= (forall ((M5 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M5) N)) (tptp.pp (tptp.aa_nat_bool P M5)))) (forall ((X5 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X5) (tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat N))) (tptp.pp (tptp.aa_nat_bool P X5)))))) (forall ((N tptp.nat) (P tptp.fun_nat_bool)) (= (exists ((M5 tptp.nat)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M5) N)) (tptp.pp (tptp.aa_nat_bool P M5)))) (exists ((X5 tptp.nat)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X5) (tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat N))) (tptp.pp (tptp.aa_nat_bool P X5)))))) (forall ((N tptp.nat)) (= (tptp.set_ord_atMost_nat N) (tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat N))) (forall ((N tptp.nat)) (= (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat tptp.aTP_Lamm_bq) (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_br 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_bq) (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 ((D3 tptp.int) (B3 tptp.set_int) (P tptp.fun_int_bool) (Q tptp.fun_int_bool)) (=> (forall ((X3 tptp.int)) (=> (forall ((Xa2 tptp.int)) (=> (tptp.member_int Xa2 (tptp.set_or1266510415728281911st_int tptp.one_one_int D3)) (forall ((Xb tptp.int)) (=> (tptp.member_int Xb B3) (not (= X3 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int Xb) Xa2))))))) (=> (tptp.pp (tptp.aa_int_bool P X3)) (tptp.pp (tptp.aa_int_bool P (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int X3) D3)))))) (=> (forall ((X3 tptp.int)) (=> (forall ((Xa2 tptp.int)) (=> (tptp.member_int Xa2 (tptp.set_or1266510415728281911st_int tptp.one_one_int D3)) (forall ((Xb tptp.int)) (=> (tptp.member_int Xb B3) (not (= X3 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int Xb) Xa2))))))) (=> (tptp.pp (tptp.aa_int_bool Q X3)) (tptp.pp (tptp.aa_int_bool Q (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int X3) D3)))))) (forall ((X4 tptp.int)) (let ((_let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int X4) D3))) (=> (forall ((Xa3 tptp.int)) (=> (tptp.member_int Xa3 (tptp.set_or1266510415728281911st_int tptp.one_one_int D3)) (forall ((Xb2 tptp.int)) (=> (tptp.member_int Xb2 B3) (not (= X4 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int Xb2) Xa3))))))) (=> (and (tptp.pp (tptp.aa_int_bool P X4)) (tptp.pp (tptp.aa_int_bool Q X4))) (and (tptp.pp (tptp.aa_int_bool P _let_1)) (tptp.pp (tptp.aa_int_bool Q _let_1)))))))))) (forall ((D3 tptp.int) (B3 tptp.set_int) (P tptp.fun_int_bool) (Q tptp.fun_int_bool)) (=> (forall ((X3 tptp.int)) (=> (forall ((Xa2 tptp.int)) (=> (tptp.member_int Xa2 (tptp.set_or1266510415728281911st_int tptp.one_one_int D3)) (forall ((Xb tptp.int)) (=> (tptp.member_int Xb B3) (not (= X3 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int Xb) Xa2))))))) (=> (tptp.pp (tptp.aa_int_bool P X3)) (tptp.pp (tptp.aa_int_bool P (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int X3) D3)))))) (=> (forall ((X3 tptp.int)) (=> (forall ((Xa2 tptp.int)) (=> (tptp.member_int Xa2 (tptp.set_or1266510415728281911st_int tptp.one_one_int D3)) (forall ((Xb tptp.int)) (=> (tptp.member_int Xb B3) (not (= X3 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int Xb) Xa2))))))) (=> (tptp.pp (tptp.aa_int_bool Q X3)) (tptp.pp (tptp.aa_int_bool Q (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int X3) D3)))))) (forall ((X4 tptp.int)) (let ((_let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int X4) D3))) (=> (forall ((Xa3 tptp.int)) (=> (tptp.member_int Xa3 (tptp.set_or1266510415728281911st_int tptp.one_one_int D3)) (forall ((Xb2 tptp.int)) (=> (tptp.member_int Xb2 B3) (not (= X4 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int Xb2) Xa3))))))) (=> (or (tptp.pp (tptp.aa_int_bool P X4)) (tptp.pp (tptp.aa_int_bool Q X4))) (or (tptp.pp (tptp.aa_int_bool P _let_1)) (tptp.pp (tptp.aa_int_bool Q _let_1)))))))))) (forall ((D3 tptp.int) (A2 tptp.set_int) (P tptp.fun_int_bool) (Q tptp.fun_int_bool)) (=> (forall ((X3 tptp.int)) (=> (forall ((Xa2 tptp.int)) (=> (tptp.member_int Xa2 (tptp.set_or1266510415728281911st_int tptp.one_one_int D3)) (forall ((Xb tptp.int)) (=> (tptp.member_int Xb A2) (not (= X3 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int Xb) Xa2))))))) (=> (tptp.pp (tptp.aa_int_bool P X3)) (tptp.pp (tptp.aa_int_bool P (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int X3) D3)))))) (=> (forall ((X3 tptp.int)) (=> (forall ((Xa2 tptp.int)) (=> (tptp.member_int Xa2 (tptp.set_or1266510415728281911st_int tptp.one_one_int D3)) (forall ((Xb tptp.int)) (=> (tptp.member_int Xb A2) (not (= X3 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int Xb) Xa2))))))) (=> (tptp.pp (tptp.aa_int_bool Q X3)) (tptp.pp (tptp.aa_int_bool Q (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int X3) D3)))))) (forall ((X4 tptp.int)) (let ((_let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int X4) D3))) (=> (forall ((Xa3 tptp.int)) (=> (tptp.member_int Xa3 (tptp.set_or1266510415728281911st_int tptp.one_one_int D3)) (forall ((Xb2 tptp.int)) (=> (tptp.member_int Xb2 A2) (not (= X4 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int Xb2) Xa3))))))) (=> (and (tptp.pp (tptp.aa_int_bool P X4)) (tptp.pp (tptp.aa_int_bool Q X4))) (and (tptp.pp (tptp.aa_int_bool P _let_1)) (tptp.pp (tptp.aa_int_bool Q _let_1)))))))))) (forall ((D3 tptp.int) (A2 tptp.set_int) (P tptp.fun_int_bool) (Q tptp.fun_int_bool)) (=> (forall ((X3 tptp.int)) (=> (forall ((Xa2 tptp.int)) (=> (tptp.member_int Xa2 (tptp.set_or1266510415728281911st_int tptp.one_one_int D3)) (forall ((Xb tptp.int)) (=> (tptp.member_int Xb A2) (not (= X3 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int Xb) Xa2))))))) (=> (tptp.pp (tptp.aa_int_bool P X3)) (tptp.pp (tptp.aa_int_bool P (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int X3) D3)))))) (=> (forall ((X3 tptp.int)) (=> (forall ((Xa2 tptp.int)) (=> (tptp.member_int Xa2 (tptp.set_or1266510415728281911st_int tptp.one_one_int D3)) (forall ((Xb tptp.int)) (=> (tptp.member_int Xb A2) (not (= X3 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int Xb) Xa2))))))) (=> (tptp.pp (tptp.aa_int_bool Q X3)) (tptp.pp (tptp.aa_int_bool Q (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int X3) D3)))))) (forall ((X4 tptp.int)) (let ((_let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int X4) D3))) (=> (forall ((Xa3 tptp.int)) (=> (tptp.member_int Xa3 (tptp.set_or1266510415728281911st_int tptp.one_one_int D3)) (forall ((Xb2 tptp.int)) (=> (tptp.member_int Xb2 A2) (not (= X4 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int Xb2) Xa3))))))) (=> (or (tptp.pp (tptp.aa_int_bool P X4)) (tptp.pp (tptp.aa_int_bool Q X4))) (or (tptp.pp (tptp.aa_int_bool P _let_1)) (tptp.pp (tptp.aa_int_bool Q _let_1)))))))))) (forall ((D tptp.int) (D3 tptp.int) (B3 tptp.set_int) (T tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int D) D3)) (forall ((X4 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int D))) (=> (forall ((Xa3 tptp.int)) (=> (tptp.member_int Xa3 (tptp.set_or1266510415728281911st_int tptp.one_one_int D3)) (forall ((Xb2 tptp.int)) (=> (tptp.member_int Xb2 B3) (not (= X4 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int Xb2) Xa3))))))) (=> (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int X4) 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 X4) D3)) T))))))))) (forall ((D tptp.int) (D3 tptp.int) (B3 tptp.set_int) (T tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int D) D3)) (forall ((X4 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int D))) (=> (forall ((Xa3 tptp.int)) (=> (tptp.member_int Xa3 (tptp.set_or1266510415728281911st_int tptp.one_one_int D3)) (forall ((Xb2 tptp.int)) (=> (tptp.member_int Xb2 B3) (not (= X4 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int Xb2) Xa3))))))) (=> (not (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int X4) 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 X4) D3)) T)))))))))) (forall ((D tptp.int) (D3 tptp.int) (A2 tptp.set_int) (T tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int D) D3)) (forall ((X4 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.plus_plus_int X4))) (let ((_let_2 (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int D))) (=> (forall ((Xa3 tptp.int)) (=> (tptp.member_int Xa3 (tptp.set_or1266510415728281911st_int tptp.one_one_int D3)) (forall ((Xb2 tptp.int)) (=> (tptp.member_int Xb2 A2) (not (= X4 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int Xb2) Xa3))))))) (=> (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 D3)) T)))))))))) (forall ((D tptp.int) (D3 tptp.int) (A2 tptp.set_int) (T tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int D) D3)) (forall ((X4 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.plus_plus_int X4))) (let ((_let_2 (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int D))) (=> (forall ((Xa3 tptp.int)) (=> (tptp.member_int Xa3 (tptp.set_or1266510415728281911st_int tptp.one_one_int D3)) (forall ((Xb2 tptp.int)) (=> (tptp.member_int Xb2 A2) (not (= X4 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int Xb2) Xa3))))))) (=> (not (tptp.pp (tptp.aa_int_bool _let_2 (tptp.aa_int_int _let_1 T)))) (not (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 D3)) T))))))))))) (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 ((X3 tptp.int) (K2 tptp.int)) (= (tptp.pp (tptp.aa_int_bool P X3)) (tptp.pp (tptp.aa_int_bool P (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int X3) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int K2) D)))))) (= (exists ((X_12 tptp.int)) (tptp.pp (tptp.aa_int_bool P X_12))) (exists ((X5 tptp.int)) (and (tptp.member_int X5 (tptp.set_or1266510415728281911st_int tptp.one_one_int D)) (tptp.pp (tptp.aa_int_bool P X5)))))))) (forall ((D3 tptp.int) (T tptp.int) (B3 tptp.set_int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) D3)) (=> (tptp.member_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int T) tptp.one_one_int) B3) (forall ((X4 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (tptp.member_int Xa3 (tptp.set_or1266510415728281911st_int tptp.one_one_int D3)) (forall ((Xb2 tptp.int)) (=> (tptp.member_int Xb2 B3) (not (= X4 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int Xb2) Xa3))))))) (=> (= X4 T) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int X4) D3) T))))))) (forall ((D3 tptp.int) (T tptp.int) (B3 tptp.set_int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) D3)) (=> (tptp.member_int T B3) (forall ((X4 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (tptp.member_int Xa3 (tptp.set_or1266510415728281911st_int tptp.one_one_int D3)) (forall ((Xb2 tptp.int)) (=> (tptp.member_int Xb2 B3) (not (= X4 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int Xb2) Xa3))))))) (=> (not (= X4 T)) (not (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int X4) D3) T)))))))) (forall ((D3 tptp.int) (B3 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) D3)) (forall ((X4 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (tptp.member_int Xa3 (tptp.set_or1266510415728281911st_int tptp.one_one_int D3)) (forall ((Xb2 tptp.int)) (=> (tptp.member_int Xb2 B3) (not (= X4 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int Xb2) Xa3))))))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X4) 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 X4) D3)) T))))))) (forall ((D3 tptp.int) (T tptp.int) (B3 tptp.set_int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) D3)) (=> (tptp.member_int T B3) (forall ((X4 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_int T))) (=> (forall ((Xa3 tptp.int)) (=> (tptp.member_int Xa3 (tptp.set_or1266510415728281911st_int tptp.one_one_int D3)) (forall ((Xb2 tptp.int)) (=> (tptp.member_int Xb2 B3) (not (= X4 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int Xb2) Xa3))))))) (=> (tptp.pp (tptp.aa_int_bool _let_1 X4)) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int X4) D3)))))))))) (forall ((D3 tptp.int) (T tptp.int) (A2 tptp.set_int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) D3)) (=> (tptp.member_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int T) tptp.one_one_int) A2) (forall ((X4 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (tptp.member_int Xa3 (tptp.set_or1266510415728281911st_int tptp.one_one_int D3)) (forall ((Xb2 tptp.int)) (=> (tptp.member_int Xb2 A2) (not (= X4 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int Xb2) Xa3))))))) (=> (= X4 T) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int X4) D3) T))))))) (forall ((D3 tptp.int) (T tptp.int) (A2 tptp.set_int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) D3)) (=> (tptp.member_int T A2) (forall ((X4 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (tptp.member_int Xa3 (tptp.set_or1266510415728281911st_int tptp.one_one_int D3)) (forall ((Xb2 tptp.int)) (=> (tptp.member_int Xb2 A2) (not (= X4 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int Xb2) Xa3))))))) (=> (not (= X4 T)) (not (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int X4) D3) T)))))))) (forall ((D3 tptp.int) (T tptp.int) (A2 tptp.set_int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) D3)) (=> (tptp.member_int T A2) (forall ((X4 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (tptp.member_int Xa3 (tptp.set_or1266510415728281911st_int tptp.one_one_int D3)) (forall ((Xb2 tptp.int)) (=> (tptp.member_int Xb2 A2) (not (= X4 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int Xb2) Xa3))))))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X4) 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 X4) D3)) T)))))))) (forall ((D3 tptp.int) (A2 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) D3)) (forall ((X4 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_int T))) (=> (forall ((Xa3 tptp.int)) (=> (tptp.member_int Xa3 (tptp.set_or1266510415728281911st_int tptp.one_one_int D3)) (forall ((Xb2 tptp.int)) (=> (tptp.member_int Xb2 A2) (not (= X4 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int Xb2) Xa3))))))) (=> (tptp.pp (tptp.aa_int_bool _let_1 X4)) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int X4) D3))))))))) (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_bq (tptp.set_or1269000886237332187st_nat (tptp.aa_nat_nat tptp.suc N) M)))))) (forall ((D3 tptp.int) (B3 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) D3)) (forall ((X4 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (tptp.member_int Xa3 (tptp.set_or1266510415728281911st_int tptp.one_one_int D3)) (forall ((Xb2 tptp.int)) (=> (tptp.member_int Xb2 B3) (not (= X4 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int Xb2) Xa3))))))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X4) 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 X4) D3)) T))))))) (forall ((D3 tptp.int) (T tptp.int) (B3 tptp.set_int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) D3)) (=> (tptp.member_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int T) tptp.one_one_int) B3) (forall ((X4 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int T))) (=> (forall ((Xa3 tptp.int)) (=> (tptp.member_int Xa3 (tptp.set_or1266510415728281911st_int tptp.one_one_int D3)) (forall ((Xb2 tptp.int)) (=> (tptp.member_int Xb2 B3) (not (= X4 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int Xb2) Xa3))))))) (=> (tptp.pp (tptp.aa_int_bool _let_1 X4)) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int X4) D3)))))))))) (forall ((D3 tptp.int) (T tptp.int) (A2 tptp.set_int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) D3)) (=> (tptp.member_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int T) tptp.one_one_int) A2) (forall ((X4 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (tptp.member_int Xa3 (tptp.set_or1266510415728281911st_int tptp.one_one_int D3)) (forall ((Xb2 tptp.int)) (=> (tptp.member_int Xb2 A2) (not (= X4 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int Xb2) Xa3))))))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X4) 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 X4) D3)) T)))))))) (forall ((D3 tptp.int) (A2 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) D3)) (forall ((X4 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int T))) (=> (forall ((Xa3 tptp.int)) (=> (tptp.member_int Xa3 (tptp.set_or1266510415728281911st_int tptp.one_one_int D3)) (forall ((Xb2 tptp.int)) (=> (tptp.member_int Xb2 A2) (not (= X4 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int Xb2) Xa3))))))) (=> (tptp.pp (tptp.aa_int_bool _let_1 X4)) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int X4) D3))))))))) (forall ((D3 tptp.int) (P tptp.fun_int_bool) (P2 tptp.fun_int_bool) (A2 tptp.set_int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) D3)) (=> (exists ((Z3 tptp.int)) (forall ((X3 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Z3) X3)) (= (tptp.pp (tptp.aa_int_bool P X3)) (tptp.pp (tptp.aa_int_bool P2 X3)))))) (=> (forall ((X3 tptp.int)) (=> (forall ((Xa2 tptp.int)) (=> (tptp.member_int Xa2 (tptp.set_or1266510415728281911st_int tptp.one_one_int D3)) (forall ((Xb tptp.int)) (=> (tptp.member_int Xb A2) (not (= X3 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int Xb) Xa2))))))) (=> (tptp.pp (tptp.aa_int_bool P X3)) (tptp.pp (tptp.aa_int_bool P (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int X3) D3)))))) (=> (forall ((X3 tptp.int) (K2 tptp.int)) (= (tptp.pp (tptp.aa_int_bool P2 X3)) (tptp.pp (tptp.aa_int_bool P2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int X3) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int K2) D3)))))) (= (exists ((X_12 tptp.int)) (tptp.pp (tptp.aa_int_bool P X_12))) (or (exists ((X5 tptp.int)) (and (tptp.member_int X5 (tptp.set_or1266510415728281911st_int tptp.one_one_int D3)) (tptp.pp (tptp.aa_int_bool P2 X5)))) (exists ((X5 tptp.int)) (and (tptp.member_int X5 (tptp.set_or1266510415728281911st_int tptp.one_one_int D3)) (exists ((Xa4 tptp.int)) (and (tptp.member_int Xa4 A2) (tptp.pp (tptp.aa_int_bool P (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int Xa4) X5)))))))))))))) (forall ((D3 tptp.int) (P tptp.fun_int_bool) (P2 tptp.fun_int_bool) (B3 tptp.set_int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) D3)) (=> (exists ((Z3 tptp.int)) (forall ((X3 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X3) Z3)) (= (tptp.pp (tptp.aa_int_bool P X3)) (tptp.pp (tptp.aa_int_bool P2 X3)))))) (=> (forall ((X3 tptp.int)) (=> (forall ((Xa2 tptp.int)) (=> (tptp.member_int Xa2 (tptp.set_or1266510415728281911st_int tptp.one_one_int D3)) (forall ((Xb tptp.int)) (=> (tptp.member_int Xb B3) (not (= X3 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int Xb) Xa2))))))) (=> (tptp.pp (tptp.aa_int_bool P X3)) (tptp.pp (tptp.aa_int_bool P (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int X3) D3)))))) (=> (forall ((X3 tptp.int) (K2 tptp.int)) (= (tptp.pp (tptp.aa_int_bool P2 X3)) (tptp.pp (tptp.aa_int_bool P2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int X3) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int K2) D3)))))) (= (exists ((X_12 tptp.int)) (tptp.pp (tptp.aa_int_bool P X_12))) (or (exists ((X5 tptp.int)) (and (tptp.member_int X5 (tptp.set_or1266510415728281911st_int tptp.one_one_int D3)) (tptp.pp (tptp.aa_int_bool P2 X5)))) (exists ((X5 tptp.int)) (and (tptp.member_int X5 (tptp.set_or1266510415728281911st_int tptp.one_one_int D3)) (exists ((Xa4 tptp.int)) (and (tptp.member_int Xa4 B3) (tptp.pp (tptp.aa_int_bool P (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int Xa4) X5)))))))))))))) (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_bq (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 ((L tptp.num) (Qr tptp.product_prod_nat_nat)) (= (tptp.unique5026877609467782581ep_nat L Qr) (tptp.aa_Pro262675715343573244at_nat (tptp.produc2626176000494625587at_nat (tptp.aTP_Lamm_bs L)) Qr))) (forall ((L tptp.num) (Qr tptp.product_prod_int_int)) (= (tptp.unique5024387138958732305ep_int L Qr) (tptp.produc4245557441103728435nt_int (tptp.aTP_Lamm_bt L) Qr))) (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_bu (tptp.set_or1266510415728281911st_int M N)) (tptp.aa_int_int (tptp.aa_int_fun_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 ((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_bv) (tptp.divmod_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) N) N)))))))) (forall ((X tptp.nat) (Y4 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 (= Y4 (tptp.vEBT_Leaf tptp.fFalse tptp.fFalse)))) (=> (= (tptp.vEBT_vebt_buildup X) Y4) (=> (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 ((Va tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat tptp.suc Va)))) (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.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 (= Y4 (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) (= Y4 (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 ((Y4 tptp.real)) (= (tptp.aa_real_real tptp.arctan Y4) (tptp.the_real (tptp.aa_rea7809428808904475482l_bool tptp.aTP_Lamm_bw Y4)))) (forall ((I tptp.nat) (J tptp.nat)) (= (tptp.groups705719431365010083at_int tptp.semiri1314217659103216013at_int (tptp.set_or1269000886237332187st_nat I J)) (tptp.groups1705073143266064639nt_int tptp.aTP_Lamm_bu (tptp.set_or1266510415728281911st_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int I) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int J))))) (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_bu (tptp.set_or1266510415728281911st_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int I) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int _let_1)))))) (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_bx)))) (forall ((Y4 tptp.real)) (= (tptp.aa_real_real tptp.arccos Y4) (tptp.the_real (tptp.aa_rea7809428808904475482l_bool tptp.aTP_Lamm_by Y4)))) (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.modulo_modulo_nat M) N)))) (= _let_42 _let_53) (= tptp.pi (tptp.aa_real_real _let_54 _let_53)) (forall ((Y4 tptp.real)) (= (tptp.aa_real_real tptp.arcsin Y4) (tptp.the_real (tptp.aa_rea7809428808904475482l_bool tptp.aTP_Lamm_ca Y4)))) (forall ((X tptp.nat) (Y4 tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat))) (let ((_let_2 (tptp.accp_nat tptp.vEBT_V1247956027447740395_p_rel))) (let ((_let_3 (= Y4 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 tptp.one))))) (=> (= (tptp.aa_nat_nat tptp.vEBT_V8346862874174094_d_u_p X) Y4) (=> (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 ((Va tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat tptp.suc Va)))) (let ((_let_2 (tptp.aa_num_num tptp.bit0 tptp.one))) (let ((_let_3 (tptp.aa_num_nat tptp.numeral_numeral_nat _let_2))) (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.vEBT_V8346862874174094_d_u_p _let_4))) (let ((_let_6 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat _let_5) tptp.one_one_nat))) (let ((_let_7 (tptp.aa_nat_nat tptp.suc _let_4))) (let ((_let_8 (tptp.power_power_nat _let_3))) (let ((_let_9 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat _let_3) _let_1)))) (=> (= X _let_1) (=> (and (=> _let_9 (= Y4 (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.plus_plus_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.aa_num_num tptp.bit0 _let_2)))) _let_5)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat _let_8 _let_4)) _let_6))))) (=> (not _let_9) (= Y4 (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_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit1 _let_2)))) (tptp.aa_nat_nat tptp.vEBT_V8346862874174094_d_u_p _let_7))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat _let_8 _let_7)) _let_6))))) (not (tptp.pp (tptp.aa_nat_bool (tptp.accp_nat tptp.vEBT_V1247956027447740395_p_rel) _let_1)))))))))))))))))))))))) (forall ((X tptp.nat) (Y4 tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat))) (let ((_let_2 (tptp.accp_nat tptp.vEBT_V5144397997797733112_d_rel))) (let ((_let_3 (= Y4 (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.vEBT_V8646137997579335489_i_l_d X) Y4) (=> (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 ((Va tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat tptp.suc Va)))) (let ((_let_2 (tptp.aa_num_num tptp.bit0 tptp.one))) (let ((_let_3 (tptp.aa_num_nat tptp.numeral_numeral_nat _let_2))) (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.vEBT_V8646137997579335489_i_l_d _let_4))) (let ((_let_6 (tptp.aa_nat_nat tptp.suc _let_4))) (let ((_let_7 (tptp.power_power_nat _let_3))) (let ((_let_8 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat _let_3) _let_1)))) (=> (= X _let_1) (=> (and (=> _let_8 (= Y4 (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.plus_plus_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.aa_num_num tptp.bit1 _let_2)))) _let_5)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat _let_7 _let_4)) _let_5))))) (=> (not _let_8) (= Y4 (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_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit1 tptp.one))))) (tptp.aa_nat_nat tptp.vEBT_V8646137997579335489_i_l_d _let_6))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat _let_7 _let_6)) _let_5))))) (not (tptp.pp (tptp.aa_nat_bool (tptp.accp_nat tptp.vEBT_V5144397997797733112_d_rel) _let_1))))))))))))))))))))))) (= tptp.nat_set_encode (tptp.groups3542108847815614940at_nat _let_52)) (forall ((N tptp.nat)) (= (tptp.aa_set_nat_nat tptp.nat_set_encode (tptp.nat_set_decode N)) 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 ((M tptp.nat) (N tptp.nat)) (= (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat tptp.aTP_Lamm_bq) (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 ((K tptp.nat)) (let ((_let_1 (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) (P tptp.fun_nat_bool)) (= (exists ((M5 tptp.nat)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M5) N)) (tptp.pp (tptp.aa_nat_bool P M5)))) (exists ((X5 tptp.nat)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X5) (tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat N))) (tptp.pp (tptp.aa_nat_bool P X5)))))) (forall ((N tptp.nat) (P tptp.fun_nat_bool)) (= (forall ((M5 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M5) N)) (tptp.pp (tptp.aa_nat_bool P M5)))) (forall ((X5 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X5) (tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat N))) (tptp.pp (tptp.aa_nat_bool P X5)))))) (forall ((L tptp.nat) (U tptp.nat)) (= (tptp.set_or4665077453230672383an_nat L (tptp.aa_nat_nat tptp.suc U)) (tptp.set_or1269000886237332187st_nat L U))) (forall ((N tptp.nat)) (= (tptp.set_ord_lessThan_nat N) (tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat N))) (forall ((N tptp.nat)) (= (tptp.groups708209901874060359at_nat tptp.suc (tptp.set_or4665077453230672383an_nat (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat) N)) (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat N))) (forall ((N tptp.nat)) (= (tptp.groups708209901874060359at_nat tptp.suc (tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat N)) (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat N))) (forall ((N tptp.nat) (A tptp.fun_nat_nat) (B 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 B J2)) (tptp.aa_nat_nat B 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_cb A) B)) _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 B) _let_1)))))))) (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 ((X21 tptp.bool) (X222 tptp.bool)) (= (tptp.aa_VEBT_VEBT_nat tptp.vEBT_size_VEBT (tptp.vEBT_Leaf X21 X222)) tptp.zero_zero_nat)) (= tptp.code_T6385005292777649522of_nat tptp.semiri1314217659103216013at_int) (forall ((X tptp.nat) (Xa tptp.nat) (Y4 tptp.product_prod_nat_nat)) (let ((_let_1 (tptp.accp_P4275260045618599050at_nat tptp.nat_pr5047031295181774490ux_rel (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat X) Xa)))) (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 Xa) X)))) (=> (= (tptp.nat_prod_decode_aux X Xa) Y4) (=> _let_1 (not (=> (and (=> _let_3 (= Y4 (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Xa) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat X) Xa)))) (=> (not _let_3) (= Y4 (tptp.nat_prod_decode_aux _let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Xa) _let_2))))) (not _let_1))))))))) (forall ((X tptp.num) (Xa tptp.num) (Y4 tptp.num)) (let ((_let_1 (= X tptp.one))) (=> (= (tptp.aa_num_num (tptp.bit_or_not_num_neg X) Xa) Y4) (=> (tptp.accp_P3113834385874906142um_num tptp.bit_or3848514188828904588eg_rel (tptp.product_Pair_num_num X Xa)) (=> (=> _let_1 (=> (= Xa tptp.one) (=> (= Y4 tptp.one) (not (tptp.accp_P3113834385874906142um_num tptp.bit_or3848514188828904588eg_rel (tptp.product_Pair_num_num tptp.one tptp.one)))))) (=> (=> _let_1 (forall ((M4 tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 M4))) (=> (= Xa _let_1) (=> (= Y4 (tptp.aa_num_num tptp.bit1 M4)) (not (tptp.accp_P3113834385874906142um_num tptp.bit_or3848514188828904588eg_rel (tptp.product_Pair_num_num tptp.one _let_1)))))))) (=> (=> _let_1 (forall ((M4 tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit1 M4))) (=> (= Xa _let_1) (=> (= Y4 _let_1) (not (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) (=> (= Xa tptp.one) (=> (= Y4 (tptp.aa_num_num tptp.bit0 tptp.one)) (not (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 ((M4 tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 M4))) (=> (= Xa _let_1) (=> (= Y4 (tptp.aa_num_num tptp.bitM (tptp.aa_num_num (tptp.bit_or_not_num_neg N2) M4))) (not (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 ((M4 tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit1 M4))) (=> (= Xa _let_1) (=> (= Y4 (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num (tptp.bit_or_not_num_neg N2) M4))) (not (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) (=> (= Xa tptp.one) (=> (= Y4 tptp.one) (not (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 ((M4 tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 M4))) (=> (= Xa _let_1) (=> (= Y4 (tptp.aa_num_num tptp.bitM (tptp.aa_num_num (tptp.bit_or_not_num_neg N2) M4))) (not (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 ((M4 tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit1 M4))) (=> (= Xa _let_1) (=> (= Y4 (tptp.aa_num_num tptp.bitM (tptp.aa_num_num (tptp.bit_or_not_num_neg N2) M4))) (not (tptp.accp_P3113834385874906142um_num tptp.bit_or3848514188828904588eg_rel (tptp.product_Pair_num_num (tptp.aa_num_num tptp.bit1 N2) _let_1)))))))))))))))))))))) (forall ((D tptp.int)) (= (tptp.int_ge_less_than D) (tptp.collec213857154873943460nt_int (tptp.produc8560705615207772305t_bool (tptp.aTP_Lamm_cc D))))) (forall ((D tptp.int)) (= (tptp.int_ge_less_than2 D) (tptp.collec213857154873943460nt_int (tptp.produc8560705615207772305t_bool (tptp.aTP_Lamm_cd D))))) (forall ((A0 tptp.int) (A1 tptp.int) (P tptp.fun_int_fun_int_bool)) (=> (tptp.accp_P1096762738010456898nt_int tptp.upto_rel (tptp.product_Pair_int_int A0 A1)) (=> (forall ((I3 tptp.int) (J2 tptp.int)) (=> (tptp.accp_P1096762738010456898nt_int tptp.upto_rel (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.code_Target_positive tptp.numeral_numeral_int) (forall ((L tptp.num) (Qr tptp.produc8923325533196201883nteger)) (= (tptp.unique4921790084139445826nteger L Qr) (tptp.produc6916734918728496179nteger (tptp.aTP_Lamm_ce L) Qr))) (tptp.pp (tptp.aa_Code_integer_bool _let_51 tptp.zero_z3403309356797280102nteger)) (forall ((K tptp.code_integer)) (= (tptp.plus_p5714425477246183910nteger K tptp.zero_z3403309356797280102nteger) K)) (forall ((L tptp.code_integer)) (= (tptp.plus_p5714425477246183910nteger tptp.zero_z3403309356797280102nteger L) L)) (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 ((L tptp.code_integer)) (= (tptp.minus_8373710615458151222nteger tptp.zero_z3403309356797280102nteger L) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger L))) (forall ((K tptp.code_integer)) (= (tptp.minus_8373710615458151222nteger K tptp.zero_z3403309356797280102nteger) K)) (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 ((Nat tptp.nat)) (= (not (= Nat tptp.zero_zero_nat)) (tptp.pp (tptp.aa_nat_bool (tptp.case_nat_bool tptp.fFalse tptp.aTP_Lamm_cf) 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_cg) Nat)))) (= tptp.zero_zero_nat tptp.zero_zero_nat) (= tptp.zero_zero_int 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 (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.aTP_Lamm_ch 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.aTP_Lamm_ci 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_bq) (tptp.aa_nat_nat _let_1 N))))) (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.numera6620942414471956472nteger _let_1)) (tptp.code_integer_of_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int K) _let_2))))) (let ((_let_4 (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.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.modulo_modulo_int K _let_2)) tptp.zero_zero_int) _let_3 (tptp.plus_p5714425477246183910nteger _let_3 tptp.one_one_Code_integer)))))))))))))) (forall ((Xa tptp.nat) (X tptp.int)) (= (tptp.bit_se1345352211410354436nteger Xa (tptp.code_integer_of_int X)) (tptp.code_integer_of_int (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_se2159334234014336723it_int Xa) X)))) (= tptp.zero_z3403309356797280102nteger (tptp.code_integer_of_int tptp.zero_zero_int)) (forall ((Xa tptp.nat) (X tptp.int)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_nat6383147911832638789nteger tptp.bit_se8260200283734997820nteger Xa) (tptp.code_integer_of_int X)) (tptp.code_integer_of_int (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_se4203085406695923979it_int Xa) X)))) (forall ((Xa tptp.int) (X tptp.int)) (= (tptp.divide6298287555418463151nteger (tptp.code_integer_of_int Xa) (tptp.code_integer_of_int X)) (tptp.code_integer_of_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int Xa) X)))) (forall ((Xa tptp.nat) (X tptp.int)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_nat6383147911832638789nteger tptp.bit_se2793503036327961859nteger Xa) (tptp.code_integer_of_int X)) (tptp.code_integer_of_int (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_se7879613467334960850it_int Xa) X)))) _let_50 (not (tptp.pp (tptp.aa_Code_integer_bool _let_49 tptp.zero_z3403309356797280102nteger))) (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 ((Xa tptp.int) (X tptp.int)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.code_integer_of_int Xa)) (tptp.code_integer_of_int X)) (tptp.code_integer_of_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int Xa) X)))) (forall ((Xa tptp.int) (X tptp.int)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.code_integer_of_int Xa)) (tptp.code_integer_of_int X))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Xa) X)))) (forall ((Xa tptp.int) (X tptp.int)) (= (tptp.minus_8373710615458151222nteger (tptp.code_integer_of_int Xa) (tptp.code_integer_of_int X)) (tptp.code_integer_of_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int Xa) X)))) (forall ((X tptp.real)) (= (tptp.aa_real_int tptp.archim6058952711729229775r_real X) (tptp.the_int (tptp.aTP_Lamm_cj X)))) (forall ((X tptp.rat)) (= (tptp.aa_rat_int tptp.archim3151403230148437115or_rat X) (tptp.the_int (tptp.aTP_Lamm_ck X)))) (forall ((N tptp.num)) (let ((_let_1 (tptp.code_integer_of_num N))) (= (tptp.code_integer_of_num (tptp.aa_num_num tptp.bit1 N)) (tptp.plus_p5714425477246183910nteger (tptp.plus_p5714425477246183910nteger _let_1 _let_1) tptp.one_one_Code_integer)))) (forall ((X tptp.rat) (Y4 tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) Y4)) (or (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) Y4)) (= X Y4)))) (forall ((R2 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) R2)) (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 ((T3 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) T3)) (not (= R2 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat S3) T3)))))))))) (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)))))) (= (tptp.code_integer_of_num tptp.one) tptp.one_one_Code_integer) (forall ((N tptp.num)) (let ((_let_1 (tptp.code_integer_of_num N))) (= (tptp.code_integer_of_num (tptp.aa_num_num tptp.bit0 N)) (tptp.plus_p5714425477246183910nteger _let_1 _let_1)))) (= (tptp.code_integer_of_num _let_1) _let_48) (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_bq) Nat))) (forall ((P3 tptp.rat)) (= (tptp.quotient_of (tptp.aa_rat_rat tptp.inverse_inverse_rat P3)) (tptp.produc4245557441103728435nt_int tptp.aTP_Lamm_cl (tptp.quotient_of P3)))) (forall ((Q2 tptp.int) (P3 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Q2) tptp.zero_zero_int)) (= (tptp.normalize (tptp.product_Pair_int_int P3 Q2)) (tptp.normalize (tptp.product_Pair_int_int (tptp.aa_int_int tptp.uminus_uminus_int P3) (tptp.aa_int_int tptp.uminus_uminus_int Q2)))))) (forall ((K tptp.code_integer)) (let ((_let_1 (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.quotient_of (tptp.aa_num_rat tptp.numeral_numeral_rat K)) (tptp.product_Pair_int_int (tptp.aa_num_int tptp.numeral_numeral_int K) tptp.one_one_int))) (forall ((P3 tptp.int)) (= (tptp.normalize (tptp.product_Pair_int_int P3 tptp.zero_zero_int)) (tptp.product_Pair_int_int tptp.zero_zero_int tptp.one_one_int))) (= (tptp.quotient_of tptp.zero_zero_rat) _let_31) (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.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))) (forall ((Q2 tptp.rat) (R2 tptp.rat)) (= (tptp.aa_rat_rat (tptp.minus_minus_rat Q2) R2) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat Q2) (tptp.aa_rat_rat tptp.uminus_uminus_rat R2)))) (forall ((P3 tptp.rat) (Q2 tptp.rat)) (= (tptp.quotient_of (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat P3) Q2)) (tptp.produc4245557441103728435nt_int (tptp.aTP_Lamm_cn Q2) (tptp.quotient_of P3)))) (forall ((P3 tptp.rat) (Q2 tptp.rat)) (= (tptp.quotient_of (tptp.aa_rat_rat (tptp.divide_divide_rat P3) Q2)) (tptp.produc4245557441103728435nt_int (tptp.aTP_Lamm_cp Q2) (tptp.quotient_of P3)))) (forall ((P3 tptp.rat) (Q2 tptp.rat)) (= (tptp.quotient_of (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat P3) Q2)) (tptp.produc4245557441103728435nt_int (tptp.aTP_Lamm_cr Q2) (tptp.quotient_of P3)))) (forall ((P3 tptp.rat) (Q2 tptp.rat)) (= (tptp.quotient_of (tptp.aa_rat_rat (tptp.minus_minus_rat P3) Q2)) (tptp.produc4245557441103728435nt_int (tptp.aTP_Lamm_ct Q2) (tptp.quotient_of P3)))) (forall ((R2 tptp.rat) (P3 tptp.int) (Q2 tptp.int)) (=> (= (tptp.quotient_of R2) (tptp.product_Pair_int_int P3 Q2)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) Q2)))) (forall ((R2 tptp.product_prod_int_int) (P3 tptp.int) (Q2 tptp.int)) (=> (= (tptp.normalize R2) (tptp.product_Pair_int_int P3 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) (S2 tptp.int) (P3 tptp.int) (R2 tptp.int)) (=> (not (= Q2 tptp.zero_zero_int)) (=> (not (= S2 tptp.zero_zero_int)) (=> (= (tptp.normalize (tptp.product_Pair_int_int P3 Q2)) (tptp.normalize (tptp.product_Pair_int_int R2 S2))) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int P3) S2) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int R2) Q2)))))) (forall ((P3 tptp.rat) (Q2 tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat P3) Q2)) (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.produc8560705615207772305t_bool (tptp.aTP_Lamm_cv Q2)) (tptp.quotient_of P3))))) (forall ((P3 tptp.rat) (Q2 tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat P3) Q2)) (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.produc8560705615207772305t_bool (tptp.aTP_Lamm_cx Q2)) (tptp.quotient_of P3))))) (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_cy K) (tptp.code_divmod_abs K (tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one)))))))))) (forall ((X tptp.nat)) (= (tptp.bezw X tptp.zero_zero_nat) (tptp.product_Pair_int_int tptp.one_one_int tptp.zero_zero_int))) (forall ((A2 tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A2)) (= (tptp.nat_set_decode (tptp.aa_set_nat_nat tptp.nat_set_encode A2)) A2))) (forall ((N tptp.nat)) (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat (tptp.nat_set_decode N)))) (forall ((A2 tptp.set_nat) (B3 tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A2)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat B3)) (= (= (tptp.aa_set_nat_nat tptp.nat_set_encode A2) (tptp.aa_set_nat_nat tptp.nat_set_encode B3)) (= A2 B3))))) (forall ((N5 tptp.set_nat)) (= (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat N5)) (exists ((M5 tptp.nat)) (forall ((X5 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X5) N5)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X5) M5))))))) (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_cz F) U)))))) (forall ((A2 tptp.set_nat)) (=> (not (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A2))) (= (tptp.aa_set_nat_nat tptp.nat_set_encode A2) tptp.zero_zero_nat))) (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_da M)))))) (forall ((N5 tptp.set_nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat N5) (tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat N))) (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat N5)))) (forall ((N5 tptp.set_nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat N5) (tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat N))) (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat N5)))) (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 ((A2 tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A2)) (= (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 A2))) (not (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat tptp.zero_zero_nat) A2)))))) (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_db K))))) (forall ((A tptp.int) (B tptp.int)) (tptp.finite_finite_int (tptp.collect_int (tptp.aa_int_fun_int_bool (tptp.aTP_Lamm_dc A) B)))) (forall ((A tptp.int) (B tptp.int)) (tptp.finite_finite_int (tptp.collect_int (tptp.aa_int_fun_int_bool (tptp.aTP_Lamm_dd A) B)))) (forall ((A tptp.int) (B tptp.int)) (tptp.finite_finite_int (tptp.collect_int (tptp.aa_int_fun_int_bool (tptp.aTP_Lamm_de A) B)))) (forall ((A tptp.int) (B tptp.int)) (tptp.finite_finite_int (tptp.collect_int (tptp.aa_int_fun_int_bool (tptp.aTP_Lamm_df A) B)))) (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.finite3207457112153483333omplex (tptp.collect_complex (tptp.aa_com1553036987509291606x_bool (tptp.aTP_Lamm_bg N) C))))) (forall ((U tptp.int)) (tptp.finite_finite_int (tptp.set_or4662586982721622107an_int tptp.zero_zero_int U))) (forall ((I tptp.int)) (=> (not (= I tptp.zero_zero_int)) (tptp.finite_finite_int (tptp.collect_int (tptp.aa_int_fun_int_bool tptp.aTP_Lamm_dg I))))) (forall ((S tptp.set_nat)) (= (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat S)) (exists ((K3 tptp.nat)) (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat S) (tptp.set_ord_atMost_nat K3)))))) (forall ((S tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat S)) (exists ((K2 tptp.nat)) (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat S) (tptp.set_ord_lessThan_nat K2)))))) (forall ((S tptp.set_nat)) (= (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat S)) (exists ((K3 tptp.nat)) (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat S) (tptp.set_ord_lessThan_nat K3)))))) (forall ((S tptp.set_int)) (= (not (tptp.finite_finite_int S)) (forall ((M5 tptp.int)) (exists ((N4 tptp.int)) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int M5) (tptp.aa_int_int tptp.abs_abs_int N4))) (tptp.member_int N4 S)))))) (forall ((S tptp.set_nat)) (= (not (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat S))) (forall ((M5 tptp.nat)) (exists ((N4 tptp.nat)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M5) N4)) (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat N4) S))))))) (forall ((K tptp.num)) (= (tptp.frct (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 ((A2 tptp.set_nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A2)) (=> (not (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat N) A2))) (= (tptp.aa_set_nat_nat tptp.nat_set_encode (tptp.insert_nat N A2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_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 A2)))))) (forall ((K tptp.nat)) (= (tptp.set_ord_lessThan_nat (tptp.aa_nat_nat tptp.suc K)) (tptp.insert_nat K (tptp.set_ord_lessThan_nat K)))) (forall ((K tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc K))) (= (tptp.set_ord_atMost_nat _let_1) (tptp.insert_nat _let_1 (tptp.set_ord_atMost_nat K))))) (forall ((N tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N))) (= (tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat _let_1) (tptp.insert_nat _let_1 (tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat N))))) (forall ((N tptp.nat)) (= (tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat (tptp.aa_nat_nat tptp.suc N)) (tptp.insert_nat N (tptp.set_or4665077453230672383an_nat tptp.zero_zero_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.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 ((A tptp.int)) (= (tptp.frct (tptp.product_Pair_int_int A tptp.zero_zero_int)) tptp.zero_zero_rat)) (forall ((A tptp.int)) (= (tptp.frct (tptp.product_Pair_int_int tptp.zero_zero_int A)) tptp.zero_zero_rat)) (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.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 ((K tptp.num)) (= (tptp.frct (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 ((K tptp.num) (L tptp.num)) (= (tptp.frct (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.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_dh 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_di L) _let_1)))))))))))))))))) (forall ((U tptp.nat)) (= (tptp.finite_card_nat (tptp.set_ord_atMost_nat U)) (tptp.aa_nat_nat tptp.suc U))) (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_db 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 ((L tptp.int) (U tptp.int)) (= (tptp.finite_card_int (tptp.set_or4662586982721622107an_int L U)) (tptp.aa_int_nat tptp.nat2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int U) L)))) (forall ((L tptp.int) (U tptp.int)) (= (tptp.finite_card_int (tptp.set_or1266510415728281911st_int L U)) (tptp.aa_int_nat tptp.nat2 (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 U) L)) tptp.one_one_int)))) (forall ((M tptp.nat) (N5 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_dj M) N5))) (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_dk M) N5)))) (tptp.finite_card_list_nat (tptp.collect_list_nat (tptp.aa_nat2079453845469346690t_bool (tptp.aTP_Lamm_dl M) N5))))))) (forall ((M tptp.nat) (N5 tptp.nat)) (= (tptp.finite_card_list_nat (tptp.collect_list_nat (tptp.aa_nat2079453845469346690t_bool (tptp.aTP_Lamm_dj M) N5))) (tptp.aa_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 N5) M)) tptp.one_one_nat)) N5))) (forall ((M10 tptp.set_nat) (I tptp.nat)) (=> (not (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat tptp.zero_zero_nat) M10))) (= (tptp.finite_card_nat (tptp.collect_nat (tptp.aa_nat_fun_nat_bool (tptp.aTP_Lamm_dm M10) I))) (tptp.finite_card_nat (tptp.collect_nat (tptp.aa_nat_fun_nat_bool (tptp.aTP_Lamm_dn M10) I)))))) (forall ((M10 tptp.set_nat) (I tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat tptp.zero_zero_nat) M10)) (= (tptp.aa_nat_nat tptp.suc (tptp.finite_card_nat (tptp.collect_nat (tptp.aa_nat_fun_nat_bool (tptp.aTP_Lamm_dm M10) I)))) (tptp.finite_card_nat (tptp.collect_nat (tptp.aa_nat_fun_nat_bool (tptp.aTP_Lamm_dn M10) I)))))) (forall ((M10 tptp.set_nat) (I tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat tptp.zero_zero_nat) M10)) (not (= (tptp.finite_card_nat (tptp.collect_nat (tptp.aa_nat_fun_nat_bool (tptp.aTP_Lamm_dn M10) I))) tptp.zero_zero_nat)))) (forall ((U tptp.int)) (= (tptp.finite_card_int (tptp.set_or4662586982721622107an_int tptp.zero_zero_int U)) (tptp.aa_int_nat tptp.nat2 U))) (forall ((A2 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 A2))))) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat A2) _let_1)) (= A2 _let_1)))) (forall ((M tptp.int) (N tptp.int)) (let ((_let_1 (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_1)) (= (tptp.set_or1266510415728281911st_int M _let_1) (tptp.insert_int _let_1 (tptp.set_or1266510415728281911st_int M N)))))) (forall ((N5 tptp.set_nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat N5) (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 N5)) N)))) (forall ((S tptp.set_nat)) (let ((_let_1 (tptp.groups3542108847815614940at_nat tptp.aTP_Lamm_bq))) (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 S)))) (tptp.aa_set_nat_nat _let_1 S))))) (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_al 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_ak N))) 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_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.aa_int_fun_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.member_int K _let_5) (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.aa_int_fun_int_int tptp.bit_se725231765392027082nd_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int K) _let_1)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int L) _let_1)))))))))))))) (forall ((X tptp.int) (Xa tptp.int) (Y4 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 Xa)))))) (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.member_int X _let_4) (tptp.member_int Xa _let_4)))) (=> (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se725231765392027082nd_int X) Xa) Y4) (and (=> _let_5 (= Y4 (tptp.aa_int_int tptp.uminus_uminus_int _let_3))) (=> (not _let_5) (= Y4 (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.aa_int_fun_int_int tptp.bit_se725231765392027082nd_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int X) _let_1)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int Xa) _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.aa_int_fun_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.member_int K _let_5) (tptp.member_int L _let_5)))) (=> (tptp.accp_P1096762738010456898nt_int tptp.bit_and_int_rel (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.aa_int_fun_int_int tptp.bit_se725231765392027082nd_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int K) _let_1)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int L) _let_1))))))))))))))) (forall ((X tptp.int) (Xa tptp.int) (Y4 tptp.int)) (let ((_let_1 (tptp.accp_P1096762738010456898nt_int tptp.bit_and_int_rel (tptp.product_Pair_int_int X Xa)))) (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 Xa)))))) (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.member_int X _let_5) (tptp.member_int Xa _let_5)))) (=> (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se725231765392027082nd_int X) Xa) Y4) (=> _let_1 (not (=> (and (=> _let_6 (= Y4 (tptp.aa_int_int tptp.uminus_uminus_int _let_4))) (=> (not _let_6) (= Y4 (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.aa_int_fun_int_int tptp.bit_se725231765392027082nd_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int X) _let_2)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int Xa) _let_2))))))) (not _let_1)))))))))))) (forall ((A0 tptp.int) (A1 tptp.int) (P tptp.fun_int_fun_int_bool)) (=> (tptp.accp_P1096762738010456898nt_int tptp.bit_and_int_rel (tptp.product_Pair_int_int A0 A1)) (=> (forall ((K2 tptp.int) (L2 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.accp_P1096762738010456898nt_int tptp.bit_and_int_rel (tptp.product_Pair_int_int K2 L2)) (=> (=> (not (and (tptp.member_int K2 _let_2) (tptp.member_int L2 _let_2))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool P (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int K2) _let_1)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int L2) _let_1)))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool P K2) L2))))))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool P A0) A1))))) (= (tptp.set_ord_lessThan_nat tptp.zero_zero_nat) tptp.bot_bot_set_nat) (= (tptp.nat_set_decode tptp.zero_zero_nat) tptp.bot_bot_set_nat) (= (tptp.aa_set_nat_nat tptp.nat_set_encode tptp.bot_bot_set_nat) tptp.zero_zero_nat) (forall ((M tptp.nat)) (= (tptp.set_or4665077453230672383an_nat M (tptp.aa_nat_nat tptp.suc M)) (tptp.insert_nat M tptp.bot_bot_set_nat))) (= (tptp.set_ord_atMost_nat tptp.zero_zero_nat) (tptp.insert_nat tptp.zero_zero_nat tptp.bot_bot_set_nat)) (= tptp.bot_bo4199563552545308370d_enat tptp.zero_z5237406670263579293d_enat) (= tptp.bot_bot_nat tptp.zero_zero_nat) (forall ((M tptp.nat)) (= (tptp.set_or4665077453230672383an_nat M tptp.zero_zero_nat) tptp.bot_bot_set_nat)) (forall ((N tptp.nat)) (= (= (tptp.set_ord_lessThan_nat N) tptp.bot_bot_set_nat) (= N tptp.zero_zero_nat))) (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 ((N tptp.nat)) (= (tptp.set_or4665077453230672383an_nat (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat) N) (tptp.minus_minus_set_nat (tptp.set_ord_lessThan_nat N) (tptp.insert_nat tptp.zero_zero_nat tptp.bot_bot_set_nat)))) (forall ((N tptp.nat)) (= (tptp.set_or1269000886237332187st_nat (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat) N) (tptp.minus_minus_set_nat (tptp.set_ord_atMost_nat N) (tptp.insert_nat tptp.zero_zero_nat tptp.bot_bot_set_nat)))) (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 ((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 ((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_bq) (tptp.set_or4665077453230672383an_nat M N))))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.map_nat_nat tptp.suc (tptp.upt M N)) (tptp.upt (tptp.aa_nat_nat tptp.suc M) (tptp.aa_nat_nat tptp.suc N)))) (forall ((N tptp.nat) (M tptp.nat)) (= (tptp.map_nat_nat (tptp.aTP_Lamm_do 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 ((M tptp.nat) (N tptp.nat)) (= (tptp.map_nat_nat tptp.aTP_Lamm_dp (tptp.upt (tptp.aa_nat_nat tptp.suc M) (tptp.aa_nat_nat tptp.suc N))) (tptp.upt M N))) (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 ((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 ((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 ((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 ((N tptp.nat) (K tptp.nat)) (= (tptp.aa_nat_nat (tptp.binomial N) K) (tptp.finite_card_set_nat (tptp.collect_set_nat (tptp.aa_nat8857836526276733660t_bool (tptp.aTP_Lamm_dq N) 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.product_fst_nat_nat (tptp.unique5055182867167087721od_nat tptp.one K)))) (forall ((K tptp.num)) (= (tptp.aa_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.product_snd_nat_nat (tptp.unique5055182867167087721od_nat tptp.one K)))) (forall ((M tptp.nat) (N tptp.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 ((M tptp.nat) (N tptp.nat)) (= (tptp.product_snd_nat_nat (tptp.divmod_nat M N)) (tptp.aa_nat_nat (tptp.modulo_modulo_nat M) N))) (forall ((R2 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 R2))))) (forall ((Y4 tptp.nat) (X tptp.nat)) (let ((_let_1 (tptp.bezw Y4 (tptp.aa_nat_nat (tptp.modulo_modulo_nat X) Y4)))) (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) Y4)) (= (tptp.bezw X Y4) (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) Y4)))))))))) (forall ((Y4 tptp.nat) (X tptp.nat)) (let ((_let_1 (tptp.bezw Y4 (tptp.aa_nat_nat (tptp.modulo_modulo_nat X) Y4)))) (let ((_let_2 (tptp.product_snd_int_int _let_1))) (let ((_let_3 (tptp.bezw X Y4))) (let ((_let_4 (= Y4 tptp.zero_zero_nat))) (and (=> _let_4 (= _let_3 (tptp.product_Pair_int_int tptp.one_one_int tptp.zero_zero_int))) (=> (not _let_4) (= _let_3 (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) Y4))))))))))))) (forall ((X tptp.nat) (Xa tptp.nat) (Y4 tptp.product_prod_int_int)) (let ((_let_1 (tptp.bezw Xa (tptp.aa_nat_nat (tptp.modulo_modulo_nat X) Xa)))) (let ((_let_2 (tptp.product_snd_int_int _let_1))) (let ((_let_3 (= Xa tptp.zero_zero_nat))) (=> (= (tptp.bezw X Xa) Y4) (and (=> _let_3 (= Y4 (tptp.product_Pair_int_int tptp.one_one_int tptp.zero_zero_int))) (=> (not _let_3) (= Y4 (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) Xa))))))))))))) (forall ((X tptp.nat) (Xa tptp.nat) (Y4 tptp.product_prod_int_int)) (let ((_let_1 (tptp.accp_P4275260045618599050at_nat tptp.bezw_rel (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat X) Xa)))) (let ((_let_2 (tptp.bezw Xa (tptp.aa_nat_nat (tptp.modulo_modulo_nat X) Xa)))) (let ((_let_3 (tptp.product_snd_int_int _let_2))) (let ((_let_4 (= Xa tptp.zero_zero_nat))) (=> (= (tptp.bezw X Xa) Y4) (=> _let_1 (not (=> (and (=> _let_4 (= Y4 (tptp.product_Pair_int_int tptp.one_one_int tptp.zero_zero_int))) (=> (not _let_4) (= Y4 (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) Xa)))))))) (not _let_1)))))))))) (forall ((N tptp.num)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int N))) (= (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.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.modulo_modulo_int (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int) _let_1) (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.modulo_modulo_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int M)) _let_1) (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.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.adjust_mod _let_1 (tptp.product_snd_int_int (tptp.unique5052692396658037445od_int M N))))))) (forall ((R2 tptp.int) (L tptp.int)) (let ((_let_1 (tptp.adjust_mod L R2))) (let ((_let_2 (= R2 tptp.zero_zero_int))) (and (=> _let_2 (= _let_1 tptp.zero_zero_int)) (=> (not _let_2) (= _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int L) R2))))))) (forall ((P3 tptp.product_prod_int_int)) (let ((_let_1 (tptp.product_snd_int_int P3))) (let ((_let_2 (tptp.product_fst_int_int P3))) (let ((_let_3 (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.aa_int_fun_int_int tptp.divide_divide_int _let_1))) (let ((_let_6 (tptp.aa_int_fun_int_int tptp.divide_divide_int _let_2))) (let ((_let_7 (tptp.normalize P3))) (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.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.product_Pair_int_int tptp.zero_zero_int tptp.one_one_int))) (=> (not _let_8) (= _let_7 (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.gcd_gcd_int M N))) (or (not (= M tptp.zero_zero_int)) (not (= N tptp.zero_zero_int))))) (forall ((N tptp.num) (X tptp.int)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int N))) (= (tptp.gcd_gcd_int (tptp.aa_int_int tptp.uminus_uminus_int _let_1) X) (tptp.gcd_gcd_int _let_1 X)))) (forall ((X tptp.int) (N tptp.num)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int N))) (= (tptp.gcd_gcd_int X (tptp.aa_int_int tptp.uminus_uminus_int _let_1)) (tptp.gcd_gcd_int X _let_1)))) (forall ((X tptp.int)) (= (tptp.gcd_gcd_int X tptp.zero_zero_int) (tptp.aa_int_int tptp.abs_abs_int X))) (forall ((X tptp.int)) (= (tptp.gcd_gcd_int tptp.zero_zero_int X) (tptp.aa_int_int tptp.abs_abs_int X))) (forall ((Y4 tptp.int) (X tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int Y4) X)) (= (tptp.gcd_gcd_int X Y4) (tptp.aa_int_int tptp.abs_abs_int Y4)))) (forall ((X tptp.int) (Y4 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int X) Y4)) (= (tptp.gcd_gcd_int X Y4) (tptp.aa_int_int tptp.abs_abs_int X)))) (forall ((X tptp.int) (Y4 tptp.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 X Y4)))) (forall ((X tptp.int) (Y4 tptp.int)) (exists ((U2 tptp.int) (V3 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 V3) Y4)) (tptp.gcd_gcd_int X Y4)))) (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.gcd_gcd_int M N)) (tptp.gcd_gcd_int (tptp.aa_int_int _let_1 M) (tptp.aa_int_int _let_1 N))))) (forall ((A tptp.int) (B 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.gcd_gcd_int A B)) A)))) (forall ((B 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) B)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.gcd_gcd_int A B)) B)))) (forall ((X tptp.int) (Y4 tptp.int) (P tptp.fun_int_bool)) (let ((_let_1 (tptp.pp (tptp.aa_int_bool P (tptp.gcd_gcd_int X Y4))))) (let ((_let_2 (tptp.aa_int_int tptp.uminus_uminus_int Y4))) (let ((_let_3 (tptp.aa_int_int tptp.uminus_uminus_int X))) (let ((_let_4 (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Y4) tptp.zero_zero_int)))) (let ((_let_5 (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X) tptp.zero_zero_int)))) (let ((_let_6 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_7 (tptp.pp (tptp.aa_int_bool _let_6 Y4)))) (let ((_let_8 (tptp.pp (tptp.aa_int_bool _let_6 X)))) (=> (=> _let_8 (=> _let_7 _let_1)) (=> (=> _let_8 (=> _let_4 (tptp.pp (tptp.aa_int_bool P (tptp.gcd_gcd_int X _let_2))))) (=> (=> _let_5 (=> _let_7 (tptp.pp (tptp.aa_int_bool P (tptp.gcd_gcd_int _let_3 Y4))))) (=> (=> _let_5 (=> _let_4 (tptp.pp (tptp.aa_int_bool P (tptp.gcd_gcd_int _let_3 _let_2))))) _let_1))))))))))))) (forall ((D tptp.int) (A tptp.int) (B 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 B)) (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 B))) (tptp.pp (tptp.aa_int_bool _let_1 D)))))) (= D (tptp.gcd_gcd_int A B))))) (forall ((Y4 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) Y4)) (= (tptp.gcd_gcd_int X Y4) (tptp.gcd_gcd_int Y4 (tptp.modulo_modulo_int X Y4))))) (forall ((K tptp.int) (L tptp.int)) (= (tptp.gcd_gcd_int K L) (tptp.aa_int_int tptp.abs_abs_int (tptp.if_int (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.fequal_int L) tptp.zero_zero_int) K (tptp.gcd_gcd_int L (tptp.modulo_modulo_int (tptp.aa_int_int tptp.abs_abs_int K) (tptp.aa_int_int tptp.abs_abs_int L))))))) (forall ((X tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.gcd_gcd_nat tptp.zero_zero_nat) X) X)) (forall ((X tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.gcd_gcd_nat X) tptp.zero_zero_nat) X)) (forall ((A tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.gcd_gcd_nat A) tptp.zero_zero_nat) A)) (forall ((A tptp.nat) (B tptp.nat)) (= (= tptp.zero_zero_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.gcd_gcd_nat A) B)) (and (= A tptp.zero_zero_nat) (= B tptp.zero_zero_nat)))) (forall ((A tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.gcd_gcd_nat tptp.zero_zero_nat) A) A)) (forall ((A tptp.nat) (B tptp.nat)) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.gcd_gcd_nat A) B) tptp.zero_zero_nat) (and (= A tptp.zero_zero_nat) (= B tptp.zero_zero_nat)))) (forall ((A tptp.nat) (B tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat A) B)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.gcd_gcd_nat A) B) A))) (forall ((B tptp.nat) (A tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat B) A)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.gcd_gcd_nat A) B) B))) (forall ((A tptp.nat) (B 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.gcd_gcd_nat B) C))) (and (tptp.pp (tptp.aa_nat_bool _let_1 B)) (tptp.pp (tptp.aa_nat_bool _let_1 C)))))) (forall ((X tptp.nat) (Y4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat X) Y4)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.gcd_gcd_nat X) Y4) X))) (forall ((Y4 tptp.nat) (X tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat Y4) X)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.gcd_gcd_nat X) Y4) Y4))) (forall ((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.gcd_gcd_nat M) _let_1) _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 ((M tptp.nat) (N tptp.nat)) (= (tptp.gcd_gcd_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int M) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N)) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.gcd_gcd_nat M) N)))) (forall ((N tptp.nat) (K tptp.int)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.gcd_gcd_nat N) (tptp.aa_int_nat tptp.nat2 (tptp.aa_int_int tptp.abs_abs_int K))) (tptp.aa_int_nat tptp.nat2 (tptp.gcd_gcd_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N) K)))) (forall ((K tptp.int) (N tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.gcd_gcd_nat (tptp.aa_int_nat tptp.nat2 (tptp.aa_int_int tptp.abs_abs_int K))) N) (tptp.aa_int_nat tptp.nat2 (tptp.gcd_gcd_int K (tptp.aa_nat_int tptp.semiri1314217659103216013at_int 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.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 ((A tptp.nat) (C tptp.nat) (B tptp.nat) (D tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat A) C)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat B) 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.gcd_gcd_nat A) B)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.gcd_gcd_nat C) D)))))) (forall ((A tptp.nat) (B tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat A) B)) (= A (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.gcd_gcd_nat A) B)))) (forall ((A tptp.nat) (B tptp.nat)) (=> (= A (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.gcd_gcd_nat A) B)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat A) B)))) (forall ((A tptp.nat) (B tptp.nat)) (=> (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat A) B)) (not (= A B))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.gcd_gcd_nat A) B) A))) (forall ((B tptp.nat) (A tptp.nat)) (=> (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat B) A)) (not (= B A))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.gcd_gcd_nat A) B) B))) (forall ((A tptp.nat) (B 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.gcd_gcd_nat B) C))) (not (=> (tptp.pp (tptp.aa_nat_bool _let_1 B)) (not (tptp.pp (tptp.aa_nat_bool _let_1 C)))))))) (forall ((A tptp.nat) (B 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 B)) (=> (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.gcd_gcd_nat B) C))))))) (forall ((A tptp.nat) (B tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat A) B)) (= A (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.gcd_gcd_nat A) B)))) (forall ((A tptp.nat) (B 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.gcd_gcd_nat A) B)) A))) (forall ((A tptp.nat) (B 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.gcd_gcd_nat A) B)) B))) (forall ((A tptp.nat) (B tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat A) B)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.gcd_gcd_nat A) B) A))) (forall ((B tptp.nat) (A tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat B) A)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.gcd_gcd_nat A) B) B))) (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat A) 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.gcd_gcd_nat A) B)) C)))) (forall ((B tptp.nat) (C tptp.nat) (A tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat B) 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.gcd_gcd_nat A) B)) C)))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat A))) (let ((_let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.gcd_gcd_nat B) C))) (=> (and (tptp.pp (tptp.aa_nat_bool _let_1 _let_2)) (not (= A _let_2))) (not (=> (and (tptp.pp (tptp.aa_nat_bool _let_1 B)) (not (= A B))) (not (and (tptp.pp (tptp.aa_nat_bool _let_1 C)) (not (= A C)))))))))) (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (not (= A B)))) (= (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat A) B)) _let_1) (and (= A (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.gcd_gcd_nat A) B)) _let_1)))) (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.gcd_gcd_nat A) B))) (=> (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat A) C)) (not (= A C))) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat _let_1) C)) (not (= _let_1 C)))))) (forall ((B tptp.nat) (C tptp.nat) (A tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.gcd_gcd_nat A) B))) (=> (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat B) C)) (not (= B C))) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat _let_1) C)) (not (= _let_1 C)))))) (forall ((D tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat D))) (= (and (tptp.pp (tptp.aa_nat_bool _let_1 A)) (tptp.pp (tptp.aa_nat_bool _let_1 B)) (forall ((E3 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat E3))) (=> (and (tptp.pp (tptp.aa_nat_bool _let_1 A)) (tptp.pp (tptp.aa_nat_bool _let_1 B))) (tptp.pp (tptp.aa_nat_bool _let_1 D)))))) (= D (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.gcd_gcd_nat A) B))))) (forall ((B tptp.nat) (A tptp.nat)) (=> (not (= B 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) B)) B)))) (forall ((A tptp.nat) (B 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) B)) 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 ((X tptp.nat) (Xa tptp.nat) (Y4 tptp.nat)) (let ((_let_1 (= Xa tptp.zero_zero_nat))) (=> (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.gcd_gcd_nat X) Xa) Y4) (and (=> _let_1 (= Y4 X)) (=> (not _let_1) (= Y4 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.gcd_gcd_nat Xa) (tptp.aa_nat_nat (tptp.modulo_modulo_nat X) Xa)))))))) (forall ((Y4 tptp.nat) (X tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.gcd_gcd_nat X) Y4))) (let ((_let_2 (= Y4 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 X)) (=> (not _let_2) (= _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.gcd_gcd_nat Y4) (tptp.aa_nat_nat (tptp.modulo_modulo_nat X) Y4)))))))) (forall ((Y4 tptp.nat) (X tptp.nat)) (=> (not (= Y4 tptp.zero_zero_nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.gcd_gcd_nat X) Y4) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.gcd_gcd_nat Y4) (tptp.aa_nat_nat (tptp.modulo_modulo_nat X) Y4))))) (forall ((K tptp.code_integer) (L tptp.code_integer)) (= (tptp.gcd_gcd_Code_integer K L) (tptp.abs_abs_Code_integer (tptp.if_Code_integer (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.fequal_Code_integer L) tptp.zero_z3403309356797280102nteger) K (tptp.gcd_gcd_Code_integer L (tptp.modulo364778990260209775nteger (tptp.abs_abs_Code_integer K) (tptp.abs_abs_Code_integer L))))))) (forall ((A tptp.nat) (B tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (exists ((X3 tptp.nat) (Y tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) X3) (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 B) Y)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.gcd_gcd_nat A) B)))))) (forall ((B tptp.nat) (A tptp.nat)) (exists ((X3 tptp.nat) (Y tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.gcd_gcd_nat A) B))) (let ((_let_2 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A))) (let ((_let_3 (tptp.aa_nat_nat _let_2 Y))) (let ((_let_4 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B))) (let ((_let_5 (tptp.aa_nat_nat _let_4 X3))) (let ((_let_6 (tptp.aa_nat_nat _let_4 Y))) (let ((_let_7 (tptp.aa_nat_nat _let_2 X3))) (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.int) (Y4 tptp.int)) (= (tptp.gcd_gcd_int X Y4) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.gcd_gcd_nat (tptp.aa_int_nat tptp.nat2 (tptp.aa_int_int tptp.abs_abs_int X))) (tptp.aa_int_nat tptp.nat2 (tptp.aa_int_int tptp.abs_abs_int Y4)))))) (forall ((X tptp.nat) (Y4 tptp.nat)) (let ((_let_1 (tptp.bezw X Y4))) (= (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.gcd_gcd_nat X) Y4)) (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 Y4)))))) (forall ((N tptp.nat) (P tptp.fun_nat_bool) (M tptp.nat)) (=> (forall ((K2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N) K2)) (tptp.pp (tptp.aa_nat_bool P K2)))) (=> (forall ((K2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K2) N)) (=> (forall ((I4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat K2) I4)) (tptp.pp (tptp.aa_nat_bool P I4)))) (tptp.pp (tptp.aa_nat_bool P K2))))) (tptp.pp (tptp.aa_nat_bool P M))))) (forall ((X tptp.nat) (Xa tptp.nat) (Y4 tptp.nat)) (let ((_let_1 (tptp.accp_P4275260045618599050at_nat tptp.gcd_nat_rel (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat X) Xa)))) (let ((_let_2 (= Xa tptp.zero_zero_nat))) (=> (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.gcd_gcd_nat X) Xa) Y4) (=> _let_1 (not (=> (and (=> _let_2 (= Y4 X)) (=> (not _let_2) (= Y4 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.gcd_gcd_nat Xa) (tptp.aa_nat_nat (tptp.modulo_modulo_nat X) Xa))))) (not _let_1)))))))) (= (tptp.complete_Sup_Sup_nat tptp.bot_bot_set_nat) tptp.zero_zero_nat) (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_dr L) _let_1))))))))))))) (forall ((L tptp.int) (U tptp.int)) (= (tptp.finite_card_int (tptp.set_or5832277885323065728an_int L U)) (tptp.aa_int_nat tptp.nat2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int U) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int L) tptp.one_one_int))))) (forall ((N tptp.nat)) (= (tptp.compow_fun_nat_nat N tptp.suc) (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N))) (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)))) (= _let_47 _let_47) (forall ((L tptp.nat) (U tptp.nat)) (= (tptp.set_or4665077453230672383an_nat (tptp.aa_nat_nat tptp.suc L) U) (tptp.set_or5834768355832116004an_nat L U))) (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)))) (= tptp.code_Target_negative (tptp.comp_int_int_num tptp.uminus_uminus_int tptp.numeral_numeral_int)) (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 ((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))) (tptp.semila1623282765462674594er_nat tptp.ord_max_nat tptp.zero_zero_nat tptp.aTP_Lamm_db tptp.aTP_Lamm_be) (forall ((K tptp.code_integer)) (= (tptp.semiri4939895301339042750nteger (tptp.code_nat_of_integer K)) (tptp.ord_max_Code_integer tptp.zero_z3403309356797280102nteger K))) (= (tptp.code_nat_of_integer tptp.zero_z3403309356797280102nteger) tptp.zero_zero_nat) (forall ((K tptp.num)) (= (tptp.code_nat_of_integer (tptp.numera6620942414471956472nteger K)) (tptp.aa_num_nat tptp.numeral_numeral_nat K))) (tptp.semila1623282765462674594er_nat tptp.gcd_gcd_nat tptp.zero_zero_nat tptp.dvd_dvd_nat tptp.aTP_Lamm_ds) (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_dt (tptp.code_divmod_integer K (tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one)))))))))) (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_du (tptp.code_divmod_integer K (tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))))))))))))) (forall ((Xa 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 Xa)) (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_dw) Xa) X)))) (= (tptp.code_int_of_integer tptp.zero_z3403309356797280102nteger) tptp.zero_zero_int) (forall ((K tptp.num)) (= (tptp.code_int_of_integer (tptp.numera6620942414471956472nteger K)) (tptp.aa_num_int tptp.numeral_numeral_int K))) (forall ((X tptp.code_integer) (Xa tptp.code_integer)) (= (tptp.code_int_of_integer (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger X) Xa)) (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 Xa)))) (forall ((X tptp.code_integer) (Xa tptp.code_integer)) (= (tptp.code_int_of_integer (tptp.minus_8373710615458151222nteger X Xa)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.code_int_of_integer X)) (tptp.code_int_of_integer Xa)))) (forall ((X tptp.code_integer) (Xa tptp.code_integer)) (= (tptp.code_int_of_integer (tptp.divide6298287555418463151nteger X Xa)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int (tptp.code_int_of_integer X)) (tptp.code_int_of_integer Xa)))) (forall ((N tptp.nat)) (= (tptp.code_int_of_integer (tptp.semiri4939895301339042750nteger N)) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N))) (forall ((Z tptp.int)) (not (forall ((X3 tptp.nat) (Y tptp.nat)) (not (= Z (tptp.aa_Pro4240683299535347697at_int tptp.abs_Integ (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat X3) Y))))))) (forall ((P tptp.fun_int_bool) (X tptp.int)) (=> (forall ((Y tptp.product_prod_nat_nat)) (tptp.pp (tptp.aa_int_bool P (tptp.aa_Pro4240683299535347697at_int tptp.abs_Integ Y)))) (tptp.pp (tptp.aa_int_bool P X)))) (forall ((X tptp.code_integer) (Xa tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger X) Xa)) (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 Xa))))) (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.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))) (forall ((X tptp.nat) (Xa tptp.code_integer)) (= (tptp.code_int_of_integer (tptp.aa_Cod1783974652533396728nteger (tptp.aa_nat6383147911832638789nteger tptp.bit_se8260200283734997820nteger X) Xa)) (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_se4203085406695923979it_int X) (tptp.code_int_of_integer Xa)))) (forall ((X tptp.nat) (Xa tptp.code_integer)) (= (tptp.code_int_of_integer (tptp.aa_Cod1783974652533396728nteger (tptp.aa_nat6383147911832638789nteger tptp.bit_se2793503036327961859nteger X) Xa)) (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_se7879613467334960850it_int X) (tptp.code_int_of_integer Xa)))) (forall ((X tptp.nat) (Xa tptp.code_integer)) (= (tptp.code_int_of_integer (tptp.bit_se1345352211410354436nteger X Xa)) (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_se2159334234014336723it_int X) (tptp.code_int_of_integer Xa)))) (= tptp.zero_zero_int (tptp.aa_Pro4240683299535347697at_int tptp.abs_Integ _let_25)) (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_dx) X)))) (= tptp.one_one_int (tptp.aa_Pro4240683299535347697at_int tptp.abs_Integ _let_23)) (forall ((Xa 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 Xa)) (tptp.aa_Pro4240683299535347697at_int tptp.abs_Integ X))) (tptp.pp (tptp.aa_Pro2232559814647311250t_bool (tptp.aa_Pro595088089689268830t_bool (tptp.produc5023667602222594023t_bool tptp.aTP_Lamm_dz) Xa) X)))) (forall ((Xa 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 Xa)) (tptp.aa_Pro4240683299535347697at_int tptp.abs_Integ X))) (tptp.pp (tptp.aa_Pro2232559814647311250t_bool (tptp.aa_Pro595088089689268830t_bool (tptp.produc5023667602222594023t_bool tptp.aTP_Lamm_eb) Xa) X)))) (forall ((Xa 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 Xa)) (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_ed) Xa) X)))) (forall ((Xa 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 Xa)) (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_ef) Xa) X)))) (forall ((M10 tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat M10)) (= (tptp.gcd_Gcd_nat M10) (tptp.gcd_Gcd_nat (tptp.minus_minus_set_nat M10 (tptp.insert_nat tptp.zero_zero_nat tptp.bot_bot_set_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) 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 ((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))) (forall ((A tptp.nat) (A2 tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat A) A2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.gcd_Gcd_nat A2)) A)))) (forall ((A2 tptp.set_nat) (A tptp.nat)) (=> (forall ((B2 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat B2) A2)) (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 A) (tptp.gcd_Gcd_nat A2))))) (forall ((L tptp.nat) (U tptp.nat)) (= (tptp.set_or1269000886237332187st_nat (tptp.aa_nat_nat tptp.suc L) U) (tptp.set_or6659071591806873216st_nat L U))) (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 ((X tptp.int) (Xa tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X) Xa)) (tptp.pp (tptp.aa_Pro2232559814647311250t_bool (tptp.aa_Pro595088089689268830t_bool (tptp.produc5023667602222594023t_bool tptp.aTP_Lamm_eb) (tptp.aa_int1417691210696471063at_nat tptp.rep_Integ X)) (tptp.aa_int1417691210696471063at_nat tptp.rep_Integ Xa))))) (forall ((X tptp.int) (Xa tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) Xa)) (tptp.pp (tptp.aa_Pro2232559814647311250t_bool (tptp.aa_Pro595088089689268830t_bool (tptp.produc5023667602222594023t_bool tptp.aTP_Lamm_dz) (tptp.aa_int1417691210696471063at_nat tptp.rep_Integ X)) (tptp.aa_int1417691210696471063at_nat tptp.rep_Integ Xa))))) (forall ((L tptp.int) (U tptp.int)) (= (tptp.finite_card_int (tptp.set_or6656581121297822940st_int L U)) (tptp.aa_int_nat tptp.nat2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int U) L)))) (forall ((A tptp.int) (A2 tptp.set_int)) (=> (tptp.member_int A A2) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.gcd_Gcd_int A2)) A)))) (forall ((A2 tptp.set_int) (A tptp.int)) (=> (forall ((B2 tptp.int)) (=> (tptp.member_int B2 A2) (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 A) (tptp.gcd_Gcd_int A2))))) (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 ((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.uminus_uminus_int (tptp.aa_fun8399641135911395862nt_int _let_46 _let_26)) (= tptp.nat_prod_encode (tptp.produc6842872674320459806at_nat tptp.aTP_Lamm_eg)) (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.product_prod_nat_nat) (Y4 tptp.product_prod_nat_nat)) (= (= (tptp.aa_Pro4243173770044397973at_nat tptp.nat_prod_encode X) (tptp.aa_Pro4243173770044397973at_nat tptp.nat_prod_encode Y4)) (= X Y4))) (forall ((Q2 tptp.num)) (= (tptp.aa_nat_num tptp.num_of_nat (tptp.aa_num_nat tptp.numeral_numeral_nat Q2)) Q2)) (= (tptp.aa_nat_num tptp.num_of_nat tptp.zero_zero_nat) tptp.one) (forall ((A tptp.nat) (B 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) B))))) (forall ((B tptp.nat) (A tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B) (tptp.aa_Pro4243173770044397973at_nat tptp.nat_prod_encode (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat A) B))))) (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 ((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.plus_plus_num (tptp.aa_nat_num tptp.num_of_nat M)) (tptp.aa_nat_num tptp.num_of_nat N))))))) (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_46 _let_27)) (= tptp.minus_minus_int (tptp.map_fu8294830438409148311nt_int tptp.rep_Integ _let_46 _let_16)) (= tptp.plus_plus_int (tptp.map_fu8294830438409148311nt_int tptp.rep_Integ _let_46 _let_18)) (= tptp.pred_nat (tptp.collec3392354462482085612at_nat (tptp.produc8955392012077580105t_bool tptp.aTP_Lamm_eh))) (forall ((X tptp.num) (Y4 tptp.num)) (let ((_let_1 (tptp.pow X))) (= (tptp.aa_num_num _let_1 (tptp.aa_num_num tptp.bit1 Y4)) (tptp.aa_num_num (tptp.times_times_num (tptp.aa_num_num tptp.sqr (tptp.aa_num_num _let_1 Y4))) X)))) (forall ((C tptp.nat) (Y4 tptp.nat) (X tptp.nat)) (let ((_let_1 (tptp.image_nat_nat (tptp.aTP_Lamm_ei C) (tptp.set_or4665077453230672383an_nat X Y4)))) (let ((_let_2 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Y4)))) (let ((_let_3 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat C) Y4)))) (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 Y4) 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))))))))) (forall ((M10 tptp.set_nat) (N5 tptp.set_nat)) (= (tptp.pp (tptp.aa_set_nat_bool (tptp.bij_betw_nat_nat tptp.suc M10) N5)) (= (tptp.image_nat_nat tptp.suc M10) N5))) (forall ((I tptp.nat) (J tptp.nat)) (= (tptp.image_nat_nat tptp.suc (tptp.set_or1269000886237332187st_nat I J)) (tptp.set_or1269000886237332187st_nat (tptp.aa_nat_nat tptp.suc I) (tptp.aa_nat_nat tptp.suc J)))) (forall ((I tptp.nat) (J tptp.nat)) (= (tptp.image_nat_nat tptp.suc (tptp.set_or4665077453230672383an_nat I J)) (tptp.set_or4665077453230672383an_nat (tptp.aa_nat_nat tptp.suc I) (tptp.aa_nat_nat tptp.suc J)))) (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 ((A2 tptp.set_nat)) (not (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat tptp.zero_zero_nat) (tptp.image_nat_nat tptp.suc A2))))) (forall ((X tptp.num)) (= (tptp.aa_num_num tptp.sqr X) (tptp.aa_num_num (tptp.times_times_num X) X))) (forall ((N tptp.nat)) (= (tptp.image_nat_nat tptp.suc (tptp.set_ord_lessThan_nat N)) (tptp.set_or1269000886237332187st_nat tptp.one_one_nat N))) (forall ((N tptp.nat)) (= (tptp.image_nat_nat tptp.suc (tptp.set_ord_atMost_nat N)) (tptp.set_or1269000886237332187st_nat tptp.one_one_nat (tptp.aa_nat_nat tptp.suc N)))) (forall ((N tptp.nat)) (= (tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat (tptp.aa_nat_nat tptp.suc N)) (tptp.insert_nat tptp.zero_zero_nat (tptp.image_nat_nat tptp.suc (tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat N))))) (forall ((N tptp.nat)) (= (tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat (tptp.aa_nat_nat tptp.suc N)) (tptp.insert_nat tptp.zero_zero_nat (tptp.image_nat_nat tptp.suc (tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat N))))) (forall ((N tptp.nat)) (= (tptp.set_ord_lessThan_nat (tptp.aa_nat_nat tptp.suc N)) (tptp.insert_nat tptp.zero_zero_nat (tptp.image_nat_nat tptp.suc (tptp.set_ord_lessThan_nat N))))) (forall ((N tptp.nat)) (= (tptp.set_ord_atMost_nat (tptp.aa_nat_nat tptp.suc N)) (tptp.insert_nat tptp.zero_zero_nat (tptp.image_nat_nat tptp.suc (tptp.set_ord_atMost_nat N))))) (forall ((X tptp.num) (Y4 tptp.num)) (let ((_let_1 (tptp.pow X))) (= (tptp.aa_num_num _let_1 (tptp.aa_num_num tptp.bit0 Y4)) (tptp.aa_num_num tptp.sqr (tptp.aa_num_num _let_1 Y4))))) (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.plus_plus_num (tptp.aa_num_num tptp.sqr N)) N))))) (forall ((N5 tptp.set_nat)) (= (tptp.gcd_Gcd_int (tptp.image_nat_int tptp.semiri1314217659103216013at_int N5)) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.gcd_Gcd_nat N5)))) (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 ((S tptp.set_int)) (= (tptp.finite_finite_int S) (exists ((K3 tptp.int)) (tptp.ord_less_eq_set_int (tptp.image_int_int tptp.abs_abs_int S) (tptp.set_ord_lessThan_int K3))))) (forall ((S tptp.set_int)) (= (tptp.finite_finite_int S) (exists ((K3 tptp.int)) (tptp.ord_less_eq_set_int (tptp.image_int_int tptp.abs_abs_int S) (tptp.set_ord_atMost_int K3))))) (forall ((A tptp.nat) (B tptp.nat)) (= (tptp.image_nat_int tptp.semiri1314217659103216013at_int (tptp.set_or1269000886237332187st_nat A B)) (tptp.set_or1266510415728281911st_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int A) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int B)))) (forall ((A tptp.nat) (B tptp.nat)) (= (tptp.image_nat_int tptp.semiri1314217659103216013at_int (tptp.set_or4665077453230672383an_nat A B)) (tptp.set_or4662586982721622107an_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int A) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int B)))) (forall ((L tptp.int) (U tptp.int)) (= (tptp.image_int_int (tptp.aTP_Lamm_ej L) (tptp.set_or4662586982721622107an_int tptp.zero_zero_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int U) L))) (tptp.set_or4662586982721622107an_int L U))) (forall ((K5 tptp.set_int)) (= (tptp.gcd_Gcd_int K5) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.gcd_Gcd_nat (tptp.image_int_nat (tptp.comp_int_nat_int tptp.nat2 tptp.abs_abs_int) K5))))) (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.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.aTP_Lamm_ek N) tptp.top_top_set_nat) (tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat N)))) (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_el X7) tptp.top_top_set_nat)))))) (= tptp.top_top_set_nat (tptp.insert_nat tptp.zero_zero_nat _let_44)) (tptp.fun_is_measure_int (tptp.comp_int_nat_int tptp.nat2 tptp.abs_abs_int)) (= (tptp.finite_card_bool tptp.top_top_set_bool) _let_2) (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)))))) (not (tptp.finite_finite_int tptp.top_top_set_int)) (tptp.pp (tptp.aa_set_nat_bool (tptp.bij_be5333170631980326235at_nat tptp.nat_prod_encode tptp.top_to4669805908274784177at_nat) tptp.top_top_set_nat)) (= (tptp.image_2486076414777270412at_nat tptp.nat_prod_encode tptp.top_to4669805908274784177at_nat) tptp.top_top_set_nat) (forall ((N tptp.nat)) (tptp.member_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N) (tptp.image_int_int tptp.abs_abs_int tptp.top_top_set_int))) (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_em N)) X))))))) (= (tptp.finite_card_char tptp.top_top_set_char) _let_38) (= tptp.top_top_set_bool (tptp.insert_bool tptp.fFalse (tptp.insert_bool tptp.fTrue tptp.bot_bot_set_bool))) (= tptp.top_top_set_char (tptp.image_nat_char tptp.unique3096191561947761185of_nat _let_39)) (forall ((X1 tptp.bool) (X2 tptp.bool) (X33 tptp.bool) (X42 tptp.bool) (X52 tptp.bool) (X62 tptp.bool) (X72 tptp.bool) (X8 tptp.bool)) (= (tptp.size_size_char (tptp.char2 X1 X2 X33 X42 X52 X62 X72 X8)) tptp.zero_zero_nat)) (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_39) (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.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.aa_bool_Code_integer tptp.zero_n356916108424825756nteger B72)) _let_1) (tptp.aa_bool_Code_integer tptp.zero_n356916108424825756nteger B62))) _let_1) (tptp.aa_bool_Code_integer tptp.zero_n356916108424825756nteger B52))) _let_1) (tptp.aa_bool_Code_integer tptp.zero_n356916108424825756nteger B42))) _let_1) (tptp.aa_bool_Code_integer tptp.zero_n356916108424825756nteger B32))) _let_1) (tptp.aa_bool_Code_integer tptp.zero_n356916108424825756nteger B22))) _let_1) (tptp.aa_bool_Code_integer tptp.zero_n356916108424825756nteger B1))) _let_1) (tptp.aa_bool_Code_integer tptp.zero_n356916108424825756nteger B0))))) (forall ((X1 tptp.bool) (X2 tptp.bool) (X33 tptp.bool) (X42 tptp.bool) (X52 tptp.bool) (X62 tptp.bool) (X72 tptp.bool) (X8 tptp.bool)) (= (tptp.size_char (tptp.char2 X1 X2 X33 X42 X52 X62 X72 X8)) tptp.zero_zero_nat)) (forall ((C tptp.char)) (= (tptp.aa_char_nat tptp.comm_s629917340098488124ar_nat (tptp.ascii_of C)) (tptp.aa_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)))) (forall ((N tptp.nat) (X tptp.real) (D3 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 (= D3 _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)) (= D3 (tptp.aa_real_real tptp.uminus_uminus_real _let_2)))) (=> (=> (not _let_4) _let_3) (tptp.has_fi5821293074295781190e_real _let_1 D3 (tptp.topolo2177554685111907308n_real X tptp.top_top_set_real)))))))))))) (forall ((F tptp.fun_real_real) (L tptp.real) (X tptp.real) (S tptp.set_real)) (=> (tptp.has_fi5821293074295781190e_real F L (tptp.topolo2177554685111907308n_real X S)) (=> (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 ((H2 tptp.real)) (let ((_let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) H2))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) H2)) (=> (tptp.member_real _let_1 S) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real H2) 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) (S tptp.set_real)) (=> (tptp.has_fi5821293074295781190e_real F L (tptp.topolo2177554685111907308n_real X S)) (=> (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 ((H2 tptp.real)) (let ((_let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) H2))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) H2)) (=> (tptp.member_real _let_1 S) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real H2) 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) (S tptp.set_real)) (=> (tptp.has_fi5821293074295781190e_real F L (tptp.topolo2177554685111907308n_real X S)) (=> (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 ((H2 tptp.real)) (let ((_let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real X) H2))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) H2)) (=> (tptp.member_real _let_1 S) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real H2) 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) (S tptp.set_real)) (=> (tptp.has_fi5821293074295781190e_real F L (tptp.topolo2177554685111907308n_real X S)) (=> (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 ((H2 tptp.real)) (let ((_let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real X) H2))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) H2)) (=> (tptp.member_real _let_1 S) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real H2) 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 ((A tptp.real) (B tptp.real) (G tptp.fun_real_real) (G2 tptp.fun_real_real)) (=> (forall ((X3 tptp.real)) (=> (tptp.member_real X3 (tptp.set_or1222579329274155063t_real A B)) (tptp.has_fi5821293074295781190e_real G (tptp.aa_real_real G2 X3) (tptp.topolo2177554685111907308n_real X3 tptp.top_top_set_real)))) (=> (forall ((X3 tptp.real)) (=> (tptp.member_real X3 (tptp.set_or1222579329274155063t_real A B)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_real_real G2 X3))))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) B)) (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 B))))))) (forall ((A tptp.real) (B tptp.real) (F tptp.fun_real_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) B)) (=> (forall ((X3 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) X3)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X3) B)) (exists ((Y3 tptp.real)) (and (tptp.has_fi5821293074295781190e_real F Y3 (tptp.topolo2177554685111907308n_real X3 tptp.top_top_set_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) Y3))))))) (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 B)))))) (forall ((A tptp.real) (B tptp.real) (F tptp.fun_real_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) B)) (=> (forall ((X3 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) X3)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X3) B)) (exists ((Y3 tptp.real)) (and (tptp.has_fi5821293074295781190e_real F Y3 (tptp.topolo2177554685111907308n_real X3 tptp.top_top_set_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y3) tptp.zero_zero_real))))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real F B)) (tptp.aa_real_real F A)))))) (forall ((A tptp.real) (B tptp.real) (F tptp.fun_real_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B)) (=> (forall ((X3 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) X3)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X3) B)) (exists ((Y3 tptp.real)) (and (tptp.has_fi5821293074295781190e_real F Y3 (tptp.topolo2177554685111907308n_real X3 tptp.top_top_set_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) Y3))))))) (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 B)))))) (forall ((A tptp.real) (B tptp.real) (F tptp.fun_real_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B)) (=> (forall ((X3 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) X3)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X3) B)) (exists ((Y3 tptp.real)) (and (tptp.has_fi5821293074295781190e_real F Y3 (tptp.topolo2177554685111907308n_real X3 tptp.top_top_set_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y3) tptp.zero_zero_real))))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real F B)) (tptp.aa_real_real F A)))))) (forall ((F tptp.fun_real_real) (X tptp.real) (Y4 tptp.real)) (=> (forall ((X3 tptp.real)) (tptp.has_fi5821293074295781190e_real F tptp.zero_zero_real (tptp.topolo2177554685111907308n_real X3 tptp.top_top_set_real))) (= (tptp.aa_real_real F X) (tptp.aa_real_real F Y4)))) (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 ((H2 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) H2)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real H2) 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) H2)))))))))))) (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 ((H2 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) H2)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real H2) 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) H2))) (tptp.aa_real_real F X))))))))))) (forall ((A tptp.real) (B tptp.real) (F tptp.fun_real_real) (K tptp.real)) (=> (not (= A B)) (=> (forall ((X3 tptp.real)) (tptp.has_fi5821293074295781190e_real F K (tptp.topolo2177554685111907308n_real X3 tptp.top_top_set_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 F B)) (tptp.aa_real_real F A))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real B) A)) K)))) (forall ((A tptp.real) (B tptp.real) (F tptp.fun_real_real) (K tptp.real)) (=> (not (= A B)) (=> (forall ((X3 tptp.real)) (tptp.has_fi5821293074295781190e_real F K (tptp.topolo2177554685111907308n_real X3 tptp.top_top_set_real))) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real F B)) (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 B) A)) K))))) (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 ((H2 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) H2)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real H2) 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) H2))) (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 ((H2 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) H2)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real H2) 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) H2)))))))))))) (forall ((A tptp.real) (B tptp.real) (X tptp.real) (Y4 tptp.real) (F tptp.fun_real_real)) (let ((_let_1 (tptp.set_or1633881224788618240n_real A B))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B)) (=> (tptp.member_real X _let_1) (=> (tptp.member_real Y4 _let_1) (=> (forall ((X3 tptp.real)) (=> (tptp.member_real X3 (tptp.set_or1633881224788618240n_real A B)) (tptp.has_fi5821293074295781190e_real F tptp.zero_zero_real (tptp.topolo2177554685111907308n_real X3 tptp.top_top_set_real)))) (= (tptp.aa_real_real F X) (tptp.aa_real_real F Y4)))))))) (forall ((A tptp.real) (B tptp.real) (F tptp.fun_real_real) (F2 tptp.fun_real_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B)) (=> (forall ((X3 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) X3)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X3) B)) (tptp.has_fi5821293074295781190e_real F (tptp.aa_real_real F2 X3) (tptp.topolo2177554685111907308n_real X3 tptp.top_top_set_real))))) (exists ((Z2 tptp.real)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) Z2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Z2) B)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real F B)) (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 B) A)) (tptp.aa_real_real F2 Z2)))))))) (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 ((Y 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) Y))) D)) (= (tptp.aa_real_real F X) (tptp.aa_real_real F Y)))) (= 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) (B 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 B)) (=> (forall ((X3 tptp.real)) (tptp.has_fi5821293074295781190e_real V K (tptp.topolo2177554685111907308n_real X3 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) B)) _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 B))) _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 ((Y 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) Y))) 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 Y))))) (= 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 ((Y 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) Y))) D)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real F Y)) (tptp.aa_real_real F X))))) (= 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) (S2 tptp.set_real)) (tptp.has_fi5821293074295781190e_real (tptp.aa_nat_fun_real_real tptp.aTP_Lamm_en 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 S2))) (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_eo 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) (R2 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_ep R2) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real R2) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.powr_real Z) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real R2) tptp.one_one_real))) (tptp.topolo2177554685111907308n_real Z tptp.top_top_set_real)))) (forall ((F tptp.fun_re4238438383274954274t_real) (F2 tptp.fun_re4238438383274954274t_real) (X0 tptp.real) (A tptp.real) (B tptp.real) (L4 tptp.fun_nat_real)) (let ((_let_1 (tptp.aa_real_fun_nat_real F2 X0))) (=> (forall ((N2 tptp.nat)) (tptp.has_fi5821293074295781190e_real (tptp.aa_nat_fun_real_real (tptp.aTP_Lamm_eq F) N2) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real F2 X0) N2) (tptp.topolo2177554685111907308n_real X0 tptp.top_top_set_real))) (=> (forall ((X3 tptp.real)) (=> (tptp.member_real X3 (tptp.set_or1633881224788618240n_real A B)) (tptp.summable_real (tptp.aa_real_fun_nat_real F X3)))) (=> (tptp.member_real X0 (tptp.set_or1633881224788618240n_real A B)) (=> (tptp.summable_real _let_1) (=> (tptp.summable_real L4) (=> (forall ((N2 tptp.nat) (X3 tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.set_or1633881224788618240n_real A B))) (=> (tptp.member_real X3 _let_1) (=> (tptp.member_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 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real F X3) N2)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real F Y) N2)))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real L4 N2)) (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real X3) Y))))))))) (tptp.has_fi5821293074295781190e_real (tptp.aTP_Lamm_er F) (tptp.suminf_real _let_1) (tptp.topolo2177554685111907308n_real X0 tptp.top_top_set_real)))))))))) (forall ((X tptp.real) (B 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 B) (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 B)) X)) (tptp.topolo2177554685111907308n_real X tptp.top_top_set_real)))) (forall ((G tptp.fun_real_real) (M tptp.real) (X tptp.real) (R2 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_es G) R2) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real R2) (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 R2) (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) (R2 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 R2 _let_1) (tptp.has_fi5821293074295781190e_real (tptp.aa_fun6946558556880649704l_real (tptp.aTP_Lamm_et 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 R2) (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) (A2 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 A2)))) (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) (A2 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 A2))) (forall ((X tptp.real) (D3 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)) (= D3 (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)) (= D3 (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 D3 (tptp.topolo2177554685111907308n_real X tptp.top_top_set_real)))))))) (forall ((X tptp.real) (A2 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 A2)))) (forall ((R tptp.real) (F tptp.fun_nat_real) (X0 tptp.real)) (=> (forall ((X3 tptp.real)) (=> (tptp.member_real X3 (tptp.set_or1633881224788618240n_real (tptp.aa_real_real tptp.uminus_uminus_real R) R)) (tptp.summable_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_eu F) X3)))) (=> (tptp.member_real X0 (tptp.set_or1633881224788618240n_real (tptp.aa_real_real tptp.uminus_uminus_real R) R)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) R)) (tptp.has_fi5821293074295781190e_real (tptp.aTP_Lamm_ew F) (tptp.suminf_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_eu F) X0)) (tptp.topolo2177554685111907308n_real X0 tptp.top_top_set_real)))))) (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)) (=> (and (= (tptp.aa_nat_fun_real_real Diff tptp.zero_zero_nat) F) (forall ((M4 tptp.nat) (X3 tptp.real)) (tptp.has_fi5821293074295781190e_real (tptp.aa_nat_fun_real_real Diff M4) (tptp.aa_real_real (tptp.aa_nat_fun_real_real Diff (tptp.aa_nat_nat tptp.suc M4)) X3) (tptp.topolo2177554685111907308n_real X3 tptp.top_top_set_real)))) (exists ((T3 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 T3)) (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.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_ex 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) T3)) (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)) (=> (= (tptp.aa_nat_fun_real_real Diff tptp.zero_zero_nat) F) (=> (forall ((M4 tptp.nat) (X3 tptp.real)) (tptp.has_fi5821293074295781190e_real (tptp.aa_nat_fun_real_real Diff M4) (tptp.aa_real_real (tptp.aa_nat_fun_real_real Diff (tptp.aa_nat_nat tptp.suc M4)) X3) (tptp.topolo2177554685111907308n_real X3 tptp.top_top_set_real))) (exists ((T3 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 T3)) (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.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_ex 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) T3)) (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 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 ((M4 tptp.nat) (T3 tptp.real)) (=> (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M4) N)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real H) T3)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real T3) tptp.zero_zero_real))) (tptp.has_fi5821293074295781190e_real (tptp.aa_nat_fun_real_real Diff M4) (tptp.aa_real_real (tptp.aa_nat_fun_real_real Diff (tptp.aa_nat_nat tptp.suc M4)) T3) (tptp.topolo2177554685111907308n_real T3 tptp.top_top_set_real)))) (exists ((T3 tptp.real)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real H) T3)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real T3) tptp.zero_zero_real)) (= (tptp.aa_real_real F H) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aa_fun1113820866546176217t_real (tptp.aTP_Lamm_ey 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) T3)) (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 ((M4 tptp.nat) (T3 tptp.real)) (=> (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M4) N)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) T3)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real T3) H))) (tptp.has_fi5821293074295781190e_real (tptp.aa_nat_fun_real_real Diff M4) (tptp.aa_real_real (tptp.aa_nat_fun_real_real Diff (tptp.aa_nat_nat tptp.suc M4)) T3) (tptp.topolo2177554685111907308n_real T3 tptp.top_top_set_real)))) (exists ((T3 tptp.real)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) T3)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real T3) H)) (= (tptp.aa_real_real F H) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aa_fun1113820866546176217t_real (tptp.aTP_Lamm_ey 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) T3)) (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 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 ((M4 tptp.nat) (T3 tptp.real)) (=> (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M4) N)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) T3)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real T3) H))) (tptp.has_fi5821293074295781190e_real (tptp.aa_nat_fun_real_real Diff M4) (tptp.aa_real_real (tptp.aa_nat_fun_real_real Diff (tptp.aa_nat_nat tptp.suc M4)) T3) (tptp.topolo2177554685111907308n_real T3 tptp.top_top_set_real)))) (exists ((T3 tptp.real)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) T3)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real T3) H)) (= (tptp.aa_real_real F H) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aa_fun1113820866546176217t_real (tptp.aTP_Lamm_ey 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) T3)) (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 ((M4 tptp.nat) (X3 tptp.real)) (tptp.has_fi5821293074295781190e_real (tptp.aa_nat_fun_real_real Diff M4) (tptp.aa_real_real (tptp.aa_nat_fun_real_real Diff (tptp.aa_nat_nat tptp.suc M4)) X3) (tptp.topolo2177554685111907308n_real X3 tptp.top_top_set_real))) (exists ((T3 tptp.real)) (let ((_let_1 (tptp.aa_real_real tptp.abs_abs_real T3))) (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.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_ex 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) T3)) (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 ((M4 tptp.nat) (T3 tptp.real)) (=> (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M4) N)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real T3)) (tptp.aa_real_real tptp.abs_abs_real X)))) (tptp.has_fi5821293074295781190e_real (tptp.aa_nat_fun_real_real Diff M4) (tptp.aa_real_real (tptp.aa_nat_fun_real_real Diff (tptp.aa_nat_nat tptp.suc M4)) T3) (tptp.topolo2177554685111907308n_real T3 tptp.top_top_set_real)))) (exists ((T3 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 T3)) (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.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_ex 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) T3)) (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) (B 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 ((M4 tptp.nat) (T3 tptp.real)) (=> (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M4) N)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) T3)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real T3) B))) (tptp.has_fi5821293074295781190e_real (tptp.aa_nat_fun_real_real Diff M4) (tptp.aa_real_real (tptp.aa_nat_fun_real_real Diff (tptp.aa_nat_nat tptp.suc M4)) T3) (tptp.topolo2177554685111907308n_real T3 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) B)) (exists ((T3 tptp.real)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) T3)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real T3) C)) (= (tptp.aa_real_real F A) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real (tptp.aa_rea7841385751566875788t_real (tptp.aTP_Lamm_ez 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) T3)) (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) (Diff tptp.fun_na6724076748692969250l_real) (F tptp.fun_real_real) (A tptp.real) (B 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 ((M4 tptp.nat) (T3 tptp.real)) (=> (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M4) N)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) T3)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real T3) B))) (tptp.has_fi5821293074295781190e_real (tptp.aa_nat_fun_real_real Diff M4) (tptp.aa_real_real (tptp.aa_nat_fun_real_real Diff (tptp.aa_nat_nat tptp.suc M4)) T3) (tptp.topolo2177554685111907308n_real T3 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) B)) (exists ((T3 tptp.real)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real C) T3)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real T3) B)) (= (tptp.aa_real_real F B) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real (tptp.aa_rea7841385751566875788t_real (tptp.aTP_Lamm_ez Diff) B) 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) T3)) (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 B) C)) N)))))))))))) (forall ((N tptp.nat) (Diff tptp.fun_na6724076748692969250l_real) (F tptp.fun_real_real) (A tptp.real) (B 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 ((M4 tptp.nat) (T3 tptp.real)) (=> (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M4) N)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) T3)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real T3) B))) (tptp.has_fi5821293074295781190e_real (tptp.aa_nat_fun_real_real Diff M4) (tptp.aa_real_real (tptp.aa_nat_fun_real_real Diff (tptp.aa_nat_nat tptp.suc M4)) T3) (tptp.topolo2177554685111907308n_real T3 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) B)) (=> (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) B)) (=> (not (= X C)) (exists ((T3 tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real T3))) (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 T3)) (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) T3)) (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.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real (tptp.aa_rea7841385751566875788t_real (tptp.aTP_Lamm_fa 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) T3)) (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) (H tptp.real) (Diff tptp.fun_na6724076748692969250l_real) (K tptp.nat) (B3 tptp.real)) (=> (forall ((M4 tptp.nat) (T3 tptp.real)) (=> (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M4) N)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) T3)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real T3) H))) (tptp.has_fi5821293074295781190e_real (tptp.aa_nat_fun_real_real Diff M4) (tptp.aa_real_real (tptp.aa_nat_fun_real_real Diff (tptp.aa_nat_nat tptp.suc M4)) T3) (tptp.topolo2177554685111907308n_real T3 tptp.top_top_set_real)))) (=> (= N (tptp.aa_nat_nat tptp.suc K)) (forall ((M2 tptp.nat) (T4 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) 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 (tptp.aa_rea1103652080130114956l_real (tptp.aa_fun2567993205388704171l_real (tptp.aTP_Lamm_fc N) Diff) B3) 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) T4)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real (tptp.aa_nat1308781354268537904t_real (tptp.aTP_Lamm_fd Diff) M2) T4)) (tptp.set_ord_lessThan_nat _let_2))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real B3) (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 T4) _let_2)) (tptp.aa_nat_real tptp.semiri2265585572941072030t_real _let_2))))) (tptp.topolo2177554685111907308n_real T4 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_fe (tptp.suminf_real (tptp.aa_real_fun_nat_real tptp.aTP_Lamm_ff X)) (tptp.topolo2177554685111907308n_real X tptp.top_top_set_real)))) (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 ((A tptp.real) (B tptp.real) (F tptp.fun_real_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) B)) (=> (forall ((X3 tptp.real)) (=> (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) X3)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X3) B))) (tptp.topolo4422821103128117721l_real (tptp.topolo2177554685111907308n_real X3 tptp.top_top_set_real) F))) (exists ((L5 tptp.real) (M8 tptp.real)) (and (forall ((X4 tptp.real)) (let ((_let_1 (tptp.aa_real_real F X4))) (=> (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) B))) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real L5) _let_1)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real _let_1) M8)))))) (forall ((Y3 tptp.real)) (=> (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real L5) Y3)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y3) M8))) (exists ((X3 tptp.real)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) X3)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X3) B)) (= (tptp.aa_real_real F X3) Y3)))))))))) (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 ((X4 tptp.real)) (=> (and (not (= X4 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) X4))) R3))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real F X4)) 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 ((X4 tptp.real)) (=> (and (not (= X4 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) X4))) R3))) (not (= (tptp.aa_real_real F X4) 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 ((X4 tptp.real)) (=> (and (not (= X4 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) X4))) R3))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) (tptp.aa_real_real F X4)))))))))) (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) (B 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) B)) (=> (forall ((Z2 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) Z2)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Z2) B)) (= (tptp.aa_real_real G (tptp.aa_real_real F Z2)) Z2)))) (=> (forall ((Z2 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) Z2)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Z2) B)) (tptp.topolo4422821103128117721l_real (tptp.topolo2177554685111907308n_real Z2 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)) (=> (not (= X tptp.zero_zero_real)) (tptp.topolo4422821103128117721l_real (tptp.topolo2177554685111907308n_real X tptp.top_top_set_real) tptp.ln_ln_real))) (tptp.filterlim_real_real tptp.aTP_Lamm_fg _let_43 (tptp.topolo2177554685111907308n_real _let_42 tptp.top_top_set_real)) (forall ((F tptp.fun_real_real) (D3 tptp.real) (G tptp.fun_real_real) (X tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (tptp.topolo2177554685111907308n_real X tptp.top_top_set_real))) (=> (tptp.has_fi5821293074295781190e_real F D3 (tptp.topolo2177554685111907308n_real (tptp.aa_real_real G X) tptp.top_top_set_real)) (=> (not (= D3 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) B)) (=> (forall ((Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) Y)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y) B)) (= (tptp.aa_real_real F (tptp.aa_real_real G Y)) Y)))) (=> (tptp.topolo4422821103128117721l_real _let_1 G) (tptp.has_fi5821293074295781190e_real G (tptp.aa_real_real tptp.inverse_inverse_real D3) _let_1))))))))) (forall ((B tptp.real) (X tptp.real) (F tptp.fun_real_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B) X)) (=> (forall ((X3 tptp.real)) (=> (tptp.member_real X3 (tptp.set_or1633881224788618240n_real B 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 X3))))) (=> (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 ((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 ((Z2 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 Z2) X))) D)) (= (tptp.aa_real_real G (tptp.aa_real_real F Z2)) Z2))) (=> (forall ((Z2 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 Z2) X))) D)) (tptp.topolo4422821103128117721l_real (tptp.topolo2177554685111907308n_real Z2 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) (B tptp.real) (F tptp.fun_real_real) (G tptp.fun_real_real) (G2 tptp.fun_real_real) (F2 tptp.fun_real_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B)) (=> (forall ((Z2 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) Z2)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Z2) B)) (tptp.topolo4422821103128117721l_real (tptp.topolo2177554685111907308n_real Z2 tptp.top_top_set_real) F)))) (=> (forall ((Z2 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) Z2)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Z2) B)) (tptp.topolo4422821103128117721l_real (tptp.topolo2177554685111907308n_real Z2 tptp.top_top_set_real) G)))) (=> (forall ((Z2 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) Z2)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Z2) B)) (tptp.has_fi5821293074295781190e_real G (tptp.aa_real_real G2 Z2) (tptp.topolo2177554685111907308n_real Z2 tptp.top_top_set_real))))) (=> (forall ((Z2 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) Z2)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Z2) B)) (tptp.has_fi5821293074295781190e_real F (tptp.aa_real_real F2 Z2) (tptp.topolo2177554685111907308n_real Z2 tptp.top_top_set_real))))) (exists ((C3 tptp.real)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) C3)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real C3) B)) (= (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 B)) (tptp.aa_real_real F A))) (tptp.aa_real_real G2 C3)) (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 B)) (tptp.aa_real_real G A))) (tptp.aa_real_real F2 C3))))))))))) (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 ((N6 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))) N6))) (let ((_let_2 (tptp.aTP_Lamm_fh A))) (let ((_let_3 (tptp.groups6591440286371151544t_real _let_2))) (tptp.member_real (tptp.suminf_real _let_2) (tptp.set_or1222579329274155063t_real (tptp.aa_set_nat_real _let_3 (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.aa_set_nat_real _let_3 (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 ((N6 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))) N6))) (let ((_let_2 (tptp.aTP_Lamm_fh A))) (let ((_let_3 (tptp.groups6591440286371151544t_real _let_2))) (tptp.member_real (tptp.suminf_real _let_2) (tptp.set_or1222579329274155063t_real (tptp.aa_set_nat_real _let_3 (tptp.set_ord_lessThan_nat _let_1)) (tptp.aa_set_nat_real _let_3 (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.filterlim_nat_nat tptp.suc 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.aTP_Lamm_fi 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.times_times_nat C) tptp.at_top_nat tptp.at_top_nat))) (forall ((X7 tptp.fun_nat_real) (B3 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))) B3))) (not (forall ((L5 tptp.real)) (not (tptp.filterlim_nat_real X7 (tptp.topolo2815343760600316023s_real L5) tptp.at_top_nat))))))) (tptp.filterlim_nat_real tptp.aTP_Lamm_fj (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_fk F) G) (tptp.topolo2815343760600316023s_real tptp.zero_zero_real) tptp.at_top_nat) (exists ((L2 tptp.real)) (let ((_let_1 (tptp.topolo2815343760600316023s_real L2))) (and (forall ((N6 tptp.nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_nat_real F N6)) L2))) (tptp.filterlim_nat_real F _let_1 tptp.at_top_nat) (forall ((N6 tptp.nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real L2) (tptp.aa_nat_real G N6)))) (tptp.filterlim_nat_real G _let_1 tptp.at_top_nat))))))))) (forall ((X7 tptp.fun_nat_real)) (=> (forall ((R3 tptp.real)) (exists ((N7 tptp.nat)) (forall ((N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N7) 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_fl X7) (tptp.topolo2815343760600316023s_real tptp.zero_zero_real) tptp.at_top_nat))) (tptp.filterlim_nat_real tptp.aTP_Lamm_fm _let_43 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_fn C) (tptp.topolo2815343760600316023s_real tptp.one_one_real) tptp.at_top_nat))) (tptp.filterlim_nat_real tptp.aTP_Lamm_fo _let_43 tptp.at_top_nat) (forall ((R2 tptp.real)) (tptp.filterlim_nat_real (tptp.aa_real_fun_nat_real tptp.aTP_Lamm_fp R2) (tptp.topolo2815343760600316023s_real R2) 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 ((E tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) E)) (exists ((N6 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 N6)) E)))))) (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_fq 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_fr X) (tptp.topolo2815343760600316023s_real tptp.zero_zero_real) tptp.at_top_nat))) (forall ((R2 tptp.real)) (tptp.filterlim_nat_real (tptp.aa_real_fun_nat_real tptp.aTP_Lamm_fs R2) (tptp.topolo2815343760600316023s_real R2) tptp.at_top_nat)) (forall ((X tptp.real)) (tptp.filterlim_nat_real (tptp.aa_real_fun_nat_real tptp.aTP_Lamm_ft X) (tptp.topolo2815343760600316023s_real (tptp.aa_real_real tptp.exp_real X)) tptp.at_top_nat)) (forall ((R2 tptp.real)) (tptp.filterlim_nat_real (tptp.aa_real_fun_nat_real tptp.aTP_Lamm_fu R2) (tptp.topolo2815343760600316023s_real R2) 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_fh 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_fh A)))))) (forall ((Theta tptp.fun_nat_real) (Theta2 tptp.real)) (=> (tptp.filterlim_nat_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_fv Theta) Theta2) (tptp.topolo2815343760600316023s_real tptp.one_one_real) tptp.at_top_nat) (not (forall ((K2 tptp.fun_nat_int)) (not (tptp.filterlim_nat_real (tptp.aa_fun4551936527957760560t_real (tptp.aTP_Lamm_fw Theta) K2) (tptp.topolo2815343760600316023s_real Theta2) tptp.at_top_nat)))))) (forall ((Theta tptp.fun_nat_real)) (=> (tptp.filterlim_nat_real (tptp.aTP_Lamm_fx Theta) (tptp.topolo2815343760600316023s_real tptp.one_one_real) tptp.at_top_nat) (exists ((K2 tptp.fun_nat_int)) (tptp.filterlim_nat_real (tptp.aa_fun4551936527957760560t_real (tptp.aTP_Lamm_fw Theta) K2) (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_fy A) (tptp.topolo2815343760600316023s_real (tptp.suminf_real (tptp.aTP_Lamm_fh 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_ag 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_fh 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.aa_set_nat_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_fy A) (tptp.topolo2815343760600316023s_real (tptp.suminf_real (tptp.aTP_Lamm_fh 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 ((L2 tptp.real)) (let ((_let_1 (tptp.topolo2815343760600316023s_real L2))) (and (forall ((N6 tptp.nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aTP_Lamm_fh 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))) N6)))) L2))) (tptp.filterlim_nat_real (tptp.aTP_Lamm_fy A) _let_1 tptp.at_top_nat) (forall ((N6 tptp.nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real L2) (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aTP_Lamm_fh 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))) N6)) tptp.one_one_nat)))))) (tptp.filterlim_nat_real (tptp.aTP_Lamm_fz 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_fz A) (tptp.topolo2815343760600316023s_real (tptp.suminf_real (tptp.aTP_Lamm_fh 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_fz A) (tptp.topolo2815343760600316023s_real (tptp.suminf_real (tptp.aTP_Lamm_fh A))) tptp.at_top_nat))))) (forall ((A tptp.fun_nat_real) (N tptp.nat)) (let ((_let_1 (tptp.aTP_Lamm_fh 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.aa_set_nat_real (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 ((F tptp.fun_real_real)) (= (tptp.real_V5970128139526366754l_real F) (exists ((C5 tptp.real)) (forall ((X5 tptp.real)) (= (tptp.aa_real_real F X5) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real X5) C5)))))) (tptp.filterlim_real_real tptp.arctan (tptp.topolo2815343760600316023s_real _let_45) tptp.at_bot_real) (forall ((X tptp.real) (Y4 tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.real_V975177566351809787t_real X) Y4) (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real X) Y4)))) (forall ((X tptp.complex) (Y4 tptp.complex)) (= (tptp.aa_complex_real (tptp.real_V3694042436643373181omplex X) Y4) (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.minus_minus_complex X Y4)))) (tptp.filterlim_real_real tptp.exp_real _let_43 tptp.at_bot_real) (tptp.filterlim_real_real tptp.inverse_inverse_real tptp.at_bot_real (tptp.topolo2177554685111907308n_real tptp.zero_zero_real (tptp.set_or5984915006950818249n_real tptp.zero_zero_real))) (forall ((B tptp.real) (F tptp.fun_real_real) (Flim tptp.real)) (=> (forall ((X3 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X3) B)) (exists ((Y3 tptp.real)) (and (tptp.has_fi5821293074295781190e_real F Y3 (tptp.topolo2177554685111907308n_real X3 tptp.top_top_set_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) Y3)))))) (=> (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 B)))))) (forall ((N tptp.nat) (F tptp.fun_real_real) (F3 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 F3) (=> (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_ga N) F) tptp.at_bot_real F3))))) (forall ((X tptp.real)) (tptp.filterlim_real_real (tptp.aa_rea7340605660300375871l_real tptp.aTP_Lamm_gb 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.ln_ln_real tptp.at_bot_real _let_12) (tptp.filterlim_real_real tptp.arcosh_real _let_43 (tptp.topolo2177554685111907308n_real tptp.one_one_real (tptp.set_or5849166863359141190n_real tptp.one_one_real))) (tptp.filterlim_real_real tptp.tan_real tptp.at_bot_real (tptp.topolo2177554685111907308n_real _let_45 (tptp.set_or5849166863359141190n_real _let_45))) (= (tptp.set_ord_atLeast_nat tptp.zero_zero_nat) tptp.top_top_set_nat) (forall ((K tptp.nat)) (= (tptp.set_ord_atLeast_nat (tptp.aa_nat_nat tptp.suc K)) (tptp.set_or1210151606488870762an_nat K))) (= (tptp.set_or1210151606488870762an_nat tptp.zero_zero_nat) _let_44) (forall ((K tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc K))) (= (tptp.set_or1210151606488870762an_nat _let_1) (tptp.minus_minus_set_nat (tptp.set_or1210151606488870762an_nat K) (tptp.insert_nat _let_1 tptp.bot_bot_set_nat))))) (forall ((K tptp.nat)) (= (tptp.set_ord_atLeast_nat (tptp.aa_nat_nat tptp.suc K)) (tptp.minus_minus_set_nat (tptp.set_ord_atLeast_nat K) (tptp.insert_nat K tptp.bot_bot_set_nat)))) (forall ((N tptp.nat) (F tptp.fun_real_real) (F3 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 F3) (=> (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_ga N) F) tptp.at_top_real F3))))) (tptp.filterlim_real_real tptp.tan_real tptp.at_top_real (tptp.topolo2177554685111907308n_real _let_42 (tptp.set_or5984915006950818249n_real _let_42))) (tptp.filterlim_real_real tptp.sqrt tptp.at_top_real tptp.at_top_real) (tptp.filterlim_nat_real tptp.semiri5074537144036343181t_real tptp.at_top_real tptp.at_top_nat) (tptp.filterlim_real_real tptp.aTP_Lamm_gc _let_43 tptp.at_top_real) (tptp.filterlim_real_real tptp.inverse_inverse_real _let_12 tptp.at_top_real) (tptp.filterlim_real_real tptp.inverse_inverse_real tptp.at_top_real _let_12) (forall ((K tptp.nat)) (tptp.filterlim_real_real (tptp.aa_nat_fun_real_real tptp.aTP_Lamm_gd K) (tptp.topolo2815343760600316023s_real tptp.zero_zero_real) tptp.at_top_real)) (forall ((X tptp.real)) (tptp.filterlim_real_real (tptp.aa_rea7340605660300375871l_real tptp.aTP_Lamm_ge X) (tptp.topolo2815343760600316023s_real (tptp.aa_real_real tptp.exp_real X)) tptp.at_top_real)) (forall ((B tptp.real) (F tptp.fun_real_real) (Flim tptp.real)) (=> (forall ((X3 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real B) X3)) (exists ((Y3 tptp.real)) (and (tptp.has_fi5821293074295781190e_real F Y3 (tptp.topolo2177554685111907308n_real X3 tptp.top_top_set_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y3) 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 B)))))) (tptp.filterlim_real_real tptp.arctan (tptp.topolo2815343760600316023s_real _let_42) tptp.at_top_real) (forall ((G tptp.fun_real_real) (X tptp.real) (G2 tptp.fun_real_real) (F tptp.fun_real_real) (F2 tptp.fun_real_real) (Y4 tptp.real)) (let ((_let_1 (tptp.topolo2177554685111907308n_real X (tptp.set_or5984915006950818249n_real X)))) (let ((_let_2 (tptp.topolo2815343760600316023s_real Y4))) (=> (tptp.filterlim_real_real G tptp.at_top_real _let_1) (=> (tptp.eventually_real (tptp.aTP_Lamm_gf G2) _let_1) (=> (tptp.eventually_real (tptp.aa_fun9137271176455094897l_bool (tptp.aTP_Lamm_gg F) F2) _let_1) (=> (tptp.eventually_real (tptp.aa_fun9137271176455094897l_bool (tptp.aTP_Lamm_gg G) G2) _let_1) (=> (tptp.filterlim_real_real (tptp.aa_fun6946558556880649704l_real (tptp.aTP_Lamm_gh G2) F2) _let_2 _let_1) (tptp.filterlim_real_real (tptp.aa_fun6946558556880649704l_real (tptp.aTP_Lamm_gh G) F) _let_2 _let_1))))))))) (tptp.ord_le4104064031414453916r_real tptp.at_top_real tptp.at_infinity_real) (tptp.ord_le4104064031414453916r_real tptp.at_bot_real tptp.at_infinity_real) (tptp.filterlim_nat_real tptp.semiri5074537144036343181t_real tptp.at_infinity_real tptp.at_top_nat) (forall ((P tptp.fun_real_bool) (A tptp.real)) (= (tptp.eventually_real P (tptp.topolo2177554685111907308n_real A (tptp.set_or5849166863359141190n_real A))) (tptp.eventually_real (tptp.aa_rea7809428808904475482l_bool (tptp.aTP_Lamm_gi P) A) (tptp.topolo2177554685111907308n_real tptp.zero_zero_real (tptp.set_or5849166863359141190n_real tptp.zero_zero_real))))) (forall ((P tptp.fun_real_bool)) (= (tptp.eventually_real P tptp.at_top_real) (tptp.eventually_real (tptp.aTP_Lamm_gj P) (tptp.topolo2177554685111907308n_real tptp.zero_zero_real (tptp.set_or5849166863359141190n_real tptp.zero_zero_real))))) (forall ((P tptp.fun_real_bool)) (= (tptp.eventually_real P (tptp.topolo2177554685111907308n_real tptp.zero_zero_real (tptp.set_or5849166863359141190n_real tptp.zero_zero_real))) (tptp.eventually_real (tptp.aTP_Lamm_gj P) tptp.at_top_real))) (forall ((F tptp.fun_real_real) (A tptp.real) (G tptp.fun_real_real) (F2 tptp.fun_real_real) (G2 tptp.fun_real_real)) (let ((_let_1 (tptp.topolo2177554685111907308n_real A tptp.top_top_set_real))) (=> (tptp.filterlim_real_real F tptp.at_top_real _let_1) (=> (tptp.filterlim_real_real G tptp.at_top_real _let_1) (=> (tptp.eventually_real (tptp.aa_fun9137271176455094897l_bool (tptp.aTP_Lamm_gg F) F2) _let_1) (=> (tptp.eventually_real (tptp.aa_fun9137271176455094897l_bool (tptp.aTP_Lamm_gg G) G2) _let_1) (=> (tptp.filterlim_real_real (tptp.aa_fun6946558556880649704l_real (tptp.aTP_Lamm_gk F2) G2) tptp.at_top_real _let_1) (tptp.filterlim_real_real (tptp.aa_fun6946558556880649704l_real (tptp.aTP_Lamm_gk F) G) tptp.at_top_real _let_1)))))))) (forall ((F tptp.fun_real_real) (X tptp.real) (G tptp.fun_real_real) (G2 tptp.fun_real_real) (F2 tptp.fun_real_real) (F3 tptp.filter_real)) (let ((_let_1 (tptp.topolo2177554685111907308n_real X tptp.top_top_set_real))) (let ((_let_2 (tptp.topolo2815343760600316023s_real tptp.zero_zero_real))) (=> (tptp.filterlim_real_real F _let_2 _let_1) (=> (tptp.filterlim_real_real G _let_2 _let_1) (=> (tptp.eventually_real (tptp.aTP_Lamm_gf G) _let_1) (=> (tptp.eventually_real (tptp.aTP_Lamm_gf G2) _let_1) (=> (tptp.eventually_real (tptp.aa_fun9137271176455094897l_bool (tptp.aTP_Lamm_gg F) F2) _let_1) (=> (tptp.eventually_real (tptp.aa_fun9137271176455094897l_bool (tptp.aTP_Lamm_gg G) G2) _let_1) (=> (tptp.filterlim_real_real (tptp.aa_fun6946558556880649704l_real (tptp.aTP_Lamm_gh G2) F2) F3 _let_1) (tptp.filterlim_real_real (tptp.aa_fun6946558556880649704l_real (tptp.aTP_Lamm_gk F) G) F3 _let_1))))))))))) (forall ((F tptp.fun_real_real) (A tptp.real) (G tptp.fun_real_real) (F2 tptp.fun_real_real) (G2 tptp.fun_real_real)) (let ((_let_1 (tptp.topolo2177554685111907308n_real A (tptp.set_or5849166863359141190n_real A)))) (=> (tptp.filterlim_real_real F tptp.at_top_real _let_1) (=> (tptp.filterlim_real_real G tptp.at_top_real _let_1) (=> (tptp.eventually_real (tptp.aa_fun9137271176455094897l_bool (tptp.aTP_Lamm_gg F) F2) _let_1) (=> (tptp.eventually_real (tptp.aa_fun9137271176455094897l_bool (tptp.aTP_Lamm_gg G) G2) _let_1) (=> (tptp.filterlim_real_real (tptp.aa_fun6946558556880649704l_real (tptp.aTP_Lamm_gk F2) G2) tptp.at_top_real _let_1) (tptp.filterlim_real_real (tptp.aa_fun6946558556880649704l_real (tptp.aTP_Lamm_gk F) G) tptp.at_top_real _let_1)))))))) (forall ((F tptp.fun_real_real) (A tptp.real) (G tptp.fun_real_real) (F2 tptp.fun_real_real) (G2 tptp.fun_real_real)) (let ((_let_1 (tptp.topolo2177554685111907308n_real A tptp.top_top_set_real))) (=> (tptp.filterlim_real_real F tptp.at_top_real _let_1) (=> (tptp.filterlim_real_real G tptp.at_bot_real _let_1) (=> (tptp.eventually_real (tptp.aa_fun9137271176455094897l_bool (tptp.aTP_Lamm_gg F) F2) _let_1) (=> (tptp.eventually_real (tptp.aa_fun9137271176455094897l_bool (tptp.aTP_Lamm_gg G) G2) _let_1) (=> (tptp.filterlim_real_real (tptp.aa_fun6946558556880649704l_real (tptp.aTP_Lamm_gk F2) G2) tptp.at_bot_real _let_1) (tptp.filterlim_real_real (tptp.aa_fun6946558556880649704l_real (tptp.aTP_Lamm_gk F) G) tptp.at_bot_real _let_1)))))))) (forall ((F tptp.fun_real_real) (A tptp.real) (G tptp.fun_real_real) (F2 tptp.fun_real_real) (G2 tptp.fun_real_real)) (let ((_let_1 (tptp.topolo2177554685111907308n_real A (tptp.set_or5984915006950818249n_real A)))) (=> (tptp.filterlim_real_real F tptp.at_top_real _let_1) (=> (tptp.filterlim_real_real G tptp.at_top_real _let_1) (=> (tptp.eventually_real (tptp.aa_fun9137271176455094897l_bool (tptp.aTP_Lamm_gg F) F2) _let_1) (=> (tptp.eventually_real (tptp.aa_fun9137271176455094897l_bool (tptp.aTP_Lamm_gg G) G2) _let_1) (=> (tptp.filterlim_real_real (tptp.aa_fun6946558556880649704l_real (tptp.aTP_Lamm_gk F2) G2) tptp.at_top_real _let_1) (tptp.filterlim_real_real (tptp.aa_fun6946558556880649704l_real (tptp.aTP_Lamm_gk F) G) tptp.at_top_real _let_1)))))))) (forall ((G tptp.fun_real_real) (G2 tptp.fun_real_real) (F tptp.fun_real_real) (F2 tptp.fun_real_real) (X tptp.real)) (let ((_let_1 (tptp.topolo2815343760600316023s_real X))) (=> (tptp.filterlim_real_real G tptp.at_top_real tptp.at_top_real) (=> (tptp.eventually_real (tptp.aTP_Lamm_gf G2) tptp.at_top_real) (=> (tptp.eventually_real (tptp.aa_fun9137271176455094897l_bool (tptp.aTP_Lamm_gg F) F2) tptp.at_top_real) (=> (tptp.eventually_real (tptp.aa_fun9137271176455094897l_bool (tptp.aTP_Lamm_gg G) G2) tptp.at_top_real) (=> (tptp.filterlim_real_real (tptp.aa_fun6946558556880649704l_real (tptp.aTP_Lamm_gh G2) F2) _let_1 tptp.at_top_real) (tptp.filterlim_real_real (tptp.aa_fun6946558556880649704l_real (tptp.aTP_Lamm_gh G) F) _let_1 tptp.at_top_real)))))))) (forall ((G tptp.fun_real_real) (X tptp.real) (G2 tptp.fun_real_real) (F tptp.fun_real_real) (F2 tptp.fun_real_real) (Y4 tptp.real)) (let ((_let_1 (tptp.topolo2177554685111907308n_real X tptp.top_top_set_real))) (let ((_let_2 (tptp.topolo2815343760600316023s_real Y4))) (=> (tptp.filterlim_real_real G tptp.at_top_real _let_1) (=> (tptp.eventually_real (tptp.aTP_Lamm_gf G2) _let_1) (=> (tptp.eventually_real (tptp.aa_fun9137271176455094897l_bool (tptp.aTP_Lamm_gg F) F2) _let_1) (=> (tptp.eventually_real (tptp.aa_fun9137271176455094897l_bool (tptp.aTP_Lamm_gg G) G2) _let_1) (=> (tptp.filterlim_real_real (tptp.aa_fun6946558556880649704l_real (tptp.aTP_Lamm_gh G2) F2) _let_2 _let_1) (tptp.filterlim_real_real (tptp.aa_fun6946558556880649704l_real (tptp.aTP_Lamm_gh G) F) _let_2 _let_1))))))))) (forall ((F0 tptp.fun_real_real) (G0 tptp.fun_real_real) (G2 tptp.fun_real_real) (F2 tptp.fun_real_real) (F3 tptp.filter_real)) (let ((_let_1 (tptp.topolo2177554685111907308n_real tptp.zero_zero_real (tptp.set_or5849166863359141190n_real tptp.zero_zero_real)))) (let ((_let_2 (tptp.topolo2815343760600316023s_real tptp.zero_zero_real))) (=> (tptp.filterlim_real_real F0 _let_2 _let_1) (=> (tptp.filterlim_real_real G0 _let_2 _let_1) (=> (tptp.eventually_real (tptp.aTP_Lamm_gf G0) _let_1) (=> (tptp.eventually_real (tptp.aTP_Lamm_gf G2) _let_1) (=> (tptp.eventually_real (tptp.aa_fun9137271176455094897l_bool (tptp.aTP_Lamm_gg F0) F2) _let_1) (=> (tptp.eventually_real (tptp.aa_fun9137271176455094897l_bool (tptp.aTP_Lamm_gg G0) G2) _let_1) (=> (tptp.filterlim_real_real (tptp.aa_fun6946558556880649704l_real (tptp.aTP_Lamm_gh G2) F2) F3 _let_1) (tptp.filterlim_real_real (tptp.aa_fun6946558556880649704l_real (tptp.aTP_Lamm_gk F0) G0) F3 _let_1))))))))))) (forall ((F tptp.fun_real_real) (X tptp.real) (G tptp.fun_real_real) (G2 tptp.fun_real_real) (F2 tptp.fun_real_real) (F3 tptp.filter_real)) (let ((_let_1 (tptp.topolo2177554685111907308n_real X (tptp.set_or5849166863359141190n_real X)))) (let ((_let_2 (tptp.topolo2815343760600316023s_real tptp.zero_zero_real))) (=> (tptp.filterlim_real_real F _let_2 _let_1) (=> (tptp.filterlim_real_real G _let_2 _let_1) (=> (tptp.eventually_real (tptp.aTP_Lamm_gf G) _let_1) (=> (tptp.eventually_real (tptp.aTP_Lamm_gf G2) _let_1) (=> (tptp.eventually_real (tptp.aa_fun9137271176455094897l_bool (tptp.aTP_Lamm_gg F) F2) _let_1) (=> (tptp.eventually_real (tptp.aa_fun9137271176455094897l_bool (tptp.aTP_Lamm_gg G) G2) _let_1) (=> (tptp.filterlim_real_real (tptp.aa_fun6946558556880649704l_real (tptp.aTP_Lamm_gh G2) F2) F3 _let_1) (tptp.filterlim_real_real (tptp.aa_fun6946558556880649704l_real (tptp.aTP_Lamm_gk F) G) F3 _let_1))))))))))) (forall ((F tptp.fun_real_real) (X tptp.real) (G tptp.fun_real_real) (G2 tptp.fun_real_real) (F2 tptp.fun_real_real) (F3 tptp.filter_real)) (let ((_let_1 (tptp.topolo2177554685111907308n_real X (tptp.set_or5984915006950818249n_real X)))) (let ((_let_2 (tptp.topolo2815343760600316023s_real tptp.zero_zero_real))) (=> (tptp.filterlim_real_real F _let_2 _let_1) (=> (tptp.filterlim_real_real G _let_2 _let_1) (=> (tptp.eventually_real (tptp.aTP_Lamm_gf G) _let_1) (=> (tptp.eventually_real (tptp.aTP_Lamm_gf G2) _let_1) (=> (tptp.eventually_real (tptp.aa_fun9137271176455094897l_bool (tptp.aTP_Lamm_gg F) F2) _let_1) (=> (tptp.eventually_real (tptp.aa_fun9137271176455094897l_bool (tptp.aTP_Lamm_gg G) G2) _let_1) (=> (tptp.filterlim_real_real (tptp.aa_fun6946558556880649704l_real (tptp.aTP_Lamm_gh G2) F2) F3 _let_1) (tptp.filterlim_real_real (tptp.aa_fun6946558556880649704l_real (tptp.aTP_Lamm_gk F) G) F3 _let_1))))))))))) (forall ((F tptp.fun_real_real) (A tptp.real) (G tptp.fun_real_real) (F2 tptp.fun_real_real) (G2 tptp.fun_real_real)) (let ((_let_1 (tptp.topolo2177554685111907308n_real A (tptp.set_or5849166863359141190n_real A)))) (=> (tptp.filterlim_real_real F tptp.at_top_real _let_1) (=> (tptp.filterlim_real_real G tptp.at_bot_real _let_1) (=> (tptp.eventually_real (tptp.aa_fun9137271176455094897l_bool (tptp.aTP_Lamm_gg F) F2) _let_1) (=> (tptp.eventually_real (tptp.aa_fun9137271176455094897l_bool (tptp.aTP_Lamm_gg G) G2) _let_1) (=> (tptp.filterlim_real_real (tptp.aa_fun6946558556880649704l_real (tptp.aTP_Lamm_gk F2) G2) tptp.at_bot_real _let_1) (tptp.filterlim_real_real (tptp.aa_fun6946558556880649704l_real (tptp.aTP_Lamm_gk F) G) tptp.at_bot_real _let_1)))))))) (forall ((F tptp.fun_real_real) (A tptp.real) (G tptp.fun_real_real) (F2 tptp.fun_real_real) (G2 tptp.fun_real_real)) (let ((_let_1 (tptp.topolo2177554685111907308n_real A (tptp.set_or5984915006950818249n_real A)))) (=> (tptp.filterlim_real_real F tptp.at_top_real _let_1) (=> (tptp.filterlim_real_real G tptp.at_bot_real _let_1) (=> (tptp.eventually_real (tptp.aa_fun9137271176455094897l_bool (tptp.aTP_Lamm_gg F) F2) _let_1) (=> (tptp.eventually_real (tptp.aa_fun9137271176455094897l_bool (tptp.aTP_Lamm_gg G) G2) _let_1) (=> (tptp.filterlim_real_real (tptp.aa_fun6946558556880649704l_real (tptp.aTP_Lamm_gk F2) G2) tptp.at_bot_real _let_1) (tptp.filterlim_real_real (tptp.aa_fun6946558556880649704l_real (tptp.aTP_Lamm_gk F) G) tptp.at_bot_real _let_1)))))))) (forall ((G tptp.fun_real_real) (X tptp.real) (G2 tptp.fun_real_real) (F tptp.fun_real_real) (F2 tptp.fun_real_real) (Y4 tptp.real)) (let ((_let_1 (tptp.topolo2177554685111907308n_real X (tptp.set_or5849166863359141190n_real X)))) (let ((_let_2 (tptp.topolo2815343760600316023s_real Y4))) (=> (tptp.filterlim_real_real G tptp.at_top_real _let_1) (=> (tptp.eventually_real (tptp.aTP_Lamm_gf G2) _let_1) (=> (tptp.eventually_real (tptp.aa_fun9137271176455094897l_bool (tptp.aTP_Lamm_gg F) F2) _let_1) (=> (tptp.eventually_real (tptp.aa_fun9137271176455094897l_bool (tptp.aTP_Lamm_gg G) G2) _let_1) (=> (tptp.filterlim_real_real (tptp.aa_fun6946558556880649704l_real (tptp.aTP_Lamm_gh G2) F2) _let_2 _let_1) (tptp.filterlim_real_real (tptp.aa_fun6946558556880649704l_real (tptp.aTP_Lamm_gh G) F) _let_2 _let_1))))))))) (forall ((G tptp.fun_real_real) (G2 tptp.fun_real_real) (F tptp.fun_real_real) (F2 tptp.fun_real_real) (X tptp.real)) (let ((_let_1 (tptp.topolo2177554685111907308n_real tptp.zero_zero_real (tptp.set_or5849166863359141190n_real tptp.zero_zero_real)))) (let ((_let_2 (tptp.topolo2815343760600316023s_real X))) (=> (tptp.filterlim_real_real G tptp.at_top_real _let_1) (=> (tptp.eventually_real (tptp.aTP_Lamm_gf G2) _let_1) (=> (tptp.eventually_real (tptp.aa_fun9137271176455094897l_bool (tptp.aTP_Lamm_gg F) F2) _let_1) (=> (tptp.eventually_real (tptp.aa_fun9137271176455094897l_bool (tptp.aTP_Lamm_gg G) G2) _let_1) (=> (tptp.filterlim_real_real (tptp.aa_fun6946558556880649704l_real (tptp.aTP_Lamm_gh G2) F2) _let_2 _let_1) (tptp.filterlim_real_real (tptp.aa_fun6946558556880649704l_real (tptp.aTP_Lamm_gh G) F) _let_2 _let_1))))))))) (forall ((P tptp.fun_nat_bool)) (= (tptp.eventually_nat (tptp.aTP_Lamm_gl P) tptp.at_top_nat) (tptp.eventually_nat P tptp.at_top_nat))) (forall ((F3 tptp.filter_nat)) (= (tptp.ord_le2510731241096832064er_nat F3 tptp.at_top_nat) (forall ((N8 tptp.nat)) (tptp.eventually_nat (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N8) F3)))) (forall ((P tptp.fun_nat_bool)) (= (tptp.eventually_nat P tptp.at_top_nat) (exists ((N8 tptp.nat)) (forall ((N4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N8) N4)) (tptp.pp (tptp.aa_nat_bool P N4))))))) (forall ((C tptp.nat) (P tptp.fun_nat_bool)) (=> (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat C) X3)) (tptp.pp (tptp.aa_nat_bool P X3)))) (tptp.eventually_nat P tptp.at_top_nat))) (tptp.filterlim_nat_int tptp.semiri1314217659103216013at_int tptp.at_top_int tptp.at_top_nat) (forall ((F tptp.fun_nat_real) (A tptp.real) (B tptp.real)) (=> (tptp.ord_less_eq_set_real (tptp.image_nat_real F tptp.top_top_set_nat) (tptp.set_or1222579329274155063t_real A B)) (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 ((P tptp.fun_nat_bool) (K tptp.nat) (B tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool P K)) (=> (forall ((Y tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool P Y)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Y) B)))) (tptp.pp (tptp.aa_nat_bool P (tptp.order_Greatest_nat P)))))) (forall ((P tptp.fun_nat_bool) (K tptp.nat) (B tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool P K)) (=> (forall ((Y tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool P Y)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Y) B)))) (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) (B tptp.nat)) (=> (exists ((X_13 tptp.nat)) (tptp.pp (tptp.aa_nat_bool P X_13))) (=> (forall ((Y tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool P Y)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Y) B)))) (tptp.pp (tptp.aa_nat_bool P (tptp.order_Greatest_nat P)))))) (forall ((A tptp.real) (B 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) B)) (=> (forall ((X3 tptp.real)) (=> (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) X3)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X3) B))) (tptp.topolo4422821103128117721l_real (tptp.topolo2177554685111907308n_real X3 tptp.top_top_set_real) F))) (=> (forall ((X3 tptp.real)) (=> (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) X3)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X3) B))) (tptp.differ6690327859849518006l_real F (tptp.topolo2177554685111907308n_real X3 tptp.top_top_set_real)))) (=> (forall ((X3 tptp.real)) (=> (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) X3)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X3) B))) (tptp.topolo4422821103128117721l_real (tptp.topolo2177554685111907308n_real X3 tptp.top_top_set_real) G))) (=> (forall ((X3 tptp.real)) (=> (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) X3)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X3) B))) (tptp.differ6690327859849518006l_real G (tptp.topolo2177554685111907308n_real X3 tptp.top_top_set_real)))) (exists ((G_c tptp.real) (F_c tptp.real) (C3 tptp.real)) (let ((_let_1 (tptp.topolo2177554685111907308n_real C3 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) C3)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real C3) B)) (= (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 B)) (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 B)) (tptp.aa_real_real G A))) F_c))))))))))) (forall ((A tptp.real) (B tptp.real) (F tptp.fun_real_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B)) (=> (tptp.topolo5044208981011980120l_real (tptp.set_or1222579329274155063t_real A B) F) (=> (forall ((X3 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) X3)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X3) B)) (tptp.differ6690327859849518006l_real F (tptp.topolo2177554685111907308n_real X3 tptp.top_top_set_real))))) (exists ((L2 tptp.real) (Z2 tptp.real)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) Z2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Z2) B)) (tptp.has_fi5821293074295781190e_real F L2 (tptp.topolo2177554685111907308n_real Z2 tptp.top_top_set_real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real F B)) (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 B) A)) L2)))))))) (forall ((A2 tptp.set_real) (F tptp.fun_real_real)) (=> (tptp.topolo5044208981011980120l_real A2 F) (=> (forall ((X3 tptp.real)) (=> (tptp.member_real X3 A2) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.one_one_real) (tptp.aa_real_real F X3))))) (tptp.topolo5044208981011980120l_real A2 (tptp.aTP_Lamm_gm F))))) (forall ((A tptp.real) (B tptp.real) (F tptp.fun_real_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) B)) (=> (tptp.topolo5044208981011980120l_real (tptp.set_or1222579329274155063t_real A B) F) (exists ((C3 tptp.real) (D2 tptp.real)) (and (= (tptp.image_real_real F (tptp.set_or1222579329274155063t_real A B)) (tptp.set_or1222579329274155063t_real C3 D2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real C3) D2))))))) (forall ((A2 tptp.set_real)) (=> (tptp.ord_less_eq_set_real A2 (tptp.set_ord_atLeast_real tptp.one_one_real)) (tptp.topolo5044208981011980120l_real A2 tptp.arcosh_real))) (forall ((A tptp.real) (B tptp.real) (F tptp.fun_real_real) (F2 tptp.fun_re7681423839302404990l_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B)) (=> (= (tptp.aa_real_real F A) (tptp.aa_real_real F B)) (=> (tptp.topolo5044208981011980120l_real (tptp.set_or1222579329274155063t_real A B) F) (=> (forall ((X3 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) X3)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X3) B)) (tptp.has_de1759254742604945161l_real F (tptp.aa_rea7340605660300375871l_real F2 X3) (tptp.topolo2177554685111907308n_real X3 tptp.top_top_set_real))))) (exists ((Z2 tptp.real)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) Z2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Z2) B)) (forall ((X4 tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real F2 Z2) X4) tptp.zero_zero_real))))))))) (forall ((A tptp.real) (B tptp.real) (F tptp.fun_real_real) (F2 tptp.fun_re7681423839302404990l_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B)) (=> (tptp.topolo5044208981011980120l_real (tptp.set_or1222579329274155063t_real A B) F) (=> (forall ((X3 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) X3)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X3) B)) (tptp.has_de1759254742604945161l_real F (tptp.aa_rea7340605660300375871l_real F2 X3) (tptp.topolo2177554685111907308n_real X3 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) B)) (not (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real F B)) (tptp.aa_real_real F A)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real F2 Xi) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real B) A)))))))))))) (forall ((A tptp.real) (B tptp.real) (F tptp.fun_real_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B)) (=> (forall ((X3 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) X3)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X3) B)) (exists ((Y3 tptp.real)) (and (tptp.has_fi5821293074295781190e_real F Y3 (tptp.topolo2177554685111907308n_real X3 tptp.top_top_set_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) Y3))))))) (=> (tptp.topolo5044208981011980120l_real (tptp.set_or1222579329274155063t_real A B) 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 B))))))) (forall ((A tptp.real) (B tptp.real) (F tptp.fun_real_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B)) (=> (forall ((X3 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) X3)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X3) B)) (exists ((Y3 tptp.real)) (and (tptp.has_fi5821293074295781190e_real F Y3 (tptp.topolo2177554685111907308n_real X3 tptp.top_top_set_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y3) tptp.zero_zero_real))))))) (=> (tptp.topolo5044208981011980120l_real (tptp.set_or1222579329274155063t_real A B) F) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real F B)) (tptp.aa_real_real F A))))))) (forall ((A tptp.real) (B tptp.real) (F tptp.fun_real_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B)) (=> (tptp.topolo5044208981011980120l_real (tptp.set_or1222579329274155063t_real A B) F) (=> (forall ((X3 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) X3)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X3) B)) (tptp.has_fi5821293074295781190e_real F tptp.zero_zero_real (tptp.topolo2177554685111907308n_real X3 tptp.top_top_set_real))))) (= (tptp.aa_real_real F B) (tptp.aa_real_real F A)))))) (forall ((A2 tptp.set_real)) (=> (tptp.ord_less_eq_set_real A2 (tptp.set_or1633881224788618240n_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real) tptp.one_one_real)) (tptp.topolo5044208981011980120l_real A2 tptp.artanh_real))) (forall ((A tptp.real) (B 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) B)) (=> (tptp.topolo5044208981011980120l_real (tptp.set_or1222579329274155063t_real A B) F) (=> (forall ((X3 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) X3)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X3) B)) (tptp.has_fi5821293074295781190e_real F tptp.zero_zero_real (tptp.topolo2177554685111907308n_real X3 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) B)) (= (tptp.aa_real_real F X) (tptp.aa_real_real F A)))))))) (forall ((A tptp.real) (B tptp.real) (F tptp.fun_real_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B)) (=> (= (tptp.aa_real_real F A) (tptp.aa_real_real F B)) (=> (tptp.topolo5044208981011980120l_real (tptp.set_or1222579329274155063t_real A B) F) (=> (forall ((X3 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) X3)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X3) B)) (tptp.differ6690327859849518006l_real F (tptp.topolo2177554685111907308n_real X3 tptp.top_top_set_real))))) (exists ((Z2 tptp.real)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) Z2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Z2) B)) (tptp.has_fi5821293074295781190e_real F tptp.zero_zero_real (tptp.topolo2177554685111907308n_real Z2 tptp.top_top_set_real))))))))) (= (tptp.image_int_nat tptp.nat_int_encode tptp.top_top_set_int) tptp.top_top_set_nat) (forall ((X tptp.int) (Y4 tptp.int)) (= (= (tptp.aa_int_nat tptp.nat_int_encode X) (tptp.aa_int_nat tptp.nat_int_encode Y4)) (= X Y4))) (tptp.pp (tptp.aa_set_nat_bool (tptp.bij_betw_int_nat tptp.nat_int_encode tptp.top_top_set_int) tptp.top_top_set_nat)) (= tptp.topolo1511823702728130853y_real (tptp.comple2936214249959783750l_real (tptp.image_2178119161166701260l_real tptp.aTP_Lamm_go _let_11))) (= tptp.topolo896644834953643431omplex (tptp.comple8358262395181532106omplex (tptp.image_5971271580939081552omplex tptp.aTP_Lamm_gq _let_11))) (= (tptp.image_int_int tptp.abs_abs_int tptp.top_top_set_int) tptp.semiring_1_Nats_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.inj_on_real_real (tptp.aa_nat_fun_real_real tptp.aTP_Lamm_em N) tptp.top_top_set_real))) (= (tptp.image_nat_int tptp.nat_int_decode tptp.top_top_set_nat) tptp.top_top_set_int) (forall ((N tptp.nat)) (= (tptp.aa_int_nat tptp.nat_int_encode (tptp.aa_nat_int tptp.nat_int_decode N)) N)) (forall ((X tptp.int)) (= (tptp.aa_nat_int tptp.nat_int_decode (tptp.aa_int_nat tptp.nat_int_encode X)) X)) (forall ((X tptp.nat) (Y4 tptp.nat)) (= (= (tptp.aa_nat_int tptp.nat_int_decode X) (tptp.aa_nat_int tptp.nat_int_decode Y4)) (= X Y4))) (tptp.bij_betw_nat_int tptp.nat_int_decode tptp.top_top_set_nat tptp.top_top_set_int) (forall ((B tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real) B)) (tptp.inj_on_real_real (tptp.aa_rea7340605660300375871l_real tptp.log B) (tptp.set_or5849166863359141190n_real tptp.zero_zero_real)))) (forall ((Z tptp.complex)) (= (tptp.member_complex Z tptp.semiri3842193898606819883omplex) (and (= (tptp.aa_complex_real tptp.im Z) tptp.zero_zero_real) (exists ((I2 tptp.nat)) (= (tptp.aa_complex_real tptp.re Z) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real I2)))))) (forall ((A2 tptp.set_int)) (tptp.inj_on_int_nat tptp.nat_int_encode A2)) (tptp.inj_on_set_nat_nat tptp.nat_set_encode (tptp.collect_set_nat tptp.finite_finite_nat)) (forall ((A2 tptp.set_Pr1261947904930325089at_nat)) (tptp.inj_on2178005380612969504at_nat tptp.nat_prod_encode A2)) (forall ((N5 tptp.set_nat)) (tptp.pp (tptp.aa_set_nat_bool (tptp.inj_on_nat_nat tptp.suc) N5))) (forall ((A2 tptp.set_nat)) (tptp.pp (tptp.aa_set_nat_bool (tptp.inj_on_nat_int tptp.nat_int_decode) A2))) (forall ((N5 tptp.set_nat) (K tptp.nat)) (=> (forall ((N2 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat N2) N5)) (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.aTP_Lamm_ei K)) N5)))) (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 ((X3 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 X3)))) (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 ((X3 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 X3)))) (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_39)) (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 ((X3 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 X3)))) (=> (forall ((X3 tptp.nat)) (=> (not (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) (tptp.image_nat_nat G tptp.top_top_set_nat)))) (= (tptp.aa_nat_real F X3) 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.power_int_real X) N))))) (forall ((X tptp.vEBT_VEBT) (Xa tptp.nat)) (=> (not (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_VEBT_valid X) Xa))) (=> (=> (exists ((Uu2 tptp.bool) (Uv2 tptp.bool)) (= X (tptp.vEBT_Leaf Uu2 Uv2))) (= Xa 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 Xa) (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.power_power_nat _let_1) _let_2)) (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_gr Deg2) TreeList2) Summary2)) Mima)))))))))) (forall ((X tptp.vEBT_VEBT) (Xa tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_VEBT_valid X) Xa)) (=> (=> (exists ((Uu2 tptp.bool) (Uv2 tptp.bool)) (= X (tptp.vEBT_Leaf Uu2 Uv2))) (not (= Xa 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 Xa) (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.power_power_nat _let_1) _let_2)) (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_gr 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 ((X5 tptp.vEBT_VEBT)) (=> (tptp.pp (tptp.aa_set8260762808118238015T_bool (tptp.aa_VEB289770264548726718T_bool tptp.member_VEBT_VEBT X5) (tptp.set_VEBT_VEBT2 TreeList))) (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 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.power_power_nat _let_1) _let_2)) (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_gr Deg) TreeList) Summary)) Mima2)))))) (forall ((X tptp.vEBT_VEBT) (Xa tptp.nat) (Y4 tptp.bool)) (let ((_let_1 (tptp.pp Y4))) (=> (= (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_VEBT_valid X) Xa)) _let_1) (=> (=> (exists ((Uu2 tptp.bool) (Uv2 tptp.bool)) (= X (tptp.vEBT_Leaf Uu2 Uv2))) (= _let_1 (not (= Xa 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 Y4) (not (and (= Deg2 Xa) (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.power_power_nat _let_1) _let_2)) (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_gr Deg2) TreeList2) Summary2)) Mima))))))))))))) (forall ((X tptp.vEBT_VEBT) (Xa tptp.nat)) (=> (not (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_VEBT_valid X) Xa))) (=> (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel (tptp.produc738532404422230701BT_nat X Xa)) (=> (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 Xa)) (= Xa 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 Xa)) (and (= Deg2 Xa) (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.power_power_nat _let_1) _let_2)) (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_gr Deg2) TreeList2) Summary2)) Mima))))))))))))) (forall ((X tptp.vEBT_VEBT) (Xa tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_VEBT_valid X) Xa)) (=> (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel (tptp.produc738532404422230701BT_nat X Xa)) (=> (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 Xa)) (not (= Xa 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 Xa)) (not (and (= Deg2 Xa) (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.power_power_nat _let_1) _let_2)) (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_gr Deg2) TreeList2) Summary2)) Mima)))))))))))))) (forall ((X7 tptp.set_int)) (= (tptp.complete_Sup_Sup_int X7) (tptp.the_int (tptp.aTP_Lamm_gs X7)))) (forall ((X tptp.vEBT_VEBT) (Xa tptp.nat) (Y4 tptp.bool)) (=> (= (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_VEBT_valid X) Xa)) (tptp.pp Y4)) (=> (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel (tptp.produc738532404422230701BT_nat X Xa)) (=> (forall ((Uu2 tptp.bool) (Uv2 tptp.bool)) (let ((_let_1 (tptp.vEBT_Leaf Uu2 Uv2))) (=> (= X _let_1) (=> (= (tptp.pp Y4) (= Xa tptp.one_one_nat)) (not (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel (tptp.produc738532404422230701BT_nat _let_1 Xa))))))) (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 Y4) (and (= Deg2 Xa) (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_3)) (= (tptp.size_s6755466524823107622T_VEBT TreeList2) (tptp.aa_nat_nat (tptp.power_power_nat _let_2) _let_3)) (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_gr Deg2) TreeList2) Summary2)) Mima))) (not (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel (tptp.produc738532404422230701BT_nat _let_1 Xa)))))))))))))) (= tptp.field_5140801741446780682s_real (tptp.collect_real tptp.aTP_Lamm_gt)) (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 ((X tptp.real) (Y4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Y4)) (exists ((X3 tptp.real)) (and (tptp.member_real X3 tptp.field_5140801741446780682s_real) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) X3)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X3) Y4)))))) (forall ((X tptp.real)) (exists ((X3 tptp.real)) (and (tptp.member_real X3 tptp.field_5140801741446780682s_real) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X3) X))))) (forall ((X tptp.real)) (exists ((X3 tptp.real)) (and (tptp.member_real X3 tptp.field_5140801741446780682s_real) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) X3))))) (= tptp.field_5140801741446780682s_real (tptp.collect_real tptp.aTP_Lamm_gu)) (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A) B))) (let ((_let_2 (tptp.aa_int_rat (tptp.aa_int_fun_int_rat tptp.fract A) B))) (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 ((A tptp.int) (B 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) B)) (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 B) D)))) (forall ((A tptp.int) (B 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) B)) (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 B) C)))) (forall ((A tptp.int) (B tptp.int)) (= (tptp.aa_rat_int tptp.archim3151403230148437115or_rat (tptp.aa_int_rat (tptp.aa_int_fun_int_rat tptp.fract A) B)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A) B))) (forall ((B 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 B) D))) (=> (not (= B 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) B)) (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) B)) _let_1)))))))) (forall ((B tptp.int) (D tptp.int) (A tptp.int) (C tptp.int)) (=> (not (= B 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) B)) (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) B))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B) D)))))) (forall ((B 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 B) D))) (=> (not (= B 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) B)) (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) B)) _let_1)))))))) (forall ((B tptp.int) (D tptp.int) (A tptp.int) (C tptp.int)) (=> (not (= B 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) B)) (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) B))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B) D)))))) (forall ((A tptp.int) (B tptp.int)) (= (tptp.aa_rat_rat tptp.sgn_sgn_rat (tptp.aa_int_rat (tptp.aa_int_fun_int_rat tptp.fract A) B)) (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.sgn_sgn_int A)) (tptp.sgn_sgn_int B))))) (forall ((P tptp.fun_rat_bool) (Q2 tptp.rat)) (=> (forall ((A3 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) B2)) (tptp.pp (tptp.aa_rat_bool P (tptp.aa_int_rat (tptp.aa_int_fun_int_rat tptp.fract A3) B2))))) (tptp.pp (tptp.aa_rat_bool P Q2)))) (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (tptp.gcd_gcd_int A B))) (= (tptp.aa_int_rat (tptp.aa_int_fun_int_rat tptp.fract (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A) _let_1)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int B) _let_1)) (tptp.aa_int_rat (tptp.aa_int_fun_int_rat tptp.fract A) B)))) (forall ((K tptp.int)) (= (tptp.aa_int_rat (tptp.aa_int_fun_int_rat tptp.fract tptp.zero_zero_int) K) tptp.zero_zero_rat)) (forall ((K tptp.int)) (= (tptp.aa_int_rat (tptp.aa_int_fun_int_rat tptp.fract K) tptp.zero_zero_int) tptp.zero_zero_rat)) (forall ((A tptp.int)) (= (tptp.aa_int_rat (tptp.aa_int_fun_int_rat tptp.fract A) tptp.zero_zero_int) (tptp.aa_int_rat (tptp.aa_int_fun_int_rat tptp.fract tptp.zero_zero_int) tptp.one_one_int))) (forall ((C tptp.int) (A tptp.int) (B 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 B)) (tptp.aa_int_rat (tptp.aa_int_fun_int_rat tptp.fract A) B))))) (forall ((B tptp.int) (D tptp.int) (A tptp.int) (C tptp.int)) (=> (not (= B tptp.zero_zero_int)) (=> (not (= D tptp.zero_zero_int)) (= (= (tptp.aa_int_rat (tptp.aa_int_fun_int_rat tptp.fract A) B) (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) B)))))) (forall ((A tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_rat tptp.fract tptp.zero_zero_int))) (= (tptp.aa_int_rat _let_1 A) (tptp.aa_int_rat _let_1 C)))) (forall ((K tptp.nat)) (= (tptp.aa_int_rat (tptp.aa_int_fun_int_rat tptp.fract (tptp.aa_nat_int tptp.semiri1314217659103216013at_int K)) tptp.one_one_int) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat K))) (= tptp.zero_zero_rat (tptp.aa_int_rat (tptp.aa_int_fun_int_rat tptp.fract tptp.zero_zero_int) tptp.one_one_int)) (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)))))) (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 ((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 ((B 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 B)) (= (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) B))) (tptp.pp (tptp.aa_int_bool _let_1 A)))))) (forall ((B 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) B)) (= (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) B)) 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 ((B 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) B)) (= (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) B)) tptp.one_one_rat)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B))))) (forall ((B 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) B)) (= (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) B))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B) A))))) (forall ((N tptp.int) (M tptp.int)) (=> (not (= N tptp.zero_zero_int)) (= (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 M) N)) N) (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 M) N)) tptp.one_one_rat)))) (forall ((B 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) B)) (= (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) B)) 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 ((B 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) B)) (= (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) B))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) A))))) (forall ((B 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) B)) (= (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) B))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B) A))))) (forall ((B 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) B)) (= (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) B)) tptp.one_one_rat)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B))))) (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)))) (= tptp.sup_sup_int tptp.ord_max_int) (= tptp.sup_su3973961784419623482d_enat tptp.ord_ma741700101516333627d_enat) (= tptp.sup_sup_nat tptp.ord_max_nat) (forall ((F tptp.fun_real_real) (F2 tptp.fun_real_real)) (=> (forall ((X3 tptp.real)) (tptp.has_fi5821293074295781190e_real F (tptp.aa_real_real F2 X3) (tptp.topolo2177554685111907308n_real X3 tptp.top_top_set_real))) (=> (forall ((X3 tptp.real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) (tptp.aa_real_real F2 X3)))) (tptp.order_7092887310737990675l_real F)))) (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_gv M) (tptp.bit_take_bit_num _let_1 N))))) (= tptp.semiri1316708129612266289at_nat tptp.id_nat) (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 ((R2 tptp.num)) (= (tptp.bit_take_bit_num (tptp.aa_num_nat tptp.numeral_numeral_nat R2) tptp.one) (tptp.some_num tptp.one))) (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.bit_take_bit_num N tptp.one) (tptp.case_nat_option_num tptp.none_num tptp.aTP_Lamm_gw N))) (= tptp.ord_less_int (tptp.map_fu2743658913401090412t_bool tptp.rep_Integ _let_36 _let_22)) (= tptp.nat2 (tptp.map_fu2345160673673942751at_nat tptp.rep_Integ tptp.id_nat _let_24)) (= tptp.ord_less_eq_int (tptp.map_fu2743658913401090412t_bool tptp.rep_Integ _let_36 _let_20)) (forall ((N tptp.nat) (M tptp.num)) (let ((_let_1 (tptp.aa_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 ((M tptp.num) (N tptp.num)) (= (tptp.aa_int_int (tptp.aa_int_fun_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 ((N tptp.num) (M tptp.num)) (= (tptp.aa_int_int (tptp.aa_int_fun_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 (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 ((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_gx (tptp.bit_take_bit_num N M)))) (forall ((R2 tptp.num) (M tptp.num)) (= (tptp.bit_take_bit_num (tptp.aa_num_nat tptp.numeral_numeral_nat R2) (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 R2) M))))) (forall ((R2 tptp.num) (M tptp.num)) (= (tptp.bit_take_bit_num (tptp.aa_num_nat tptp.numeral_numeral_nat R2) (tptp.aa_num_num tptp.bit0 M)) (tptp.case_o6005452278849405969um_num tptp.none_num tptp.aTP_Lamm_gx (tptp.bit_take_bit_num (tptp.aa_num_nat tptp.pred_numeral R2) M)))) (forall ((N tptp.num) (M tptp.num)) (= (tptp.aa_int_int (tptp.aa_int_fun_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 ((M tptp.num) (N tptp.num)) (= (tptp.aa_int_int (tptp.aa_int_fun_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 ((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_gy (tptp.bit_and_not_num M N)))) (= (tptp.bit_and_not_num tptp.one tptp.one) tptp.none_num) (forall ((N tptp.num)) (= (tptp.bit_and_not_num tptp.one (tptp.aa_num_num tptp.bit1 N)) tptp.none_num)) (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 ((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_gz 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.aa_int_fun_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 ((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_ha M) N))) (forall ((M tptp.num) (N tptp.num)) (= (= (tptp.bit_and_not_num M N) tptp.none_num) (= (tptp.aa_int_int (tptp.aa_int_fun_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.aa_int_fun_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 ((M tptp.num) (N tptp.num)) (= (tptp.aa_int_int (tptp.aa_int_fun_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 ((A tptp.int) (B tptp.int)) (= (tptp.pp (tptp.aa_rat_bool tptp.positive (tptp.aa_int_rat (tptp.aa_int_fun_int_rat tptp.fract A) B))) (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) B))))) (not (tptp.pp (tptp.aa_rat_bool tptp.positive tptp.zero_zero_rat))) (forall ((X tptp.rat)) (=> (not (tptp.pp (tptp.aa_rat_bool tptp.positive X))) (=> (not (= X tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool tptp.positive (tptp.aa_rat_rat tptp.uminus_uminus_rat X)))))) (forall ((X tptp.rat) (Y4 tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) Y4)) (tptp.pp (tptp.aa_rat_bool tptp.positive (tptp.aa_rat_rat (tptp.minus_minus_rat Y4) X))))) (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))))))) (forall ((X tptp.num) (Xa tptp.num) (Y4 tptp.option_num)) (let ((_let_1 (not (= Y4 tptp.none_num)))) (let ((_let_2 (= X tptp.one))) (=> (= (tptp.bit_and_not_num X Xa) Y4) (=> (=> _let_2 (=> (= Xa tptp.one) _let_1)) (=> (=> _let_2 (=> (exists ((N2 tptp.num)) (= Xa (tptp.aa_num_num tptp.bit0 N2))) (not (= Y4 (tptp.some_num tptp.one))))) (=> (=> _let_2 (=> (exists ((N2 tptp.num)) (= Xa (tptp.aa_num_num tptp.bit1 N2))) _let_1)) (=> (forall ((M4 tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 M4))) (=> (= X _let_1) (=> (= Xa tptp.one) (not (= Y4 (tptp.some_num _let_1))))))) (=> (forall ((M4 tptp.num)) (=> (= X (tptp.aa_num_num tptp.bit0 M4)) (forall ((N2 tptp.num)) (=> (= Xa (tptp.aa_num_num tptp.bit0 N2)) (not (= Y4 (tptp.map_option_num_num tptp.bit0 (tptp.bit_and_not_num M4 N2)))))))) (=> (forall ((M4 tptp.num)) (=> (= X (tptp.aa_num_num tptp.bit0 M4)) (forall ((N2 tptp.num)) (=> (= Xa (tptp.aa_num_num tptp.bit1 N2)) (not (= Y4 (tptp.map_option_num_num tptp.bit0 (tptp.bit_and_not_num M4 N2)))))))) (=> (forall ((M4 tptp.num)) (=> (= X (tptp.aa_num_num tptp.bit1 M4)) (=> (= Xa tptp.one) (not (= Y4 (tptp.some_num (tptp.aa_num_num tptp.bit0 M4))))))) (=> (forall ((M4 tptp.num)) (=> (= X (tptp.aa_num_num tptp.bit1 M4)) (forall ((N2 tptp.num)) (=> (= Xa (tptp.aa_num_num tptp.bit0 N2)) (not (= Y4 (tptp.case_o6005452278849405969um_num (tptp.some_num tptp.one) tptp.aTP_Lamm_gy (tptp.bit_and_not_num M4 N2)))))))) (not (forall ((M4 tptp.num)) (=> (= X (tptp.aa_num_num tptp.bit1 M4)) (forall ((N2 tptp.num)) (=> (= Xa (tptp.aa_num_num tptp.bit1 N2)) (not (= Y4 (tptp.map_option_num_num tptp.bit0 (tptp.bit_and_not_num M4 N2))))))))))))))))))))) (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.bit1 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.bit0 M) (tptp.aa_num_num tptp.bit1 N)) (tptp.map_option_num_num tptp.bit0 (tptp.bit_and_not_num M N)))) (forall ((X tptp.num) (Xa tptp.num) (Y4 tptp.option_num)) (let ((_let_1 (= X tptp.one))) (=> (= (tptp.bit_and_not_num X Xa) Y4) (=> (tptp.accp_P3113834385874906142um_num tptp.bit_and_not_num_rel (tptp.product_Pair_num_num X Xa)) (=> (=> _let_1 (=> (= Xa tptp.one) (=> (= Y4 tptp.none_num) (not (tptp.accp_P3113834385874906142um_num tptp.bit_and_not_num_rel (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))) (=> (= Xa _let_1) (=> (= Y4 (tptp.some_num tptp.one)) (not (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))) (=> (= Xa _let_1) (=> (= Y4 tptp.none_num) (not (tptp.accp_P3113834385874906142um_num tptp.bit_and_not_num_rel (tptp.product_Pair_num_num tptp.one _let_1)))))))) (=> (forall ((M4 tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 M4))) (=> (= X _let_1) (=> (= Xa tptp.one) (=> (= Y4 (tptp.some_num _let_1)) (not (tptp.accp_P3113834385874906142um_num tptp.bit_and_not_num_rel (tptp.product_Pair_num_num _let_1 tptp.one)))))))) (=> (forall ((M4 tptp.num)) (=> (= X (tptp.aa_num_num tptp.bit0 M4)) (forall ((N2 tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 N2))) (=> (= Xa _let_1) (=> (= Y4 (tptp.map_option_num_num tptp.bit0 (tptp.bit_and_not_num M4 N2))) (not (tptp.accp_P3113834385874906142um_num tptp.bit_and_not_num_rel (tptp.product_Pair_num_num (tptp.aa_num_num tptp.bit0 M4) _let_1))))))))) (=> (forall ((M4 tptp.num)) (=> (= X (tptp.aa_num_num tptp.bit0 M4)) (forall ((N2 tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit1 N2))) (=> (= Xa _let_1) (=> (= Y4 (tptp.map_option_num_num tptp.bit0 (tptp.bit_and_not_num M4 N2))) (not (tptp.accp_P3113834385874906142um_num tptp.bit_and_not_num_rel (tptp.product_Pair_num_num (tptp.aa_num_num tptp.bit0 M4) _let_1))))))))) (=> (forall ((M4 tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit1 M4))) (=> (= X _let_1) (=> (= Xa tptp.one) (=> (= Y4 (tptp.some_num (tptp.aa_num_num tptp.bit0 M4))) (not (tptp.accp_P3113834385874906142um_num tptp.bit_and_not_num_rel (tptp.product_Pair_num_num _let_1 tptp.one)))))))) (=> (forall ((M4 tptp.num)) (=> (= X (tptp.aa_num_num tptp.bit1 M4)) (forall ((N2 tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 N2))) (=> (= Xa _let_1) (=> (= Y4 (tptp.case_o6005452278849405969um_num (tptp.some_num tptp.one) tptp.aTP_Lamm_gy (tptp.bit_and_not_num M4 N2))) (not (tptp.accp_P3113834385874906142um_num tptp.bit_and_not_num_rel (tptp.product_Pair_num_num (tptp.aa_num_num tptp.bit1 M4) _let_1))))))))) (not (forall ((M4 tptp.num)) (=> (= X (tptp.aa_num_num tptp.bit1 M4)) (forall ((N2 tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit1 N2))) (=> (= Xa _let_1) (=> (= Y4 (tptp.map_option_num_num tptp.bit0 (tptp.bit_and_not_num M4 N2))) (not (tptp.accp_P3113834385874906142um_num tptp.bit_and_not_num_rel (tptp.product_Pair_num_num (tptp.aa_num_num tptp.bit1 M4) _let_1)))))))))))))))))))))) (= tptp.positive (tptp.map_fu5118516228767806217l_bool tptp.rep_Rat tptp.id_bool tptp.aTP_Lamm_hb)) (forall ((X tptp.num) (Xa tptp.num) (Y4 tptp.option_num)) (let ((_let_1 (not (= Y4 (tptp.some_num tptp.one))))) (let ((_let_2 (= Xa tptp.one))) (let ((_let_3 (=> _let_2 _let_1))) (let ((_let_4 (not (= Y4 tptp.none_num)))) (let ((_let_5 (= X tptp.one))) (=> (= (tptp.aa_num_option_num (tptp.aa_num6390622462783740633on_num tptp.bit_un7362597486090784418nd_num X) Xa) Y4) (=> (=> _let_5 _let_3) (=> (=> _let_5 (=> (exists ((N2 tptp.num)) (= Xa (tptp.aa_num_num tptp.bit0 N2))) _let_4)) (=> (=> _let_5 (=> (exists ((N2 tptp.num)) (= Xa (tptp.aa_num_num tptp.bit1 N2))) _let_1)) (=> (=> (exists ((M4 tptp.num)) (= X (tptp.aa_num_num tptp.bit0 M4))) (=> _let_2 _let_4)) (=> (forall ((M4 tptp.num)) (=> (= X (tptp.aa_num_num tptp.bit0 M4)) (forall ((N2 tptp.num)) (=> (= Xa (tptp.aa_num_num tptp.bit0 N2)) (not (= Y4 (tptp.map_option_num_num tptp.bit0 (tptp.aa_num_option_num (tptp.aa_num6390622462783740633on_num tptp.bit_un7362597486090784418nd_num M4) N2)))))))) (=> (forall ((M4 tptp.num)) (=> (= X (tptp.aa_num_num tptp.bit0 M4)) (forall ((N2 tptp.num)) (=> (= Xa (tptp.aa_num_num tptp.bit1 N2)) (not (= Y4 (tptp.map_option_num_num tptp.bit0 (tptp.aa_num_option_num (tptp.aa_num6390622462783740633on_num tptp.bit_un7362597486090784418nd_num M4) N2)))))))) (=> (=> (exists ((M4 tptp.num)) (= X (tptp.aa_num_num tptp.bit1 M4))) _let_3) (=> (forall ((M4 tptp.num)) (=> (= X (tptp.aa_num_num tptp.bit1 M4)) (forall ((N2 tptp.num)) (=> (= Xa (tptp.aa_num_num tptp.bit0 N2)) (not (= Y4 (tptp.map_option_num_num tptp.bit0 (tptp.aa_num_option_num (tptp.aa_num6390622462783740633on_num tptp.bit_un7362597486090784418nd_num M4) N2)))))))) (not (forall ((M4 tptp.num)) (=> (= X (tptp.aa_num_num tptp.bit1 M4)) (forall ((N2 tptp.num)) (=> (= Xa (tptp.aa_num_num tptp.bit1 N2)) (not (= Y4 (tptp.case_o6005452278849405969um_num (tptp.some_num tptp.one) tptp.aTP_Lamm_gy (tptp.aa_num_option_num (tptp.aa_num6390622462783740633on_num tptp.bit_un7362597486090784418nd_num M4) N2)))))))))))))))))))))))) (forall ((X tptp.num) (Xa tptp.num) (Y4 tptp.option_num)) (let ((_let_1 (= X tptp.one))) (=> (= (tptp.aa_num_option_num (tptp.aa_num6390622462783740633on_num tptp.bit_un2480387367778600638or_num X) Xa) Y4) (=> (=> _let_1 (=> (= Xa tptp.one) (not (= Y4 tptp.none_num)))) (=> (=> _let_1 (forall ((N2 tptp.num)) (=> (= Xa (tptp.aa_num_num tptp.bit0 N2)) (not (= Y4 (tptp.some_num (tptp.aa_num_num tptp.bit1 N2))))))) (=> (=> _let_1 (forall ((N2 tptp.num)) (=> (= Xa (tptp.aa_num_num tptp.bit1 N2)) (not (= Y4 (tptp.some_num (tptp.aa_num_num tptp.bit0 N2))))))) (=> (forall ((M4 tptp.num)) (=> (= X (tptp.aa_num_num tptp.bit0 M4)) (=> (= Xa tptp.one) (not (= Y4 (tptp.some_num (tptp.aa_num_num tptp.bit1 M4))))))) (=> (forall ((M4 tptp.num)) (=> (= X (tptp.aa_num_num tptp.bit0 M4)) (forall ((N2 tptp.num)) (=> (= Xa (tptp.aa_num_num tptp.bit0 N2)) (not (= Y4 (tptp.map_option_num_num tptp.bit0 (tptp.aa_num_option_num (tptp.aa_num6390622462783740633on_num tptp.bit_un2480387367778600638or_num M4) N2)))))))) (=> (forall ((M4 tptp.num)) (=> (= X (tptp.aa_num_num tptp.bit0 M4)) (forall ((N2 tptp.num)) (=> (= Xa (tptp.aa_num_num tptp.bit1 N2)) (not (= Y4 (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 M4) N2))))))))) (=> (forall ((M4 tptp.num)) (=> (= X (tptp.aa_num_num tptp.bit1 M4)) (=> (= Xa tptp.one) (not (= Y4 (tptp.some_num (tptp.aa_num_num tptp.bit0 M4))))))) (=> (forall ((M4 tptp.num)) (=> (= X (tptp.aa_num_num tptp.bit1 M4)) (forall ((N2 tptp.num)) (=> (= Xa (tptp.aa_num_num tptp.bit0 N2)) (not (= Y4 (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 M4) N2))))))))) (not (forall ((M4 tptp.num)) (=> (= X (tptp.aa_num_num tptp.bit1 M4)) (forall ((N2 tptp.num)) (=> (= Xa (tptp.aa_num_num tptp.bit1 N2)) (not (= Y4 (tptp.map_option_num_num tptp.bit0 (tptp.aa_num_option_num (tptp.aa_num6390622462783740633on_num tptp.bit_un2480387367778600638or_num M4) N2)))))))))))))))))))) (= (tptp.aa_num_option_num (tptp.aa_num6390622462783740633on_num tptp.bit_un7362597486090784418nd_num tptp.one) tptp.one) (tptp.some_num tptp.one)) (= (tptp.aa_num_option_num (tptp.aa_num6390622462783740633on_num tptp.bit_un2480387367778600638or_num tptp.one) tptp.one) tptp.none_num) (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_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 ((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 ((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.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.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.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_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 ((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 ((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 ((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 ((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) (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_gy (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_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.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 ((X tptp.num) (Xa tptp.num) (Y4 tptp.option_num)) (let ((_let_1 (= X tptp.one))) (=> (= (tptp.aa_num_option_num (tptp.aa_num6390622462783740633on_num tptp.bit_un7362597486090784418nd_num X) Xa) Y4) (=> (tptp.accp_P3113834385874906142um_num tptp.bit_un4731106466462545111um_rel (tptp.product_Pair_num_num X Xa)) (=> (=> _let_1 (=> (= Xa tptp.one) (=> (= Y4 (tptp.some_num tptp.one)) (not (tptp.accp_P3113834385874906142um_num tptp.bit_un4731106466462545111um_rel (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))) (=> (= Xa _let_1) (=> (= Y4 tptp.none_num) (not (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))) (=> (= Xa _let_1) (=> (= Y4 (tptp.some_num tptp.one)) (not (tptp.accp_P3113834385874906142um_num tptp.bit_un4731106466462545111um_rel (tptp.product_Pair_num_num tptp.one _let_1)))))))) (=> (forall ((M4 tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 M4))) (=> (= X _let_1) (=> (= Xa tptp.one) (=> (= Y4 tptp.none_num) (not (tptp.accp_P3113834385874906142um_num tptp.bit_un4731106466462545111um_rel (tptp.product_Pair_num_num _let_1 tptp.one)))))))) (=> (forall ((M4 tptp.num)) (=> (= X (tptp.aa_num_num tptp.bit0 M4)) (forall ((N2 tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 N2))) (=> (= Xa _let_1) (=> (= Y4 (tptp.map_option_num_num tptp.bit0 (tptp.aa_num_option_num (tptp.aa_num6390622462783740633on_num tptp.bit_un7362597486090784418nd_num M4) N2))) (not (tptp.accp_P3113834385874906142um_num tptp.bit_un4731106466462545111um_rel (tptp.product_Pair_num_num (tptp.aa_num_num tptp.bit0 M4) _let_1))))))))) (=> (forall ((M4 tptp.num)) (=> (= X (tptp.aa_num_num tptp.bit0 M4)) (forall ((N2 tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit1 N2))) (=> (= Xa _let_1) (=> (= Y4 (tptp.map_option_num_num tptp.bit0 (tptp.aa_num_option_num (tptp.aa_num6390622462783740633on_num tptp.bit_un7362597486090784418nd_num M4) N2))) (not (tptp.accp_P3113834385874906142um_num tptp.bit_un4731106466462545111um_rel (tptp.product_Pair_num_num (tptp.aa_num_num tptp.bit0 M4) _let_1))))))))) (=> (forall ((M4 tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit1 M4))) (=> (= X _let_1) (=> (= Xa tptp.one) (=> (= Y4 (tptp.some_num tptp.one)) (not (tptp.accp_P3113834385874906142um_num tptp.bit_un4731106466462545111um_rel (tptp.product_Pair_num_num _let_1 tptp.one)))))))) (=> (forall ((M4 tptp.num)) (=> (= X (tptp.aa_num_num tptp.bit1 M4)) (forall ((N2 tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 N2))) (=> (= Xa _let_1) (=> (= Y4 (tptp.map_option_num_num tptp.bit0 (tptp.aa_num_option_num (tptp.aa_num6390622462783740633on_num tptp.bit_un7362597486090784418nd_num M4) N2))) (not (tptp.accp_P3113834385874906142um_num tptp.bit_un4731106466462545111um_rel (tptp.product_Pair_num_num (tptp.aa_num_num tptp.bit1 M4) _let_1))))))))) (not (forall ((M4 tptp.num)) (=> (= X (tptp.aa_num_num tptp.bit1 M4)) (forall ((N2 tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit1 N2))) (=> (= Xa _let_1) (=> (= Y4 (tptp.case_o6005452278849405969um_num (tptp.some_num tptp.one) tptp.aTP_Lamm_gy (tptp.aa_num_option_num (tptp.aa_num6390622462783740633on_num tptp.bit_un7362597486090784418nd_num M4) N2))) (not (tptp.accp_P3113834385874906142um_num tptp.bit_un4731106466462545111um_rel (tptp.product_Pair_num_num (tptp.aa_num_num tptp.bit1 M4) _let_1)))))))))))))))))))))) (forall ((X tptp.num) (Xa tptp.num) (Y4 tptp.option_num)) (let ((_let_1 (= X tptp.one))) (=> (= (tptp.aa_num_option_num (tptp.aa_num6390622462783740633on_num tptp.bit_un2480387367778600638or_num X) Xa) Y4) (=> (tptp.accp_P3113834385874906142um_num tptp.bit_un2901131394128224187um_rel (tptp.product_Pair_num_num X Xa)) (=> (=> _let_1 (=> (= Xa tptp.one) (=> (= Y4 tptp.none_num) (not (tptp.accp_P3113834385874906142um_num tptp.bit_un2901131394128224187um_rel (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))) (=> (= Xa _let_1) (=> (= Y4 (tptp.some_num (tptp.aa_num_num tptp.bit1 N2))) (not (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))) (=> (= Xa _let_1) (=> (= Y4 (tptp.some_num (tptp.aa_num_num tptp.bit0 N2))) (not (tptp.accp_P3113834385874906142um_num tptp.bit_un2901131394128224187um_rel (tptp.product_Pair_num_num tptp.one _let_1)))))))) (=> (forall ((M4 tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 M4))) (=> (= X _let_1) (=> (= Xa tptp.one) (=> (= Y4 (tptp.some_num (tptp.aa_num_num tptp.bit1 M4))) (not (tptp.accp_P3113834385874906142um_num tptp.bit_un2901131394128224187um_rel (tptp.product_Pair_num_num _let_1 tptp.one)))))))) (=> (forall ((M4 tptp.num)) (=> (= X (tptp.aa_num_num tptp.bit0 M4)) (forall ((N2 tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 N2))) (=> (= Xa _let_1) (=> (= Y4 (tptp.map_option_num_num tptp.bit0 (tptp.aa_num_option_num (tptp.aa_num6390622462783740633on_num tptp.bit_un2480387367778600638or_num M4) N2))) (not (tptp.accp_P3113834385874906142um_num tptp.bit_un2901131394128224187um_rel (tptp.product_Pair_num_num (tptp.aa_num_num tptp.bit0 M4) _let_1))))))))) (=> (forall ((M4 tptp.num)) (=> (= X (tptp.aa_num_num tptp.bit0 M4)) (forall ((N2 tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit1 N2))) (=> (= Xa _let_1) (=> (= Y4 (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 M4) N2)))) (not (tptp.accp_P3113834385874906142um_num tptp.bit_un2901131394128224187um_rel (tptp.product_Pair_num_num (tptp.aa_num_num tptp.bit0 M4) _let_1))))))))) (=> (forall ((M4 tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit1 M4))) (=> (= X _let_1) (=> (= Xa tptp.one) (=> (= Y4 (tptp.some_num (tptp.aa_num_num tptp.bit0 M4))) (not (tptp.accp_P3113834385874906142um_num tptp.bit_un2901131394128224187um_rel (tptp.product_Pair_num_num _let_1 tptp.one)))))))) (=> (forall ((M4 tptp.num)) (=> (= X (tptp.aa_num_num tptp.bit1 M4)) (forall ((N2 tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 N2))) (=> (= Xa _let_1) (=> (= Y4 (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 M4) N2)))) (not (tptp.accp_P3113834385874906142um_num tptp.bit_un2901131394128224187um_rel (tptp.product_Pair_num_num (tptp.aa_num_num tptp.bit1 M4) _let_1))))))))) (not (forall ((M4 tptp.num)) (=> (= X (tptp.aa_num_num tptp.bit1 M4)) (forall ((N2 tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit1 N2))) (=> (= Xa _let_1) (=> (= Y4 (tptp.map_option_num_num tptp.bit0 (tptp.aa_num_option_num (tptp.aa_num6390622462783740633on_num tptp.bit_un2480387367778600638or_num M4) N2))) (not (tptp.accp_P3113834385874906142um_num tptp.bit_un2901131394128224187um_rel (tptp.product_Pair_num_num (tptp.aa_num_num tptp.bit1 M4) _let_1)))))))))))))))))))))) (= tptp.bit_un4731106466462545111um_rel tptp.bit_un5425074673868309765um_rel) (= tptp.bit_un2901131394128224187um_rel tptp.bit_un3595099601533988841um_rel) (= tptp.bit_un2480387367778600638or_num tptp.bit_un6178654185764691216or_num) (= tptp.bit_un7362597486090784418nd_num tptp.bit_un1837492267222099188nd_num) (forall ((N tptp.nat) (M tptp.num)) (= (tptp.bit_take_bit_num N M) (tptp.produc478579273971653890on_num tptp.aTP_Lamm_hf (tptp.product_Pair_nat_num N M)))) (forall ((X tptp.real) (Y4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Y4)) (exists ((Q4 tptp.rat)) (let ((_let_1 (tptp.aa_rat_real tptp.field_7254667332652039916t_real Q4))) (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) Y4))))))) (= tptp.plus_plus_rat (tptp.map_fu5968964422797239547at_rat tptp.rep_Rat _let_35 tptp.aTP_Lamm_hg)) (= tptp.inverse_inverse_rat (tptp.aa_fun7041730090766645614at_rat _let_35 tptp.aTP_Lamm_hh)) (forall ((Xa tptp.int) (X tptp.int)) (= (tptp.aa_int_rat (tptp.aa_int_fun_int_rat tptp.fract Xa) X) (tptp.aa_Pro6166618844887768661nt_rat tptp.abs_Rat (tptp.if_Pro3027730157355071871nt_int (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.fequal_int X) tptp.zero_zero_int) (tptp.product_Pair_int_int tptp.zero_zero_int tptp.one_one_int) (tptp.product_Pair_int_int Xa X))))) (= tptp.zero_zero_rat (tptp.aa_Pro6166618844887768661nt_rat tptp.abs_Rat _let_31)) (= tptp.times_times_rat (tptp.map_fu5968964422797239547at_rat tptp.rep_Rat _let_35 tptp.aTP_Lamm_hi)) (forall ((Xa 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 Xa))) (=> (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.aa_Pro1534211998248933470t_bool tptp.ratrel Xa) Xa)) (=> (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 Xa)) (tptp.aa_Pro6166618844887768661nt_rat tptp.abs_Rat X)) (tptp.aa_Pro6166618844887768661nt_rat tptp.abs_Rat (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 Xa)) _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)) (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.if_Pro3027730157355071871nt_int (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.fequal_int _let_1) tptp.zero_zero_int) (tptp.product_Pair_int_int tptp.zero_zero_int tptp.one_one_int) (tptp.product_Pair_int_int (tptp.product_snd_int_int X) _let_1))))))) (forall ((X tptp.product_prod_int_int) (Y4 tptp.product_prod_int_int)) (let ((_let_1 (tptp.product_snd_int_int X))) (let ((_let_2 (tptp.product_snd_int_int Y4))) (= (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.aa_Pro1534211998248933470t_bool tptp.ratrel X) Y4)) (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 Y4)) _let_1))))))) (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.aa_Pro1534211998248933470t_bool tptp.ratrel _let_31) _let_31)) (forall ((X4 tptp.product_prod_int_int) (Xa2 tptp.product_prod_int_int)) (let ((_let_1 (tptp.product_snd_int_int X4))) (let ((_let_2 (tptp.product_snd_int_int Xa2))) (= (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.aa_Pro1534211998248933470t_bool tptp.ratrel X4) Xa2)) (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 X4)) _let_2) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.product_fst_int_int Xa2)) _let_1))))))) (forall ((Xa tptp.product_prod_int_int) (X tptp.product_prod_int_int)) (=> (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.aa_Pro1534211998248933470t_bool tptp.ratrel Xa) Xa)) (=> (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 Xa)) (tptp.aa_Pro6166618844887768661nt_rat tptp.abs_Rat X)) (tptp.aa_Pro6166618844887768661nt_rat tptp.abs_Rat (tptp.product_Pair_int_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.product_fst_int_int Xa)) (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 Xa)) (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 ((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_hj (tptp.code_divmod_integer K (tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one)))))))))) (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 ((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 N) tptp.zero_zero_nat) tptp.zero_zero_nat)) (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) (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))))) (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)))) (= tptp.inf_inf_nat tptp.ord_min_nat) (forall ((M tptp.nat) (N tptp.nat) (K tptp.int) (L tptp.int) (R2 tptp.int)) (= (tptp.aa_int_int (tptp.bit_concat_bit M (tptp.aa_int_int (tptp.bit_concat_bit N K) L)) R2) (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) R2)))) (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)) (= (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 ((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.aTP_Lamm_hk N)) M))) (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.aTP_Lamm_hl N)) M))) (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)) (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)) (= tptp.inf_inf_int tptp.ord_min_int) (forall ((N tptp.nat)) (=> (not (= N tptp.zero_zero_nat)) (= (tptp.lattic8265883725875713057ax_nat (tptp.collect_nat (tptp.aa_nat_fun_nat_bool tptp.aTP_Lamm_da N))) N))) (= tptp.inf_in1870772243966228564d_enat tptp.ord_mi8085742599997312461d_enat) (forall ((S tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat S)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.finite_card_nat S)) (tptp.aa_nat_nat tptp.suc (tptp.lattic8265883725875713057ax_nat S)))))) (forall ((X7 tptp.set_nat)) (let ((_let_1 (tptp.complete_Sup_Sup_nat X7))) (let ((_let_2 (= X7 tptp.bot_bot_set_nat))) (and (=> _let_2 (= _let_1 tptp.zero_zero_nat)) (=> (not _let_2) (= _let_1 (tptp.lattic8265883725875713057ax_nat X7))))))) (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_hm 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_hn N) M)))))) (forall ((M10 tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat M10)) (=> (not (= M10 tptp.bot_bot_set_nat)) (=> (not (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat tptp.zero_zero_nat) M10))) (= (tptp.gcd_Gcd_nat M10) (tptp.lattic8265883725875713057ax_nat (tptp.comple7806235888213564991et_nat (tptp.image_nat_set_nat tptp.aTP_Lamm_ho M10)))))))) (forall ((N tptp.int)) (=> (not (= N tptp.zero_zero_int)) (= (tptp.lattic8263393255366662781ax_int (tptp.collect_int (tptp.aa_int_fun_int_bool tptp.aTP_Lamm_dg N))) (tptp.aa_int_int tptp.abs_abs_int N)))) (forall ((M tptp.nat) (N tptp.nat) (Ns tptp.list_nat) (Q2 tptp.nat)) (let ((_let_1 (tptp.cons_nat N Ns))) (= (= (tptp.cons_nat M _let_1) (tptp.upt M Q2)) (= _let_1 (tptp.upt (tptp.aa_nat_nat tptp.suc M) Q2))))) (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 ((N tptp.int) (M tptp.int)) (=> (not (= N tptp.zero_zero_int)) (= (tptp.gcd_gcd_int M N) (tptp.lattic8263393255366662781ax_int (tptp.collect_int (tptp.aa_int_fun_int_bool (tptp.aTP_Lamm_hp N) M)))))) (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 ((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.nat) (Xs tptp.list_nat)) (= (tptp.aa_list_nat_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.aa_list_nat_nat tptp.nat_list_encode Xs)))))) (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 ((K tptp.nat)) (= (tptp.linord2614967742042102400et_nat (tptp.set_ord_lessThan_nat (tptp.aa_nat_nat tptp.suc K))) (tptp.append_nat (tptp.linord2614967742042102400et_nat (tptp.set_ord_lessThan_nat K)) (tptp.cons_nat K tptp.nil_nat)))) (forall ((K tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc K))) (= (tptp.linord2614967742042102400et_nat (tptp.set_ord_atMost_nat _let_1)) (tptp.append_nat (tptp.linord2614967742042102400et_nat (tptp.set_ord_atMost_nat K)) (tptp.cons_nat _let_1 tptp.nil_nat))))) (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 ((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 ((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 ((X tptp.list_nat)) (=> (not (= X tptp.nil_nat)) (not (forall ((X3 tptp.nat) (Xs2 tptp.list_nat)) (not (= X (tptp.cons_nat X3 Xs2))))))) (= (tptp.aa_list_nat_nat tptp.nat_list_encode tptp.nil_nat) tptp.zero_zero_nat) (forall ((I tptp.nat)) (= (tptp.upt I tptp.zero_zero_nat) tptp.nil_nat)) (forall ((A2 tptp.set_list_nat)) (tptp.inj_on_list_nat_nat tptp.nat_list_encode A2)) (forall ((X tptp.list_nat) (Y4 tptp.list_nat)) (= (= (tptp.aa_list_nat_nat tptp.nat_list_encode X) (tptp.aa_list_nat_nat tptp.nat_list_encode Y4)) (= X Y4))) (tptp.pp (tptp.aa_set_nat_bool (tptp.bij_be8532844293280997160at_nat tptp.nat_list_encode tptp.top_top_set_list_nat) tptp.top_top_set_nat)) (= (tptp.image_list_nat_nat tptp.nat_list_encode tptp.top_top_set_list_nat) tptp.top_top_set_nat) (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 ((X tptp.list_nat) (Y4 tptp.nat)) (=> (= (tptp.aa_list_nat_nat tptp.nat_list_encode X) Y4) (=> (=> (= X tptp.nil_nat) (not (= Y4 tptp.zero_zero_nat))) (not (forall ((X3 tptp.nat) (Xs2 tptp.list_nat)) (=> (= X (tptp.cons_nat X3 Xs2)) (not (= Y4 (tptp.aa_nat_nat tptp.suc (tptp.aa_Pro4243173770044397973at_nat tptp.nat_prod_encode (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat X3) (tptp.aa_list_nat_nat tptp.nat_list_encode Xs2)))))))))))) (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 ((X tptp.list_nat) (Y4 tptp.nat)) (let ((_let_1 (tptp.accp_list_nat tptp.nat_list_encode_rel))) (=> (= (tptp.aa_list_nat_nat tptp.nat_list_encode X) Y4) (=> (tptp.pp (tptp.aa_list_nat_bool _let_1 X)) (=> (=> (= X tptp.nil_nat) (=> (= Y4 tptp.zero_zero_nat) (not (tptp.pp (tptp.aa_list_nat_bool _let_1 tptp.nil_nat))))) (not (forall ((X3 tptp.nat) (Xs2 tptp.list_nat)) (let ((_let_1 (tptp.cons_nat X3 Xs2))) (=> (= X _let_1) (=> (= Y4 (tptp.aa_nat_nat tptp.suc (tptp.aa_Pro4243173770044397973at_nat tptp.nat_prod_encode (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat X3) (tptp.aa_list_nat_nat 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 ((X tptp.int) (Xa tptp.int) (Y4 tptp.list_int)) (let ((_let_1 (tptp.accp_P1096762738010456898nt_int tptp.upto_rel (tptp.product_Pair_int_int X Xa)))) (let ((_let_2 (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X) Xa)))) (=> (= (tptp.upto X Xa) Y4) (=> _let_1 (not (=> (and (=> _let_2 (= Y4 (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) Xa)))) (=> (not _let_2) (= Y4 tptp.nil_int))) (not _let_1)))))))) (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 ((I tptp.int) (J tptp.int)) (= (tptp.size_size_list_int (tptp.upto I J)) (tptp.aa_int_nat tptp.nat2 (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 J) I)) 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))) (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 ((M tptp.int) (N tptp.int)) (tptp.sorted_wrt_int tptp.ord_less_eq_int (tptp.upto M N))) (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.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)) (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) (Xa tptp.int) (Y4 tptp.list_int)) (let ((_let_1 (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X) Xa)))) (=> (= (tptp.upto X Xa) Y4) (and (=> _let_1 (= Y4 (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) Xa)))) (=> (not _let_1) (= Y4 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.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)) (=> (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)) (= (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 ((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.accp_P1096762738010456898nt_int tptp.upto_rel (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 ((M tptp.nat) (N tptp.nat)) (= (tptp.tl_nat (tptp.upt M N)) (tptp.upt (tptp.aa_nat_nat tptp.suc M) N))) (forall ((X tptp.rat)) (= (tptp.quotient_of X) (tptp.the_Pr4378521158711661632nt_int (tptp.aTP_Lamm_hq 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) (P3 tptp.int)) (let ((_let_1 (tptp.product_Pair_int_int P3 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 P3) Q2)) (= (tptp.normalize _let_1) _let_1))))) (tptp.order_mono_nat_nat tptp.suc) (forall ((A tptp.int) (D tptp.int) (B 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 B))) (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 B) 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 ((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 ((A tptp.int) (B 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) B)) (=> (tptp.pp (tptp.aa_int_bool _let_1 A)) (=> (tptp.pp (tptp.aa_int_bool _let_1 B)) (= (tptp.aa_int_int tptp.abs_abs_int X) tptp.one_one_int)))))) (forall ((Q2 tptp.rat)) (not (forall ((A3 tptp.int) (B2 tptp.int)) (=> (= Q2 (tptp.aa_int_rat (tptp.aa_int_fun_int_rat tptp.fract A3) B2)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) B2)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.algebr932160517623751201me_int A3) B2)))))))) (forall ((P tptp.fun_rat_bool) (Q2 tptp.rat)) (=> (forall ((A3 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) B2)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.algebr932160517623751201me_int A3) B2)) (tptp.pp (tptp.aa_rat_bool P (tptp.aa_int_rat (tptp.aa_int_fun_int_rat tptp.fract A3) B2)))))) (tptp.pp (tptp.aa_rat_bool P Q2)))) (forall ((Q2 tptp.rat)) (=> (forall ((A3 tptp.int) (B2 tptp.int)) (=> (= Q2 (tptp.aa_int_rat (tptp.aa_int_fun_int_rat tptp.fract A3) B2)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) B2)) (=> (not (= A3 tptp.zero_zero_int)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.algebr932160517623751201me_int A3) B2))))))) (= Q2 tptp.zero_zero_rat))) (forall ((R2 tptp.rat)) (exists ((X3 tptp.product_prod_int_int)) (let ((_let_1 (tptp.product_snd_int_int X3))) (let ((_let_2 (tptp.product_fst_int_int X3))) (and (= R2 (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 ((Y3 tptp.product_prod_int_int)) (let ((_let_1 (tptp.product_snd_int_int Y3))) (let ((_let_2 (tptp.product_fst_int_int Y3))) (=> (and (= R2 (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))) (= Y3 X3)))))))))) (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.aTP_Lamm_hr K)))) (forall ((F tptp.fun_real_real) (Y4 tptp.real)) (let ((_let_1 (tptp.topolo2815343760600316023s_real Y4))) (=> (tptp.order_mono_real_real F) (=> (tptp.filterlim_nat_real (tptp.aTP_Lamm_hs F) _let_1 tptp.at_top_nat) (tptp.filterlim_real_real F _let_1 tptp.at_top_real))))) (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 ((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) (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 ((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 ((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 ((A tptp.nat) (D tptp.nat) (B 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 B) 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 B) D)) (and (= A B) (= C D)))))) (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 N)) 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 N)))) (forall ((A tptp.nat) (B 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) B)) (=> (tptp.pp (tptp.aa_nat_bool _let_1 A)) (=> (tptp.pp (tptp.aa_nat_bool _let_1 B)) (= X tptp.one_one_nat)))))) (forall ((X7 tptp.fun_nat_real) (B3 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)) B3))) (tptp.bfun_nat_real X7 tptp.at_top_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 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 ((X7 tptp.fun_nat_real) (B3 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)) B3))) (not (forall ((L5 tptp.real)) (=> (tptp.filterlim_nat_real X7 (tptp.topolo2815343760600316023s_real L5) tptp.at_top_nat) (not (forall ((I4 tptp.nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_nat_real X7 I4)) L5)))))))))) (forall ((X tptp.real)) (=> (tptp.member_real X tptp.field_5140801741446780682s_real) (not (forall ((M4 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 M4)) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N2))) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.algebr934650988132801477me_nat M4) N2))))))))) (forall ((F tptp.fun_nat_real) (G tptp.fun_nat_nat)) (=> (forall ((X3 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 X3)))) (=> (tptp.order_mono_nat_real F) (=> (tptp.order_5726023648592871131at_nat G) (= (tptp.bfun_nat_real (tptp.aa_fun1538629612289296340t_real (tptp.aTP_Lamm_ht F) G) tptp.at_top_nat) (tptp.bfun_nat_real F tptp.at_top_nat)))))) (tptp.bNF_re1394333895916556125l_bool tptp.ratrel tptp.fequal_bool tptp.aTP_Lamm_hb tptp.aTP_Lamm_hb) (forall ((X7 tptp.fun_nat_rat) (Y6 tptp.fun_nat_rat)) (=> (exists ((A6 tptp.rat)) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) A6)) (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))) A6))))) (=> (tptp.pp (tptp.vanishes Y6)) (tptp.pp (tptp.vanishes (tptp.aa_fun765758790203053448at_rat (tptp.aa_fun3638354034882855594at_rat tptp.aTP_Lamm_hu X7) Y6)))))) (forall ((C tptp.rat)) (= (tptp.pp (tptp.vanishes (tptp.aTP_Lamm_hv C))) (= C tptp.zero_zero_rat))) (forall ((X7 tptp.fun_nat_rat) (Y6 tptp.fun_nat_rat)) (=> (tptp.pp (tptp.vanishes X7)) (=> (tptp.pp (tptp.vanishes Y6)) (tptp.pp (tptp.vanishes (tptp.aa_fun765758790203053448at_rat (tptp.aTP_Lamm_hw X7) Y6)))))) (forall ((X7 tptp.fun_nat_rat) (Y6 tptp.fun_nat_rat)) (=> (tptp.pp (tptp.vanishes X7)) (=> (tptp.pp (tptp.vanishes Y6)) (tptp.pp (tptp.vanishes (tptp.aa_fun765758790203053448at_rat (tptp.aa_fun3638354034882855594at_rat tptp.aTP_Lamm_hx X7) Y6)))))) (forall ((X7 tptp.fun_nat_rat)) (=> (tptp.pp (tptp.vanishes X7)) (tptp.pp (tptp.vanishes (tptp.aa_fun765758790203053448at_rat tptp.aTP_Lamm_hy X7))))) (forall ((X7 tptp.fun_nat_rat)) (= (tptp.pp (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 ((K3 tptp.nat)) (forall ((N4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K3) N4)) (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 N4))) 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.pp (tptp.vanishes X7)))) (forall ((X7 tptp.fun_nat_rat) (R2 tptp.rat)) (=> (tptp.pp (tptp.vanishes X7)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) R2)) (exists ((K2 tptp.nat)) (forall ((N6 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K2) N6)) (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 N6))) R2)))))))) (tptp.bNF_re4808202430149235895nt_int tptp.fequal_int (tptp.bNF_re6250860962936578807nt_int tptp.fequal_int tptp.ratrel) tptp.aTP_Lamm_hz tptp.aTP_Lamm_hz) (tptp.bNF_re6650684261131312217nt_int tptp.fequal_nat tptp.fequal_int tptp.semiri1314217659103216013at_int tptp.semiri1314217659103216013at_int) (tptp.bNF_re5780769757191362231t_bool tptp.fequal_int (tptp.bNF_re9007465950226028919l_bool tptp.fequal_int tptp.fequal_bool) tptp.ord_less_eq_int tptp.ord_less_eq_int) (tptp.bNF_re1480548845665215743t_bool tptp.fequal_nat (tptp.bNF_re6223507645442431167l_bool tptp.fequal_nat tptp.fequal_bool) tptp.ord_less_eq_nat tptp.ord_less_eq_nat) (tptp.bNF_re5162689864697376059at_nat tptp.fequal_nat _let_33 tptp.times_times_nat tptp.times_times_nat) (tptp.bNF_re5717476210804479843nt_int tptp.fequal_int _let_34 tptp.times_times_int tptp.times_times_int) (tptp.bNF_re5717476210804479843nt_int tptp.fequal_int _let_34 tptp.divide_divide_int tptp.divide_divide_int) (tptp.bNF_re5162689864697376059at_nat tptp.fequal_nat _let_33 tptp.divide_divide_nat tptp.divide_divide_nat) (tptp.bNF_re5162689864697376059at_nat tptp.fequal_nat _let_33 tptp.bit_se7882103937844011126it_nat tptp.bit_se7882103937844011126it_nat) (tptp.bNF_re5651586111134833323nt_int tptp.fequal_nat _let_34 tptp.bit_se7879613467334960850it_int tptp.bit_se7879613467334960850it_int) (tptp.bNF_re5162689864697376059at_nat tptp.fequal_nat _let_33 tptp.bit_se4205575877204974255it_nat tptp.bit_se4205575877204974255it_nat) (tptp.bNF_re5651586111134833323nt_int tptp.fequal_nat _let_34 tptp.bit_se4203085406695923979it_int tptp.bit_se4203085406695923979it_int) (tptp.bNF_re5162689864697376059at_nat tptp.fequal_nat _let_33 tptp.bit_se2161824704523386999it_nat tptp.bit_se2161824704523386999it_nat) (tptp.bNF_re5651586111134833323nt_int tptp.fequal_nat _let_34 tptp.bit_se2159334234014336723it_int tptp.bit_se2159334234014336723it_int) (tptp.pp (tptp.aa_fun_nat_nat_bool (tptp.aa_fun3185460345579526648t_bool _let_33 tptp.suc) tptp.suc)) (tptp.bNF_re5717476210804479843nt_int tptp.fequal_int _let_34 tptp.minus_minus_int tptp.minus_minus_int) (tptp.bNF_re5162689864697376059at_nat tptp.fequal_nat _let_33 tptp.minus_minus_nat tptp.minus_minus_nat) (tptp.bNF_re6378542964492772123um_int tptp.fequal_num (tptp.bNF_re1822329894187522285nt_int tptp.fequal_num tptp.fequal_int) tptp.aTP_Lamm_ia tptp.aTP_Lamm_ia) (tptp.bNF_re4734134812813710757nt_int tptp.ratrel _let_32 tptp.aTP_Lamm_hi tptp.aTP_Lamm_hi) (tptp.bNF_re4734134812813710757nt_int tptp.ratrel _let_32 tptp.aTP_Lamm_hg tptp.aTP_Lamm_hg) (tptp.pp (tptp.aa_fun1403452029515102102t_bool (tptp.aa_fun8298786006102058668t_bool _let_32 tptp.aTP_Lamm_hh) tptp.aTP_Lamm_hh)) (tptp.bNF_re6323452265856231590at_rat tptp.pcr_rat _let_30 tptp.aTP_Lamm_hg tptp.plus_plus_rat) (tptp.pp (tptp.aa_fun_rat_rat_bool (tptp.aa_fun2103967415933125506t_bool _let_30 tptp.aTP_Lamm_hh) tptp.inverse_inverse_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_Pro6332413336323567195t_bool tptp.pcr_rat _let_31) tptp.zero_zero_rat)) (tptp.bNF_re2486238095283335024nt_rat tptp.fequal_int (tptp.bNF_re2214769303045360666nt_rat tptp.fequal_int tptp.pcr_rat) tptp.aTP_Lamm_hz tptp.fract) (tptp.bNF_re6323452265856231590at_rat tptp.pcr_rat _let_30 tptp.aTP_Lamm_hi tptp.times_times_rat) (tptp.bNF_re3535474257078034868l_bool tptp.pcr_rat tptp.fequal_bool tptp.aTP_Lamm_hb tptp.positive) (tptp.bNF_re8869769828555196650nt_int tptp.pcr_int _let_29 _let_27 tptp.times_times_int) (tptp.pp (tptp.aa_int_bool (tptp.aa_Pro2928840338864870335t_bool tptp.pcr_int _let_25) tptp.zero_zero_int)) (tptp.bNF_re6830278522597306478at_int tptp.fequal_nat tptp.pcr_int tptp.aTP_Lamm_ib tptp.semiri1314217659103216013at_int) (tptp.pp (tptp.aa_fun_int_int_bool (tptp.aa_fun7527181275634263258t_bool _let_29 _let_26) tptp.uminus_uminus_int)) (tptp.bNF_re4555766996558763186at_nat tptp.pcr_int tptp.fequal_nat _let_24 tptp.nat2) (tptp.pp (tptp.aa_int_bool (tptp.aa_Pro2928840338864870335t_bool tptp.pcr_int _let_23) tptp.one_one_int)) (tptp.bNF_re2632563231991741785t_bool tptp.pcr_int _let_19 _let_22 tptp.ord_less_int) (tptp.bNF_re2632563231991741785t_bool tptp.pcr_int _let_19 _let_20 tptp.ord_less_eq_int) (tptp.bNF_re8869769828555196650nt_int tptp.pcr_int _let_29 _let_18 tptp.plus_plus_int) (tptp.bNF_re8869769828555196650nt_int tptp.pcr_int _let_29 _let_16 tptp.minus_minus_int) (forall ((A2 tptp.set_nat) (M tptp.nat)) (= (tptp.produc457027306803732586at_nat A2 (tptp.aTP_Lamm_ic M)) (tptp.sup_su6327502436637775413at_nat (tptp.produc457027306803732586at_nat A2 (tptp.aTP_Lamm_id M)) (tptp.produc457027306803732586at_nat A2 (tptp.aTP_Lamm_ie M))))) (forall ((M tptp.nat)) (= (tptp.collec3392354462482085612at_nat (tptp.produc8955392012077580105t_bool (tptp.aTP_Lamm_if M))) (tptp.produc457027306803732586at_nat (tptp.set_ord_atMost_nat M) (tptp.aTP_Lamm_id M)))) (tptp.pp (tptp.aa_fun9137951878280015556l_bool (tptp.aa_fun9159459243913713430l_bool _let_28 tptp.aTP_Lamm_ii) tptp.inverse_inverse_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_fun5258240734392065441l_bool tptp.pcr_real tptp.aTP_Lamm_ig) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_fun5258240734392065441l_bool tptp.pcr_real tptp.aTP_Lamm_ij) tptp.one_one_real)) (tptp.pp (tptp.aa_fun9137951878280015556l_bool (tptp.aa_fun9159459243913713430l_bool _let_28 tptp.aTP_Lamm_hy) tptp.uminus_uminus_real)) (tptp.bNF_re1162444993429354318l_real tptp.pcr_real _let_28 tptp.aTP_Lamm_hx tptp.plus_plus_real) (tptp.bNF_re1162444993429354318l_real tptp.pcr_real _let_28 tptp.aTP_Lamm_hu tptp.times_times_real) (forall ((P3 tptp.rat)) (= (tptp.aa_rat_int tptp.archim3151403230148437115or_rat P3) (tptp.produc8211389475949308722nt_int tptp.divide_divide_int (tptp.quotient_of P3)))) (forall ((Qr tptp.product_prod_int_int)) (= (tptp.adjust_div Qr) (tptp.produc8211389475949308722nt_int tptp.aTP_Lamm_ik Qr))) (tptp.pp (tptp.aa_fun3352386287069783311l_bool (tptp.aa_fun7221085148252759141l_bool _let_15 tptp.aTP_Lamm_il) tptp.positive2)) (tptp.bNF_re6214786843070381989at_nat tptp.intrel _let_17 _let_27 _let_27) (forall ((X tptp.nat) (Y4 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) Y4)) (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) Y4)))) (tptp.pp (tptp.aa_fun4519828053337421206t_bool (tptp.aa_fun2399787666232550060t_bool _let_17 _let_26) _let_26)) (tptp.pp (tptp.aa_Pro2232559814647311250t_bool (tptp.aa_Pro595088089689268830t_bool tptp.intrel _let_25) _let_25)) (forall ((X tptp.product_prod_nat_nat) (Y4 tptp.product_prod_nat_nat)) (= (= (tptp.aa_Pro4240683299535347697at_int tptp.abs_Integ X) (tptp.aa_Pro4240683299535347697at_int tptp.abs_Integ Y4)) (tptp.pp (tptp.aa_Pro2232559814647311250t_bool (tptp.aa_Pro595088089689268830t_bool tptp.intrel X) Y4)))) (forall ((X tptp.real) (Y4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool tptp.positive2 X)) (=> (tptp.pp (tptp.aa_real_bool tptp.positive2 Y4)) (tptp.pp (tptp.aa_real_bool tptp.positive2 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real X) Y4)))))) (not (tptp.pp (tptp.aa_real_bool tptp.positive2 tptp.zero_zero_real))) (forall ((X tptp.real) (Y4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool tptp.positive2 X)) (=> (tptp.pp (tptp.aa_real_bool tptp.positive2 Y4)) (tptp.pp (tptp.aa_real_bool tptp.positive2 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) Y4)))))) (forall ((X tptp.real)) (=> (not (tptp.pp (tptp.aa_real_bool tptp.positive2 X))) (=> (not (= X tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool tptp.positive2 (tptp.aa_real_real tptp.uminus_uminus_real X)))))) (tptp.bNF_re8246922863344978751at_nat tptp.intrel tptp.fequal_nat _let_24 _let_24) (forall ((X tptp.real) (Y4 tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Y4)) (tptp.pp (tptp.aa_real_bool tptp.positive2 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real Y4) X))))) (tptp.pp (tptp.aa_Pro2232559814647311250t_bool (tptp.aa_Pro595088089689268830t_bool tptp.intrel _let_23) _let_23)) (= tptp.intrel (tptp.produc5023667602222594023t_bool tptp.aTP_Lamm_in)) (tptp.bNF_re2219331435504962769t_bool tptp.intrel _let_21 _let_22 _let_22) (tptp.bNF_re2219331435504962769t_bool tptp.intrel _let_21 _let_20 _let_20) (tptp.bNF_re2632563231991741785t_bool tptp.pcr_int _let_19 tptp.intrel tptp.fequal_int) (tptp.bNF_re6214786843070381989at_nat tptp.intrel _let_17 _let_18 _let_18) (tptp.bNF_re6214786843070381989at_nat tptp.intrel _let_17 _let_16 _let_16) (forall ((X tptp.real)) (= (tptp.pp (tptp.aa_real_bool tptp.positive2 X)) (exists ((R5 tptp.rat)) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) R5)) (exists ((K3 tptp.nat)) (forall ((N4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K3) N4)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat R5) (tptp.aa_nat_rat (tptp.aa_real_fun_nat_rat tptp.rep_real X) N4)))))))))) (tptp.bNF_re2717234250851183977l_bool tptp.realrel tptp.fequal_bool tptp.aTP_Lamm_il tptp.aTP_Lamm_il) (tptp.bNF_re769765379126235449at_rat tptp.realrel _let_14 tptp.aTP_Lamm_hu tptp.aTP_Lamm_hu) (tptp.bNF_re769765379126235449at_rat tptp.realrel _let_14 tptp.aTP_Lamm_hx tptp.aTP_Lamm_hx) (tptp.pp (tptp.aa_fun1696419067750587730t_bool (tptp.aa_fun4901480949278917796t_bool _let_14 tptp.aTP_Lamm_hy) tptp.aTP_Lamm_hy)) (tptp.pp (tptp.aa_fun_nat_rat_bool (tptp.aa_fun6650786570619099624t_bool tptp.realrel tptp.aTP_Lamm_ig) tptp.aTP_Lamm_ig)) (tptp.pp (tptp.aa_fun_nat_rat_bool (tptp.aa_fun6650786570619099624t_bool tptp.realrel tptp.aTP_Lamm_ij) tptp.aTP_Lamm_ij)) (tptp.bNF_re8935275315890131625l_bool tptp.pcr_real _let_15 tptp.realrel tptp.fequal_real) (tptp.pp (tptp.aa_fun1696419067750587730t_bool (tptp.aa_fun4901480949278917796t_bool _let_14 tptp.aTP_Lamm_ii) tptp.aTP_Lamm_ii)) (= tptp.positive2 (tptp.map_fu1722713901878115497l_bool tptp.rep_real tptp.id_bool tptp.aTP_Lamm_il)) (forall ((X tptp.fun_nat_rat)) (=> (tptp.pp (tptp.aa_fun_nat_rat_bool (tptp.aa_fun6650786570619099624t_bool tptp.realrel X) X)) (= (tptp.aa_real_real tptp.inverse_inverse_real (tptp.aa_fun_nat_rat_real tptp.real2 X)) (tptp.aa_fun_nat_rat_real tptp.real2 (tptp.if_fun_nat_rat (tptp.vanishes X) tptp.aTP_Lamm_ig (tptp.aTP_Lamm_ih X)))))) (forall ((P tptp.fun_real_bool) (X tptp.real)) (=> (forall ((Y tptp.fun_nat_rat)) (=> (tptp.pp (tptp.aa_fun_nat_rat_bool (tptp.aa_fun6650786570619099624t_bool tptp.realrel Y) Y)) (tptp.pp (tptp.aa_real_bool P (tptp.aa_fun_nat_rat_real tptp.real2 Y))))) (tptp.pp (tptp.aa_real_bool P X)))) (forall ((X tptp.int)) (= (tptp.aa_int_real tptp.ring_1_of_int_real X) (tptp.aa_fun_nat_rat_real tptp.real2 (tptp.aTP_Lamm_io X)))) (forall ((X tptp.rat)) (= (tptp.aa_rat_real tptp.field_7254667332652039916t_real X) (tptp.aa_fun_nat_rat_real tptp.real2 (tptp.aTP_Lamm_hv X)))) (= tptp.one_one_real (tptp.aa_fun_nat_rat_real tptp.real2 tptp.aTP_Lamm_ij)) (= tptp.zero_zero_real (tptp.aa_fun_nat_rat_real tptp.real2 tptp.aTP_Lamm_ig)) (forall ((X tptp.nat)) (= (tptp.aa_nat_real tptp.semiri5074537144036343181t_real X) (tptp.aa_fun_nat_rat_real tptp.real2 (tptp.aTP_Lamm_ip X)))) (forall ((X tptp.fun_nat_rat)) (=> (tptp.pp (tptp.aa_fun_nat_rat_bool (tptp.aa_fun6650786570619099624t_bool tptp.realrel X) X)) (= (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_fun_nat_rat_real tptp.real2 X)) (tptp.aa_fun_nat_rat_real tptp.real2 (tptp.aa_fun765758790203053448at_rat tptp.aTP_Lamm_hy X))))) (forall ((Xa tptp.fun_nat_rat) (X tptp.fun_nat_rat)) (=> (tptp.pp (tptp.aa_fun_nat_rat_bool (tptp.aa_fun6650786570619099624t_bool tptp.realrel Xa) Xa)) (=> (tptp.pp (tptp.aa_fun_nat_rat_bool (tptp.aa_fun6650786570619099624t_bool tptp.realrel X) X)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_fun_nat_rat_real tptp.real2 Xa)) (tptp.aa_fun_nat_rat_real tptp.real2 X)) (tptp.aa_fun_nat_rat_real tptp.real2 (tptp.aa_fun765758790203053448at_rat (tptp.aa_fun3638354034882855594at_rat tptp.aTP_Lamm_hx Xa) X)))))) (forall ((Xa tptp.fun_nat_rat) (X tptp.fun_nat_rat)) (=> (tptp.pp (tptp.aa_fun_nat_rat_bool (tptp.aa_fun6650786570619099624t_bool tptp.realrel Xa) Xa)) (=> (tptp.pp (tptp.aa_fun_nat_rat_bool (tptp.aa_fun6650786570619099624t_bool tptp.realrel X) X)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_fun_nat_rat_real tptp.real2 Xa)) (tptp.aa_fun_nat_rat_real tptp.real2 X)) (tptp.aa_fun_nat_rat_real tptp.real2 (tptp.aa_fun765758790203053448at_rat (tptp.aa_fun3638354034882855594at_rat tptp.aTP_Lamm_hu Xa) X)))))) (forall ((X tptp.fun_nat_rat)) (=> (tptp.pp (tptp.aa_fun_nat_rat_bool (tptp.aa_fun6650786570619099624t_bool tptp.realrel X) X)) (= (tptp.pp (tptp.aa_real_bool tptp.positive2 (tptp.aa_fun_nat_rat_real tptp.real2 X))) (exists ((R5 tptp.rat)) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) R5)) (exists ((K3 tptp.nat)) (forall ((N4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K3) N4)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat R5) (tptp.aa_nat_rat X N4))))))))))) (= tptp.inverse_inverse_real (tptp.aa_fun8686829112900759002l_real _let_13 tptp.aTP_Lamm_ii)) (forall ((X7 tptp.fun_nat_rat) (Y6 tptp.fun_nat_rat)) (=> (tptp.cauchy X7) (=> (tptp.cauchy Y6) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_fun_nat_rat_real tptp.real2 X7)) (tptp.aa_fun_nat_rat_real tptp.real2 Y6))) (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 ((K3 tptp.nat)) (forall ((N4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K3) N4)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat X7 N4)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_nat_rat Y6 N4)) R5)))))))))))) (forall ((X4 tptp.fun_nat_rat) (Xa2 tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_fun5258240734392065441l_bool tptp.pcr_real X4) Xa2)) (and (tptp.cauchy X4) (= (tptp.aa_fun_nat_rat_real tptp.real2 X4) Xa2)))) (forall ((P tptp.fun_real_bool) (X tptp.real)) (=> (forall ((X9 tptp.fun_nat_rat)) (=> (tptp.cauchy X9) (tptp.pp (tptp.aa_real_bool P (tptp.aa_fun_nat_rat_real tptp.real2 X9))))) (tptp.pp (tptp.aa_real_bool P X)))) (forall ((X7 tptp.fun_nat_rat)) (=> (tptp.cauchy X7) (=> (not (tptp.pp (tptp.vanishes X7))) (tptp.cauchy (tptp.aTP_Lamm_ih X7))))) (forall ((X7 tptp.fun_nat_rat) (Y6 tptp.fun_nat_rat)) (=> (tptp.cauchy X7) (=> (tptp.cauchy Y6) (tptp.cauchy (tptp.aa_fun765758790203053448at_rat (tptp.aa_fun3638354034882855594at_rat tptp.aTP_Lamm_hx X7) Y6))))) (forall ((X7 tptp.fun_nat_rat)) (=> (tptp.cauchy X7) (tptp.cauchy (tptp.aa_fun765758790203053448at_rat tptp.aTP_Lamm_hy X7)))) (forall ((X tptp.rat)) (tptp.cauchy (tptp.aTP_Lamm_hv X))) (forall ((X7 tptp.fun_nat_rat) (Y6 tptp.fun_nat_rat)) (=> (tptp.cauchy X7) (=> (tptp.cauchy Y6) (tptp.cauchy (tptp.aa_fun765758790203053448at_rat (tptp.aa_fun3638354034882855594at_rat tptp.aTP_Lamm_hu X7) Y6))))) (forall ((X7 tptp.fun_nat_rat) (Y6 tptp.fun_nat_rat)) (=> (tptp.cauchy X7) (=> (tptp.cauchy Y6) (tptp.cauchy (tptp.aa_fun765758790203053448at_rat (tptp.aTP_Lamm_hw X7) Y6))))) (forall ((X7 tptp.fun_nat_rat)) (=> (tptp.cauchy X7) (tptp.pp (tptp.aa_fun_nat_rat_bool (tptp.aa_fun6650786570619099624t_bool tptp.realrel X7) X7)))) (forall ((X7 tptp.fun_nat_rat)) (=> (tptp.cauchy X7) (exists ((B2 tptp.rat)) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) B2)) (forall ((N6 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 N6))) B2))))))) (forall ((Y6 tptp.fun_nat_rat) (X tptp.real)) (=> (tptp.cauchy Y6) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) (tptp.aa_fun_nat_rat_real tptp.real2 Y6))) (exists ((N2 tptp.nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) (tptp.aa_rat_real tptp.field_7254667332652039916t_real (tptp.aa_nat_rat Y6 N2)))))))) (forall ((X7 tptp.fun_nat_rat) (Y4 tptp.real)) (=> (tptp.cauchy X7) (=> (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_rat_real tptp.field_7254667332652039916t_real (tptp.aa_nat_rat X7 N2))) Y4))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_fun_nat_rat_real tptp.real2 X7)) Y4))))) (forall ((Y6 tptp.fun_nat_rat) (X tptp.real)) (=> (tptp.cauchy Y6) (=> (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) (tptp.aa_rat_real tptp.field_7254667332652039916t_real (tptp.aa_nat_rat Y6 N2))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) (tptp.aa_fun_nat_rat_real tptp.real2 Y6)))))) (forall ((X7 tptp.fun_nat_rat)) (=> (tptp.cauchy X7) (= (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_fun_nat_rat_real tptp.real2 X7)) (tptp.aa_fun_nat_rat_real tptp.real2 (tptp.aa_fun765758790203053448at_rat tptp.aTP_Lamm_hy X7))))) (forall ((X7 tptp.fun_nat_rat) (Y6 tptp.fun_nat_rat)) (=> (tptp.cauchy X7) (=> (tptp.cauchy Y6) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_fun_nat_rat_real tptp.real2 X7)) (tptp.aa_fun_nat_rat_real tptp.real2 Y6)) (tptp.aa_fun_nat_rat_real tptp.real2 (tptp.aa_fun765758790203053448at_rat (tptp.aa_fun3638354034882855594at_rat tptp.aTP_Lamm_hx X7) Y6)))))) (forall ((X7 tptp.fun_nat_rat) (Y6 tptp.fun_nat_rat)) (=> (tptp.cauchy X7) (=> (tptp.cauchy Y6) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_fun_nat_rat_real tptp.real2 X7)) (tptp.aa_fun_nat_rat_real tptp.real2 Y6)) (tptp.aa_fun_nat_rat_real tptp.real2 (tptp.aa_fun765758790203053448at_rat (tptp.aa_fun3638354034882855594at_rat tptp.aTP_Lamm_hu X7) Y6)))))) (forall ((X7 tptp.fun_nat_rat) (Y6 tptp.fun_nat_rat)) (=> (tptp.cauchy X7) (=> (tptp.cauchy Y6) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_fun_nat_rat_real tptp.real2 X7)) (tptp.aa_fun_nat_rat_real tptp.real2 Y6)) (tptp.aa_fun_nat_rat_real tptp.real2 (tptp.aa_fun765758790203053448at_rat (tptp.aTP_Lamm_hw X7) Y6)))))) (forall ((X7 tptp.fun_nat_rat) (Y6 tptp.fun_nat_rat)) (=> (tptp.cauchy X7) (=> (tptp.cauchy Y6) (=> (tptp.pp (tptp.vanishes (tptp.aa_fun765758790203053448at_rat (tptp.aTP_Lamm_hw X7) Y6))) (tptp.pp (tptp.aa_fun_nat_rat_bool (tptp.aa_fun6650786570619099624t_bool tptp.realrel X7) Y6)))))) (forall ((X7 tptp.fun_nat_rat) (Y6 tptp.fun_nat_rat)) (=> (tptp.cauchy X7) (=> (tptp.cauchy Y6) (= (= (tptp.aa_fun_nat_rat_real tptp.real2 X7) (tptp.aa_fun_nat_rat_real tptp.real2 Y6)) (tptp.pp (tptp.vanishes (tptp.aa_fun765758790203053448at_rat (tptp.aTP_Lamm_hw X7) Y6))))))) (forall ((X7 tptp.fun_nat_rat) (Y6 tptp.fun_nat_rat)) (=> (tptp.cauchy X7) (=> (not (tptp.pp (tptp.vanishes X7))) (=> (tptp.cauchy Y6) (=> (not (tptp.pp (tptp.vanishes Y6))) (=> (tptp.pp (tptp.vanishes (tptp.aa_fun765758790203053448at_rat (tptp.aTP_Lamm_hw X7) Y6))) (tptp.pp (tptp.vanishes (tptp.aa_fun765758790203053448at_rat (tptp.aTP_Lamm_iq X7) Y6))))))))) (forall ((X4 tptp.fun_nat_rat) (Xa2 tptp.fun_nat_rat)) (= (tptp.pp (tptp.aa_fun_nat_rat_bool (tptp.aa_fun6650786570619099624t_bool tptp.realrel X4) Xa2)) (and (tptp.cauchy X4) (tptp.cauchy Xa2) (tptp.pp (tptp.vanishes (tptp.aa_fun765758790203053448at_rat (tptp.aTP_Lamm_hw X4) Xa2)))))) (forall ((X7 tptp.fun_nat_rat)) (=> (tptp.cauchy X7) (=> (not (tptp.pp (tptp.vanishes X7))) (exists ((B2 tptp.rat)) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) B2)) (exists ((K2 tptp.nat)) (or (forall ((N6 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K2) N6)) (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 (tptp.aa_nat_rat X7 N6)))))) (forall ((N6 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K2) N6)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B2) (tptp.aa_nat_rat X7 N6)))))))))))) (forall ((X7 tptp.fun_nat_rat)) (=> (tptp.cauchy X7) (= (tptp.pp (tptp.aa_real_bool tptp.positive2 (tptp.aa_fun_nat_rat_real tptp.real2 X7))) (exists ((R5 tptp.rat)) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) R5)) (exists ((K3 tptp.nat)) (forall ((N4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K3) N4)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat R5) (tptp.aa_nat_rat X7 N4))))))))))) (= tptp.uminus_uminus_real (tptp.aa_fun8686829112900759002l_real _let_13 tptp.aTP_Lamm_hy)) (forall ((X7 tptp.fun_nat_rat)) (=> (tptp.cauchy X7) (=> (not (tptp.pp (tptp.vanishes X7))) (exists ((B2 tptp.rat)) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) B2)) (exists ((K2 tptp.nat)) (forall ((N6 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K2) N6)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B2) (tptp.aa_rat_rat tptp.abs_abs_rat (tptp.aa_nat_rat X7 N6)))))))))))) (forall ((X7 tptp.fun_nat_rat) (R2 tptp.rat)) (=> (tptp.cauchy X7) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) R2)) (exists ((K2 tptp.nat)) (forall ((M2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K2) M2)) (forall ((N6 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K2) N6)) (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 (tptp.aa_nat_rat X7 M2)) (tptp.aa_nat_rat X7 N6)))) R2)))))))))) (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 ((M4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K4) M4)) (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_rat_rat (tptp.minus_minus_rat (tptp.aa_nat_rat X7 M4)) (tptp.aa_nat_rat X7 N2)))) R3))))))))) (tptp.cauchy X7))) (forall ((X7 tptp.fun_nat_rat)) (= (tptp.cauchy 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 ((K3 tptp.nat)) (forall ((M5 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K3) M5)) (forall ((N4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K3) N4)) (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 (tptp.aa_nat_rat X7 M5)) (tptp.aa_nat_rat X7 N4)))) R5))))))))))) (forall ((X7 tptp.fun_nat_rat)) (let ((_let_1 (tptp.aa_real_real tptp.inverse_inverse_real (tptp.aa_fun_nat_rat_real tptp.real2 X7)))) (let ((_let_2 (tptp.pp (tptp.vanishes X7)))) (=> (tptp.cauchy X7) (and (=> _let_2 (= _let_1 tptp.zero_zero_real)) (=> (not _let_2) (= _let_1 (tptp.aa_fun_nat_rat_real tptp.real2 (tptp.aTP_Lamm_ih X7))))))))) (forall ((X7 tptp.fun_nat_rat)) (=> (tptp.cauchy X7) (= (not (tptp.pp (tptp.aa_real_bool tptp.positive2 (tptp.aa_fun_nat_rat_real tptp.real2 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 ((K3 tptp.nat)) (forall ((N4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K3) N4)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat X7 N4)) R5)))))))))) (= tptp.times_times_real (tptp.map_fu2502140041903272327l_real tptp.rep_real _let_13 tptp.aTP_Lamm_hu)) (= tptp.plus_plus_real (tptp.map_fu2502140041903272327l_real tptp.rep_real _let_13 tptp.aTP_Lamm_hx)) (forall ((X4 tptp.fun_nat_rat) (Xa2 tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_fun5258240734392065441l_bool tptp.cr_real X4) Xa2)) (and (tptp.pp (tptp.aa_fun_nat_rat_bool (tptp.aa_fun6650786570619099624t_bool tptp.realrel X4) X4)) (= (tptp.aa_fun_nat_rat_real tptp.real2 X4) Xa2)))) (tptp.bi_tot896582865486249351at_int tptp.pcr_int) (= tptp.pcr_real tptp.cr_real) (forall ((R2 tptp.real) (A tptp.real)) (= (tptp.invers8013647133539491842omplex (tptp.rcis R2 A)) (tptp.rcis (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.one_one_real) R2) (tptp.aa_real_real tptp.uminus_uminus_real A)))) (forall ((R2 tptp.real)) (= (tptp.rcis R2 tptp.zero_zero_real) (tptp.real_V4546457046886955230omplex R2))) (forall ((R2 tptp.real) (A tptp.real)) (= (= (tptp.rcis R2 A) tptp.zero_zero_complex) (= R2 tptp.zero_zero_real))) (forall ((A tptp.real)) (= (tptp.rcis tptp.zero_zero_real A) tptp.zero_zero_complex)) (forall ((R2 tptp.real) (A tptp.real)) (= (tptp.aa_complex_real tptp.re (tptp.rcis R2 A)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real R2) (tptp.aa_real_real tptp.cos_real A)))) (forall ((R2 tptp.real) (A tptp.real)) (= (tptp.aa_complex_real tptp.im (tptp.rcis R2 A)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real R2) (tptp.aa_real_real tptp.sin_real A)))) (forall ((R1 tptp.real) (A tptp.real) (R22 tptp.real) (B tptp.real)) (= (tptp.aa_complex_complex (tptp.times_times_complex (tptp.rcis R1 A)) (tptp.rcis R22 B)) (tptp.rcis (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real R1) R22) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) B)))) (forall ((R1 tptp.real) (A tptp.real) (R22 tptp.real) (B tptp.real)) (= (tptp.divide1717551699836669952omplex (tptp.rcis R1 A) (tptp.rcis R22 B)) (tptp.rcis (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real R1) R22) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A) B)))) (forall ((R2 tptp.real) (A tptp.real) (N tptp.nat)) (= (tptp.aa_nat_complex (tptp.power_power_complex (tptp.rcis R2 A)) N) (tptp.rcis (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real R2) N) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N)) A)))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.member8440522571783428010at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat M) N) (tptp.transi2905341329935302413cl_nat tptp.pred_nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)))) (forall ((S tptp.set_nat) (N tptp.nat)) (=> (not (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat S))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N) (tptp.aa_nat_nat (tptp.infini8530281810654367211te_nat S) N))))) (forall ((S tptp.set_nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat S)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N) (tptp.finite_card_nat S))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N) (tptp.aa_nat_nat (tptp.infini8530281810654367211te_nat S) N)))))) (forall ((P tptp.fun_nat_bool)) (=> (tptp.pp (tptp.aa_nat_bool P tptp.zero_zero_nat)) (= (tptp.ord_Least_nat P) tptp.zero_zero_nat))) (forall ((P tptp.fun_nat_bool) (N tptp.nat) (Q tptp.fun_nat_bool) (M tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool P N)) (=> (tptp.pp (tptp.aa_nat_bool Q M)) (=> (not (tptp.pp (tptp.aa_nat_bool P tptp.zero_zero_nat))) (=> (forall ((K2 tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool P (tptp.aa_nat_nat tptp.suc K2))) (tptp.pp (tptp.aa_nat_bool Q K2)))) (= (tptp.ord_Least_nat P) (tptp.aa_nat_nat tptp.suc (tptp.ord_Least_nat Q)))))))) (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))) (= (tptp.ord_Least_nat P) (tptp.aa_nat_nat tptp.suc (tptp.ord_Least_nat (tptp.aTP_Lamm_gl P))))))) (forall ((X7 tptp.set_real)) (= (tptp.comple1385675409528146559p_real X7) (tptp.ord_Least_real (tptp.aTP_Lamm_ir X7)))) (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.last_nat (tptp.upt I J)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat J) tptp.one_one_nat)))) (forall ((A2 tptp.set_nat)) (= (tptp.vimage_nat_nat tptp.suc (tptp.insert_nat tptp.zero_zero_nat A2)) (tptp.vimage_nat_nat tptp.suc A2))) (forall ((N tptp.nat) (A2 tptp.set_nat)) (= (tptp.vimage_nat_nat tptp.suc (tptp.insert_nat (tptp.aa_nat_nat tptp.suc N) A2)) (tptp.insert_nat N (tptp.vimage_nat_nat tptp.suc A2)))) (forall ((F3 tptp.set_nat)) (= (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat (tptp.vimage_nat_nat tptp.suc F3))) (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat F3)))) (forall ((X tptp.nat)) (= (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)))) (tptp.vimage_nat_nat tptp.suc (tptp.nat_set_decode X)))) (forall ((A2 tptp.set_nat)) (= (tptp.aa_set_nat_nat tptp.nat_set_encode (tptp.vimage_nat_nat tptp.suc A2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_set_nat_nat tptp.nat_set_encode A2)) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (forall ((F tptp.fun_nat_real) (M10 tptp.nat)) (=> (tptp.bfun_nat_real (tptp.aa_nat_fun_nat_real (tptp.aTP_Lamm_is F) M10) tptp.at_top_nat) (=> (forall ((M4 tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M10) M4)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M4) N2)) (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 M4)))))) (tptp.topolo7531315842566124627t_real F)))) (forall ((X7 tptp.fun_nat_real)) (=> (tptp.bfun_nat_real X7 tptp.at_top_nat) (=> (forall ((M4 tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M4) N2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_nat_real X7 M4)) (tptp.aa_nat_real X7 N2))))) (tptp.topolo7531315842566124627t_real X7)))) (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.topolo7531315842566124627t_real (tptp.aa_real_fun_nat_real tptp.power_power_real X))))) (forall ((F tptp.fun_nat_real) (M10 tptp.nat)) (=> (tptp.bfun_nat_real (tptp.aa_nat_fun_nat_real (tptp.aTP_Lamm_is F) M10) tptp.at_top_nat) (=> (forall ((M4 tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M10) M4)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M4) N2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_nat_real F M4)) (tptp.aa_nat_real F N2)))))) (tptp.topolo7531315842566124627t_real F)))) (forall ((A tptp.nat) (B tptp.nat) (S2 tptp.nat) (T tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat S2) T)) (tptp.member8206827879206165904at_nat (tptp.produc6161850002892822231at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat A) S2) (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat B) T)) tptp.fun_pair_less)))) (forall ((A tptp.nat) (B tptp.nat) (S2 tptp.nat) (T tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat S2) T)) (tptp.member8206827879206165904at_nat (tptp.produc6161850002892822231at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat A) S2) (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat B) T)) tptp.fun_pair_leq)))) (forall ((D tptp.real) (A tptp.real)) (let ((_let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A) D))) (= (tptp.filtermap_real_real (tptp.aa_rea7340605660300375871l_real tptp.aTP_Lamm_it D) (tptp.topolo2177554685111907308n_real A (tptp.set_or5849166863359141190n_real A))) (tptp.topolo2177554685111907308n_real _let_1 (tptp.set_or5849166863359141190n_real _let_1))))) (forall ((A tptp.real)) (= (tptp.topolo2177554685111907308n_real A (tptp.set_or5849166863359141190n_real A)) (tptp.filtermap_real_real (tptp.aa_rea7340605660300375871l_real tptp.aTP_Lamm_iu A) (tptp.topolo2177554685111907308n_real tptp.zero_zero_real (tptp.set_or5849166863359141190n_real tptp.zero_zero_real))))) (= _let_12 (tptp.filtermap_real_real tptp.inverse_inverse_real tptp.at_top_real)) (= tptp.at_top_real (tptp.filtermap_real_real tptp.inverse_inverse_real _let_12)) (= (tptp.filtermap_real_real tptp.ln_ln_real _let_12) tptp.at_bot_real) (tptp.pp (tptp.aa_nat_bool (tptp.ordering_top_nat tptp.dvd_dvd_nat tptp.aTP_Lamm_ds) tptp.zero_zero_nat)) (tptp.pp (tptp.aa_nat_bool (tptp.ordering_top_nat tptp.aTP_Lamm_db tptp.aTP_Lamm_be) tptp.zero_zero_nat)) (forall ((Uu tptp.product_prod_int_int)) (let ((_let_1 (tptp.product_fst_int_int Uu))) (= (tptp.aa_Pro6970504127699319548nt_int tptp.aTP_Lamm_hh Uu) (tptp.if_Pro3027730157355071871nt_int (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.fequal_int _let_1) tptp.zero_zero_int) (tptp.product_Pair_int_int tptp.zero_zero_int tptp.one_one_int) (tptp.product_Pair_int_int (tptp.product_snd_int_int Uu) _let_1))))) (forall ((Uu tptp.fun_nat_rat)) (= (tptp.aa_fun765758790203053448at_rat tptp.aTP_Lamm_ii Uu) (tptp.if_fun_nat_rat (tptp.vanishes Uu) tptp.aTP_Lamm_ig (tptp.aTP_Lamm_ih Uu)))) (forall ((Uu tptp.nat)) (= (tptp.aa_nat_real tptp.aTP_Lamm_ai 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_ap 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_bz 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.nat)) (= (tptp.aa_nat_real tptp.aTP_Lamm_bj 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_fg 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.real)) (= (tptp.aa_real_real tptp.aTP_Lamm_gc Uu) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real tptp.ln_ln_real Uu)) Uu))) (forall ((Uu tptp.nat)) (= (tptp.aa_nat_real tptp.aTP_Lamm_fj 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_dp 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.nat)) (= (tptp.aa_nat7603221163087113075at_nat tptp.aTP_Lamm_ib 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_hb 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.nat)) (= (tptp.aa_nat_real tptp.aTP_Lamm_fm Uu) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.one_one_real) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real Uu)))) (forall ((Uu tptp.real)) (= (tptp.aa_real_real tptp.aTP_Lamm_fe Uu) (tptp.suminf_real (tptp.aa_real_fun_nat_real tptp.aTP_Lamm_aj Uu)))) (forall ((Uu tptp.nat)) (= (tptp.aa_nat_set_nat tptp.aTP_Lamm_ho Uu) (tptp.collect_nat (tptp.aa_nat_fun_nat_bool tptp.aTP_Lamm_da Uu)))) (forall ((Uu tptp.real)) (= (tptp.aa_rea5117059003799598681omplex tptp.aTP_Lamm_gq Uu) (tptp.princi3496590319149328850omplex (tptp.collec8663557070575231912omplex (tptp.produc9214369023355538061x_bool (tptp.aTP_Lamm_gp Uu)))))) (forall ((Uu tptp.real)) (= (tptp.aa_rea5428163979925208277l_real tptp.aTP_Lamm_go Uu) (tptp.princi6114159922880469582l_real (tptp.collec3799799289383736868l_real (tptp.produc5257810830037637649l_bool (tptp.aTP_Lamm_gn Uu)))))) (forall ((Uu tptp.nat)) (= (tptp.aa_nat_real tptp.aTP_Lamm_fo Uu) (tptp.aa_real_real tptp.inverse_inverse_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real (tptp.aa_nat_nat tptp.suc Uu))))) (forall ((Uu tptp.num)) (= (tptp.aa_num_option_num tptp.aTP_Lamm_gy Uu) (tptp.some_num (tptp.aa_num_num tptp.bit1 Uu)))) (forall ((Uu tptp.num)) (= (tptp.aa_num_option_num tptp.aTP_Lamm_gx Uu) (tptp.some_num (tptp.aa_num_num tptp.bit0 Uu)))) (forall ((Uu tptp.nat)) (= (tptp.aa_nat8803788312118491388at_nat tptp.aTP_Lamm_bv Uu) (tptp.product_Pair_nat_nat (tptp.aa_nat_nat tptp.suc Uu)))) (forall ((Uu tptp.fun_nat_rat)) (= (tptp.pp (tptp.aa_fun_nat_rat_bool tptp.aTP_Lamm_il Uu)) (exists ((R5 tptp.rat)) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) R5)) (exists ((K3 tptp.nat)) (forall ((N4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K3) N4)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat R5) (tptp.aa_nat_rat Uu N4)))))))))) (forall ((Uu tptp.real)) (= (tptp.pp (tptp.aa_real_bool tptp.aTP_Lamm_gt Uu)) (exists ((I2 tptp.int) (N4 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 I2)) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N4))) (not (= N4 tptp.zero_zero_nat)))))) (forall ((Uu tptp.real)) (= (tptp.pp (tptp.aa_real_bool tptp.aTP_Lamm_gu Uu)) (exists ((I2 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 I2)) (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_gw Uu) (tptp.some_num tptp.one))) (forall ((Uu tptp.num) (Uua tptp.nat)) (= (tptp.aa_nat_option_num (tptp.aTP_Lamm_he Uu) Uua) (tptp.case_num_option_num (tptp.some_num tptp.one) (tptp.aTP_Lamm_hc Uua) (tptp.aTP_Lamm_hd Uua) Uu))) (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_aq 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_du Uu) Uua) (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.code_integer) (Uua tptp.code_integer)) (let ((_let_1 (tptp.code_num_of_integer Uu))) (let ((_let_2 (tptp.aa_num_num (tptp.plus_plus_num _let_1) _let_1))) (= (tptp.aa_Code_integer_num (tptp.aa_Cod6128727250572145423er_num tptp.aTP_Lamm_hj Uu) Uua) (tptp.aa_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.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_dt Uu) Uua) (tptp.aa_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_cl Uu) Uua) (tptp.if_Pro3027730157355071871nt_int (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.fequal_int Uu) tptp.zero_zero_int) (tptp.product_Pair_int_int tptp.zero_zero_int tptp.one_one_int) (tptp.product_Pair_int_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_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_hz Uu) Uua) (tptp.if_Pro3027730157355071871nt_int (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.fequal_int Uua) tptp.zero_zero_int) (tptp.product_Pair_int_int tptp.zero_zero_int tptp.one_one_int) (tptp.product_Pair_int_int Uu Uua)))) (forall ((Uu tptp.nat) (Uua tptp.num)) (= (tptp.aa_num_option_num (tptp.aa_nat3713591252005393295on_num tptp.aTP_Lamm_hf Uu) Uua) (tptp.case_nat_option_num tptp.none_num (tptp.aTP_Lamm_he Uua) Uu))) (forall ((Uu tptp.nat) (Uua tptp.num)) (= (tptp.aa_num_option_num (tptp.aTP_Lamm_hc Uu) Uua) (tptp.case_o6005452278849405969um_num tptp.none_num tptp.aTP_Lamm_gx (tptp.bit_take_bit_num Uu Uua)))) (forall ((Uu tptp.num) (Uua tptp.nat)) (= (tptp.aa_nat_option_num (tptp.aTP_Lamm_gz Uu) Uua) (tptp.case_o6005452278849405969um_num tptp.none_num tptp.aTP_Lamm_gx (tptp.bit_take_bit_num Uua Uu)))) (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_hg Uu) Uua) (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_ah 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_ao 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_as 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.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_ca 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_bw 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.aTP_Lamm_at Uu) Uua)) (and (= (tptp.sgn_sgn_complex Uu) (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_hi Uu) Uua) (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.aTP_Lamm_cj 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_ck 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_aj 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_ff 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_fh 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.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_hq 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.nat) (Uua tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.aTP_Lamm_ds Uu) Uua)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat Uu) Uua)) (not (= Uu Uua))))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat_nat (tptp.aTP_Lamm_bc Uu) Uua) (tptp.aa_nat_nat (tptp.power_power_nat (tptp.aa_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_gs Uu) Uua)) (and (tptp.member_int Uua Uu) (forall ((X5 tptp.int)) (=> (tptp.member_int X5 Uu) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X5) Uua))))))) (forall ((Uu tptp.real) (Uua tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.aTP_Lamm_bo 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.nat) (Uua tptp.real)) (= (tptp.aa_real_real (tptp.aa_nat_fun_real_real tptp.aTP_Lamm_gd 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 Uua) Uu)) (tptp.aa_real_real tptp.exp_real Uua)))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat_set_nat (tptp.aTP_Lamm_ie Uu) Uua) (tptp.set_or6659071591806873216st_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uu) Uua) Uu))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat_nat (tptp.aTP_Lamm_hr Uu) Uua) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat (tptp.power_power_nat Uu) Uua)) Uua))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat_nat (tptp.aTP_Lamm_au Uu) Uua) (tptp.aa_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_ak Uu) Uua)) (= (tptp.aa_nat_complex (tptp.power_power_complex Uua) Uu) tptp.one_one_complex))) (forall ((Uu tptp.real) (Uua tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.aTP_Lamm_ft Uu) Uua) (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 Uu) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real Uua)))) Uua))) (forall ((Uu tptp.real) (Uua tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.aTP_Lamm_gb 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.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.aTP_Lamm_ge 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.divide_divide_real Uu) Uua))) 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_ag 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_by 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)) (= (tptp.aa_nat_real (tptp.aTP_Lamm_fz Uu) Uua) (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aTP_Lamm_fh 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_fy Uu) Uua) (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aTP_Lamm_fh 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_eg 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.num) (Uua tptp.num)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat Uu))) (= (tptp.aa_num_int (tptp.aTP_Lamm_gv 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_em 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_bi 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_bh 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_ia 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_nat (tptp.aTP_Lamm_bd Uu) Uua) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat Uua) (tptp.aa_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_fu 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.int) (Uua tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.aTP_Lamm_ik Uu) Uua) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int Uu) (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 Uua) tptp.zero_zero_int)))))) (forall ((Uu tptp.real) (Uua tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.aTP_Lamm_fs Uu) Uua) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real Uu) (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.real) (Uua tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.aTP_Lamm_fp Uu) Uua) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real Uu) (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_el Uu) Uua) (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real Uu) (tptp.set_ord_lessThan_nat Uua)))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.aTP_Lamm_eh Uu) Uua)) (= Uua (tptp.aa_nat_nat tptp.suc Uu)))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.aTP_Lamm_db Uu) Uua)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Uua) Uu)))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat_nat (tptp.aTP_Lamm_ek Uu) Uua) (tptp.aa_nat_nat (tptp.modulo_modulo_nat Uua) Uu))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.aTP_Lamm_be Uu) Uua)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Uua) Uu)))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat_nat (tptp.aTP_Lamm_fi Uu) Uua) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat Uua) Uu))) (forall ((Uu tptp.real) (Uua tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.aTP_Lamm_it Uu) Uua) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real Uua) Uu))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat_nat (tptp.aTP_Lamm_ei 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_en Uu) Uua) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Uua) Uu))) (forall ((Uu tptp.real) (Uua tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.aTP_Lamm_iu Uu) Uua) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real Uua) Uu))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat_nat (tptp.aTP_Lamm_do Uu) Uua) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Uua) Uu))) (forall ((Uu tptp.int) (Uua tptp.int)) (= (tptp.aa_int_int (tptp.aTP_Lamm_ej Uu) Uua) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int Uua) Uu))) (forall ((Uu tptp.real) (Uua tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.aTP_Lamm_ep Uu) Uua) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.powr_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_da 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_dg 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_dx Uu) Uua) (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Uua) Uu))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat_nat (tptp.aTP_Lamm_av Uu) Uua) (tptp.aa_nat_nat (tptp.binomial Uua) Uu))) (forall ((Uu tptp.real) (Uua tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.aTP_Lamm_fn 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.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_set_nat) (Uua tptp.set_nat)) (= (tptp.pp (tptp.aa_set_nat_bool (tptp.aTP_Lamm_ac Uu) Uua)) (tptp.member_set_nat Uua Uu))) (forall ((Uu tptp.set_nat) (Uua tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aTP_Lamm_ad 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_ae Uu) Uua)) (tptp.member_int Uua Uu))) (forall ((Uu tptp.fun_nat_real) (Uua tptp.nat)) (= (tptp.aa_nat_real (tptp.aTP_Lamm_bn 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_bm 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_real_bool) (Uua tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aTP_Lamm_gj Uu) Uua)) (tptp.pp (tptp.aa_real_bool Uu (tptp.aa_real_real tptp.inverse_inverse_real Uua))))) (forall ((Uu tptp.fun_real_real) (Uua tptp.nat)) (= (tptp.aa_nat_real (tptp.aTP_Lamm_hs Uu) Uua) (tptp.aa_real_real Uu (tptp.aa_nat_real tptp.semiri5074537144036343181t_real Uua)))) (forall ((Uu tptp.fun_nat_bool) (Uua tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aTP_Lamm_gl Uu) Uua)) (tptp.pp (tptp.aa_nat_bool Uu (tptp.aa_nat_nat tptp.suc Uua))))) (forall ((Uu tptp.nat) (Uua tptp.num)) (= (tptp.aa_num_option_num (tptp.aTP_Lamm_hd 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_ha 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_in Uu) Uua) (tptp.produc8955392012077580105t_bool (tptp.aa_nat8637530788439456283t_bool (tptp.aTP_Lamm_im Uu) Uua)))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat7997280740862404369at_nat (tptp.aa_nat5682243440470347102at_nat tptp.aTP_Lamm_ef Uu) Uua) (tptp.produc2626176000494625587at_nat (tptp.aa_nat4158579785191972357at_nat (tptp.aTP_Lamm_ee Uu) Uua)))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat7997280740862404369at_nat (tptp.aa_nat5682243440470347102at_nat tptp.aTP_Lamm_ed Uu) Uua) (tptp.produc2626176000494625587at_nat (tptp.aa_nat4158579785191972357at_nat (tptp.aTP_Lamm_ec Uu) Uua)))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat4401263874371387303t_bool (tptp.aa_nat4909001760120733684t_bool tptp.aTP_Lamm_eb Uu) Uua) (tptp.produc8955392012077580105t_bool (tptp.aa_nat8637530788439456283t_bool (tptp.aTP_Lamm_ea Uu) Uua)))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat4401263874371387303t_bool (tptp.aa_nat4909001760120733684t_bool tptp.aTP_Lamm_dz Uu) Uua) (tptp.produc8955392012077580105t_bool (tptp.aa_nat8637530788439456283t_bool (tptp.aTP_Lamm_dy Uu) Uua)))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat7997280740862404369at_nat (tptp.aa_nat5682243440470347102at_nat tptp.aTP_Lamm_dw Uu) Uua) (tptp.produc2626176000494625587at_nat (tptp.aa_nat4158579785191972357at_nat (tptp.aTP_Lamm_dv Uu) Uua)))) (forall ((Uu tptp.fun_nat_real) (Uua tptp.real)) (= (tptp.aa_real_real (tptp.aTP_Lamm_ew Uu) Uua) (tptp.suminf_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_ev Uu) Uua)))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat_complex (tptp.aTP_Lamm_bp Uu) Uua) (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.fun_real_real) (Uua tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aTP_Lamm_gf Uu) Uua)) (not (= (tptp.aa_real_real Uu Uua) tptp.zero_zero_real)))) (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_af 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.power_power_nat _let_1) Uua)))))))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat_set_nat (tptp.aTP_Lamm_id Uu) Uua) (tptp.set_ord_atMost_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uu) Uua)))) (forall ((Uu tptp.real) (Uua tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.aTP_Lamm_fr 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.aTP_Lamm_hl 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.aTP_Lamm_hk 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.aTP_Lamm_ci 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.aTP_Lamm_ch 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_nat_real) (Uua tptp.nat)) (= (tptp.aa_nat_real (tptp.aTP_Lamm_fl Uu) Uua) (tptp.aa_real_real tptp.inverse_inverse_real (tptp.aa_nat_real Uu Uua)))) (forall ((Uu tptp.fun_nat_rat) (Uua tptp.nat)) (= (tptp.aa_nat_rat (tptp.aTP_Lamm_ih Uu) Uua) (tptp.aa_rat_rat tptp.inverse_inverse_rat (tptp.aa_nat_rat Uu Uua)))) (forall ((Uu tptp.fun_nat_rat) (Uua tptp.nat)) (= (tptp.aa_nat_rat (tptp.aa_fun765758790203053448at_rat tptp.aTP_Lamm_hy Uu) Uua) (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_nat_rat Uu Uua)))) (forall ((Uu tptp.fun_real_real) (Uua tptp.real)) (= (tptp.aa_real_real (tptp.aTP_Lamm_gm 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_am Uu) Uua) (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_nat_real Uu Uua)))) (forall ((Uu tptp.fun_nat_real) (Uua tptp.nat)) (= (tptp.aa_nat_real (tptp.aTP_Lamm_fx 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_er Uu) Uua) (tptp.suminf_real (tptp.aa_real_fun_nat_real Uu Uua)))) (forall ((Uu tptp.set_real) (Uua tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aTP_Lamm_ir Uu) Uua)) (forall ((X5 tptp.real)) (=> (tptp.member_real X5 Uu) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X5) Uua)))))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat_set_nat (tptp.aTP_Lamm_ic Uu) Uua) (tptp.set_ord_atMost_nat Uu))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat_rat (tptp.aTP_Lamm_ip Uu) Uua) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat Uu))) (forall ((Uu tptp.int) (Uua tptp.nat)) (= (tptp.aa_nat_rat (tptp.aTP_Lamm_io Uu) Uua) (tptp.aa_int_rat tptp.ring_1_of_int_rat 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_ar 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_bl 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.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))) Uua))) (let ((_let_2 (tptp.numera6620942414471956472nteger Uu))) (= (tptp.aa_Cod6977894654539884864nteger (tptp.aa_Cod8380929501330563836nteger (tptp.aTP_Lamm_ce 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_bs Uu) Uua) Uub) (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_bt Uu) Uua) Uub) (tptp.if_Pro3027730157355071871nt_int (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int _let_2) Uub) (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.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_di 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_dr 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_dh 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_real_real) (Uua tptp.fun_real_real) (Uub tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_fun9137271176455094897l_bool (tptp.aTP_Lamm_gg Uu) Uua) Uub)) (tptp.has_fi5821293074295781190e_real Uu (tptp.aa_real_real Uua Uub) (tptp.topolo2177554685111907308n_real Uub tptp.top_top_set_real)))) (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_eq Uu) Uua) Uub) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real Uu Uub) Uua))) (forall ((Uu tptp.code_integer) (Uua tptp.code_integer) (Uub tptp.code_integer)) (= (tptp.aa_Cod2825494507867081354r_bool (tptp.aa_Cod4981436349852597092r_bool (tptp.aTP_Lamm_cy 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_cx Uu) Uua) Uub)) (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.produc8560705615207772305t_bool (tptp.aa_int2327297053056786951t_bool (tptp.aTP_Lamm_cw 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_cv Uu) Uua) Uub)) (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.produc8560705615207772305t_bool (tptp.aa_int2327297053056786951t_bool (tptp.aTP_Lamm_cu 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_ct Uu) Uua) Uub) (tptp.produc4245557441103728435nt_int (tptp.aa_int1966403025003302569nt_int (tptp.aTP_Lamm_cs 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_cr Uu) Uua) Uub) (tptp.produc4245557441103728435nt_int (tptp.aa_int1966403025003302569nt_int (tptp.aTP_Lamm_cq 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_cp Uu) Uua) Uub) (tptp.produc4245557441103728435nt_int (tptp.aa_int1966403025003302569nt_int (tptp.aTP_Lamm_co 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_cn Uu) Uua) Uub) (tptp.produc4245557441103728435nt_int (tptp.aa_int1966403025003302569nt_int (tptp.aTP_Lamm_cm 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_ex 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_na6724076748692969250l_real) (Uub tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_fun1113820866546176217t_real (tptp.aTP_Lamm_ey 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.fun_nat_real) (Uua tptp.real) (Uub tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_eu 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_bk 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_dk 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.nat) (Uua tptp.nat) (Uub tptp.list_nat)) (= (tptp.pp (tptp.aa_list_nat_bool (tptp.aa_nat2079453845469346690t_bool (tptp.aTP_Lamm_dl 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.nat) (Uua tptp.nat) (Uub tptp.list_nat)) (= (tptp.pp (tptp.aa_list_nat_bool (tptp.aa_nat2079453845469346690t_bool (tptp.aTP_Lamm_dj 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_dm 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.set_nat)) (= (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_nat8857836526276733660t_bool (tptp.aTP_Lamm_dq Uu) Uua) Uub)) (and (tptp.member_set_nat Uub (tptp.pow_nat (tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat Uu))) (= (tptp.finite_card_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_dn 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.nat) (Uua tptp.nat) (Uub tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.aTP_Lamm_aw Uu) Uua) Uub) (tptp.aa_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_cc 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_dc 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_cd 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_de 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_df 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_dd 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_hn 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.int) (Uua tptp.int) (Uub tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int Uub))) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool (tptp.aTP_Lamm_hp Uu) Uua) Uub)) (and (tptp.pp (tptp.aa_int_bool _let_1 Uua)) (tptp.pp (tptp.aa_int_bool _let_1 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_hm 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_if 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_gp 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_gn 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.complex) (Uub tptp.complex)) (= (tptp.pp (tptp.aa_complex_bool (tptp.aa_com1553036987509291606x_bool (tptp.aTP_Lamm_bg 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_al Uu) Uua) Uub)) (= (tptp.aa_nat_complex (tptp.power_power_complex Uub) Uua) Uu))) (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_fw 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_ev 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_real) (Uua tptp.real) (Uub tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_an 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_nat) (Uua tptp.nat) (Uub tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.aTP_Lamm_az 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.power_power_nat 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_gk Uu) Uua) Uub) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real Uu Uub)) (tptp.aa_real_real 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_gh Uu) Uua) Uub) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real Uua Uub)) (tptp.aa_real_real 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.aa_fun3638354034882855594at_rat tptp.aTP_Lamm_hu 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_cb 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_real) (Uua tptp.fun_nat_real) (Uub tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_fun1839206346889086768t_real (tptp.aTP_Lamm_fk 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_hw 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_nat_rat) (Uua tptp.fun_nat_rat) (Uub tptp.nat)) (= (tptp.aa_nat_rat (tptp.aa_fun765758790203053448at_rat (tptp.aa_fun3638354034882855594at_rat tptp.aTP_Lamm_hx 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_real_real) (Uua tptp.fun_real_real) (Uub tptp.real)) (= (tptp.aa_real_real (tptp.aa_fun6946558556880649704l_real (tptp.aTP_Lamm_et 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_cz 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_real_real) (Uua tptp.nat) (Uub tptp.real)) (= (tptp.aa_real_real (tptp.aa_nat_fun_real_real (tptp.aTP_Lamm_eo 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.nat) (Uua tptp.fun_real_real) (Uub tptp.real)) (= (tptp.aa_real_real (tptp.aa_fun6946558556880649704l_real (tptp.aTP_Lamm_ga 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_es Uu) Uua) Uub) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.powr_real (tptp.aa_real_real Uu 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_iq Uu) Uua) Uub) (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_rat_rat tptp.inverse_inverse_rat (tptp.aa_nat_rat Uu Uub))) (tptp.aa_rat_rat tptp.inverse_inverse_rat (tptp.aa_nat_rat Uua Uub))))) (forall ((Uu tptp.real) (Uua tptp.real) (Uub tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_fq 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.nat) (Uua tptp.nat) (Uub tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.aTP_Lamm_br 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.fun_real_bool) (Uua tptp.real) (Uub tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool (tptp.aTP_Lamm_gi Uu) Uua) Uub)) (tptp.pp (tptp.aa_real_bool Uu (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real 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_is 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_real) (Uua tptp.fun_nat_nat) (Uub tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_fun1538629612289296340t_real (tptp.aTP_Lamm_ht Uu) Uua) Uub) (tptp.aa_nat_real Uu (tptp.aa_nat_nat 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_fv 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_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_bb 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_ba Uu) Uua) Uuc)) (tptp.set_ord_atMost_nat Uuc))) (tptp.aa_nat_nat (tptp.power_power_nat 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_fd 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_fb 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_fa 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_ez 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.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_dv 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.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_ay 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.binomial Uub) Uuc))) (tptp.aa_nat_nat (tptp.power_power_nat Uu) Uuc))) (tptp.aa_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.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_ax Uu) Uua) Uub) Uuc) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.binomial Uu) Uuc)) (tptp.aa_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_cw 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_ea 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_cu 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_dy 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_ec 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_ee 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_im 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.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_ba 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.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_cs Uu) Uua) Uub) Uuc) (tptp.normalize (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_cq Uu) Uua) Uub) Uuc) (tptp.normalize (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_cm Uu) Uua) Uub) Uuc) (tptp.normalize (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_co Uu) Uua) Uub) Uuc) (tptp.normalize (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.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_fc 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.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real (tptp.aa_nat1308781354268537904t_real (tptp.aTP_Lamm_fb 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.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_gr 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.power_power_nat _let_1) Uu))) (forall ((I2 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 I2) (tptp.aa_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_12 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions (tptp.nth_VEBT_VEBT Uua I2)) X_12))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions Uub) I2)))))) (=> _let_2 (forall ((X5 tptp.vEBT_VEBT)) (=> (tptp.pp (tptp.aa_set8260762808118238015T_bool (tptp.aa_VEB289770264548726718T_bool tptp.member_VEBT_VEBT X5) (tptp.set_VEBT_VEBT2 Uua))) (not (exists ((X_12 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions X5) X_12))))))) (=> (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 ((X5 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 X5) (tptp.aa_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) X5)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Uuc) X5)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X5) Uud)))))))))))))) (forall ((Uu tptp.rat) (Uua tptp.nat)) (= (tptp.aa_nat_rat (tptp.aTP_Lamm_hv Uu) Uua) Uu)) (forall ((Uu tptp.complex)) (= (tptp.aa_complex_complex tptp.aTP_Lamm_bf Uu) Uu)) (forall ((Uu tptp.nat)) (= (tptp.aa_nat_nat tptp.aTP_Lamm_bq Uu) Uu)) (forall ((Uu tptp.int)) (= (tptp.aa_int_int tptp.aTP_Lamm_bu Uu) Uu)) (forall ((Uu tptp.nat)) (= (tptp.aa_nat_rat tptp.aTP_Lamm_ig Uu) tptp.zero_zero_rat)) (forall ((Uu tptp.nat)) (= (tptp.aa_nat_rat tptp.aTP_Lamm_ij Uu) tptp.one_one_rat)) (forall ((Uu tptp.real)) (= (tptp.pp (tptp.aa_real_bool tptp.aTP_Lamm_bx Uu)) false)) (forall ((Uu tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool tptp.aTP_Lamm_cg Uu)) false)) (forall ((Uu tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool tptp.aTP_Lamm_cf 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) (Y4 tptp.int)) (= (tptp.if_int tptp.fFalse X Y4) Y4)) (forall ((X tptp.int) (Y4 tptp.int)) (= (tptp.if_int tptp.fTrue X Y4) X)) (forall ((X tptp.nat) (Y4 tptp.nat)) (= (tptp.aa_nat_nat (tptp.if_nat tptp.fFalse X) Y4) Y4)) (forall ((X tptp.nat) (Y4 tptp.nat)) (= (tptp.aa_nat_nat (tptp.if_nat tptp.fTrue X) Y4) X)) (forall ((X tptp.num) (Y4 tptp.num)) (= (tptp.aa_num_num (tptp.if_num tptp.fFalse X) Y4) Y4)) (forall ((X tptp.num) (Y4 tptp.num)) (= (tptp.aa_num_num (tptp.if_num tptp.fTrue X) Y4) 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) (Y4 tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real (tptp.if_real tptp.fFalse) X) Y4) Y4)) (forall ((X tptp.real) (Y4 tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real (tptp.if_real tptp.fTrue) X) Y4) X)) (forall ((X tptp.int) (Y4 tptp.int)) (or (not (= X Y4)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.fequal_int X) Y4)))) (forall ((X tptp.int) (Y4 tptp.int)) (or (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.fequal_int X) Y4))) (= X Y4))) (forall ((X tptp.nat) (Y4 tptp.nat)) (or (not (= X Y4)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.fequal_nat X) Y4)))) (forall ((X tptp.nat) (Y4 tptp.nat)) (or (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.fequal_nat X) Y4))) (= X Y4))) (forall ((X tptp.num) (Y4 tptp.num)) (or (not (= X Y4)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.fequal_num X) Y4)))) (forall ((X tptp.num) (Y4 tptp.num)) (or (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.fequal_num X) Y4))) (= X Y4))) (forall ((X tptp.rat) (Y4 tptp.rat)) (or (not (= X Y4)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.fequal_rat X) Y4)))) (forall ((X tptp.rat) (Y4 tptp.rat)) (or (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.fequal_rat X) Y4))) (= X Y4))) (forall ((X tptp.bool) (Y4 tptp.bool)) (or (not (= X Y4)) (tptp.pp (tptp.aa_bool_bool (tptp.aa_boo8970175072276269406l_bool tptp.fequal_bool X) Y4)))) (forall ((X tptp.bool) (Y4 tptp.bool)) (or (not (tptp.pp (tptp.aa_bool_bool (tptp.aa_boo8970175072276269406l_bool tptp.fequal_bool X) Y4))) (= X Y4))) (forall ((X tptp.real) (Y4 tptp.real)) (or (not (= X Y4)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.fequal_real X) Y4)))) (forall ((X tptp.real) (Y4 tptp.real)) (or (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.fequal_real X) Y4))) (= X Y4))) (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) (Y4 tptp.complex)) (or (not (= X Y4)) (tptp.pp (tptp.aa_complex_bool (tptp.fequal_complex X) Y4)))) (forall ((X tptp.complex) (Y4 tptp.complex)) (or (not (tptp.pp (tptp.aa_complex_bool (tptp.fequal_complex X) Y4))) (= X Y4))) (forall ((X tptp.code_integer) (Y4 tptp.code_integer)) (= (tptp.if_Code_integer tptp.fFalse X Y4) Y4)) (forall ((X tptp.code_integer) (Y4 tptp.code_integer)) (= (tptp.if_Code_integer tptp.fTrue X Y4) 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) (Y4 tptp.code_integer)) (or (not (= X Y4)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.fequal_Code_integer X) Y4)))) (forall ((X tptp.code_integer) (Y4 tptp.code_integer)) (or (not (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.fequal_Code_integer X) Y4))) (= X Y4))) (forall ((X tptp.fun_int_int) (Y4 tptp.fun_int_int)) (= (tptp.if_fun_int_int tptp.fFalse X Y4) Y4)) (forall ((X tptp.fun_int_int) (Y4 tptp.fun_int_int)) (= (tptp.if_fun_int_int tptp.fTrue X Y4) X)) (forall ((X tptp.fun_nat_rat) (Y4 tptp.fun_nat_rat)) (= (tptp.if_fun_nat_rat tptp.fFalse X Y4) Y4)) (forall ((X tptp.fun_nat_rat) (Y4 tptp.fun_nat_rat)) (= (tptp.if_fun_nat_rat tptp.fTrue X Y4) X)) (forall ((X tptp.product_prod_int_int) (Y4 tptp.product_prod_int_int)) (= (tptp.if_Pro3027730157355071871nt_int tptp.fFalse X Y4) Y4)) (forall ((X tptp.product_prod_int_int) (Y4 tptp.product_prod_int_int)) (= (tptp.if_Pro3027730157355071871nt_int tptp.fTrue X Y4) X)) (forall ((X tptp.product_prod_nat_nat) (Y4 tptp.product_prod_nat_nat)) (= (tptp.if_Pro6206227464963214023at_nat tptp.fFalse X Y4) Y4)) (forall ((X tptp.product_prod_nat_nat) (Y4 tptp.product_prod_nat_nat)) (= (tptp.if_Pro6206227464963214023at_nat tptp.fTrue X Y4) X)) (forall ((X tptp.fun_nat_fun_int_int) (Y4 tptp.fun_nat_fun_int_int)) (= (tptp.if_fun5757141600869472092nt_int tptp.fFalse X Y4) Y4)) (forall ((X tptp.fun_nat_fun_int_int) (Y4 tptp.fun_nat_fun_int_int)) (= (tptp.if_fun5757141600869472092nt_int tptp.fTrue X Y4) X)) (forall ((X tptp.fun_nat_fun_nat_nat) (Y4 tptp.fun_nat_fun_nat_nat)) (= (tptp.if_fun6060303171108177060at_nat tptp.fFalse X Y4) Y4)) (forall ((X tptp.fun_nat_fun_nat_nat) (Y4 tptp.fun_nat_fun_nat_nat)) (= (tptp.if_fun6060303171108177060at_nat tptp.fTrue X Y4) X)) (forall ((P tptp.fun_bool_bool) (Q tptp.fun_VEBT_VEBT_bool) (R tptp.vEBT_VEBT)) (= (tptp.aa_VEBT_VEBT_bool (tptp.cOMBB_3745307990312268622T_VEBT P Q) R) (tptp.aa_bool_bool P (tptp.aa_VEBT_VEBT_bool Q R)))) (forall ((P tptp.fun_VE2066785035971159626l_bool) (Q tptp.fun_VEBT_VEBT_bool) (R tptp.vEBT_VEBT)) (= (tptp.aa_VEBT_VEBT_bool (tptp.cOMBS_6222329278419335549l_bool P Q) R) (tptp.aa_bool_bool (tptp.aa_VEB8047906998784800507l_bool P R) (tptp.aa_VEBT_VEBT_bool Q R)))) (forall ((X tptp.produc8923325533196201883nteger) (Y4 tptp.produc8923325533196201883nteger)) (= (tptp.if_Pro6119634080678213985nteger tptp.fFalse X Y4) Y4)) (forall ((X tptp.produc8923325533196201883nteger) (Y4 tptp.produc8923325533196201883nteger)) (= (tptp.if_Pro6119634080678213985nteger tptp.fTrue X Y4) X)) (forall ((P tptp.fun_fu7168253649841883962l_bool) (Q tptp.fun_VE3763956218935105199t_bool) (R tptp.vEBT_VEBT)) (= (tptp.aa_VEBT_VEBT_bool (tptp.cOMBB_2885587777813823575T_VEBT P Q) R) (tptp.aa_fun_nat_bool_bool P (tptp.aa_VEB4832260192069861672t_bool Q R)))) (forall ((P tptp.fun_bo1841576699660343469l_bool) (Q tptp.fun_VEBT_VEBT_bool) (R tptp.vEBT_VEBT)) (= (tptp.aa_VEB8047906998784800507l_bool (tptp.cOMBB_3438363824644082366T_VEBT P Q) R) (tptp.aa_boo8970175072276269406l_bool P (tptp.aa_VEBT_VEBT_bool Q R)))) (forall ((P tptp.bool)) (or (= P tptp.fTrue) (= P tptp.fFalse))) (forall ((X tptp.fun_na7078387940644931716nteger) (Y4 tptp.fun_na7078387940644931716nteger)) (= (tptp.if_fun4784160582202652222nteger tptp.fFalse X Y4) Y4)) (forall ((X tptp.fun_na7078387940644931716nteger) (Y4 tptp.fun_na7078387940644931716nteger)) (= (tptp.if_fun4784160582202652222nteger tptp.fTrue X Y4) X)) (forall ((P tptp.fun_VE7346385682144900493T_bool) (Q tptp.set_VEBT_VEBT) (R tptp.vEBT_VEBT)) (= (tptp.aa_VEBT_VEBT_bool (tptp.cOMBC_771164880915498576T_bool P Q) R) (tptp.aa_set8260762808118238015T_bool (tptp.aa_VEB289770264548726718T_bool P R) Q))) _let_10 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 19.17/19.53 )
% 19.17/19.53 % SZS output end Proof for ITP280_1
% 19.17/19.53 % cvc5---1.0.5 exiting
% 19.41/19.54 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------