%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : ITP220_1 : TPTP v8.1.2. Released v8.0.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n005.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 03:21:01 EDT 2023

% Result   : Theorem 18.53s 18.74s
% Output   : Proof 18.53s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 3.99/4.05  % Problem    : ITP220_1 : TPTP v8.1.2. Released v8.0.0.
% 3.99/4.06  % Command    : do_cvc5 %s %d
% 4.09/4.26  % Computer : n005.cluster.edu
% 4.09/4.26  % Model    : x86_64 x86_64
% 4.09/4.26  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 4.09/4.26  % Memory   : 8042.1875MB
% 4.09/4.26  % OS       : Linux 3.10.0-693.el7.x86_64
% 4.09/4.26  % CPULimit   : 300
% 4.09/4.26  % WCLimit    : 300
% 4.09/4.26  % DateTime   : Sun Aug 27 16:09:42 EDT 2023
% 4.09/4.26  % CPUTime    : 
% 8.01/8.22  %----Proving TF0_NAR, FOF, or CNF
% 18.53/18.74  ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.1UkoSTZI0W/cvc5---1.0.5_24932.p...
% 18.53/18.74  ------- get file name : TPTP file name is ITP220_1
% 18.53/18.74  ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_24932.smt2...
% 18.53/18.74  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 18.53/18.74  % SZS status Theorem for ITP220_1
% 18.53/18.74  % SZS output start Proof for ITP220_1
% 18.53/18.74  (
% 18.53/18.74  (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 tptp.va)))) (let ((_let_4 (tptp.vEBT_VEBT_membermima (tptp.vEBT_vebt_buildup (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat _let_3) _let_2))))) (let ((_let_5 (tptp.pp (tptp.aa_nat_bool _let_4 tptp.y)))) (let ((_let_6 (not _let_5))) (let ((_let_7 (not _let_6))) (let ((_let_8 (tptp.bNF_re3704215830270325841atural tptp.code_pcr_natural tptp.code_pcr_natural))) (let ((_let_9 (tptp.bNF_re3379532845092657523nteger tptp.code_pcr_integer tptp.code_pcr_integer))) (let ((_let_10 (tptp.map_fu1239815594074539274atural tptp.code_nat_of_natural tptp.code_natural_of_nat))) (let ((_let_11 (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat))) (let ((_let_12 (tptp.aa_num_nat tptp.nat_of_num tptp.one))) (let ((_let_13 (tptp.code_Pos tptp.one))) (let ((_let_14 (tptp.numera6620942414471956472nteger tptp.one))) (let ((_let_15 (tptp.map_fu2599414010547811884nteger tptp.code_int_of_integer tptp.code_integer_of_int))) (let ((_let_16 (tptp.bNF_re4712519889275205905nt_int tptp.fequal_int tptp.fequal_int))) (let ((_let_17 (= (tptp.aa_nat_list_nat tptp.nat_list_decode tptp.zero_zero_nat) tptp.nil_nat))) (let ((_let_18 (tptp.comp_int_nat_int tptp.nat2 tptp.abs_abs_int))) (let ((_let_19 (tptp.map_fu3926683916856352828t_real tptp.rep_real tptp.real2))) (let ((_let_20 (tptp.bNF_re1458715823057739248l_bool tptp.pcr_real tptp.fequal_bool))) (let ((_let_21 (tptp.bNF_re237660433471117187t_real tptp.pcr_real tptp.pcr_real))) (let ((_let_22 (tptp.bNF_re9178625837396562677at_rat tptp.realrel tptp.realrel))) (let ((_let_23 (tptp.produc4528391901023682385at_nat tptp.aTP_Lamm_dt))) (let ((_let_24 (tptp.bNF_re2241393799969408733at_nat tptp.intrel tptp.intrel))) (let ((_let_25 (tptp.produc4528391901023682385at_nat tptp.aTP_Lamm_dv))) (let ((_let_26 (tptp.produc5023667602222594023t_bool tptp.aTP_Lamm_dr))) (let ((_let_27 (tptp.bNF_re3189209160384574813l_bool tptp.intrel tptp.fequal_bool))) (let ((_let_28 (tptp.produc5023667602222594023t_bool tptp.aTP_Lamm_dp))) (let ((_let_29 (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat tptp.one_one_nat) tptp.zero_zero_nat))) (let ((_let_30 (tptp.produc6842872674320459806at_nat tptp.minus_minus_nat))) (let ((_let_31 (tptp.produc2626176000494625587at_nat tptp.aTP_Lamm_dn))) (let ((_let_32 (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat tptp.zero_zero_nat) tptp.zero_zero_nat))) (let ((_let_33 (tptp.bNF_re1498568104593929552l_bool tptp.pcr_int tptp.fequal_bool))) (let ((_let_34 (tptp.produc4528391901023682385at_nat tptp.aTP_Lamm_dm))) (let ((_let_35 (tptp.bNF_re7400052026677387805at_int tptp.pcr_int tptp.pcr_int))) (let ((_let_36 (tptp.bNF_re8279943556446156061nt_rat tptp.pcr_rat tptp.pcr_rat))) (let ((_let_37 (tptp.product_Pair_int_int tptp.zero_zero_int tptp.one_one_int))) (let ((_let_38 (tptp.product_Pair_int_int tptp.one_one_int tptp.one_one_int))) (let ((_let_39 (tptp.bNF_re7145576690424134365nt_int tptp.ratrel tptp.ratrel))) (let ((_let_40 (tptp.bNF_re5653821019739307937at_nat tptp.fequal_nat tptp.fequal_nat))) (let ((_let_41 (tptp.aa_num_num tptp.bit0 _let_1))) (let ((_let_42 (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_41))))))))) (let ((_let_43 (tptp.aa_nat_set_nat (tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) _let_42))) (let ((_let_44 (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real))) (let ((_let_45 (tptp.set_or1222579329274155063t_real _let_44 tptp.one_one_real))) (let ((_let_46 (tptp.numeral_numeral_real _let_1))) (let ((_let_47 (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi))) (let ((_let_48 (tptp.aa_real_real _let_47 _let_46))) (let ((_let_49 (tptp.topolo2815343760600316023s_real tptp.zero_zero_real))) (let ((_let_50 (tptp.topolo2815343760600316023s_real tptp.one_one_real))) (let ((_let_51 (tptp.image_nat_nat tptp.suc tptp.top_top_set_nat))) (let ((_let_52 (tptp.aa_real_real tptp.uminus_uminus_real _let_48))) (let ((_let_53 (tptp.map_fu5673905371560938248nt_rat tptp.rep_Rat tptp.abs_Rat))) (let ((_let_54 (tptp.map_fu6608131713810608381l_bool tptp.rep_Integ tptp.id_bool))) (let ((_let_55 (tptp.map_fu3667384564859982768at_int tptp.rep_Integ tptp.abs_Integ))) (let ((_let_56 (tptp.uminus_uminus_rat tptp.one_one_rat))) (let ((_let_57 (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int))) (let ((_let_58 (tptp.comp_nat_nat_nat tptp.suc tptp.suc))) (let ((_let_59 (tptp.numera6620942414471956472nteger _let_1))) (let ((_let_60 (tptp.vEBT_Leaf tptp.fFalse tptp.fFalse))) (let ((_let_61 (tptp.the_real tptp.aTP_Lamm_cj))) (let ((_let_62 (tptp.aa_rea7340605660300375871l_real tptp.times_times_real _let_46))) (let ((_let_63 (tptp.numeral_numeral_real _let_41))) (let ((_let_64 (tptp.aa_real_real _let_47 _let_63))) (let ((_let_65 (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (let ((_let_66 (tptp.aa_int_int tptp.bit_ri7919022796975470100ot_int tptp.zero_zero_int))) (let ((_let_67 (tptp.aa_int_int tptp.bit_ri7919022796975470100ot_int tptp.one_one_int))) (let ((_let_68 (tptp.aa_num_int tptp.numeral_numeral_int _let_1))) (let ((_let_69 (tptp.aa_int_int tptp.uminus_uminus_int _let_68))) (let ((_let_70 (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger _let_59))) (let ((_let_71 (tptp.aa_real_real tptp.sqrt _let_46))) (let ((_let_72 (tptp.uminus1482373934393186551omplex tptp.imaginary_unit))) (let ((_let_73 (tptp.numeral_numeral_rat tptp.one))) (let ((_let_74 (tptp.numera6690914467698888265omplex tptp.one))) (let ((_let_75 (tptp.numeral_numeral_real tptp.one))) (let ((_let_76 (= (tptp.aa_rat_rat tptp.inverse_inverse_rat tptp.zero_zero_rat) tptp.zero_zero_rat))) (let ((_let_77 (= (tptp.invers8013647133539491842omplex tptp.zero_zero_complex) tptp.zero_zero_complex))) (let ((_let_78 (= (tptp.aa_real_real tptp.inverse_inverse_real tptp.zero_zero_real) tptp.zero_zero_real))) (let ((_let_79 (tptp.uminus1482373934393186551omplex tptp.one_one_complex))) (let ((_let_80 (tptp.real_V4546457046886955230omplex tptp.pi))) (let ((_let_81 (tptp.times_times_complex tptp.imaginary_unit))) (let ((_let_82 (tptp.times_times_complex _let_80))) (let ((_let_83 (tptp.numera6690914467698888265omplex _let_1))) (let ((_let_84 (tptp.aa_real_real _let_62 tptp.pi))) (let ((_let_85 (tptp.aa_nat_nat tptp.suc _let_11))) (let ((_let_86 (tptp.aa_int_nat tptp.nat2 tptp.one_one_int))) (let ((_let_87 (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.one_one_real))) (let ((_let_88 (tptp.aa_real_real _let_87 _let_46))) (let ((_let_89 (tptp.aa_num_num tptp.bit1 tptp.one))) (let ((_let_90 (tptp.numeral_numeral_real _let_89))) (let ((_let_91 (tptp.aa_real_real tptp.sqrt _let_90))) (let ((_let_92 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real _let_91) _let_46))) (let ((_let_93 (tptp.aa_real_real _let_47 _let_90))) (let ((_let_94 (tptp.aa_real_real _let_47 (tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 _let_89))))) (let ((_let_95 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real _let_71) _let_46))) (let ((_let_96 (tptp.aa_real_real tptp.cos_real _let_46))) (let ((_let_97 (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real _let_90))) (let ((_let_98 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real _let_97 _let_46)) tptp.pi))) (let ((_let_99 (tptp.divide1717551699836669952omplex _let_80 _let_83))) (let ((_let_100 (tptp.aa_real_real tptp.real_V1803761363581548252l_real tptp.pi))) (let ((_let_101 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real _let_100) _let_46))) (let ((_let_102 (tptp.aa_num_num tptp.bit1 _let_89))) (let ((_let_103 (tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit1 _let_1)))) (let ((_let_104 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (let ((_let_105 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real))) (let ((_let_106 (tptp.aa_num_int tptp.numeral_numeral_int _let_89))) (let ((_let_107 (tptp.numeral_numeral_rat _let_89))) (let ((_let_108 (tptp.numera6690914467698888265omplex _let_89))) (let ((_let_109 (= (tptp.aa_int_int tptp.uminus_uminus_int tptp.zero_zero_int) tptp.zero_zero_int))) (let ((_let_110 (= (tptp.aa_int_int tptp.abs_abs_int tptp.one_one_int) tptp.one_one_int))) (let ((_let_111 (= (tptp.abs_abs_rat tptp.one_one_rat) tptp.one_one_rat))) (let ((_let_112 (= (tptp.aa_real_real tptp.abs_abs_real tptp.one_one_real) tptp.one_one_real))) (let ((_let_113 (= (tptp.abs_abs_Code_integer tptp.one_one_Code_integer) tptp.one_one_Code_integer))) (let ((_let_114 (= (tptp.aa_int_int tptp.abs_abs_int tptp.zero_zero_int) tptp.zero_zero_int))) (let ((_let_115 (= (tptp.abs_abs_rat tptp.zero_zero_rat) tptp.zero_zero_rat))) (let ((_let_116 (= (tptp.aa_real_real tptp.abs_abs_real tptp.zero_zero_real) tptp.zero_zero_real))) (let ((_let_117 (= (tptp.abs_abs_Code_integer tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger))) (let ((_let_118 (tptp.aa_num_int tptp.numeral_numeral_int tptp.one))) (let ((_let_119 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat))) (let ((_let_120 (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int))) (let ((_let_121 (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger _let_65))) (let ((_let_122 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat _let_56))) (let ((_let_123 (tptp.aa_int_fun_int_bool tptp.ord_less_int _let_57))) (let ((_let_124 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real _let_44))) (let ((_let_125 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_126 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat))) (let ((_let_127 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int _let_57))) (let ((_let_128 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat _let_56))) (let ((_let_129 (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger _let_65))) (let ((_let_130 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real _let_44))) (let ((_let_131 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.one_one_rat))) (let ((_let_132 (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.one_one_int))) (let ((_let_133 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real))) (let ((_let_134 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.one_one_int))) (let ((_let_135 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.one_one_rat))) (let ((_let_136 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.one_one_real))) (let ((_let_137 (tptp.numeral_numeral_rat _let_1))) (let ((_let_138 (tptp.uminus_uminus_rat _let_137))) (let ((_let_139 (tptp.uminus1482373934393186551omplex _let_83))) (let ((_let_140 (tptp.aa_real_real tptp.uminus_uminus_real _let_46))) (let ((_let_141 (= (tptp.modulo364778990260209775nteger _let_65 _let_59) tptp.one_one_Code_integer))) (let ((_let_142 (= (tptp.modulo_modulo_int _let_57 _let_68) tptp.one_one_int))) (let ((_let_143 (tptp.aa_int_fun_int_int tptp.minus_minus_int tptp.one_one_int))) (let ((_let_144 (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real tptp.one_one_real))) (let ((_let_145 (tptp.aa_Cod4161879620478718930nteger tptp.minus_8373710615458151222nteger _let_65))) (let ((_let_146 (tptp.aa_int_fun_int_int tptp.minus_minus_int _let_57))) (let ((_let_147 (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real _let_44))) (let ((_let_148 (tptp.aa_Cod4161879620478718930nteger tptp.plus_p5714425477246183910nteger _let_65))) (let ((_let_149 (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat _let_56))) (let ((_let_150 (tptp.aa_int_fun_int_int tptp.plus_plus_int _let_57))) (let ((_let_151 (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real _let_44))) (let ((_let_152 (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat tptp.one_one_rat))) (let ((_let_153 (tptp.aa_int_fun_int_int tptp.plus_plus_int tptp.one_one_int))) (let ((_let_154 (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real tptp.one_one_real))) (let ((_let_155 (= (tptp.sgn_sgn_complex tptp.one_one_complex) tptp.one_one_complex))) (let ((_let_156 (= (tptp.aa_real_real tptp.sgn_sgn_real tptp.one_one_real) tptp.one_one_real))) (let ((_let_157 (= (tptp.aa_real_real tptp.sgn_sgn_real tptp.zero_zero_real) tptp.zero_zero_real))) (let ((_let_158 (= (tptp.sgn_sgn_complex tptp.zero_zero_complex) tptp.zero_zero_complex))) (let ((_let_159 (= (tptp.modulo8411746178871703098atural tptp.one_one_Code_natural (tptp.numera5444537566228673987atural _let_1)) tptp.one_one_Code_natural))) (let ((_let_160 (= (tptp.modulo364778990260209775nteger tptp.one_one_Code_integer _let_59) tptp.one_one_Code_integer))) (let ((_let_161 (= (tptp.modulo_modulo_int tptp.one_one_int _let_68) tptp.one_one_int))) (let ((_let_162 (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat tptp.one_one_nat) _let_2) tptp.one_one_nat))) (let ((_let_163 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat))) (let ((_let_164 (tptp.aa_int_int _let_153 tptp.one_one_int))) (let ((_let_165 (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat tptp.one_one_nat))) (let ((_let_166 (tptp.aa_nat_nat _let_165 tptp.one_one_nat))) (let ((_let_167 (tptp.aa_rat_rat _let_152 tptp.one_one_rat))) (let ((_let_168 (tptp.aa_real_real _let_154 tptp.one_one_real))) (let ((_let_169 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.one_one_nat))) (let ((_let_170 (tptp.pp (tptp.aa_int_bool _let_125 tptp.one_one_int)))) (let ((_let_171 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat))) (let ((_let_172 (tptp.pp (tptp.aa_nat_bool _let_171 tptp.one_one_nat)))) (let ((_let_173 (tptp.pp (tptp.aa_rat_bool _let_126 tptp.one_one_rat)))) (let ((_let_174 (tptp.pp (tptp.aa_real_bool _let_104 tptp.one_one_real)))) (let ((_let_175 (tptp.pp (tptp.aa_int_bool _let_120 tptp.one_one_int)))) (let ((_let_176 (tptp.pp (tptp.aa_nat_bool _let_163 tptp.one_one_nat)))) (let ((_let_177 (tptp.pp (tptp.aa_rat_bool _let_119 tptp.one_one_rat)))) (let ((_let_178 (tptp.pp (tptp.aa_real_bool _let_105 tptp.one_one_real)))) (let ((_let_179 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.one_one_nat))) (let ((_let_180 (tptp.pp (tptp.aa_int_bool _let_125 tptp.zero_zero_int)))) (let ((_let_181 (not (tptp.pp (tptp.aa_int_bool _let_120 tptp.zero_zero_int))))) (let ((_let_182 (= _let_166 _let_2))) (let ((_let_183 (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int _let_68))) (let ((_let_184 (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat _let_2))) (let ((_let_185 (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer _let_59))) (let ((_let_186 (tptp.aa_num_nat tptp.numeral_numeral_nat tptp.one))) (let ((_let_187 (= _let_186 tptp.one_one_nat))) (let ((_let_188 (= (tptp.aa_nat_int tptp.semiri1314217659103216013at_int tptp.one_one_nat) tptp.one_one_int))) (let ((_let_189 (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int tptp.one_one_int) _let_68) tptp.zero_zero_int))) (let ((_let_190 (= (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_191 (= (tptp.aa_nat_int tptp.semiri1314217659103216013at_int tptp.zero_zero_nat) tptp.zero_zero_int))) (let ((_let_192 (forall ((X tptp.nat) (Xa 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)) (not (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_VEBT_membermima (tptp.vEBT_vebt_buildup X)) Xa)))))))))) (let ((_let_193 (tptp.pp (tptp.aa_nat_bool _let_184 _let_3)))) (let ((_let_194 (forall ((Xa tptp.nat)) (not (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_VEBT_membermima (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))))) Xa)))))) (let ((_let_195 (_let_194))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_195) :args (tptp.y QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.aa_nat_bool _let_4 Xa)))) :args _let_195)) :args ((or _let_6 (not _let_194)))) (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (ASSUME :args (_let_192)) (MACRO_SR_EQ_INTRO :args (_let_192 SB_DEFAULT SBA_FIXPOINT))) (ASSUME :args (_let_193)) :args (_let_194 false _let_193)) :args (false false _let_5 false _let_194)) :args (_let_193 _let_192 (forall ((X tptp.nat) (Xa 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)) (not (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_VEBT_membermima (tptp.vEBT_vebt_buildup (tptp.aa_nat_nat tptp.suc X))) Xa)))))))) (forall ((X tptp.nat) (Xa 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)) (not (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_VEBT_membermima (tptp.vEBT_vebt_buildup X)) Xa)))))))) (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))))) (forall ((M tptp.num)) (not (= (tptp.aa_num_num tptp.bit0 M) tptp.one))) (forall ((N tptp.num)) (not (= tptp.one (tptp.aa_num_num tptp.bit0 N)))) (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.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.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat _let_1) N))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat tptp.suc N)) _let_1) (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat N) _let_1)))))) (forall ((N tptp.nat)) (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_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat tptp.suc N))) (not (tptp.pp (tptp.aa_nat_bool _let_1 N)))))) (forall ((N tptp.nat)) (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 ((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.numeral_numeral_real tptp.one)) A)) (forall ((A tptp.rat)) (= (tptp.divide_divide_rat A (tptp.numeral_numeral_rat tptp.one)) A)) (forall ((X2 tptp.nat) (Y2 tptp.nat)) (= (= (tptp.aa_nat_nat tptp.suc X2) (tptp.aa_nat_nat tptp.suc Y2)) (= X2 Y2))) (forall ((Nat tptp.nat) (Nat2 tptp.nat)) (= (= (tptp.aa_nat_nat tptp.suc Nat) (tptp.aa_nat_nat tptp.suc Nat2)) (= Nat Nat2))) (forall ((M tptp.num) (N tptp.num)) (= (= (tptp.numera6690914467698888265omplex M) (tptp.numera6690914467698888265omplex N)) (= M N))) (forall ((M tptp.num) (N tptp.num)) (= (= (tptp.numeral_numeral_real M) (tptp.numeral_numeral_real N)) (= M N))) (forall ((M tptp.num) (N tptp.num)) (= (= (tptp.numeral_numeral_rat M) (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.bit0 M) (tptp.aa_num_num tptp.bit0 N)) (= 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 ((N tptp.nat)) (not (= N (tptp.aa_nat_nat tptp.suc N)))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (= (tptp.aa_nat_nat tptp.suc X) (tptp.aa_nat_nat tptp.suc Y)) (= X Y))) (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 ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat _let_1))) (=> (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat X) _let_1) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat Y) _let_1)) (=> (= (tptp.pp (tptp.aa_nat_bool _let_2 X)) (tptp.pp (tptp.aa_nat_bool _let_2 Y))) (= X Y)))))) (forall ((A tptp.code_integer) (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.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.divide6298287555418463151nteger B) A)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger 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.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.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.divide6298287555418463151nteger A) _let_1) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger 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 ((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 ((X2 tptp.num) (Y2 tptp.num)) (= (= (tptp.aa_num_num tptp.bit0 X2) (tptp.aa_num_num tptp.bit0 Y2)) (= X2 Y2))) (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 ((D tptp.code_integer) (B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod4161879620478718930nteger tptp.divide6298287555418463151nteger A))) (=> (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.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.divide6298287555418463151nteger (tptp.aa_Cod1783974652533396728nteger _let_1 D)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.divide6298287555418463151nteger B) D)) (tptp.aa_Cod1783974652533396728nteger _let_1 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 ((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.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.divide6298287555418463151nteger A) C) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger 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.divide_divide_rat A C) (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 ((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.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.divide6298287555418463151nteger A) C) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger 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.divide_divide_rat A C) (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 ((X2 tptp.num)) (not (= tptp.one (tptp.aa_num_num tptp.bit0 X2)))) (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.aa_nat_set_nat tptp.nat_set_decode X))) (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat N) (tptp.aa_nat_set_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)))))))) (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 ((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.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.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.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.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.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.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))) (= (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_191 (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 ((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))) (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.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.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.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 ((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 ((X tptp.nat)) (= (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat tptp.zero_zero_nat) (tptp.aa_nat_set_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 ((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 ((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 ((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 ((X tptp.nat)) (=> (not (= X tptp.zero_zero_nat)) (not (forall ((N2 tptp.nat)) (not (= X (tptp.aa_nat_nat tptp.suc N2))))))) (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.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 ((N tptp.num)) (not (= tptp.zero_zero_complex (tptp.numera6690914467698888265omplex N)))) (forall ((N tptp.num)) (not (= tptp.zero_zero_real (tptp.numeral_numeral_real N)))) (forall ((N tptp.num)) (not (= tptp.zero_zero_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 ((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 ((Y tptp.nat)) (=> (not (= Y tptp.zero_zero_nat)) (not (forall ((Nat3 tptp.nat)) (not (= Y (tptp.aa_nat_nat tptp.suc Nat3))))))) (forall ((P tptp.fun_nat_bool) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool P tptp.zero_zero_nat)) (=> (forall ((N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool P N2)) (tptp.pp (tptp.aa_nat_bool P (tptp.aa_nat_nat tptp.suc N2))))) (tptp.pp (tptp.aa_nat_bool P N))))) (forall ((P tptp.fun_nat_fun_nat_bool) (M tptp.nat) (N tptp.nat)) (=> (forall ((X3 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool P X3) tptp.zero_zero_nat))) (=> (forall ((Y3 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 Y3)))) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool P X3) Y3)) (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 Y3))))) (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 ((M2 tptp.nat)) (= N (tptp.aa_nat_nat tptp.suc M2))))) (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.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger 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.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 ((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 ((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) (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))) (= _let_186 _let_11) (tptp.pp (tptp.aa_Code_integer_bool _let_185 tptp.zero_z3403309356797280102nteger)) (tptp.pp (tptp.aa_nat_bool _let_184 tptp.zero_zero_nat)) (tptp.pp (tptp.aa_int_bool _let_183 tptp.zero_zero_int)) (= _let_2 _let_85) (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 ((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.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)) (= (= (tptp.divide_divide_rat C A) (tptp.divide_divide_rat C 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.divide_divide_rat A C) (tptp.divide_divide_rat B C)) (or (= C tptp.zero_zero_rat) (= A B)))) (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.divide_divide_rat A tptp.zero_zero_rat) tptp.zero_zero_rat)) (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_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_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.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.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_se8260200283734997820nteger M A))) (or (tptp.pp (tptp.aa_Code_integer_bool _let_1 A)) (= M tptp.zero_zero_nat))))) (forall ((M tptp.nat) (A tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.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) (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 ((N tptp.nat)) (=> (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N))) (= (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat))) N))) (forall ((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 ((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.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.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A) tptp.zero_zero_real) A)) (forall ((A tptp.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.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A) tptp.zero_zero_real) A)) (forall ((A tptp.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.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A) A) tptp.zero_zero_real)) (forall ((A tptp.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 ((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.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.divide6298287555418463151nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.minus_8373710615458151222nteger A) B)) C) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.minus_8373710615458151222nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.divide6298287555418463151nteger A) C)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger 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_int tptp.semiri1314217659103216013at_int M) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N)) (= M N))) (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.aa_nat_fun_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))))))) (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 ((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.minus_minus_rat A B) (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)) (= (tptp.minus_minus_rat (tptp.minus_minus_rat A C) B) (tptp.minus_minus_rat (tptp.minus_minus_rat A 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.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.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 ((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.divide_divide_rat (tptp.minus_minus_rat A B) C) (tptp.minus_minus_rat (tptp.divide_divide_rat A C) (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.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.minus_8373710615458151222nteger C) B))) (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger 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) (Y tptp.code_integer) (Z tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer X))) (=> (tptp.pp (tptp.aa_Code_integer_bool _let_1 Y)) (=> (tptp.pp (tptp.aa_Code_integer_bool _let_1 Z)) (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.minus_8373710615458151222nteger Y) Z))))))) (forall ((X tptp.real) (Y tptp.real) (Z tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.dvd_dvd_real X))) (=> (tptp.pp (tptp.aa_real_bool _let_1 Y)) (=> (tptp.pp (tptp.aa_real_bool _let_1 Z)) (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real Y) Z))))))) (forall ((X tptp.rat) (Y tptp.rat) (Z tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.dvd_dvd_rat X))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 Y)) (=> (tptp.pp (tptp.aa_rat_bool _let_1 Z)) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.minus_minus_rat Y Z))))))) (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int X))) (=> (tptp.pp (tptp.aa_int_bool _let_1 Y)) (=> (tptp.pp (tptp.aa_int_bool _let_1 Z)) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int Y) Z))))))) (forall ((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.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))))))) _let_191 (forall ((X tptp.literal)) (= (= tptp.zero_zero_literal X) (= X tptp.zero_zero_literal))) (forall ((X tptp.real)) (= (= tptp.zero_zero_real X) (= X tptp.zero_zero_real))) (forall ((X tptp.rat)) (= (= tptp.zero_zero_rat X) (= X tptp.zero_zero_rat))) (forall ((X tptp.nat)) (= (= tptp.zero_zero_nat X) (= X tptp.zero_zero_nat))) (forall ((X tptp.int)) (= (= tptp.zero_zero_int X) (= X tptp.zero_zero_int))) (forall ((A tptp.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 ((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.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 ((P tptp.fun_nat_bool)) (=> (not (tptp.pp (tptp.aa_nat_bool P tptp.zero_zero_nat))) (=> (exists ((X_1 tptp.nat)) (tptp.pp (tptp.aa_nat_bool P X_1))) (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)))))))) _let_190 _let_189 _let_190 _let_189 (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.aa_nat_fun_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 ((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.aa_nat_fun_int_int 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.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_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.code_natural)) (let ((_let_1 (tptp.numera5444537566228673987atural (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.pp (tptp.dvd_dvd_Code_natural _let_1 (tptp.aa_Cod4272041906116450446atural (tptp.aa_nat5282697797315388251atural tptp.bit_se6611745700429515170atural N) A))) (or (not (= N tptp.zero_zero_nat)) (tptp.pp (tptp.dvd_dvd_Code_natural _let_1 A)))))) (forall ((M tptp.num) (N tptp.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.times_times_num M N))))) (forall ((N tptp.num)) (= (tptp.times_times_num tptp.one N) N)) (forall ((M tptp.num)) (= (tptp.times_times_num M tptp.one) M)) (forall ((M tptp.nat) (N tptp.nat)) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat M) N) tptp.zero_zero_nat) (or (= M tptp.zero_zero_nat) (= N tptp.zero_zero_nat)))) (forall ((M tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat M) tptp.zero_zero_nat) tptp.zero_zero_nat)) (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat K))) (= (= (tptp.aa_nat_nat _let_1 M) (tptp.aa_nat_nat _let_1 N)) (or (= M N) (= K tptp.zero_zero_nat))))) (forall ((M tptp.nat) (K tptp.nat) (N tptp.nat)) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat M) K) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat N) K)) (or (= M N) (= K tptp.zero_zero_nat)))) (forall ((M tptp.nat)) (= (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) (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 ((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.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.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.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 ((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.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.numeral_numeral_real V)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.numeral_numeral_real W)) Z)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.numeral_numeral_real (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.numeral_numeral_rat V)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.numeral_numeral_rat W)) Z)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.numeral_numeral_rat (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.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.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.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.numeral_numeral_real M)) (tptp.numeral_numeral_real N)) (tptp.numeral_numeral_real (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.numeral_numeral_rat M)) (tptp.numeral_numeral_rat N)) (tptp.numeral_numeral_rat (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.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.times_times_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 ((N tptp.num)) (= (tptp.times_times_num (tptp.aa_num_num tptp.bit0 tptp.one) N) (tptp.aa_num_num tptp.bit0 N))) (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.divide_divide_rat B C)) A) (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)) (= (tptp.divide_divide_rat (tptp.divide_divide_rat A B) C) (tptp.divide_divide_rat A (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.divide_divide_rat A (tptp.divide_divide_rat B C)) (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.divide_divide_rat B C)) (tptp.divide_divide_rat (tptp.aa_rat_rat _let_1 B) C)))) (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.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 ((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)))) (= (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_188 (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))) (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 ((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 ((N tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat tptp.suc N)) tptp.one_one_nat) N)) (forall ((K tptp.nat) (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 ((N tptp.nat) (A tptp.nat)) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se547839408752420682it_nat N) A) tptp.zero_zero_nat) (= A tptp.zero_zero_nat))) (forall ((N tptp.nat) (A tptp.int)) (= (= (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_se545348938243370406it_int N) A) tptp.zero_zero_int) (= A tptp.zero_zero_int))) (forall ((N tptp.nat) (A tptp.code_integer)) (= (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_nat6383147911832638789nteger tptp.bit_se7788150548672797655nteger N) A) tptp.zero_z3403309356797280102nteger) (= A tptp.zero_z3403309356797280102nteger))) (forall ((N tptp.nat) (A tptp.code_natural)) (= (= (tptp.aa_Cod4272041906116450446atural (tptp.aa_nat5282697797315388251atural tptp.bit_se6611745700429515170atural N) A) tptp.zero_z2226904508553997617atural) (= A tptp.zero_z2226904508553997617atural))) (forall ((N tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se547839408752420682it_nat N) tptp.zero_zero_nat) tptp.zero_zero_nat)) (forall ((N tptp.nat)) (= (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_se545348938243370406it_int N) tptp.zero_zero_int) tptp.zero_zero_int)) (forall ((N tptp.nat)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_nat6383147911832638789nteger tptp.bit_se7788150548672797655nteger N) tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger)) (forall ((N tptp.nat)) (= (tptp.aa_Cod4272041906116450446atural (tptp.aa_nat5282697797315388251atural tptp.bit_se6611745700429515170atural N) tptp.zero_z2226904508553997617atural) tptp.zero_z2226904508553997617atural)) (forall ((A tptp.complex) (C tptp.complex)) (= (= (tptp.aa_complex_complex (tptp.times_times_complex A) C) C) (or (= C tptp.zero_zero_complex) (= A tptp.one_one_complex)))) (forall ((A tptp.real) (C tptp.real)) (= (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) C) C) (or (= C tptp.zero_zero_real) (= A tptp.one_one_real)))) (forall ((A tptp.rat) (C tptp.rat)) (= (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) C) C) (or (= C tptp.zero_zero_rat) (= A tptp.one_one_rat)))) (forall ((A tptp.int) (C tptp.int)) (= (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) C) C) (or (= C tptp.zero_zero_int) (= A tptp.one_one_int)))) (forall ((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 ((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 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)))) (= (tptp.minus_minus_complex tptp.one_one_complex tptp.one_one_complex) tptp.zero_zero_complex) (= (tptp.aa_real_real _let_144 tptp.one_one_real) tptp.zero_zero_real) (= (tptp.minus_minus_rat tptp.one_one_rat tptp.one_one_rat) tptp.zero_zero_rat) (= (tptp.aa_int_int _let_143 tptp.one_one_int) tptp.zero_zero_int) (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.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.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))) (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.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))) (=> (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.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.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.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.divide_divide_rat (tptp.aa_rat_rat _let_1 A) (tptp.aa_rat_rat _let_1 B)) (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.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.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.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.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.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.divide_divide_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.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.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.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.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.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.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.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.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.divide_divide_rat tptp.one_one_rat A)) (= A tptp.zero_zero_rat))) (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.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.numeral_numeral_rat V)))) (= (tptp.aa_rat_rat _let_1 (tptp.minus_minus_rat B C)) (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.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.numeral_numeral_rat V))) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.minus_minus_rat A B)) _let_1) (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 ((N tptp.num)) (= (= (tptp.numera6690914467698888265omplex N) tptp.one_one_complex) (= N tptp.one))) (forall ((N tptp.num)) (= (= (tptp.numeral_numeral_real N) tptp.one_one_real) (= N tptp.one))) (forall ((N tptp.num)) (= (= (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.numeral_numeral_real N)) (= tptp.one N))) (forall ((N tptp.num)) (= (= tptp.one_one_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 ((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.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.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 ((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) B)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger 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) (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.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger 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) 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.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.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger 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)) (let ((_let_1 (tptp.aa_Cod4161879620478718930nteger tptp.divide6298287555418463151nteger tptp.one_one_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 _let_1 (tptp.aa_Cod1783974652533396728nteger _let_1 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 ((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.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.numeral_numeral_rat W))) (let ((_let_2 (= _let_1 tptp.zero_zero_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.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.numeral_numeral_rat W))) (let ((_let_2 (= _let_1 tptp.zero_zero_rat))) (= (= A (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 ((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.divide_divide_rat A (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) B)) (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.divide_divide_rat B (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) B)) (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 (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger 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 ((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.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.divide6298287555418463151nteger tptp.one_one_Code_integer) A)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger 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)))) (= (tptp.aa_nat_nat tptp.suc tptp.one_one_nat) _let_2) (forall ((N tptp.nat) (K tptp.num)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_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.aa_nat_fun_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.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_se545348938243370406it_int (tptp.aa_nat_nat tptp.suc N)) (tptp.aa_num_int tptp.numeral_numeral_int K)) (tptp.aa_int_int (tptp.aa_nat_fun_int_int 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_Cod1783974652533396728nteger (tptp.aa_nat6383147911832638789nteger tptp.bit_se7788150548672797655nteger (tptp.aa_nat_nat tptp.suc N)) (tptp.numera6620942414471956472nteger K)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_nat6383147911832638789nteger tptp.bit_se7788150548672797655nteger N) (tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 K))))) (forall ((N tptp.nat) (K tptp.num)) (= (tptp.aa_Cod4272041906116450446atural (tptp.aa_nat5282697797315388251atural tptp.bit_se6611745700429515170atural (tptp.aa_nat_nat tptp.suc N)) (tptp.numera5444537566228673987atural K)) (tptp.aa_Cod4272041906116450446atural (tptp.aa_nat5282697797315388251atural tptp.bit_se6611745700429515170atural N) (tptp.numera5444537566228673987atural (tptp.aa_num_num tptp.bit0 K))))) (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 ((N tptp.nat) (A tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se547839408752420682it_nat (tptp.aa_nat_nat tptp.suc N)) A) (tptp.aa_nat_nat (tptp.aa_nat_fun_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) (A tptp.int)) (= (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_se545348938243370406it_int (tptp.aa_nat_nat tptp.suc N)) A) (tptp.aa_int_int (tptp.aa_nat_fun_int_int 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.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_nat6383147911832638789nteger tptp.bit_se7788150548672797655nteger (tptp.aa_nat_nat tptp.suc N)) A) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_nat6383147911832638789nteger tptp.bit_se7788150548672797655nteger N) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) (tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one)))))) (forall ((N tptp.nat) (A tptp.code_natural)) (= (tptp.aa_Cod4272041906116450446atural (tptp.aa_nat5282697797315388251atural tptp.bit_se6611745700429515170atural (tptp.aa_nat_nat tptp.suc N)) A) (tptp.aa_Cod4272041906116450446atural (tptp.aa_nat5282697797315388251atural tptp.bit_se6611745700429515170atural N) (tptp.aa_Cod4272041906116450446atural (tptp.aa_Cod5141017464274028979atural tptp.times_2397367101498566445atural A) (tptp.numera5444537566228673987atural (tptp.aa_num_num tptp.bit0 tptp.one)))))) (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 ((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 ((K tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int K) tptp.zero_zero_int) K)) (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.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.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)) (= (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))) (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.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 ((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)))))) (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 ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat 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 ((N tptp.nat) (M tptp.nat)) (= (tptp.aa_int_int (tptp.aa_nat_fun_int_int 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.aa_nat_fun_nat_nat tptp.bit_se547839408752420682it_nat N) M)))) (forall ((N tptp.nat) (M tptp.nat)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_nat6383147911832638789nteger tptp.bit_se7788150548672797655nteger N) (tptp.semiri4939895301339042750nteger M)) (tptp.semiri4939895301339042750nteger (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se547839408752420682it_nat N) M)))) (forall ((N tptp.nat) (M tptp.nat)) (= (tptp.aa_Cod4272041906116450446atural (tptp.aa_nat5282697797315388251atural tptp.bit_se6611745700429515170atural N) (tptp.semiri3763490453095760265atural M)) (tptp.semiri3763490453095760265atural (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se547839408752420682it_nat N) M)))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat 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 ((M tptp.nat) (N tptp.nat)) (= (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se547839408752420682it_nat M) N)) (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_se545348938243370406it_int M) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N)))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.semiri4939895301339042750nteger (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se547839408752420682it_nat M) N)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_nat6383147911832638789nteger tptp.bit_se7788150548672797655nteger M) (tptp.semiri4939895301339042750nteger N)))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.semiri3763490453095760265atural (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se547839408752420682it_nat M) N)) (tptp.aa_Cod4272041906116450446atural (tptp.aa_nat5282697797315388251atural tptp.bit_se6611745700429515170atural M) (tptp.semiri3763490453095760265atural 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 (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 ((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.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)))) _let_188 (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 ((B2 tptp.nat) (C2 tptp.nat)) (and (= A (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B2) C2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat B2) B)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat C2) 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 ((B2 tptp.int) (C2 tptp.int)) (and (= A (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B2) C2)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int B2) B)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int C2) C)))))) (forall ((P2 tptp.nat) (A tptp.nat) (B tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat P2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) B))) (not (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (= P2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat X3) Y3)) (=> (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 Y3) B))))))))) (forall ((P2 tptp.int) (A tptp.int) (B tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int P2) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) B))) (not (forall ((X3 tptp.int) (Y3 tptp.int)) (=> (= P2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int X3) Y3)) (=> (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 Y3) 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) 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 ((B tptp.code_integer) (C tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod4161879620478718930nteger tptp.divide6298287555418463151nteger 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 (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer C) tptp.one_one_Code_integer)) (= (tptp.aa_Cod1783974652533396728nteger _let_1 (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B) C)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.divide6298287555418463151nteger (tptp.aa_Cod1783974652533396728nteger _let_1 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 ((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.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.divide6298287555418463151nteger B) C)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger 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) (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.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.divide6298287555418463151nteger A) B)) C) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger 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) (B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod4161879620478718930nteger tptp.divide6298287555418463151nteger A))) (=> (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.aa_Cod1783974652533396728nteger _let_1 (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B) C)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger 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.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)) (= (= A (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger 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 ((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.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 ((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 ((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 ((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 ((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.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.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.minus_minus_rat A B)) C) (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.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.minus_minus_rat B C)) (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 ((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.minus_minus_rat B C)) A) (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.minus_minus_rat B C)) (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 ((X tptp.complex) (Y tptp.complex) (Z tptp.complex) (W tptp.complex)) (= (tptp.aa_complex_complex (tptp.times_times_complex (tptp.divide1717551699836669952omplex X Y)) (tptp.divide1717551699836669952omplex Z W)) (tptp.divide1717551699836669952omplex (tptp.aa_complex_complex (tptp.times_times_complex X) Z) (tptp.aa_complex_complex (tptp.times_times_complex Y) W)))) (forall ((X tptp.real) (Y tptp.real) (Z tptp.real) (W tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real X) Y)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real Z) W)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real X) Z)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real Y) W)))) (forall ((X tptp.rat) (Y tptp.rat) (Z tptp.rat) (W tptp.rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.divide_divide_rat X Y)) (tptp.divide_divide_rat Z W)) (tptp.divide_divide_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat X) Z) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat Y) W)))) (forall ((X tptp.complex) (Y tptp.complex) (Z tptp.complex) (W tptp.complex)) (= (tptp.divide1717551699836669952omplex (tptp.divide1717551699836669952omplex X Y) (tptp.divide1717551699836669952omplex Z W)) (tptp.divide1717551699836669952omplex (tptp.aa_complex_complex (tptp.times_times_complex X) W) (tptp.aa_complex_complex (tptp.times_times_complex Y) Z)))) (forall ((X tptp.real) (Y tptp.real) (Z tptp.real) (W tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real X) Y)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real Z) W)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real X) W)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real Y) Z)))) (forall ((X tptp.rat) (Y tptp.rat) (Z tptp.rat) (W tptp.rat)) (= (tptp.divide_divide_rat (tptp.divide_divide_rat X Y) (tptp.divide_divide_rat Z W)) (tptp.divide_divide_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat X) W) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat Y) Z)))) (forall ((A tptp.complex) (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)) (= (tptp.divide_divide_rat (tptp.divide_divide_rat A B) C) (tptp.divide_divide_rat A (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat C) B)))) (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 ((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 ((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) (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)) (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)) (=> (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) (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) (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 ((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 ((K2 tptp.code_integer)) (= 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)) (exists ((K2 tptp.real)) (= 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)) (exists ((K2 tptp.rat)) (= 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)) (exists ((K2 tptp.nat)) (= 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)) (exists ((K2 tptp.int)) (= 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)) (not (forall ((K3 tptp.code_integer)) (not (= 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)) (not (forall ((K3 tptp.real)) (not (= 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)) (not (forall ((K3 tptp.rat)) (not (= 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)) (not (forall ((K3 tptp.nat)) (not (= 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)) (not (forall ((K3 tptp.int)) (not (= A (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B) K3))))))) (forall ((N tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat tptp.zero_zero_nat) N) tptp.zero_zero_nat)) (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat K))) (= (= (tptp.aa_nat_nat _let_1 M) (tptp.aa_nat_nat _let_1 N)) (or (= K tptp.zero_zero_nat) (= M N))))) (forall ((X tptp.nat) (Y tptp.complex)) (let ((_let_1 (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex X))) (= (tptp.aa_complex_complex (tptp.times_times_complex _let_1) Y) (tptp.aa_complex_complex (tptp.times_times_complex Y) _let_1)))) (forall ((X tptp.nat) (Y tptp.real)) (let ((_let_1 (tptp.aa_nat_real tptp.semiri5074537144036343181t_real X))) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real _let_1) Y) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real Y) _let_1)))) (forall ((X tptp.nat) (Y tptp.rat)) (let ((_let_1 (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat X))) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat _let_1) Y) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat Y) _let_1)))) (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat X))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat _let_1) Y) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat Y) _let_1)))) (forall ((X tptp.nat) (Y tptp.int)) (let ((_let_1 (tptp.aa_nat_int tptp.semiri1314217659103216013at_int X))) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int _let_1) Y) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int Y) _let_1)))) (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 ((Z tptp.int)) (not (forall ((M2 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 M2)) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N2))))))) (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 ((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 ((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 ((K tptp.int) (M tptp.int) (N tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.times_times_int K))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_int_int _let_1 M)) (tptp.aa_int_int _let_1 N))) (=> (not (= K tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int M) N)))))) (forall ((A tptp.nat) (B tptp.nat)) (exists ((D2 tptp.nat) (X3 tptp.nat) (Y3 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 Y3)) 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 Y3)) D2)))))))) (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_fun_nat_nat 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 ((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_nat_fun_int_int tptp.bit_se545348938243370406it_int N))) (= (tptp.aa_int_int _let_2 (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.aa_int_int _let_2 A)) _let_1))))) (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.aa_nat6383147911832638789nteger tptp.bit_se7788150548672797655nteger N))) (= (tptp.aa_Cod1783974652533396728nteger _let_2 (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) _let_1)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger _let_2 A)) _let_1))))) (forall ((N tptp.nat) (A tptp.code_natural)) (let ((_let_1 (tptp.numera5444537566228673987atural (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_nat5282697797315388251atural tptp.bit_se6611745700429515170atural N))) (= (tptp.aa_Cod4272041906116450446atural _let_2 (tptp.aa_Cod4272041906116450446atural (tptp.aa_Cod5141017464274028979atural tptp.times_2397367101498566445atural A) _let_1)) (tptp.aa_Cod4272041906116450446atural (tptp.aa_Cod5141017464274028979atural tptp.times_2397367101498566445atural (tptp.aa_Cod4272041906116450446atural _let_2 A)) _let_1))))) (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.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.divide6298287555418463151nteger A) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B) A)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger 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))))) (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.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.divide6298287555418463151nteger A) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) B)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger 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) (C tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer)) (not (=> (not (= A tptp.zero_z3403309356797280102nteger)) (forall ((B3 tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod4161879620478718930nteger tptp.divide6298287555418463151nteger tptp.one_one_Code_integer))) (=> (not (= B3 tptp.zero_z3403309356797280102nteger)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer B3) tptp.one_one_Code_integer)) (=> (= (tptp.aa_Cod1783974652533396728nteger _let_1 A) B3) (=> (= (tptp.aa_Cod1783974652533396728nteger _let_1 B3) A) (=> (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) B3) tptp.one_one_Code_integer) (not (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.divide6298287555418463151nteger C) A) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger C) B3)))))))))))))) (forall ((A tptp.nat) (C tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat A) tptp.one_one_nat)) (not (=> (not (= A tptp.zero_zero_nat)) (forall ((B3 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat tptp.one_one_nat))) (=> (not (= B3 tptp.zero_zero_nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat B3) tptp.one_one_nat)) (=> (= (tptp.aa_nat_nat _let_1 A) B3) (=> (= (tptp.aa_nat_nat _let_1 B3) A) (=> (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) B3) tptp.one_one_nat) (not (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat C) A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat C) B3)))))))))))))) (forall ((A tptp.int) (C tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int A) tptp.one_one_int)) (not (=> (not (= A tptp.zero_zero_int)) (forall ((B3 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.divide_divide_int tptp.one_one_int))) (=> (not (= B3 tptp.zero_zero_int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int B3) tptp.one_one_int)) (=> (= (tptp.aa_int_int _let_1 A) B3) (=> (= (tptp.aa_int_int _let_1 B3) A) (=> (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) B3) tptp.one_one_int) (not (= (tptp.aa_int_int (tptp.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) B3)))))))))))))) (forall ((Y tptp.complex) (Z tptp.complex) (X tptp.complex) (W tptp.complex)) (=> (not (= Y tptp.zero_zero_complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (= (tptp.divide1717551699836669952omplex X Y) (tptp.divide1717551699836669952omplex W Z)) (= (tptp.aa_complex_complex (tptp.times_times_complex X) Z) (tptp.aa_complex_complex (tptp.times_times_complex W) Y)))))) (forall ((Y tptp.real) (Z tptp.real) (X tptp.real) (W tptp.real)) (=> (not (= Y tptp.zero_zero_real)) (=> (not (= Z tptp.zero_zero_real)) (= (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real X) Y) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real W) Z)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real X) Z) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real W) Y)))))) (forall ((Y tptp.rat) (Z tptp.rat) (X tptp.rat) (W tptp.rat)) (=> (not (= Y tptp.zero_zero_rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (= (tptp.divide_divide_rat X Y) (tptp.divide_divide_rat W Z)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat X) Z) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat W) Y)))))) (forall ((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.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.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.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.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.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.divide_divide_rat B C)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) C) B)))) (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.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.numeral_numeral_rat tptp.one)) A) A)) (forall ((A tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat tptp.one)) A) A)) (forall ((A tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_num_int tptp.numeral_numeral_int tptp.one)) A) A)) (forall ((A tptp.complex)) (= (tptp.aa_complex_complex (tptp.times_times_complex A) (tptp.numera6690914467698888265omplex tptp.one)) A)) (forall ((A tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) (tptp.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.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.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.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.times_times_num K L)))))) (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.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.divide6298287555418463151nteger B) C)) A) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger 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.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.divide6298287555418463151nteger B) C)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger 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)) (let ((_let_1 (tptp.aa_Cod4161879620478718930nteger tptp.divide6298287555418463151nteger A))) (=> (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.aa_Cod1783974652533396728nteger _let_1 (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.divide6298287555418463151nteger B) C)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (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.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_Cod4161879620478718930nteger tptp.divide6298287555418463151nteger A))) (let ((_let_2 (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_2) A)) (= (tptp.aa_Cod1783974652533396728nteger _let_1 _let_2) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.divide6298287555418463151nteger (tptp.aa_Cod1783974652533396728nteger _let_1 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.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger 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.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.divide6298287555418463151nteger A) B)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.divide6298287555418463151nteger C) D)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger 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 ((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 ((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.divide_divide_rat A B) tptp.one_one_rat) (= A B)))) (= _let_74 tptp.one_one_complex) (= _let_75 tptp.one_one_real) (= _let_73 tptp.one_one_rat) _let_187 (= _let_118 tptp.one_one_int) (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 ((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.divide6298287555418463151nteger B) A) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger 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.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger 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.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger 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)))))) _let_187 (= tptp.one_one_nat _let_11) (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 ((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.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.numeral_numeral_rat W))) (let ((_let_2 (= C tptp.zero_zero_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.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.numeral_numeral_rat W))) (let ((_let_2 (= C tptp.zero_zero_rat))) (= (= _let_1 (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.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.minus_minus_rat A (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.divide_divide_rat (tptp.minus_minus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) Z) B) Z))))))) (forall ((Y tptp.complex) (Z tptp.complex) (X tptp.complex) (W tptp.complex)) (=> (not (= Y tptp.zero_zero_complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (tptp.minus_minus_complex (tptp.divide1717551699836669952omplex X Y) (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) Y)) (tptp.aa_complex_complex (tptp.times_times_complex Y) Z)))))) (forall ((Y tptp.real) (Z tptp.real) (X tptp.real) (W tptp.real)) (=> (not (= Y tptp.zero_zero_real)) (=> (not (= Z tptp.zero_zero_real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real X) Y)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real W) Z)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real X) Z)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real W) Y))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real Y) Z)))))) (forall ((Y tptp.rat) (Z tptp.rat) (X tptp.rat) (W tptp.rat)) (=> (not (= Y tptp.zero_zero_rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (tptp.minus_minus_rat (tptp.divide_divide_rat X Y) (tptp.divide_divide_rat W Z)) (tptp.divide_divide_rat (tptp.minus_minus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat X) Z) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat W) Y)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat Y) Z)))))) (forall ((Z tptp.complex) (X tptp.complex) (Y tptp.complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (tptp.minus_minus_complex X (tptp.divide1717551699836669952omplex Y Z)) (tptp.divide1717551699836669952omplex (tptp.minus_minus_complex (tptp.aa_complex_complex (tptp.times_times_complex X) Z) Y) Z)))) (forall ((Z tptp.real) (X tptp.real) (Y tptp.real)) (=> (not (= Z tptp.zero_zero_real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real Y) Z)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real X) Z)) Y)) Z)))) (forall ((Z tptp.rat) (X tptp.rat) (Y tptp.rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (tptp.minus_minus_rat X (tptp.divide_divide_rat Y Z)) (tptp.divide_divide_rat (tptp.minus_minus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat X) Z) Y) Z)))) (forall ((Z tptp.complex) (X tptp.complex) (Y tptp.complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (tptp.minus_minus_complex (tptp.divide1717551699836669952omplex X Z) Y) (tptp.divide1717551699836669952omplex (tptp.minus_minus_complex X (tptp.aa_complex_complex (tptp.times_times_complex Y) Z)) Z)))) (forall ((Z tptp.real) (X tptp.real) (Y tptp.real)) (=> (not (= Z tptp.zero_zero_real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real X) Z)) Y) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real Y) Z))) Z)))) (forall ((Z tptp.rat) (X tptp.rat) (Y tptp.rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (tptp.minus_minus_rat (tptp.divide_divide_rat X Z) Y) (tptp.divide_divide_rat (tptp.minus_minus_rat X (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat Y) Z)) Z)))) (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.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.divide6298287555418463151nteger B) A) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger 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)))))))) (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.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger 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 ((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.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger 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 ((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.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger 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)) (=> (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.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 ((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 ((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 ((B3 tptp.code_integer)) (not (= A (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))) B3))))))) (forall ((A tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) A)) (not (forall ((B3 tptp.nat)) (not (= A (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) B3))))))) (forall ((A tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) A)) (not (forall ((B3 tptp.int)) (not (= A (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) B3))))))) (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)))))) (not (tptp.pp (tptp.aa_Code_integer_bool _let_185 tptp.one_one_Code_integer))) (not (tptp.pp (tptp.aa_nat_bool _let_184 tptp.one_one_nat))) (not (tptp.pp (tptp.aa_int_bool _let_183 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.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger _let_1) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger 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)))) (= (tptp.neg_nu7009210354673126013omplex tptp.one_one_complex) _let_83) (= (tptp.aa_real_real tptp.neg_numeral_dbl_real tptp.one_one_real) _let_46) (= (tptp.neg_numeral_dbl_rat tptp.one_one_rat) _let_137) (= (tptp.neg_numeral_dbl_int tptp.one_one_int) _let_68) (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 ((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 ((R tptp.real) (A tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.times_times_real R))) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real _let_1 A)) (tptp.aa_real_real _let_1 R)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real A) R)))) (forall ((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.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger _let_1) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger 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 ((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.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger 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.aa_nat_fun_nat_nat tptp.power_power_nat _let_1) N)) tptp.one_one_nat))) (= N tptp.zero_zero_nat)))) (forall ((N tptp.nat)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int _let_1) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_nat_int (tptp.power_power_int _let_1) N)) tptp.one_one_int))) (= N tptp.zero_zero_nat)))) (forall ((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.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.divide6298287555418463151nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer) A)) _let_1) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger 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 ((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.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.divide6298287555418463151nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.plus_p5714425477246183910nteger A) tptp.one_one_Code_integer)) _let_1) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger 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.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.divide6298287555418463151nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.plus_p5714425477246183910nteger A) tptp.one_one_Code_integer)) _let_1) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger 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 ((P tptp.fun_real_bool) (D3 tptp.real) (Q tptp.fun_real_bool)) (=> (forall ((X3 tptp.real) (K3 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 K3) D3)))))) (=> (forall ((X3 tptp.real) (K3 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 K3) 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) (K3 tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool P X3)) (tptp.pp (tptp.aa_rat_bool P (tptp.minus_minus_rat X3 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat K3) D3)))))) (=> (forall ((X3 tptp.rat) (K3 tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool Q X3)) (tptp.pp (tptp.aa_rat_bool Q (tptp.minus_minus_rat X3 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat K3) D3)))))) (forall ((X4 tptp.rat) (K4 tptp.rat)) (let ((_let_1 (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) (K3 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 K3) D3)))))) (=> (forall ((X3 tptp.int) (K3 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 K3) 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 ((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 ((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 _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 ((M tptp.num) (N tptp.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.plus_plus_num M N)))) (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)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) tptp.zero_zero_nat) M)) (forall ((M tptp.nat) (N tptp.nat)) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) N) tptp.zero_zero_nat) (and (= M tptp.zero_zero_nat) (= N tptp.zero_zero_nat)))) (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat I))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat _let_1 J)) K) (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat J) K))))) (forall ((M tptp.nat) (N tptp.nat) (A tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se547839408752420682it_nat M) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se547839408752420682it_nat N) A)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se547839408752420682it_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.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_se545348938243370406it_int M) (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_se545348938243370406it_int N) A)) (tptp.aa_int_int (tptp.aa_nat_fun_int_int 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.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_nat6383147911832638789nteger tptp.bit_se7788150548672797655nteger M) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_nat6383147911832638789nteger tptp.bit_se7788150548672797655nteger N) A)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_nat6383147911832638789nteger tptp.bit_se7788150548672797655nteger (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.code_natural)) (= (tptp.aa_Cod4272041906116450446atural (tptp.aa_nat5282697797315388251atural tptp.bit_se6611745700429515170atural M) (tptp.aa_Cod4272041906116450446atural (tptp.aa_nat5282697797315388251atural tptp.bit_se6611745700429515170atural N) A)) (tptp.aa_Cod4272041906116450446atural (tptp.aa_nat5282697797315388251atural tptp.bit_se6611745700429515170atural (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) N)) A))) (forall ((A tptp.literal)) (= (tptp.plus_plus_literal A tptp.zero_zero_literal) 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.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 ((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) (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 ((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.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 ((X tptp.nat) (Y tptp.nat)) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat X) Y) tptp.zero_zero_nat) (and (= X tptp.zero_zero_nat) (= Y tptp.zero_zero_nat)))) (forall ((X tptp.nat) (Y tptp.nat)) (= (= tptp.zero_zero_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat X) Y)) (and (= X tptp.zero_zero_nat) (= Y tptp.zero_zero_nat)))) (forall ((A tptp.literal)) (= (tptp.plus_plus_literal tptp.zero_zero_literal A) A)) (forall ((A tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real tptp.zero_zero_real) A) A)) (forall ((A tptp.rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat tptp.zero_zero_rat) A) A)) (forall ((A tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat tptp.zero_zero_nat) A) A)) (forall ((A tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int tptp.zero_zero_int) A) A)) (forall ((A tptp.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 ((M tptp.num) (N tptp.num)) (= (tptp.plus_plus_complex (tptp.numera6690914467698888265omplex M) (tptp.numera6690914467698888265omplex N)) (tptp.numera6690914467698888265omplex (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.numeral_numeral_real M)) (tptp.numeral_numeral_real N)) (tptp.numeral_numeral_real (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.numeral_numeral_rat M)) (tptp.numeral_numeral_rat N)) (tptp.numeral_numeral_rat (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.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.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.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.numeral_numeral_real V)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.numeral_numeral_real W)) Z)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.numeral_numeral_real (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.numeral_numeral_rat V)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.numeral_numeral_rat W)) Z)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.numeral_numeral_rat (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.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.plus_plus_num V W))) Z))) (= (tptp.plus_plus_num tptp.one tptp.one) _let_1) (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.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 ((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.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 ((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.minus_minus_rat (tptp.aa_rat_rat _let_1 A) (tptp.aa_rat_rat _let_1 B)) (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.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.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 ((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.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.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)) B) A)) (forall ((A tptp.rat) (B tptp.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.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.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger 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 ((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.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger 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 ((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_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 ((M tptp.nat) (N tptp.nat)) (= (= tptp.one_one_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat M) N)) (and (= M tptp.one_one_nat) (= N tptp.one_one_nat)))) (forall ((M tptp.nat) (N tptp.nat)) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat M) N) tptp.one_one_nat) (and (= M tptp.one_one_nat) (= N tptp.one_one_nat)))) (= (tptp.aa_real_real tptp.neg_numeral_dbl_real tptp.zero_zero_real) tptp.zero_zero_real) (= (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) (forall ((N tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N))) (= (tptp.aa_nat_nat tptp.nat_triangle _let_1) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat tptp.nat_triangle N)) _let_1)))) (= (tptp.aa_nat_nat tptp.nat_triangle tptp.zero_zero_nat) tptp.zero_zero_nat) (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.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.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.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.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) (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.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger 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 ((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.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger 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 ((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.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.divide6298287555418463151nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.plus_p5714425477246183910nteger A) B)) C) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.divide6298287555418463151nteger A) C)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger 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 ((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.plus_plus_num N tptp.one)))) (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.numeral_numeral_real K)) (tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 K)))) (forall ((K tptp.num)) (= (tptp.neg_numeral_dbl_rat (tptp.numeral_numeral_rat K)) (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)))) (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 ((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) (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) (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 ((N tptp.num)) (= (tptp.plus_plus_complex tptp.one_one_complex (tptp.numera6690914467698888265omplex N)) (tptp.numera6690914467698888265omplex (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.numeral_numeral_real N)) (tptp.numeral_numeral_real (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.numeral_numeral_rat N)) (tptp.numeral_numeral_rat (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.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.plus_plus_num tptp.one N)))) (forall ((N tptp.num)) (= (tptp.plus_plus_complex (tptp.numera6690914467698888265omplex N) tptp.one_one_complex) (tptp.numera6690914467698888265omplex (tptp.plus_plus_num N tptp.one)))) (forall ((N tptp.num)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.numeral_numeral_real N)) tptp.one_one_real) (tptp.numeral_numeral_real (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.numeral_numeral_rat N)) tptp.one_one_rat) (tptp.numeral_numeral_rat (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.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.plus_plus_num N tptp.one)))) (forall ((N tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat tptp.suc N)))) (forall ((N tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N) (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat tptp.suc N)))) (forall ((M tptp.nat)) (= (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 ((M tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) M)) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) M)) (= (tptp.plus_plus_complex tptp.one_one_complex tptp.one_one_complex) _let_83) (= _let_168 _let_46) (= _let_167 _let_137) _let_182 (= _let_164 _let_68) (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.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 ((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.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger 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)) (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.plus_p5714425477246183910nteger A) tptp.one_one_Code_integer))) (not (tptp.pp (tptp.aa_Code_integer_bool _let_1 A)))))) (forall ((A tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) tptp.one_one_nat))) (not (tptp.pp (tptp.aa_nat_bool _let_1 A)))))) (forall ((A tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) tptp.one_one_int))) (not (tptp.pp (tptp.aa_int_bool _let_1 A)))))) (forall ((A tptp.code_integer) (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.minus_8373710615458151222nteger A) B))) (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger 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 ((N tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se547839408752420682it_nat N) tptp.one_one_nat) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N))) (forall ((N tptp.nat)) (= (tptp.aa_int_int (tptp.aa_nat_fun_int_int 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_Cod1783974652533396728nteger (tptp.aa_nat6383147911832638789nteger tptp.bit_se7788150548672797655nteger N) tptp.one_one_Code_integer) (tptp.power_8256067586552552935nteger (tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one)) N))) (forall ((N tptp.nat)) (= (tptp.aa_Cod4272041906116450446atural (tptp.aa_nat5282697797315388251atural tptp.bit_se6611745700429515170atural N) tptp.one_one_Code_natural) (tptp.power_7079662738309270450atural (tptp.numera5444537566228673987atural (tptp.aa_num_num tptp.bit0 tptp.one)) N))) (forall ((N tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se547839408752420682it_nat N) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N))) (forall ((W tptp.int) (Z1 tptp.int) (Z2 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) Z2)) (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 Z2))))) (forall ((Z1 tptp.int) (Z2 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) Z2)) 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 Z2) W)))) (forall ((W tptp.int) (Z1 tptp.int) (Z2 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) Z2)) (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 Z2))))) (forall ((Z1 tptp.int) (Z2 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) Z2)) 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 Z2) W)))) (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 ((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 ((N tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat N) tptp.one_one_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 (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 ((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 ((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.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 ((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 ((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 _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)) (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)) (= (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)) (= (= (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) (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 ((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 ((B4 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))) (=> (= B4 (tptp.aa_real_real _let_2 B)) (= (tptp.aa_real_real _let_1 B4) (tptp.aa_real_real _let_2 (tptp.aa_real_real _let_1 B))))))) (forall ((B4 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))) (=> (= B4 (tptp.aa_rat_rat _let_2 B)) (= (tptp.aa_rat_rat _let_1 B4) (tptp.aa_rat_rat _let_2 (tptp.aa_rat_rat _let_1 B))))))) (forall ((B4 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))) (=> (= B4 (tptp.aa_nat_nat _let_2 B)) (= (tptp.aa_nat_nat _let_1 B4) (tptp.aa_nat_nat _let_2 (tptp.aa_nat_nat _let_1 B))))))) (forall ((B4 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))) (=> (= B4 (tptp.aa_int_int _let_2 B)) (= (tptp.aa_int_int _let_1 B4) (tptp.aa_int_int _let_2 (tptp.aa_int_int _let_1 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.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 ((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 ((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 ((M tptp.nat) (N tptp.nat) (Z tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int M)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N)) Z)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) N))) Z))) (forall ((N tptp.nat) (M tptp.nat)) (= (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N) M)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N)) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int M)))) (forall ((A tptp.nat) (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 ((A tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real tptp.zero_zero_real) A) A)) (forall ((A tptp.rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat tptp.zero_zero_rat) A) A)) (forall ((A tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat tptp.zero_zero_nat) A) A)) (forall ((A tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int tptp.zero_zero_int) A) A)) (forall ((A tptp.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.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.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.real) (E 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) E)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real B) E)) C)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) B)) E)) C))) (forall ((A tptp.rat) (E 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) E)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat B) E)) C)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) B)) E)) C))) (forall ((A tptp.nat) (E 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) E)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B) E)) C)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) B)) E)) C))) (forall ((A tptp.int) (E 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) E)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B) E)) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) B)) E)) 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) (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.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 ((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.minus_minus_rat A2 B) (tptp.aa_rat_rat _let_1 (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) (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.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 ((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.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)) (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.minus_minus_rat B C)) (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) (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.minus_minus_rat A (tptp.minus_minus_rat B C)) (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)) (= (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.minus_minus_rat A B)) C) (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)) (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)) (= (tptp.minus_minus_rat A (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat B) C)) (tptp.minus_minus_rat (tptp.minus_minus_rat A 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 ((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.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) (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.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.minus_minus_rat A B)) (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.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)) (= (tptp.minus_minus_rat (tptp.minus_minus_rat A B) C) (tptp.minus_minus_rat A (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 ((N tptp.num)) (= (tptp.plus_plus_num tptp.one N) (tptp.plus_plus_num N tptp.one))) (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.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.divide_divide_rat A C)) (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 C)) (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger 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 ((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.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 (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger 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 ((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 ((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 ((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 ((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))) (= _let_165 tptp.suc) (forall ((N tptp.nat)) (= (tptp.aa_nat_nat tptp.suc N) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat tptp.one_one_nat) N))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat tptp.suc M)) N) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat M) N)))) (forall ((M tptp.nat) (N tptp.nat)) (=> (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) N) M) (= N tptp.zero_zero_nat))) (forall ((N tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat tptp.zero_zero_nat) N) N)) (forall ((P tptp.fun_nat_fun_nat_bool) (A tptp.nat) (B tptp.nat)) (=> (forall ((A3 tptp.nat) (B3 tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool P A3) B3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool P B3) A3)))) (=> (forall ((A3 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool P A3) tptp.zero_zero_nat))) (=> (forall ((A3 tptp.nat) (B3 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool P A3))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 B3)) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A3) B3)))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool P A) B)))))) (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 ((K tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int K) tptp.zero_zero_int) K)) (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 ((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 ((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) (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 ((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 ((D tptp.nat) (A tptp.nat) (B tptp.nat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A))) (let ((_let_2 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat 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 Y)) D)) (= (tptp.aa_nat_nat _let_2 X) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat _let_1 Y)) D))) (exists ((X3 tptp.nat) (Y3 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 Y3)) 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 Y3)) D)))))))))))))))) (forall ((A tptp.nat) (B tptp.nat)) (exists ((D2 tptp.nat) (X3 tptp.nat) (Y3 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 Y3)) 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 Y3)) D2))))))))) (forall ((A tptp.int) (D tptp.int) (X tptp.int) (T tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.plus_plus_int X))) (let ((_let_2 (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int A))) (=> (tptp.pp (tptp.aa_int_bool _let_2 D)) (= (tptp.pp (tptp.aa_int_bool _let_2 (tptp.aa_int_int _let_1 T))) (tptp.pp (tptp.aa_int_bool _let_2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int C) D))) T)))))))) (forall ((K tptp.int) (N tptp.int) (M tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int K))) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int N) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int K) M)))) (tptp.pp (tptp.aa_int_bool _let_1 N))))) (forall ((N tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat 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) (A tptp.int) (B tptp.int)) (let ((_let_1 (tptp.aa_nat_fun_int_int tptp.bit_se545348938243370406it_int N))) (= (tptp.aa_int_int _let_1 (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 _let_1 A)) (tptp.aa_int_int _let_1 B))))) (forall ((N tptp.nat) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (tptp.aa_nat6383147911832638789nteger tptp.bit_se7788150548672797655nteger N))) (= (tptp.aa_Cod1783974652533396728nteger _let_1 (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.plus_p5714425477246183910nteger A) B)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger _let_1 A)) (tptp.aa_Cod1783974652533396728nteger _let_1 B))))) (forall ((N tptp.nat) (A tptp.code_natural) (B tptp.code_natural)) (let ((_let_1 (tptp.aa_nat5282697797315388251atural tptp.bit_se6611745700429515170atural N))) (= (tptp.aa_Cod4272041906116450446atural _let_1 (tptp.aa_Cod4272041906116450446atural (tptp.aa_Cod5141017464274028979atural tptp.plus_p4538020629002901425atural A) B)) (tptp.aa_Cod4272041906116450446atural (tptp.aa_Cod5141017464274028979atural tptp.plus_p4538020629002901425atural (tptp.aa_Cod4272041906116450446atural _let_1 A)) (tptp.aa_Cod4272041906116450446atural _let_1 B))))) (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.plus_plus_num V tptp.one))) N))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (=> (not (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) N)) tptp.zero_zero_nat)) (not (= (tptp.aa_nat_nat _let_1 N) tptp.zero_zero_nat))))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))))) (=> (not (= (tptp.aa_nat_int _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) N)) tptp.zero_zero_int)) (not (= (tptp.aa_nat_int _let_1 N) tptp.zero_zero_int))))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (=> (not (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) N)) tptp.zero_zero_nat)) (not (= (tptp.aa_nat_nat _let_1 M) tptp.zero_zero_nat))))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))))) (=> (not (= (tptp.aa_nat_int _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) N)) tptp.zero_zero_int)) (not (= (tptp.aa_nat_int _let_1 M) tptp.zero_zero_int))))) (forall ((A tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_2 (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat _let_2 (tptp.aa_nat_nat _let_1 M))) (tptp.aa_nat_nat _let_1 N)) (tptp.aa_nat_nat _let_2 (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) N))))))) (forall ((A tptp.int) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_2 (tptp.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_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.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.plus_p5714425477246183910nteger X5) tptp.zero_z3403309356797280102nteger))) (tptp.pp (tptp.aa_Code_integer_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 ((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.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.numeral_numeral_real _let_1)) X)) _let_2))))) (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.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.plus_p5714425477246183910nteger X4) T)))) (not (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger 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.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 ((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.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.plus_p5714425477246183910nteger X4) T))) (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger 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.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 ((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.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.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 ((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.numeral_numeral_real N))) (= (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.numeral_numeral_rat N))) (= (tptp.numeral_numeral_rat (tptp.aa_num_num tptp.bit0 N)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat _let_1) _let_1)))) (forall ((N tptp.num)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat N))) (= (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 N)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat _let_1) _let_1)))) (forall ((N tptp.num)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int N))) (= (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 N)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int _let_1) _let_1)))) (forall ((X tptp.real) (Y tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real X) X)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real Y) Y)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) Y)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real X) Y)))) (forall ((X tptp.rat) (Y tptp.rat)) (= (tptp.minus_minus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat X) X) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat Y) Y)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat X) Y)) (tptp.minus_minus_rat X Y)))) (forall ((X tptp.int) (Y tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int X) X)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int Y) Y)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int X) Y)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int X) Y)))) (forall ((A tptp.real) (E 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) E)) C) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real B) E)) D)) (= C (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real B) A)) E)) D)))) (forall ((A tptp.rat) (E 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) E)) C) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat B) E)) D)) (= C (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.minus_minus_rat B A)) E)) D)))) (forall ((A tptp.int) (E 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) E)) C) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B) E)) D)) (= C (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int B) A)) E)) D)))) (forall ((A tptp.real) (E 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) E)) C) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real B) E)) D)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A) B)) E)) C) D))) (forall ((A tptp.rat) (E 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) E)) C) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat B) E)) D)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.minus_minus_rat A B)) E)) C) D))) (forall ((A tptp.int) (E 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) E)) C) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B) E)) D)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) B)) E)) C) D))) (forall ((X tptp.real) (Y 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 Y)) (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 Y) 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) (Y tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_rat tptp.times_times_rat X))) (= (tptp.minus_minus_rat (tptp.aa_rat_rat _let_1 Y) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) B)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat _let_1 (tptp.minus_minus_rat Y B))) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.minus_minus_rat X A)) B))))) (forall ((X tptp.int) (Y 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 Y)) (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 Y) 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 ((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.divide6298287555418463151nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.plus_p5714425477246183910nteger A) B)) C) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.divide6298287555418463151nteger A) C)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger 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 ((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.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.divide6298287555418463151nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.plus_p5714425477246183910nteger A) B)) C) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.divide6298287555418463151nteger A) C)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger 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 ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat))) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) N) _let_1) (or (and (= M _let_1) (= N tptp.zero_zero_nat)) (and (= M tptp.zero_zero_nat) (= N _let_1)))))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat))) (= (= _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) N)) (or (and (= M _let_1) (= N tptp.zero_zero_nat)) (and (= M tptp.zero_zero_nat) (= N _let_1)))))) (forall ((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 ((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 ((A tptp.nat)) (= (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_nat tptp.suc A)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int A)) tptp.one_one_int))) (forall ((N tptp.nat)) (= (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_nat tptp.suc N)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N)) tptp.one_one_int))) (forall ((A tptp.nat) (B tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (exists ((D2 tptp.nat) (X3 tptp.nat) (Y3 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) Y3)) D2))))))) (forall ((Z tptp.complex) (X tptp.complex) (Y tptp.complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (tptp.plus_plus_complex (tptp.divide1717551699836669952omplex X Z) Y) (tptp.divide1717551699836669952omplex (tptp.plus_plus_complex X (tptp.aa_complex_complex (tptp.times_times_complex Y) Z)) Z)))) (forall ((Z tptp.real) (X tptp.real) (Y tptp.real)) (=> (not (= Z tptp.zero_zero_real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real X) Z)) Y) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real Y) Z))) Z)))) (forall ((Z tptp.rat) (X tptp.rat) (Y tptp.rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.divide_divide_rat X Z)) Y) (tptp.divide_divide_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat X) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat Y) Z)) Z)))) (forall ((Z tptp.complex) (X tptp.complex) (Y tptp.complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (tptp.plus_plus_complex X (tptp.divide1717551699836669952omplex Y Z)) (tptp.divide1717551699836669952omplex (tptp.plus_plus_complex (tptp.aa_complex_complex (tptp.times_times_complex X) Z) Y) Z)))) (forall ((Z tptp.real) (X tptp.real) (Y tptp.real)) (=> (not (= Z tptp.zero_zero_real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real Y) Z)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real X) Z)) Y)) Z)))) (forall ((Z tptp.rat) (X tptp.rat) (Y tptp.rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat X) (tptp.divide_divide_rat Y Z)) (tptp.divide_divide_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat X) Z)) Y) Z)))) (forall ((Y tptp.complex) (Z tptp.complex) (X tptp.complex)) (=> (not (= Y tptp.zero_zero_complex)) (= (tptp.plus_plus_complex Z (tptp.divide1717551699836669952omplex X Y)) (tptp.divide1717551699836669952omplex (tptp.plus_plus_complex X (tptp.aa_complex_complex (tptp.times_times_complex Z) Y)) Y)))) (forall ((Y tptp.real) (Z tptp.real) (X tptp.real)) (=> (not (= Y tptp.zero_zero_real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real Z) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real X) Y)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real Z) Y))) Y)))) (forall ((Y tptp.rat) (Z tptp.rat) (X tptp.rat)) (=> (not (= Y tptp.zero_zero_rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat Z) (tptp.divide_divide_rat X Y)) (tptp.divide_divide_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat X) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat Z) Y)) Y)))) (forall ((Y tptp.complex) (X tptp.complex) (Z tptp.complex)) (=> (not (= Y tptp.zero_zero_complex)) (= (tptp.plus_plus_complex (tptp.divide1717551699836669952omplex X Y) Z) (tptp.divide1717551699836669952omplex (tptp.plus_plus_complex X (tptp.aa_complex_complex (tptp.times_times_complex Z) Y)) Y)))) (forall ((Y tptp.real) (X tptp.real) (Z tptp.real)) (=> (not (= Y tptp.zero_zero_real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real X) Y)) Z) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real Z) Y))) Y)))) (forall ((Y tptp.rat) (X tptp.rat) (Z tptp.rat)) (=> (not (= Y tptp.zero_zero_rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.divide_divide_rat X Y)) Z) (tptp.divide_divide_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat X) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat Z) Y)) Y)))) (forall ((Y tptp.complex) (Z tptp.complex) (X tptp.complex) (W tptp.complex)) (=> (not (= Y tptp.zero_zero_complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (tptp.plus_plus_complex (tptp.divide1717551699836669952omplex X Y) (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) Y)) (tptp.aa_complex_complex (tptp.times_times_complex Y) Z)))))) (forall ((Y tptp.real) (Z tptp.real) (X tptp.real) (W tptp.real)) (=> (not (= Y tptp.zero_zero_real)) (=> (not (= Z tptp.zero_zero_real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real X) Y)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real W) Z)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real X) Z)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real W) Y))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real Y) Z)))))) (forall ((Y tptp.rat) (Z tptp.rat) (X tptp.rat) (W tptp.rat)) (=> (not (= Y tptp.zero_zero_rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.divide_divide_rat X Y)) (tptp.divide_divide_rat W Z)) (tptp.divide_divide_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat X) Z)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat W) Y)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat Y) Z)))))) (forall ((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.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.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 ((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.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.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 ((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.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.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.minus_minus_rat X tptp.one_one_rat)))) (forall ((X tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int X) X)) tptp.one_one_int) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int X) tptp.one_one_int)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int X) tptp.one_one_int)))) (forall ((N tptp.nat) (M tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se547839408752420682it_nat N) M) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat M) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N)))) (forall ((N tptp.nat) (K tptp.int)) (= (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_se545348938243370406it_int N) K) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int K) (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) N)))) _let_182 (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 ((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.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.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 ((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.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.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 ((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.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.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 ((X tptp.real)) (let ((_let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real X) (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.divide_divide_rat X (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.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger 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 ((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 ((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 ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (=> (not (= (tptp.aa_nat_nat _let_1 N) tptp.zero_zero_nat)) (not (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) M)) tptp.zero_zero_nat))))) (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))))) (=> (not (= (tptp.aa_nat_int _let_1 N) tptp.zero_zero_int)) (not (= (tptp.aa_nat_int _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) M)) tptp.zero_zero_int))))) (forall ((N tptp.nat) (A tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_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.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N)))) (forall ((N tptp.nat) (A tptp.int)) (= (tptp.aa_int_int (tptp.aa_nat_fun_int_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.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_nat6383147911832638789nteger tptp.bit_se7788150548672797655nteger N) A) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) (tptp.power_8256067586552552935nteger (tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one)) N)))) (forall ((N tptp.nat) (A tptp.code_natural)) (= (tptp.aa_Cod4272041906116450446atural (tptp.aa_nat5282697797315388251atural tptp.bit_se6611745700429515170atural N) A) (tptp.aa_Cod4272041906116450446atural (tptp.aa_Cod5141017464274028979atural tptp.times_2397367101498566445atural A) (tptp.power_7079662738309270450atural (tptp.numera5444537566228673987atural (tptp.aa_num_num tptp.bit0 tptp.one)) 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_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N)) A)) (not (forall ((B3 tptp.nat)) (not (= A (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se547839408752420682it_nat N) B3))))))) (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 ((B3 tptp.int)) (not (= A (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_se545348938243370406it_int N) B3))))))) (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 ((B3 tptp.code_integer)) (not (= A (tptp.aa_Cod1783974652533396728nteger (tptp.aa_nat6383147911832638789nteger tptp.bit_se7788150548672797655nteger N) B3))))))) (forall ((N tptp.nat) (A tptp.code_natural)) (=> (tptp.pp (tptp.dvd_dvd_Code_natural (tptp.power_7079662738309270450atural (tptp.numera5444537566228673987atural (tptp.aa_num_num tptp.bit0 tptp.one)) N) A)) (not (forall ((B3 tptp.code_natural)) (not (= A (tptp.aa_Cod4272041906116450446atural (tptp.aa_nat5282697797315388251atural tptp.bit_se6611745700429515170atural N) B3))))))) (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 ((B3 tptp.code_integer)) (not (= A (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))) B3)) tptp.one_one_Code_integer))))))) (forall ((A tptp.nat)) (=> (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) A))) (not (forall ((B3 tptp.nat)) (not (= A (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) B3)) tptp.one_one_nat))))))) (forall ((A tptp.int)) (=> (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) A))) (not (forall ((B3 tptp.int)) (not (= A (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) B3)) tptp.one_one_int))))))) (forall ((P tptp.fun_real_bool) (D3 tptp.real) (Q tptp.fun_real_bool)) (=> (forall ((X3 tptp.real) (K3 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 K3) D3)))))) (=> (forall ((X3 tptp.real) (K3 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 K3) 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) (K3 tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool P X3)) (tptp.pp (tptp.aa_rat_bool P (tptp.minus_minus_rat X3 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat K3) D3)))))) (=> (forall ((X3 tptp.rat) (K3 tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool Q X3)) (tptp.pp (tptp.aa_rat_bool Q (tptp.minus_minus_rat X3 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat K3) D3)))))) (forall ((X4 tptp.rat) (K4 tptp.rat)) (let ((_let_1 (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) (K3 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 K3) D3)))))) (=> (forall ((X3 tptp.int) (K3 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 K3) 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 ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_nat_rat (tptp.power_power_rat X) _let_1)) (tptp.aa_nat_rat (tptp.power_power_rat Y) _let_1)) tptp.zero_zero_rat) (and (= X tptp.zero_zero_rat) (= Y tptp.zero_zero_rat))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) _let_1)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Y) _let_1)) tptp.zero_zero_real) (and (= X tptp.zero_zero_real) (= Y tptp.zero_zero_real))))) (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_nat_int (tptp.power_power_int X) _let_1)) (tptp.aa_nat_int (tptp.power_power_int Y) _let_1)) tptp.zero_zero_int) (and (= X tptp.zero_zero_int) (= Y tptp.zero_zero_int))))) (forall ((A tptp.rat)) (= (= (tptp.aa_nat_rat (tptp.power_power_rat A) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))) (forall ((A tptp.nat)) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) tptp.zero_zero_nat) (= A tptp.zero_zero_nat))) (forall ((A tptp.real)) (= (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real A) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) tptp.zero_zero_real) (= A tptp.zero_zero_real))) (forall ((A tptp.int)) (= (= (tptp.aa_nat_int (tptp.power_power_int A) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) tptp.zero_zero_int) (= A tptp.zero_zero_int))) (forall ((A tptp.complex)) (= (= (tptp.aa_nat_complex (tptp.power_power_complex A) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) tptp.zero_zero_complex) (= A tptp.zero_zero_complex))) (forall ((Y tptp.nat) (X tptp.num) (N tptp.nat)) (= (= (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex Y) (tptp.aa_nat_complex (tptp.power_power_complex (tptp.numera6690914467698888265omplex X)) N)) (= Y (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat X)) N)))) (forall ((Y tptp.nat) (X tptp.num) (N tptp.nat)) (= (= (tptp.aa_nat_real tptp.semiri5074537144036343181t_real Y) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.numeral_numeral_real X)) N)) (= Y (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat X)) N)))) (forall ((Y tptp.nat) (X tptp.num) (N tptp.nat)) (= (= (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat Y) (tptp.aa_nat_rat (tptp.power_power_rat (tptp.numeral_numeral_rat X)) N)) (= Y (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat X)) N)))) (forall ((Y tptp.nat) (X tptp.num) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat X)) N))) (= (= (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat Y) _let_1) (= Y _let_1)))) (forall ((Y tptp.nat) (X tptp.num) (N tptp.nat)) (= (= (tptp.aa_nat_int tptp.semiri1314217659103216013at_int Y) (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int X)) N)) (= Y (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat X)) N)))) (forall ((X tptp.num) (N tptp.nat) (Y tptp.nat)) (= (= (tptp.aa_nat_complex (tptp.power_power_complex (tptp.numera6690914467698888265omplex X)) N) (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex Y)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat X)) N) Y))) (forall ((X tptp.num) (N tptp.nat) (Y tptp.nat)) (= (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.numeral_numeral_real X)) N) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real Y)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat X)) N) Y))) (forall ((X tptp.num) (N tptp.nat) (Y tptp.nat)) (= (= (tptp.aa_nat_rat (tptp.power_power_rat (tptp.numeral_numeral_rat X)) N) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat Y)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat X)) N) Y))) (forall ((X tptp.num) (N tptp.nat) (Y tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat X)) N))) (= (= _let_1 (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat Y)) (= _let_1 Y)))) (forall ((X tptp.num) (N tptp.nat) (Y tptp.nat)) (= (= (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int X)) N) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int Y)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat X)) N) Y))) (forall ((A tptp.nat) (M tptp.num) (N tptp.num)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_nat_nat _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat M))) (tptp.aa_num_nat tptp.numeral_numeral_nat N)) (tptp.aa_nat_nat _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.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.times_times_num M N)))))) (forall ((A tptp.int) (M tptp.num) (N tptp.num)) (let ((_let_1 (tptp.power_power_int A))) (= (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_nat_int _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat M))) (tptp.aa_num_nat tptp.numeral_numeral_nat N)) (tptp.aa_nat_int _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.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.times_times_num M N)))))) (forall ((X tptp.complex) (Y tptp.complex)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (let ((_let_2 (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1))) (= (tptp.aa_nat_complex (tptp.power_power_complex (tptp.minus_minus_complex X Y)) _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 Y) _let_2)) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_complex_complex (tptp.times_times_complex (tptp.numera6690914467698888265omplex _let_1)) X)) Y)))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (let ((_let_2 (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1))) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real X) Y)) _let_2) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) _let_2)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Y) _let_2))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.numeral_numeral_real _let_1)) X)) Y)))))) (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (let ((_let_2 (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1))) (= (tptp.aa_nat_rat (tptp.power_power_rat (tptp.minus_minus_rat X Y)) _let_2) (tptp.minus_minus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_nat_rat (tptp.power_power_rat X) _let_2)) (tptp.aa_nat_rat (tptp.power_power_rat Y) _let_2)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.numeral_numeral_rat _let_1)) X)) Y)))))) (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (let ((_let_2 (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1))) (= (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int X) Y)) _let_2) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_nat_int (tptp.power_power_int X) _let_2)) (tptp.aa_nat_int (tptp.power_power_int Y) _let_2))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_num_int tptp.numeral_numeral_int _let_1)) X)) Y)))))) (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (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 ((B tptp.real) (A tptp.real)) (let ((_let_1 (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.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)) A)) (forall ((A tptp.real)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real A) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)) A)) (forall ((A tptp.int)) (= (tptp.aa_nat_int (tptp.power_power_int A) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)) A)) (forall ((A tptp.complex)) (= (tptp.aa_nat_complex (tptp.power_power_complex A) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)) A)) (forall ((A tptp.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.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.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.plus_plus_num M N)))))) (forall ((A tptp.nat) (M tptp.num) (N tptp.num)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat M))) (tptp.aa_nat_nat _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat N))) (tptp.aa_nat_nat _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.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.plus_plus_num M N)))))) (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.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.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.plus_plus_num M N)))) B)))) (forall ((A tptp.nat) (M tptp.num) (N tptp.num) (B tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat M))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat N))) 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.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.plus_plus_num M N)))) B)))) (forall ((N tptp.nat)) (= (tptp.aa_nat_rat (tptp.power_power_rat tptp.one_one_rat) N) tptp.one_one_rat)) (forall ((N tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat tptp.one_one_nat) N) tptp.one_one_nat)) (forall ((N tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real tptp.one_one_real) N) tptp.one_one_real)) (forall ((N tptp.nat)) (= (tptp.aa_nat_int (tptp.power_power_int tptp.one_one_int) N) tptp.one_one_int)) (forall ((N tptp.nat)) (= (tptp.aa_nat_complex (tptp.power_power_complex tptp.one_one_complex) N) tptp.one_one_complex)) (forall ((A tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A) tptp.one_one_nat) A)) (forall ((A tptp.real)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real A) tptp.one_one_nat) A)) (forall ((A tptp.int)) (= (tptp.aa_nat_int (tptp.power_power_int A) tptp.one_one_nat) A)) (forall ((A tptp.complex)) (= (tptp.aa_nat_complex (tptp.power_power_complex A) tptp.one_one_nat) A)) (forall ((X tptp.real) (Y tptp.real)) (= (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real X) X)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real Y) Y)) tptp.zero_zero_real) (and (= X tptp.zero_zero_real) (= Y tptp.zero_zero_real)))) (forall ((X tptp.rat) (Y tptp.rat)) (= (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat X) X)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat Y) Y)) tptp.zero_zero_rat) (and (= X tptp.zero_zero_rat) (= Y tptp.zero_zero_rat)))) (forall ((X tptp.int) (Y tptp.int)) (= (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int X) X)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int Y) Y)) tptp.zero_zero_int) (and (= X tptp.zero_zero_int) (= Y tptp.zero_zero_int)))) (forall ((N tptp.nat)) (= (tptp.aa_nat_rat (tptp.power_power_rat tptp.zero_zero_rat) (tptp.aa_nat_nat tptp.suc N)) tptp.zero_zero_rat)) (forall ((N tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat tptp.zero_zero_nat) (tptp.aa_nat_nat tptp.suc N)) tptp.zero_zero_nat)) (forall ((N tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real tptp.zero_zero_real) (tptp.aa_nat_nat tptp.suc N)) tptp.zero_zero_real)) (forall ((N tptp.nat)) (= (tptp.aa_nat_int (tptp.power_power_int tptp.zero_zero_int) (tptp.aa_nat_nat tptp.suc N)) tptp.zero_zero_int)) (forall ((N tptp.nat)) (= (tptp.aa_nat_complex (tptp.power_power_complex tptp.zero_zero_complex) (tptp.aa_nat_nat tptp.suc N)) tptp.zero_zero_complex)) (forall ((K tptp.num)) (= (tptp.aa_nat_rat (tptp.power_power_rat tptp.zero_zero_rat) (tptp.aa_num_nat tptp.numeral_numeral_nat K)) tptp.zero_zero_rat)) (forall ((K tptp.num)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat tptp.zero_zero_nat) (tptp.aa_num_nat tptp.numeral_numeral_nat K)) tptp.zero_zero_nat)) (forall ((K tptp.num)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real tptp.zero_zero_real) (tptp.aa_num_nat tptp.numeral_numeral_nat K)) tptp.zero_zero_real)) (forall ((K tptp.num)) (= (tptp.aa_nat_int (tptp.power_power_int tptp.zero_zero_int) (tptp.aa_num_nat tptp.numeral_numeral_nat K)) tptp.zero_zero_int)) (forall ((K tptp.num)) (= (tptp.aa_nat_complex (tptp.power_power_complex tptp.zero_zero_complex) (tptp.aa_num_nat tptp.numeral_numeral_nat K)) tptp.zero_zero_complex)) (forall ((X tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat))) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat X) M) _let_1) (or (= M tptp.zero_zero_nat) (= X _let_1))))) (forall ((N tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat _let_1) N) _let_1))) (forall ((X tptp.nat) (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.aa_nat_fun_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.aa_nat_fun_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.aa_nat_fun_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.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat B)) W)) (= X (tptp.aa_nat_nat (tptp.aa_nat_fun_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.aa_nat_fun_nat_nat tptp.power_power_nat B) W)))) (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.aa_nat_fun_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.aa_nat_fun_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.aa_nat_fun_nat_nat tptp.power_power_nat B) W) X))) (forall ((B tptp.nat) (W tptp.nat) (X tptp.nat)) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat B)) W) (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat X)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_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.aa_nat_fun_nat_nat tptp.power_power_nat B) W) X))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat M) N)) (tptp.aa_nat_complex (tptp.power_power_complex (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex M)) N))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.aa_nat_real tptp.semiri5074537144036343181t_real (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat M) N)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real M)) N))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat (tptp.aa_nat_nat (tptp.aa_nat_fun_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.aa_nat_fun_nat_nat tptp.power_power_nat M) N)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat M)) N))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat M) N)) (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int M)) N))) (forall ((A tptp.rat) (N tptp.nat)) (=> (not (= A tptp.zero_zero_rat)) (not (= (tptp.aa_nat_rat (tptp.power_power_rat A) N) tptp.zero_zero_rat)))) (forall ((A tptp.nat) (N tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (not (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A) N) tptp.zero_zero_nat)))) (forall ((A tptp.real) (N tptp.nat)) (=> (not (= A tptp.zero_zero_real)) (not (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real A) N) tptp.zero_zero_real)))) (forall ((A tptp.int) (N tptp.nat)) (=> (not (= A tptp.zero_zero_int)) (not (= (tptp.aa_nat_int (tptp.power_power_int A) N) tptp.zero_zero_int)))) (forall ((A tptp.complex) (N tptp.nat)) (=> (not (= A tptp.zero_zero_complex)) (not (= (tptp.aa_nat_complex (tptp.power_power_complex A) N) tptp.zero_zero_complex)))) (forall ((X tptp.complex) (Y tptp.complex) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_complex (tptp.power_power_complex X) N))) (let ((_let_2 (tptp.times_times_complex Y))) (=> (= (tptp.aa_complex_complex (tptp.times_times_complex X) Y) (tptp.aa_complex_complex _let_2 X)) (= (tptp.aa_complex_complex (tptp.times_times_complex _let_1) Y) (tptp.aa_complex_complex _let_2 _let_1)))))) (forall ((X tptp.real) (Y tptp.real) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) N))) (let ((_let_2 (tptp.aa_rea7340605660300375871l_real tptp.times_times_real Y))) (=> (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real X) Y) (tptp.aa_real_real _let_2 X)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real _let_1) Y) (tptp.aa_real_real _let_2 _let_1)))))) (forall ((X tptp.rat) (Y tptp.rat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_rat (tptp.power_power_rat X) N))) (let ((_let_2 (tptp.aa_rat_fun_rat_rat tptp.times_times_rat Y))) (=> (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat X) Y) (tptp.aa_rat_rat _let_2 X)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat _let_1) Y) (tptp.aa_rat_rat _let_2 _let_1)))))) (forall ((X tptp.nat) (Y tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat X) N))) (let ((_let_2 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat Y))) (=> (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat X) Y) (tptp.aa_nat_nat _let_2 X)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat _let_1) Y) (tptp.aa_nat_nat _let_2 _let_1)))))) (forall ((X tptp.int) (Y tptp.int) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_int (tptp.power_power_int X) N))) (let ((_let_2 (tptp.aa_int_fun_int_int tptp.times_times_int Y))) (=> (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int X) Y) (tptp.aa_int_int _let_2 X)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int _let_1) Y) (tptp.aa_int_int _let_2 _let_1)))))) (forall ((A tptp.complex) (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.aa_nat_fun_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.aa_nat_fun_nat_nat tptp.power_power_nat A) N)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat 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.aa_nat_fun_nat_nat tptp.power_power_nat A) N))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat _let_1) A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) _let_1)))) (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_int (tptp.power_power_int A) N))) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int _let_1) A) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) _let_1)))) (forall ((A tptp.complex) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.power_power_complex A))) (= (tptp.aa_nat_complex _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) N)) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_nat_complex _let_1 M)) (tptp.aa_nat_complex _let_1 N))))) (forall ((A tptp.real) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_real_fun_nat_real tptp.power_power_real A))) (= (tptp.aa_nat_real _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) N)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real _let_1 M)) (tptp.aa_nat_real _let_1 N))))) (forall ((A tptp.rat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.power_power_rat A))) (= (tptp.aa_nat_rat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) N)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat _let_1 M)) (tptp.aa_nat_rat _let_1 N))))) (forall ((A tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A))) (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) N)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat _let_1 M)) (tptp.aa_nat_nat _let_1 N))))) (forall ((A tptp.int) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.power_power_int A))) (= (tptp.aa_nat_int _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) N)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int _let_1 M)) (tptp.aa_nat_int _let_1 N))))) (forall ((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.divide_divide_rat A B)) N) (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) (Y tptp.code_integer) (N tptp.nat)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer X) Y)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.power_8256067586552552935nteger X N)) (tptp.power_8256067586552552935nteger Y N))))) (forall ((X tptp.nat) (Y tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat X) Y)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat X) N)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat Y) N))))) (forall ((X tptp.real) (Y tptp.real) (N tptp.nat)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.dvd_dvd_real X) Y)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.dvd_dvd_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) N)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Y) N))))) (forall ((X tptp.int) (Y tptp.int) (N tptp.nat)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int X) Y)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_nat_int (tptp.power_power_int X) N)) (tptp.aa_nat_int (tptp.power_power_int Y) N))))) (forall ((X tptp.complex) (Y tptp.complex) (N tptp.nat)) (=> (tptp.pp (tptp.aa_complex_bool (tptp.dvd_dvd_complex X) Y)) (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 Y) N))))) (forall ((A tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A))) (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat M) N)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_nat_nat _let_1 M)) N)))) (forall ((A tptp.real) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_real_fun_nat_real tptp.power_power_real A))) (= (tptp.aa_nat_real _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat M) N)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_nat_real _let_1 M)) N)))) (forall ((A tptp.int) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.power_power_int A))) (= (tptp.aa_nat_int _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat M) N)) (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_nat_int _let_1 M)) N)))) (forall ((A tptp.complex) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.power_power_complex A))) (= (tptp.aa_nat_complex _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat M) N)) (tptp.aa_nat_complex (tptp.power_power_complex (tptp.aa_nat_complex _let_1 M)) N)))) (forall ((X tptp.complex) (Y tptp.complex) (N tptp.nat)) (=> (= (tptp.aa_complex_complex (tptp.times_times_complex X) Y) tptp.one_one_complex) (= (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_nat_complex (tptp.power_power_complex X) N)) (tptp.aa_nat_complex (tptp.power_power_complex Y) N)) tptp.one_one_complex))) (forall ((X tptp.real) (Y tptp.real) (N tptp.nat)) (=> (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real X) Y) tptp.one_one_real) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) N)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Y) N)) tptp.one_one_real))) (forall ((X tptp.rat) (Y tptp.rat) (N tptp.nat)) (=> (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat X) Y) tptp.one_one_rat) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat (tptp.power_power_rat X) N)) (tptp.aa_nat_rat (tptp.power_power_rat Y) N)) tptp.one_one_rat))) (forall ((X tptp.nat) (Y tptp.nat) (N tptp.nat)) (=> (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat X) Y) tptp.one_one_nat) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat X) N)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat Y) N)) tptp.one_one_nat))) (forall ((X tptp.int) (Y tptp.int) (N tptp.nat)) (=> (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int X) Y) tptp.one_one_int) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int (tptp.power_power_int X) N)) (tptp.aa_nat_int (tptp.power_power_int Y) N)) tptp.one_one_int))) (forall ((A tptp.complex) (N tptp.nat)) (= (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)) (= (tptp.aa_nat_rat (tptp.power_power_rat (tptp.divide_divide_rat tptp.one_one_rat A)) N) (tptp.divide_divide_rat tptp.one_one_rat (tptp.aa_nat_rat (tptp.power_power_rat A) N)))) (forall ((A tptp.complex) (N tptp.nat)) (let ((_let_1 (tptp.power_power_complex A))) (= (tptp.aa_nat_complex _let_1 (tptp.aa_nat_nat tptp.suc N)) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_nat_complex _let_1 N)) A)))) (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (tptp.aa_real_fun_nat_real tptp.power_power_real A))) (= (tptp.aa_nat_real _let_1 (tptp.aa_nat_nat tptp.suc N)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real _let_1 N)) A)))) (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (tptp.power_power_rat A))) (= (tptp.aa_nat_rat _let_1 (tptp.aa_nat_nat tptp.suc N)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat _let_1 N)) A)))) (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A))) (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat tptp.suc N)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat _let_1 N)) A)))) (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (tptp.power_power_int A))) (= (tptp.aa_nat_int _let_1 (tptp.aa_nat_nat tptp.suc N)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int _let_1 N)) A)))) (forall ((A tptp.complex) (N tptp.nat)) (let ((_let_1 (tptp.power_power_complex A))) (= (tptp.aa_nat_complex _let_1 (tptp.aa_nat_nat tptp.suc N)) (tptp.aa_complex_complex (tptp.times_times_complex A) (tptp.aa_nat_complex _let_1 N))))) (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (tptp.aa_real_fun_nat_real tptp.power_power_real A))) (= (tptp.aa_nat_real _let_1 (tptp.aa_nat_nat tptp.suc N)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) (tptp.aa_nat_real _let_1 N))))) (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (tptp.power_power_rat A))) (= (tptp.aa_nat_rat _let_1 (tptp.aa_nat_nat tptp.suc N)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) (tptp.aa_nat_rat _let_1 N))))) (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A))) (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat tptp.suc N)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) (tptp.aa_nat_nat _let_1 N))))) (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (tptp.power_power_int A))) (= (tptp.aa_nat_int _let_1 (tptp.aa_nat_nat tptp.suc N)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) (tptp.aa_nat_int _let_1 N))))) (forall ((A tptp.rat)) (= (tptp.aa_nat_rat (tptp.power_power_rat A) tptp.zero_zero_nat) tptp.one_one_rat)) (forall ((A tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A) tptp.zero_zero_nat) tptp.one_one_nat)) (forall ((A tptp.real)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real A) tptp.zero_zero_nat) tptp.one_one_real)) (forall ((A tptp.int)) (= (tptp.aa_nat_int (tptp.power_power_int A) tptp.zero_zero_nat) tptp.one_one_int)) (forall ((A tptp.complex)) (= (tptp.aa_nat_complex (tptp.power_power_complex A) tptp.zero_zero_nat) tptp.one_one_complex)) (forall ((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.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.divide6298287555418463151nteger A) B) N) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger 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.aa_nat_fun_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.aa_nat_fun_nat_nat tptp.power_power_nat A) N)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat 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)) (let ((_let_1 (tptp.aa_nat_rat (tptp.power_power_rat tptp.zero_zero_rat) N))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_rat)) (=> (not _let_2) (= _let_1 tptp.zero_zero_rat)))))) (forall ((N tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat tptp.zero_zero_nat) N))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_nat)) (=> (not _let_2) (= _let_1 tptp.zero_zero_nat)))))) (forall ((N tptp.nat)) (let ((_let_1 (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real tptp.zero_zero_real) N))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_real)) (=> (not _let_2) (= _let_1 tptp.zero_zero_real)))))) (forall ((N tptp.nat)) (let ((_let_1 (tptp.aa_nat_int (tptp.power_power_int tptp.zero_zero_int) N))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_int)) (=> (not _let_2) (= _let_1 tptp.zero_zero_int)))))) (forall ((N tptp.nat)) (let ((_let_1 (tptp.aa_nat_complex (tptp.power_power_complex tptp.zero_zero_complex) N))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_complex)) (=> (not _let_2) (= _let_1 tptp.zero_zero_complex)))))) (forall ((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.nat) (N tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A) N)) tptp.one_one_nat)) (or (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat A) tptp.one_one_nat)) (= N tptp.zero_zero_nat)))) (forall ((A tptp.int) (N tptp.nat)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_nat_int (tptp.power_power_int A) N)) tptp.one_one_int)) (or (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int A) tptp.one_one_int)) (= N tptp.zero_zero_nat)))) (= (tptp.aa_nat_rat (tptp.power_power_rat tptp.zero_zero_rat) _let_2) tptp.zero_zero_rat) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat tptp.zero_zero_nat) _let_2) tptp.zero_zero_nat) (= (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_int (tptp.power_power_int tptp.zero_zero_int) _let_2) tptp.zero_zero_int) (= (tptp.aa_nat_complex (tptp.power_power_complex tptp.zero_zero_complex) _let_2) tptp.zero_zero_complex) (forall ((X tptp.complex)) (= (tptp.aa_nat_complex (tptp.power_power_complex X) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit0 tptp.one)))) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_complex_complex (tptp.times_times_complex X) X)) X)) X))) (forall ((X tptp.real)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit0 tptp.one)))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real X) X)) X)) X))) (forall ((X tptp.rat)) (= (tptp.aa_nat_rat (tptp.power_power_rat X) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit0 tptp.one)))) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat X) X)) X)) X))) (forall ((X tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat X) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit0 tptp.one)))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat X) X)) X)) X))) (forall ((X tptp.int)) (= (tptp.aa_nat_int (tptp.power_power_int X) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit0 tptp.one)))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int X) X)) X)) X))) (forall ((A tptp.complex)) (= (tptp.aa_nat_complex (tptp.power_power_complex A) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_complex_complex (tptp.times_times_complex A) A))) (forall ((A tptp.real)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real A) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) A))) (forall ((A tptp.rat)) (= (tptp.aa_nat_rat (tptp.power_power_rat A) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) A))) (forall ((A tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) A))) (forall ((A tptp.int)) (= (tptp.aa_nat_int (tptp.power_power_int A) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) A))) (= (tptp.aa_nat_rat (tptp.power_power_rat tptp.one_one_rat) _let_2) tptp.one_one_rat) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat tptp.one_one_nat) _let_2) tptp.one_one_nat) (= (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_int (tptp.power_power_int tptp.one_one_int) _let_2) tptp.one_one_int) (= (tptp.aa_nat_complex (tptp.power_power_complex tptp.one_one_complex) _let_2) tptp.one_one_complex) (forall ((X tptp.complex) (Y tptp.complex)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.aa_nat_complex (tptp.power_power_complex (tptp.minus_minus_complex X Y)) _let_1) (tptp.aa_nat_complex (tptp.power_power_complex (tptp.minus_minus_complex Y X)) _let_1)))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real X) Y)) _let_1) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real Y) X)) _let_1)))) (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.aa_nat_rat (tptp.power_power_rat (tptp.minus_minus_rat X Y)) _let_1) (tptp.aa_nat_rat (tptp.power_power_rat (tptp.minus_minus_rat Y X)) _let_1)))) (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int X) Y)) _let_1) (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int Y) X)) _let_1)))) (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A))) (= (tptp.aa_nat_nat _let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat _let_1) N)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_nat_nat _let_2 N)) _let_1))))) (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_real_fun_nat_real tptp.power_power_real A))) (= (tptp.aa_nat_real _let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat _let_1) N)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_nat_real _let_2 N)) _let_1))))) (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.power_power_int A))) (= (tptp.aa_nat_int _let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat _let_1) N)) (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_nat_int _let_2 N)) _let_1))))) (forall ((A tptp.complex) (N tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.power_power_complex A))) (= (tptp.aa_nat_complex _let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat _let_1) N)) (tptp.aa_nat_complex (tptp.power_power_complex (tptp.aa_nat_complex _let_2 N)) _let_1))))) (forall ((M tptp.nat) (P2 tptp.complex)) (let ((_let_1 (tptp.power_power_complex P2))) (let ((_let_2 (tptp.aa_nat_complex _let_1 M))) (let ((_let_3 (= M tptp.zero_zero_nat))) (and (=> _let_3 (= _let_2 tptp.one_one_complex)) (=> (not _let_3) (= _let_2 (tptp.aa_complex_complex (tptp.times_times_complex P2) (tptp.aa_nat_complex _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) tptp.one_one_nat)))))))))) (forall ((M tptp.nat) (P2 tptp.real)) (let ((_let_1 (tptp.aa_real_fun_nat_real tptp.power_power_real P2))) (let ((_let_2 (tptp.aa_nat_real _let_1 M))) (let ((_let_3 (= M tptp.zero_zero_nat))) (and (=> _let_3 (= _let_2 tptp.one_one_real)) (=> (not _let_3) (= _let_2 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real P2) (tptp.aa_nat_real _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) tptp.one_one_nat)))))))))) (forall ((M tptp.nat) (P2 tptp.rat)) (let ((_let_1 (tptp.power_power_rat P2))) (let ((_let_2 (tptp.aa_nat_rat _let_1 M))) (let ((_let_3 (= M tptp.zero_zero_nat))) (and (=> _let_3 (= _let_2 tptp.one_one_rat)) (=> (not _let_3) (= _let_2 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat P2) (tptp.aa_nat_rat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) tptp.one_one_nat)))))))))) (forall ((M tptp.nat) (P2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat P2))) (let ((_let_2 (tptp.aa_nat_nat _let_1 M))) (let ((_let_3 (= M tptp.zero_zero_nat))) (and (=> _let_3 (= _let_2 tptp.one_one_nat)) (=> (not _let_3) (= _let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat P2) (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) tptp.one_one_nat)))))))))) (forall ((M tptp.nat) (P2 tptp.int)) (let ((_let_1 (tptp.power_power_int P2))) (let ((_let_2 (tptp.aa_nat_int _let_1 M))) (let ((_let_3 (= M tptp.zero_zero_nat))) (and (=> _let_3 (= _let_2 tptp.one_one_int)) (=> (not _let_3) (= _let_2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int P2) (tptp.aa_nat_int _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) tptp.one_one_nat)))))))))) (forall ((X tptp.complex) (Y tptp.complex)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (let ((_let_2 (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1))) (= (tptp.aa_nat_complex (tptp.power_power_complex (tptp.plus_plus_complex X Y)) _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 Y) _let_2)) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_complex_complex (tptp.times_times_complex (tptp.numera6690914467698888265omplex _let_1)) X)) Y)))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (let ((_let_2 (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1))) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) Y)) _let_2) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) _let_2)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Y) _let_2))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.numeral_numeral_real _let_1)) X)) Y)))))) (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (let ((_let_2 (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1))) (= (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat X) Y)) _let_2) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_nat_rat (tptp.power_power_rat X) _let_2)) (tptp.aa_nat_rat (tptp.power_power_rat Y) _let_2))) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.numeral_numeral_rat _let_1)) X)) Y)))))) (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat X) Y)) _let_1) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat X) _let_1)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat Y) _let_1))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat _let_1) X)) Y))))) (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (let ((_let_2 (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1))) (= (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int X) Y)) _let_2) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_nat_int (tptp.power_power_int X) _let_2)) (tptp.aa_nat_int (tptp.power_power_int Y) _let_2))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_num_int tptp.numeral_numeral_int _let_1)) X)) Y)))))) (forall ((A tptp.complex) (N tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.power_power_complex A))) (= (tptp.aa_nat_complex _let_2 (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat _let_1) N))) (tptp.aa_complex_complex (tptp.times_times_complex A) (tptp.aa_nat_complex (tptp.power_power_complex (tptp.aa_nat_complex _let_2 N)) _let_1)))))) (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_real_fun_nat_real tptp.power_power_real A))) (= (tptp.aa_nat_real _let_2 (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat _let_1) N))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_nat_real _let_2 N)) _let_1)))))) (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.power_power_rat A))) (= (tptp.aa_nat_rat _let_2 (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat _let_1) N))) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_nat_rat _let_2 N)) _let_1)))))) (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A))) (= (tptp.aa_nat_nat _let_2 (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat _let_1) N))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_nat_nat _let_2 N)) _let_1)))))) (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.power_power_int A))) (= (tptp.aa_nat_int _let_2 (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat _let_1) N))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_nat_int _let_2 N)) _let_1)))))) (forall ((X tptp.nat) (N tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high X) N) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat X) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N)))) (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.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.divide6298287555418463151nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer) A)) _let_2) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.divide6298287555418463151nteger A) _let_2))))))) (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat _let_1) N))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat _let_1) A)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat tptp.one_one_nat) A)) _let_2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) _let_2))))))) (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_nat_int (tptp.power_power_int _let_1) N))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int _let_1) A)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (= (tptp.aa_int_int (tptp.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 ((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.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger 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.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.divide6298287555418463151nteger A) _let_1)))))) (forall ((A tptp.int)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.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 ((R 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 R))) (=> (not (= R 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 ((R 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 R))) (=> (not (= R 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 ((R 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 R))) (=> (not (= R 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 ((R 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 R))) (=> (not (= R 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 ((X2 tptp.num)) (= (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.size_num X2)) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)))) (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.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.numeral_numeral_real K)) (tptp.aa_num_nat tptp.numeral_numeral_nat L)) (tptp.numeral_numeral_real (tptp.pow K L)))) (forall ((K tptp.num) (L tptp.num)) (= (tptp.aa_nat_rat (tptp.power_power_rat (tptp.numeral_numeral_rat K)) (tptp.aa_num_nat tptp.numeral_numeral_nat L)) (tptp.numeral_numeral_rat (tptp.pow K L)))) (forall ((K tptp.num) (L tptp.num)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_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.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.pow K L)))) (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.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.divide6298287555418463151nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger 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.aa_nat_fun_nat_nat tptp.power_power_nat _let_1))) (let ((_let_3 (tptp.aa_nat_nat _let_2 N))) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat _let_1) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat _let_2 M)) tptp.one_one_nat)) _let_3))) (or (= _let_3 tptp.zero_zero_nat) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)))))))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.power_power_int _let_1))) (let ((_let_3 (tptp.aa_nat_int _let_2 N))) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int _let_1) (tptp.aa_int_int (tptp.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 ((U tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (let ((_let_2 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real U) (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real X) Y)) (=> (tptp.pp (tptp.aa_real_bool _let_2 X)) (=> (tptp.pp (tptp.aa_real_bool _let_2 Y)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real U) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) Y)) (tptp.numeral_numeral_real _let_1)))))))))) (forall ((U tptp.rat) (X tptp.rat) (Y tptp.rat)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (let ((_let_2 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (= (tptp.aa_nat_rat (tptp.power_power_rat U) (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat X) Y)) (=> (tptp.pp (tptp.aa_rat_bool _let_2 X)) (=> (tptp.pp (tptp.aa_rat_bool _let_2 Y)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat U) (tptp.divide_divide_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat X) Y) (tptp.numeral_numeral_rat _let_1)))))))))) (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 ((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 ((M tptp.num) (N tptp.num)) (= (tptp.pp (tptp.aa_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.ord_less_num M) N)))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.pp (tptp.aa_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.ord_less_eq_num M) N)))) (forall ((M tptp.num)) (not (tptp.pp (tptp.aa_num_bool (tptp.ord_less_num M) tptp.one)))) (forall ((N tptp.num)) (tptp.pp (tptp.aa_num_bool (tptp.ord_less_eq_num 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.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.bit_se2159334234014336723it_int N K)) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int K) tptp.zero_zero_int)))) (forall ((N tptp.nat) (K tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.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)) (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.bit_se2159334234014336723it_int N K))) (tptp.pp (tptp.aa_int_bool _let_1 K))))) (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_se4203085406695923979it_int N) K))) (tptp.pp (tptp.aa_int_bool _let_1 K))))) (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 ((Ma tptp.nat) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Ma) (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N) M)))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high Ma) N)) (tptp.aa_nat_nat _let_1 M)))))) (forall ((N tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N) tptp.zero_zero_nat)) (= N tptp.zero_zero_nat))) (forall ((N tptp.nat)) (= (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N))) (= N tptp.zero_zero_nat))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.numeral_numeral_real M)) (tptp.numeral_numeral_real N))) (tptp.pp (tptp.aa_num_bool (tptp.ord_less_eq_num M) N)))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.numeral_numeral_rat M)) (tptp.numeral_numeral_rat N))) (tptp.pp (tptp.aa_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.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.ord_less_eq_num M) N)))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.numeral_numeral_real M)) (tptp.numeral_numeral_real N))) (tptp.pp (tptp.aa_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.numeral_numeral_rat M)) (tptp.numeral_numeral_rat N))) (tptp.pp (tptp.aa_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.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.ord_less_num M) N)))) (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.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 ((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 ((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 ((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 ((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 ((N tptp.num)) (tptp.pp (tptp.aa_num_bool (tptp.ord_less_num tptp.one) (tptp.aa_num_num tptp.bit0 N)))) (forall ((M tptp.num)) (not (tptp.pp (tptp.aa_num_bool (tptp.ord_less_eq_num (tptp.aa_num_num tptp.bit0 M)) tptp.one)))) (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 ((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 ((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 ((N tptp.nat)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N) tptp.zero_zero_nat)))) (forall ((N tptp.nat)) (= (not (= N tptp.zero_zero_nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)))) (forall ((A tptp.nat)) (= (not (= A tptp.zero_zero_nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) A)))) (forall ((N tptp.nat) (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 ((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 ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat K))) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat _let_1 M)) (tptp.aa_nat_nat _let_1 N))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N))))) (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat K))) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat _let_1 M)) (tptp.aa_nat_nat _let_1 N))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N))))) (forall ((I tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I) N)) (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat _let_1 I)) I)))) (forall ((P tptp.bool) (Q tptp.bool)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.zero_n2052037380579107095ol_rat P)) (tptp.zero_n2052037380579107095ol_rat Q))) (=> (tptp.pp P) (tptp.pp Q)))) (forall ((P tptp.bool) (Q tptp.bool)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.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)))) (= (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)) (= (= (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)))) (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 ((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 ((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 ((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 ((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 ((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_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) (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_se545348938243370406it_int N) K))) (tptp.pp (tptp.aa_int_bool _let_1 K))))) (forall ((A tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (= (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) A))) (tptp.pp (tptp.aa_real_bool _let_1 A))))) (forall ((A tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat))) (= (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) A))) (tptp.pp (tptp.aa_rat_bool _let_1 A))))) (forall ((A tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) A))) (tptp.pp (tptp.aa_int_bool _let_1 A))))) (forall ((A tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) A)) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) tptp.zero_zero_real)))) (forall ((A tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) A)) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) tptp.zero_zero_rat)))) (forall ((A tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) A)) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) tptp.zero_zero_int)))) (forall ((A tptp.real) (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 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 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 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 (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 ((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 ((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.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 ((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 ((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.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)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real))) (= (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) A))) (tptp.pp (tptp.aa_real_bool _let_1 A))))) (forall ((A tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat))) (= (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) A))) (tptp.pp (tptp.aa_rat_bool _let_1 A))))) (forall ((A tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int))) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) A))) (tptp.pp (tptp.aa_int_bool _let_1 A))))) (forall ((A tptp.real)) (= (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) (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) (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 (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 ((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.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.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 ((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 ((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.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 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 B) (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 ((A tptp.real) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_real_fun_nat_real tptp.power_power_real A))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real) A)) (= (= (tptp.aa_nat_real _let_1 M) (tptp.aa_nat_real _let_1 N)) (= M N))))) (forall ((A tptp.rat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.power_power_rat A))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.one_one_rat) A)) (= (= (tptp.aa_nat_rat _let_1 M) (tptp.aa_nat_rat _let_1 N)) (= M N))))) (forall ((A tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.one_one_nat) A)) (= (= (tptp.aa_nat_nat _let_1 M) (tptp.aa_nat_nat _let_1 N)) (= M N))))) (forall ((A tptp.int) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.power_power_int A))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.one_one_int) A)) (= (= (tptp.aa_nat_int _let_1 M) (tptp.aa_nat_int _let_1 N)) (= M N))))) (forall ((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_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real M)) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat M)) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat N))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat M)) (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat N))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int M)) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)))) (forall ((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)) (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 ((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 ((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 ((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 ((M tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) N) tptp.zero_zero_nat))) (forall ((M tptp.nat) (N tptp.nat)) (= (= (tptp.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 ((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 ((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 ((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.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.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.minus_8373710615458151222nteger tptp.one_one_Code_integer) (tptp.aa_bool_Code_integer tptp.zero_n356916108424825756nteger P)))) (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 ((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 ((X tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat))) (= (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat X) N))) (or (tptp.pp (tptp.aa_nat_bool _let_1 X)) (= N tptp.zero_zero_nat))))) (forall ((A tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (= (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.one_one_real) A))) (tptp.pp (tptp.aa_real_bool _let_1 A))))) (forall ((A tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat))) (= (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.divide_divide_rat tptp.one_one_rat A))) (tptp.pp (tptp.aa_rat_bool _let_1 A))))) (forall ((A tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.one_one_real) A)) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) tptp.zero_zero_real)))) (forall ((A tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.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 ((N tptp.num)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.numeral_numeral_real N)) tptp.one_one_real)) (tptp.pp (tptp.aa_num_bool (tptp.ord_less_eq_num N) tptp.one)))) (forall ((N tptp.num)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.numeral_numeral_rat N)) tptp.one_one_rat)) (tptp.pp (tptp.aa_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.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.ord_less_eq_num N) 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 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.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.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.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.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.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.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 ((A tptp.real) (B tptp.real) (W tptp.num)) (let ((_let_1 (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.numeral_numeral_rat W))) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) (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 ((B tptp.real) (W tptp.num) (A tptp.real)) (let ((_let_1 (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.numeral_numeral_rat W))) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_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 ((N tptp.num)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real) (tptp.numeral_numeral_real N))) (tptp.pp (tptp.aa_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.numeral_numeral_rat N))) (tptp.pp (tptp.aa_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.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.ord_less_num tptp.one) N)))) (forall ((A tptp.real) (B tptp.real) (W tptp.num)) (let ((_let_1 (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.numeral_numeral_rat W))) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) (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 ((B tptp.real) (W tptp.num) (A tptp.real)) (let ((_let_1 (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.numeral_numeral_rat W))) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_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 ((M tptp.nat)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real M)) tptp.zero_zero_real)) (= M tptp.zero_zero_nat))) (forall ((M tptp.nat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat M)) tptp.zero_zero_rat)) (= M tptp.zero_zero_nat))) (forall ((M tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat M)) tptp.zero_zero_nat)) (= M tptp.zero_zero_nat))) (forall ((M tptp.nat)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int M)) tptp.zero_zero_int)) (= M tptp.zero_zero_nat))) (forall ((B tptp.real) (X tptp.nat) (Y 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_real (tptp.aa_nat_real _let_1 X)) (tptp.aa_nat_real _let_1 Y))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Y)))))) (forall ((B tptp.rat) (X tptp.nat) (Y 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_rat (tptp.aa_nat_rat _let_1 X)) (tptp.aa_nat_rat _let_1 Y))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Y)))))) (forall ((B tptp.nat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat 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_nat (tptp.aa_nat_nat _let_1 X)) (tptp.aa_nat_nat _let_1 Y))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Y)))))) (forall ((B tptp.int) (X tptp.nat) (Y 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_int (tptp.aa_nat_int _let_1 X)) (tptp.aa_nat_int _let_1 Y))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Y)))))) (forall ((A tptp.rat) (N tptp.nat)) (= (= (tptp.aa_nat_rat (tptp.power_power_rat A) N) tptp.zero_zero_rat) (and (= A tptp.zero_zero_rat) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N))))) (forall ((A tptp.nat) (N tptp.nat)) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A) N) tptp.zero_zero_nat) (and (= A tptp.zero_zero_nat) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N))))) (forall ((A tptp.real) (N tptp.nat)) (= (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real A) N) tptp.zero_zero_real) (and (= A tptp.zero_zero_real) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N))))) (forall ((A tptp.int) (N tptp.nat)) (= (= (tptp.aa_nat_int (tptp.power_power_int A) N) tptp.zero_zero_int) (and (= A tptp.zero_zero_int) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N))))) (forall ((A tptp.complex) (N tptp.nat)) (= (= (tptp.aa_nat_complex (tptp.power_power_complex A) N) tptp.zero_zero_complex) (and (= A tptp.zero_zero_complex) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N))))) (forall ((N tptp.nat) (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.aa_nat_fun_nat_nat tptp.power_power_nat A) N)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat B) N))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat 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)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (= (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat))) N))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)))) (= (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat M) N))) (and (tptp.pp (tptp.aa_nat_bool _let_1 M)) (tptp.pp (tptp.aa_nat_bool _let_1 N)))))) (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat K))) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat _let_1 M)) (tptp.aa_nat_nat _let_1 N))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) K)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)))))) (forall ((M tptp.nat) (K tptp.nat) (N tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat M) K)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat N) K))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) K)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N))))) (forall ((K tptp.nat) (J tptp.nat) (I tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) J)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat J) K))) I) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat tptp.suc J)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat K) I))))) (forall ((K tptp.nat) (J tptp.nat) (I tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) J)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat I) (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat J) K))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat I) K)) (tptp.aa_nat_nat tptp.suc J))))) (forall ((N tptp.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 ((W tptp.num) (N tptp.nat)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.numeral_numeral_real W)) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_num_nat tptp.numeral_numeral_nat W)) N)))) (forall ((N tptp.nat) (W tptp.num)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N)) (tptp.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 ((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 ((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.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 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 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.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 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 tptp.zero_zero_rat) A)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_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 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 A) tptp.zero_zero_rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_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 ((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.aa_nat_fun_nat_nat 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.real) (X tptp.nat) (Y 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 Y))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X) Y)))))) (forall ((B tptp.rat) (X tptp.nat) (Y 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 Y))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X) Y)))))) (forall ((B tptp.nat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat 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 Y))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X) Y)))))) (forall ((B tptp.int) (X tptp.nat) (Y 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 Y))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X) Y)))))) (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 ((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.aa_nat_fun_nat_nat tptp.power_power_nat A) N)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat 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 ((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)))) (forall ((P2 tptp.bool)) (= (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_bool_nat tptp.zero_n2687167440665602831ol_nat P2)))) (tptp.pp P2))) (forall ((P2 tptp.bool)) (= (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_bool_int tptp.zero_n2684676970156552555ol_int P2)))) (tptp.pp P2))) (forall ((P2 tptp.bool)) (= (not (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_bool_Code_integer tptp.zero_n356916108424825756nteger P2)))) (tptp.pp P2))) (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.aa_nat_fun_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.aa_nat_fun_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.aa_nat_fun_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.aa_nat_fun_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.aa_nat_fun_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.aa_nat_fun_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.aa_nat_fun_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.aa_nat_fun_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.aa_nat_fun_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.aa_nat_fun_nat_nat tptp.power_power_nat B) W))))) (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.aa_nat_fun_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_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.aa_nat_fun_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.aa_nat_fun_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.aa_nat_fun_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.aa_nat_fun_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_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.aa_nat_fun_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.aa_nat_fun_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.aa_nat_fun_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.aa_nat_fun_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.aa_nat_fun_nat_nat tptp.power_power_nat B) W))))) (forall ((N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (= (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) tptp.one_one_nat)) N))) (forall ((K tptp.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 ((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 ((N tptp.num) (M tptp.nat)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_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 ((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 ((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.aa_nat_fun_nat_nat 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 ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool _let_2 X)) (=> (tptp.pp (tptp.aa_real_bool _let_2 Y)) (= (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) _let_1) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Y) _let_1)) (= X Y))))))) (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (tptp.pp (tptp.aa_rat_bool _let_2 X)) (=> (tptp.pp (tptp.aa_rat_bool _let_2 Y)) (= (= (tptp.aa_nat_rat (tptp.power_power_rat X) _let_1) (tptp.aa_nat_rat (tptp.power_power_rat Y) _let_1)) (= X Y))))))) (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (tptp.pp (tptp.aa_nat_bool _let_2 X)) (=> (tptp.pp (tptp.aa_nat_bool _let_2 Y)) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat X) _let_1) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat Y) _let_1)) (= X Y))))))) (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.pp (tptp.aa_int_bool _let_2 X)) (=> (tptp.pp (tptp.aa_int_bool _let_2 Y)) (= (= (tptp.aa_nat_int (tptp.power_power_int X) _let_1) (tptp.aa_nat_int (tptp.power_power_int Y) _let_1)) (= X Y))))))) (forall ((A tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real A) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) tptp.zero_zero_real)) (= A tptp.zero_zero_real))) (forall ((A tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat (tptp.power_power_rat A) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) tptp.zero_zero_rat)) (= A tptp.zero_zero_rat))) (forall ((A tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int (tptp.power_power_int A) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) tptp.zero_zero_int)) (= A tptp.zero_zero_int))) (forall ((A tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real A) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (not (= A tptp.zero_zero_real)))) (forall ((A tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) (tptp.aa_nat_rat (tptp.power_power_rat A) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (not (= A tptp.zero_zero_rat)))) (forall ((A tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) (tptp.aa_nat_int (tptp.power_power_int A) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (not (= A tptp.zero_zero_int)))) (forall ((X tptp.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.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat X)) N))) (or (tptp.pp (tptp.aa_nat_bool _let_1 X)) (= N tptp.zero_zero_nat))))) (forall ((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 ((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.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger 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 ((A tptp.real) (W tptp.num)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (let ((_let_2 (tptp.aa_num_nat tptp.numeral_numeral_nat W))) (let ((_let_3 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) _let_2)))) (= (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real A) _let_2))) (or _let_3 (and (not _let_3) (tptp.pp (tptp.aa_real_bool _let_1 A))))))))) (forall ((A tptp.rat) (W tptp.num)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat))) (let ((_let_2 (tptp.aa_num_nat tptp.numeral_numeral_nat W))) (let ((_let_3 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) _let_2)))) (= (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_nat_rat (tptp.power_power_rat A) _let_2))) (or _let_3 (and (not _let_3) (tptp.pp (tptp.aa_rat_bool _let_1 A))))))))) (forall ((A tptp.int) (W tptp.num)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_2 (tptp.aa_num_nat tptp.numeral_numeral_nat W))) (let ((_let_3 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) _let_2)))) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_nat_int (tptp.power_power_int A) _let_2))) (or _let_3 (and (not _let_3) (tptp.pp (tptp.aa_int_bool _let_1 A))))))))) (forall ((A tptp.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.aa_nat_fun_nat_nat tptp.power_power_nat A) N))) (and (tptp.pp (tptp.aa_nat_bool _let_1 A)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)))))) (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_nat_int (tptp.power_power_int A) N))) (and (tptp.pp (tptp.aa_int_bool _let_1 A)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)))))) (forall ((A tptp.real) (W tptp.num)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat W))) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real A) _let_1)) tptp.zero_zero_real)) (and (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) _let_1))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) tptp.zero_zero_real)))))) (forall ((A tptp.rat) (W tptp.num)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat W))) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_nat_rat (tptp.power_power_rat A) _let_1)) tptp.zero_zero_rat)) (and (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) _let_1))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) tptp.zero_zero_rat)))))) (forall ((A tptp.int) (W tptp.num)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat W))) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_nat_int (tptp.power_power_int A) _let_1)) tptp.zero_zero_int)) (and (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) _let_1))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) tptp.zero_zero_int)))))) (forall ((A tptp.real) (N tptp.nat)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real A) N)) tptp.zero_zero_real)) (and (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) tptp.zero_zero_real))))) (forall ((A tptp.rat) (N tptp.nat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_nat_rat (tptp.power_power_rat A) N)) tptp.zero_zero_rat)) (and (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) tptp.zero_zero_rat))))) (forall ((A tptp.int) (N tptp.nat)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_nat_int (tptp.power_power_int A) N)) tptp.zero_zero_int)) (and (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) tptp.zero_zero_int))))) (forall ((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.numeral_numeral_real I)) N))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat I)) N))))) (forall ((X tptp.nat) (I tptp.num) (N tptp.nat)) (= (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.numeral_numeral_rat I)) N))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat I)) N))))) (forall ((X tptp.nat) (I tptp.num) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat I)) N))) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat X)) _let_1)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) _let_1))))) (forall ((X tptp.nat) (I tptp.num) (N tptp.nat)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int X)) (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int I)) N))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat I)) N))))) (forall ((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.numeral_numeral_real I)) N)) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real X))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat I)) N)) X)))) (forall ((I tptp.num) (N tptp.nat) (X tptp.nat)) (= (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.numeral_numeral_rat I)) N)) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat X))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat I)) N)) X)))) (forall ((I tptp.num) (N tptp.nat) (X tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat I)) N)))) (= (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat X))) (tptp.pp (tptp.aa_nat_bool _let_1 X))))) (forall ((I tptp.num) (N tptp.nat) (X tptp.nat)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int I)) N)) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int X))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat I)) N)) X)))) (forall ((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.numeral_numeral_real I)) N))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat I)) N))))) (forall ((X tptp.nat) (I tptp.num) (N tptp.nat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat X)) (tptp.aa_nat_rat (tptp.power_power_rat (tptp.numeral_numeral_rat I)) N))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat I)) N))))) (forall ((X tptp.nat) (I tptp.num) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat I)) N))) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat X)) _let_1)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X) _let_1))))) (forall ((X tptp.nat) (I tptp.num) (N tptp.nat)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int X)) (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int I)) N))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat I)) N))))) (forall ((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.numeral_numeral_real I)) N)) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real X))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat I)) N)) X)))) (forall ((I tptp.num) (N tptp.nat) (X tptp.nat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat (tptp.power_power_rat (tptp.numeral_numeral_rat I)) N)) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat X))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat I)) N)) X)))) (forall ((I tptp.num) (N tptp.nat) (X tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat I)) N)))) (= (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat X))) (tptp.pp (tptp.aa_nat_bool _let_1 X))))) (forall ((I tptp.num) (N tptp.nat) (X tptp.nat)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int I)) N)) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int X))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat I)) N)) X)))) (forall ((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 ((N tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat tptp.one_one_nat) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N)) (tptp.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.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger 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.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N)) (tptp.aa_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.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger 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 ((A tptp.real) (W tptp.num)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat W))) (let ((_let_2 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) _let_1)))) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real A) _let_1)) tptp.zero_zero_real)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) _let_1)) (or (and (not _let_2) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) tptp.zero_zero_real))) (and _let_2 (= A tptp.zero_zero_real)))))))) (forall ((A tptp.rat) (W tptp.num)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat W))) (let ((_let_2 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) _let_1)))) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat (tptp.power_power_rat A) _let_1)) tptp.zero_zero_rat)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) _let_1)) (or (and (not _let_2) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) tptp.zero_zero_rat))) (and _let_2 (= A tptp.zero_zero_rat)))))))) (forall ((A tptp.int) (W tptp.num)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat W))) (let ((_let_2 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) _let_1)))) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int (tptp.power_power_int A) _let_1)) tptp.zero_zero_int)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) _let_1)) (or (and (not _let_2) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) tptp.zero_zero_int))) (and _let_2 (= A tptp.zero_zero_int)))))))) (forall ((P tptp.bool)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.zero_n3304061248610475627l_real P)))) (forall ((P tptp.bool)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.zero_n2052037380579107095ol_rat P)))) (forall ((P tptp.bool)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) (tptp.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 ((P tptp.bool)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.zero_n3304061248610475627l_real P)) tptp.one_one_real))) (forall ((P tptp.bool)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.zero_n2052037380579107095ol_rat P)) tptp.one_one_rat))) (forall ((P tptp.bool)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.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 ((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.ord_less_eq_num A) B))) (not (tptp.pp (tptp.aa_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 ((X tptp.real) (Y tptp.real)) (=> (not (= X Y)) (=> (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Y))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y) X))))) (forall ((X tptp.rat) (Y tptp.rat)) (=> (not (= X Y)) (=> (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) Y))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Y) X))))) (forall ((X tptp.int) (Y tptp.int)) (=> (not (= X Y)) (=> (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) Y))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Y) X))))) (forall ((P2 tptp.bool) (Q2 tptp.bool)) (= (= (tptp.aa_bool_nat tptp.zero_n2687167440665602831ol_nat P2) (tptp.aa_bool_nat tptp.zero_n2687167440665602831ol_nat Q2)) (= (tptp.pp P2) (tptp.pp Q2)))) (forall ((P2 tptp.bool) (Q2 tptp.bool)) (= (= (tptp.aa_bool_int tptp.zero_n2684676970156552555ol_int P2) (tptp.aa_bool_int tptp.zero_n2684676970156552555ol_int Q2)) (= (tptp.pp P2) (tptp.pp Q2)))) (forall ((P2 tptp.bool) (Q2 tptp.bool)) (= (= (tptp.aa_bool_Code_integer tptp.zero_n356916108424825756nteger P2) (tptp.aa_bool_Code_integer tptp.zero_n356916108424825756nteger Q2)) (= (tptp.pp P2) (tptp.pp Q2)))) (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.ord_less_num A) A)))) (forall ((A tptp.nat)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) A)))) (forall ((A tptp.int)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) A)))) (forall ((A tptp.set_nat)) (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat 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.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 ((B5 tptp.real) (A4 tptp.real)) (= (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real B5) A4))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A4) B5)))) (forall ((B5 tptp.rat) (A4 tptp.rat)) (= (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B5) A4))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A4) B5)))) (forall ((B5 tptp.num) (A4 tptp.num)) (= (not (tptp.pp (tptp.aa_num_bool (tptp.ord_less_eq_num B5) A4))) (tptp.pp (tptp.aa_num_bool (tptp.ord_less_num A4) B5)))) (forall ((B5 tptp.nat) (A4 tptp.nat)) (= (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B5) A4))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A4) B5)))) (forall ((B5 tptp.int) (A4 tptp.int)) (= (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B5) A4))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A4) B5)))) (forall ((F tptp.fun_nat_nat) (I tptp.nat) (J tptp.nat)) (=> (forall ((I2 tptp.nat) (J2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I2) J2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat F I2)) (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 ((P tptp.fun_nat_bool) (K tptp.nat) (B tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool P K)) (=> (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) B)))) (exists ((X3 tptp.nat)) (and (tptp.pp (tptp.aa_nat_bool P X3)) (forall ((Y4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool P Y4)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Y4) X3))))))))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (not (= X Y)) (=> (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Y))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Y) X))))) (forall ((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 ((P tptp.fun_nat_bool) (N tptp.nat)) (=> (forall ((N2 tptp.nat)) (=> (not (tptp.pp (tptp.aa_nat_bool P N2))) (exists ((M3 tptp.nat)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M3) N2)) (not (tptp.pp (tptp.aa_nat_bool P M3))))))) (tptp.pp (tptp.aa_nat_bool P N)))) (forall ((P tptp.fun_nat_bool) (N tptp.nat)) (=> (forall ((N2 tptp.nat)) (=> (forall ((M3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M3) N2)) (tptp.pp (tptp.aa_nat_bool P M3)))) (tptp.pp (tptp.aa_nat_bool P N2)))) (tptp.pp (tptp.aa_nat_bool P N)))) (forall ((N tptp.nat)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat 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 M) N)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)))) (forall ((S tptp.nat) (T tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat S) T)) (not (= S T)))) (forall ((N tptp.nat) (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 ((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 ((N tptp.nat)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N) N)))) (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 ((M tptp.nat) (N tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)) (not (= M N))))) (forall ((M tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_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)) (=> (= M 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_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 ((N tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N) N))) (forall ((X tptp.real) (Y tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) Y)) (or (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Y)) (= X Y)))) (forall ((S2 tptp.set_real)) (=> (exists ((X4 tptp.real)) (tptp.member_real X4 S2)) (=> (exists ((Z3 tptp.real)) (forall ((X3 tptp.real)) (=> (tptp.member_real X3 S2) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X3) Z3))))) (exists ((Y3 tptp.real)) (and (forall ((X4 tptp.real)) (=> (tptp.member_real X4 S2) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X4) Y3)))) (forall ((Z3 tptp.real)) (=> (forall ((X3 tptp.real)) (=> (tptp.member_real X3 S2) (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 Y3) Z3))))))))) (forall ((X4 tptp.real)) (exists ((X_12 tptp.real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X4) X_12)))) (forall ((X4 tptp.rat)) (exists ((X_12 tptp.rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X4) X_12)))) (forall ((X4 tptp.real)) (exists ((Y3 tptp.real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y3) X4)))) (forall ((X4 tptp.rat)) (exists ((Y3 tptp.rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Y3) X4)))) (forall ((P tptp.fun_real_bool) (P3 tptp.fun_real_bool) (Q tptp.fun_real_bool) (Q3 tptp.fun_real_bool)) (=> (exists ((Z3 tptp.real)) (forall ((X3 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Z3) X3)) (= (tptp.pp (tptp.aa_real_bool P X3)) (tptp.pp (tptp.aa_real_bool P3 X3)))))) (=> (exists ((Z3 tptp.real)) (forall ((X3 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Z3) X3)) (= (tptp.pp (tptp.aa_real_bool Q X3)) (tptp.pp (tptp.aa_real_bool Q3 X3)))))) (exists ((Z4 tptp.real)) (forall ((X4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Z4) X4)) (= (and (tptp.pp (tptp.aa_real_bool P X4)) (tptp.pp (tptp.aa_real_bool Q X4))) (and (tptp.pp (tptp.aa_real_bool P3 X4)) (tptp.pp (tptp.aa_real_bool Q3 X4)))))))))) (forall ((P tptp.fun_rat_bool) (P3 tptp.fun_rat_bool) (Q tptp.fun_rat_bool) (Q3 tptp.fun_rat_bool)) (=> (exists ((Z3 tptp.rat)) (forall ((X3 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Z3) X3)) (= (tptp.pp (tptp.aa_rat_bool P X3)) (tptp.pp (tptp.aa_rat_bool P3 X3)))))) (=> (exists ((Z3 tptp.rat)) (forall ((X3 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Z3) X3)) (= (tptp.pp (tptp.aa_rat_bool Q X3)) (tptp.pp (tptp.aa_rat_bool Q3 X3)))))) (exists ((Z4 tptp.rat)) (forall ((X4 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Z4) X4)) (= (and (tptp.pp (tptp.aa_rat_bool P X4)) (tptp.pp (tptp.aa_rat_bool Q X4))) (and (tptp.pp (tptp.aa_rat_bool P3 X4)) (tptp.pp (tptp.aa_rat_bool Q3 X4)))))))))) (forall ((P tptp.fun_num_bool) (P3 tptp.fun_num_bool) (Q tptp.fun_num_bool) (Q3 tptp.fun_num_bool)) (=> (exists ((Z3 tptp.num)) (forall ((X3 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.ord_less_num Z3) X3)) (= (tptp.pp (tptp.aa_num_bool P X3)) (tptp.pp (tptp.aa_num_bool P3 X3)))))) (=> (exists ((Z3 tptp.num)) (forall ((X3 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.ord_less_num Z3) X3)) (= (tptp.pp (tptp.aa_num_bool Q X3)) (tptp.pp (tptp.aa_num_bool Q3 X3)))))) (exists ((Z4 tptp.num)) (forall ((X4 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.ord_less_num Z4) X4)) (= (and (tptp.pp (tptp.aa_num_bool P X4)) (tptp.pp (tptp.aa_num_bool Q X4))) (and (tptp.pp (tptp.aa_num_bool P3 X4)) (tptp.pp (tptp.aa_num_bool Q3 X4)))))))))) (forall ((P tptp.fun_nat_bool) (P3 tptp.fun_nat_bool) (Q tptp.fun_nat_bool) (Q3 tptp.fun_nat_bool)) (=> (exists ((Z3 tptp.nat)) (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Z3) X3)) (= (tptp.pp (tptp.aa_nat_bool P X3)) (tptp.pp (tptp.aa_nat_bool P3 X3)))))) (=> (exists ((Z3 tptp.nat)) (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Z3) X3)) (= (tptp.pp (tptp.aa_nat_bool Q X3)) (tptp.pp (tptp.aa_nat_bool Q3 X3)))))) (exists ((Z4 tptp.nat)) (forall ((X4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Z4) X4)) (= (and (tptp.pp (tptp.aa_nat_bool P X4)) (tptp.pp (tptp.aa_nat_bool Q X4))) (and (tptp.pp (tptp.aa_nat_bool P3 X4)) (tptp.pp (tptp.aa_nat_bool Q3 X4)))))))))) (forall ((P tptp.fun_int_bool) (P3 tptp.fun_int_bool) (Q tptp.fun_int_bool) (Q3 tptp.fun_int_bool)) (=> (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 P3 X3)))))) (=> (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 Q X3)) (tptp.pp (tptp.aa_int_bool Q3 X3)))))) (exists ((Z4 tptp.int)) (forall ((X4 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Z4) X4)) (= (and (tptp.pp (tptp.aa_int_bool P X4)) (tptp.pp (tptp.aa_int_bool Q X4))) (and (tptp.pp (tptp.aa_int_bool P3 X4)) (tptp.pp (tptp.aa_int_bool Q3 X4)))))))))) (forall ((P tptp.fun_real_bool) (P3 tptp.fun_real_bool) (Q tptp.fun_real_bool) (Q3 tptp.fun_real_bool)) (=> (exists ((Z3 tptp.real)) (forall ((X3 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Z3) X3)) (= (tptp.pp (tptp.aa_real_bool P X3)) (tptp.pp (tptp.aa_real_bool P3 X3)))))) (=> (exists ((Z3 tptp.real)) (forall ((X3 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Z3) X3)) (= (tptp.pp (tptp.aa_real_bool Q X3)) (tptp.pp (tptp.aa_real_bool Q3 X3)))))) (exists ((Z4 tptp.real)) (forall ((X4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Z4) X4)) (= (or (tptp.pp (tptp.aa_real_bool P X4)) (tptp.pp (tptp.aa_real_bool Q X4))) (or (tptp.pp (tptp.aa_real_bool P3 X4)) (tptp.pp (tptp.aa_real_bool Q3 X4)))))))))) (forall ((P tptp.fun_rat_bool) (P3 tptp.fun_rat_bool) (Q tptp.fun_rat_bool) (Q3 tptp.fun_rat_bool)) (=> (exists ((Z3 tptp.rat)) (forall ((X3 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Z3) X3)) (= (tptp.pp (tptp.aa_rat_bool P X3)) (tptp.pp (tptp.aa_rat_bool P3 X3)))))) (=> (exists ((Z3 tptp.rat)) (forall ((X3 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Z3) X3)) (= (tptp.pp (tptp.aa_rat_bool Q X3)) (tptp.pp (tptp.aa_rat_bool Q3 X3)))))) (exists ((Z4 tptp.rat)) (forall ((X4 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Z4) X4)) (= (or (tptp.pp (tptp.aa_rat_bool P X4)) (tptp.pp (tptp.aa_rat_bool Q X4))) (or (tptp.pp (tptp.aa_rat_bool P3 X4)) (tptp.pp (tptp.aa_rat_bool Q3 X4)))))))))) (forall ((P tptp.fun_num_bool) (P3 tptp.fun_num_bool) (Q tptp.fun_num_bool) (Q3 tptp.fun_num_bool)) (=> (exists ((Z3 tptp.num)) (forall ((X3 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.ord_less_num Z3) X3)) (= (tptp.pp (tptp.aa_num_bool P X3)) (tptp.pp (tptp.aa_num_bool P3 X3)))))) (=> (exists ((Z3 tptp.num)) (forall ((X3 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.ord_less_num Z3) X3)) (= (tptp.pp (tptp.aa_num_bool Q X3)) (tptp.pp (tptp.aa_num_bool Q3 X3)))))) (exists ((Z4 tptp.num)) (forall ((X4 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.ord_less_num Z4) X4)) (= (or (tptp.pp (tptp.aa_num_bool P X4)) (tptp.pp (tptp.aa_num_bool Q X4))) (or (tptp.pp (tptp.aa_num_bool P3 X4)) (tptp.pp (tptp.aa_num_bool Q3 X4)))))))))) (forall ((P tptp.fun_nat_bool) (P3 tptp.fun_nat_bool) (Q tptp.fun_nat_bool) (Q3 tptp.fun_nat_bool)) (=> (exists ((Z3 tptp.nat)) (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Z3) X3)) (= (tptp.pp (tptp.aa_nat_bool P X3)) (tptp.pp (tptp.aa_nat_bool P3 X3)))))) (=> (exists ((Z3 tptp.nat)) (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Z3) X3)) (= (tptp.pp (tptp.aa_nat_bool Q X3)) (tptp.pp (tptp.aa_nat_bool Q3 X3)))))) (exists ((Z4 tptp.nat)) (forall ((X4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Z4) X4)) (= (or (tptp.pp (tptp.aa_nat_bool P X4)) (tptp.pp (tptp.aa_nat_bool Q X4))) (or (tptp.pp (tptp.aa_nat_bool P3 X4)) (tptp.pp (tptp.aa_nat_bool Q3 X4)))))))))) (forall ((P tptp.fun_int_bool) (P3 tptp.fun_int_bool) (Q tptp.fun_int_bool) (Q3 tptp.fun_int_bool)) (=> (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 P3 X3)))))) (=> (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 Q X3)) (tptp.pp (tptp.aa_int_bool Q3 X3)))))) (exists ((Z4 tptp.int)) (forall ((X4 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Z4) X4)) (= (or (tptp.pp (tptp.aa_int_bool P X4)) (tptp.pp (tptp.aa_int_bool Q X4))) (or (tptp.pp (tptp.aa_int_bool P3 X4)) (tptp.pp (tptp.aa_int_bool Q3 X4)))))))))) (forall ((T tptp.real)) (exists ((Z4 tptp.real)) (forall ((X4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Z4) X4)) (not (= X4 T)))))) (forall ((T tptp.rat)) (exists ((Z4 tptp.rat)) (forall ((X4 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Z4) X4)) (not (= X4 T)))))) (forall ((T tptp.num)) (exists ((Z4 tptp.num)) (forall ((X4 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.ord_less_num Z4) X4)) (not (= X4 T)))))) (forall ((T tptp.nat)) (exists ((Z4 tptp.nat)) (forall ((X4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Z4) X4)) (not (= X4 T)))))) (forall ((T tptp.int)) (exists ((Z4 tptp.int)) (forall ((X4 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Z4) X4)) (not (= X4 T)))))) (forall ((T tptp.real)) (exists ((Z4 tptp.real)) (forall ((X4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Z4) X4)) (not (= X4 T)))))) (forall ((T tptp.rat)) (exists ((Z4 tptp.rat)) (forall ((X4 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Z4) X4)) (not (= X4 T)))))) (forall ((T tptp.num)) (exists ((Z4 tptp.num)) (forall ((X4 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.ord_less_num Z4) X4)) (not (= X4 T)))))) (forall ((T tptp.nat)) (exists ((Z4 tptp.nat)) (forall ((X4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Z4) X4)) (not (= X4 T)))))) (forall ((T tptp.int)) (exists ((Z4 tptp.int)) (forall ((X4 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Z4) X4)) (not (= X4 T)))))) (forall ((T tptp.real)) (exists ((Z4 tptp.real)) (forall ((X4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Z4) X4)) (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X4) T))))))) (forall ((T tptp.rat)) (exists ((Z4 tptp.rat)) (forall ((X4 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Z4) X4)) (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X4) T))))))) (forall ((T tptp.num)) (exists ((Z4 tptp.num)) (forall ((X4 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.ord_less_num Z4) X4)) (not (tptp.pp (tptp.aa_num_bool (tptp.ord_less_num X4) T))))))) (forall ((T tptp.nat)) (exists ((Z4 tptp.nat)) (forall ((X4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Z4) X4)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X4) T))))))) (forall ((T tptp.int)) (exists ((Z4 tptp.int)) (forall ((X4 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Z4) X4)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X4) T))))))) (forall ((T tptp.real)) (exists ((Z4 tptp.real)) (forall ((X4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Z4) X4)) (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X4) T))))))) (forall ((T tptp.rat)) (exists ((Z4 tptp.rat)) (forall ((X4 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Z4) 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 ((Z4 tptp.num)) (forall ((X4 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.ord_less_num Z4) X4)) (not (tptp.pp (tptp.aa_num_bool (tptp.ord_less_eq_num X4) T))))))) (forall ((T tptp.nat)) (exists ((Z4 tptp.nat)) (forall ((X4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Z4) 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 ((Z4 tptp.int)) (forall ((X4 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Z4) 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 ((Z4 tptp.real)) (forall ((X4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Z4) X4)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real T) X4)))))) (forall ((T tptp.rat)) (exists ((Z4 tptp.rat)) (forall ((X4 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Z4) X4)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat T) X4)))))) (forall ((T tptp.num)) (exists ((Z4 tptp.num)) (forall ((X4 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.ord_less_num Z4) X4)) (tptp.pp (tptp.aa_num_bool (tptp.ord_less_num T) X4)))))) (forall ((T tptp.nat)) (exists ((Z4 tptp.nat)) (forall ((X4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Z4) X4)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat T) X4)))))) (forall ((T tptp.int)) (exists ((Z4 tptp.int)) (forall ((X4 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Z4) X4)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int T) X4)))))) (forall ((T tptp.real)) (exists ((Z4 tptp.real)) (forall ((X4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Z4) X4)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real T) X4)))))) (forall ((T tptp.rat)) (exists ((Z4 tptp.rat)) (forall ((X4 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Z4) 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 ((Z4 tptp.num)) (forall ((X4 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.ord_less_num Z4) X4)) (tptp.pp (tptp.aa_num_bool (tptp.ord_less_eq_num T) X4)))))) (forall ((T tptp.nat)) (exists ((Z4 tptp.nat)) (forall ((X4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Z4) 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 ((Z4 tptp.int)) (forall ((X4 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Z4) X4)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int T) X4)))))) (forall ((P tptp.fun_real_bool) (P3 tptp.fun_real_bool) (Q tptp.fun_real_bool) (Q3 tptp.fun_real_bool)) (=> (exists ((Z3 tptp.real)) (forall ((X3 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X3) Z3)) (= (tptp.pp (tptp.aa_real_bool P X3)) (tptp.pp (tptp.aa_real_bool P3 X3)))))) (=> (exists ((Z3 tptp.real)) (forall ((X3 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X3) Z3)) (= (tptp.pp (tptp.aa_real_bool Q X3)) (tptp.pp (tptp.aa_real_bool Q3 X3)))))) (exists ((Z4 tptp.real)) (forall ((X4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X4) Z4)) (= (and (tptp.pp (tptp.aa_real_bool P X4)) (tptp.pp (tptp.aa_real_bool Q X4))) (and (tptp.pp (tptp.aa_real_bool P3 X4)) (tptp.pp (tptp.aa_real_bool Q3 X4)))))))))) (forall ((P tptp.fun_rat_bool) (P3 tptp.fun_rat_bool) (Q tptp.fun_rat_bool) (Q3 tptp.fun_rat_bool)) (=> (exists ((Z3 tptp.rat)) (forall ((X3 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X3) Z3)) (= (tptp.pp (tptp.aa_rat_bool P X3)) (tptp.pp (tptp.aa_rat_bool P3 X3)))))) (=> (exists ((Z3 tptp.rat)) (forall ((X3 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X3) Z3)) (= (tptp.pp (tptp.aa_rat_bool Q X3)) (tptp.pp (tptp.aa_rat_bool Q3 X3)))))) (exists ((Z4 tptp.rat)) (forall ((X4 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X4) Z4)) (= (and (tptp.pp (tptp.aa_rat_bool P X4)) (tptp.pp (tptp.aa_rat_bool Q X4))) (and (tptp.pp (tptp.aa_rat_bool P3 X4)) (tptp.pp (tptp.aa_rat_bool Q3 X4)))))))))) (forall ((P tptp.fun_num_bool) (P3 tptp.fun_num_bool) (Q tptp.fun_num_bool) (Q3 tptp.fun_num_bool)) (=> (exists ((Z3 tptp.num)) (forall ((X3 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.ord_less_num X3) Z3)) (= (tptp.pp (tptp.aa_num_bool P X3)) (tptp.pp (tptp.aa_num_bool P3 X3)))))) (=> (exists ((Z3 tptp.num)) (forall ((X3 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.ord_less_num X3) Z3)) (= (tptp.pp (tptp.aa_num_bool Q X3)) (tptp.pp (tptp.aa_num_bool Q3 X3)))))) (exists ((Z4 tptp.num)) (forall ((X4 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.ord_less_num X4) Z4)) (= (and (tptp.pp (tptp.aa_num_bool P X4)) (tptp.pp (tptp.aa_num_bool Q X4))) (and (tptp.pp (tptp.aa_num_bool P3 X4)) (tptp.pp (tptp.aa_num_bool Q3 X4)))))))))) (forall ((P tptp.fun_nat_bool) (P3 tptp.fun_nat_bool) (Q tptp.fun_nat_bool) (Q3 tptp.fun_nat_bool)) (=> (exists ((Z3 tptp.nat)) (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X3) Z3)) (= (tptp.pp (tptp.aa_nat_bool P X3)) (tptp.pp (tptp.aa_nat_bool P3 X3)))))) (=> (exists ((Z3 tptp.nat)) (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X3) Z3)) (= (tptp.pp (tptp.aa_nat_bool Q X3)) (tptp.pp (tptp.aa_nat_bool Q3 X3)))))) (exists ((Z4 tptp.nat)) (forall ((X4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X4) Z4)) (= (and (tptp.pp (tptp.aa_nat_bool P X4)) (tptp.pp (tptp.aa_nat_bool Q X4))) (and (tptp.pp (tptp.aa_nat_bool P3 X4)) (tptp.pp (tptp.aa_nat_bool Q3 X4)))))))))) (forall ((P tptp.fun_int_bool) (P3 tptp.fun_int_bool) (Q tptp.fun_int_bool) (Q3 tptp.fun_int_bool)) (=> (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 P3 X3)))))) (=> (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 Q X3)) (tptp.pp (tptp.aa_int_bool Q3 X3)))))) (exists ((Z4 tptp.int)) (forall ((X4 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X4) Z4)) (= (and (tptp.pp (tptp.aa_int_bool P X4)) (tptp.pp (tptp.aa_int_bool Q X4))) (and (tptp.pp (tptp.aa_int_bool P3 X4)) (tptp.pp (tptp.aa_int_bool Q3 X4)))))))))) (forall ((P tptp.fun_real_bool) (P3 tptp.fun_real_bool) (Q tptp.fun_real_bool) (Q3 tptp.fun_real_bool)) (=> (exists ((Z3 tptp.real)) (forall ((X3 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X3) Z3)) (= (tptp.pp (tptp.aa_real_bool P X3)) (tptp.pp (tptp.aa_real_bool P3 X3)))))) (=> (exists ((Z3 tptp.real)) (forall ((X3 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X3) Z3)) (= (tptp.pp (tptp.aa_real_bool Q X3)) (tptp.pp (tptp.aa_real_bool Q3 X3)))))) (exists ((Z4 tptp.real)) (forall ((X4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X4) Z4)) (= (or (tptp.pp (tptp.aa_real_bool P X4)) (tptp.pp (tptp.aa_real_bool Q X4))) (or (tptp.pp (tptp.aa_real_bool P3 X4)) (tptp.pp (tptp.aa_real_bool Q3 X4)))))))))) (forall ((P tptp.fun_rat_bool) (P3 tptp.fun_rat_bool) (Q tptp.fun_rat_bool) (Q3 tptp.fun_rat_bool)) (=> (exists ((Z3 tptp.rat)) (forall ((X3 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X3) Z3)) (= (tptp.pp (tptp.aa_rat_bool P X3)) (tptp.pp (tptp.aa_rat_bool P3 X3)))))) (=> (exists ((Z3 tptp.rat)) (forall ((X3 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X3) Z3)) (= (tptp.pp (tptp.aa_rat_bool Q X3)) (tptp.pp (tptp.aa_rat_bool Q3 X3)))))) (exists ((Z4 tptp.rat)) (forall ((X4 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X4) Z4)) (= (or (tptp.pp (tptp.aa_rat_bool P X4)) (tptp.pp (tptp.aa_rat_bool Q X4))) (or (tptp.pp (tptp.aa_rat_bool P3 X4)) (tptp.pp (tptp.aa_rat_bool Q3 X4)))))))))) (forall ((P tptp.fun_num_bool) (P3 tptp.fun_num_bool) (Q tptp.fun_num_bool) (Q3 tptp.fun_num_bool)) (=> (exists ((Z3 tptp.num)) (forall ((X3 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.ord_less_num X3) Z3)) (= (tptp.pp (tptp.aa_num_bool P X3)) (tptp.pp (tptp.aa_num_bool P3 X3)))))) (=> (exists ((Z3 tptp.num)) (forall ((X3 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.ord_less_num X3) Z3)) (= (tptp.pp (tptp.aa_num_bool Q X3)) (tptp.pp (tptp.aa_num_bool Q3 X3)))))) (exists ((Z4 tptp.num)) (forall ((X4 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.ord_less_num X4) Z4)) (= (or (tptp.pp (tptp.aa_num_bool P X4)) (tptp.pp (tptp.aa_num_bool Q X4))) (or (tptp.pp (tptp.aa_num_bool P3 X4)) (tptp.pp (tptp.aa_num_bool Q3 X4)))))))))) (forall ((P tptp.fun_nat_bool) (P3 tptp.fun_nat_bool) (Q tptp.fun_nat_bool) (Q3 tptp.fun_nat_bool)) (=> (exists ((Z3 tptp.nat)) (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X3) Z3)) (= (tptp.pp (tptp.aa_nat_bool P X3)) (tptp.pp (tptp.aa_nat_bool P3 X3)))))) (=> (exists ((Z3 tptp.nat)) (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X3) Z3)) (= (tptp.pp (tptp.aa_nat_bool Q X3)) (tptp.pp (tptp.aa_nat_bool Q3 X3)))))) (exists ((Z4 tptp.nat)) (forall ((X4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X4) Z4)) (= (or (tptp.pp (tptp.aa_nat_bool P X4)) (tptp.pp (tptp.aa_nat_bool Q X4))) (or (tptp.pp (tptp.aa_nat_bool P3 X4)) (tptp.pp (tptp.aa_nat_bool Q3 X4)))))))))) (forall ((P tptp.fun_int_bool) (P3 tptp.fun_int_bool) (Q tptp.fun_int_bool) (Q3 tptp.fun_int_bool)) (=> (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 P3 X3)))))) (=> (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 Q X3)) (tptp.pp (tptp.aa_int_bool Q3 X3)))))) (exists ((Z4 tptp.int)) (forall ((X4 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X4) Z4)) (= (or (tptp.pp (tptp.aa_int_bool P X4)) (tptp.pp (tptp.aa_int_bool Q X4))) (or (tptp.pp (tptp.aa_int_bool P3 X4)) (tptp.pp (tptp.aa_int_bool Q3 X4)))))))))) (forall ((T tptp.real)) (exists ((Z4 tptp.real)) (forall ((X4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X4) Z4)) (not (= X4 T)))))) (forall ((T tptp.rat)) (exists ((Z4 tptp.rat)) (forall ((X4 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X4) Z4)) (not (= X4 T)))))) (forall ((T tptp.num)) (exists ((Z4 tptp.num)) (forall ((X4 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.ord_less_num X4) Z4)) (not (= X4 T)))))) (forall ((T tptp.nat)) (exists ((Z4 tptp.nat)) (forall ((X4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X4) Z4)) (not (= X4 T)))))) (forall ((T tptp.int)) (exists ((Z4 tptp.int)) (forall ((X4 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X4) Z4)) (not (= X4 T)))))) (forall ((T tptp.real)) (exists ((Z4 tptp.real)) (forall ((X4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X4) Z4)) (not (= X4 T)))))) (forall ((T tptp.rat)) (exists ((Z4 tptp.rat)) (forall ((X4 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X4) Z4)) (not (= X4 T)))))) (forall ((T tptp.num)) (exists ((Z4 tptp.num)) (forall ((X4 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.ord_less_num X4) Z4)) (not (= X4 T)))))) (forall ((T tptp.nat)) (exists ((Z4 tptp.nat)) (forall ((X4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X4) Z4)) (not (= X4 T)))))) (forall ((T tptp.int)) (exists ((Z4 tptp.int)) (forall ((X4 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X4) Z4)) (not (= X4 T)))))) (forall ((T tptp.real)) (exists ((Z4 tptp.real)) (forall ((X4 tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X4))) (=> (tptp.pp (tptp.aa_real_bool _let_1 Z4)) (tptp.pp (tptp.aa_real_bool _let_1 T))))))) (forall ((T tptp.rat)) (exists ((Z4 tptp.rat)) (forall ((X4 tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X4))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 Z4)) (tptp.pp (tptp.aa_rat_bool _let_1 T))))))) (forall ((T tptp.num)) (exists ((Z4 tptp.num)) (forall ((X4 tptp.num)) (let ((_let_1 (tptp.ord_less_num X4))) (=> (tptp.pp (tptp.aa_num_bool _let_1 Z4)) (tptp.pp (tptp.aa_num_bool _let_1 T))))))) (forall ((T tptp.nat)) (exists ((Z4 tptp.nat)) (forall ((X4 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X4))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 Z4)) (tptp.pp (tptp.aa_nat_bool _let_1 T))))))) (forall ((T tptp.int)) (exists ((Z4 tptp.int)) (forall ((X4 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_int X4))) (=> (tptp.pp (tptp.aa_int_bool _let_1 Z4)) (tptp.pp (tptp.aa_int_bool _let_1 T))))))) (forall ((T tptp.real)) (exists ((Z4 tptp.real)) (forall ((X4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X4) Z4)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X4) T)))))) (forall ((T tptp.rat)) (exists ((Z4 tptp.rat)) (forall ((X4 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X4) Z4)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X4) T)))))) (forall ((T tptp.num)) (exists ((Z4 tptp.num)) (forall ((X4 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.ord_less_num X4) Z4)) (tptp.pp (tptp.aa_num_bool (tptp.ord_less_eq_num X4) T)))))) (forall ((T tptp.nat)) (exists ((Z4 tptp.nat)) (forall ((X4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X4) Z4)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X4) T)))))) (forall ((T tptp.int)) (exists ((Z4 tptp.int)) (forall ((X4 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X4) Z4)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X4) T)))))) (forall ((T tptp.real)) (exists ((Z4 tptp.real)) (forall ((X4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X4) Z4)) (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real T) X4))))))) (forall ((T tptp.rat)) (exists ((Z4 tptp.rat)) (forall ((X4 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X4) Z4)) (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat T) X4))))))) (forall ((T tptp.num)) (exists ((Z4 tptp.num)) (forall ((X4 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.ord_less_num X4) Z4)) (not (tptp.pp (tptp.aa_num_bool (tptp.ord_less_num T) X4))))))) (forall ((T tptp.nat)) (exists ((Z4 tptp.nat)) (forall ((X4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X4) Z4)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat T) X4))))))) (forall ((T tptp.int)) (exists ((Z4 tptp.int)) (forall ((X4 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X4) Z4)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int T) X4))))))) (forall ((T tptp.real)) (exists ((Z4 tptp.real)) (forall ((X4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X4) Z4)) (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real T) X4))))))) (forall ((T tptp.rat)) (exists ((Z4 tptp.rat)) (forall ((X4 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X4) Z4)) (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 ((Z4 tptp.num)) (forall ((X4 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.ord_less_num X4) Z4)) (not (tptp.pp (tptp.aa_num_bool (tptp.ord_less_eq_num T) X4))))))) (forall ((T tptp.nat)) (exists ((Z4 tptp.nat)) (forall ((X4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X4) Z4)) (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 ((Z4 tptp.int)) (forall ((X4 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X4) Z4)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int T) X4))))))) (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 ((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_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_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 ((I tptp.real) (J tptp.real) (K tptp.real) (L tptp.real)) (=> (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real I) J)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real K) L))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real I) K)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real J) L))))) (forall ((I tptp.rat) (J tptp.rat) (K tptp.rat) (L tptp.rat)) (=> (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat I) J)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat K) L))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat I) K)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat J) L))))) (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I) J)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) L))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat I) K)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat J) L))))) (forall ((I tptp.int) (J tptp.int) (K tptp.int) (L tptp.int)) (=> (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int I) J)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int K) L))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int I) K)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int J) L))))) (forall ((I tptp.real) (J tptp.real) (K tptp.real) (L tptp.real)) (=> (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real I) J)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real K) L))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real I) K)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real J) L))))) (forall ((I tptp.rat) (J tptp.rat) (K tptp.rat) (L tptp.rat)) (=> (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat I) J)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat K) L))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat I) K)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat J) L))))) (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I) J)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat K) L))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat I) K)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat J) L))))) (forall ((I tptp.int) (J tptp.int) (K tptp.int) (L tptp.int)) (=> (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int I) J)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int K) L))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int I) K)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int J) L))))) (forall ((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.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.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 ((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.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.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_set_nat) (N tptp.nat) (N3 tptp.nat)) (=> (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat (tptp.aa_nat_set_nat F N2)) (tptp.aa_nat_set_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_set_nat_bool (tptp.ord_less_eq_set_nat (tptp.aa_nat_set_nat F N)) (tptp.aa_nat_set_nat 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.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.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_set_nat) (N tptp.nat) (N3 tptp.nat)) (=> (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat (tptp.aa_nat_set_nat F (tptp.aa_nat_nat tptp.suc N2))) (tptp.aa_nat_set_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_set_nat_bool (tptp.ord_less_eq_set_nat (tptp.aa_nat_set_nat F N3)) (tptp.aa_nat_set_nat 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.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.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 ((M tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat tptp.suc M)) N)))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat tptp.suc M)) N)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N)))) (forall ((I tptp.nat) (J tptp.nat) (P tptp.fun_nat_bool)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I) J)) (=> (tptp.pp (tptp.aa_nat_bool P I)) (=> (forall ((N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I) N2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) J)) (=> (tptp.pp (tptp.aa_nat_bool P N2)) (tptp.pp (tptp.aa_nat_bool P (tptp.aa_nat_nat tptp.suc N2))))))) (tptp.pp (tptp.aa_nat_bool P J)))))) (forall ((I tptp.nat) (J tptp.nat) (P tptp.fun_nat_bool)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I) J)) (=> (tptp.pp (tptp.aa_nat_bool P J)) (=> (forall ((N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I) N2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) J)) (=> (tptp.pp (tptp.aa_nat_bool P (tptp.aa_nat_nat tptp.suc N2))) (tptp.pp (tptp.aa_nat_bool P N2)))))) (tptp.pp (tptp.aa_nat_bool P I)))))) (forall ((M tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat tptp.suc M)) N)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N)))) (forall ((M tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N) (tptp.aa_nat_nat tptp.suc M))) (= N M)))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) (tptp.aa_nat_nat tptp.suc N))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)))) (forall ((N tptp.nat) (M tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N) M)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat tptp.suc N)) M)))) (forall ((M tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) (tptp.aa_nat_nat tptp.suc N))))) (forall ((P tptp.fun_nat_bool) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool P N)) (=> (not (tptp.pp (tptp.aa_nat_bool P tptp.zero_zero_nat))) (exists ((K3 tptp.nat)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K3) N)) (forall ((I3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I3) K3)) (not (tptp.pp (tptp.aa_nat_bool P I3))))) (tptp.pp (tptp.aa_nat_bool P K3))))))) (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 ((I tptp.nat) (J tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I) J)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real I)) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real J))))) (forall ((I tptp.nat) (J tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I) J)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat I)) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat J))))) (forall ((I tptp.nat) (J tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I) J)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat I)) (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat J))))) (forall ((I tptp.nat) (J tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I) J)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int I)) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int J))))) (forall ((F tptp.fun_nat_nat) (M tptp.nat) (K tptp.nat)) (=> (forall ((M2 tptp.nat) (N2 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 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat F M2)) (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 ((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 ((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 ((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.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 ((A tptp.real) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_real_fun_nat_real tptp.power_power_real A))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real) A)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_nat_real _let_1 M)) (tptp.aa_nat_real _let_1 N))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)))))) (forall ((A tptp.rat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.power_power_rat A))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.one_one_rat) A)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat _let_1 M)) (tptp.aa_nat_rat _let_1 N))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)))))) (forall ((A tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.one_one_nat) A)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat _let_1 M)) (tptp.aa_nat_nat _let_1 N))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)))))) (forall ((A tptp.int) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.power_power_int A))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.one_one_int) A)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int _let_1 M)) (tptp.aa_nat_int _let_1 N))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)))))) (forall ((M tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat (tptp.aa_nat_set_nat tptp.nat_set_decode M)) (tptp.aa_nat_set_nat 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 ((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 ((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.aa_nat_fun_nat_nat tptp.power_power_nat A) N)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat 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 ((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 ((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 ((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 ((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 ((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 ((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 ((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 ((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 ((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 ((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 ((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) (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) (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) (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) (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 ((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 ((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 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 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_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_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 ((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 ((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) (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) (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_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_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 ((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)) (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)) (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)) (=> (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) (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)) (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)) (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)) (=> (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)) (=> (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)) (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)) (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)) (=> (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 ((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 ((X tptp.real) (Y tptp.real)) (=> (forall ((E2 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) E2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real Y) E2))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) Y)))) (forall ((X tptp.rat) (Y tptp.rat)) (=> (forall ((E2 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) E2)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat Y) E2))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) Y)))) (forall ((X tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) tptp.zero_zero_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) Y)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real X) Y)) tptp.zero_zero_real))))) (forall ((X tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) tptp.zero_zero_rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) Y)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.divide_divide_rat X Y)) tptp.zero_zero_rat))))) (forall ((X tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) tptp.zero_zero_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real X) Y)))))) (forall ((X tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) tptp.zero_zero_rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Y) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.divide_divide_rat X Y)))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool _let_1 X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) Y)) (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real X) Y))))))) (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 X)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) Y)) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.divide_divide_rat X Y))))))) (forall ((X tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real X) Y)) tptp.zero_zero_real))))) (forall ((X tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) X)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Y) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.divide_divide_rat X Y)) tptp.zero_zero_rat))))) (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 ((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.divide_divide_rat A C)) (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 ((X tptp.real) (Y tptp.real) (W tptp.real) (Z tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool _let_1 X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) Y)) (=> (tptp.pp (tptp.aa_real_bool _let_1 W)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real W) Z)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real X) Z)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real Y) W))))))))) (forall ((X tptp.rat) (Y tptp.rat) (W tptp.rat) (Z tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 X)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) Y)) (=> (tptp.pp (tptp.aa_rat_bool _let_1 W)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat W) Z)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.divide_divide_rat X Z)) (tptp.divide_divide_rat Y W))))))))) (forall ((X tptp.real) (Y tptp.real) (W tptp.real) (Z tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Y)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) W)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real W) Z)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real X) Z)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real Y) W)))))))) (forall ((X tptp.rat) (Y tptp.rat) (W tptp.rat) (Z tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) X)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) Y)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) W)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat W) Z)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.divide_divide_rat X Z)) (tptp.divide_divide_rat Y W)))))))) (forall ((Y tptp.real) (X tptp.real) (W tptp.real) (Z tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) Y)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) Y)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) W)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real W) Z)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real X) Z)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real Y) W)))))))) (forall ((Y tptp.rat) (X tptp.rat) (W tptp.rat) (Z tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) Y)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) Y)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) W)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat W) Z)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.divide_divide_rat X Z)) (tptp.divide_divide_rat Y W)))))))) (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 ((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 ((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) (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.aa_nat_fun_nat_nat tptp.power_power_nat A) N)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat 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.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)))) (forall ((N tptp.nat) (N4 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) N4)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real) A)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_nat_real _let_1 N)) (tptp.aa_nat_real _let_1 N4))))))) (forall ((N tptp.nat) (N4 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) N4)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.one_one_rat) A)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_nat_rat _let_1 N)) (tptp.aa_nat_rat _let_1 N4))))))) (forall ((N tptp.nat) (N4 tptp.nat) (A tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N) N4)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.one_one_nat) A)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat _let_1 N)) (tptp.aa_nat_nat _let_1 N4))))))) (forall ((N tptp.nat) (N4 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) N4)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.one_one_int) A)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_nat_int _let_1 N)) (tptp.aa_nat_int _let_1 N4))))))) (forall ((A tptp.real) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_real_fun_nat_real tptp.power_power_real A))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real) A)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_nat_real _let_1 M)) (tptp.aa_nat_real _let_1 N))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N)))))) (forall ((A tptp.rat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.power_power_rat A))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.one_one_rat) A)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_nat_rat _let_1 M)) (tptp.aa_nat_rat _let_1 N))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N)))))) (forall ((A tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.one_one_nat) A)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat _let_1 M)) (tptp.aa_nat_nat _let_1 N))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N)))))) (forall ((A tptp.int) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.power_power_int A))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.one_one_int) A)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_nat_int _let_1 M)) (tptp.aa_nat_int _let_1 N))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N)))))) (forall ((N tptp.nat) (N4 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) N4)) (=> (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 N4))))))) (forall ((N tptp.nat) (N4 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) N4)) (=> (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 N4))))))) (forall ((N tptp.nat) (N4 tptp.nat) (A tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N) N4)) (=> (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 N4))))))) (forall ((N tptp.nat) (N4 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) N4)) (=> (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 N4))))))) (forall ((P tptp.fun_nat_bool) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool P N)) (=> (not (tptp.pp (tptp.aa_nat_bool P tptp.zero_zero_nat))) (exists ((K3 tptp.nat)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat K3) N)) (forall ((I3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I3) K3)) (not (tptp.pp (tptp.aa_nat_bool P I3))))) (tptp.pp (tptp.aa_nat_bool P (tptp.aa_nat_nat tptp.suc K3)))))))) (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 ((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 ((Y4 tptp.real)) (=> (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) Y4)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Y4) N) A)) (= Y4 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 ((R2 tptp.real)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) R2)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real R2) N) A)))))) (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 ((K tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat K) N)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) N))))) (forall ((K tptp.nat) (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 ((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 ((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 ((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) (B5 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) B5)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B5) 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 B5)))))))) (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) (B5 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) B5)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B5) B)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int _let_1 B5)) (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 ((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 ((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 ((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 ((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.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)) (= (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 ((D1 tptp.real) (D22 tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool _let_1 D1)) (=> (tptp.pp (tptp.aa_real_bool _let_1 D22)) (exists ((E2 tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real E2))) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) E2)) (tptp.pp (tptp.aa_real_bool _let_1 D1)) (tptp.pp (tptp.aa_real_bool _let_1 D22))))))))) (forall ((D1 tptp.rat) (D22 tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 D1)) (=> (tptp.pp (tptp.aa_rat_bool _let_1 D22)) (exists ((E2 tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat E2))) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) E2)) (tptp.pp (tptp.aa_rat_bool _let_1 D1)) (tptp.pp (tptp.aa_rat_bool _let_1 D22))))))))) (not (tptp.pp (tptp.aa_real_bool _let_105 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_163 tptp.zero_zero_nat))) _let_181 (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))) (tptp.pp (tptp.aa_real_bool _let_104 tptp.zero_zero_real)) (tptp.pp (tptp.aa_rat_bool _let_126 tptp.zero_zero_rat)) (tptp.pp (tptp.aa_nat_bool _let_171 tptp.zero_zero_nat)) _let_180 (not (tptp.pp (tptp.aa_real_bool _let_133 tptp.one_one_real))) (not (tptp.pp (tptp.aa_rat_bool _let_131 tptp.one_one_rat))) (not (tptp.pp (tptp.aa_nat_bool _let_179 tptp.one_one_nat))) (not (tptp.pp (tptp.aa_int_bool _let_132 tptp.one_one_int))) (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 ((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) (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 ((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) (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 ((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 ((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)) (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 ((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.minus_minus_rat A C)) (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 ((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.minus_minus_rat A B) (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 ((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)) (=> (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.minus_minus_rat C A)) (tptp.minus_minus_rat C 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)) (=> (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.minus_minus_rat A C)) (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))))) (tptp.pp (tptp.aa_real_bool _let_136 tptp.one_one_real)) (tptp.pp (tptp.aa_rat_bool _let_135 tptp.one_one_rat)) (tptp.pp (tptp.aa_nat_bool _let_169 tptp.one_one_nat)) (tptp.pp (tptp.aa_int_bool _let_134 tptp.one_one_int)) (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.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 ((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 ((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 ((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 ((C4 tptp.nat)) (= B (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) C4))))) (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.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.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.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.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) (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) (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 ((I tptp.real) (J tptp.real) (K tptp.real) (L tptp.real)) (=> (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real I) J)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real K) L))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real I) K)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real J) L))))) (forall ((I tptp.rat) (J tptp.rat) (K tptp.rat) (L tptp.rat)) (=> (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat I) J)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat K) L))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat I) K)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat J) L))))) (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I) J)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) L))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat I) K)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat J) L))))) (forall ((I tptp.int) (J tptp.int) (K tptp.int) (L tptp.int)) (=> (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int I) J)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int K) L))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int I) K)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int J) L))))) (forall ((I tptp.real) (J tptp.real) (K tptp.real) (L tptp.real)) (=> (and (= I J) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real K) L))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real I) K)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real J) L))))) (forall ((I tptp.rat) (J tptp.rat) (K tptp.rat) (L tptp.rat)) (=> (and (= I J) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat K) L))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat I) K)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat J) L))))) (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (= I J) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) L))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat I) K)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat J) L))))) (forall ((I tptp.int) (J tptp.int) (K tptp.int) (L tptp.int)) (=> (and (= I J) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int K) L))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int I) K)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int J) L))))) (forall ((I tptp.real) (J tptp.real) (K tptp.real) (L tptp.real)) (=> (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real I) J)) (= K L)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real I) K)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real J) L))))) (forall ((I tptp.rat) (J tptp.rat) (K tptp.rat) (L tptp.rat)) (=> (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat I) J)) (= K L)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat I) K)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat J) L))))) (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I) J)) (= K L)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat I) K)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat J) L))))) (forall ((I tptp.int) (J tptp.int) (K tptp.int) (L tptp.int)) (=> (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int I) J)) (= K L)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int I) K)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int J) L))))) (forall ((X tptp.num)) (= (tptp.pp (tptp.aa_num_bool (tptp.ord_less_eq_num X) tptp.one)) (= X tptp.one))) (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.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.minus_minus_rat A C)) (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 ((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 ((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 (tptp.minus_minus_rat C A)) (tptp.minus_minus_rat C 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 ((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 ((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.minus_minus_rat A C)) (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) (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) (D tptp.rat)) (=> (= (tptp.minus_minus_rat A B) (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 ((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 ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N))) (=> (not (tptp.pp (tptp.aa_nat_bool _let_1 M))) (= (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat tptp.suc M))) (= N M))))) (forall ((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 ((I2 tptp.nat)) (=> (= J (tptp.aa_nat_nat tptp.suc I2)) (tptp.pp (tptp.aa_nat_bool P I2)))) (=> (forall ((I2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I2) J)) (=> (tptp.pp (tptp.aa_nat_bool P (tptp.aa_nat_nat tptp.suc I2))) (tptp.pp (tptp.aa_nat_bool P I2))))) (tptp.pp (tptp.aa_nat_bool P I)))))) (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 ((I2 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool P I2) (tptp.aa_nat_nat tptp.suc I2)))) (=> (forall ((I2 tptp.nat) (J2 tptp.nat) (K3 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool P I2))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I2) J2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat J2) K3)) (=> (tptp.pp (tptp.aa_nat_bool _let_1 J2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool P J2) K3)) (tptp.pp (tptp.aa_nat_bool _let_1 K3)))))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool P I) J)))))) (forall ((I tptp.nat) (J tptp.nat) (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 ((M tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat tptp.suc M)) (tptp.aa_nat_nat tptp.suc N))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N)))) (forall ((N tptp.nat) (M tptp.nat)) (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 ((N tptp.nat) (M tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat tptp.suc N)) M)) (exists ((M4 tptp.nat)) (and (= M (tptp.aa_nat_nat tptp.suc M4)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N) M4)))))) (forall ((N tptp.nat) (P tptp.fun_nat_bool)) (= (forall ((I4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I4) (tptp.aa_nat_nat tptp.suc N))) (tptp.pp (tptp.aa_nat_bool P I4)))) (and (tptp.pp (tptp.aa_nat_bool P N)) (forall ((I4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I4) N)) (tptp.pp (tptp.aa_nat_bool P I4))))))) (forall ((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 ((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 ((N tptp.nat) (P tptp.fun_nat_bool)) (= (exists ((I4 tptp.nat)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I4) (tptp.aa_nat_nat tptp.suc N))) (tptp.pp (tptp.aa_nat_bool P I4)))) (or (tptp.pp (tptp.aa_nat_bool P N)) (exists ((I4 tptp.nat)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I4) N)) (tptp.pp (tptp.aa_nat_bool P I4))))))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 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_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_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 ((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)) (=> (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 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 ((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 ((M3 tptp.nat)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M3) N2)) (not (tptp.pp (tptp.aa_nat_bool P M3)))))))) (tptp.pp (tptp.aa_nat_bool P N))))) (forall ((M tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N)) (not (= N tptp.zero_zero_nat)))) (forall ((N tptp.nat)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N) tptp.zero_zero_nat)))) (forall ((N tptp.nat)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N) tptp.zero_zero_nat)))) (forall ((N tptp.nat)) (= (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N))) (= N tptp.zero_zero_nat))) (forall ((N tptp.nat)) (=> (not (= N tptp.zero_zero_nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)))) (forall ((A tptp.nat)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) tptp.zero_zero_nat)))) (forall ((M tptp.nat) (N tptp.nat) (R3 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 R3 X3) X3))) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat) (Z4 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool R3 X3))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 Y3)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool R3 Y3) Z4)) (tptp.pp (tptp.aa_nat_bool _let_1 Z4)))))) (=> (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool R3 N2) (tptp.aa_nat_nat tptp.suc N2)))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool R3 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 ((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 M3)) N2)) (tptp.pp (tptp.aa_nat_bool P M3)))) (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) (M5 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat tptp.suc N)) M5)) (exists ((M2 tptp.nat)) (= M5 (tptp.aa_nat_nat tptp.suc M2))))) (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 ((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 ((X tptp.real)) (exists ((N2 tptp.nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N2))))) (forall ((X tptp.rat)) (exists ((N2 tptp.nat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat N2))))) _let_181 (forall ((X tptp.int) (X6 tptp.int) (P tptp.bool) (P3 tptp.bool)) (let ((_let_1 (tptp.pp P3))) (let ((_let_2 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_3 (tptp.pp (tptp.aa_int_bool _let_2 X6)))) (let ((_let_4 (tptp.pp P))) (=> (= X X6) (=> (=> _let_3 (= _let_4 _let_1)) (= (=> (tptp.pp (tptp.aa_int_bool _let_2 X)) _let_4) (=> _let_3 _let_1))))))))) (forall ((X tptp.int) (X6 tptp.int) (P tptp.bool) (P3 tptp.bool)) (let ((_let_1 (tptp.pp P3))) (let ((_let_2 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_3 (tptp.pp (tptp.aa_int_bool _let_2 X6)))) (let ((_let_4 (tptp.pp P))) (=> (= X X6) (=> (=> _let_3 (= _let_4 _let_1)) (= (and (tptp.pp (tptp.aa_int_bool _let_2 X)) _let_4) (and _let_3 _let_1))))))))) _let_180 (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat I) J)) K)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I) K)))) (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I) J)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat K) L)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat I) K)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat J) L)))))) (forall ((I tptp.nat) (J tptp.nat)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat I) J)) I)))) (forall ((J tptp.nat) (I tptp.nat)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat J) I)) I)))) (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I) J)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat I) K)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat J) K))))) (forall ((I tptp.nat) (J tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 J)) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat J) M)))))) (forall ((I tptp.nat) (J tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 J)) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) J)))))) (forall ((K tptp.nat) (L tptp.nat) (M tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat K) L)) (=> (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) L) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat K) N)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N))))) (forall ((M tptp.nat) (K tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) K)) N)) (not (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) N))))))) (forall ((N tptp.nat) (M tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N) M)))) (forall ((N tptp.nat) (M tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) N)))) (forall ((M tptp.nat) (K tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) K)) N)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)))) (forall ((M tptp.nat) (K tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) K)) N)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) N)))) (forall ((K tptp.nat) (L tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) L)) (exists ((N2 tptp.nat)) (= L (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat K) N2))))) (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I) J)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) L)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat I) K)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat J) L)))))) (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I) J)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat I) K)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat J) K))))) (forall ((I tptp.nat) (J tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 J)) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat J) M)))))) (forall ((I tptp.nat) (J tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 J)) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) J)))))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)) (exists ((K2 tptp.nat)) (= N (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) K2))))) (forall ((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 ((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 ((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 ((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)) (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 ((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 ((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 ((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_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 ((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 ((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 ((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 ((X tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real) X)) (exists ((N2 tptp.nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) N2)))))) (forall ((Y tptp.real) (X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) Y)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) tptp.one_one_real)) (exists ((N2 tptp.nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) N2)) Y)))))) (forall ((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 ((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) (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) (A tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real C) A)) C)) (and (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) C)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) tptp.one_one_real))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real C) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.one_one_real) A)))))) (forall ((C tptp.rat) (A tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat C) A)) C)) (and (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) C)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) tptp.one_one_rat))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat C) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.one_one_rat) A)))))) (forall ((C tptp.int) (A tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int C) A)) C)) (and (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) C)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) tptp.one_one_int))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int C) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.one_one_int) A)))))) (forall ((C tptp.real) (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 ((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 ((A tptp.real) (C tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) C)) C)) (and (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) C)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) tptp.one_one_real))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real C) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.one_one_real) A)))))) (forall ((A tptp.rat) (C tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) C)) C)) (and (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) C)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) tptp.one_one_rat))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat C) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.one_one_rat) A)))))) (forall ((A tptp.int) (C tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) C)) C)) (and (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) C)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) tptp.one_one_int))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int C) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.one_one_int) A)))))) (forall ((C tptp.real) (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) (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) (A tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real C) A)) C)) (and (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) C)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) tptp.one_one_real))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real C) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real) A)))))) (forall ((C tptp.rat) (A tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat C) A)) C)) (and (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) C)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) tptp.one_one_rat))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat C) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.one_one_rat) A)))))) (forall ((C tptp.int) (A tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int C) A)) C)) (and (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) C)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) tptp.one_one_int))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int C) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.one_one_int) A)))))) (forall ((C tptp.real) (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 ((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 ((A tptp.real) (C tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) C)) C)) (and (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) C)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) tptp.one_one_real))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real C) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real) A)))))) (forall ((A tptp.rat) (C tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) C)) C)) (and (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) C)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) tptp.one_one_rat))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat C) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.one_one_rat) A)))))) (forall ((A tptp.int) (C tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) C)) C)) (and (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) C)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) tptp.one_one_int))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int C) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.one_one_int) A)))))) (forall ((X tptp.real) (Y tptp.real)) (=> (forall ((Z4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) Z4)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Z4) tptp.one_one_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real Z4) X)) Y))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) Y)))) (forall ((X tptp.rat) (Y tptp.rat)) (=> (forall ((Z4 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) Z4)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Z4) tptp.one_one_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat Z4) X)) Y))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) Y)))) (forall ((A tptp.real) (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 ((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_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.divide_divide_rat C A)) (tptp.divide_divide_rat C B))))))) (forall ((Y tptp.real) (Z tptp.real) (X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) Y)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real Z) Y)) X)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Z) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real X) Y)))))) (forall ((Y tptp.rat) (Z tptp.rat) (X tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) Y)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat Z) Y)) X)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat Z) (tptp.divide_divide_rat X Y)))))) (forall ((Y tptp.real) (X tptp.real) (Z tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) Y)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real Z) Y))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real X) Y)) Z))))) (forall ((Y tptp.rat) (X tptp.rat) (Z tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) Y)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat Z) Y))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.divide_divide_rat X Y)) Z))))) (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 ((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.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) (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) (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.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) (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) (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.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) (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) (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.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 ((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 ((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 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.divide_divide_rat C A)) (tptp.divide_divide_rat C B))))))) (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 ((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.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 ((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 ((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.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) (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 ((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.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.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.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 ((N tptp.nat) (N4 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) N4)) (=> (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 N4)) (tptp.aa_nat_real _let_1 N)))))))) (forall ((N tptp.nat) (N4 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) N4)) (=> (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 N4)) (tptp.aa_nat_rat _let_1 N)))))))) (forall ((N tptp.nat) (N4 tptp.nat) (A tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N) N4)) (=> (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 N4)) (tptp.aa_nat_nat _let_1 N)))))))) (forall ((N tptp.nat) (N4 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) N4)) (=> (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 N4)) (tptp.aa_nat_int _let_1 N)))))))) (forall ((N tptp.nat) (N4 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) N4)) (=> (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 N4)) (tptp.aa_nat_real _let_1 N)))))))) (forall ((N tptp.nat) (N4 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) N4)) (=> (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 N4)) (tptp.aa_nat_rat _let_1 N)))))))) (forall ((N tptp.nat) (N4 tptp.nat) (A tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N) N4)) (=> (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 N4)) (tptp.aa_nat_nat _let_1 N)))))))) (forall ((N tptp.nat) (N4 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) N4)) (=> (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 N4)) (tptp.aa_nat_int _let_1 N)))))))) (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.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.aa_nat_fun_nat_nat tptp.power_power_nat A) N) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat 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 ((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 ((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.aa_nat_fun_nat_nat tptp.power_power_nat A) N) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat 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 ((A tptp.real) (N tptp.nat)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real))) (=> (tptp.pp (tptp.aa_real_bool _let_1 A)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real A) N))))))) (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.one_one_rat))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 A)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_nat_rat (tptp.power_power_rat A) N))))))) (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.one_one_nat))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 A)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A) N))))))) (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.one_one_int))) (=> (tptp.pp (tptp.aa_int_bool _let_1 A)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_nat_int (tptp.power_power_int A) N))))))) (forall ((A tptp.real) (N tptp.nat)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.one_one_real) A)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real A) N)))))) (forall ((A tptp.rat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.one_one_rat) A)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) (tptp.aa_nat_rat (tptp.power_power_rat A) N)))))) (forall ((A tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.one_one_nat) A)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A) N)))))) (forall ((A tptp.int) (N tptp.nat)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.one_one_int) A)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) (tptp.aa_nat_int (tptp.power_power_int A) N)))))) (forall ((K tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) K)) (exists ((N2 tptp.nat)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)) (= K (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N2)))))) (forall ((K tptp.int)) (=> (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 ((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 ((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 ((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 ((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 ((B tptp.int) (Q4 tptp.int) (R4 tptp.int) (Q2 tptp.int) (R 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 Q4)) R4)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int _let_2 Q2)) R))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int R) tptp.zero_zero_int)) (=> (tptp.pp (tptp.aa_int_bool _let_1 R)) (=> (tptp.pp (tptp.aa_int_bool _let_1 R4)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Q2) Q4))))))))) (forall ((B tptp.int) (Q4 tptp.int) (R4 tptp.int) (Q2 tptp.int) (R 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 Q4)) R4)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int _let_1 Q2)) R))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) R4)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int R4) B)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int R) B)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Q4) Q2)))))))) (forall ((B tptp.int) (Q2 tptp.int) (R tptp.int) (B5 tptp.int) (Q4 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 B5) Q4)) 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)) R) _let_1) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int _let_1) tptp.zero_zero_int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int R) 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) B5)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B5) B)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Q4) Q2)))))))))) (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 ((B tptp.int) (Q2 tptp.int) (R tptp.int) (B5 tptp.int) (Q4 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 B5) Q4)) 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)) R) _let_2) (=> (tptp.pp (tptp.aa_int_bool _let_1 _let_2)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int R4) B5)) (=> (tptp.pp (tptp.aa_int_bool _let_1 R)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) B5)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B5) B)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Q2) Q4))))))))))) (forall ((B5 tptp.int) (Q4 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 B5) Q4)) R4))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int R4) B5)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) B5)) (tptp.pp (tptp.aa_int_bool _let_1 Q4))))))) (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 ((M2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) M2)) (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 M2)) X)) C)))) (= X tptp.zero_zero_real)))))) (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 ((I tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat I))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_nat_nat _let_1 M)) (tptp.aa_nat_nat _let_1 N))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.one_one_nat) I)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)))))) (forall ((X tptp.real) (A tptp.real) (Y tptp.real) (U tptp.real) (V tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) A)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y) A)) (=> (tptp.pp (tptp.aa_real_bool _let_1 U)) (=> (tptp.pp (tptp.aa_real_bool _let_1 V)) (=> (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real U) V) tptp.one_one_real) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real U) X)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real V) Y))) A))))))))) (forall ((X tptp.rat) (A tptp.rat) (Y tptp.rat) (U tptp.rat) (V tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) A)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Y) A)) (=> (tptp.pp (tptp.aa_rat_bool _let_1 U)) (=> (tptp.pp (tptp.aa_rat_bool _let_1 V)) (=> (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat U) V) tptp.one_one_rat) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat U) X)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat V) Y))) A))))))))) (forall ((X tptp.int) (A tptp.int) (Y tptp.int) (U tptp.int) (V tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) A)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Y) A)) (=> (tptp.pp (tptp.aa_int_bool _let_1 U)) (=> (tptp.pp (tptp.aa_int_bool _let_1 V)) (=> (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int U) V) tptp.one_one_int) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int U) X)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int V) Y))) A))))))))) (forall ((B tptp.real) (C tptp.real) (W tptp.num)) (let ((_let_1 (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 ((B tptp.rat) (C tptp.rat) (W tptp.num)) (let ((_let_1 (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.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 ((W tptp.num) (B tptp.real) (C tptp.real)) (let ((_let_1 (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 ((W tptp.num) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (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.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 ((P2 tptp.bool)) (let ((_let_1 (tptp.zero_n1201886186963655149omplex P2))) (let ((_let_2 (tptp.pp P2))) (and (=> _let_2 (= _let_1 tptp.one_one_complex)) (=> (not _let_2) (= _let_1 tptp.zero_zero_complex)))))) (forall ((P2 tptp.bool)) (let ((_let_1 (tptp.zero_n3304061248610475627l_real P2))) (let ((_let_2 (tptp.pp P2))) (and (=> _let_2 (= _let_1 tptp.one_one_real)) (=> (not _let_2) (= _let_1 tptp.zero_zero_real)))))) (forall ((P2 tptp.bool)) (let ((_let_1 (tptp.zero_n2052037380579107095ol_rat P2))) (let ((_let_2 (tptp.pp P2))) (and (=> _let_2 (= _let_1 tptp.one_one_rat)) (=> (not _let_2) (= _let_1 tptp.zero_zero_rat)))))) (forall ((P2 tptp.bool)) (let ((_let_1 (tptp.aa_bool_nat tptp.zero_n2687167440665602831ol_nat P2))) (let ((_let_2 (tptp.pp P2))) (and (=> _let_2 (= _let_1 tptp.one_one_nat)) (=> (not _let_2) (= _let_1 tptp.zero_zero_nat)))))) (forall ((P2 tptp.bool)) (let ((_let_1 (tptp.aa_bool_int tptp.zero_n2684676970156552555ol_int P2))) (let ((_let_2 (tptp.pp P2))) (and (=> _let_2 (= _let_1 tptp.one_one_int)) (=> (not _let_2) (= _let_1 tptp.zero_zero_int)))))) (forall ((P2 tptp.bool)) (let ((_let_1 (tptp.aa_bool_Code_integer tptp.zero_n356916108424825756nteger P2))) (let ((_let_2 (tptp.pp P2))) (and (=> _let_2 (= _let_1 tptp.one_one_Code_integer)) (=> (not _let_2) (= _let_1 tptp.zero_z3403309356797280102nteger)))))) (forall ((P tptp.fun_complex_bool) (P2 tptp.bool)) (let ((_let_1 (tptp.pp P2))) (= (tptp.pp (tptp.aa_complex_bool P (tptp.zero_n1201886186963655149omplex P2))) (and (=> _let_1 (tptp.pp (tptp.aa_complex_bool P tptp.one_one_complex))) (=> (not _let_1) (tptp.pp (tptp.aa_complex_bool P tptp.zero_zero_complex))))))) (forall ((P tptp.fun_real_bool) (P2 tptp.bool)) (let ((_let_1 (tptp.pp P2))) (= (tptp.pp (tptp.aa_real_bool P (tptp.zero_n3304061248610475627l_real P2))) (and (=> _let_1 (tptp.pp (tptp.aa_real_bool P tptp.one_one_real))) (=> (not _let_1) (tptp.pp (tptp.aa_real_bool P tptp.zero_zero_real))))))) (forall ((P tptp.fun_rat_bool) (P2 tptp.bool)) (let ((_let_1 (tptp.pp P2))) (= (tptp.pp (tptp.aa_rat_bool P (tptp.zero_n2052037380579107095ol_rat P2))) (and (=> _let_1 (tptp.pp (tptp.aa_rat_bool P tptp.one_one_rat))) (=> (not _let_1) (tptp.pp (tptp.aa_rat_bool P tptp.zero_zero_rat))))))) (forall ((P tptp.fun_nat_bool) (P2 tptp.bool)) (let ((_let_1 (tptp.pp P2))) (= (tptp.pp (tptp.aa_nat_bool P (tptp.aa_bool_nat tptp.zero_n2687167440665602831ol_nat P2))) (and (=> _let_1 (tptp.pp (tptp.aa_nat_bool P tptp.one_one_nat))) (=> (not _let_1) (tptp.pp (tptp.aa_nat_bool P tptp.zero_zero_nat))))))) (forall ((P tptp.fun_int_bool) (P2 tptp.bool)) (let ((_let_1 (tptp.pp P2))) (= (tptp.pp (tptp.aa_int_bool P (tptp.aa_bool_int tptp.zero_n2684676970156552555ol_int P2))) (and (=> _let_1 (tptp.pp (tptp.aa_int_bool P tptp.one_one_int))) (=> (not _let_1) (tptp.pp (tptp.aa_int_bool P tptp.zero_zero_int))))))) (forall ((P tptp.fun_Co8822979462182099027r_bool) (P2 tptp.bool)) (let ((_let_1 (tptp.pp P2))) (= (tptp.pp (tptp.aa_Code_integer_bool P (tptp.aa_bool_Code_integer tptp.zero_n356916108424825756nteger P2))) (and (=> _let_1 (tptp.pp (tptp.aa_Code_integer_bool P tptp.one_one_Code_integer))) (=> (not _let_1) (tptp.pp (tptp.aa_Code_integer_bool P tptp.zero_z3403309356797280102nteger))))))) (forall ((P tptp.fun_complex_bool) (P2 tptp.bool)) (let ((_let_1 (tptp.pp P2))) (= (tptp.pp (tptp.aa_complex_bool P (tptp.zero_n1201886186963655149omplex P2))) (not (or (and _let_1 (not (tptp.pp (tptp.aa_complex_bool P tptp.one_one_complex)))) (and (not _let_1) (not (tptp.pp (tptp.aa_complex_bool P tptp.zero_zero_complex))))))))) (forall ((P tptp.fun_real_bool) (P2 tptp.bool)) (let ((_let_1 (tptp.pp P2))) (= (tptp.pp (tptp.aa_real_bool P (tptp.zero_n3304061248610475627l_real P2))) (not (or (and _let_1 (not (tptp.pp (tptp.aa_real_bool P tptp.one_one_real)))) (and (not _let_1) (not (tptp.pp (tptp.aa_real_bool P tptp.zero_zero_real))))))))) (forall ((P tptp.fun_rat_bool) (P2 tptp.bool)) (let ((_let_1 (tptp.pp P2))) (= (tptp.pp (tptp.aa_rat_bool P (tptp.zero_n2052037380579107095ol_rat P2))) (not (or (and _let_1 (not (tptp.pp (tptp.aa_rat_bool P tptp.one_one_rat)))) (and (not _let_1) (not (tptp.pp (tptp.aa_rat_bool P tptp.zero_zero_rat))))))))) (forall ((P tptp.fun_nat_bool) (P2 tptp.bool)) (let ((_let_1 (tptp.pp P2))) (= (tptp.pp (tptp.aa_nat_bool P (tptp.aa_bool_nat tptp.zero_n2687167440665602831ol_nat P2))) (not (or (and _let_1 (not (tptp.pp (tptp.aa_nat_bool P tptp.one_one_nat)))) (and (not _let_1) (not (tptp.pp (tptp.aa_nat_bool P tptp.zero_zero_nat))))))))) (forall ((P tptp.fun_int_bool) (P2 tptp.bool)) (let ((_let_1 (tptp.pp P2))) (= (tptp.pp (tptp.aa_int_bool P (tptp.aa_bool_int tptp.zero_n2684676970156552555ol_int P2))) (not (or (and _let_1 (not (tptp.pp (tptp.aa_int_bool P tptp.one_one_int)))) (and (not _let_1) (not (tptp.pp (tptp.aa_int_bool P tptp.zero_zero_int))))))))) (forall ((P tptp.fun_Co8822979462182099027r_bool) (P2 tptp.bool)) (let ((_let_1 (tptp.pp P2))) (= (tptp.pp (tptp.aa_Code_integer_bool P (tptp.aa_bool_Code_integer tptp.zero_n356916108424825756nteger P2))) (not (or (and _let_1 (not (tptp.pp (tptp.aa_Code_integer_bool P tptp.one_one_Code_integer)))) (and (not _let_1) (not (tptp.pp (tptp.aa_Code_integer_bool P tptp.zero_z3403309356797280102nteger))))))))) (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.one_one_real))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N) M)) (=> (not (= N tptp.zero_zero_nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real _let_1 (tptp.aa_nat_real tptp.semiri5074537144036343181t_real M))) (tptp.aa_real_real _let_1 (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N)))))))) (forall ((N tptp.nat) (M tptp.nat)) (=> (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.divide_divide_rat tptp.one_one_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat M))) (tptp.divide_divide_rat tptp.one_one_rat (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_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 ((Q5 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 Q5)) 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 Q5)))) (tptp.pp (tptp.aa_nat_bool P Q5)))))))) (forall ((N tptp.num)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_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.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 ((N tptp.num)) (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_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.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 ((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 ((P tptp.fun_int_bool) (X tptp.nat) (Y tptp.nat)) (= (tptp.pp (tptp.aa_int_bool P (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat X) Y)))) (and (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Y) X)) (tptp.pp (tptp.aa_int_bool P (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int X)) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int Y))))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Y)) (tptp.pp (tptp.aa_int_bool P tptp.zero_zero_int)))))) (forall ((A tptp.int) (B tptp.int) (Q2 tptp.int) (R tptp.int)) (=> (= A (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B) Q2)) R)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) R)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int R) 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) (R tptp.int)) (=> (= A (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B) Q2)) R)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int R) tptp.zero_zero_int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B) R)) (= (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 ((I4 tptp.int) (J3 tptp.int)) (=> (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) J3)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int J3) K)) (= N (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int K) I4)) J3))) (tptp.pp (tptp.aa_int_bool P I4))))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int K) tptp.zero_zero_int)) (forall ((I4 tptp.int) (J3 tptp.int)) (=> (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int K) J3)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int J3) tptp.zero_zero_int)) (= N (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int K) I4)) J3))) (tptp.pp (tptp.aa_int_bool P I4)))))))) _let_178 _let_177 _let_176 _let_175 (not (tptp.pp (tptp.aa_real_bool _let_133 tptp.zero_zero_real))) (not (tptp.pp (tptp.aa_rat_bool _let_131 tptp.zero_zero_rat))) (not (tptp.pp (tptp.aa_nat_bool _let_179 tptp.zero_zero_nat))) (not (tptp.pp (tptp.aa_int_bool _let_132 tptp.zero_zero_int))) _let_178 _let_177 _let_176 _let_175 (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 ((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)) (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.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 ((X tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) Y)) tptp.zero_zero_real)) (or (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y) tptp.zero_zero_real))))) (forall ((X tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat X) Y)) tptp.zero_zero_rat)) (or (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Y) tptp.zero_zero_rat))))) (forall ((X tptp.int) (Y tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int X) Y)) tptp.zero_zero_int)) (or (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Y) tptp.zero_zero_int))))) (forall ((A tptp.real) (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.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 ((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.divide_divide_rat A C)) (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_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.divide_divide_rat A C)) (tptp.divide_divide_rat B C)))))) (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.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) (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.divide_divide_rat A C)) (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 (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.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 ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool _let_1 X)) (=> (tptp.pp (tptp.aa_real_bool _let_1 Y)) (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real X) Y))))))) (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 X)) (=> (tptp.pp (tptp.aa_rat_bool _let_1 Y)) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.divide_divide_rat X Y))))))) (forall ((X tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real X) Y)) tptp.zero_zero_real))))) (forall ((X tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) X)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Y) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.divide_divide_rat X Y)) tptp.zero_zero_rat))))) (forall ((X tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) tptp.zero_zero_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) Y)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real X) Y)) tptp.zero_zero_real))))) (forall ((X tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) tptp.zero_zero_rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) Y)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.divide_divide_rat X Y)) tptp.zero_zero_rat))))) (forall ((X tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) tptp.zero_zero_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real X) Y)))))) (forall ((X tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) tptp.zero_zero_rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Y) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) (tptp.divide_divide_rat X Y)))))) (forall ((N tptp.num)) (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_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.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 ((N tptp.num)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.numeral_numeral_real N)))) (forall ((N tptp.num)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.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)) (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.numeral_numeral_real N)) tptp.zero_zero_real)))) (forall ((N tptp.num)) (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.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 ((A tptp.real) (N tptp.nat)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool _let_1 A)) (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real A) N)))))) (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 A)) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_nat_rat (tptp.power_power_rat A) N)))))) (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 A)) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A) N)))))) (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int))) (=> (tptp.pp (tptp.aa_int_bool _let_1 A)) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_nat_int (tptp.power_power_int A) N)))))) (forall ((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 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 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) (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)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) A)))) (forall ((A tptp.rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) A)))) (forall ((A tptp.int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) A)))) (forall ((A tptp.real) (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 ((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 ((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 ((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 ((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)) (=> (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) (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) (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 ((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 ((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 ((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) (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)) (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))) (= (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))) (=> (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))) (=> (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))) (=> (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_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)) (=> (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 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 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 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 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)) (=> (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)) (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)) (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) (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) (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)) (=> (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 ((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)))) _let_174 _let_173 _let_172 _let_170 _let_174 _let_173 _let_172 _let_170 (not (tptp.pp (tptp.aa_real_bool _let_136 tptp.zero_zero_real))) (not (tptp.pp (tptp.aa_rat_bool _let_135 tptp.zero_zero_rat))) (not (tptp.pp (tptp.aa_nat_bool _let_169 tptp.zero_zero_nat))) (not (tptp.pp (tptp.aa_int_bool _let_134 tptp.zero_zero_int))) (forall ((X tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) tptp.zero_zero_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y) tptp.zero_zero_real)) (= (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) Y) tptp.zero_zero_real) (and (= X tptp.zero_zero_real) (= Y tptp.zero_zero_real)))))) (forall ((X tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) tptp.zero_zero_rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat Y) tptp.zero_zero_rat)) (= (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat X) Y) tptp.zero_zero_rat) (and (= X tptp.zero_zero_rat) (= Y tptp.zero_zero_rat)))))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X) tptp.zero_zero_nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Y) tptp.zero_zero_nat)) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat X) Y) tptp.zero_zero_nat) (and (= X tptp.zero_zero_nat) (= Y tptp.zero_zero_nat)))))) (forall ((X tptp.int) (Y tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X) tptp.zero_zero_int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Y) tptp.zero_zero_int)) (= (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int X) Y) tptp.zero_zero_int) (and (= X tptp.zero_zero_int) (= Y tptp.zero_zero_int)))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool _let_1 X)) (=> (tptp.pp (tptp.aa_real_bool _let_1 Y)) (= (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) Y) tptp.zero_zero_real) (and (= X tptp.zero_zero_real) (= Y tptp.zero_zero_real))))))) (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 X)) (=> (tptp.pp (tptp.aa_rat_bool _let_1 Y)) (= (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat X) Y) tptp.zero_zero_rat) (and (= X tptp.zero_zero_rat) (= Y tptp.zero_zero_rat))))))) (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 X)) (=> (tptp.pp (tptp.aa_nat_bool _let_1 Y)) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat X) Y) tptp.zero_zero_nat) (and (= X tptp.zero_zero_nat) (= Y tptp.zero_zero_nat))))))) (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.pp (tptp.aa_int_bool _let_1 X)) (=> (tptp.pp (tptp.aa_int_bool _let_1 Y)) (= (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int X) Y) tptp.zero_zero_int) (and (= X tptp.zero_zero_int) (= Y tptp.zero_zero_int))))))) (forall ((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)) (=> (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)) (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 ((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 ((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) (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) (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 ((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 ((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) (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) (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 ((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) (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.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 ((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.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) (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.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)) (= (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)))) (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.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 ((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)))) (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 ((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.divide_divide_rat B C)) (tptp.divide_divide_rat A C)))))) (forall ((X tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) tptp.zero_zero_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real X) Y)))))) (forall ((X tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) tptp.zero_zero_rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat Y) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.divide_divide_rat X Y)))))) (forall ((X tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) tptp.zero_zero_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) Y)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real X) Y)) tptp.zero_zero_real))))) (forall ((X tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) tptp.zero_zero_rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) Y)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.divide_divide_rat X Y)) tptp.zero_zero_rat))))) (forall ((X tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real X) Y)) tptp.zero_zero_real))))) (forall ((X tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) X)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat Y) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.divide_divide_rat X Y)) tptp.zero_zero_rat))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool _let_1 X)) (=> (tptp.pp (tptp.aa_real_bool _let_1 Y)) (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real X) Y))))))) (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 X)) (=> (tptp.pp (tptp.aa_rat_bool _let_1 Y)) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.divide_divide_rat X Y))))))) (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 ((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.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) (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) (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.divide_divide_rat A C)) (tptp.divide_divide_rat B C)))))) (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)) (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.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 ((N tptp.num)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.one_one_real) (tptp.numeral_numeral_real N)))) (forall ((N tptp.num)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.one_one_rat) (tptp.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 ((A tptp.real) (N tptp.nat)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool _let_1 A)) (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real A) N)))))) (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 A)) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_nat_rat (tptp.power_power_rat A) N)))))) (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 A)) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A) N)))))) (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.pp (tptp.aa_int_bool _let_1 A)) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_nat_int (tptp.power_power_int A) N)))))) (forall ((A tptp.real) (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) (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.aa_nat_fun_nat_nat tptp.power_power_nat A) N)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat 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 ((D tptp.code_integer) (S tptp.code_integer)) (exists ((Z4 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.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.plus_p5714425477246183910nteger X4) S))))) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger Z4) X4)) (= _let_1 _let_1)))))) (forall ((D tptp.real) (S tptp.real)) (exists ((Z4 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) S))))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Z4) X4)) (= _let_1 _let_1)))))) (forall ((D tptp.rat) (S tptp.rat)) (exists ((Z4 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) S))))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Z4) X4)) (= _let_1 _let_1)))))) (forall ((D tptp.nat) (S tptp.nat)) (exists ((Z4 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) S))))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Z4) X4)) (= _let_1 _let_1)))))) (forall ((D tptp.int) (S tptp.int)) (exists ((Z4 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) S))))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Z4) X4)) (= _let_1 _let_1)))))) (forall ((D tptp.code_integer) (S tptp.code_integer)) (exists ((Z4 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.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.plus_p5714425477246183910nteger X4) S)))))) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger Z4) X4)) (= _let_1 _let_1)))))) (forall ((D tptp.real) (S tptp.real)) (exists ((Z4 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) S)))))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Z4) X4)) (= _let_1 _let_1)))))) (forall ((D tptp.rat) (S tptp.rat)) (exists ((Z4 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) S)))))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Z4) X4)) (= _let_1 _let_1)))))) (forall ((D tptp.nat) (S tptp.nat)) (exists ((Z4 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) S)))))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Z4) X4)) (= _let_1 _let_1)))))) (forall ((D tptp.int) (S tptp.int)) (exists ((Z4 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) S)))))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Z4) X4)) (= _let_1 _let_1)))))) (forall ((D tptp.code_integer) (S tptp.code_integer)) (exists ((Z4 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.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.plus_p5714425477246183910nteger X4) S))))) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger X4) Z4)) (= _let_1 _let_1)))))) (forall ((D tptp.real) (S tptp.real)) (exists ((Z4 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) S))))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X4) Z4)) (= _let_1 _let_1)))))) (forall ((D tptp.rat) (S tptp.rat)) (exists ((Z4 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) S))))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X4) Z4)) (= _let_1 _let_1)))))) (forall ((D tptp.nat) (S tptp.nat)) (exists ((Z4 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) S))))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X4) Z4)) (= _let_1 _let_1)))))) (forall ((D tptp.int) (S tptp.int)) (exists ((Z4 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) S))))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X4) Z4)) (= _let_1 _let_1)))))) (forall ((D tptp.code_integer) (S tptp.code_integer)) (exists ((Z4 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.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.plus_p5714425477246183910nteger X4) S)))))) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger X4) Z4)) (= _let_1 _let_1)))))) (forall ((D tptp.real) (S tptp.real)) (exists ((Z4 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) S)))))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X4) Z4)) (= _let_1 _let_1)))))) (forall ((D tptp.rat) (S tptp.rat)) (exists ((Z4 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) S)))))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X4) Z4)) (= _let_1 _let_1)))))) (forall ((D tptp.nat) (S tptp.nat)) (exists ((Z4 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) S)))))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X4) Z4)) (= _let_1 _let_1)))))) (forall ((D tptp.int) (S tptp.int)) (exists ((Z4 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) S)))))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X4) Z4)) (= _let_1 _let_1)))))) (forall ((I tptp.real) (K tptp.real) (N tptp.real) (J tptp.real)) (let ((_let_1 (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real N) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real J) K))))) (let ((_let_2 (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real I) K)) N)))) (=> _let_2 (=> _let_1 (=> _let_2 (=> _let_1 (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real N) K)) J))))))))) (forall ((I tptp.rat) (K tptp.rat) (N tptp.rat) (J tptp.rat)) (let ((_let_1 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat N) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat J) K))))) (let ((_let_2 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat I) K)) N)))) (=> _let_2 (=> _let_1 (=> _let_2 (=> _let_1 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.minus_minus_rat N K)) J))))))))) (forall ((I tptp.nat) (K tptp.nat) (N tptp.nat) (J tptp.nat)) (let ((_let_1 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat J) K))))) (let ((_let_2 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat I) K)) N)))) (=> _let_2 (=> _let_1 (=> _let_2 (=> _let_1 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) K)) J))))))))) (forall ((I tptp.int) (K tptp.int) (N tptp.int) (J tptp.int)) (let ((_let_1 (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int N) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int J) K))))) (let ((_let_2 (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int I) K)) N)))) (=> _let_2 (=> _let_1 (=> _let_2 (=> _let_1 (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int N) K)) J))))))))) (forall ((I tptp.real) (K tptp.real) (N tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real I) K)) N)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real I) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real N) K))))) (forall ((I tptp.rat) (K tptp.rat) (N tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat I) K)) N)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat I) (tptp.minus_minus_rat N K))))) (forall ((I tptp.nat) (K tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat I) K)) N)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) K))))) (forall ((I tptp.int) (K tptp.int) (N tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int I) K)) N)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int I) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int N) K))))) (forall ((A tptp.real) (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) (B tptp.rat) (C tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_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) (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.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.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.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 ((N tptp.nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N)))) (forall ((N tptp.nat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat N)))) (forall ((N tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat N)))) (forall ((N tptp.nat)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N)))) (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.one_one_real))) (=> (tptp.pp (tptp.aa_real_bool _let_1 A)) (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real A) N)))))) (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.one_one_rat))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 A)) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_nat_rat (tptp.power_power_rat A) N)))))) (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.one_one_nat))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 A)) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A) N)))))) (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.one_one_int))) (=> (tptp.pp (tptp.aa_int_bool _let_1 A)) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_nat_int (tptp.power_power_int A) N)))))) (forall ((N tptp.nat) (P tptp.fun_nat_bool)) (= (exists ((I4 tptp.nat)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I4) (tptp.aa_nat_nat tptp.suc N))) (tptp.pp (tptp.aa_nat_bool P I4)))) (or (tptp.pp (tptp.aa_nat_bool P tptp.zero_zero_nat)) (exists ((I4 tptp.nat)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I4) N)) (tptp.pp (tptp.aa_nat_bool P (tptp.aa_nat_nat tptp.suc I4)))))))) (forall ((N tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (exists ((M6 tptp.nat)) (= N (tptp.aa_nat_nat tptp.suc M6))))) (forall ((N tptp.nat) (P tptp.fun_nat_bool)) (= (forall ((I4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I4) (tptp.aa_nat_nat tptp.suc N))) (tptp.pp (tptp.aa_nat_bool P I4)))) (and (tptp.pp (tptp.aa_nat_bool P tptp.zero_zero_nat)) (forall ((I4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I4) N)) (tptp.pp (tptp.aa_nat_bool P (tptp.aa_nat_nat tptp.suc I4)))))))) (forall ((N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (exists ((M2 tptp.nat)) (= N (tptp.aa_nat_nat tptp.suc M2))))) (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 ((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.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_nat_nat _let_1 M)) (tptp.aa_nat_nat _let_1 N)))))) (forall ((M tptp.nat) (N tptp.nat) (A tptp.real)) (let ((_let_1 (tptp.aa_real_fun_nat_real tptp.power_power_real A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.dvd_dvd_real (tptp.aa_nat_real _let_1 M)) (tptp.aa_nat_real _let_1 N)))))) (forall ((M tptp.nat) (N tptp.nat) (A tptp.int)) (let ((_let_1 (tptp.power_power_int A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_nat_int _let_1 M)) (tptp.aa_nat_int _let_1 N)))))) (forall ((M tptp.nat) (N tptp.nat) (A tptp.complex)) (let ((_let_1 (tptp.power_power_complex A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)) (tptp.pp (tptp.aa_complex_bool (tptp.dvd_dvd_complex (tptp.aa_nat_complex _let_1 M)) (tptp.aa_nat_complex _let_1 N)))))) (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.nat) (N tptp.nat) (B tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_nat_nat _let_1 N)) 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.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.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.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 ((X tptp.code_integer) (Y tptp.code_integer) (N tptp.nat) (M tptp.nat)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer X) Y)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N) M)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.power_8256067586552552935nteger X N)) (tptp.power_8256067586552552935nteger Y M)))))) (forall ((X tptp.nat) (Y tptp.nat) (N tptp.nat) (M tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat X) Y)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N) M)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat X) N)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat Y) M)))))) (forall ((X tptp.real) (Y tptp.real) (N tptp.nat) (M tptp.nat)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.dvd_dvd_real X) Y)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N) M)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.dvd_dvd_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) N)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Y) M)))))) (forall ((X tptp.int) (Y tptp.int) (N tptp.nat) (M tptp.nat)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int X) Y)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N) M)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_nat_int (tptp.power_power_int X) N)) (tptp.aa_nat_int (tptp.power_power_int Y) M)))))) (forall ((X tptp.complex) (Y tptp.complex) (N tptp.nat) (M tptp.nat)) (=> (tptp.pp (tptp.aa_complex_bool (tptp.dvd_dvd_complex X) Y)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N) M)) (tptp.pp (tptp.aa_complex_bool (tptp.dvd_dvd_complex (tptp.aa_nat_complex (tptp.power_power_complex X) N)) (tptp.aa_nat_complex (tptp.power_power_complex Y) 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 ((Q6 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) Q6)))))))) (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 ((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 ((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) (J tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I) J)) (exists ((K3 tptp.nat)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) K3)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat I) K3) J))))) (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 ((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_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 (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 ((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 ((N tptp.nat) (M tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N) M)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat tptp.suc M)) N) (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) N))))) (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat tptp.suc K)))) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat _let_1 M)) (tptp.aa_nat_nat _let_1 N))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N))))) (forall ((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 ((R2 tptp.real)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) R2)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real R2) (tptp.aa_nat_nat tptp.suc N)) A))))) (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 ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 N)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat M) N)) (tptp.pp (tptp.aa_nat_bool _let_1 M)))))) (forall ((M tptp.nat) (N tptp.nat)) (=> (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) N)) M))) (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat J) K))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat I) K)) J)))) (forall ((I tptp.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 ((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 ((M tptp.nat) (N tptp.nat)) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat M) N) tptp.zero_zero_nat) (or (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N)) (= N tptp.zero_zero_nat)))) (forall ((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 ((I tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat I))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) I)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat _let_1 M)) (tptp.aa_nat_nat _let_1 N))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N)))))) (forall ((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 ((I2 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int K) I2)) (=> (tptp.pp (tptp.aa_int_bool P I2)) (tptp.pp (tptp.aa_int_bool P (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int I2) 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)) (=> (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 ((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 ((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 ((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 ((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))))))) (forall ((M tptp.int) (N tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) M)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int M) N)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int N) M)))))) (forall ((K tptp.int) (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 ((I2 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int K) I2)) (=> (tptp.pp (tptp.aa_int_bool P I2)) (tptp.pp (tptp.aa_int_bool P (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int I2) tptp.one_one_int)))))) (tptp.pp (tptp.aa_int_bool P I)))))) (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 ((I2 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int I2) K)) (=> (tptp.pp (tptp.aa_int_bool P I2)) (tptp.pp (tptp.aa_int_bool P (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int I2) tptp.one_one_int)))))) (tptp.pp (tptp.aa_int_bool P I)))))) (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)) (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 ((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 ((X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) X)) (forall ((Y4 tptp.real)) (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 ((W tptp.int) (Z tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int W) Z)) (exists ((N5 tptp.nat)) (= Z (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int W) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N5)))))) (forall ((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 ((I2 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int I2) K)) (=> (tptp.pp (tptp.aa_int_bool P I2)) (tptp.pp (tptp.aa_int_bool P (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int I2) tptp.one_one_int)))))) (tptp.pp (tptp.aa_int_bool P I)))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) _let_1)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Y) _let_1))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) Y)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Y)))))) (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_nat_rat (tptp.power_power_rat X) _let_1)) (tptp.aa_nat_rat (tptp.power_power_rat Y) _let_1))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) Y)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) Y)))))) (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat X) _let_1)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat Y) _let_1))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) Y)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Y)))))) (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_nat_int (tptp.power_power_int X) _let_1)) (tptp.aa_nat_int (tptp.power_power_int Y) _let_1))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) Y)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) Y)))))) (forall ((X tptp.num)) (= (tptp.pow X tptp.one) X)) (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 ((X tptp.real) (Y tptp.real)) (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real X) X)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real Y) Y))) tptp.zero_zero_real)))) (forall ((X tptp.rat) (Y tptp.rat)) (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat X) X)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat Y) Y))) tptp.zero_zero_rat)))) (forall ((X tptp.int) (Y tptp.int)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int X) X)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int Y) Y))) tptp.zero_zero_int)))) (forall ((X tptp.real) (Y tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real X) X)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real Y) Y)))) (or (not (= X tptp.zero_zero_real)) (not (= Y tptp.zero_zero_real))))) (forall ((X tptp.rat) (Y tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat X) X)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat Y) Y)))) (or (not (= X tptp.zero_zero_rat)) (not (= Y tptp.zero_zero_rat))))) (forall ((X tptp.int) (Y tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int X) X)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int Y) Y)))) (or (not (= X tptp.zero_zero_int)) (not (= Y tptp.zero_zero_int))))) (tptp.pp (tptp.aa_real_bool _let_105 _let_168)) (tptp.pp (tptp.aa_rat_bool _let_119 _let_167)) (tptp.pp (tptp.aa_nat_bool _let_163 _let_166)) (tptp.pp (tptp.aa_int_bool _let_120 _let_164)) (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.aa_nat_fun_nat_nat 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 ((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.aa_nat_fun_nat_nat 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 ((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)) (=> (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.divide_divide_rat C A)) (tptp.divide_divide_rat C B))))))) (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.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_1 C)) (=> (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 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.divide_divide_rat C A)) (tptp.divide_divide_rat C B)))))))) (forall ((Y tptp.real) (Z tptp.real) (X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) Y)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real Z) Y)) X)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Z) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real X) Y)))))) (forall ((Y tptp.rat) (Z tptp.rat) (X tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) Y)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat Z) Y)) X)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Z) (tptp.divide_divide_rat X Y)))))) (forall ((Y tptp.real) (X tptp.real) (Z tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) Y)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real Z) Y))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real X) Y)) Z))))) (forall ((Y tptp.rat) (X tptp.rat) (Z tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) Y)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat Z) Y))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.divide_divide_rat X Y)) Z))))) (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.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 ((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.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 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.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 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.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 ((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.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 ((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.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 ((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.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.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 ((A tptp.real) (E 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) E)) C)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real B) E)) D))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A) B)) E)) C)) D)))) (forall ((A tptp.rat) (E 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) E)) C)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat B) E)) D))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.minus_minus_rat A B)) E)) C)) D)))) (forall ((A tptp.int) (E 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) E)) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B) E)) D))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) B)) E)) C)) D)))) (forall ((A tptp.real) (E 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) E)) C)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real B) E)) D))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real C) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real B) A)) E)) D))))) (forall ((A tptp.rat) (E 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) E)) C)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat B) E)) D))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat C) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.minus_minus_rat B A)) E)) D))))) (forall ((A tptp.int) (E 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) E)) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B) E)) D))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int C) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int B) A)) E)) D))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool _let_1 X)) (=> (tptp.pp (tptp.aa_real_bool _let_1 Y)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y) tptp.one_one_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real Y) X)) X))))))) (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 X)) (=> (tptp.pp (tptp.aa_rat_bool _let_1 Y)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat Y) tptp.one_one_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat Y) X)) X))))))) (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.pp (tptp.aa_int_bool _let_1 X)) (=> (tptp.pp (tptp.aa_int_bool _let_1 Y)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Y) tptp.one_one_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int Y) X)) X))))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool _let_1 X)) (=> (tptp.pp (tptp.aa_real_bool _let_1 Y)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y) tptp.one_one_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real X) Y)) X))))))) (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 X)) (=> (tptp.pp (tptp.aa_rat_bool _let_1 Y)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat Y) tptp.one_one_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat X) Y)) X))))))) (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.pp (tptp.aa_int_bool _let_1 X)) (=> (tptp.pp (tptp.aa_int_bool _let_1 Y)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Y) tptp.one_one_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int X) Y)) X))))))) (forall ((A tptp.real) (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 ((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 ((C tptp.real) (A tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real C) tptp.one_one_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) A)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) C)) A))))) (forall ((C tptp.rat) (A tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat C) tptp.one_one_rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) A)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) C)) A))))) (forall ((C tptp.nat) (A tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat C) tptp.one_one_nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) A)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) C)) A))))) (forall ((C tptp.int) (A tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int C) tptp.one_one_int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) A)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) C)) A))))) (forall ((X tptp.real) (Y tptp.real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real X) X)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real Y) Y))))) (forall ((X tptp.rat) (Y tptp.rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat X) X)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat Y) Y))))) (forall ((X tptp.int) (Y tptp.int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int X) X)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int Y) Y))))) (forall ((X tptp.real) (Y tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real X) X)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real Y) Y))) tptp.zero_zero_real)) (and (= X tptp.zero_zero_real) (= Y tptp.zero_zero_real)))) (forall ((X tptp.rat) (Y tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat X) X)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat Y) Y))) tptp.zero_zero_rat)) (and (= X tptp.zero_zero_rat) (= Y tptp.zero_zero_rat)))) (forall ((X tptp.int) (Y tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int X) X)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int Y) Y))) tptp.zero_zero_int)) (and (= X tptp.zero_zero_int) (= Y tptp.zero_zero_int)))) (forall ((X tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) X)) (exists ((N2 tptp.nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N2)) X)))))) (forall ((X tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) X)) (exists ((N2 tptp.nat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Y) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat N2)) X)))))) (forall ((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.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.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 ((A tptp.real) (N tptp.nat)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real))) (=> (tptp.pp (tptp.aa_real_bool _let_1 A)) (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real A) N))))))) (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.one_one_rat))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 A)) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) (tptp.aa_nat_rat (tptp.power_power_rat A) N))))))) (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.one_one_nat))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 A)) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A) N))))))) (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.one_one_int))) (=> (tptp.pp (tptp.aa_int_bool _let_1 A)) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) (tptp.aa_nat_int (tptp.power_power_int A) N))))))) (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real A) N))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real) A)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real _let_1) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) _let_1)))))) (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_rat (tptp.power_power_rat A) N))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.one_one_rat) A)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat _let_1) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) _let_1)))))) (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A) N))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.one_one_nat) A)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_1) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) _let_1)))))) (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_int (tptp.power_power_int A) N))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.one_one_int) A)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int _let_1) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) _let_1)))))) (forall ((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 ((A tptp.real) (N tptp.nat)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) A)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) tptp.one_one_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real A) N)) tptp.one_one_real))))) (forall ((A tptp.rat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) A)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) tptp.one_one_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat (tptp.power_power_rat A) N)) tptp.one_one_rat))))) (forall ((A tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) A)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) tptp.one_one_nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A) N)) tptp.one_one_nat))))) (forall ((A tptp.int) (N tptp.nat)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) A)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) tptp.one_one_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int (tptp.power_power_int A) N)) tptp.one_one_int))))) (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real))) (=> (tptp.pp (tptp.aa_real_bool _let_1 A)) (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real A) (tptp.aa_nat_nat tptp.suc N))))))) (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.one_one_rat))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 A)) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_nat_rat (tptp.power_power_rat A) (tptp.aa_nat_nat tptp.suc N))))))) (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.one_one_nat))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 A)) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A) (tptp.aa_nat_nat tptp.suc N))))))) (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.one_one_int))) (=> (tptp.pp (tptp.aa_int_bool _let_1 A)) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_nat_int (tptp.power_power_int A) (tptp.aa_nat_nat tptp.suc N))))))) (forall ((A tptp.real) (E 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) E)) C)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real B) E)) D))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A) B)) E)) C)) D)))) (forall ((A tptp.rat) (E 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) E)) C)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat B) E)) D))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.minus_minus_rat A B)) E)) C)) D)))) (forall ((A tptp.int) (E 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) E)) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B) E)) D))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) B)) E)) C)) D)))) (forall ((A tptp.real) (E 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) E)) C)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real B) E)) D))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real C) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real B) A)) E)) D))))) (forall ((A tptp.rat) (E 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) E)) C)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat B) E)) D))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat C) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.minus_minus_rat B A)) E)) D))))) (forall ((A tptp.int) (E 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) E)) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B) E)) D))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int C) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int B) A)) E)) D))))) (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.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.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.aa_nat_fun_nat_nat tptp.power_power_nat A) _let_2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat 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_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_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.aa_nat_fun_nat_nat tptp.power_power_nat A) _let_1)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat 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 ((N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (= (tptp.aa_nat_rat (tptp.power_power_rat tptp.zero_zero_rat) N) tptp.zero_zero_rat))) (forall ((N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat tptp.zero_zero_nat) N) tptp.zero_zero_nat))) (forall ((N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real tptp.zero_zero_real) N) tptp.zero_zero_real))) (forall ((N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (= (tptp.aa_nat_int (tptp.power_power_int tptp.zero_zero_int) N) tptp.zero_zero_int))) (forall ((N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (= (tptp.aa_nat_complex (tptp.power_power_complex tptp.zero_zero_complex) N) tptp.zero_zero_complex))) (forall ((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 ((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.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 ((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 ((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 ((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 ((N tptp.nat) (K tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)) N)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat K) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat N) K))))) (forall ((W tptp.int) (Z tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int W) Z)) (exists ((N5 tptp.nat)) (= Z (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int W) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_nat tptp.suc N5))))))) (forall ((I tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 I)) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat I) N)))))) (forall ((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 ((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 ((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 ((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 ((J tptp.nat) (I tptp.nat) (U tptp.nat) (M tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat J) I)) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat I) U)) M) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat J) U)) N)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat I) J)) U)) M) N)))) (forall ((I tptp.nat) (J tptp.nat) (U tptp.nat) (M tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I) J)) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat I) U)) M) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat J) U)) N)) (= M (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat J) I)) U)) N))))) (forall ((J tptp.nat) (I tptp.nat) (U tptp.nat) (M tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat J) I)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat I) U)) M)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat J) U)) N))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat I) J)) U)) M)) N))))) (forall ((I tptp.nat) (J tptp.nat) (U tptp.nat) (M tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I) J)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat I) U)) M)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat J) U)) N))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat J) I)) U)) N)))))) (forall ((J tptp.nat) (I tptp.nat) (U tptp.nat) (M tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat J) I)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat I) U)) M)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat J) U)) N)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat I) J)) U)) M)) N)))) (forall ((I tptp.nat) (J tptp.nat) (U tptp.nat) (M tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I) J)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat I) U)) M)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat J) U)) N)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat J) I)) U)) N))))) (forall ((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 ((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 ((D tptp.int) (P3 tptp.fun_int_bool) (P tptp.fun_int_bool)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) D)) (=> (forall ((X3 tptp.int) (K3 tptp.int)) (= (tptp.pp (tptp.aa_int_bool P3 X3)) (tptp.pp (tptp.aa_int_bool P3 (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 K3) 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 P3 X3)))))) (=> (exists ((X_1 tptp.int)) (tptp.pp (tptp.aa_int_bool P3 X_1))) (exists ((X_12 tptp.int)) (tptp.pp (tptp.aa_int_bool P X_12)))))))) (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) (K3 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 K3) 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_1 tptp.int)) (tptp.pp (tptp.aa_int_bool P1 X_1))) (exists ((X_12 tptp.int)) (tptp.pp (tptp.aa_int_bool P X_12)))))))) (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 ((P tptp.fun_int_bool) (K tptp.int) (I tptp.int)) (=> (tptp.pp (tptp.aa_int_bool P K)) (=> (forall ((I2 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int K) I2)) (=> (tptp.pp (tptp.aa_int_bool P I2)) (tptp.pp (tptp.aa_int_bool P (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int I2) tptp.one_one_int)))))) (=> (forall ((I2 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int I2) K)) (=> (tptp.pp (tptp.aa_int_bool P I2)) (tptp.pp (tptp.aa_int_bool P (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int I2) tptp.one_one_int)))))) (tptp.pp (tptp.aa_int_bool P I)))))) (forall ((N tptp.nat) (X tptp.nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat N) X))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N)) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real X))))) (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N)))) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real A) N)) tptp.zero_zero_real)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (or (and (not _let_1) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) tptp.zero_zero_real))) (and _let_1 (= A tptp.zero_zero_real))))))) (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N)))) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat (tptp.power_power_rat A) N)) tptp.zero_zero_rat)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (or (and (not _let_1) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) tptp.zero_zero_rat))) (and _let_1 (= A tptp.zero_zero_rat))))))) (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N)))) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int (tptp.power_power_int A) N)) tptp.zero_zero_int)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (or (and (not _let_1) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) tptp.zero_zero_int))) (and _let_1 (= A tptp.zero_zero_int))))))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_2 (tptp.aa_nat_nat _let_1 M))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat _let_2) (tptp.aa_nat_nat _let_1 N)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.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.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger 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 ((W tptp.num) (B tptp.real) (C tptp.real)) (let ((_let_1 (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.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.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 ((B tptp.real) (C tptp.real) (W tptp.num)) (let ((_let_1 (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.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.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 ((Y tptp.real) (Z tptp.real) (X tptp.real) (W tptp.real)) (=> (not (= Y tptp.zero_zero_real)) (=> (not (= Z tptp.zero_zero_real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real X) Y)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real W) Z))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real X) Z)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real W) Y))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real Y) Z))) tptp.zero_zero_real)))))) (forall ((Y tptp.rat) (Z tptp.rat) (X tptp.rat) (W tptp.rat)) (=> (not (= Y tptp.zero_zero_rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.divide_divide_rat X Y)) (tptp.divide_divide_rat W Z))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.divide_divide_rat (tptp.minus_minus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat X) Z) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat W) Y)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat Y) Z))) tptp.zero_zero_rat)))))) (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real A) N))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) A)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) tptp.one_one_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) _let_1)) _let_1)))))) (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_rat (tptp.power_power_rat A) N))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) A)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) tptp.one_one_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) _let_1)) _let_1)))))) (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A) N))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) A)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) tptp.one_one_nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) _let_1)) _let_1)))))) (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_int (tptp.power_power_int A) N))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) A)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) tptp.one_one_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) _let_1)) _let_1)))))) (forall ((A tptp.real) (N tptp.nat)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) A)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) tptp.one_one_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real A) (tptp.aa_nat_nat tptp.suc N))) tptp.one_one_real))))) (forall ((A tptp.rat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) A)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) tptp.one_one_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_nat_rat (tptp.power_power_rat A) (tptp.aa_nat_nat tptp.suc N))) tptp.one_one_rat))))) (forall ((A tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) A)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) tptp.one_one_nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A) (tptp.aa_nat_nat tptp.suc N))) tptp.one_one_nat))))) (forall ((A tptp.int) (N tptp.nat)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) A)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) tptp.one_one_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_nat_int (tptp.power_power_int A) (tptp.aa_nat_nat tptp.suc N))) tptp.one_one_int))))) (forall ((X tptp.real) (A tptp.real) (Y tptp.real) (U tptp.real) (V tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) A)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y) A)) (=> (tptp.pp (tptp.aa_real_bool _let_1 U)) (=> (tptp.pp (tptp.aa_real_bool _let_1 V)) (=> (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real U) V) tptp.one_one_real) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real U) X)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real V) Y))) A))))))))) (forall ((X tptp.rat) (A tptp.rat) (Y tptp.rat) (U tptp.rat) (V tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) A)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat Y) A)) (=> (tptp.pp (tptp.aa_rat_bool _let_1 U)) (=> (tptp.pp (tptp.aa_rat_bool _let_1 V)) (=> (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat U) V) tptp.one_one_rat) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat U) X)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat V) Y))) A))))))))) (forall ((X tptp.int) (A tptp.int) (Y tptp.int) (U tptp.int) (V tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X) A)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Y) A)) (=> (tptp.pp (tptp.aa_int_bool _let_1 U)) (=> (tptp.pp (tptp.aa_int_bool _let_1 V)) (=> (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int U) V) tptp.one_one_int) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int U) X)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int V) Y))) A))))))))) (forall ((Y tptp.real) (Z tptp.real) (X tptp.real) (W tptp.real)) (=> (not (= Y tptp.zero_zero_real)) (=> (not (= Z tptp.zero_zero_real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real X) Y)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real W) Z))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real X) Z)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real W) Y))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real Y) Z))) tptp.zero_zero_real)))))) (forall ((Y tptp.rat) (Z tptp.rat) (X tptp.rat) (W tptp.rat)) (=> (not (= Y tptp.zero_zero_rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.divide_divide_rat X Y)) (tptp.divide_divide_rat W Z))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.divide_divide_rat (tptp.minus_minus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat X) Z) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat W) Y)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat Y) Z))) tptp.zero_zero_rat)))))) (forall ((A tptp.real) (N tptp.nat)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) A)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) tptp.one_one_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real A) (tptp.aa_nat_nat tptp.suc N))) A))))) (forall ((A tptp.rat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) A)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) tptp.one_one_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat (tptp.power_power_rat A) (tptp.aa_nat_nat tptp.suc N))) A))))) (forall ((A tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) A)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) tptp.one_one_nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A) (tptp.aa_nat_nat tptp.suc N))) A))))) (forall ((A tptp.int) (N tptp.nat)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) A)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) tptp.one_one_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int (tptp.power_power_int A) (tptp.aa_nat_nat tptp.suc N))) A))))) (forall ((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.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat X))) (=> (not (= X tptp.zero_zero_nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_nat_nat _let_1 M)) (tptp.aa_nat_nat _let_1 N))) (or (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat X) tptp.one_one_nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N))))))) (forall ((X tptp.int) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.power_power_int X))) (=> (not (= X tptp.zero_zero_int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_nat_int _let_1 M)) (tptp.aa_nat_int _let_1 N))) (or (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int X) tptp.one_one_int)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N))))))) (tptp.pp (tptp.aa_nat_bool _let_163 _let_2)) (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.nat)) (=> (or (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (= X tptp.one_one_nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat X) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat X) N))))) (forall ((N tptp.nat) (X tptp.real)) (=> (or (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (= X tptp.one_one_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.dvd_dvd_real X) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) N))))) (forall ((N tptp.nat) (X tptp.int)) (=> (or (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (= X tptp.one_one_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int X) (tptp.aa_nat_int (tptp.power_power_int X) N))))) (forall ((N tptp.nat) (X tptp.complex)) (=> (or (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (= X tptp.one_one_complex)) (tptp.pp (tptp.aa_complex_bool (tptp.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.divide_divide_rat (tptp.aa_nat_rat _let_1 M) (tptp.aa_nat_rat _let_1 N))))))) (forall ((A tptp.nat) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A))) (=> (not (= A tptp.zero_zero_nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N) M)) (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) N)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat _let_1 M)) (tptp.aa_nat_nat _let_1 N))))))) (forall ((A tptp.int) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.power_power_int A))) (=> (not (= A tptp.zero_zero_int)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N) M)) (= (tptp.aa_nat_int _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) N)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int (tptp.aa_nat_int _let_1 M)) (tptp.aa_nat_int _let_1 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.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N)))) (forall ((M tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat M) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) N)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat M) _let_1)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat N) _let_1))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N))))) (forall ((K tptp.nat) (M tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) K)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat K) M))))) (forall ((N tptp.nat)) (tptp.pp (tptp.aa_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.numeral_numeral_real (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.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 ((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 ((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) (M tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat N) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat M) N))))))) (forall ((N tptp.nat) (M tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat M) N)) N)))))) (forall ((P tptp.fun_nat_bool) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (= N tptp.zero_zero_nat))) (= (tptp.pp (tptp.aa_nat_bool P (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat M) N))) (and (=> _let_1 (tptp.pp (tptp.aa_nat_bool P tptp.zero_zero_nat))) (=> (not _let_1) (forall ((I4 tptp.nat) (J3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat J3) N)) (=> (= M (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat N) I4)) J3)) (tptp.pp (tptp.aa_nat_bool P I4)))))))))) (forall ((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 ((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 ((Q2 tptp.nat) (N tptp.nat) (R tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat R) M))) (let ((_let_2 (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat M))) (let ((_let_3 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Q2))) (=> (tptp.pp (tptp.aa_nat_bool _let_3 N)) (=> (tptp.pp (tptp.aa_nat_bool _let_3 _let_1)) (= (tptp.pp (tptp.aa_nat_bool _let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) Q2))) (tptp.pp (tptp.aa_nat_bool _let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat _let_1) Q2))))))))))) (forall ((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.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger 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.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger 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.aa_nat_fun_nat_nat tptp.power_power_nat _let_1))) (let ((_let_3 (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat _let_1))) (let ((_let_4 (tptp.aa_nat_nat _let_2 N))) (= (tptp.pp (tptp.aa_nat_bool _let_3 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) (tptp.aa_nat_nat _let_2 M))) _let_4))) (or (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N) M)) (= _let_4 tptp.zero_zero_nat) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)) (tptp.pp (tptp.aa_nat_bool _let_3 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) (tptp.aa_nat_nat _let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) M))))))))))))) (forall ((A tptp.int) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.power_power_int _let_1))) (let ((_let_3 (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int _let_1))) (let ((_let_4 (tptp.aa_nat_int _let_2 N))) (= (tptp.pp (tptp.aa_int_bool _let_3 (tptp.aa_int_int (tptp.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) (X tptp.nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N)) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real X))) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat N) X)))))) (forall ((N tptp.nat) (X tptp.nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N)) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real X))) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat N) X)))) tptp.one_one_real))) (forall ((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.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.divide_divide_rat A (tptp.numeral_numeral_rat (tptp.aa_num_num tptp.bit0 tptp.one))))) (tptp.pp (tptp.aa_rat_bool _let_1 A))))) (forall ((A tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool _let_1 A)) (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real A) (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.divide_divide_rat A (tptp.numeral_numeral_rat (tptp.aa_num_num tptp.bit0 tptp.one)))))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X))) (=> (tptp.pp (tptp.aa_real_bool _let_1 Y)) (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) Y)) (tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))))))) (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 Y)) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.divide_divide_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat X) Y) (tptp.numeral_numeral_rat (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 ((E tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) E)) (not (forall ((N2 tptp.nat)) (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.one_one_real) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real (tptp.aa_nat_nat tptp.suc N2)))) E))))))) (forall ((E tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) E)) (not (forall ((N2 tptp.nat)) (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.divide_divide_rat tptp.one_one_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat (tptp.aa_nat_nat tptp.suc N2)))) E))))))) (forall ((U tptp.real) (V tptp.real) (R tptp.real) (S tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real U) V)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) R)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real R) S)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real U) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real R) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real V) U))) S))) V)))))) (forall ((U tptp.rat) (V tptp.rat) (R tptp.rat) (S tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat U) V)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) R)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat R) S)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat U) (tptp.divide_divide_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat R) (tptp.minus_minus_rat V U)) S))) V)))))) (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.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.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 ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) _let_1)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Y) _let_1))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) Y)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) Y)))))) (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat (tptp.power_power_rat X) _let_1)) (tptp.aa_nat_rat (tptp.power_power_rat Y) _let_1))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) Y)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) Y)))))) (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat X) _let_1)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat Y) _let_1))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) Y)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X) Y)))))) (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int (tptp.power_power_int X) _let_1)) (tptp.aa_nat_int (tptp.power_power_int Y) _let_1))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) Y)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X) Y)))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (let ((_let_2 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) _let_2) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Y) _let_2)) (=> (tptp.pp (tptp.aa_real_bool _let_1 X)) (=> (tptp.pp (tptp.aa_real_bool _let_1 Y)) (= X Y))))))) (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat))) (let ((_let_2 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (= (tptp.aa_nat_rat (tptp.power_power_rat X) _let_2) (tptp.aa_nat_rat (tptp.power_power_rat Y) _let_2)) (=> (tptp.pp (tptp.aa_rat_bool _let_1 X)) (=> (tptp.pp (tptp.aa_rat_bool _let_1 Y)) (= X Y))))))) (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat))) (let ((_let_2 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat X) _let_2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat Y) _let_2)) (=> (tptp.pp (tptp.aa_nat_bool _let_1 X)) (=> (tptp.pp (tptp.aa_nat_bool _let_1 Y)) (= X Y))))))) (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_2 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (= (tptp.aa_nat_int (tptp.power_power_int X) _let_2) (tptp.aa_nat_int (tptp.power_power_int Y) _let_2)) (=> (tptp.pp (tptp.aa_int_bool _let_1 X)) (=> (tptp.pp (tptp.aa_int_bool _let_1 Y)) (= X Y))))))) (forall ((A tptp.real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real A) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))))) (forall ((A tptp.rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_nat_rat (tptp.power_power_rat A) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))))) (forall ((A tptp.int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.aa_nat_int (tptp.power_power_int A) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))))) (= (tptp.size_num tptp.one) 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)) (=> (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 ((A tptp.nat) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A))) (let ((_let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat _let_1 M)) (tptp.aa_nat_nat _let_1 N)))) (let ((_let_3 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N) M)))) (=> (not (= A tptp.zero_zero_nat)) (and (=> _let_3 (= _let_2 (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) N)))) (=> (not _let_3) (= _let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat tptp.one_one_nat) (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) M))))))))))) (forall ((A tptp.int) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.power_power_int A))) (let ((_let_2 (tptp.aa_int_int (tptp.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.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 ((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)) (=> (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) (A tptp.complex)) (let ((_let_1 (tptp.power_power_complex A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (= (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_nat_complex _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) tptp.one_one_nat))) A) (tptp.aa_nat_complex _let_1 N))))) (forall ((N tptp.nat) (A tptp.real)) (let ((_let_1 (tptp.aa_real_fun_nat_real tptp.power_power_real A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) tptp.one_one_nat))) A) (tptp.aa_nat_real _let_1 N))))) (forall ((N tptp.nat) (A tptp.rat)) (let ((_let_1 (tptp.power_power_rat A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) tptp.one_one_nat))) A) (tptp.aa_nat_rat _let_1 N))))) (forall ((N tptp.nat) (A tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) tptp.one_one_nat))) A) (tptp.aa_nat_nat _let_1 N))))) (forall ((N tptp.nat) (A tptp.int)) (let ((_let_1 (tptp.power_power_int A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) tptp.one_one_nat))) A) (tptp.aa_nat_int _let_1 N))))) (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat K))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) K)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) N)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat _let_1 M)) (tptp.aa_nat_nat _let_1 N))))))) (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat K))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) K)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_nat_nat _let_1 M)) (tptp.aa_nat_nat _let_1 N))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)))))) (forall ((N tptp.nat)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) N)) tptp.zero_zero_int)))) (forall ((P tptp.fun_nat_bool) (A tptp.nat)) (=> (forall ((A3 tptp.nat)) (=> (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A3) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) A3) (tptp.pp (tptp.aa_nat_bool P A3)))) (=> (forall ((A3 tptp.nat) (B3 tptp.bool)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_bool_nat tptp.zero_n2687167440665602831ol_nat B3)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat _let_1) A3)))) (=> (tptp.pp (tptp.aa_nat_bool P A3)) (=> (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat _let_2) _let_1) A3) (tptp.pp (tptp.aa_nat_bool P _let_2))))))) (tptp.pp (tptp.aa_nat_bool P A))))) (forall ((P tptp.fun_int_bool) (A tptp.int)) (=> (forall ((A3 tptp.int)) (=> (= (tptp.aa_int_int (tptp.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) (B3 tptp.bool)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_bool_int tptp.zero_n2684676970156552555ol_int B3)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int _let_1) A3)))) (=> (tptp.pp (tptp.aa_int_bool P A3)) (=> (= (tptp.aa_int_int (tptp.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.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger 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) (B3 tptp.bool)) (let ((_let_1 (tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.plus_p5714425477246183910nteger (tptp.aa_bool_Code_integer tptp.zero_n356916108424825756nteger B3)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger _let_1) A3)))) (=> (tptp.pp (tptp.aa_Code_integer_bool P A3)) (=> (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger 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 ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) _let_1)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Y) _let_1)))) (or (not (= X tptp.zero_zero_real)) (not (= Y tptp.zero_zero_real)))))) (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_nat_rat (tptp.power_power_rat X) _let_1)) (tptp.aa_nat_rat (tptp.power_power_rat Y) _let_1)))) (or (not (= X tptp.zero_zero_rat)) (not (= Y tptp.zero_zero_rat)))))) (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_nat_int (tptp.power_power_int X) _let_1)) (tptp.aa_nat_int (tptp.power_power_int Y) _let_1)))) (or (not (= X tptp.zero_zero_int)) (not (= Y tptp.zero_zero_int)))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) _let_1)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Y) _let_1))) tptp.zero_zero_real))))) (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_nat_rat (tptp.power_power_rat X) _let_1)) (tptp.aa_nat_rat (tptp.power_power_rat Y) _let_1))) tptp.zero_zero_rat))))) (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_nat_int (tptp.power_power_int X) _let_1)) (tptp.aa_nat_int (tptp.power_power_int Y) _let_1))) tptp.zero_zero_int))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) _let_1)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Y) _let_1))) tptp.zero_zero_real)) (and (= X tptp.zero_zero_real) (= Y tptp.zero_zero_real))))) (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_nat_rat (tptp.power_power_rat X) _let_1)) (tptp.aa_nat_rat (tptp.power_power_rat Y) _let_1))) tptp.zero_zero_rat)) (and (= X tptp.zero_zero_rat) (= Y tptp.zero_zero_rat))))) (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_nat_int (tptp.power_power_int X) _let_1)) (tptp.aa_nat_int (tptp.power_power_int Y) _let_1))) tptp.zero_zero_int)) (and (= X tptp.zero_zero_int) (= Y tptp.zero_zero_int))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) _let_1)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Y) _let_1)))))) (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_nat_rat (tptp.power_power_rat X) _let_1)) (tptp.aa_nat_rat (tptp.power_power_rat Y) _let_1)))))) (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_nat_int (tptp.power_power_int X) _let_1)) (tptp.aa_nat_int (tptp.power_power_int Y) _let_1)))))) (forall ((A tptp.real) (N tptp.nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N))))) (forall ((A tptp.rat) (N tptp.nat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_nat_rat (tptp.power_power_rat A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N))))) (forall ((A tptp.int) (N tptp.nat)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.aa_nat_int (tptp.power_power_int A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N))))) (forall ((N tptp.nat) (A tptp.real)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real A) N))))) (forall ((N tptp.nat) (A tptp.rat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_nat_rat (tptp.power_power_rat A) N))))) (forall ((N tptp.nat) (A tptp.int)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.aa_nat_int (tptp.power_power_int A) N))))) (forall ((N tptp.nat) (A tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N))) (= (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real A) N))) (tptp.pp (tptp.aa_real_bool _let_1 A)))))) (forall ((N tptp.nat) (A tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N))) (= (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_nat_rat (tptp.power_power_rat A) N))) (tptp.pp (tptp.aa_rat_bool _let_1 A)))))) (forall ((N tptp.nat) (A tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N))) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_nat_int (tptp.power_power_int A) N))) (tptp.pp (tptp.aa_int_bool _let_1 A)))))) (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (let ((_let_2 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N)))) (= (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real A) N))) (or _let_2 (and (not _let_2) (tptp.pp (tptp.aa_real_bool _let_1 A)))))))) (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat))) (let ((_let_2 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N)))) (= (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_nat_rat (tptp.power_power_rat A) N))) (or _let_2 (and (not _let_2) (tptp.pp (tptp.aa_rat_bool _let_1 A)))))))) (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_2 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N)))) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_nat_int (tptp.power_power_int A) N))) (or _let_2 (and (not _let_2) (tptp.pp (tptp.aa_int_bool _let_1 A)))))))) (forall ((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)) (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 ((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 ((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) (Y tptp.real) (X tptp.real) (Z tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.times_times_real X))) (let ((_let_2 (tptp.aa_rea7340605660300375871l_real tptp.times_times_real W))) (= (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real _let_2 Y)) (tptp.aa_real_real _let_1 Z)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real _let_2 Z)) (tptp.aa_real_real _let_1 Y))) (or (= W X) (= Y Z)))))) (forall ((W tptp.rat) (Y tptp.rat) (X tptp.rat) (Z tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_rat tptp.times_times_rat X))) (let ((_let_2 (tptp.aa_rat_fun_rat_rat tptp.times_times_rat W))) (= (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat _let_2 Y)) (tptp.aa_rat_rat _let_1 Z)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat _let_2 Z)) (tptp.aa_rat_rat _let_1 Y))) (or (= W X) (= Y Z)))))) (forall ((W tptp.nat) (Y tptp.nat) (X tptp.nat) (Z tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat X))) (let ((_let_2 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat W))) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat _let_2 Y)) (tptp.aa_nat_nat _let_1 Z)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat _let_2 Z)) (tptp.aa_nat_nat _let_1 Y))) (or (= W X) (= Y Z)))))) (forall ((W tptp.int) (Y tptp.int) (X tptp.int) (Z tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.times_times_int X))) (let ((_let_2 (tptp.aa_int_fun_int_int tptp.times_times_int W))) (= (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int _let_2 Y)) (tptp.aa_int_int _let_1 Z)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int _let_2 Z)) (tptp.aa_int_int _let_1 Y))) (or (= W X) (= Y Z)))))) (forall ((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 ((A tptp.real) (N tptp.nat)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real A) (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N)))) tptp.zero_zero_real)))) (forall ((A tptp.rat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_nat_rat (tptp.power_power_rat A) (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N)))) tptp.zero_zero_rat)))) (forall ((A tptp.int) (N tptp.nat)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_nat_int (tptp.power_power_int A) (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N)))) tptp.zero_zero_int)))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (let ((_let_2 (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.numeral_numeral_real _let_1)) X)) Y)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) _let_2)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Y) _let_2))))))) (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (let ((_let_2 (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.numeral_numeral_rat _let_1)) X)) Y)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_nat_rat (tptp.power_power_rat X) _let_2)) (tptp.aa_nat_rat (tptp.power_power_rat Y) _let_2))))))) (forall ((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 ((A tptp.real) (N tptp.nat)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real A) (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N))))) (tptp.pp (tptp.aa_real_bool _let_1 A))))) (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_nat_rat (tptp.power_power_rat A) (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N))))) (tptp.pp (tptp.aa_rat_bool _let_1 A))))) (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_nat_int (tptp.power_power_int A) (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N))))) (tptp.pp (tptp.aa_int_bool _let_1 A))))) (forall ((A tptp.real) (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.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 ((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.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.divide6298287555418463151nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger 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.aa_nat_fun_nat_nat tptp.power_power_nat _let_1))) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat _let_1) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat _let_2 M)) tptp.one_one_nat)) (tptp.aa_nat_nat _let_2 N)))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)))))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.power_power_int _let_1))) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int _let_1) (tptp.aa_int_int (tptp.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 ((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 ((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 ((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 ((M tptp.num) (N tptp.num)) (= (tptp.ord_le2932123472753598470d_enat (tptp.numera1916890842035813515d_enat M) (tptp.numera1916890842035813515d_enat N)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_num_nat tptp.numeral_numeral_nat M)) (tptp.aa_num_nat tptp.numeral_numeral_nat N))))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.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 ((Z tptp.real) (X tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) Z)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real X) Z)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real Y) Z))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) Y))))) (forall ((Z tptp.rat) (X tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) Z)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat X) Z)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat Y) Z))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) Y))))) (forall ((Z tptp.int) (X tptp.int) (Y tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) Z)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int X) Z)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int Y) Z))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X) Y))))) (forall ((Z tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.times_times_real Z))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) Z)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real _let_1 X)) (tptp.aa_real_real _let_1 Y))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) Y)))))) (forall ((Z tptp.rat) (X tptp.rat) (Y tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_rat tptp.times_times_rat Z))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) Z)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat _let_1 X)) (tptp.aa_rat_rat _let_1 Y))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) Y)))))) (forall ((Z tptp.int) (X tptp.int) (Y tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.times_times_int Z))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) Z)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int _let_1 X)) (tptp.aa_int_int _let_1 Y))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X) Y)))))) (forall ((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.real_V1022390504157884413omplex Z)) K5)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.real_V1022390504157884413omplex _let_4)) K5)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_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.real_V1022390504157884413omplex H)))))))))))) (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat _let_1) N))) (let ((_let_3 (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat tptp.one_one_nat))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat _let_1) A)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat _let_3 A)) _let_2) (tptp.aa_nat_nat _let_3 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A) _let_2))))))))) (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_nat_int (tptp.power_power_int _let_1) N))) (let ((_let_3 (tptp.aa_int_fun_int_int tptp.plus_plus_int tptp.one_one_int))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int _let_1) A)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (= (tptp.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))) (let ((_let_3 (tptp.aa_Cod4161879620478718930nteger tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer))) (=> (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.aa_Cod1783974652533396728nteger _let_3 A) _let_2) (tptp.aa_Cod1783974652533396728nteger _let_3 (tptp.modulo364778990260209775nteger A _let_2))))))))) (forall ((A tptp.code_natural) (N tptp.nat)) (let ((_let_1 (tptp.numera5444537566228673987atural (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.power_7079662738309270450atural _let_1 N))) (let ((_let_3 (tptp.aa_Cod5141017464274028979atural tptp.plus_p4538020629002901425atural tptp.one_one_Code_natural))) (=> (tptp.pp (tptp.dvd_dvd_Code_natural _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.modulo8411746178871703098atural (tptp.aa_Cod4272041906116450446atural _let_3 A) _let_2) (tptp.aa_Cod4272041906116450446atural _let_3 (tptp.modulo8411746178871703098atural A _let_2))))))))) (forall ((M tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat M) N) M))) (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A) B))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_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.code_natural) (B tptp.code_natural)) (let ((_let_1 (tptp.modulo8411746178871703098atural A B))) (= (tptp.modulo8411746178871703098atural _let_1 B) _let_1))) (forall ((A tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)) (forall ((A tptp.int)) (= (tptp.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.code_natural)) (= (tptp.modulo8411746178871703098atural tptp.zero_z2226904508553997617atural A) tptp.zero_z2226904508553997617atural)) (forall ((A tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A) A) tptp.zero_zero_nat)) (forall ((A tptp.int)) (= (tptp.modulo_modulo_int A A) tptp.zero_zero_int)) (forall ((A tptp.code_integer)) (= (tptp.modulo364778990260209775nteger A A) tptp.zero_z3403309356797280102nteger)) (forall ((A tptp.code_natural)) (= (tptp.modulo8411746178871703098atural A A) tptp.zero_z2226904508553997617atural)) (forall ((A tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A) tptp.zero_zero_nat) A)) (forall ((A tptp.int)) (= (tptp.modulo_modulo_int A tptp.zero_zero_int) A)) (forall ((A tptp.code_integer)) (= (tptp.modulo364778990260209775nteger A tptp.zero_z3403309356797280102nteger) A)) (forall ((A tptp.code_natural)) (= (tptp.modulo8411746178871703098atural A tptp.zero_z2226904508553997617atural) A)) (forall ((A tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)) (forall ((A tptp.int)) (= (tptp.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.code_natural)) (= (tptp.modulo8411746178871703098atural tptp.zero_z2226904508553997617atural A) tptp.zero_z2226904508553997617atural)) (forall ((M tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat M) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)) tptp.zero_zero_nat)) (forall ((B tptp.nat) (A tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat B) A)) B) (tptp.aa_nat_nat (tptp.aa_nat_fun_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.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.plus_p5714425477246183910nteger B) A) B) (tptp.modulo364778990260209775nteger A B))) (forall ((B tptp.code_natural) (A tptp.code_natural)) (= (tptp.modulo8411746178871703098atural (tptp.aa_Cod4272041906116450446atural (tptp.aa_Cod5141017464274028979atural tptp.plus_p4538020629002901425atural B) A) B) (tptp.modulo8411746178871703098atural A B))) (forall ((A tptp.nat) (B tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) B)) B) (tptp.aa_nat_nat (tptp.aa_nat_fun_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.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.plus_p5714425477246183910nteger A) B) B) (tptp.modulo364778990260209775nteger A B))) (forall ((A tptp.code_natural) (B tptp.code_natural)) (= (tptp.modulo8411746178871703098atural (tptp.aa_Cod4272041906116450446atural (tptp.aa_Cod5141017464274028979atural tptp.plus_p4538020629002901425atural A) B) B) (tptp.modulo8411746178871703098atural 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.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.minus_8373710615458151222nteger A) B) B) (tptp.modulo364778990260209775nteger A B))) (forall ((B tptp.nat) (A tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat 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 ((B tptp.code_natural) (A tptp.code_natural)) (= (tptp.modulo8411746178871703098atural (tptp.aa_Cod4272041906116450446atural (tptp.aa_Cod5141017464274028979atural tptp.times_2397367101498566445atural B) A) B) tptp.zero_z2226904508553997617atural)) (forall ((A tptp.nat) (B tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) 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.code_natural) (B tptp.code_natural)) (= (tptp.modulo8411746178871703098atural (tptp.aa_Cod4272041906116450446atural (tptp.aa_Cod5141017464274028979atural tptp.times_2397367101498566445atural A) B) B) tptp.zero_z2226904508553997617atural)) (forall ((A tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A) tptp.one_one_nat) tptp.zero_zero_nat)) (forall ((A tptp.int)) (= (tptp.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.code_natural)) (= (tptp.modulo8411746178871703098atural A tptp.one_one_Code_natural) tptp.zero_z2226904508553997617atural)) (forall ((A tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A) tptp.one_one_nat) tptp.zero_zero_nat)) (forall ((A tptp.int)) (= (tptp.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.code_natural)) (= (tptp.modulo8411746178871703098atural A tptp.one_one_Code_natural) tptp.zero_z2226904508553997617atural)) (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.aa_nat_fun_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.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.divide6298287555418463151nteger (tptp.modulo364778990260209775nteger A B)) B) tptp.zero_z3403309356797280102nteger)) (forall ((A tptp.code_natural) (B tptp.code_natural)) (= (tptp.aa_Cod4272041906116450446atural (tptp.aa_Cod5141017464274028979atural tptp.divide5121882707175180666atural (tptp.modulo8411746178871703098atural A B)) B) tptp.zero_z2226904508553997617atural)) (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.aa_nat_fun_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.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.divide6298287555418463151nteger (tptp.modulo364778990260209775nteger A B)) B) tptp.zero_z3403309356797280102nteger)) (forall ((A tptp.code_natural) (B tptp.code_natural)) (= (tptp.aa_Cod4272041906116450446atural (tptp.aa_Cod5141017464274028979atural tptp.divide5121882707175180666atural (tptp.modulo8411746178871703098atural A B)) B) tptp.zero_z2226904508553997617atural)) (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat C) B))) B) (tptp.aa_nat_nat (tptp.aa_nat_fun_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.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.plus_p5714425477246183910nteger A) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger C) B)) B) (tptp.modulo364778990260209775nteger A B))) (forall ((A tptp.code_natural) (C tptp.code_natural) (B tptp.code_natural)) (= (tptp.modulo8411746178871703098atural (tptp.aa_Cod4272041906116450446atural (tptp.aa_Cod5141017464274028979atural tptp.plus_p4538020629002901425atural A) (tptp.aa_Cod4272041906116450446atural (tptp.aa_Cod5141017464274028979atural tptp.times_2397367101498566445atural C) B)) B) (tptp.modulo8411746178871703098atural A B))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B) C))) B) (tptp.aa_nat_nat (tptp.aa_nat_fun_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.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.plus_p5714425477246183910nteger A) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B) C)) B) (tptp.modulo364778990260209775nteger A B))) (forall ((A tptp.code_natural) (B tptp.code_natural) (C tptp.code_natural)) (= (tptp.modulo8411746178871703098atural (tptp.aa_Cod4272041906116450446atural (tptp.aa_Cod5141017464274028979atural tptp.plus_p4538020629002901425atural A) (tptp.aa_Cod4272041906116450446atural (tptp.aa_Cod5141017464274028979atural tptp.times_2397367101498566445atural B) C)) B) (tptp.modulo8411746178871703098atural A B))) (forall ((C tptp.nat) (B tptp.nat) (A tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat C) B)) A)) B) (tptp.aa_nat_nat (tptp.aa_nat_fun_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.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger C) B)) A) B) (tptp.modulo364778990260209775nteger A B))) (forall ((C tptp.code_natural) (B tptp.code_natural) (A tptp.code_natural)) (= (tptp.modulo8411746178871703098atural (tptp.aa_Cod4272041906116450446atural (tptp.aa_Cod5141017464274028979atural tptp.plus_p4538020629002901425atural (tptp.aa_Cod4272041906116450446atural (tptp.aa_Cod5141017464274028979atural tptp.times_2397367101498566445atural C) B)) A) B) (tptp.modulo8411746178871703098atural A B))) (forall ((B tptp.nat) (C tptp.nat) (A tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B) C)) A)) B) (tptp.aa_nat_nat (tptp.aa_nat_fun_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.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B) C)) A) B) (tptp.modulo364778990260209775nteger A B))) (forall ((B tptp.code_natural) (C tptp.code_natural) (A tptp.code_natural)) (= (tptp.modulo8411746178871703098atural (tptp.aa_Cod4272041906116450446atural (tptp.aa_Cod5141017464274028979atural tptp.plus_p4538020629002901425atural (tptp.aa_Cod4272041906116450446atural (tptp.aa_Cod5141017464274028979atural tptp.times_2397367101498566445atural B) C)) A) B) (tptp.modulo8411746178871703098atural 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.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.code_natural) (B tptp.code_natural)) (=> (tptp.pp (tptp.dvd_dvd_Code_natural A B)) (= (tptp.modulo8411746178871703098atural B A) tptp.zero_z2226904508553997617atural))) (forall ((M tptp.nat) (K tptp.nat) (N tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat K) N)))) N) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat tptp.suc M)) N))) (forall ((M tptp.nat) (N tptp.nat) (K tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat N) K)))) N) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat tptp.suc M)) N))) (forall ((K tptp.nat) (N tptp.nat) (M tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat K) N)) M))) N) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat tptp.suc M)) N))) (forall ((N tptp.nat) (K tptp.nat) (M tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat N) K)) M))) N) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat tptp.suc M)) N))) (forall ((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 ((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 ((N tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat _let_1) N) (tptp.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)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat tptp.suc M))) _let_1) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat M) _let_1)))) (forall ((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 ((K tptp.num) (N tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat K))) (=> (not (= _let_1 tptp.one_one_nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat _let_1) N))) _let_1) tptp.one_one_nat)))) _let_162 _let_161 _let_160 _let_159 _let_162 _let_161 _let_160 _let_159 (forall ((N tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat N) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (not (= _let_1 (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat))) (= _let_1 tptp.zero_zero_nat)))) (forall ((A tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat _let_1))) (= (tptp.pp (tptp.aa_nat_bool _let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A) _let_1))) (tptp.pp (tptp.aa_nat_bool _let_2 A)))))) (forall ((A tptp.int)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int _let_1))) (= (tptp.pp (tptp.aa_int_bool _let_2 (tptp.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 ((A tptp.code_natural)) (let ((_let_1 (tptp.numera5444537566228673987atural (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.pp (tptp.dvd_dvd_Code_natural _let_1 (tptp.modulo8411746178871703098atural A _let_1))) (tptp.pp (tptp.dvd_dvd_Code_natural _let_1 A))))) (forall ((M tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) M)) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) tptp.zero_zero_nat)) (forall ((A tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (not (= _let_1 tptp.zero_zero_nat)) (= _let_1 tptp.one_one_nat)))) (forall ((A tptp.int)) (let ((_let_1 (tptp.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 ((A tptp.code_natural)) (let ((_let_1 (tptp.modulo8411746178871703098atural A (tptp.numera5444537566228673987atural (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (not (= _let_1 tptp.zero_z2226904508553997617atural)) (= _let_1 tptp.one_one_Code_natural)))) (forall ((A tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (not (= _let_1 tptp.one_one_nat)) (= _let_1 tptp.zero_zero_nat)))) (forall ((A tptp.int)) (let ((_let_1 (tptp.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.code_natural)) (let ((_let_1 (tptp.modulo8411746178871703098atural A (tptp.numera5444537566228673987atural (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (not (= _let_1 tptp.one_one_Code_natural)) (= _let_1 tptp.zero_z2226904508553997617atural)))) (forall ((M tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat M) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) _let_1)) (= _let_1 tptp.one_one_nat)))) (forall ((N tptp.nat)) (= (tptp.modulo8411746178871703098atural tptp.one_one_Code_natural (tptp.power_7079662738309270450atural (tptp.numera5444537566228673987atural (tptp.aa_num_num tptp.bit0 tptp.one)) N)) (tptp.zero_n8403883297036319079atural (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.aa_nat_fun_nat_nat tptp.modulo_modulo_nat tptp.one_one_nat) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N)) (tptp.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 ((Z tptp.extended_enat) (Y tptp.extended_enat) (X tptp.extended_enat)) (=> (tptp.ord_le2932123472753598470d_enat Z Y) (= (tptp.plus_p3455044024723400733d_enat X (tptp.minus_3235023915231533773d_enat Y Z)) (tptp.minus_3235023915231533773d_enat (tptp.plus_p3455044024723400733d_enat X Y) Z)))) (forall ((A tptp.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)))) (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 ((M tptp.extended_enat) (N tptp.extended_enat)) (= (tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat (tptp.times_7803423173614009249d_enat M N)) (and (tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat M) (tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat N)))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.semiri4939895301339042750nteger (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat M) N)) (tptp.modulo364778990260209775nteger (tptp.semiri4939895301339042750nteger M) (tptp.semiri4939895301339042750nteger N)))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.semiri3763490453095760265atural (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat M) N)) (tptp.modulo8411746178871703098atural (tptp.semiri3763490453095760265atural M) (tptp.semiri3763490453095760265atural N)))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat M) N)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat M)) (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat N)))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_nat (tptp.aa_nat_fun_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 ((A tptp.nat) (B tptp.nat)) (= (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_nat (tptp.aa_nat_fun_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 ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A) C)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat B) C))) C) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) 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.code_natural) (C tptp.code_natural) (B tptp.code_natural)) (= (tptp.modulo8411746178871703098atural (tptp.aa_Cod4272041906116450446atural (tptp.aa_Cod5141017464274028979atural tptp.times_2397367101498566445atural (tptp.modulo8411746178871703098atural A C)) (tptp.modulo8411746178871703098atural B C)) C) (tptp.modulo8411746178871703098atural (tptp.aa_Cod4272041906116450446atural (tptp.aa_Cod5141017464274028979atural tptp.times_2397367101498566445atural A) B) C))) (forall ((A tptp.nat) (C tptp.nat) (A4 tptp.nat) (B tptp.nat) (B5 tptp.nat)) (=> (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A) C) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A4) C)) (=> (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat B) C) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat B5) C)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) B)) C) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A4) B5)) C))))) (forall ((A tptp.int) (C tptp.int) (A4 tptp.int) (B tptp.int) (B5 tptp.int)) (=> (= (tptp.modulo_modulo_int A C) (tptp.modulo_modulo_int A4 C)) (=> (= (tptp.modulo_modulo_int B C) (tptp.modulo_modulo_int B5 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) B5) C))))) (forall ((A tptp.code_integer) (C tptp.code_integer) (A4 tptp.code_integer) (B tptp.code_integer) (B5 tptp.code_integer)) (=> (= (tptp.modulo364778990260209775nteger A C) (tptp.modulo364778990260209775nteger A4 C)) (=> (= (tptp.modulo364778990260209775nteger B C) (tptp.modulo364778990260209775nteger B5 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) B5) C))))) (forall ((A tptp.code_natural) (C tptp.code_natural) (A4 tptp.code_natural) (B tptp.code_natural) (B5 tptp.code_natural)) (=> (= (tptp.modulo8411746178871703098atural A C) (tptp.modulo8411746178871703098atural A4 C)) (=> (= (tptp.modulo8411746178871703098atural B C) (tptp.modulo8411746178871703098atural B5 C)) (= (tptp.modulo8411746178871703098atural (tptp.aa_Cod4272041906116450446atural (tptp.aa_Cod5141017464274028979atural tptp.times_2397367101498566445atural A) B) C) (tptp.modulo8411746178871703098atural (tptp.aa_Cod4272041906116450446atural (tptp.aa_Cod5141017464274028979atural tptp.times_2397367101498566445atural A4) B5) C))))) (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) C)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B) C)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A) 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.code_natural) (C tptp.code_natural) (B tptp.code_natural)) (= (tptp.modulo8411746178871703098atural (tptp.aa_Cod4272041906116450446atural (tptp.aa_Cod5141017464274028979atural tptp.times_2397367101498566445atural A) C) (tptp.aa_Cod4272041906116450446atural (tptp.aa_Cod5141017464274028979atural tptp.times_2397367101498566445atural B) C)) (tptp.aa_Cod4272041906116450446atural (tptp.aa_Cod5141017464274028979atural tptp.times_2397367101498566445atural (tptp.modulo8411746178871703098atural 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.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A) B)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat _let_1 A)) (tptp.aa_nat_nat _let_1 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 ((C tptp.code_natural) (A tptp.code_natural) (B tptp.code_natural)) (let ((_let_1 (tptp.aa_Cod5141017464274028979atural tptp.times_2397367101498566445atural C))) (= (tptp.aa_Cod4272041906116450446atural _let_1 (tptp.modulo8411746178871703098atural A B)) (tptp.modulo8411746178871703098atural (tptp.aa_Cod4272041906116450446atural _let_1 A) (tptp.aa_Cod4272041906116450446atural _let_1 B))))) (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A) C)) B)) C) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) 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 ((A tptp.code_natural) (C tptp.code_natural) (B tptp.code_natural)) (= (tptp.modulo8411746178871703098atural (tptp.aa_Cod4272041906116450446atural (tptp.aa_Cod5141017464274028979atural tptp.times_2397367101498566445atural (tptp.modulo8411746178871703098atural A C)) B) C) (tptp.modulo8411746178871703098atural (tptp.aa_Cod4272041906116450446atural (tptp.aa_Cod5141017464274028979atural tptp.times_2397367101498566445atural A) 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.modulo_modulo_nat (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat B) C))) C) (tptp.aa_nat_nat (tptp.aa_nat_fun_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.code_natural) (B tptp.code_natural) (C tptp.code_natural)) (let ((_let_1 (tptp.aa_Cod5141017464274028979atural tptp.times_2397367101498566445atural A))) (= (tptp.modulo8411746178871703098atural (tptp.aa_Cod4272041906116450446atural _let_1 (tptp.modulo8411746178871703098atural B C)) C) (tptp.modulo8411746178871703098atural (tptp.aa_Cod4272041906116450446atural _let_1 B) C)))) (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A) C)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat B) C))) C) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) 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.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.plus_p5714425477246183910nteger (tptp.modulo364778990260209775nteger A C)) (tptp.modulo364778990260209775nteger B C)) C) (tptp.modulo364778990260209775nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.plus_p5714425477246183910nteger A) B) C))) (forall ((A tptp.code_natural) (C tptp.code_natural) (B tptp.code_natural)) (= (tptp.modulo8411746178871703098atural (tptp.aa_Cod4272041906116450446atural (tptp.aa_Cod5141017464274028979atural tptp.plus_p4538020629002901425atural (tptp.modulo8411746178871703098atural A C)) (tptp.modulo8411746178871703098atural B C)) C) (tptp.modulo8411746178871703098atural (tptp.aa_Cod4272041906116450446atural (tptp.aa_Cod5141017464274028979atural tptp.plus_p4538020629002901425atural A) B) C))) (forall ((A tptp.nat) (C tptp.nat) (A4 tptp.nat) (B tptp.nat) (B5 tptp.nat)) (=> (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A) C) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A4) C)) (=> (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat B) C) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat B5) C)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) B)) C) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A4) B5)) C))))) (forall ((A tptp.int) (C tptp.int) (A4 tptp.int) (B tptp.int) (B5 tptp.int)) (=> (= (tptp.modulo_modulo_int A C) (tptp.modulo_modulo_int A4 C)) (=> (= (tptp.modulo_modulo_int B C) (tptp.modulo_modulo_int B5 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) B5) C))))) (forall ((A tptp.code_integer) (C tptp.code_integer) (A4 tptp.code_integer) (B tptp.code_integer) (B5 tptp.code_integer)) (=> (= (tptp.modulo364778990260209775nteger A C) (tptp.modulo364778990260209775nteger A4 C)) (=> (= (tptp.modulo364778990260209775nteger B C) (tptp.modulo364778990260209775nteger B5 C)) (= (tptp.modulo364778990260209775nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.plus_p5714425477246183910nteger A) B) C) (tptp.modulo364778990260209775nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.plus_p5714425477246183910nteger A4) B5) C))))) (forall ((A tptp.code_natural) (C tptp.code_natural) (A4 tptp.code_natural) (B tptp.code_natural) (B5 tptp.code_natural)) (=> (= (tptp.modulo8411746178871703098atural A C) (tptp.modulo8411746178871703098atural A4 C)) (=> (= (tptp.modulo8411746178871703098atural B C) (tptp.modulo8411746178871703098atural B5 C)) (= (tptp.modulo8411746178871703098atural (tptp.aa_Cod4272041906116450446atural (tptp.aa_Cod5141017464274028979atural tptp.plus_p4538020629002901425atural A) B) C) (tptp.modulo8411746178871703098atural (tptp.aa_Cod4272041906116450446atural (tptp.aa_Cod5141017464274028979atural tptp.plus_p4538020629002901425atural A4) B5) C))))) (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A) C)) B)) C) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) 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.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.plus_p5714425477246183910nteger (tptp.modulo364778990260209775nteger A C)) B) C) (tptp.modulo364778990260209775nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.plus_p5714425477246183910nteger A) B) C))) (forall ((A tptp.code_natural) (C tptp.code_natural) (B tptp.code_natural)) (= (tptp.modulo8411746178871703098atural (tptp.aa_Cod4272041906116450446atural (tptp.aa_Cod5141017464274028979atural tptp.plus_p4538020629002901425atural (tptp.modulo8411746178871703098atural A C)) B) C) (tptp.modulo8411746178871703098atural (tptp.aa_Cod4272041906116450446atural (tptp.aa_Cod5141017464274028979atural tptp.plus_p4538020629002901425atural 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.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat B) C))) C) (tptp.aa_nat_nat (tptp.aa_nat_fun_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)) (let ((_let_1 (tptp.aa_Cod4161879620478718930nteger tptp.plus_p5714425477246183910nteger 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.code_natural) (B tptp.code_natural) (C tptp.code_natural)) (let ((_let_1 (tptp.aa_Cod5141017464274028979atural tptp.plus_p4538020629002901425atural A))) (= (tptp.modulo8411746178871703098atural (tptp.aa_Cod4272041906116450446atural _let_1 (tptp.modulo8411746178871703098atural B C)) C) (tptp.modulo8411746178871703098atural (tptp.aa_Cod4272041906116450446atural _let_1 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)) (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.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.minus_8373710615458151222nteger (tptp.modulo364778990260209775nteger A C)) (tptp.modulo364778990260209775nteger B C)) C) (tptp.modulo364778990260209775nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.minus_8373710615458151222nteger A) B) C))) (forall ((A tptp.int) (C tptp.int) (A4 tptp.int) (B tptp.int) (B5 tptp.int)) (=> (= (tptp.modulo_modulo_int A C) (tptp.modulo_modulo_int A4 C)) (=> (= (tptp.modulo_modulo_int B C) (tptp.modulo_modulo_int B5 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) B5) C))))) (forall ((A tptp.code_integer) (C tptp.code_integer) (A4 tptp.code_integer) (B tptp.code_integer) (B5 tptp.code_integer)) (=> (= (tptp.modulo364778990260209775nteger A C) (tptp.modulo364778990260209775nteger A4 C)) (=> (= (tptp.modulo364778990260209775nteger B C) (tptp.modulo364778990260209775nteger B5 C)) (= (tptp.modulo364778990260209775nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.minus_8373710615458151222nteger A) B) C) (tptp.modulo364778990260209775nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.minus_8373710615458151222nteger A4) B5) 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.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.minus_8373710615458151222nteger (tptp.modulo364778990260209775nteger A C)) B) C) (tptp.modulo364778990260209775nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.minus_8373710615458151222nteger 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)) (let ((_let_1 (tptp.aa_Cod4161879620478718930nteger tptp.minus_8373710615458151222nteger 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) (B tptp.nat) (N tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A) B)) N)) B) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A) N)) 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 ((A tptp.code_natural) (B tptp.code_natural) (N tptp.nat)) (= (tptp.modulo8411746178871703098atural (tptp.power_7079662738309270450atural (tptp.modulo8411746178871703098atural A B) N) B) (tptp.modulo8411746178871703098atural (tptp.power_7079662738309270450atural A N) 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 (tptp.aa_nat_nat (tptp.aa_nat_fun_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 ((C tptp.code_natural) (A tptp.code_natural) (B tptp.code_natural)) (=> (tptp.pp (tptp.dvd_dvd_Code_natural C (tptp.modulo8411746178871703098atural A B))) (=> (tptp.pp (tptp.dvd_dvd_Code_natural C B)) (tptp.pp (tptp.dvd_dvd_Code_natural C A))))) (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.aa_nat_fun_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.code_natural) (B tptp.code_natural) (A tptp.code_natural)) (=> (tptp.pp (tptp.dvd_dvd_Code_natural C B)) (= (tptp.pp (tptp.dvd_dvd_Code_natural C (tptp.modulo8411746178871703098atural A B))) (tptp.pp (tptp.dvd_dvd_Code_natural C A))))) (forall ((C tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat C) B)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_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.code_natural) (B tptp.code_natural) (A tptp.code_natural)) (=> (tptp.pp (tptp.dvd_dvd_Code_natural C B)) (= (tptp.modulo8411746178871703098atural (tptp.modulo8411746178871703098atural A B) C) (tptp.modulo8411746178871703098atural A C)))) (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat K))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 M)) (=> (tptp.pp (tptp.aa_nat_bool _let_1 N)) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat M) N))))))) (forall ((K tptp.int) (M tptp.int) (N tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int K))) (=> (tptp.pp (tptp.aa_int_bool _let_1 M)) (=> (tptp.pp (tptp.aa_int_bool _let_1 N)) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.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 ((K tptp.code_natural) (M tptp.code_natural) (N tptp.code_natural)) (=> (tptp.pp (tptp.dvd_dvd_Code_natural K M)) (=> (tptp.pp (tptp.dvd_dvd_Code_natural K N)) (tptp.pp (tptp.dvd_dvd_Code_natural K (tptp.modulo8411746178871703098atural M N)))))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat M) N))) N) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat tptp.suc M)) N))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat M) N)))) N) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat tptp.suc M))) N))) (forall ((M tptp.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 ((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 ((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 ((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 ((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 ((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 ((M tptp.nat) (N tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat M) N)) M))) (forall ((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.aa_nat_fun_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.aa_nat_fun_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 ((A tptp.nat) (B tptp.nat)) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_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.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.divide6298287555418463151nteger A) B) tptp.zero_z3403309356797280102nteger))) (forall ((A tptp.code_natural) (B tptp.code_natural)) (= (= (tptp.modulo8411746178871703098atural A B) A) (= (tptp.aa_Cod4272041906116450446atural (tptp.aa_Cod5141017464274028979atural tptp.divide5121882707175180666atural A) B) tptp.zero_z2226904508553997617atural))) (forall ((M tptp.num) (Q2 tptp.num) (N tptp.num)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat Q2))) (let ((_let_2 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 Q2)))) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 M))) _let_2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 N))) _let_2)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_num_nat tptp.numeral_numeral_nat M)) _let_1) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_num_nat tptp.numeral_numeral_nat N)) _let_1)))))) (forall ((M tptp.num) (Q2 tptp.num) (N tptp.num)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int Q2))) (let ((_let_2 (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 Q2)))) (= (= (tptp.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 ((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.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.plus_p5714425477246183910nteger A) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger C) D2)))))))) (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat tptp.one))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_num_nat tptp.numeral_numeral_nat M)) _let_1) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_num_nat tptp.numeral_numeral_nat N)) _let_1)))) (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int tptp.one))) (= (tptp.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.nat) (B tptp.nat)) (=> (= (tptp.aa_nat_nat (tptp.aa_nat_fun_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.code_natural) (B tptp.code_natural)) (=> (= (tptp.modulo8411746178871703098atural A B) tptp.zero_z2226904508553997617atural) (tptp.pp (tptp.dvd_dvd_Code_natural 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.aa_nat_fun_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.code_natural) (B tptp.code_natural)) (= (tptp.pp (tptp.dvd_dvd_Code_natural A B)) (= (tptp.modulo8411746178871703098atural B A) tptp.zero_z2226904508553997617atural))) (forall ((A tptp.nat) (B tptp.nat)) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_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.code_natural) (B tptp.code_natural)) (= (= (tptp.modulo8411746178871703098atural A B) tptp.zero_z2226904508553997617atural) (tptp.pp (tptp.dvd_dvd_Code_natural 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.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A) C)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat 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.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.divide6298287555418463151nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.plus_p5714425477246183910nteger A) B)) C) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.divide6298287555418463151nteger A) C)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.divide6298287555418463151nteger B) C))) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.divide6298287555418463151nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.plus_p5714425477246183910nteger (tptp.modulo364778990260209775nteger A C)) (tptp.modulo364778990260209775nteger B C))) C)))) (forall ((A tptp.code_natural) (B tptp.code_natural) (C tptp.code_natural)) (= (tptp.aa_Cod4272041906116450446atural (tptp.aa_Cod5141017464274028979atural tptp.divide5121882707175180666atural (tptp.aa_Cod4272041906116450446atural (tptp.aa_Cod5141017464274028979atural tptp.plus_p4538020629002901425atural A) B)) C) (tptp.aa_Cod4272041906116450446atural (tptp.aa_Cod5141017464274028979atural tptp.plus_p4538020629002901425atural (tptp.aa_Cod4272041906116450446atural (tptp.aa_Cod5141017464274028979atural tptp.plus_p4538020629002901425atural (tptp.aa_Cod4272041906116450446atural (tptp.aa_Cod5141017464274028979atural tptp.divide5121882707175180666atural A) C)) (tptp.aa_Cod4272041906116450446atural (tptp.aa_Cod5141017464274028979atural tptp.divide5121882707175180666atural B) C))) (tptp.aa_Cod4272041906116450446atural (tptp.aa_Cod5141017464274028979atural tptp.divide5121882707175180666atural (tptp.aa_Cod4272041906116450446atural (tptp.aa_Cod5141017464274028979atural tptp.plus_p4538020629002901425atural (tptp.modulo8411746178871703098atural A C)) (tptp.modulo8411746178871703098atural B C))) 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.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A) 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.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.minus_8373710615458151222nteger A) (tptp.modulo364778990260209775nteger A B))))) (forall ((B tptp.code_natural) (A tptp.code_natural)) (tptp.pp (tptp.dvd_dvd_Code_natural B (tptp.aa_Cod4272041906116450446atural (tptp.aa_Cod5141017464274028979atural tptp.minus_7197305767214868737atural A) (tptp.modulo8411746178871703098atural A B))))) (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.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.minus_8373710615458151222nteger A) B))))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat M) N)))) (let ((_let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat tptp.suc M)) N))) (let ((_let_3 (= _let_1 N))) (and (=> _let_3 (= _let_2 tptp.zero_zero_nat)) (=> (not _let_3) (= _let_2 _let_1))))))) (forall ((P tptp.fun_nat_bool) (N tptp.nat) (P2 tptp.nat) (M tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool P N)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N) P2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) P2)) (=> (forall ((N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) P2)) (=> (tptp.pp (tptp.aa_nat_bool P N2)) (tptp.pp (tptp.aa_nat_bool P (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat tptp.suc N2)) P2)))))) (tptp.pp (tptp.aa_nat_bool P M))))))) (forall ((P tptp.fun_nat_fun_nat_bool) (M tptp.nat) (N tptp.nat)) (=> (forall ((M2 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool P M2) tptp.zero_zero_nat))) (=> (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool P N2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat M2) N2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool P M2) N2))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool P M) N))))) (forall ((N tptp.nat) (M tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_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_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat M) (tptp.aa_nat_nat tptp.suc N))) N))) (forall ((M tptp.nat) (D tptp.nat)) (=> (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat M) D) tptp.zero_zero_nat) (exists ((Q6 tptp.nat)) (= M (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat D) Q6))))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat M) N))) (let ((_let_2 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N)))) (and (=> _let_2 (= _let_1 M)) (=> (not _let_2) (= _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) N)) N))))))) (forall ((M tptp.nat) (N tptp.nat)) (=> (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat M) N) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) N)) N)))) (forall ((N tptp.nat) (M tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N) M)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat M) N) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) N)) N)))) (forall ((M tptp.int) (D tptp.int)) (= (= (tptp.modulo_modulo_int M D) tptp.zero_zero_int) (exists ((Q5 tptp.int)) (= M (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int D) Q5))))) (forall ((M tptp.int) (D tptp.int)) (=> (= (tptp.modulo_modulo_int M D) tptp.zero_zero_int) (exists ((Q6 tptp.int)) (= M (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int D) Q6))))) (forall ((X tptp.nat) (N tptp.nat) (Y tptp.nat)) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat X) N) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat Y) N)) (exists ((Q1 tptp.nat) (Q22 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat N))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat X) (tptp.aa_nat_nat _let_1 Q1)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Y) (tptp.aa_nat_nat _let_1 Q22))))))) (forall ((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 ((A2 tptp.int) (B4 tptp.int) (N tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A2) B4)) (=> (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 B4 N) tptp.zero_zero_int) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.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 B4) N)))))))) (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 ((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.aa_nat_fun_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 ((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.aa_nat_fun_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 ((N tptp.num) (Q2 tptp.num)) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 N))) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 Q2))) tptp.zero_zero_nat) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_num_nat tptp.numeral_numeral_nat N)) (tptp.aa_num_nat tptp.numeral_numeral_nat Q2)) tptp.zero_zero_nat))) (forall ((N tptp.num) (Q2 tptp.num)) (= (= (tptp.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.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_num_nat tptp.numeral_numeral_nat N)) (tptp.aa_num_nat tptp.numeral_numeral_nat tptp.one)) tptp.zero_zero_nat)) (forall ((N tptp.num)) (= (tptp.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 ((M tptp.num) (Q2 tptp.num)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 Q2)))) (not (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 M))) _let_1) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_num_nat tptp.numeral_numeral_nat tptp.one)) _let_1))))) (forall ((M tptp.num) (Q2 tptp.num)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 Q2)))) (not (= (tptp.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 ((Q2 tptp.num) (N tptp.num)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 Q2)))) (not (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_num_nat tptp.numeral_numeral_nat tptp.one)) _let_1) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 N))) _let_1))))) (forall ((Q2 tptp.num) (N tptp.num)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 Q2)))) (not (= (tptp.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 ((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.aa_nat_fun_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.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.divide6298287555418463151nteger A) B))) (tptp.modulo364778990260209775nteger A B))) C) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.plus_p5714425477246183910nteger A) C))) (forall ((B tptp.code_natural) (A tptp.code_natural) (C tptp.code_natural)) (= (tptp.aa_Cod4272041906116450446atural (tptp.aa_Cod5141017464274028979atural tptp.plus_p4538020629002901425atural (tptp.aa_Cod4272041906116450446atural (tptp.aa_Cod5141017464274028979atural tptp.plus_p4538020629002901425atural (tptp.aa_Cod4272041906116450446atural (tptp.aa_Cod5141017464274028979atural tptp.times_2397367101498566445atural B) (tptp.aa_Cod4272041906116450446atural (tptp.aa_Cod5141017464274028979atural tptp.divide5121882707175180666atural A) B))) (tptp.modulo8411746178871703098atural A B))) C) (tptp.aa_Cod4272041906116450446atural (tptp.aa_Cod5141017464274028979atural tptp.plus_p4538020629002901425atural A) C))) (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.aa_nat_fun_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.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.divide6298287555418463151nteger A) B)) B)) (tptp.modulo364778990260209775nteger A B))) C) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.plus_p5714425477246183910nteger A) C))) (forall ((A tptp.code_natural) (B tptp.code_natural) (C tptp.code_natural)) (= (tptp.aa_Cod4272041906116450446atural (tptp.aa_Cod5141017464274028979atural tptp.plus_p4538020629002901425atural (tptp.aa_Cod4272041906116450446atural (tptp.aa_Cod5141017464274028979atural tptp.plus_p4538020629002901425atural (tptp.aa_Cod4272041906116450446atural (tptp.aa_Cod5141017464274028979atural tptp.times_2397367101498566445atural (tptp.aa_Cod4272041906116450446atural (tptp.aa_Cod5141017464274028979atural tptp.divide5121882707175180666atural A) B)) B)) (tptp.modulo8411746178871703098atural A B))) C) (tptp.aa_Cod4272041906116450446atural (tptp.aa_Cod5141017464274028979atural tptp.plus_p4538020629002901425atural A) C))) (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.aa_nat_fun_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.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.divide6298287555418463151nteger A) B)) B)) (tptp.modulo364778990260209775nteger A B)))) (forall ((A tptp.code_natural) (B tptp.code_natural)) (= A (tptp.aa_Cod4272041906116450446atural (tptp.aa_Cod5141017464274028979atural tptp.plus_p4538020629002901425atural (tptp.aa_Cod4272041906116450446atural (tptp.aa_Cod5141017464274028979atural tptp.times_2397367101498566445atural (tptp.aa_Cod4272041906116450446atural (tptp.aa_Cod5141017464274028979atural tptp.divide5121882707175180666atural A) B)) B)) (tptp.modulo8411746178871703098atural A B)))) (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.aa_nat_fun_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.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.divide6298287555418463151nteger A) B)) B)) (tptp.modulo364778990260209775nteger A B)) A)) (forall ((A tptp.code_natural) (B tptp.code_natural)) (= (tptp.aa_Cod4272041906116450446atural (tptp.aa_Cod5141017464274028979atural tptp.plus_p4538020629002901425atural (tptp.aa_Cod4272041906116450446atural (tptp.aa_Cod5141017464274028979atural tptp.times_2397367101498566445atural (tptp.aa_Cod4272041906116450446atural (tptp.aa_Cod5141017464274028979atural tptp.divide5121882707175180666atural A) B)) B)) (tptp.modulo8411746178871703098atural 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.aa_nat_fun_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.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.plus_p5714425477246183910nteger (tptp.modulo364778990260209775nteger A B)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.divide6298287555418463151nteger A) B)) B)) A)) (forall ((A tptp.code_natural) (B tptp.code_natural)) (= (tptp.aa_Cod4272041906116450446atural (tptp.aa_Cod5141017464274028979atural tptp.plus_p4538020629002901425atural (tptp.modulo8411746178871703098atural A B)) (tptp.aa_Cod4272041906116450446atural (tptp.aa_Cod5141017464274028979atural tptp.times_2397367101498566445atural (tptp.aa_Cod4272041906116450446atural (tptp.aa_Cod5141017464274028979atural tptp.divide5121882707175180666atural 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.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.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.plus_p5714425477246183910nteger (tptp.modulo364778990260209775nteger A B)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.divide6298287555418463151nteger A) B))) A)) (forall ((A tptp.code_natural) (B tptp.code_natural)) (= (tptp.aa_Cod4272041906116450446atural (tptp.aa_Cod5141017464274028979atural tptp.plus_p4538020629002901425atural (tptp.modulo8411746178871703098atural A B)) (tptp.aa_Cod4272041906116450446atural (tptp.aa_Cod5141017464274028979atural tptp.times_2397367101498566445atural B) (tptp.aa_Cod4272041906116450446atural (tptp.aa_Cod5141017464274028979atural tptp.divide5121882707175180666atural A) B))) A)) (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.aa_nat_fun_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.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.divide6298287555418463151nteger A) B))) (tptp.modulo364778990260209775nteger A B)) A)) (forall ((B tptp.code_natural) (A tptp.code_natural)) (= (tptp.aa_Cod4272041906116450446atural (tptp.aa_Cod5141017464274028979atural tptp.plus_p4538020629002901425atural (tptp.aa_Cod4272041906116450446atural (tptp.aa_Cod5141017464274028979atural tptp.times_2397367101498566445atural B) (tptp.aa_Cod4272041906116450446atural (tptp.aa_Cod5141017464274028979atural tptp.divide5121882707175180666atural A) B))) (tptp.modulo8411746178871703098atural A B)) A)) (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.aa_nat_fun_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.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.divide6298287555418463151nteger (tptp.aa_Cod1783974652533396728nteger _let_1 B)) C) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger _let_1 (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.divide6298287555418463151nteger B) C))) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.divide6298287555418463151nteger (tptp.aa_Cod1783974652533396728nteger _let_1 (tptp.modulo364778990260209775nteger B C))) C))))) (forall ((A tptp.code_natural) (B tptp.code_natural) (C tptp.code_natural)) (let ((_let_1 (tptp.aa_Cod5141017464274028979atural tptp.times_2397367101498566445atural A))) (= (tptp.aa_Cod4272041906116450446atural (tptp.aa_Cod5141017464274028979atural tptp.divide5121882707175180666atural (tptp.aa_Cod4272041906116450446atural _let_1 B)) C) (tptp.aa_Cod4272041906116450446atural (tptp.aa_Cod5141017464274028979atural tptp.plus_p4538020629002901425atural (tptp.aa_Cod4272041906116450446atural _let_1 (tptp.aa_Cod4272041906116450446atural (tptp.aa_Cod5141017464274028979atural tptp.divide5121882707175180666atural B) C))) (tptp.aa_Cod4272041906116450446atural (tptp.aa_Cod5141017464274028979atural tptp.divide5121882707175180666atural (tptp.aa_Cod4272041906116450446atural _let_1 (tptp.modulo8411746178871703098atural B C))) 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.aa_nat_fun_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 ((B tptp.code_natural) (A tptp.code_natural)) (=> (tptp.pp (tptp.dvd_dvd_Code_natural B tptp.one_one_Code_natural)) (= (tptp.modulo8411746178871703098atural A B) tptp.zero_z2226904508553997617atural))) (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.aa_nat_fun_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.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.minus_8373710615458151222nteger A) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.divide6298287555418463151nteger A) B))) (tptp.modulo364778990260209775nteger A B))) (forall ((A tptp.code_natural) (B tptp.code_natural)) (= (tptp.aa_Cod4272041906116450446atural (tptp.aa_Cod5141017464274028979atural tptp.minus_7197305767214868737atural A) (tptp.aa_Cod4272041906116450446atural (tptp.aa_Cod5141017464274028979atural tptp.times_2397367101498566445atural B) (tptp.aa_Cod4272041906116450446atural (tptp.aa_Cod5141017464274028979atural tptp.divide5121882707175180666atural A) B))) (tptp.modulo8411746178871703098atural 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.aa_nat_fun_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.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.minus_8373710615458151222nteger A) (tptp.modulo364778990260209775nteger A B)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.divide6298287555418463151nteger A) B)))) (forall ((A tptp.code_natural) (B tptp.code_natural)) (= (tptp.aa_Cod4272041906116450446atural (tptp.aa_Cod5141017464274028979atural tptp.minus_7197305767214868737atural A) (tptp.modulo8411746178871703098atural A B)) (tptp.aa_Cod4272041906116450446atural (tptp.aa_Cod5141017464274028979atural tptp.times_2397367101498566445atural B) (tptp.aa_Cod4272041906116450446atural (tptp.aa_Cod5141017464274028979atural tptp.divide5121882707175180666atural 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.aa_nat_fun_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.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.minus_8373710615458151222nteger A) (tptp.modulo364778990260209775nteger A B)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.divide6298287555418463151nteger A) B)) B))) (forall ((A tptp.code_natural) (B tptp.code_natural)) (= (tptp.aa_Cod4272041906116450446atural (tptp.aa_Cod5141017464274028979atural tptp.minus_7197305767214868737atural A) (tptp.modulo8411746178871703098atural A B)) (tptp.aa_Cod4272041906116450446atural (tptp.aa_Cod5141017464274028979atural tptp.times_2397367101498566445atural (tptp.aa_Cod4272041906116450446atural (tptp.aa_Cod5141017464274028979atural tptp.divide5121882707175180666atural 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.aa_nat_fun_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.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.minus_8373710615458151222nteger A) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.divide6298287555418463151nteger A) B)) B)) (tptp.modulo364778990260209775nteger A B))) (forall ((A tptp.code_natural) (B tptp.code_natural)) (= (tptp.aa_Cod4272041906116450446atural (tptp.aa_Cod5141017464274028979atural tptp.minus_7197305767214868737atural A) (tptp.aa_Cod4272041906116450446atural (tptp.aa_Cod5141017464274028979atural tptp.times_2397367101498566445atural (tptp.aa_Cod4272041906116450446atural (tptp.aa_Cod5141017464274028979atural tptp.divide5121882707175180666atural A) B)) B)) (tptp.modulo8411746178871703098atural A B))) (forall ((N tptp.nat) (M tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat M) N)) N)))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat M) N))) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat N) M))))) (forall ((A2 tptp.nat) (B4 tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A2) B4)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (=> (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A2) N) tptp.zero_zero_nat) (=> (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat B4) N) tptp.zero_zero_nat) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A2) N)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat B4) N)))))))) (forall ((X tptp.nat) (N tptp.nat) (Y tptp.nat)) (=> (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat X) N) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat Y) N)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Y) X)) (exists ((Q6 tptp.nat)) (= X (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Y) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat N) Q6))))))) (forall ((M tptp.nat) (Q2 tptp.nat) (N tptp.nat)) (=> (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat M) Q2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat N) Q2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)) (not (forall ((S3 tptp.nat)) (not (= N (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat Q2) S3))))))))) (forall ((M tptp.nat) (Q2 tptp.nat) (N tptp.nat)) (=> (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat M) Q2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat N) Q2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N) M)) (not (forall ((S3 tptp.nat)) (not (= M (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat Q2) S3))))))))) (forall ((N tptp.nat) (M tptp.nat) (Q2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N) M)) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat M) Q2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat N) Q2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat Q2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) N)))))) (forall ((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 ((I4 tptp.int) (J3 tptp.int)) (=> (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) J3)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int J3) K)) (= N (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int K) I4)) J3))) (tptp.pp (tptp.aa_int_bool P J3))))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int K) tptp.zero_zero_int)) (forall ((I4 tptp.int) (J3 tptp.int)) (=> (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int K) J3)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int J3) tptp.zero_zero_int)) (= N (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int K) I4)) J3))) (tptp.pp (tptp.aa_int_bool P J3)))))))) (forall ((A tptp.int) (B tptp.int) (Q2 tptp.int) (R tptp.int)) (=> (= A (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B) Q2)) R)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int R) tptp.zero_zero_int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B) R)) (= (tptp.modulo_modulo_int A B) R))))) (forall ((A tptp.int) (B tptp.int) (Q2 tptp.int) (R tptp.int)) (=> (= A (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B) Q2)) R)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) R)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int R) B)) (= (tptp.modulo_modulo_int A B) R))))) (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.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A2) N)))) (forall ((M tptp.nat) (N tptp.nat) (Q2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat M))) (let ((_let_2 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat N))) (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat _let_2 Q2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat _let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat M) N)) Q2))) (tptp.aa_nat_nat _let_1 N)))))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat M) N) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat M) N)) N)))) (forall ((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 ((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.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger _let_3 (tptp.modulo364778990260209775nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.divide6298287555418463151nteger A) _let_1) _let_2))) (tptp.modulo364778990260209775nteger A _let_1))))))) (forall ((A tptp.code_natural) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.semiri3763490453095760265atural M))) (let ((_let_2 (tptp.semiri3763490453095760265atural N))) (let ((_let_3 (tptp.aa_Cod5141017464274028979atural tptp.times_2397367101498566445atural _let_1))) (= (tptp.modulo8411746178871703098atural A (tptp.aa_Cod4272041906116450446atural _let_3 _let_2)) (tptp.aa_Cod4272041906116450446atural (tptp.aa_Cod5141017464274028979atural tptp.plus_p4538020629002901425atural (tptp.aa_Cod4272041906116450446atural _let_3 (tptp.modulo8411746178871703098atural (tptp.aa_Cod4272041906116450446atural (tptp.aa_Cod5141017464274028979atural tptp.divide5121882707175180666atural A) _let_1) _let_2))) (tptp.modulo8411746178871703098atural 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.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A))) (let ((_let_3 (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat N))) (let ((_let_4 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat _let_1))) (= (tptp.aa_nat_nat _let_2 (tptp.aa_nat_nat _let_4 _let_3)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat _let_4 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) _let_1)) _let_3))) (tptp.aa_nat_nat _let_2 _let_1)))))))) (forall ((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.aa_nat_fun_nat_nat tptp.modulo_modulo_nat N) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 _let_1))))))))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.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.aa_nat_fun_nat_nat tptp.modulo_modulo_nat M) N))) (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex N)))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.aa_nat_real tptp.semiri5074537144036343181t_real (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat M) N)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real M)) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat M) N)))) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N)))) (forall ((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.divide_divide_rat (tptp.minus_minus_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat M) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat M) N))) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat N)))) (forall ((P tptp.fun_nat_bool) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (= N tptp.zero_zero_nat))) (= (tptp.pp (tptp.aa_nat_bool P (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat M) N))) (and (=> _let_1 (tptp.pp (tptp.aa_nat_bool P M))) (=> (not _let_1) (forall ((I4 tptp.nat) (J3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat J3) N)) (=> (= M (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat N) I4)) J3)) (tptp.pp (tptp.aa_nat_bool P J3)))))))))) (forall ((R tptp.nat) (N tptp.nat) (M tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat R) N)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat R) M)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat N) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) R))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat M) N) R))))) (forall ((A2 tptp.int) (B4 tptp.int) (N tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A2) B4)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) N)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.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 B4 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 B4) N)))))) (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 ((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 ((I4 tptp.int) (J3 tptp.int)) (=> (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int K) J3)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int J3) tptp.zero_zero_int)) (= N (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int K) I4)) J3))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool P I4) J3))))))) (forall ((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 ((I4 tptp.int) (J3 tptp.int)) (=> (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) J3)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int J3) K)) (= N (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int K) I4)) J3))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool P I4) J3))))))) (forall ((X tptp.nat) (D tptp.nat)) (let ((_let_1 (tptp.aa_nat_real tptp.semiri5074537144036343181t_real D))) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real X)) _let_1) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat X) D))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat X) D))) _let_1))))) (forall ((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.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger _let_1 (tptp.modulo364778990260209775nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.divide6298287555418463151nteger A) B) C))) (tptp.modulo364778990260209775nteger A B)))))) (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A))) (let ((_let_2 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat 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.aa_nat_fun_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.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A) _let_1) tptp.zero_zero_nat)))) (forall ((A tptp.int)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int _let_1) A)) (= (tptp.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 ((A tptp.code_natural)) (let ((_let_1 (tptp.numera5444537566228673987atural (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.pp (tptp.dvd_dvd_Code_natural _let_1 A)) (= (tptp.modulo8411746178871703098atural A _let_1) tptp.zero_z2226904508553997617atural)))) (forall ((A tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat _let_1) A))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A) _let_1) tptp.one_one_nat)))) (forall ((A tptp.int)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int _let_1) A))) (= (tptp.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 ((A tptp.code_natural)) (let ((_let_1 (tptp.numera5444537566228673987atural (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (not (tptp.pp (tptp.dvd_dvd_Code_natural _let_1 A))) (= (tptp.modulo8411746178871703098atural A _let_1) tptp.one_one_Code_natural)))) (forall ((A tptp.code_natural)) (let ((_let_1 (tptp.numera5444537566228673987atural (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.zero_n8403883297036319079atural (tptp.aa_bool_bool tptp.fNot (tptp.dvd_dvd_Code_natural _let_1 A))) (tptp.modulo8411746178871703098atural 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_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.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A) _let_1)))) (forall ((A tptp.int)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.aa_bool_int tptp.zero_n2684676970156552555ol_int (tptp.aa_bool_bool tptp.fNot (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int _let_1) A))) (tptp.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 ((M tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)) M)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat M) N))) M) tptp.one_one_nat))) (forall ((B tptp.nat) (A tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A))) (let ((_let_2 (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) 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.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A) _let_1)) tptp.zero_zero_nat)))) (forall ((A tptp.int)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (= (tptp.aa_int_int (tptp.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.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.divide6298287555418463151nteger A) _let_1) A) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.plus_p5714425477246183910nteger A) (tptp.modulo364778990260209775nteger A _let_1)) tptp.zero_z3403309356797280102nteger)))) (forall ((A tptp.code_natural)) (let ((_let_1 (tptp.numera5444537566228673987atural (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (= (tptp.aa_Cod4272041906116450446atural (tptp.aa_Cod5141017464274028979atural tptp.divide5121882707175180666atural A) _let_1) A) (= (tptp.aa_Cod4272041906116450446atural (tptp.aa_Cod5141017464274028979atural tptp.plus_p4538020629002901425atural A) (tptp.modulo8411746178871703098atural A _let_1)) tptp.zero_z2226904508553997617atural)))) (forall ((A tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A) _let_1))) (let ((_let_3 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat _let_1) A)))) (and (=> _let_3 (= _let_2 tptp.zero_zero_nat)) (=> (not _let_3) (= _let_2 tptp.one_one_nat))))))) (forall ((A tptp.int)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.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.code_natural)) (let ((_let_1 (tptp.numera5444537566228673987atural (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.modulo8411746178871703098atural A _let_1))) (let ((_let_3 (tptp.pp (tptp.dvd_dvd_Code_natural _let_1 A)))) (and (=> _let_3 (= _let_2 tptp.zero_z2226904508553997617atural)) (=> (not _let_3) (= _let_2 tptp.one_one_Code_natural))))))) (forall ((A tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A) _let_1))) (let ((_let_3 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat _let_1) A)))) (=> (=> _let_3 (not (= _let_2 tptp.zero_zero_nat))) (not (=> (not _let_3) (not (= _let_2 tptp.one_one_nat))))))))) (forall ((A tptp.int)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.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.code_natural)) (let ((_let_1 (tptp.numera5444537566228673987atural (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.modulo8411746178871703098atural A _let_1))) (let ((_let_3 (tptp.pp (tptp.dvd_dvd_Code_natural _let_1 A)))) (=> (=> _let_3 (not (= _let_2 tptp.zero_z2226904508553997617atural))) (not (=> (not _let_3) (not (= _let_2 tptp.one_one_Code_natural))))))))) (forall ((A tptp.nat) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_2 (tptp.aa_nat_nat _let_1 N))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) _let_2)) (tptp.aa_nat_nat _let_1 M)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A) (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N) M)))) _let_2))))) (forall ((A tptp.int) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_2 (tptp.aa_nat_int _let_1 N))) (= (tptp.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.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.divide6298287555418463151nteger A) _let_2) (tptp.power_8256067586552552935nteger _let_1 M)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger 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 ((A tptp.code_natural) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.numera5444537566228673987atural (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.power_7079662738309270450atural _let_1 N))) (= (tptp.modulo8411746178871703098atural (tptp.aa_Cod4272041906116450446atural (tptp.aa_Cod5141017464274028979atural tptp.divide5121882707175180666atural A) _let_2) (tptp.power_7079662738309270450atural _let_1 M)) (tptp.aa_Cod4272041906116450446atural (tptp.aa_Cod5141017464274028979atural tptp.divide5121882707175180666atural (tptp.modulo8411746178871703098atural A (tptp.power_7079662738309270450atural _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N) M)))) _let_2))))) (forall ((A2 tptp.nat) (B4 tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A2) B4)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A2) N)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.if_nat (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.fequal_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat B4) N)) tptp.zero_zero_nat)) tptp.one_one_nat) tptp.zero_zero_nat))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat B4) N)))))) (forall ((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.aa_nat_fun_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.divide6298287555418463151nteger A))) (let ((_let_2 (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_3 (tptp.aa_Cod1783974652533396728nteger _let_2 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_3)) B)) (= (tptp.aa_Cod1783974652533396728nteger _let_2 (tptp.aa_Cod1783974652533396728nteger _let_1 _let_3)) (tptp.aa_Cod1783974652533396728nteger _let_1 B)))))))) (forall ((M tptp.nat) (N tptp.nat) (A tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_2 (tptp.aa_nat_nat _let_1 M))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) _let_2)) (tptp.aa_nat_nat _let_1 N)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A) (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) M)))) _let_2)))))) (forall ((M tptp.nat) (N tptp.nat) (A tptp.int)) (let ((_let_1 (tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_2 (tptp.aa_nat_int _let_1 M))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)) (= (tptp.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.nat) (N tptp.nat) (A tptp.code_natural)) (let ((_let_1 (tptp.numera5444537566228673987atural (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.power_7079662738309270450atural _let_1 M))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)) (= (tptp.modulo8411746178871703098atural (tptp.aa_Cod4272041906116450446atural (tptp.aa_Cod5141017464274028979atural tptp.times_2397367101498566445atural A) _let_2) (tptp.power_7079662738309270450atural _let_1 N)) (tptp.aa_Cod4272041906116450446atural (tptp.aa_Cod5141017464274028979atural tptp.times_2397367101498566445atural (tptp.modulo8411746178871703098atural A (tptp.power_7079662738309270450atural _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)) (let ((_let_1 (tptp.numera5444537566228673987atural (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.power_7079662738309270450atural _let_1 M))) (= (tptp.modulo8411746178871703098atural _let_2 (tptp.power_7079662738309270450atural _let_1 N)) (tptp.aa_Cod4272041906116450446atural (tptp.aa_Cod5141017464274028979atural tptp.times_2397367101498566445atural (tptp.zero_n8403883297036319079atural (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.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_2 (tptp.aa_nat_nat _let_1 M))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat _let_2) (tptp.aa_nat_nat _let_1 N)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.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 ((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.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) (B3 tptp.real) (C3 tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool P A3))) (=> (tptp.pp (tptp.aa_real_bool _let_1 B3)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool P B3) C3)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A3) B3)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real B3) 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) (B3 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) B3)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real B3) A3)) D5))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool P A3) B3))))))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool P A) B)))))) (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.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.plus_p5714425477246183910nteger _let_1) M)))))))) (forall ((M tptp.nat) (X tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat X))) (let ((_let_2 (tptp.aa_nat_nat _let_1 M))) (let ((_let_3 (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) M)))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) M)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) X)) (or (= _let_3 _let_2) (= _let_3 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat _let_2) M))))))))) (forall ((M tptp.int) (X tptp.int)) (let ((_let_1 (tptp.modulo_modulo_int X 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.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.minus_8373710615458151222nteger _let_1) B) (tptp.modulo364778990260209775nteger A B))))))) (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A))) (let ((_let_2 (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) 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.code_integer)) (let ((_let_1 (tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.bit_se8260200283734997820nteger (tptp.aa_nat_nat tptp.suc N) A) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.plus_p5714425477246183910nteger (tptp.modulo364778990260209775nteger A _let_1)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger _let_1) (tptp.bit_se8260200283734997820nteger N (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.divide6298287555418463151nteger A) _let_1))))))) (forall ((N tptp.nat) (A tptp.code_natural)) (let ((_let_1 (tptp.numera5444537566228673987atural (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.bit_se7083795435491715335atural (tptp.aa_nat_nat tptp.suc N) A) (tptp.aa_Cod4272041906116450446atural (tptp.aa_Cod5141017464274028979atural tptp.plus_p4538020629002901425atural (tptp.modulo8411746178871703098atural A _let_1)) (tptp.aa_Cod4272041906116450446atural (tptp.aa_Cod5141017464274028979atural tptp.times_2397367101498566445atural _let_1) (tptp.bit_se7083795435491715335atural N (tptp.aa_Cod4272041906116450446atural (tptp.aa_Cod5141017464274028979atural tptp.divide5121882707175180666atural 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_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.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A) _let_1)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat _let_1) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se4205575877204974255it_nat N) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) _let_1))))))) (forall ((N tptp.nat) (A tptp.code_integer)) (let ((_let_1 (tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.bit_se2793503036327961859nteger (tptp.aa_nat_nat tptp.suc N) A) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.plus_p5714425477246183910nteger (tptp.modulo364778990260209775nteger A _let_1)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger _let_1) (tptp.bit_se2793503036327961859nteger N (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.divide6298287555418463151nteger A) _let_1))))))) (forall ((N tptp.nat) (A tptp.code_natural)) (let ((_let_1 (tptp.numera5444537566228673987atural (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.bit_se1617098188084679374atural (tptp.aa_nat_nat tptp.suc N) A) (tptp.aa_Cod4272041906116450446atural (tptp.aa_Cod5141017464274028979atural tptp.plus_p4538020629002901425atural (tptp.modulo8411746178871703098atural A _let_1)) (tptp.aa_Cod4272041906116450446atural (tptp.aa_Cod5141017464274028979atural tptp.times_2397367101498566445atural _let_1) (tptp.bit_se1617098188084679374atural N (tptp.aa_Cod4272041906116450446atural (tptp.aa_Cod5141017464274028979atural tptp.divide5121882707175180666atural 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.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A) _let_1)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat _let_1) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se7882103937844011126it_nat N) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) _let_1))))))) (forall ((N tptp.nat) (A tptp.code_integer)) (let ((_let_1 (tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.bit_se1345352211410354436nteger (tptp.aa_nat_nat tptp.suc N) A) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.plus_p5714425477246183910nteger (tptp.modulo364778990260209775nteger A _let_1)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger _let_1) (tptp.bit_se1345352211410354436nteger N (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.divide6298287555418463151nteger A) _let_1))))))) (forall ((N tptp.nat) (A tptp.code_natural)) (let ((_let_1 (tptp.numera5444537566228673987atural (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.bit_se168947363167071951atural (tptp.aa_nat_nat tptp.suc N) A) (tptp.aa_Cod4272041906116450446atural (tptp.aa_Cod5141017464274028979atural tptp.plus_p4538020629002901425atural (tptp.modulo8411746178871703098atural A _let_1)) (tptp.aa_Cod4272041906116450446atural (tptp.aa_Cod5141017464274028979atural tptp.times_2397367101498566445atural _let_1) (tptp.bit_se168947363167071951atural N (tptp.aa_Cod4272041906116450446atural (tptp.aa_Cod5141017464274028979atural tptp.divide5121882707175180666atural 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.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.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.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A) _let_1)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat _let_1) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se2161824704523386999it_nat N) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) _let_1))))))) (forall ((N tptp.nat)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (let ((_let_2 (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1))) (let ((_let_3 (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat))) (=> (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat N) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 _let_1))) _let_3) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat _let_2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) _let_3)) _let_2)))))))) (forall ((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 ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod4161879620478718930nteger tptp.divide6298287555418463151nteger A))) (let ((_let_2 (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_3 (tptp.aa_Cod1783974652533396728nteger _let_2 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_3))) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger _let_2 (tptp.aa_Cod1783974652533396728nteger _let_1 _let_3))) tptp.one_one_Code_integer) (tptp.aa_Cod1783974652533396728nteger _let_1 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.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A) _let_3))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat _let_2 (tptp.aa_nat_nat _let_1 _let_3))) tptp.one_one_nat) (tptp.aa_nat_nat _let_1 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 ((Z tptp.real) (X tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) Z)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real X) Z)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real Y) Z))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Y))))) (forall ((Z tptp.rat) (X tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) Z)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat X) Z)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat Y) Z))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) Y))))) (forall ((Z tptp.int) (X tptp.int) (Y tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) Z)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int X) Z)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int Y) Z))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) Y))))) (forall ((A tptp.real) (W tptp.num)) (let ((_let_1 (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.real_V1022390504157884413omplex (tptp.divide1717551699836669952omplex A (tptp.numera6690914467698888265omplex W))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.real_V1022390504157884413omplex A)) (tptp.numeral_numeral_real W)))) (forall ((A tptp.real) (W tptp.num)) (let ((_let_1 (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.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.real_V1022390504157884413omplex A)) (tptp.numeral_numeral_real W)))) (forall ((W tptp.num) (A tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.times_times_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.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.numeral_numeral_real W)) (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.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.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.real_V1022390504157884413omplex (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex N)) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N))) (forall ((W tptp.num)) (let ((_let_1 (tptp.numeral_numeral_real W))) (= (tptp.aa_real_real tptp.real_V7735802525324610683m_real _let_1) _let_1))) (forall ((W tptp.num)) (= (tptp.real_V1022390504157884413omplex (tptp.numera6690914467698888265omplex W)) (tptp.numeral_numeral_real W))) (= (tptp.aa_real_real tptp.real_V7735802525324610683m_real tptp.one_one_real) tptp.one_one_real) (= (tptp.real_V1022390504157884413omplex tptp.one_one_complex) tptp.one_one_real) (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)) (= (tptp.aa_real_real tptp.real_V7735802525324610683m_real tptp.zero_zero_real) tptp.zero_zero_real) (= (tptp.real_V1022390504157884413omplex tptp.zero_zero_complex) tptp.zero_zero_real) (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.real_V1022390504157884413omplex X) tptp.zero_zero_real) (= X tptp.zero_zero_complex))) (not (= tptp.zero_z5237406670263579293d_enat tptp.one_on7984719198319812577d_enat)) (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 ((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 ((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.real_V1022390504157884413omplex (tptp.minus_minus_complex A B)) (tptp.real_V1022390504157884413omplex (tptp.minus_minus_complex B A)))) (forall ((X tptp.real) (Y tptp.real)) (= (tptp.aa_real_real tptp.real_V7735802525324610683m_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real X) Y)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real X)) (tptp.aa_real_real tptp.real_V7735802525324610683m_real Y)))) (forall ((X tptp.complex) (Y tptp.complex)) (= (tptp.real_V1022390504157884413omplex (tptp.aa_complex_complex (tptp.times_times_complex X) Y)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.real_V1022390504157884413omplex X)) (tptp.real_V1022390504157884413omplex Y)))) (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.real_V1022390504157884413omplex (tptp.divide1717551699836669952omplex A B)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.real_V1022390504157884413omplex A)) (tptp.real_V1022390504157884413omplex B)))) (forall ((X tptp.real) (N tptp.nat)) (= (tptp.aa_real_real tptp.real_V7735802525324610683m_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) N)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real X)) N))) (forall ((X tptp.complex) (N tptp.nat)) (= (tptp.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.real_V1022390504157884413omplex X)) N))) (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.real_V1022390504157884413omplex (tptp.divide1717551699836669952omplex A B)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.real_V1022390504157884413omplex A)) (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.real_V1022390504157884413omplex W) (tptp.real_V1022390504157884413omplex Z))))) (forall ((X tptp.real) (R tptp.real) (Y tptp.real) (S tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real X)) R)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real Y)) S)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real X) Y))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real R) S)))))) (forall ((X tptp.complex) (R tptp.real) (Y tptp.complex) (S tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.real_V1022390504157884413omplex X)) R)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.real_V1022390504157884413omplex Y)) S)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.real_V1022390504157884413omplex (tptp.aa_complex_complex (tptp.times_times_complex X) Y))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real R) S)))))) (forall ((X tptp.real) (Y tptp.real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real X) Y))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real X)) (tptp.aa_real_real tptp.real_V7735802525324610683m_real Y))))) (forall ((X tptp.complex) (Y tptp.complex)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.real_V1022390504157884413omplex (tptp.aa_complex_complex (tptp.times_times_complex X) Y))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.real_V1022390504157884413omplex X)) (tptp.real_V1022390504157884413omplex Y))))) (forall ((X tptp.real) (Y tptp.real) (E tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real X)) (tptp.aa_real_real tptp.real_V7735802525324610683m_real Y))) E)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) Y))) E)))) (forall ((X tptp.complex) (Y tptp.complex) (E tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.real_V1022390504157884413omplex X)) (tptp.real_V1022390504157884413omplex Y))) E)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.real_V1022390504157884413omplex (tptp.plus_plus_complex X Y))) E)))) (forall ((X tptp.real) (R tptp.real) (Y tptp.real) (S tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real X)) R)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real Y)) S)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) Y))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real R) S)))))) (forall ((X tptp.complex) (R tptp.real) (Y tptp.complex) (S tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.real_V1022390504157884413omplex X)) R)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.real_V1022390504157884413omplex Y)) S)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.real_V1022390504157884413omplex (tptp.plus_plus_complex X Y))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real R) S)))))) (forall ((A tptp.real) (R tptp.real) (B tptp.real) (S tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real A)) R)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real B)) S)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) B))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real R) S)))))) (forall ((A tptp.complex) (R tptp.real) (B tptp.complex) (S tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.real_V1022390504157884413omplex A)) R)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.real_V1022390504157884413omplex B)) S)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.real_V1022390504157884413omplex (tptp.plus_plus_complex A B))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real R) S)))))) (forall ((X tptp.real) (Y tptp.real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) Y))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real X)) (tptp.aa_real_real tptp.real_V7735802525324610683m_real Y))))) (forall ((X tptp.complex) (Y tptp.complex)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.real_V1022390504157884413omplex (tptp.plus_plus_complex X Y))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.real_V1022390504157884413omplex X)) (tptp.real_V1022390504157884413omplex Y))))) (forall ((X tptp.real) (Y tptp.real) (E tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real X)) (tptp.aa_real_real tptp.real_V7735802525324610683m_real Y))) E)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) Y))) E)))) (forall ((X tptp.complex) (Y tptp.complex) (E tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.real_V1022390504157884413omplex X)) (tptp.real_V1022390504157884413omplex Y))) E)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.real_V1022390504157884413omplex (tptp.plus_plus_complex X Y))) E)))) (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.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.real_V1022390504157884413omplex B)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.real_V1022390504157884413omplex A)) C))))) (forall ((X tptp.real) (Y tptp.real) (E1 tptp.real) (Z tptp.real) (E22 tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real X))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real (tptp.aa_real_real _let_1 Y))) E1)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real Y) Z))) E22)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real (tptp.aa_real_real _let_1 Z))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real E1) E22))))))) (forall ((X tptp.complex) (Y tptp.complex) (E1 tptp.real) (Z tptp.complex) (E22 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.real_V1022390504157884413omplex (tptp.minus_minus_complex X Y))) E1)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.real_V1022390504157884413omplex (tptp.minus_minus_complex Y Z))) E22)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_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) (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.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.real_V1022390504157884413omplex X)) N)))) (forall ((X tptp.real) (Y tptp.real) (E tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real X)) (tptp.aa_real_real tptp.real_V7735802525324610683m_real Y))) E)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real X) Y))) E)))) (forall ((X tptp.complex) (Y tptp.complex) (E tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.real_V1022390504157884413omplex X)) (tptp.real_V1022390504157884413omplex Y))) E)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.real_V1022390504157884413omplex (tptp.minus_minus_complex X Y))) E)))) (forall ((X tptp.real) (Y tptp.real) (E1 tptp.real) (Z tptp.real) (E22 tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real X))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real (tptp.aa_real_real _let_1 Y))) E1)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real Y) Z))) E22)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real (tptp.aa_real_real _let_1 Z))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real E1) E22))))))) (forall ((X tptp.complex) (Y tptp.complex) (E1 tptp.real) (Z tptp.complex) (E22 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.real_V1022390504157884413omplex (tptp.minus_minus_complex X Y))) E1)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.real_V1022390504157884413omplex (tptp.minus_minus_complex Y Z))) E22)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_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 ((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.real_V1022390504157884413omplex (tptp.minus_minus_complex A B))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.real_V1022390504157884413omplex A)) (tptp.real_V1022390504157884413omplex B))))) (forall ((X tptp.real) (Y tptp.real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real X)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real Y)) (tptp.aa_real_real tptp.real_V7735802525324610683m_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real X) Y)))))) (forall ((X tptp.complex) (Y tptp.complex)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.real_V1022390504157884413omplex X)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.real_V1022390504157884413omplex Y)) (tptp.real_V1022390504157884413omplex (tptp.minus_minus_complex X Y)))))) (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.real_V1022390504157884413omplex A)) (tptp.real_V1022390504157884413omplex B))) (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.real_V1022390504157884413omplex A)) (tptp.real_V1022390504157884413omplex B))) (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.real_V1022390504157884413omplex W) tptp.one_one_real) (= N tptp.zero_zero_nat)))) (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.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.real_V1022390504157884413omplex (tptp.minus_minus_complex A C))) (tptp.real_V1022390504157884413omplex (tptp.minus_minus_complex B D)))))) (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.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.real_V1022390504157884413omplex Z)) tptp.one_one_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_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.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.real_V1022390504157884413omplex (tptp.minus_minus_complex Z W)))))))) (= (tptp.aa_real_real tptp.arcosh_real tptp.one_one_real) tptp.zero_zero_real) (forall ((X tptp.nat) (N tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low X) N) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat X) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N)))) (= (tptp.aa_real_real tptp.arsinh_real tptp.zero_zero_real) tptp.zero_zero_real) (= (tptp.aa_real_real tptp.artanh_real tptp.zero_zero_real) tptp.zero_zero_real) (forall ((Z tptp.complex) (N tptp.nat)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (let ((_let_2 (tptp.numera6690914467698888265omplex _let_1))) (let ((_let_3 (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1))) (let ((_let_4 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat _let_3) N))) (= (tptp.aa_nat_complex (tptp.comm_s2602460028002588243omplex (tptp.aa_complex_complex (tptp.times_times_complex _let_2) Z)) _let_4) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat _let_3) _let_4))) (tptp.aa_nat_complex (tptp.comm_s2602460028002588243omplex Z) N))) (tptp.aa_nat_complex (tptp.comm_s2602460028002588243omplex (tptp.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.numeral_numeral_real _let_1))) (let ((_let_3 (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1))) (let ((_let_4 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat _let_3) N))) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.comm_s7457072308508201937r_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real _let_2) Z)) _let_4) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat _let_3) _let_4))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.comm_s7457072308508201937r_real Z) N))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.comm_s7457072308508201937r_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real Z) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.one_one_real) _let_2))) N)))))))) (forall ((Z tptp.rat) (N tptp.nat)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (let ((_let_2 (tptp.numeral_numeral_rat _let_1))) (let ((_let_3 (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1))) (let ((_let_4 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat _let_3) N))) (= (tptp.aa_nat_rat (tptp.comm_s4028243227959126397er_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat _let_2) Z)) _let_4) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat _let_3) _let_4))) (tptp.aa_nat_rat (tptp.comm_s4028243227959126397er_rat Z) N))) (tptp.aa_nat_rat (tptp.comm_s4028243227959126397er_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat Z) (tptp.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.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.numeral_numeral_real _let_1)) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N)))) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1)) N)) N))))))) (forall ((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.aa_nat_fun_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 ((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.aa_nat_fun_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.aa_nat_fun_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.aa_nat_fun_nat_nat tptp.comm_s4663373288045622133er_nat X) N)))) (forall ((X tptp.nat) (N tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_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.aa_nat_fun_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.aa_nat_fun_nat_nat tptp.comm_s4663373288045622133er_nat X) N)))) (forall ((X tptp.real) (N tptp.nat)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool _let_1 X)) (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.comm_s7457072308508201937r_real X) N)))))) (forall ((X tptp.rat) (N tptp.nat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 X)) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_nat_rat (tptp.comm_s4028243227959126397er_rat X) N)))))) (forall ((X tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 X)) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.comm_s4663373288045622133er_nat X) N)))))) (forall ((X tptp.int) (N tptp.nat)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int))) (=> (tptp.pp (tptp.aa_int_bool _let_1 X)) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_nat_int (tptp.comm_s4660882817536571857er_int X) N)))))) (forall ((A tptp.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.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 ((X tptp.real) (N tptp.nat)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) X)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.comm_s7457072308508201937r_real X) N))))) (forall ((X tptp.rat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) X)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_nat_rat (tptp.comm_s4028243227959126397er_rat X) N))))) (forall ((X tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) X)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.comm_s4663373288045622133er_nat X) N))))) (forall ((X tptp.int) (N tptp.nat)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) X)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.aa_nat_int (tptp.comm_s4660882817536571857er_int X) N))))) (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.aa_nat_fun_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 ((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.aa_nat_fun_nat_nat tptp.comm_s4663373288045622133er_nat A) (tptp.aa_nat_nat tptp.suc N)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.comm_s4663373288045622133er_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) tptp.one_one_nat)) N)))) (forall ((A tptp.int) (N tptp.nat)) (= (tptp.aa_nat_int (tptp.comm_s4660882817536571857er_int A) (tptp.aa_nat_nat tptp.suc N)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) (tptp.aa_nat_int (tptp.comm_s4660882817536571857er_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) tptp.one_one_int)) N)))) (forall ((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.aa_nat_fun_nat_nat tptp.comm_s4663373288045622133er_nat Z))) (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat tptp.suc N)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Z) (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat N))) (tptp.aa_nat_nat _let_1 N))))) (forall ((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.aa_nat_fun_nat_nat tptp.comm_s4663373288045622133er_nat A))) (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat tptp.suc N)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat _let_1 N)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat N)))))) (forall ((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 ((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.aa_nat_fun_nat_nat tptp.comm_s4663373288045622133er_nat Z))) (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N) M)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat _let_1 N)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.comm_s4663373288045622133er_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Z) (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat N))) M))))) (forall ((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 ((K tptp.nat) (K6 tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.binomial N))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) K6)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) K6)) N)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat _let_1 K)) (tptp.aa_nat_nat _let_1 K6))))))) (forall ((N tptp.nat) (K tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.binomial (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N)))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat _let_1 K)) (tptp.aa_nat_nat _let_1 N))))) (forall ((N tptp.nat) (K tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.binomial N))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat _let_1 K)) (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat N) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))))))) (forall ((K tptp.nat) (K6 tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.binomial N))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) K6)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat N) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) K)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K6) N)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat _let_1 K6)) (tptp.aa_nat_nat _let_1 K)))))))) (forall ((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.aa_nat_fun_nat_nat tptp.comm_s4663373288045622133er_nat Z))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)) (= (tptp.aa_nat_nat _let_1 N) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat _let_1 M)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.comm_s4663373288045622133er_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Z) (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat M))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) M))))))) (forall ((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.aa_nat_fun_nat_nat tptp.binomial N))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat K) K6)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) K6)) N)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat _let_1 K)) (tptp.aa_nat_nat _let_1 K6))))))) (forall ((K tptp.nat) (K6 tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.binomial N))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat K) K6)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) K))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K6) N)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat _let_1 K6)) (tptp.aa_nat_nat _let_1 K)))))))) (forall ((K tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.binomial N))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat K) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat N) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat _let_1 K)) (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat tptp.suc K))))))) (forall ((N tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat N) _let_1))) (let ((_let_3 (tptp.aa_nat_fun_nat_nat tptp.binomial N))) (=> (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat _let_1) N))) (= (tptp.aa_nat_nat _let_3 (tptp.aa_nat_nat tptp.suc _let_2)) (tptp.aa_nat_nat _let_3 _let_2))))))) (forall ((N tptp.nat) (K tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial N) K))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) N)))) (forall ((N tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial N) _let_1) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat N) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) tptp.one_one_nat))) _let_1)))) (forall ((N tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_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.aa_nat_fun_nat_nat tptp.binomial N))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial (tptp.aa_nat_nat tptp.suc N)) _let_1) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat _let_2 K)) (tptp.aa_nat_nat _let_2 _let_1)))))) (forall ((N tptp.nat) (K tptp.nat)) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial N) K) tptp.zero_zero_nat) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N) K)))) (forall ((K tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial tptp.zero_zero_nat) (tptp.aa_nat_nat tptp.suc K)) tptp.zero_zero_nat)) (forall ((N tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial N) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)) N)) (forall ((N tptp.nat) (K tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.binomial (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) tptp.one_one_nat)))) (let ((_let_2 (tptp.aa_nat_nat tptp.suc K))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial N) _let_2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat _let_1 _let_2)) (tptp.aa_nat_nat _let_1 K))))))) (forall ((N tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial _let_1) N) _let_1))) (forall ((N tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial N) N) tptp.one_one_nat)) (forall ((N tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial N) tptp.one_one_nat) N)) (forall ((N tptp.nat) (K tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N) K)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial N) K) tptp.zero_zero_nat))) (forall ((K tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N))) (let ((_let_2 (tptp.aa_nat_nat tptp.suc K))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat _let_2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial _let_1) _let_2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat _let_1) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial N) K)))))) (forall ((N tptp.nat) (K tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc K))) (let ((_let_2 (tptp.aa_nat_nat tptp.suc N))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat _let_2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial N) K)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial _let_2) _let_1)) _let_1))))) (forall ((K tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.binomial N))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) N)) (= (tptp.aa_nat_nat _let_1 K) (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) K)))))) (forall ((M tptp.nat) (R tptp.nat) (K tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M))) (let ((_let_2 (tptp.aa_nat_nat _let_1 R))) (let ((_let_3 (tptp.aa_nat_fun_nat_nat tptp.binomial (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat _let_2) K)))) (let ((_let_4 (tptp.aa_nat_nat _let_1 K))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat _let_3 _let_4)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial _let_4) K)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat _let_3 K)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial _let_2) M)))))))) (forall ((R tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat R) N)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial N) R)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat N) R))))) (forall ((K tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) N)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial N) K))))) (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.binomial (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) 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.aa_nat_fun_nat_nat tptp.binomial N))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) M)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat _let_1 M)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial M) K)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat _let_1 K)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) K)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) K)))))))) (forall ((N tptp.nat) (K tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc K))) (let ((_let_2 (tptp.aa_nat_nat tptp.suc N))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial _let_2) _let_1) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat _let_2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial N) K))) _let_1))))) (forall ((N tptp.nat) (K tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat _let_1 K)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial N) K)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat N) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial (tptp.aa_nat_nat _let_1 tptp.one_one_nat)) K))))) (forall ((K tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc K))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat _let_1) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial N) _let_1)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat N) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) tptp.one_one_nat)) K))))) (forall ((K tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) N)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N)) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real K))) K)) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial N) K)))))) (forall ((K tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) N)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat (tptp.power_power_rat (tptp.divide_divide_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat N) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat K))) K)) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial N) K)))))) (forall ((N tptp.nat) (K tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial N) K)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N)))) (forall ((N tptp.nat) (K tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.binomial (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) tptp.one_one_nat)))) (let ((_let_2 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat))) (=> (tptp.pp (tptp.aa_nat_bool _let_2 N)) (=> (tptp.pp (tptp.aa_nat_bool _let_2 K)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial N) K) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat K) tptp.one_one_nat))) (tptp.aa_nat_nat _let_1 K)))))))) (forall ((K tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) K)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat K) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial N) K)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat N) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) tptp.one_one_nat)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat K) tptp.one_one_nat)))))) (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.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))))) (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 ((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.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.plus_p5714425477246183910nteger (tptp.modulo364778990260209775nteger A _let_1)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger _let_1) (tptp.bit_ri6519982836138164636nteger N (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger 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 ((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 ((N tptp.nat)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (let ((_let_2 (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.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.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 ((L tptp.int) (K tptp.int) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat M) N)))) (let ((_let_2 (tptp.aa_int_int tptp.sgn_sgn_int L))) (let ((_let_3 (tptp.aa_int_fun_int_int tptp.times_times_int _let_2))) (let ((_let_4 (tptp.aa_int_int tptp.sgn_sgn_int K))) (let ((_let_5 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int _let_4) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int M)))) (let ((_let_6 (tptp.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.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.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger 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.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.divide6298287555418463151nteger A) _let_1))) _let_1)) (tptp.modulo364778990260209775nteger A _let_1))))))))) (forall ((N tptp.nat) (A tptp.code_natural)) (let ((_let_1 (tptp.numera5444537566228673987atural (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.bit_se569199155075624693atural N A))) (let ((_let_3 (= N tptp.zero_zero_nat))) (and (=> _let_3 (= _let_2 tptp.zero_z2226904508553997617atural)) (=> (not _let_3) (= _let_2 (tptp.aa_Cod4272041906116450446atural (tptp.aa_Cod5141017464274028979atural tptp.plus_p4538020629002901425atural (tptp.aa_Cod4272041906116450446atural (tptp.aa_Cod5141017464274028979atural tptp.times_2397367101498566445atural (tptp.bit_se569199155075624693atural (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) tptp.one_one_nat) (tptp.aa_Cod4272041906116450446atural (tptp.aa_Cod5141017464274028979atural tptp.divide5121882707175180666atural A) _let_1))) _let_1)) (tptp.modulo8411746178871703098atural 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.aa_nat_fun_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.aa_nat_fun_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.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A) _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_eq_nat M) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1)) N))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) M)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.log2 (tptp.numeral_numeral_real _let_1)) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real M))) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N))))))) (forall ((A tptp.int)) (let ((_let_1 (tptp.aa_int_int tptp.sgn_sgn_int A))) (= (tptp.aa_int_int 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.rat)) (let ((_let_1 (tptp.sgn_sgn_rat A))) (= (tptp.sgn_sgn_rat _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 ((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.aa_nat_fun_nat_nat tptp.bit_se2925701944663578781it_nat N) tptp.zero_zero_nat) tptp.zero_zero_nat)) _let_158 (= (tptp.aa_Cod1783974652533396728nteger tptp.sgn_sgn_Code_integer tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger) _let_157 (= (tptp.sgn_sgn_rat tptp.zero_zero_rat) tptp.zero_zero_rat) (= (tptp.aa_int_int tptp.sgn_sgn_int tptp.zero_zero_int) tptp.zero_zero_int) _let_158 _let_157 (= (tptp.aa_int_int tptp.sgn_sgn_int tptp.one_one_int) tptp.one_one_int) _let_156 _let_155 (= (tptp.sgn_sgn_rat tptp.one_one_rat) tptp.one_one_rat) (= (tptp.aa_Cod1783974652533396728nteger tptp.sgn_sgn_Code_integer tptp.one_one_Code_integer) tptp.one_one_Code_integer) _let_156 _let_155 (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.sgn_sgn_rat (tptp.divide_divide_rat A B)) (tptp.divide_divide_rat (tptp.sgn_sgn_rat A) (tptp.sgn_sgn_rat B)))) (forall ((A tptp.rat) (N tptp.nat)) (= (tptp.sgn_sgn_rat (tptp.aa_nat_rat (tptp.power_power_rat A) N)) (tptp.aa_nat_rat (tptp.power_power_rat (tptp.sgn_sgn_rat A)) N))) (forall ((A tptp.code_integer) (N tptp.nat)) (= (tptp.aa_Cod1783974652533396728nteger tptp.sgn_sgn_Code_integer (tptp.power_8256067586552552935nteger A N)) (tptp.power_8256067586552552935nteger (tptp.aa_Cod1783974652533396728nteger tptp.sgn_sgn_Code_integer A) N))) (forall ((A tptp.real) (N tptp.nat)) (= (tptp.aa_real_real tptp.sgn_sgn_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real A) N)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real tptp.sgn_sgn_real A)) N))) (forall ((A tptp.int) (N tptp.nat)) (= (tptp.aa_int_int tptp.sgn_sgn_int (tptp.aa_nat_int (tptp.power_power_int A) N)) (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_int_int tptp.sgn_sgn_int A)) 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_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_int_int (tptp.bit_ri631733984087533419it_int N) tptp.zero_zero_int) tptp.zero_zero_int)) (forall ((K tptp.int) (L tptp.int)) (= (tptp.aa_int_int (tptp.bit_concat_bit tptp.zero_zero_nat K) L) L)) (forall ((N tptp.nat) (K tptp.int)) (= (tptp.aa_int_int (tptp.bit_concat_bit N K) tptp.zero_zero_int) (tptp.aa_int_int (tptp.bit_se2923211474154528505it_int N) K))) (forall ((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.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.aa_int_int tptp.sgn_sgn_int A))) (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.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.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.aa_int_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.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.aa_nat_fun_nat_nat tptp.bit_se2925701944663578781it_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)) (forall ((X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) X)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.ln_ln_real X)) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) tptp.one_one_real))))) (forall ((X tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool _let_1 X)) (= (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real tptp.ln_ln_real X))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real) X)))))) (forall ((X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) X)) (= (= (tptp.aa_real_real tptp.ln_ln_real X) tptp.zero_zero_real) (= X tptp.one_one_real)))) (forall ((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.sgn_sgn_rat B))) (= (tptp.divide_divide_rat A _let_1) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) _let_1)))) (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.aa_nat_fun_nat_nat tptp.bit_se2925701944663578781it_nat (tptp.aa_nat_nat tptp.suc N)) tptp.one_one_nat) tptp.one_one_nat)) (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.aa_nat_fun_nat_nat tptp.bit_se2925701944663578781it_nat (tptp.aa_num_nat tptp.numeral_numeral_nat L)) tptp.one_one_nat) tptp.one_one_nat)) (= (tptp.aa_real_real tptp.ln_ln_real tptp.one_one_real) tptp.zero_zero_real) (= (tptp.aa_nat_complex tptp.semiri5044797733671781792omplex tptp.zero_zero_nat) tptp.one_one_complex) (= (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.one_one_nat) tptp.one_one_complex) (= (tptp.aa_nat_rat tptp.semiri773545260158071498ct_rat tptp.one_one_nat) tptp.one_one_rat) (= (tptp.aa_nat_int tptp.semiri1406184849735516958ct_int tptp.one_one_nat) tptp.one_one_int) (= (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat tptp.one_one_nat) tptp.one_one_nat) (= (tptp.aa_nat_real tptp.semiri2265585572941072030t_real tptp.one_one_nat) tptp.one_one_real) (forall ((N tptp.nat)) (= (tptp.aa_int_int (tptp.bit_ri631733984087533419it_int (tptp.aa_nat_nat tptp.suc N)) tptp.one_one_int) tptp.one_one_int)) (forall ((K tptp.num)) (= (tptp.aa_int_int (tptp.bit_ri631733984087533419it_int (tptp.aa_num_nat tptp.numeral_numeral_nat K)) tptp.one_one_int) tptp.one_one_int)) (forall ((A tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.log2 A) tptp.one_one_real) 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 ((N tptp.nat) (L tptp.int)) (= (tptp.aa_int_int (tptp.bit_concat_bit N tptp.zero_zero_int) L) (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_se545348938243370406it_int N) L))) (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.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.aa_int_int tptp.sgn_sgn_int A) tptp.one_one_int))) (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.aa_nat_fun_nat_nat tptp.bit_se2925701944663578781it_nat N) tptp.one_one_nat) tptp.zero_zero_nat) (= N tptp.zero_zero_nat))) (forall ((X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) X)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.ln_ln_real X)) tptp.zero_zero_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.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))))) (= (tptp.aa_nat_complex tptp.semiri5044797733671781792omplex _let_11) tptp.one_one_complex) (= (tptp.aa_nat_rat tptp.semiri773545260158071498ct_rat _let_11) tptp.one_one_rat) (= (tptp.aa_nat_int tptp.semiri1406184849735516958ct_int _let_11) tptp.one_one_int) (= (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat _let_11) tptp.one_one_nat) (= (tptp.aa_nat_real tptp.semiri2265585572941072030t_real _let_11) tptp.one_one_real) (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))))) (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 ((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.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.aa_int_int 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)))))) (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.log2 A) X))) (tptp.pp (tptp.aa_real_bool _let_1 X)))))))) (forall ((A tptp.real) (X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real) A)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) X)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.log2 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))) (=> (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.log2 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.log2 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) (Y tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.log2 A))) (let ((_let_2 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real) A)) (=> (tptp.pp (tptp.aa_real_bool _let_2 X)) (=> (tptp.pp (tptp.aa_real_bool _let_2 Y)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real _let_1 X)) (tptp.aa_real_real _let_1 Y))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Y))))))))) (forall ((A tptp.real)) (=> (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.log2 A) A) tptp.one_one_real)))) (forall ((N tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se2925701944663578781it_nat N) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)) (tptp.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 ((R tptp.int) (L tptp.int) (K tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int tptp.sgn_sgn_int R)) L)) K)) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int L) K)) (=> (= R tptp.zero_zero_int) (= K tptp.zero_zero_int))))) (forall ((L tptp.int) (R tptp.int) (K tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int L) (tptp.aa_int_int tptp.sgn_sgn_int R))) K)) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int L) K)) (=> (= R tptp.zero_zero_int) (= K tptp.zero_zero_int))))) (forall ((L tptp.int) (R tptp.int) (K tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int L))) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int tptp.sgn_sgn_int R)) K))) (or (tptp.pp (tptp.aa_int_bool _let_1 K)) (= R tptp.zero_zero_int))))) (forall ((L tptp.int) (K tptp.int) (R tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int L))) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int K) (tptp.aa_int_int tptp.sgn_sgn_int R)))) (or (tptp.pp (tptp.aa_int_bool _let_1 K)) (= R tptp.zero_zero_int))))) (= (tptp.aa_nat_complex tptp.semiri5044797733671781792omplex _let_2) _let_83) (= (tptp.aa_nat_rat tptp.semiri773545260158071498ct_rat _let_2) _let_137) (= (tptp.aa_nat_int tptp.semiri1406184849735516958ct_int _let_2) _let_68) (= (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat _let_2) _let_2) (= (tptp.aa_nat_real tptp.semiri2265585572941072030t_real _let_2) _let_46) (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)) (= (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.aa_nat_fun_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 ((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.log2 A) X))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.one_one_real) X)))))) (forall ((A tptp.real) (X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real) A)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) X)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.log2 A) X)) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) tptp.one_one_real)))))) (forall ((A tptp.real) (X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real) A)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) X)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.one_one_real) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.log2 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.log2 A) X)) tptp.one_one_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) A)))))) (forall ((A tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.log2 A))) (let ((_let_2 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real) A)) (=> (tptp.pp (tptp.aa_real_bool _let_2 X)) (=> (tptp.pp (tptp.aa_real_bool _let_2 Y)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real _let_1 X)) (tptp.aa_real_real _let_1 Y))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) Y))))))))) (forall ((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.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.aa_int_int 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) (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.aa_nat_fun_nat_nat tptp.bit_se2925701944663578781it_nat N) A))) (or (= N tptp.zero_zero_nat) (tptp.pp (tptp.aa_nat_bool _let_1 A)))))) (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.log2 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 ((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.code_natural)) (= (tptp.bit_se569199155075624693atural (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat) A) (tptp.modulo8411746178871703098atural A (tptp.numera5444537566228673987atural (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.aa_nat_fun_nat_nat tptp.bit_se2925701944663578781it_nat (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)) A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (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.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se2925701944663578781it_nat 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.aa_nat_fun_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) (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.aa_nat_fun_nat_nat tptp.bit_se2925701944663578781it_nat N) M)))) (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat 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 ((N tptp.nat) (K tptp.int) (L tptp.int) (R tptp.int) (S tptp.int)) (let ((_let_1 (tptp.bit_se2923211474154528505it_int N))) (= (= (tptp.aa_int_int (tptp.bit_concat_bit N K) L) (tptp.aa_int_int (tptp.bit_concat_bit N R) S)) (and (= (tptp.aa_int_int _let_1 K) (tptp.aa_int_int _let_1 R)) (= L S))))) (forall ((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 ((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 ((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 ((A tptp.real) (X tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.log2 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)))) (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.aa_nat_fun_nat_nat 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.aa_nat_fun_nat_nat tptp.bit_se2925701944663578781it_nat M))) (let ((_let_2 (tptp.aa_nat_fun_nat_nat 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 ((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 ((N tptp.nat) (M tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se2925701944663578781it_nat N) M)) M))) (forall ((M tptp.nat) (N tptp.nat) (Q2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se2925701944663578781it_nat M) Q2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se2925701944663578781it_nat N) Q2))))) (forall ((A tptp.complex)) (= (= (tptp.sgn_sgn_complex A) tptp.zero_zero_complex) (= A tptp.zero_zero_complex))) (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.sgn_sgn_rat A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))) (forall ((A tptp.int)) (= (= (tptp.aa_int_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.real)) (= (= (tptp.aa_real_real tptp.sgn_sgn_real A) tptp.zero_zero_real) (= A tptp.zero_zero_real))) (forall ((A tptp.rat)) (= (= (tptp.sgn_sgn_rat A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))) (forall ((A tptp.int)) (= (= (tptp.aa_int_int tptp.sgn_sgn_int A) tptp.zero_zero_int) (= A tptp.zero_zero_int))) (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.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.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.sgn_sgn_rat A)) (tptp.sgn_sgn_rat B)))) (forall ((A tptp.int) (B tptp.int)) (= (tptp.aa_int_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.aa_int_int tptp.sgn_sgn_int A)) (tptp.aa_int_int tptp.sgn_sgn_int B)))) (forall ((X tptp.complex) (Y tptp.complex)) (= (tptp.sgn_sgn_complex (tptp.aa_complex_complex (tptp.times_times_complex X) Y)) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.sgn_sgn_complex X)) (tptp.sgn_sgn_complex Y)))) (forall ((X tptp.real) (Y tptp.real)) (= (tptp.aa_real_real tptp.sgn_sgn_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real X) Y)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real tptp.sgn_sgn_real X)) (tptp.aa_real_real tptp.sgn_sgn_real Y)))) (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.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger 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.sgn_sgn_rat A))) (=> (= (tptp.sgn_sgn_rat B) _let_1) (= (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.aa_int_int tptp.sgn_sgn_int A))) (=> (= (tptp.aa_int_int tptp.sgn_sgn_int B) _let_1) (= (tptp.aa_int_int tptp.sgn_sgn_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) B)) _let_1)))) (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) (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) (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 ((N tptp.nat) (K tptp.int) (L tptp.int)) (= (tptp.aa_int_int (tptp.bit_concat_bit N K) L) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.bit_se2923211474154528505it_int N) K)) (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_se545348938243370406it_int N) L)))) (forall ((N tptp.nat) (K tptp.int) (M tptp.nat) (L tptp.int) (R tptp.int)) (let ((_let_1 (tptp.bit_concat_bit N K))) (= (tptp.aa_int_int _let_1 (tptp.aa_int_int (tptp.bit_concat_bit M L) R)) (tptp.aa_int_int (tptp.bit_concat_bit (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) N) (tptp.aa_int_int _let_1 L)) R)))) (forall ((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) (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 ((N tptp.nat) (K tptp.int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.aa_int_int (tptp.bit_se2923211474154528505it_int N) K)))) (forall ((N tptp.nat) (K tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.bit_se2923211474154528505it_int N) K)) K)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) K)))) (forall ((N tptp.nat) (K tptp.int)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.bit_se2923211474154528505it_int N) K)) tptp.zero_zero_int)))) (forall ((K tptp.int) (N tptp.nat)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_int K))) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.bit_se2923211474154528505it_int N) K))) (tptp.pp (tptp.aa_int_bool _let_1 tptp.zero_zero_int))))) (forall ((M tptp.nat) (N tptp.nat) (A tptp.code_integer)) (let ((_let_1 (tptp.aa_nat6383147911832638789nteger tptp.bit_se7788150548672797655nteger M))) (= (tptp.aa_Cod1783974652533396728nteger _let_1 (tptp.bit_se1745604003318907178nteger N A)) (tptp.bit_se1745604003318907178nteger (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) N) (tptp.aa_Cod1783974652533396728nteger _let_1 A))))) (forall ((M tptp.nat) (N tptp.nat) (A tptp.code_natural)) (let ((_let_1 (tptp.aa_nat5282697797315388251atural tptp.bit_se6611745700429515170atural M))) (= (tptp.aa_Cod4272041906116450446atural _let_1 (tptp.bit_se569199155075624693atural N A)) (tptp.bit_se569199155075624693atural (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) N) (tptp.aa_Cod4272041906116450446atural _let_1 A))))) (forall ((M tptp.nat) (N tptp.nat) (A tptp.int)) (let ((_let_1 (tptp.aa_nat_fun_int_int tptp.bit_se545348938243370406it_int M))) (= (tptp.aa_int_int _let_1 (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.aa_int_int _let_1 A))))) (forall ((M tptp.nat) (N tptp.nat) (A tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.bit_se547839408752420682it_nat M))) (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se2925701944663578781it_nat N) A)) (tptp.aa_nat_nat (tptp.aa_nat_fun_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 ((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 ((M tptp.nat) (N tptp.nat) (A tptp.code_integer)) (let ((_let_1 (tptp.aa_nat6383147911832638789nteger tptp.bit_se7788150548672797655nteger N))) (= (tptp.bit_se1745604003318907178nteger M (tptp.aa_Cod1783974652533396728nteger _let_1 A)) (tptp.aa_Cod1783974652533396728nteger _let_1 (tptp.bit_se1745604003318907178nteger (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.code_natural)) (let ((_let_1 (tptp.aa_nat5282697797315388251atural tptp.bit_se6611745700429515170atural N))) (= (tptp.bit_se569199155075624693atural M (tptp.aa_Cod4272041906116450446atural _let_1 A)) (tptp.aa_Cod4272041906116450446atural _let_1 (tptp.bit_se569199155075624693atural (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.int)) (let ((_let_1 (tptp.aa_nat_fun_int_int tptp.bit_se545348938243370406it_int N))) (= (tptp.aa_int_int (tptp.bit_se2923211474154528505it_int M) (tptp.aa_int_int _let_1 A)) (tptp.aa_int_int _let_1 (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.aa_nat_fun_nat_nat tptp.bit_se547839408752420682it_nat N))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_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.aa_nat_fun_nat_nat tptp.bit_se2925701944663578781it_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) N)) A))))) (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 ((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.aa_int_int tptp.sgn_sgn_int L2)) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N2))))))) (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 ((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.aa_nat_fun_nat_nat 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.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.aa_nat_fun_nat_nat 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.int)) (let ((_let_1 (tptp.bit_se2923211474154528505it_int N))) (let ((_let_2 (tptp.aa_int_int _let_1 A))) (let ((_let_3 (tptp.aa_int_int _let_1 (tptp.bit_se2159334234014336723it_int M 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_2)) (=> (not _let_4) (= _let_3 (tptp.bit_se2159334234014336723it_int M _let_2))))))))) (forall ((N tptp.nat) (M tptp.nat) (A tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat 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 ((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)) (= (tptp.aa_nat_complex tptp.semiri5044797733671781792omplex N) (tptp.aa_nat_complex (tptp.comm_s2602460028002588243omplex tptp.one_one_complex) N))) (forall ((N tptp.nat)) (= (tptp.aa_nat_rat tptp.semiri773545260158071498ct_rat N) (tptp.aa_nat_rat (tptp.comm_s4028243227959126397er_rat tptp.one_one_rat) N))) (forall ((N tptp.nat)) (= (tptp.aa_nat_int tptp.semiri1406184849735516958ct_int N) (tptp.aa_nat_int (tptp.comm_s4660882817536571857er_int tptp.one_one_int) N))) (forall ((N tptp.nat)) (= (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat N) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.comm_s4663373288045622133er_nat tptp.one_one_nat) N))) (forall ((N tptp.nat)) (= (tptp.aa_nat_real tptp.semiri2265585572941072030t_real N) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.comm_s7457072308508201937r_real tptp.one_one_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.log2 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.log2 B) X)))))))))) (forall ((X tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real tptp.ln_ln_real X))) (=> (tptp.pp (tptp.aa_real_bool _let_1 X)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real) X)))))) (forall ((X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) tptp.one_one_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.ln_ln_real X)) tptp.zero_zero_real))))) (forall ((X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real) X)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) (tptp.aa_real_real tptp.ln_ln_real X))))) (forall ((X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.one_one_real) X)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_real_real tptp.ln_ln_real X))))) (forall ((N tptp.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 ((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.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.aa_int_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 ((M tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.one_one_nat) M)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat M) (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat N)))))) (forall ((N tptp.nat) (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) (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 ((L tptp.int) (K tptp.int)) (=> (not (= L tptp.zero_zero_int)) (=> (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int L) K))) (= (tptp.aa_int_int tptp.sgn_sgn_int (tptp.modulo_modulo_int K L)) (tptp.aa_int_int tptp.sgn_sgn_int L))))) (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.modulo8411746178871703098atural (tptp.semiri2447717529341329178atural N) (tptp.semiri2447717529341329178atural M)) tptp.zero_z2226904508553997617atural))) (forall ((M tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat N)) (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat M)) tptp.zero_zero_nat))) (forall ((N tptp.nat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat tptp.semiri773545260158071498ct_rat N)) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat N) N))))) (forall ((N tptp.nat)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int tptp.semiri1406184849735516958ct_int N)) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat N) N))))) (forall ((N tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat N)) (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat N) N))))) (forall ((N tptp.nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_nat_real tptp.semiri2265585572941072030t_real N)) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat N) N))))) (forall ((N tptp.nat) (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 ((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) (Y tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool _let_1 X)) (=> (tptp.pp (tptp.aa_real_bool _let_1 Y)) (= (tptp.aa_real_real tptp.ln_ln_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real X) Y)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real tptp.ln_ln_real X)) (tptp.aa_real_real tptp.ln_ln_real Y))))))) (forall ((X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) X)) (=> (= (tptp.aa_real_real tptp.ln_ln_real X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real X) tptp.one_one_real)) (= X tptp.one_one_real)))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool _let_1 X)) (=> (tptp.pp (tptp.aa_real_bool _let_1 Y)) (= (tptp.aa_real_real tptp.ln_ln_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real X) Y)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real tptp.ln_ln_real X)) (tptp.aa_real_real tptp.ln_ln_real Y))))))) (forall ((A tptp.real) (B tptp.real) (X tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.log2 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.log2 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 ((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.log2 B) M)))))) (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.log2 B) _let_1)))))) (forall ((R tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat R) N)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat N)) (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) R)))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat N) R))))) (forall ((K tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) N)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat K)) (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) K)))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial N) K)) (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat N)))) (forall ((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.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 ((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 ((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.aa_nat_fun_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.aa_nat_fun_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.code_natural)) (= (tptp.bit_se569199155075624693atural N A) (tptp.modulo8411746178871703098atural A (tptp.power_7079662738309270450atural (tptp.numera5444537566228673987atural (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.aa_nat_fun_nat_nat tptp.bit_se2925701944663578781it_nat N) A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N)))) (forall ((M tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se2925701944663578781it_nat N) M) M))) (forall ((N tptp.nat) (M tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se2925701944663578781it_nat N) M)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N)))) (forall ((N tptp.nat) (M tptp.nat)) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se2925701944663578781it_nat N) M) M) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N))))) (forall ((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) (Y tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool _let_1 X)) (=> (tptp.pp (tptp.aa_real_bool _let_1 Y)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real tptp.ln_ln_real X)) (tptp.aa_real_real tptp.ln_ln_real Y))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real X) Y)) Y))))))) (forall ((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 ((N tptp.nat) (M tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se2925701944663578781it_nat N) M) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat M) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N)))) (forall ((A tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.log2 A))) (let ((_let_2 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool _let_2 A)) (=> (not (= A tptp.one_one_real)) (=> (tptp.pp (tptp.aa_real_bool _let_2 X)) (=> (tptp.pp (tptp.aa_real_bool _let_2 Y)) (= (tptp.aa_real_real _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real X) Y)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real _let_1 X)) (tptp.aa_real_real _let_1 Y)))))))))) (forall ((A tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.log2 A))) (let ((_let_2 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool _let_2 A)) (=> (not (= A tptp.one_one_real)) (=> (tptp.pp (tptp.aa_real_bool _let_2 X)) (=> (tptp.pp (tptp.aa_real_bool _let_2 Y)) (= (tptp.aa_real_real _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real X) Y)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real _let_1 X)) (tptp.aa_real_real _let_1 Y)))))))))) (forall ((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.log2 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.log2 (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.log2 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.log2 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)))))) (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 ((K tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) N)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial N) K) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat N)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat K)) (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) K))))))) (forall ((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 ((N tptp.nat) (K tptp.int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.bit_ri631733984087533419it_int N) K)) (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) N)))) (forall ((M tptp.nat) (A tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.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) (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.aa_nat_fun_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.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N)) A)))) (forall ((N tptp.nat) (M tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se2925701944663578781it_nat N) M)) M)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N)) M)))) (forall ((N tptp.nat)) (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) (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.log2 B) _let_1)) (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))) (=> (= M (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1)) N)) (= (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.log2 (tptp.numeral_numeral_real _let_1)) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real M)))))) (forall ((N tptp.nat) (K tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.bit_se2923211474154528505it_int N) K)) K)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) N)) K)))) (forall ((K tptp.int) (N tptp.nat)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int K) (tptp.aa_int_int (tptp.bit_se2923211474154528505it_int N) K))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int K) (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) N))))) (forall ((M tptp.nat)) (let ((_let_1 (tptp.aa_nat_complex tptp.semiri5044797733671781792omplex M))) (let ((_let_2 (= M tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_complex)) (=> (not _let_2) (= _let_1 (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex M)) (tptp.aa_nat_complex tptp.semiri5044797733671781792omplex (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) tptp.one_one_nat))))))))) (forall ((M tptp.nat)) (let ((_let_1 (tptp.aa_nat_rat tptp.semiri773545260158071498ct_rat M))) (let ((_let_2 (= M tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_rat)) (=> (not _let_2) (= _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat M)) (tptp.aa_nat_rat tptp.semiri773545260158071498ct_rat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) tptp.one_one_nat))))))))) (forall ((M tptp.nat)) (let ((_let_1 (tptp.aa_nat_int tptp.semiri1406184849735516958ct_int M))) (let ((_let_2 (= M tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_int)) (=> (not _let_2) (= _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int M)) (tptp.aa_nat_int tptp.semiri1406184849735516958ct_int (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) tptp.one_one_nat))))))))) (forall ((M tptp.nat)) (let ((_let_1 (tptp.aa_nat_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 ((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)) (=> (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) (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_complex_complex (tptp.times_times_complex (tptp.aa_nat_complex tptp.semiri5044797733671781792omplex K)) (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial N) K))) (tptp.divide1717551699836669952omplex (tptp.aa_nat_complex tptp.semiri5044797733671781792omplex N) (tptp.aa_nat_complex tptp.semiri5044797733671781792omplex (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) K)))))) (forall ((K tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) N)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat tptp.semiri773545260158071498ct_rat K)) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial N) K))) (tptp.divide_divide_rat (tptp.aa_nat_rat tptp.semiri773545260158071498ct_rat N) (tptp.aa_nat_rat tptp.semiri773545260158071498ct_rat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) K)))))) (forall ((K tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) N)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real tptp.semiri2265585572941072030t_real K)) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial N) K))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_nat_real tptp.semiri2265585572941072030t_real N)) (tptp.aa_nat_real tptp.semiri2265585572941072030t_real (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) K)))))) (forall ((K tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) N)) (= (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial N) K)) (tptp.divide1717551699836669952omplex (tptp.aa_nat_complex tptp.semiri5044797733671781792omplex N) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_nat_complex tptp.semiri5044797733671781792omplex K)) (tptp.aa_nat_complex tptp.semiri5044797733671781792omplex (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) K))))))) (forall ((K tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) N)) (= (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial N) K)) (tptp.divide_divide_rat (tptp.aa_nat_rat tptp.semiri773545260158071498ct_rat N) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat tptp.semiri773545260158071498ct_rat K)) (tptp.aa_nat_rat tptp.semiri773545260158071498ct_rat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) K))))))) (forall ((K tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) N)) (= (tptp.aa_nat_real tptp.semiri5074537144036343181t_real (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial N) K)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_nat_real tptp.semiri2265585572941072030t_real N)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real tptp.semiri2265585572941072030t_real K)) (tptp.aa_nat_real tptp.semiri2265585572941072030t_real (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) K))))))) (forall ((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.log2 B) _let_1)) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N)))))))) (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 ((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)) (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 ((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.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.bit_se1745604003318907178nteger N (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.divide6298287555418463151nteger A) _let_1))) _let_1)) (tptp.modulo364778990260209775nteger A _let_1))))) (forall ((N tptp.nat) (A tptp.code_natural)) (let ((_let_1 (tptp.numera5444537566228673987atural (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.bit_se569199155075624693atural (tptp.aa_nat_nat tptp.suc N) A) (tptp.aa_Cod4272041906116450446atural (tptp.aa_Cod5141017464274028979atural tptp.plus_p4538020629002901425atural (tptp.aa_Cod4272041906116450446atural (tptp.aa_Cod5141017464274028979atural tptp.times_2397367101498566445atural (tptp.bit_se569199155075624693atural N (tptp.aa_Cod4272041906116450446atural (tptp.aa_Cod5141017464274028979atural tptp.divide5121882707175180666atural A) _let_1))) _let_1)) (tptp.modulo8411746178871703098atural 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.aa_nat_fun_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.aa_nat_fun_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.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A) _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.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1)) N)) M)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.log2 (tptp.numeral_numeral_real _let_1)) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real M))))))) (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1)) N)) M)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.log2 (tptp.numeral_numeral_real _let_1)) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real M))))))) (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 ((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.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.divide6298287555418463151nteger A) _let_1) A) (and (=> _let_3 (= _let_2 tptp.zero_z3403309356797280102nteger)) (=> (not _let_3) (= _let_2 (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger 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.aa_nat_fun_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.aa_nat_fun_nat_nat tptp.power_power_nat _let_1) N)) tptp.one_one_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.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 ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1)) N))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) M)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.log2 (tptp.numeral_numeral_real _let_1)) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real M))) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N))))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.ln_ln_real _let_46)) tptp.one_one_real)) (forall ((N tptp.nat) (K tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) K))) (let ((_let_2 (tptp.aa_nat_fun_nat_nat tptp.binomial N))) (let ((_let_3 (tptp.aa_nat_nat _let_2 K))) (let ((_let_4 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N))) (let ((_let_5 (tptp.pp (tptp.aa_nat_bool _let_4 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) K))))) (let ((_let_6 (tptp.pp (tptp.aa_nat_bool _let_4 K)))) (and (=> _let_6 (= _let_3 tptp.zero_zero_nat)) (=> (not _let_6) (and (=> _let_5 (= _let_3 (tptp.aa_nat_nat _let_2 _let_1))) (=> (not _let_5) (= _let_3 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.set_fo2584398358068434914at_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat _let_1) tptp.one_one_nat)) N) tptp.one_one_nat)) (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat K)))))))))))))) (forall ((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 ((B tptp.nat) (K tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat 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.archim7802044766580827645g_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.log2 (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 ((B tptp.nat) (N tptp.nat) (K tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat 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.archim7802044766580827645g_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.log2 (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.log2 (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.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.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 ((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.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 ((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.rat)) (= (tptp.uminus_uminus_rat (tptp.uminus_uminus_rat B)) B)) (forall ((B tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger B)) B)) (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.rat) (B tptp.rat)) (= (= (tptp.uminus_uminus_rat A) (tptp.uminus_uminus_rat 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.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.rat)) (= (tptp.uminus_uminus_rat (tptp.uminus_uminus_rat A)) A)) (forall ((A tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A)) 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_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 ((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.uminus_uminus_rat B)) (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)))) (= (tptp.aa_real_real tptp.uminus_uminus_real tptp.zero_zero_real) tptp.zero_zero_real) _let_109 (= (tptp.uminus1482373934393186551omplex tptp.zero_zero_complex) tptp.zero_zero_complex) (= (tptp.uminus_uminus_rat tptp.zero_zero_rat) tptp.zero_zero_rat) (= (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger) (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.rat)) (= (= tptp.zero_zero_rat (tptp.uminus_uminus_rat A)) (= tptp.zero_zero_rat A))) (forall ((A tptp.code_integer)) (= (= tptp.zero_z3403309356797280102nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A)) (= tptp.zero_z3403309356797280102nteger A))) (forall ((A tptp.real)) (= (= (tptp.aa_real_real tptp.uminus_uminus_real A) tptp.zero_zero_real) (= A tptp.zero_zero_real))) (forall ((A tptp.int)) (= (= (tptp.aa_int_int tptp.uminus_uminus_int A) tptp.zero_zero_int) (= A tptp.zero_zero_int))) (forall ((A tptp.complex)) (= (= (tptp.uminus1482373934393186551omplex A) tptp.zero_zero_complex) (= A tptp.zero_zero_complex))) (forall ((A tptp.rat)) (= (= (tptp.uminus_uminus_rat A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))) (forall ((A tptp.code_integer)) (= (= (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A) tptp.zero_z3403309356797280102nteger) (= A tptp.zero_z3403309356797280102nteger))) (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.rat)) (= (= A (tptp.uminus_uminus_rat A)) (= A tptp.zero_zero_rat))) (forall ((A tptp.code_integer)) (= (= A (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A)) (= A tptp.zero_z3403309356797280102nteger))) (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.rat)) (= (= (tptp.uminus_uminus_rat A) A) (= A tptp.zero_zero_rat))) (forall ((A tptp.code_integer)) (= (= (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A) A) (= A tptp.zero_z3403309356797280102nteger))) (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.rat) (A tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.uminus_uminus_rat B)) (tptp.uminus_uminus_rat A))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat 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 ((M tptp.num) (N tptp.num)) (= (= (tptp.aa_real_real tptp.uminus_uminus_real (tptp.numeral_numeral_real M)) (tptp.aa_real_real tptp.uminus_uminus_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.uminus_uminus_rat (tptp.numeral_numeral_rat M)) (tptp.uminus_uminus_rat (tptp.numeral_numeral_rat 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 ((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.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.uminus_uminus_rat B)) (tptp.uminus_uminus_rat (tptp.aa_rat_rat _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.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.rat) (B tptp.rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.uminus_uminus_rat A)) (tptp.uminus_uminus_rat B)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat 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.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.rat) (B tptp.rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.uminus_uminus_rat A)) B) (tptp.uminus_uminus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat 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.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.rat) (B tptp.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.uminus_uminus_rat A)) (tptp.uminus_uminus_rat B)))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.plus_p5714425477246183910nteger A) B)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A)) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger 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.rat) (B tptp.rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_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.code_integer) (B tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.plus_p5714425477246183910nteger A) B)) 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.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.uminus_uminus_rat A)) B)) B)) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.plus_p5714425477246183910nteger A) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger 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.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.rat) (B tptp.rat)) (= (tptp.uminus_uminus_rat (tptp.minus_minus_rat A B)) (tptp.minus_minus_rat B A))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.minus_8373710615458151222nteger A) B)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.minus_8373710615458151222nteger 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.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.divide6298287555418463151nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A)) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger B)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.divide6298287555418463151nteger A) B))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.dvd_dvd_real X))) (= (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real tptp.uminus_uminus_real Y))) (tptp.pp (tptp.aa_real_bool _let_1 Y))))) (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int X))) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int tptp.uminus_uminus_int Y))) (tptp.pp (tptp.aa_int_bool _let_1 Y))))) (forall ((X tptp.complex) (Y tptp.complex)) (let ((_let_1 (tptp.dvd_dvd_complex X))) (= (tptp.pp (tptp.aa_complex_bool _let_1 (tptp.uminus1482373934393186551omplex Y))) (tptp.pp (tptp.aa_complex_bool _let_1 Y))))) (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.dvd_dvd_rat X))) (= (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.uminus_uminus_rat Y))) (tptp.pp (tptp.aa_rat_bool _let_1 Y))))) (forall ((X tptp.code_integer) (Y tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer X))) (= (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger Y))) (tptp.pp (tptp.aa_Code_integer_bool _let_1 Y))))) (forall ((X tptp.real) (Y tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.dvd_dvd_real (tptp.aa_real_real tptp.uminus_uminus_real X)) Y)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.dvd_dvd_real X) Y)))) (forall ((X tptp.int) (Y tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_int_int tptp.uminus_uminus_int X)) Y)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int X) Y)))) (forall ((X tptp.complex) (Y tptp.complex)) (= (tptp.pp (tptp.aa_complex_bool (tptp.dvd_dvd_complex (tptp.uminus1482373934393186551omplex X)) Y)) (tptp.pp (tptp.aa_complex_bool (tptp.dvd_dvd_complex X) Y)))) (forall ((X tptp.rat) (Y tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.dvd_dvd_rat (tptp.uminus_uminus_rat X)) Y)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.dvd_dvd_rat X) Y)))) (forall ((X tptp.code_integer) (Y tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger X)) Y)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer X) Y)))) (forall ((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 ((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.aa_int_int tptp.sgn_sgn_int (tptp.aa_int_int tptp.uminus_uminus_int A)) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_int_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.rat)) (= (tptp.sgn_sgn_rat (tptp.uminus_uminus_rat A)) (tptp.uminus_uminus_rat (tptp.sgn_sgn_rat 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)))) (= (tptp.aa_real_real tptp.tanh_real tptp.zero_zero_real) tptp.zero_zero_real) (forall ((A tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real A)) A)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) A)))) (forall ((A tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A)) A)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A)))) (forall ((A tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.uminus_uminus_rat A)) A)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) A)))) (forall ((A tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.uminus_uminus_int A)) A)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) A)))) (forall ((A tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A))) (= (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real tptp.uminus_uminus_real A))) (tptp.pp (tptp.aa_real_bool _let_1 tptp.zero_zero_real))))) (forall ((A tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger A))) (= (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A))) (tptp.pp (tptp.aa_Code_integer_bool _let_1 tptp.zero_z3403309356797280102nteger))))) (forall ((A tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A))) (= (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.uminus_uminus_rat A))) (tptp.pp (tptp.aa_rat_bool _let_1 tptp.zero_zero_rat))))) (forall ((A tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A))) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int tptp.uminus_uminus_int A))) (tptp.pp (tptp.aa_int_bool _let_1 tptp.zero_zero_int))))) (forall ((A tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real A)) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) A)))) (forall ((A tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A)) tptp.zero_z3403309356797280102nteger)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A)))) (forall ((A tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.uminus_uminus_rat A)) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) A)))) (forall ((A tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.uminus_uminus_int A)) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) A)))) (forall ((A tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_real_real tptp.uminus_uminus_real A))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) tptp.zero_zero_real)))) (forall ((A tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A))) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger A) tptp.zero_z3403309356797280102nteger)))) (forall ((A tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.uminus_uminus_rat A))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) tptp.zero_zero_rat)))) (forall ((A tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.aa_int_int tptp.uminus_uminus_int A))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) tptp.zero_zero_int)))) (forall ((A tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.uminus_uminus_real A)) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) A)))) (forall ((A tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int tptp.uminus_uminus_int A)) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) A)))) (forall ((A tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_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.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.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.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_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.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.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.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_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.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.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.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A))) (= (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.uminus_uminus_rat A))) (tptp.pp (tptp.aa_rat_bool _let_1 tptp.zero_zero_rat))))) (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.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.rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.uminus_uminus_rat A)) A) tptp.zero_zero_rat)) (forall ((A tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A)) A) tptp.zero_z3403309356797280102nteger)) (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.rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) (tptp.uminus_uminus_rat A)) tptp.zero_zero_rat)) (forall ((A tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.plus_p5714425477246183910nteger A) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A)) tptp.zero_z3403309356797280102nteger)) (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.rat)) (= (tptp.minus_minus_rat tptp.zero_zero_rat A) (tptp.uminus_uminus_rat A))) (forall ((A tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.minus_8373710615458151222nteger tptp.zero_z3403309356797280102nteger) A) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A))) (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.rat)) (= (tptp.minus_minus_rat tptp.zero_zero_rat B) (tptp.uminus_uminus_rat B))) (forall ((B tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.minus_8373710615458151222nteger tptp.zero_z3403309356797280102nteger) B) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger B))) (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (tptp.numeral_numeral_real N))) (let ((_let_2 (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.numeral_numeral_rat N))) (let ((_let_2 (tptp.numeral_numeral_rat M))) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.uminus_uminus_rat _let_2)) (tptp.uminus_uminus_rat _let_1)) (tptp.uminus_uminus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat _let_2) _let_1)))))) (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (tptp.numera6620942414471956472nteger N))) (let ((_let_2 (tptp.numera6620942414471956472nteger M))) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger _let_2)) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger _let_1)) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.plus_p5714425477246183910nteger _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.rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat Z) (tptp.uminus_uminus_rat tptp.one_one_rat)) (tptp.uminus_uminus_rat 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.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.rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.uminus_uminus_rat tptp.one_one_rat)) Z) (tptp.uminus_uminus_rat 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 ((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.rat) (B tptp.rat)) (= (tptp.minus_minus_rat A (tptp.uminus_uminus_rat B)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) B))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.minus_8373710615458151222nteger A) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger B)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.plus_p5714425477246183910nteger 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.rat) (B tptp.rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.uminus_uminus_rat A)) B) (tptp.minus_minus_rat B A))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A)) B) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.minus_8373710615458151222nteger B) 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.divide_divide_rat X (tptp.uminus_uminus_rat tptp.one_one_rat)) (tptp.uminus_uminus_rat X))) (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.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.divide6298287555418463151nteger A) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A))) (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.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.minus_8373710615458151222nteger B) A) B) (tptp.modulo364778990260209775nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A) B))) (= (tptp.archim2889992004027027881ng_rat tptp.zero_zero_rat) tptp.zero_zero_int) (= (tptp.archim7802044766580827645g_real tptp.zero_zero_real) tptp.zero_zero_int) (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 ((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 ((V tptp.num)) (= (tptp.archim7802044766580827645g_real (tptp.numeral_numeral_real V)) (tptp.aa_num_int tptp.numeral_numeral_int V))) (forall ((V tptp.num)) (= (tptp.archim2889992004027027881ng_rat (tptp.numeral_numeral_rat V)) (tptp.aa_num_int tptp.numeral_numeral_int V))) (= (tptp.archim2889992004027027881ng_rat tptp.one_one_rat) tptp.one_one_int) (= (tptp.archim7802044766580827645g_real tptp.one_one_real) tptp.one_one_int) (forall ((N tptp.nat)) (= (tptp.archim7802044766580827645g_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N)) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N))) (forall ((N tptp.nat)) (= (tptp.archim2889992004027027881ng_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat N)) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N))) (forall ((K tptp.num)) (let ((_let_1 (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.numeral_numeral_rat K))) (= (tptp.neg_numeral_dbl_rat (tptp.uminus_uminus_rat _let_1)) (tptp.uminus_uminus_rat (tptp.neg_numeral_dbl_rat _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))))) (= (tptp.aa_real_real _let_154 _let_44) tptp.zero_zero_real) (= (tptp.aa_int_int _let_153 _let_57) tptp.zero_zero_int) (= (tptp.plus_plus_complex tptp.one_one_complex _let_79) tptp.zero_zero_complex) (= (tptp.aa_rat_rat _let_152 _let_56) tptp.zero_zero_rat) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer) _let_65) tptp.zero_z3403309356797280102nteger) (= (tptp.aa_real_real _let_151 tptp.one_one_real) tptp.zero_zero_real) (= (tptp.aa_int_int _let_150 tptp.one_one_int) tptp.zero_zero_int) (= (tptp.plus_plus_complex _let_79 tptp.one_one_complex) tptp.zero_zero_complex) (= (tptp.aa_rat_rat _let_149 tptp.one_one_rat) tptp.zero_zero_rat) (= (tptp.aa_Cod1783974652533396728nteger _let_148 tptp.one_one_Code_integer) tptp.zero_z3403309356797280102nteger) (= (tptp.aa_real_real _let_147 _let_44) tptp.zero_zero_real) (= (tptp.aa_int_int _let_146 _let_57) tptp.zero_zero_int) (= (tptp.minus_minus_complex _let_79 _let_79) tptp.zero_zero_complex) (= (tptp.minus_minus_rat _let_56 _let_56) tptp.zero_zero_rat) (= (tptp.aa_Cod1783974652533396728nteger _let_145 _let_65) tptp.zero_z3403309356797280102nteger) (forall ((N tptp.num)) (= (= (tptp.aa_real_real tptp.uminus_uminus_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.uminus_uminus_rat (tptp.numeral_numeral_rat N)) (tptp.uminus_uminus_rat tptp.one_one_rat)) (= 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_real_real tptp.uminus_uminus_real tptp.one_one_real) (tptp.aa_real_real tptp.uminus_uminus_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.uminus_uminus_rat tptp.one_one_rat) (tptp.uminus_uminus_rat (tptp.numeral_numeral_rat 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.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.aa_nat_rat (tptp.power_power_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)) (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) (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.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat (tptp.power_power_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 ((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 ((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.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.real_V1022390504157884413omplex (tptp.uminus1482373934393186551omplex (tptp.numera6690914467698888265omplex W))) (tptp.numeral_numeral_real W))) (forall ((V tptp.num) (W tptp.num) (Y tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real tptp.uminus_uminus_real (tptp.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.numeral_numeral_real W))) Y)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real tptp.uminus_uminus_real (tptp.numeral_numeral_real (tptp.plus_plus_num V W)))) Y))) (forall ((V tptp.num) (W tptp.num) (Y tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int V))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int W))) Y)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.plus_plus_num V W)))) Y))) (forall ((V tptp.num) (W tptp.num) (Y tptp.complex)) (= (tptp.plus_plus_complex (tptp.uminus1482373934393186551omplex (tptp.numera6690914467698888265omplex V)) (tptp.plus_plus_complex (tptp.uminus1482373934393186551omplex (tptp.numera6690914467698888265omplex W)) Y)) (tptp.plus_plus_complex (tptp.uminus1482373934393186551omplex (tptp.numera6690914467698888265omplex (tptp.plus_plus_num V W))) Y))) (forall ((V tptp.num) (W tptp.num) (Y tptp.rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.uminus_uminus_rat (tptp.numeral_numeral_rat V))) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.uminus_uminus_rat (tptp.numeral_numeral_rat W))) Y)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.uminus_uminus_rat (tptp.numeral_numeral_rat (tptp.plus_plus_num V W)))) Y))) (forall ((V tptp.num) (W tptp.num) (Y tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.numera6620942414471956472nteger V))) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.numera6620942414471956472nteger W))) Y)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.numera6620942414471956472nteger (tptp.plus_plus_num V W)))) Y))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real tptp.uminus_uminus_real (tptp.numeral_numeral_real M))) (tptp.numeral_numeral_real N)) (tptp.aa_real_real tptp.uminus_uminus_real (tptp.numeral_numeral_real (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.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.plus_plus_num M N))))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.minus_minus_rat (tptp.uminus_uminus_rat (tptp.numeral_numeral_rat M)) (tptp.numeral_numeral_rat N)) (tptp.uminus_uminus_rat (tptp.numeral_numeral_rat (tptp.plus_plus_num M N))))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.minus_8373710615458151222nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.numera6620942414471956472nteger M))) (tptp.numera6620942414471956472nteger N)) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.numera6620942414471956472nteger (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.numeral_numeral_real M)) (tptp.aa_real_real tptp.uminus_uminus_real (tptp.numeral_numeral_real N))) (tptp.numeral_numeral_real (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.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.plus_plus_num M N)))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.minus_minus_rat (tptp.numeral_numeral_rat M) (tptp.uminus_uminus_rat (tptp.numeral_numeral_rat N))) (tptp.numeral_numeral_rat (tptp.plus_plus_num M N)))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.minus_8373710615458151222nteger (tptp.numera6620942414471956472nteger M)) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.numera6620942414471956472nteger N))) (tptp.numera6620942414471956472nteger (tptp.plus_plus_num M N)))) (forall ((V tptp.num)) (= (tptp.archim7802044766580827645g_real (tptp.aa_real_real tptp.uminus_uminus_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.archim2889992004027027881ng_rat (tptp.uminus_uminus_rat (tptp.numeral_numeral_rat V))) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int V)))) (forall ((V tptp.num) (W tptp.num) (Y tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real tptp.uminus_uminus_real (tptp.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.numeral_numeral_real W))) Y)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.numeral_numeral_real (tptp.times_times_num V W))) Y))) (forall ((V tptp.num) (W tptp.num) (Y tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int V))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int W))) Y)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.times_times_num V W))) Y))) (forall ((V tptp.num) (W tptp.num) (Y tptp.complex)) (= (tptp.aa_complex_complex (tptp.times_times_complex (tptp.uminus1482373934393186551omplex (tptp.numera6690914467698888265omplex V))) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.uminus1482373934393186551omplex (tptp.numera6690914467698888265omplex W))) Y)) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.numera6690914467698888265omplex (tptp.times_times_num V W))) Y))) (forall ((V tptp.num) (W tptp.num) (Y tptp.rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.uminus_uminus_rat (tptp.numeral_numeral_rat V))) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.uminus_uminus_rat (tptp.numeral_numeral_rat W))) Y)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.numeral_numeral_rat (tptp.times_times_num V W))) Y))) (forall ((V tptp.num) (W tptp.num) (Y tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.numera6620942414471956472nteger V))) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.numera6620942414471956472nteger W))) Y)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.numera6620942414471956472nteger (tptp.times_times_num V W))) Y))) (forall ((V tptp.num) (W tptp.num) (Y tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.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.numeral_numeral_real W))) Y)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real tptp.uminus_uminus_real (tptp.numeral_numeral_real (tptp.times_times_num V W)))) Y))) (forall ((V tptp.num) (W tptp.num) (Y tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_num_int tptp.numeral_numeral_int V)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int W))) Y)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.times_times_num V W)))) Y))) (forall ((V tptp.num) (W tptp.num) (Y tptp.complex)) (= (tptp.aa_complex_complex (tptp.times_times_complex (tptp.numera6690914467698888265omplex V)) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.uminus1482373934393186551omplex (tptp.numera6690914467698888265omplex W))) Y)) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.uminus1482373934393186551omplex (tptp.numera6690914467698888265omplex (tptp.times_times_num V W)))) Y))) (forall ((V tptp.num) (W tptp.num) (Y tptp.rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.numeral_numeral_rat V)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.uminus_uminus_rat (tptp.numeral_numeral_rat W))) Y)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.uminus_uminus_rat (tptp.numeral_numeral_rat (tptp.times_times_num V W)))) Y))) (forall ((V tptp.num) (W tptp.num) (Y tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.numera6620942414471956472nteger V)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.numera6620942414471956472nteger W))) Y)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.numera6620942414471956472nteger (tptp.times_times_num V W)))) Y))) (forall ((V tptp.num) (W tptp.num) (Y tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real tptp.uminus_uminus_real (tptp.numeral_numeral_real V))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.numeral_numeral_real W)) Y)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real tptp.uminus_uminus_real (tptp.numeral_numeral_real (tptp.times_times_num V W)))) Y))) (forall ((V tptp.num) (W tptp.num) (Y tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int V))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_num_int tptp.numeral_numeral_int W)) Y)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.times_times_num V W)))) Y))) (forall ((V tptp.num) (W tptp.num) (Y tptp.complex)) (= (tptp.aa_complex_complex (tptp.times_times_complex (tptp.uminus1482373934393186551omplex (tptp.numera6690914467698888265omplex V))) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.numera6690914467698888265omplex W)) Y)) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.uminus1482373934393186551omplex (tptp.numera6690914467698888265omplex (tptp.times_times_num V W)))) Y))) (forall ((V tptp.num) (W tptp.num) (Y tptp.rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.uminus_uminus_rat (tptp.numeral_numeral_rat V))) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.numeral_numeral_rat W)) Y)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.uminus_uminus_rat (tptp.numeral_numeral_rat (tptp.times_times_num V W)))) Y))) (forall ((V tptp.num) (W tptp.num) (Y tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.numera6620942414471956472nteger V))) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.numera6620942414471956472nteger W)) Y)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.numera6620942414471956472nteger (tptp.times_times_num V W)))) Y))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.numeral_numeral_real M)) (tptp.aa_real_real tptp.uminus_uminus_real (tptp.numeral_numeral_real N))) (tptp.aa_real_real tptp.uminus_uminus_real (tptp.numeral_numeral_real (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.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.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.numeral_numeral_rat M)) (tptp.uminus_uminus_rat (tptp.numeral_numeral_rat N))) (tptp.uminus_uminus_rat (tptp.numeral_numeral_rat (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.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.numeral_numeral_real M))) (tptp.numeral_numeral_real N)) (tptp.aa_real_real tptp.uminus_uminus_real (tptp.numeral_numeral_real (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.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.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.uminus_uminus_rat (tptp.numeral_numeral_rat M))) (tptp.numeral_numeral_rat N)) (tptp.uminus_uminus_rat (tptp.numeral_numeral_rat (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.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.numeral_numeral_real M))) (tptp.aa_real_real tptp.uminus_uminus_real (tptp.numeral_numeral_real N))) (tptp.numeral_numeral_real (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.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.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.uminus_uminus_rat (tptp.numeral_numeral_rat M))) (tptp.uminus_uminus_rat (tptp.numeral_numeral_rat N))) (tptp.numeral_numeral_rat (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.times_times_num M N)))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real (tptp.numeral_numeral_real M))) (tptp.aa_real_real tptp.uminus_uminus_real (tptp.numeral_numeral_real N)))) (tptp.pp (tptp.aa_num_bool (tptp.ord_less_eq_num N) M)))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.numera6620942414471956472nteger M))) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.numera6620942414471956472nteger N)))) (tptp.pp (tptp.aa_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.uminus_uminus_rat (tptp.numeral_numeral_rat M))) (tptp.uminus_uminus_rat (tptp.numeral_numeral_rat N)))) (tptp.pp (tptp.aa_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.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.numeral_numeral_real M))) (tptp.aa_real_real tptp.uminus_uminus_real (tptp.numeral_numeral_real N)))) (tptp.pp (tptp.aa_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.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.uminus_uminus_rat (tptp.numeral_numeral_rat M))) (tptp.uminus_uminus_rat (tptp.numeral_numeral_rat N)))) (tptp.pp (tptp.aa_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.ord_less_num N) M)))) (forall ((M tptp.num)) (= (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)) (tptp.aa_real_real tptp.uminus_uminus_real (tptp.numeral_numeral_real M))))) (not (= M tptp.one)))) (forall ((M tptp.num)) (= (not (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.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.uminus_uminus_rat tptp.one_one_rat)) (tptp.uminus_uminus_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 ((A tptp.real) (B tptp.real) (W tptp.num)) (let ((_let_1 (tptp.aa_real_real tptp.uminus_uminus_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 ((A tptp.rat) (B tptp.rat) (W tptp.num)) (let ((_let_1 (tptp.uminus_uminus_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.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 ((B tptp.real) (W tptp.num) (A tptp.real)) (let ((_let_1 (tptp.aa_real_real tptp.uminus_uminus_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 ((B tptp.rat) (W tptp.num) (A tptp.rat)) (let ((_let_1 (tptp.uminus_uminus_rat (tptp.numeral_numeral_rat W)))) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_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 ((A tptp.real) (B tptp.real) (W tptp.num)) (let ((_let_1 (tptp.aa_real_real tptp.uminus_uminus_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.uminus_uminus_rat (tptp.numeral_numeral_rat W)))) (let ((_let_2 (= _let_1 tptp.zero_zero_rat))) (= (= A (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 ((B tptp.real) (W tptp.num) (A tptp.real)) (let ((_let_1 (tptp.aa_real_real tptp.uminus_uminus_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.uminus_uminus_rat (tptp.numeral_numeral_rat W)))) (let ((_let_2 (= _let_1 tptp.zero_zero_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 ((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.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_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.uminus_uminus_rat (tptp.numeral_numeral_rat M))) (tptp.uminus_uminus_rat tptp.one_one_rat))) (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 ((A tptp.real) (B tptp.real) (W tptp.num)) (let ((_let_1 (tptp.aa_real_real tptp.uminus_uminus_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.uminus_uminus_rat (tptp.numeral_numeral_rat W)))) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) (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 ((B tptp.real) (W tptp.num) (A tptp.real)) (let ((_let_1 (tptp.aa_real_real tptp.uminus_uminus_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.uminus_uminus_rat (tptp.numeral_numeral_rat W)))) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_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)) (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.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.uminus_uminus_rat A)) _let_1) (tptp.aa_nat_rat (tptp.power_power_rat 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.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.aa_int_int tptp.sgn_sgn_int A) (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int)))) (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.sgn_sgn_rat A) (tptp.uminus_uminus_rat tptp.one_one_rat)))) (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 ((N tptp.nat) (K tptp.num)) (= (tptp.aa_int_int (tptp.aa_nat_fun_int_int 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.aa_int_int (tptp.aa_nat_fun_int_int 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 ((N tptp.nat) (K tptp.num)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_nat6383147911832638789nteger tptp.bit_se7788150548672797655nteger (tptp.aa_nat_nat tptp.suc N)) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.numera6620942414471956472nteger K))) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_nat6383147911832638789nteger tptp.bit_se7788150548672797655nteger N) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 K)))))) (forall ((X tptp.real)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_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.rat)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_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.rat)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_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.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) (V tptp.num)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_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.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_eq_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.numeral_numeral_rat V))))) (forall ((X tptp.real)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_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_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.rat)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.one_one_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.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.archim7802044766580827645g_real X))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_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.archim2889992004027027881ng_rat X))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_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_eq_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.rat)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_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.rat)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.one_one_int) (tptp.archim2889992004027027881ng_rat X))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_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_int tptp.one_one_int) (tptp.archim7802044766580827645g_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) (V tptp.num)) (= (tptp.archim7802044766580827645g_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) (tptp.numeral_numeral_real V))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.archim7802044766580827645g_real X)) (tptp.aa_num_int tptp.numeral_numeral_int V)))) (forall ((X tptp.rat) (V tptp.num)) (= (tptp.archim2889992004027027881ng_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat X) (tptp.numeral_numeral_rat V))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.archim2889992004027027881ng_rat X)) (tptp.aa_num_int tptp.numeral_numeral_int V)))) (forall ((X tptp.rat)) (= (tptp.archim2889992004027027881ng_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat X) tptp.one_one_rat)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.archim2889992004027027881ng_rat X)) tptp.one_one_int))) (forall ((X tptp.real)) (= (tptp.archim7802044766580827645g_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) tptp.one_one_real)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.archim7802044766580827645g_real X)) tptp.one_one_int))) (forall ((X tptp.real) (V tptp.num)) (= (tptp.archim7802044766580827645g_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real X) (tptp.numeral_numeral_real V))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.archim7802044766580827645g_real X)) (tptp.aa_num_int tptp.numeral_numeral_int V)))) (forall ((X tptp.rat) (V tptp.num)) (= (tptp.archim2889992004027027881ng_rat (tptp.minus_minus_rat X (tptp.numeral_numeral_rat V))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.archim2889992004027027881ng_rat X)) (tptp.aa_num_int tptp.numeral_numeral_int V)))) (forall ((X tptp.rat)) (= (tptp.archim2889992004027027881ng_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.archim2889992004027027881ng_rat X)) tptp.one_one_int))) (forall ((X tptp.real)) (= (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.archim7802044766580827645g_real X)) tptp.one_one_int))) (forall ((X tptp.num) (N tptp.nat)) (= (tptp.archim7802044766580827645g_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_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.archim2889992004027027881ng_rat (tptp.aa_nat_rat (tptp.power_power_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))) (= (tptp.aa_real_real _let_151 _let_44) _let_140) (= (tptp.aa_int_int _let_150 _let_57) _let_69) (= (tptp.plus_plus_complex _let_79 _let_79) _let_139) (= (tptp.aa_rat_rat _let_149 _let_56) _let_138) (= (tptp.aa_Cod1783974652533396728nteger _let_148 _let_65) _let_70) (= (tptp.aa_real_real _let_147 tptp.one_one_real) _let_140) (= (tptp.aa_int_int _let_146 tptp.one_one_int) _let_69) (= (tptp.minus_minus_complex _let_79 tptp.one_one_complex) _let_139) (= (tptp.minus_minus_rat _let_56 tptp.one_one_rat) _let_138) (= (tptp.aa_Cod1783974652533396728nteger _let_145 tptp.one_one_Code_integer) _let_70) (= (tptp.aa_real_real _let_144 _let_44) _let_46) (= (tptp.aa_int_int _let_143 _let_57) _let_68) (= (tptp.minus_minus_complex tptp.one_one_complex _let_79) _let_83) (= (tptp.minus_minus_rat tptp.one_one_rat _let_56) _let_137) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.minus_8373710615458151222nteger tptp.one_one_Code_integer) _let_65) _let_59) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int _let_57) _let_68) _let_57) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.divide6298287555418463151nteger _let_65) _let_59) _let_65) _let_142 _let_141 _let_142 _let_141 (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.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.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)) (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 ((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.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.uminus_uminus_rat A)) N) (tptp.aa_nat_rat (tptp.power_power_rat 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.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.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.uminus_uminus_rat A)) N) (tptp.uminus_uminus_rat (tptp.aa_nat_rat (tptp.power_power_rat 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 ((M tptp.num)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real tptp.uminus_uminus_real (tptp.numeral_numeral_real M))) tptp.one_one_real) (tptp.aa_real_real tptp.uminus_uminus_real (tptp.numeral_numeral_real (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.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.plus_plus_num M tptp.one))))) (forall ((M tptp.num)) (= (tptp.minus_minus_rat (tptp.uminus_uminus_rat (tptp.numeral_numeral_rat M)) tptp.one_one_rat) (tptp.uminus_uminus_rat (tptp.numeral_numeral_rat (tptp.plus_plus_num M tptp.one))))) (forall ((M tptp.num)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.minus_8373710615458151222nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.numera6620942414471956472nteger M))) tptp.one_one_Code_integer) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.numera6620942414471956472nteger (tptp.plus_plus_num M tptp.one))))) (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.numeral_numeral_real N))) (tptp.numeral_numeral_real (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.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.plus_plus_num tptp.one N)))) (forall ((N tptp.num)) (= (tptp.minus_minus_rat tptp.one_one_rat (tptp.uminus_uminus_rat (tptp.numeral_numeral_rat N))) (tptp.numeral_numeral_rat (tptp.plus_plus_num tptp.one N)))) (forall ((N tptp.num)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.minus_8373710615458151222nteger tptp.one_one_Code_integer) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.numera6620942414471956472nteger N))) (tptp.numera6620942414471956472nteger (tptp.plus_plus_num tptp.one N)))) (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.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.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_eq_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.uminus_uminus_rat (tptp.numeral_numeral_rat V)))))) (forall ((X tptp.real)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_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.rat)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_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.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_eq_int tptp.zero_zero_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.archim2889992004027027881ng_rat X))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.uminus_uminus_rat 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_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int V))) (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.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.archim2889992004027027881ng_rat X))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.uminus_uminus_rat (tptp.numeral_numeral_rat V))) X)))) (= (tptp.aa_real_real tptp.neg_numeral_dbl_real _let_44) _let_140) (= (tptp.neg_numeral_dbl_int _let_57) _let_69) (= (tptp.neg_nu7009210354673126013omplex _let_79) _let_139) (= (tptp.neg_numeral_dbl_rat _let_56) _let_138) (= (tptp.neg_nu8804712462038260780nteger _let_65) _let_70) (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.aa_nat_rat (tptp.power_power_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)) (= (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.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.aa_nat_rat (tptp.power_power_rat (tptp.uminus_uminus_rat tptp.one_one_rat)) N) tptp.one_one_rat))) (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)) (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.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)) (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 ((X tptp.real) (V tptp.num)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_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.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_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.minus_minus_rat (tptp.numeral_numeral_rat V) tptp.one_one_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.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.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.archim2889992004027027881ng_rat X))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.minus_minus_rat (tptp.numeral_numeral_rat V) tptp.one_one_rat)) X)))) (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.num)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat N))) (= (tptp.aa_int_int (tptp.aa_nat_fun_int_int 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.num)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat N))) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_nat6383147911832638789nteger 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 ((X tptp.real) (V tptp.num)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_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.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_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.minus_minus_rat (tptp.uminus_uminus_rat (tptp.numeral_numeral_rat V)) tptp.one_one_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_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int V))) (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.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.archim2889992004027027881ng_rat X))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.minus_minus_rat (tptp.uminus_uminus_rat (tptp.numeral_numeral_rat V)) tptp.one_one_rat)) X)))) (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.rat) (B tptp.rat)) (=> (= A B) (= (tptp.uminus_uminus_rat A) (tptp.uminus_uminus_rat 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.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.rat) (B tptp.rat)) (= (= (tptp.uminus_uminus_rat A) B) (= (tptp.uminus_uminus_rat 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.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.rat) (B tptp.rat)) (= (= A (tptp.uminus_uminus_rat B)) (= B (tptp.uminus_uminus_rat 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 ((X tptp.real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)) (tptp.aa_real_real tptp.tanh_real X)))) (forall ((A tptp.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.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.uminus_uminus_rat B)) (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 (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 (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.uminus_uminus_rat A)) B)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_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 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 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.uminus_uminus_rat B))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) (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_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.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.uminus_uminus_rat B)) (tptp.uminus_uminus_rat 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.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.rat) (B tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.uminus_uminus_rat A)) B)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.uminus_uminus_rat 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.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.rat) (B tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) (tptp.uminus_uminus_rat B))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) (tptp.uminus_uminus_rat 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 ((M tptp.num) (N tptp.num)) (not (= (tptp.numeral_numeral_real M) (tptp.aa_real_real tptp.uminus_uminus_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.numeral_numeral_rat M) (tptp.uminus_uminus_rat (tptp.numeral_numeral_rat 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_real_real tptp.uminus_uminus_real (tptp.numeral_numeral_real M)) (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.uminus_uminus_rat (tptp.numeral_numeral_rat M)) (tptp.numeral_numeral_rat N)))) (forall ((M tptp.num) (N tptp.num)) (not (= (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.numera6620942414471956472nteger M)) (tptp.numera6620942414471956472nteger 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.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.rat) (B tptp.rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.uminus_uminus_rat A)) B) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) (tptp.uminus_uminus_rat 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.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.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.uminus_uminus_rat 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))))) (not (= tptp.one_one_real _let_44)) (not (= tptp.one_one_int _let_57)) (not (= tptp.one_one_complex _let_79)) (not (= tptp.one_one_rat _let_56)) (not (= tptp.one_one_Code_integer _let_65)) (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.rat) (B tptp.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.uminus_uminus_rat B)) (tptp.uminus_uminus_rat A)))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.plus_p5714425477246183910nteger A) B)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger B)) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger 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.rat) (B tptp.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.uminus_uminus_rat B)) (tptp.uminus_uminus_rat A)))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.plus_p5714425477246183910nteger A) B)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger B)) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A)))) (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.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.uminus_uminus_rat A2) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.uminus_uminus_rat K)) (tptp.uminus_uminus_rat A))))) (forall ((A2 tptp.code_integer) (K tptp.code_integer) (A tptp.code_integer)) (=> (= A2 (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.plus_p5714425477246183910nteger K) A)) (= (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A2) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger K)) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A))))) (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.rat) (A tptp.rat)) (= (tptp.minus_minus_rat (tptp.uminus_uminus_rat B) A) (tptp.minus_minus_rat (tptp.uminus_uminus_rat A) B))) (forall ((B tptp.code_integer) (A tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.minus_8373710615458151222nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger B)) A) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.minus_8373710615458151222nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger 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.rat) (B tptp.rat)) (= (tptp.minus_minus_rat (tptp.uminus_uminus_rat A) (tptp.uminus_uminus_rat B)) (tptp.uminus_uminus_rat (tptp.minus_minus_rat A B)))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.minus_8373710615458151222nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A)) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger B)) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.minus_8373710615458151222nteger 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.uminus_uminus_rat (tptp.divide_divide_rat A B)) (tptp.divide_divide_rat (tptp.uminus_uminus_rat A) 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.divide_divide_rat (tptp.uminus_uminus_rat A) (tptp.uminus_uminus_rat B)) (tptp.divide_divide_rat 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)) (= (tptp.uminus_uminus_rat (tptp.divide_divide_rat A B)) (tptp.divide_divide_rat A (tptp.uminus_uminus_rat 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.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.divide6298287555418463151nteger A) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger B)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.divide6298287555418463151nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A)) 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)))) (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 (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 ((N tptp.nat) (A tptp.int)) (let ((_let_1 (tptp.aa_nat_fun_int_int tptp.bit_se545348938243370406it_int N))) (= (tptp.aa_int_int _let_1 (tptp.aa_int_int tptp.uminus_uminus_int A)) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_int_int _let_1 A))))) (forall ((N tptp.nat) (A tptp.code_integer)) (let ((_let_1 (tptp.aa_nat6383147911832638789nteger tptp.bit_se7788150548672797655nteger N))) (= (tptp.aa_Cod1783974652533396728nteger _let_1 (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A)) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_Cod1783974652533396728nteger _let_1 A))))) (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 ((Y tptp.real) (X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y) X)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.archim7802044766580827645g_real Y)) (tptp.archim7802044766580827645g_real X))))) (forall ((Y tptp.rat) (X tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat Y) X)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.archim2889992004027027881ng_rat Y)) (tptp.archim2889992004027027881ng_rat X))))) (forall ((X tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.archim2889992004027027881ng_rat X)) (tptp.archim2889992004027027881ng_rat Y))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) Y)))) (forall ((X tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.archim7802044766580827645g_real X)) (tptp.archim7802044766580827645g_real Y))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Y)))) (forall ((M tptp.num) (N tptp.num)) (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.numeral_numeral_real M)) (tptp.aa_real_real tptp.uminus_uminus_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.numeral_numeral_rat M)) (tptp.uminus_uminus_rat (tptp.numeral_numeral_rat N)))))) (forall ((M tptp.num) (N tptp.num)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_num_int tptp.numeral_numeral_int M)) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int N)))))) (forall ((M tptp.num) (N tptp.num)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real (tptp.numeral_numeral_real M))) (tptp.numeral_numeral_real N)))) (forall ((M tptp.num) (N tptp.num)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.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.uminus_uminus_rat (tptp.numeral_numeral_rat M))) (tptp.numeral_numeral_rat N)))) (forall ((M tptp.num) (N tptp.num)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int M))) (tptp.aa_num_int tptp.numeral_numeral_int N)))) (forall ((N tptp.num)) (not (= tptp.zero_zero_real (tptp.aa_real_real tptp.uminus_uminus_real (tptp.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_zero_rat (tptp.uminus_uminus_rat (tptp.numeral_numeral_rat N))))) (forall ((N tptp.num)) (not (= tptp.zero_z3403309356797280102nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.numera6620942414471956472nteger N))))) (forall ((M tptp.num) (N tptp.num)) (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.numeral_numeral_real M)) (tptp.aa_real_real tptp.uminus_uminus_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_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.numeral_numeral_rat M)) (tptp.uminus_uminus_rat (tptp.numeral_numeral_rat 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)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.uminus_uminus_real (tptp.numeral_numeral_real M))) (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_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.uminus_uminus_rat (tptp.numeral_numeral_rat M))) (tptp.numeral_numeral_rat 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)))) (tptp.pp (tptp.aa_real_bool _let_130 tptp.one_one_real)) (tptp.pp (tptp.aa_Code_integer_bool _let_129 tptp.one_one_Code_integer)) (tptp.pp (tptp.aa_rat_bool _let_128 tptp.one_one_rat)) (tptp.pp (tptp.aa_int_bool _let_127 tptp.one_one_int)) (not (tptp.pp (tptp.aa_real_bool _let_136 _let_44))) (not (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) _let_65))) (not (tptp.pp (tptp.aa_rat_bool _let_135 _let_56))) (not (tptp.pp (tptp.aa_int_bool _let_134 _let_57))) (not (= tptp.zero_zero_real _let_44)) (not (= tptp.zero_zero_int _let_57)) (not (= tptp.zero_zero_complex _let_79)) (not (= tptp.zero_zero_rat _let_56)) (not (= tptp.zero_z3403309356797280102nteger _let_65)) (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.rat) (B tptp.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.code_integer) (B tptp.code_integer)) (= (= (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A) B) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.plus_p5714425477246183910nteger A) B) tptp.zero_z3403309356797280102nteger))) (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.rat) (B tptp.rat)) (= (= A (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.code_integer) (B tptp.code_integer)) (= (= A (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger B)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.plus_p5714425477246183910nteger A) B) tptp.zero_z3403309356797280102nteger))) (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.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.uminus_uminus_rat A) B))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.plus_p5714425477246183910nteger A) B) tptp.zero_z3403309356797280102nteger) (= (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger 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.rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.uminus_uminus_rat A)) A) tptp.zero_zero_rat)) (forall ((A tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A)) A) tptp.zero_z3403309356797280102nteger)) (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.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.uminus_uminus_rat A)))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.plus_p5714425477246183910nteger A) B) tptp.zero_z3403309356797280102nteger) (= B (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A)))) (not (tptp.pp (tptp.aa_real_bool _let_133 _let_44))) (not (tptp.pp (tptp.aa_int_bool _let_132 _let_57))) (not (tptp.pp (tptp.aa_rat_bool _let_131 _let_56))) (not (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) _let_65))) (tptp.pp (tptp.aa_real_bool _let_124 tptp.one_one_real)) (tptp.pp (tptp.aa_int_bool _let_123 tptp.one_one_int)) (tptp.pp (tptp.aa_rat_bool _let_122 tptp.one_one_rat)) (tptp.pp (tptp.aa_Code_integer_bool _let_121 tptp.one_one_Code_integer)) (forall ((W tptp.num) (X tptp.real)) (let ((_let_1 (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.rat)) (let ((_let_1 (tptp.numeral_numeral_rat W))) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat _let_1) (tptp.uminus_uminus_rat X)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat X) (tptp.uminus_uminus_rat _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 ((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.divide_divide_rat (tptp.uminus_uminus_rat A) (tptp.uminus_uminus_rat B)) (tptp.divide_divide_rat A B)))) (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)) (=> (not (= B tptp.zero_zero_rat)) (= (tptp.uminus_uminus_rat (tptp.divide_divide_rat A B)) (tptp.divide_divide_rat A (tptp.uminus_uminus_rat B))))) (forall ((N tptp.num)) (not (= (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.numeral_numeral_rat N) (tptp.uminus_uminus_rat tptp.one_one_rat)))) (forall ((N tptp.num)) (not (= (tptp.numera6620942414471956472nteger N) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))) (forall ((N tptp.num)) (not (= tptp.one_one_real (tptp.aa_real_real tptp.uminus_uminus_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_rat (tptp.uminus_uminus_rat (tptp.numeral_numeral_rat N))))) (forall ((N tptp.num)) (not (= tptp.one_one_Code_integer (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.numera6620942414471956472nteger N))))) (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.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.uminus_uminus_rat tptp.one_one_rat))))) (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 ((B4 tptp.real) (K tptp.real) (B tptp.real) (A tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A))) (=> (= B4 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real K) B)) (= (tptp.aa_real_real _let_1 B4) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real tptp.uminus_uminus_real K)) (tptp.aa_real_real _let_1 B)))))) (forall ((B4 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))) (=> (= B4 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int K) B)) (= (tptp.aa_int_int _let_1 B4) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int tptp.uminus_uminus_int K)) (tptp.aa_int_int _let_1 B)))))) (forall ((B4 tptp.complex) (K tptp.complex) (B tptp.complex) (A tptp.complex)) (=> (= B4 (tptp.plus_plus_complex K B)) (= (tptp.minus_minus_complex A B4) (tptp.plus_plus_complex (tptp.uminus1482373934393186551omplex K) (tptp.minus_minus_complex A B))))) (forall ((B4 tptp.rat) (K tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (= B4 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat K) B)) (= (tptp.minus_minus_rat A B4) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.uminus_uminus_rat K)) (tptp.minus_minus_rat A B))))) (forall ((B4 tptp.code_integer) (K tptp.code_integer) (B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod4161879620478718930nteger tptp.minus_8373710615458151222nteger A))) (=> (= B4 (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.plus_p5714425477246183910nteger K) B)) (= (tptp.aa_Cod1783974652533396728nteger _let_1 B4) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger K)) (tptp.aa_Cod1783974652533396728nteger _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.rat) (B tptp.rat)) (= (tptp.minus_minus_rat A B) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) (tptp.uminus_uminus_rat B)))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.minus_8373710615458151222nteger A) B) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.plus_p5714425477246183910nteger A) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger 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.rat) (B tptp.rat)) (= (tptp.minus_minus_rat A B) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) (tptp.uminus_uminus_rat B)))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.minus_8373710615458151222nteger A) B) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.plus_p5714425477246183910nteger A) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger 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.rat) (A tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.dvd_dvd_rat B) A)) (= (tptp.divide_divide_rat (tptp.uminus_uminus_rat A) B) (tptp.uminus_uminus_rat (tptp.divide_divide_rat 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.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.divide6298287555418463151nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A)) B) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.divide6298287555418463151nteger A) 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.rat) (A tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.dvd_dvd_rat B) A)) (= (tptp.divide_divide_rat A (tptp.uminus_uminus_rat B)) (tptp.uminus_uminus_rat (tptp.divide_divide_rat A B))))) (forall ((B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod4161879620478718930nteger tptp.divide6298287555418463151nteger A))) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer B) A)) (= (tptp.aa_Cod1783974652533396728nteger _let_1 (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger B)) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_Cod1783974652533396728nteger _let_1 B)))))) (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.aa_int_int tptp.sgn_sgn_int B))) (let ((_let_2 (tptp.aa_int_int 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.rat) (A tptp.rat)) (let ((_let_1 (tptp.sgn_sgn_rat B))) (let ((_let_2 (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.uminus_uminus_rat _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)))))))) (= (tptp.aa_real_real tptp.sgn_sgn_real _let_44) _let_44) (= (tptp.aa_int_int tptp.sgn_sgn_int _let_57) _let_57) (= (tptp.sgn_sgn_complex _let_79) _let_79) (= (tptp.sgn_sgn_rat _let_56) _let_56) (= (tptp.aa_Cod1783974652533396728nteger tptp.sgn_sgn_Code_integer _let_65) _let_65) (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 ((X tptp.real) (Y tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real X) Y) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) (tptp.aa_real_real tptp.uminus_uminus_real Y)))) (forall ((X tptp.real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.tanh_real X)) tptp.one_one_real))) (forall ((X tptp.rat) (Y tptp.rat)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.archim2889992004027027881ng_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat X) Y))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.archim2889992004027027881ng_rat X)) (tptp.archim2889992004027027881ng_rat Y))))) (forall ((X tptp.real) (Y tptp.real)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.archim7802044766580827645g_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) Y))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.archim7802044766580827645g_real X)) (tptp.archim7802044766580827645g_real Y))))) (forall ((N tptp.num)) (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_real_real tptp.uminus_uminus_real (tptp.numeral_numeral_real N)))))) (forall ((N tptp.num)) (not (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.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.uminus_uminus_rat (tptp.numeral_numeral_rat N)))))) (forall ((N tptp.num)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int N)))))) (forall ((N tptp.num)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real (tptp.numeral_numeral_real N))) tptp.zero_zero_real))) (forall ((N tptp.num)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.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.uminus_uminus_rat (tptp.numeral_numeral_rat N))) tptp.zero_zero_rat))) (forall ((N tptp.num)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int N))) tptp.zero_zero_int))) (forall ((N tptp.num)) (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) (tptp.aa_real_real tptp.uminus_uminus_real (tptp.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_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) (tptp.uminus_uminus_rat (tptp.numeral_numeral_rat 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)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.uminus_uminus_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_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.uminus_uminus_rat (tptp.numeral_numeral_rat N))) tptp.zero_zero_rat))) (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))) (tptp.pp (tptp.aa_real_bool _let_130 tptp.zero_zero_real)) (tptp.pp (tptp.aa_Code_integer_bool _let_129 tptp.zero_z3403309356797280102nteger)) (tptp.pp (tptp.aa_rat_bool _let_128 tptp.zero_zero_rat)) (tptp.pp (tptp.aa_int_bool _let_127 tptp.zero_zero_int)) (not (tptp.pp (tptp.aa_real_bool _let_104 _let_44))) (not (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) _let_65))) (not (tptp.pp (tptp.aa_rat_bool _let_126 _let_56))) (not (tptp.pp (tptp.aa_int_bool _let_125 _let_57))) (tptp.pp (tptp.aa_real_bool _let_124 tptp.zero_zero_real)) (tptp.pp (tptp.aa_int_bool _let_123 tptp.zero_zero_int)) (tptp.pp (tptp.aa_rat_bool _let_122 tptp.zero_zero_rat)) (tptp.pp (tptp.aa_Code_integer_bool _let_121 tptp.zero_z3403309356797280102nteger)) (not (tptp.pp (tptp.aa_real_bool _let_105 _let_44))) (not (tptp.pp (tptp.aa_int_bool _let_120 _let_57))) (not (tptp.pp (tptp.aa_rat_bool _let_119 _let_56))) (not (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) _let_65))) (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.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.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.uminus_uminus_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.one_one_real)) (tptp.numeral_numeral_real M)))) (forall ((M tptp.num)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (tptp.numera6620942414471956472nteger M)))) (forall ((M tptp.num)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.uminus_uminus_rat tptp.one_one_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.numeral_numeral_real M))) (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)))) (forall ((M tptp.num)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.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.uminus_uminus_rat (tptp.numeral_numeral_rat M))) (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)) (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_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.numeral_numeral_rat M)) (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.one_one_real) (tptp.aa_real_real tptp.uminus_uminus_real (tptp.numeral_numeral_real M)))))) (forall ((M tptp.num)) (not (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.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.uminus_uminus_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)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.uminus_uminus_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_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.uminus_uminus_rat (tptp.numeral_numeral_rat M))) tptp.one_one_rat))) (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_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_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_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.uminus_uminus_rat tptp.one_one_rat)) (tptp.numeral_numeral_rat 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)) (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_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_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.numeral_numeral_rat M)) (tptp.uminus_uminus_rat tptp.one_one_rat))))) (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_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real) (tptp.aa_real_real tptp.uminus_uminus_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_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.one_one_rat) (tptp.uminus_uminus_rat (tptp.numeral_numeral_rat 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_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.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_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.uminus_uminus_rat tptp.one_one_rat)) (tptp.uminus_uminus_rat (tptp.numeral_numeral_rat 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 ((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.uminus_uminus_rat (tptp.divide_divide_rat A B))) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat C) B) (tptp.uminus_uminus_rat A))))) (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.uminus_uminus_rat (tptp.divide_divide_rat A B)) C) (= (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)) (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.uminus_uminus_rat (tptp.divide_divide_rat B C)) A) (and (=> (not _let_1) (= (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 ((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.uminus_uminus_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.uminus_uminus_rat B))) (=> _let_1 (= A tptp.zero_zero_rat)))))) (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.divide_divide_rat A B) (tptp.uminus_uminus_rat tptp.one_one_rat)) (and (not (= B tptp.zero_zero_rat)) (= A (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.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.rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.uminus_uminus_rat (tptp.numeral_numeral_rat tptp.one))) B) (tptp.uminus_uminus_rat 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.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real B) (tptp.aa_real_real tptp.uminus_uminus_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.rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat B) (tptp.uminus_uminus_rat (tptp.numeral_numeral_rat tptp.one))) (tptp.uminus_uminus_rat 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))) (= (tptp.aa_real_real tptp.uminus_uminus_real _let_75) _let_44) (= (tptp.aa_int_int tptp.uminus_uminus_int _let_118) _let_57) (= (tptp.uminus1482373934393186551omplex _let_74) _let_79) (= (tptp.uminus_uminus_rat _let_73) _let_56) (= (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger _let_14) _let_65) (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.rat) (N tptp.nat)) (= (tptp.aa_nat_rat (tptp.power_power_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.uminus_uminus_rat tptp.one_one_rat)) N)) (tptp.aa_nat_rat (tptp.power_power_rat 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 ((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.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.uminus_uminus_rat X)) _let_1) (tptp.aa_nat_rat (tptp.power_power_rat 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.real) (Y tptp.real)) (= (tptp.aa_real_real tptp.real_V7735802525324610683m_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real tptp.uminus_uminus_real X)) Y)) (tptp.aa_real_real tptp.real_V7735802525324610683m_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) Y)))) (forall ((X tptp.complex) (Y tptp.complex)) (= (tptp.real_V1022390504157884413omplex (tptp.minus_minus_complex (tptp.uminus1482373934393186551omplex X) Y)) (tptp.real_V1022390504157884413omplex (tptp.plus_plus_complex X Y)))) (forall ((X tptp.real) (Y tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) Y))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.uminus_uminus_real X)) Y)))) (forall ((X tptp.real) (Y tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) Y)) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y) (tptp.aa_real_real tptp.uminus_uminus_real X))))) (forall ((X tptp.real) (Y tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) Y))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real X)) Y)))) (forall ((X tptp.real) (Y tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) Y)) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y) (tptp.aa_real_real tptp.uminus_uminus_real X))))) (forall ((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.uminus_uminus_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.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 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.uminus_uminus_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.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_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.uminus_uminus_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.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 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.uminus_uminus_rat (tptp.divide_divide_rat B C)))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_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) (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.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.uminus_uminus_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 ((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.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.uminus_uminus_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 ((W tptp.num) (B tptp.real) (C tptp.real)) (let ((_let_1 (tptp.aa_real_real tptp.uminus_uminus_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.uminus_uminus_rat (tptp.numeral_numeral_rat W)))) (let ((_let_2 (= C tptp.zero_zero_rat))) (= (= _let_1 (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 ((B tptp.real) (C tptp.real) (W tptp.num)) (let ((_let_1 (tptp.aa_real_real tptp.uminus_uminus_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.uminus_uminus_rat (tptp.numeral_numeral_rat W)))) (let ((_let_2 (= C tptp.zero_zero_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 ((Z tptp.real) (X tptp.real) (Y tptp.real)) (=> (not (= Z tptp.zero_zero_real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real X) Z))) Y) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real tptp.uminus_uminus_real X)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real Y) Z))) Z)))) (forall ((Z tptp.complex) (X tptp.complex) (Y tptp.complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (tptp.plus_plus_complex (tptp.uminus1482373934393186551omplex (tptp.divide1717551699836669952omplex X Z)) Y) (tptp.divide1717551699836669952omplex (tptp.plus_plus_complex (tptp.uminus1482373934393186551omplex X) (tptp.aa_complex_complex (tptp.times_times_complex Y) Z)) Z)))) (forall ((Z tptp.rat) (X tptp.rat) (Y tptp.rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.uminus_uminus_rat (tptp.divide_divide_rat X Z))) Y) (tptp.divide_divide_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.uminus_uminus_rat X)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat Y) Z)) Z)))) (forall ((Z tptp.real) (A tptp.real) (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.uminus_uminus_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.divide_divide_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_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) (Y tptp.real)) (=> (not (= Z tptp.zero_zero_real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real X) Z))) Y) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real tptp.uminus_uminus_real X)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real Y) Z))) Z)))) (forall ((Z tptp.complex) (X tptp.complex) (Y tptp.complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (tptp.minus_minus_complex (tptp.uminus1482373934393186551omplex (tptp.divide1717551699836669952omplex X Z)) Y) (tptp.divide1717551699836669952omplex (tptp.minus_minus_complex (tptp.uminus1482373934393186551omplex X) (tptp.aa_complex_complex (tptp.times_times_complex Y) Z)) Z)))) (forall ((Z tptp.rat) (X tptp.rat) (Y tptp.rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (tptp.minus_minus_rat (tptp.uminus_uminus_rat (tptp.divide_divide_rat X Z)) Y) (tptp.divide_divide_rat (tptp.minus_minus_rat (tptp.uminus_uminus_rat X) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat Y) Z)) Z)))) (forall ((Z tptp.real) (A tptp.real) (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.minus_minus_rat (tptp.divide_divide_rat A Z) B))) (let ((_let_2 (= Z tptp.zero_zero_rat))) (and (=> _let_2 (= _let_1 (tptp.uminus_uminus_rat B))) (=> (not _let_2) (= _let_1 (tptp.divide_divide_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) (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.minus_minus_rat (tptp.uminus_uminus_rat (tptp.divide_divide_rat A Z)) B))) (let ((_let_2 (= Z tptp.zero_zero_rat))) (and (=> _let_2 (= _let_1 (tptp.uminus_uminus_rat B))) (=> (not _let_2) (= _let_1 (tptp.divide_divide_rat (tptp.minus_minus_rat (tptp.uminus_uminus_rat A) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat B) 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 ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) _let_1) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Y) _let_1)) (or (= X Y) (= X (tptp.aa_real_real tptp.uminus_uminus_real Y)))))) (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (= (tptp.aa_nat_int (tptp.power_power_int X) _let_1) (tptp.aa_nat_int (tptp.power_power_int Y) _let_1)) (or (= X Y) (= X (tptp.aa_int_int tptp.uminus_uminus_int Y)))))) (forall ((X tptp.complex) (Y tptp.complex)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (= (tptp.aa_nat_complex (tptp.power_power_complex X) _let_1) (tptp.aa_nat_complex (tptp.power_power_complex Y) _let_1)) (or (= X Y) (= X (tptp.uminus1482373934393186551omplex Y)))))) (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (= (tptp.aa_nat_rat (tptp.power_power_rat X) _let_1) (tptp.aa_nat_rat (tptp.power_power_rat Y) _let_1)) (or (= X Y) (= X (tptp.uminus_uminus_rat Y)))))) (forall ((X tptp.code_integer) (Y tptp.code_integer)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (= (tptp.power_8256067586552552935nteger X _let_1) (tptp.power_8256067586552552935nteger Y _let_1)) (or (= X Y) (= X (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger Y)))))) (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.aa_int_int 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.rat)) (let ((_let_1 (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.uminus_uminus_rat tptp.one_one_rat)))))))))) (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 ((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.aa_int_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.rat)) (= (= (tptp.sgn_sgn_rat A) (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 ((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 ((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.uminus_uminus_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat N))) K) tptp.zero_zero_rat))) (forall ((N tptp.nat) (K tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N) K)) (= (tptp.aa_nat_int (tptp.comm_s4660882817536571857er_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N))) K) tptp.zero_zero_int))) (forall ((N tptp.nat) (K tptp.nat)) (= (= (tptp.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.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 ((A tptp.complex) (N tptp.nat)) (= (= (tptp.aa_nat_complex (tptp.comm_s2602460028002588243omplex A) N) tptp.zero_zero_complex) (exists ((K2 tptp.nat)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat K2) N)) (= A (tptp.uminus1482373934393186551omplex (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex K2))))))) (forall ((A tptp.real) (N tptp.nat)) (= (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.comm_s7457072308508201937r_real A) N) tptp.zero_zero_real) (exists ((K2 tptp.nat)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat K2) N)) (= A (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real K2))))))) (forall ((A tptp.rat) (N tptp.nat)) (= (= (tptp.aa_nat_rat (tptp.comm_s4028243227959126397er_rat A) N) tptp.zero_zero_rat) (exists ((K2 tptp.nat)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat K2) N)) (= A (tptp.uminus_uminus_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat K2))))))) (forall ((K tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) N)) (not (= (tptp.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.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 ((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 ((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.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.archim7802044766580827645g_real A)) (tptp.archim7802044766580827645g_real 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.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.archim2889992004027027881ng_rat A)) (tptp.archim2889992004027027881ng_rat B)))))))) (forall ((X tptp.fun_nat_fun_nat_nat) (Xa tptp.nat) (Xb tptp.nat) (Xc tptp.nat) (Y tptp.nat)) (let ((_let_1 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Xb) Xa)))) (=> (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.set_fo2584398358068434914at_nat X Xa) Xb) Xc) Y) (and (=> _let_1 (= Y Xc)) (=> (not _let_1) (= Y (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.set_fo2584398358068434914at_nat X (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Xa) tptp.one_one_nat)) Xb) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat X Xa) Xc)))))))) (forall ((B tptp.nat) (A tptp.nat) (F tptp.fun_nat_fun_nat_nat) (Acc tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.set_fo2584398358068434914at_nat F A) B) Acc))) (let ((_let_2 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat B) A)))) (and (=> _let_2 (= _let_1 Acc)) (=> (not _let_2) (= _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.set_fo2584398358068434914at_nat F (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) tptp.one_one_nat)) B) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat F A) Acc)))))))) (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 ((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.uminus_uminus_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.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 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) (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.uminus_uminus_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.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) (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.uminus_uminus_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.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 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) (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.uminus_uminus_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.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) (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 ((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.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.uminus_uminus_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 ((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 ((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.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.uminus_uminus_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 ((B tptp.real) (C tptp.real) (W tptp.num)) (let ((_let_1 (tptp.aa_real_real tptp.uminus_uminus_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.uminus_uminus_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.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.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.uminus_uminus_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.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.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.uminus_uminus_rat tptp.one_one_rat))))) (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 ((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.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.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.uminus_uminus_rat _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 ((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.power_power_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 ((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 ((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 ((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 ((W tptp.num) (B tptp.real) (C tptp.real)) (let ((_let_1 (tptp.aa_real_real tptp.uminus_uminus_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 ((W tptp.num) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.uminus_uminus_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.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 ((B tptp.real) (C tptp.real) (W tptp.num)) (let ((_let_1 (tptp.aa_real_real tptp.uminus_uminus_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 ((B tptp.rat) (C tptp.rat) (W tptp.num)) (let ((_let_1 (tptp.uminus_uminus_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.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 ((X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) tptp.one_one_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) tptp.one_one_real))))) (forall ((X tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) X)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger X) tptp.one_one_Code_integer)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.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.uminus_uminus_rat tptp.one_one_rat)) X)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) tptp.one_one_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat (tptp.power_power_rat X) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) tptp.one_one_rat))))) (forall ((X tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int)) X)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X) tptp.one_one_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int (tptp.power_power_int X) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) tptp.one_one_int))))) (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real tptp.uminus_uminus_real A)) N))) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real _let_1) _let_1) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N))))) (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_int_int tptp.uminus_uminus_int A)) N))) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int _let_1) _let_1) (tptp.aa_nat_int (tptp.power_power_int A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N))))) (forall ((A tptp.complex) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_complex (tptp.power_power_complex (tptp.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.rat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_rat (tptp.power_power_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 ((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 ((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.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 ((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 ((R tptp.code_integer) (K tptp.nat)) (let ((_let_1 (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger R))) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.minus_8373710615458151222nteger R) (tptp.semiri4939895301339042750nteger K))) (tptp.comm_s8582702949713902594nteger _let_1 K)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger R) (tptp.comm_s8582702949713902594nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.plus_p5714425477246183910nteger _let_1) tptp.one_one_Code_integer) K))))) (forall ((R tptp.complex) (K tptp.nat)) (let ((_let_1 (tptp.uminus1482373934393186551omplex R))) (= (tptp.aa_complex_complex (tptp.times_times_complex (tptp.minus_minus_complex R (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex K))) (tptp.aa_nat_complex (tptp.comm_s2602460028002588243omplex _let_1) K)) (tptp.aa_complex_complex (tptp.times_times_complex R) (tptp.aa_nat_complex (tptp.comm_s2602460028002588243omplex (tptp.plus_plus_complex _let_1 tptp.one_one_complex)) K))))) (forall ((R tptp.real) (K tptp.nat)) (let ((_let_1 (tptp.aa_real_real tptp.uminus_uminus_real R))) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real R) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real K))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.comm_s7457072308508201937r_real _let_1) K)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real R) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.comm_s7457072308508201937r_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real _let_1) tptp.one_one_real)) K))))) (forall ((R tptp.rat) (K tptp.nat)) (let ((_let_1 (tptp.uminus_uminus_rat R))) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.minus_minus_rat R (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat K))) (tptp.aa_nat_rat (tptp.comm_s4028243227959126397er_rat _let_1) K)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat R) (tptp.aa_nat_rat (tptp.comm_s4028243227959126397er_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat _let_1) tptp.one_one_rat)) K))))) (forall ((R tptp.int) (K tptp.nat)) (let ((_let_1 (tptp.aa_int_int tptp.uminus_uminus_int R))) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int R) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int K))) (tptp.aa_nat_int (tptp.comm_s4660882817536571857er_int _let_1) K)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int R) (tptp.aa_nat_int (tptp.comm_s4660882817536571857er_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int _let_1) tptp.one_one_int)) K))))) (forall ((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_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)) (= (tptp.aa_nat_rat (tptp.comm_s4028243227959126397er_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.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 ((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_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.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 ((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 ((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.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger 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.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.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.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.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger 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.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.uminus_uminus_rat tptp.one_one_rat)) K)) (tptp.aa_nat_rat (tptp.comm_s4028243227959126397er_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 ((X tptp.real) (Y tptp.real) (Z tptp.real)) (= (= X (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real Y) Z)) (= Y (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) Z)))) (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.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger 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 ((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.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger 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)) (= (tptp.aa_nat_complex tptp.semiri5044797733671781792omplex N) (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.set_fo2584398358068434914at_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N) tptp.one_one_nat)))) (forall ((N tptp.nat)) (= (tptp.aa_nat_rat tptp.semiri773545260158071498ct_rat N) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.set_fo2584398358068434914at_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N) tptp.one_one_nat)))) (forall ((N tptp.nat)) (= (tptp.aa_nat_int tptp.semiri1406184849735516958ct_int N) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.set_fo2584398358068434914at_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N) tptp.one_one_nat)))) (forall ((N tptp.nat)) (= (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat N) (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.set_fo2584398358068434914at_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N) tptp.one_one_nat)))) (forall ((N tptp.nat)) (= (tptp.aa_nat_real tptp.semiri2265585572941072030t_real N) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.set_fo2584398358068434914at_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N) tptp.one_one_nat)))) (forall ((N tptp.nat) (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.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger 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.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger 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)))))))))))) (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.real)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (let ((_let_2 (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.real)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (let ((_let_2 (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 ((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.archim7802044766580827645g_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.log2 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 ((B tptp.nat) (K tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat 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.archim6058952711729229775r_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.log2 (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)))))))))) (forall ((L tptp.int) (K tptp.int) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat M) N))) (let ((_let_2 (tptp.aa_int_int tptp.sgn_sgn_int L))) (let ((_let_3 (tptp.aa_int_int tptp.sgn_sgn_int K))) (let ((_let_4 (tptp.aa_int_int (tptp.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 ((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.abs_abs_rat A))) (= (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.abs_abs_rat A))) (= (tptp.abs_abs_rat _let_1) _let_1))) _let_117 _let_116 _let_115 _let_114 _let_117 _let_116 _let_115 _let_114 (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.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.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 ((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.numeral_numeral_real N))) (= (tptp.aa_real_real tptp.abs_abs_real _let_1) _let_1))) (forall ((N tptp.num)) (let ((_let_1 (tptp.numeral_numeral_rat N))) (= (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.abs_abs_rat A))) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat _let_1) _let_1) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) A)))) (forall ((A tptp.int)) (let ((_let_1 (tptp.aa_int_int tptp.abs_abs_int A))) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int _let_1) _let_1) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) A)))) _let_113 (= (tptp.abs_abs_complex tptp.one_one_complex) tptp.one_one_complex) _let_112 _let_111 _let_110 (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger 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.abs_abs_rat A)) (tptp.abs_abs_rat B)))) (= (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))) (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.rat)) (= (tptp.abs_abs_rat (tptp.uminus_uminus_rat A)) (tptp.abs_abs_rat 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.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.rat)) (= (tptp.abs_abs_rat (tptp.uminus_uminus_rat A)) (tptp.abs_abs_rat 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.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.abs_abs_rat (tptp.divide_divide_rat A B)) (tptp.divide_divide_rat (tptp.abs_abs_rat A) (tptp.abs_abs_rat 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.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.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.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 ((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)) (forall ((A tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.powr_real tptp.one_one_real) A) tptp.one_one_real)) (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.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))) (forall ((A tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A)) (= (tptp.abs_abs_Code_integer A) A))) (forall ((A tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) A)) (= (tptp.aa_real_real tptp.abs_abs_real A) A))) (forall ((A tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) A)) (= (tptp.abs_abs_rat A) A))) (forall ((A tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) A)) (= (tptp.aa_int_int tptp.abs_abs_int A) A))) (forall ((A tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.abs_abs_Code_integer A)) A)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A)))) (forall ((A tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real A)) A)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) A)))) (forall ((A tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.abs_abs_rat A)) A)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) A)))) (forall ((A tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.abs_abs_int A)) A)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) A)))) (forall ((A tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.abs_abs_Code_integer A)) tptp.zero_z3403309356797280102nteger)) (= A tptp.zero_z3403309356797280102nteger))) (forall ((A tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real A)) tptp.zero_zero_real)) (= A tptp.zero_zero_real))) (forall ((A tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.abs_abs_rat A)) tptp.zero_zero_rat)) (= A tptp.zero_zero_rat))) (forall ((A tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.abs_abs_int A)) tptp.zero_zero_int)) (= A tptp.zero_zero_int))) (forall ((A tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_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.abs_abs_rat A))) (not (= A tptp.zero_zero_rat)))) (forall ((A tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) (tptp.aa_int_int tptp.abs_abs_int A))) (not (= A tptp.zero_zero_int)))) (forall ((N tptp.num)) (let ((_let_1 (tptp.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.numeral_numeral_rat N))) (= (tptp.abs_abs_rat (tptp.uminus_uminus_rat _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))) (= (tptp.aa_real_real tptp.abs_abs_real _let_44) tptp.one_one_real) (= (tptp.aa_int_int tptp.abs_abs_int _let_57) tptp.one_one_int) (= (tptp.abs_abs_rat _let_56) tptp.one_one_rat) (= (tptp.abs_abs_Code_integer _let_65) tptp.one_one_Code_integer) (forall ((A tptp.real) (N tptp.nat)) (= (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real tptp.uminus_uminus_real A)) N)) (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real A) N)))) (forall ((A tptp.int) (N tptp.nat)) (= (tptp.aa_int_int tptp.abs_abs_int (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_int_int tptp.uminus_uminus_int A)) N)) (tptp.aa_int_int tptp.abs_abs_int (tptp.aa_nat_int (tptp.power_power_int A) N)))) (forall ((A tptp.rat) (N tptp.nat)) (= (tptp.abs_abs_rat (tptp.aa_nat_rat (tptp.power_power_rat (tptp.uminus_uminus_rat A)) N)) (tptp.abs_abs_rat (tptp.aa_nat_rat (tptp.power_power_rat A) N)))) (forall ((A tptp.code_integer) (N tptp.nat)) (= (tptp.abs_abs_Code_integer (tptp.power_8256067586552552935nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A) N)) (tptp.abs_abs_Code_integer (tptp.power_8256067586552552935nteger A N)))) (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)))))) (= (tptp.archim6058952711729229775r_real tptp.zero_zero_real) tptp.zero_zero_int) (= (tptp.archim3151403230148437115or_rat tptp.zero_zero_rat) tptp.zero_zero_int) (forall ((V tptp.num)) (= (tptp.archim6058952711729229775r_real (tptp.numeral_numeral_real V)) (tptp.aa_num_int tptp.numeral_numeral_int V))) (forall ((V tptp.num)) (= (tptp.archim3151403230148437115or_rat (tptp.numeral_numeral_rat V)) (tptp.aa_num_int tptp.numeral_numeral_int V))) (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)))) (= (tptp.archim6058952711729229775r_real tptp.one_one_real) tptp.one_one_int) (= (tptp.archim3151403230148437115or_rat tptp.one_one_rat) tptp.one_one_int) (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_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 ((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 ((N tptp.nat)) (= (tptp.archim6058952711729229775r_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N)) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N))) (forall ((N tptp.nat)) (= (tptp.archim3151403230148437115or_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat N)) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N))) (= (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 ((A tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) tptp.zero_zero_real)) (= (tptp.aa_real_real tptp.abs_abs_real A) (tptp.aa_real_real tptp.uminus_uminus_real A)))) (forall ((A tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger A) tptp.zero_z3403309356797280102nteger)) (= (tptp.abs_abs_Code_integer A) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A)))) (forall ((A tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) tptp.zero_zero_rat)) (= (tptp.abs_abs_rat A) (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) (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)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.divide_divide_rat A (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)) (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.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.divide_divide_rat A (tptp.abs_abs_rat B)))) (or (tptp.pp (tptp.aa_rat_bool _let_1 A)) (= B tptp.zero_zero_rat))))) (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.abs_abs_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.aa_int_int tptp.sgn_sgn_int A)) tptp.one_one_int))) (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 ((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 ((X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.abs_abs_real X)) tptp.one_one_real)) (= (tptp.aa_real_real tptp.artanh_real (tptp.aa_real_real tptp.uminus_uminus_real X)) (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_real_real tptp.artanh_real X))))) (forall ((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.sgn_sgn_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.aa_int_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 ((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.abs_abs_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.aa_int_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 ((M tptp.num) (N tptp.num)) (let ((_let_1 (tptp.numeral_numeral_real M))) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.powr_real _let_1) (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.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.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.abs_abs_rat _let_1) _let_1))) (forall ((A tptp.real)) (let ((_let_1 (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real A) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.aa_real_real tptp.abs_abs_real _let_1) _let_1))) (forall ((A tptp.int)) (let ((_let_1 (tptp.aa_nat_int (tptp.power_power_int A) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.aa_int_int tptp.abs_abs_int _let_1) _let_1))) (forall ((A tptp.code_integer)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.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.abs_abs_rat A)) _let_1) (tptp.aa_nat_rat (tptp.power_power_rat A) _let_1)))) (forall ((A tptp.real)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real tptp.abs_abs_real A)) _let_1) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real A) _let_1)))) (forall ((A tptp.int)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_int_int tptp.abs_abs_int A)) _let_1) (tptp.aa_nat_int (tptp.power_power_int A) _let_1)))) (forall ((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.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.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.real)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_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.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.archim6058952711729229775r_real X))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_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.archim3151403230148437115or_rat X))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_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.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.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.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.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.real) (V tptp.num)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_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.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.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.numeral_numeral_rat V))))) (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.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.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_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.one_one_real)))) (forall ((X tptp.rat)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_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.one_one_rat)))) (forall ((V tptp.num)) (= (tptp.archim6058952711729229775r_real (tptp.aa_real_real tptp.uminus_uminus_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.archim3151403230148437115or_rat (tptp.uminus_uminus_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) (V tptp.num)) (= (tptp.archim6058952711729229775r_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real X) (tptp.numeral_numeral_real V))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.archim6058952711729229775r_real X)) (tptp.aa_num_int tptp.numeral_numeral_int V)))) (forall ((X tptp.rat) (V tptp.num)) (= (tptp.archim3151403230148437115or_rat (tptp.minus_minus_rat X (tptp.numeral_numeral_rat V))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.archim3151403230148437115or_rat X)) (tptp.aa_num_int tptp.numeral_numeral_int V)))) (forall ((X tptp.real)) (= (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.archim6058952711729229775r_real X)) tptp.one_one_int))) (forall ((X tptp.rat)) (= (tptp.archim3151403230148437115or_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.archim3151403230148437115or_rat X)) tptp.one_one_int))) (forall ((X tptp.num) (N tptp.nat)) (= (tptp.archim6058952711729229775r_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_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.archim3151403230148437115or_rat (tptp.aa_nat_rat (tptp.power_power_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 ((A tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) A)) (=> (not (= A tptp.one_one_real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.log2 A) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.powr_real A) Y)) Y)))) (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.log2 A) X)) X)))))) (forall ((A tptp.num) (B tptp.num)) (= (tptp.archim6058952711729229775r_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.numeral_numeral_real A)) (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 ((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.abs_abs_rat A)) _let_1) (tptp.aa_nat_rat (tptp.power_power_rat A) _let_1))))) (forall ((W tptp.num) (A tptp.real)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat W))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) _let_1)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real tptp.abs_abs_real A)) _let_1) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real A) _let_1))))) (forall ((W tptp.num) (A tptp.int)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat W))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) _let_1)) (= (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_int_int tptp.abs_abs_int A)) _let_1) (tptp.aa_nat_int (tptp.power_power_int A) _let_1))))) (forall ((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.numeral_numeral_real N)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) (tptp.aa_num_nat tptp.numeral_numeral_nat N))))) (forall ((A tptp.num) (B tptp.num)) (= (tptp.archim7802044766580827645g_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.numeral_numeral_real A)) (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.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.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.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.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.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.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.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.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.archim6058952711729229775r_real X))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_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.archim3151403230148437115or_rat X))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_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.archim6058952711729229775r_real X)) tptp.one_one_int)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) (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.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.numeral_numeral_rat (tptp.aa_num_num tptp.bit0 tptp.one)))))) (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.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.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.archim3151403230148437115or_rat X))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.uminus_uminus_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.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.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.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.uminus_uminus_rat (tptp.numeral_numeral_rat V)))))) (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 ((B tptp.num)) (= (tptp.archim6058952711729229775r_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.one_one_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.archim6058952711729229775r_real (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.numeral_numeral_real A)) (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.archim7802044766580827645g_real (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.numeral_numeral_real A)) (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 ((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.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.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.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.uminus_uminus_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.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.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.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.uminus_uminus_rat (tptp.numeral_numeral_rat V))) tptp.one_one_rat))))) (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.numeral_numeral_real _let_1))) (tptp.aa_real_real tptp.abs_abs_real X)))) (forall ((B tptp.num)) (= (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.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)))) (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) (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.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)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) (tptp.aa_real_real tptp.abs_abs_real A)))) (forall ((A tptp.code_integer)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger A) (tptp.abs_abs_Code_integer A)))) (forall ((A tptp.rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) (tptp.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.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.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.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.abs_abs_rat A)) (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_113 _let_112 _let_111 _let_110 (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (tptp.abs_abs_Code_integer (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.minus_8373710615458151222nteger A) B)) (tptp.abs_abs_Code_integer (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger 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.abs_abs_rat (tptp.minus_minus_rat A B)) (tptp.abs_abs_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 ((X tptp.real) (Y tptp.real)) (= (= (tptp.aa_real_real tptp.abs_abs_real X) (tptp.aa_real_real tptp.abs_abs_real Y)) (or (= X Y) (= X (tptp.aa_real_real tptp.uminus_uminus_real Y))))) (forall ((X tptp.int) (Y tptp.int)) (= (= (tptp.aa_int_int tptp.abs_abs_int X) (tptp.aa_int_int tptp.abs_abs_int Y)) (or (= X Y) (= X (tptp.aa_int_int tptp.uminus_uminus_int Y))))) (forall ((X tptp.rat) (Y tptp.rat)) (= (= (tptp.abs_abs_rat X) (tptp.abs_abs_rat Y)) (or (= X Y) (= X (tptp.uminus_uminus_rat Y))))) (forall ((X tptp.code_integer) (Y tptp.code_integer)) (= (= (tptp.abs_abs_Code_integer X) (tptp.abs_abs_Code_integer Y)) (or (= X Y) (= X (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger Y))))) (forall ((A tptp.code_integer) (N tptp.nat)) (= (tptp.abs_abs_Code_integer (tptp.power_8256067586552552935nteger A N)) (tptp.power_8256067586552552935nteger (tptp.abs_abs_Code_integer A) N))) (forall ((A tptp.rat) (N tptp.nat)) (= (tptp.abs_abs_rat (tptp.aa_nat_rat (tptp.power_power_rat A) N)) (tptp.aa_nat_rat (tptp.power_power_rat (tptp.abs_abs_rat A)) N))) (forall ((A tptp.real) (N tptp.nat)) (= (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real A) N)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real tptp.abs_abs_real A)) N))) (forall ((A tptp.int) (N tptp.nat)) (= (tptp.aa_int_int tptp.abs_abs_int (tptp.aa_nat_int (tptp.power_power_int A) N)) (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_int_int tptp.abs_abs_int A)) N))) (forall ((L tptp.real) (K tptp.real)) (=> (= (tptp.aa_real_real tptp.abs_abs_real L) (tptp.aa_real_real tptp.abs_abs_real K)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.dvd_dvd_real L) K)))) (forall ((L tptp.int) (K tptp.int)) (=> (= (tptp.aa_int_int tptp.abs_abs_int L) (tptp.aa_int_int tptp.abs_abs_int K)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int L) K)))) (forall ((L tptp.code_integer) (K tptp.code_integer)) (=> (= (tptp.abs_abs_Code_integer L) (tptp.abs_abs_Code_integer K)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer L) K)))) (forall ((L tptp.rat) (K tptp.rat)) (=> (= (tptp.abs_abs_rat L) (tptp.abs_abs_rat K)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.dvd_dvd_rat L) K)))) (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 ((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)))) _let_109 (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 ((N tptp.nat) (K tptp.int)) (let ((_let_1 (tptp.bit_se2923211474154528505it_int N))) (= (tptp.aa_int_int _let_1 (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_int_int _let_1 K))) (tptp.aa_int_int _let_1 (tptp.aa_int_int tptp.uminus_uminus_int K))))) (forall ((N tptp.nat) (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.code_integer)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (tptp.abs_abs_Code_integer A)))) (forall ((A tptp.real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_real_real tptp.abs_abs_real A)))) (forall ((A tptp.rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.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 ((X tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) Y)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.archim6058952711729229775r_real X)) (tptp.archim6058952711729229775r_real Y))))) (forall ((X tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) Y)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.archim3151403230148437115or_rat X)) (tptp.archim3151403230148437115or_rat Y))))) (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.abs_abs_rat A)) tptp.zero_zero_rat)))) (forall ((A tptp.int)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int tptp.abs_abs_int A)) tptp.zero_zero_int)))) (forall ((A tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A)) (= (tptp.abs_abs_Code_integer A) A))) (forall ((A tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) A)) (= (tptp.aa_real_real tptp.abs_abs_real A) A))) (forall ((A tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) A)) (= (tptp.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 ((X tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.archim6058952711729229775r_real X)) (tptp.archim6058952711729229775r_real Y))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Y)))) (forall ((X tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.archim3151403230148437115or_rat X)) (tptp.archim3151403230148437115or_rat Y))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) Y)))) (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.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.plus_p5714425477246183910nteger A) B))) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.plus_p5714425477246183910nteger (tptp.abs_abs_Code_integer A)) (tptp.abs_abs_Code_integer 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.rat) (B tptp.rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_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.abs_abs_rat A)) (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.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.abs_abs_rat B))) (let ((_let_2 (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.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.minus_8373710615458151222nteger (tptp.abs_abs_Code_integer A)) (tptp.abs_abs_Code_integer B))) (tptp.abs_abs_Code_integer (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.minus_8373710615458151222nteger 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.rat) (B tptp.rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.minus_minus_rat (tptp.abs_abs_rat A) (tptp.abs_abs_rat B))) (tptp.abs_abs_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.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.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.minus_8373710615458151222nteger (tptp.abs_abs_Code_integer A)) (tptp.abs_abs_Code_integer B)))) (tptp.abs_abs_Code_integer (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.minus_8373710615458151222nteger 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.rat) (B tptp.rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.abs_abs_rat (tptp.minus_minus_rat (tptp.abs_abs_rat A) (tptp.abs_abs_rat B)))) (tptp.abs_abs_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.code_integer) (B tptp.code_integer)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.minus_8373710615458151222nteger (tptp.abs_abs_Code_integer A)) (tptp.abs_abs_Code_integer B))) (tptp.abs_abs_Code_integer (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.minus_8373710615458151222nteger 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 ((A tptp.rat) (B tptp.rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.minus_minus_rat (tptp.abs_abs_rat A) (tptp.abs_abs_rat B))) (tptp.abs_abs_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 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.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.uminus_uminus_rat A)) B)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_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 (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 (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.abs_abs_rat A)) B)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_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)) (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)) (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.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.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)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real A)) (tptp.aa_real_real tptp.abs_abs_real A)))) (forall ((A tptp.code_integer)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A)) (tptp.abs_abs_Code_integer A)))) (forall ((A tptp.rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.uminus_uminus_rat A)) (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 ((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.abs_abs_rat (tptp.divide_divide_rat A B)) (tptp.divide_divide_rat (tptp.abs_abs_rat A) (tptp.abs_abs_rat 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.rat) (B tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_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.uminus_uminus_rat 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 ((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.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.one_one_real) X)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B)))))) (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_real A) B)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real) X)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real _let_1 A)) (tptp.aa_real_real _let_1 B))))))) (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 ((X tptp.real)) (= (tptp.archim7802044766580827645g_real X) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.archim6058952711729229775r_real (tptp.aa_real_real tptp.uminus_uminus_real X))))) (forall ((X tptp.rat)) (= (tptp.archim2889992004027027881ng_rat X) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.archim3151403230148437115or_rat (tptp.uminus_uminus_rat X))))) (forall ((X tptp.real)) (= (tptp.archim6058952711729229775r_real (tptp.aa_real_real tptp.uminus_uminus_real X)) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.archim7802044766580827645g_real X)))) (forall ((X tptp.rat)) (= (tptp.archim3151403230148437115or_rat (tptp.uminus_uminus_rat X)) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.archim2889992004027027881ng_rat X)))) (forall ((X tptp.real)) (= (tptp.archim7802044766580827645g_real (tptp.aa_real_real tptp.uminus_uminus_real X)) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.archim6058952711729229775r_real X)))) (forall ((X tptp.rat)) (= (tptp.archim2889992004027027881ng_rat (tptp.uminus_uminus_rat X)) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.archim3151403230148437115or_rat X)))) (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.abs_abs_rat K) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat K) (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.aa_int_int 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.abs_abs_rat A)) (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.aa_int_int 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.sgn_sgn_rat A)) (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.aa_int_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.sgn_sgn_rat X)) (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.aa_int_int tptp.sgn_sgn_int X)) (tptp.aa_int_int tptp.abs_abs_int X)) X)) (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.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.plus_p5714425477246183910nteger A) B)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger 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.sgn_sgn_rat B) (tptp.sgn_sgn_rat A)) (= (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.abs_abs_rat A)) (tptp.abs_abs_rat B))))) (forall ((B tptp.int) (A tptp.int)) (=> (= (tptp.aa_int_int tptp.sgn_sgn_int B) (tptp.aa_int_int 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 ((X tptp.real)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.archim6058952711729229775r_real X)) (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.archim3151403230148437115or_rat X)) (tptp.archim2889992004027027881ng_rat 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)) (=> (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int M) N) tptp.one_one_int) (or (= M tptp.one_one_int) (= M (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int))))) (forall ((M tptp.int) (N tptp.int)) (let ((_let_1 (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int))) (= (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int M) N) tptp.one_one_int) (or (and (= M tptp.one_one_int) (= N tptp.one_one_int)) (and (= M _let_1) (= N _let_1)))))) (forall ((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 ((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 ((X tptp.real)) (=> (forall ((E2 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) E2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real X)) E2)))) (= X tptp.zero_zero_real))) (forall ((X tptp.rat)) (=> (forall ((E2 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) E2)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.abs_abs_rat X)) E2)))) (= X tptp.zero_zero_rat))) (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.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.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.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.abs_abs_rat A)) (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 ((X tptp.code_integer) (Y tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) X)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.abs_abs_Code_integer Y)) X) (tptp.abs_abs_Code_integer (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger Y) X))))) (forall ((X tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) X)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real tptp.abs_abs_real Y)) X) (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real Y) X))))) (forall ((X tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) X)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.abs_abs_rat Y)) X) (tptp.abs_abs_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat Y) X))))) (forall ((X tptp.int) (Y tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) X)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int tptp.abs_abs_int Y)) X) (tptp.aa_int_int tptp.abs_abs_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int Y) X))))) (forall ((A tptp.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) (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.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.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)) (= (= 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)) (= (= 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.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.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)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_real_real tptp.abs_abs_real A))) tptp.zero_zero_real))) (forall ((A tptp.code_integer)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.abs_abs_Code_integer A))) tptp.zero_z3403309356797280102nteger))) (forall ((A tptp.rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.uminus_uminus_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.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.real) (N tptp.nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real tptp.abs_abs_real A)) N)))) (forall ((A tptp.rat) (N tptp.nat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_nat_rat (tptp.power_power_rat (tptp.abs_abs_rat A)) N)))) (forall ((A tptp.int) (N tptp.nat)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_int_int tptp.abs_abs_int A)) N)))) (forall ((A tptp.real)) (let ((_let_1 (tptp.aa_real_real tptp.abs_abs_real A))) (let ((_let_2 (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) tptp.zero_zero_real)))) (and (=> _let_2 (= _let_1 (tptp.aa_real_real tptp.uminus_uminus_real A))) (=> (not _let_2) (= _let_1 A)))))) (forall ((A tptp.int)) (let ((_let_1 (tptp.aa_int_int tptp.abs_abs_int A))) (let ((_let_2 (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) tptp.zero_zero_int)))) (and (=> _let_2 (= _let_1 (tptp.aa_int_int tptp.uminus_uminus_int A))) (=> (not _let_2) (= _let_1 A)))))) (forall ((A tptp.rat)) (let ((_let_1 (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.uminus_uminus_rat 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.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.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) tptp.zero_zero_rat)) (= (tptp.abs_abs_rat A) (tptp.uminus_uminus_rat 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 ((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.rat)) (let ((_let_1 (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.uminus_uminus_rat 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 ((Y tptp.real) (X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) Y)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real tptp.abs_abs_real X)) Y) (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real X) Y))))) (forall ((Y tptp.rat) (X tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) Y)) (= (tptp.divide_divide_rat (tptp.abs_abs_rat X) Y) (tptp.abs_abs_rat (tptp.divide_divide_rat X Y))))) (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.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.minus_8373710615458151222nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.plus_p5714425477246183910nteger A) B)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.plus_p5714425477246183910nteger C) D)))) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.plus_p5714425477246183910nteger (tptp.abs_abs_Code_integer (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.minus_8373710615458151222nteger A) C))) (tptp.abs_abs_Code_integer (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.minus_8373710615458151222nteger 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 ((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.abs_abs_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.abs_abs_rat (tptp.minus_minus_rat A C))) (tptp.abs_abs_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.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.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.minus_8373710615458151222nteger A) B))) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.plus_p5714425477246183910nteger (tptp.abs_abs_Code_integer A)) (tptp.abs_abs_Code_integer 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.rat) (B tptp.rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.abs_abs_rat (tptp.minus_minus_rat A B))) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.abs_abs_rat A)) (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 ((X tptp.code_integer) (A tptp.code_integer) (R tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.abs_abs_Code_integer (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.minus_8373710615458151222nteger X) A))) R)) (and (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.minus_8373710615458151222nteger A) R)) X)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger X) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.plus_p5714425477246183910nteger A) R)))))) (forall ((X tptp.real) (A tptp.real) (R tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real X) A))) R)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A) R)) X)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) R)))))) (forall ((X tptp.rat) (A tptp.rat) (R tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.abs_abs_rat (tptp.minus_minus_rat X A))) R)) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.minus_minus_rat A R)) X)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) R)))))) (forall ((X tptp.int) (A tptp.int) (R tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.abs_abs_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int X) A))) R)) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) R)) X)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) R)))))) (forall ((X tptp.code_integer) (A tptp.code_integer) (R tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.abs_abs_Code_integer (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.minus_8373710615458151222nteger X) A))) R)) (and (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.minus_8373710615458151222nteger A) R)) X)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger X) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.plus_p5714425477246183910nteger A) R)))))) (forall ((X tptp.real) (A tptp.real) (R tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real X) A))) R)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A) R)) X)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) R)))))) (forall ((X tptp.rat) (A tptp.rat) (R tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.abs_abs_rat (tptp.minus_minus_rat X A))) R)) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.minus_minus_rat A R)) X)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) R)))))) (forall ((X tptp.int) (A tptp.int) (R tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int tptp.abs_abs_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int X) A))) R)) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) R)) X)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) R)))))) (forall ((X tptp.real) (Y 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.archim6058952711729229775r_real X)) (tptp.archim6058952711729229775r_real Y))) (tptp.archim6058952711729229775r_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) Y))))) (forall ((X tptp.rat) (Y 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.archim3151403230148437115or_rat X)) (tptp.archim3151403230148437115or_rat Y))) (tptp.archim3151403230148437115or_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat X) Y))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real))) (=> (tptp.pp (tptp.aa_real_bool _let_1 X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) Y)) (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.powr_real X) Y))))))) (forall ((A tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.powr_real A))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) A)) (=> (not (= A tptp.one_one_real)) (= (= (tptp.aa_real_real _let_1 X) (tptp.aa_real_real _let_1 Y)) (= X Y)))))) (forall ((X tptp.real) (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) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) A)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) 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) Y)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.powr_real X) A)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.powr_real Y) 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) (Y tptp.real) (A tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool _let_1 X)) (=> (tptp.pp (tptp.aa_real_bool _let_1 Y)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.powr_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real X) Y)) A) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.powr_real X) A)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.powr_real Y) A))))))) (forall ((X tptp.real) (Y tptp.real) (A tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool _let_1 X)) (=> (tptp.pp (tptp.aa_real_bool _let_1 Y)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.powr_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real X) Y)) A) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.powr_real X) A)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.powr_real Y) A))))))) (forall ((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.abs_abs_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.aa_int_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 ((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 ((A tptp.real) (B tptp.real) (X tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.log2 (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.log2 A) X)) B)))) (forall ((X tptp.real) (Y tptp.real)) (=> (not (= X tptp.zero_zero_real)) (= (tptp.aa_real_real tptp.ln_ln_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.powr_real X) Y)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real Y) (tptp.aa_real_real tptp.ln_ln_real X))))) (forall ((X tptp.real) (B tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.log2 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) Y)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real Y) (tptp.aa_real_real _let_1 X)))))) (forall ((A tptp.real)) (let ((_let_1 (tptp.aa_real_real tptp.abs_abs_real A))) (let ((_let_2 (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) tptp.zero_zero_real)))) (and (=> _let_2 (= _let_1 (tptp.aa_real_real tptp.uminus_uminus_real A))) (=> (not _let_2) (= _let_1 A)))))) (forall ((A tptp.real) (X tptp.real) (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 ((Y4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real X) Y4))) D2)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) Y4)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y4) B)))))))))) (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) (Z2 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) Z2)) (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 Z2))))) (forall ((X tptp.real) (Y tptp.real) (U tptp.real) (V tptp.real)) (=> (= X Y) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real U)) V)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) U)) Y))) V))))) (forall ((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 ((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 ((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 ((N tptp.nat)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N))) tptp.zero_zero_int))) (forall ((K tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int K) tptp.zero_zero_int)) (not (forall ((N2 tptp.nat)) (not (= K (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N2)))))))) (forall ((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 ((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 ((X tptp.code_integer)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger 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.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 ((X tptp.real)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.archim6058952711729229775r_real X)) tptp.one_one_int) (tptp.archim6058952711729229775r_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) tptp.one_one_real)))) (forall ((X tptp.rat)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.archim3151403230148437115or_rat X)) tptp.one_one_int) (tptp.archim3151403230148437115or_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat X) tptp.one_one_rat)))) (forall ((M tptp.nat) (N tptp.nat)) (= (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.archim3151403230148437115or_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) (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) (Y 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 Y) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.log2 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) Y)) X)))))) (forall ((B tptp.real) (X tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real) 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.log2 B) X)) Y)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.powr_real B) Y))))))) (forall ((B tptp.real) (X tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real) 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) Y))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.log2 B) X)) Y)))))) (forall ((B tptp.real) (X tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real) 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) Y)) X)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.log2 B) X))))))) (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.archim7802044766580827645g_real X)) (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.archim2889992004027027881ng_rat X)) (tptp.archim3151403230148437115or_rat X))) tptp.one_one_int))) (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 ((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 ((Y4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real X) Y4))) D2)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) Y4)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y4) 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.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.real_V1022390504157884413omplex A)) (tptp.real_V1022390504157884413omplex B)))) (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 ((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) (B4 tptp.int) (N tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A2) B4)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) (tptp.aa_int_int tptp.uminus_uminus_int N))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int B4) 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 ((I tptp.int)) (let ((_let_1 (tptp.aa_int_int tptp.sgn_sgn_int I))) (let ((_let_2 (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) I)))) (let ((_let_3 (= I tptp.zero_zero_int))) (and (=> _let_3 (= _let_1 tptp.zero_zero_int)) (=> (not _let_3) (and (=> _let_2 (= _let_1 tptp.one_one_int)) (=> (not _let_2) (= _let_1 (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int)))))))))) (forall ((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 ((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.archim6058952711729229775r_real A)) (tptp.archim6058952711729229775r_real B))) (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.archim3151403230148437115or_rat A)) (tptp.archim3151403230148437115or_rat B))) (tptp.archim3151403230148437115or_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) B)))))))) (forall ((X tptp.code_integer) (Y tptp.code_integer)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.abs_abs_Code_integer X)) (tptp.abs_abs_Code_integer Y))) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.power_8256067586552552935nteger X _let_1)) (tptp.power_8256067586552552935nteger Y _let_1)))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real X)) (tptp.aa_real_real tptp.abs_abs_real Y))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) _let_1)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Y) _let_1)))))) (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.abs_abs_rat X)) (tptp.abs_abs_rat Y))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat (tptp.power_power_rat X) _let_1)) (tptp.aa_nat_rat (tptp.power_power_rat Y) _let_1)))))) (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.abs_abs_int X)) (tptp.aa_int_int tptp.abs_abs_int Y))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int (tptp.power_power_int X) _let_1)) (tptp.aa_nat_int (tptp.power_power_int Y) _let_1)))))) (forall ((X tptp.code_integer)) (= (= (tptp.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.abs_abs_rat X) tptp.one_one_rat))) (forall ((X tptp.real)) (= (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) tptp.one_one_real) (= (tptp.aa_real_real tptp.abs_abs_real X) tptp.one_one_real))) (forall ((X tptp.int)) (= (= (tptp.aa_nat_int (tptp.power_power_int X) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) tptp.one_one_int) (= (tptp.aa_int_int tptp.abs_abs_int X) tptp.one_one_int))) (forall ((N tptp.nat) (A tptp.code_integer)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N)) (= (tptp.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.abs_abs_rat A)) N) (tptp.aa_nat_rat (tptp.power_power_rat A) N)))) (forall ((N tptp.nat) (A tptp.real)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real tptp.abs_abs_real A)) N) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real A) N)))) (forall ((N tptp.nat) (A tptp.int)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N)) (= (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_int_int tptp.abs_abs_int A)) N) (tptp.aa_nat_int (tptp.power_power_int A) N)))) (forall ((X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) X)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.powr_real X) (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.one_one_real) X)))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.powr_real X))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) X)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real X) (tptp.aa_real_real _let_1 Y)) (tptp.aa_real_real _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real tptp.one_one_real) Y)))))) (forall ((B tptp.real) (X tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real) 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) Y)) X)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.log2 B) X))))))) (forall ((B tptp.real) (X tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real) 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) Y))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.log2 B) X)) Y)))))) (forall ((B tptp.real) (X tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real) 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.log2 B) X)) Y)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.powr_real B) Y))))))) (forall ((B tptp.real) (X tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real) 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 Y) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.log2 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) Y)) X)))))) (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 ((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_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 ((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 ((Y tptp.code_integer) (X tptp.code_integer)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) Y)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.power_8256067586552552935nteger X _let_1)) (tptp.power_8256067586552552935nteger Y _let_1))) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.abs_abs_Code_integer X)) Y)))))) (forall ((Y tptp.real) (X tptp.real)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) Y)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) _let_1)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Y) _let_1))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real X)) Y)))))) (forall ((Y tptp.rat) (X tptp.rat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) Y)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat (tptp.power_power_rat X) _let_1)) (tptp.aa_nat_rat (tptp.power_power_rat Y) _let_1))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.abs_abs_rat X)) Y)))))) (forall ((Y tptp.int) (X tptp.int)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) Y)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int (tptp.power_power_int X) _let_1)) (tptp.aa_nat_int (tptp.power_power_int Y) _let_1))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.abs_abs_int X)) Y)))))) (forall ((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.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) tptp.one_one_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real X)) tptp.one_one_real)))) (forall ((X tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat (tptp.power_power_rat X) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) tptp.one_one_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.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.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.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.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 ((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.abs_abs_rat A)) (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 ((X tptp.real) (A tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.one_one_real) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) A)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.ln_ln_real X)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.powr_real X) A)) A)))))) (forall ((X tptp.real) (A tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) A)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.powr_real (tptp.aa_real_real tptp.ln_ln_real X)) A)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.powr_real A) A)) X)))))) (forall ((B tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.log2 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 Y) (tptp.aa_real_real _let_1 X)) (tptp.aa_real_real _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.powr_real B) Y)) X))))))))) (forall ((B tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.log2 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)) Y) (tptp.aa_real_real _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.powr_real B) Y)))))))))) (forall ((B tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.log2 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 Y) (tptp.aa_real_real _let_1 X)) (tptp.aa_real_real _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.powr_real B) Y)) X))))))))) (forall ((N tptp.nat) (K tptp.num)) (= (tptp.aa_int_int (tptp.bit_se2923211474154528505it_int (tptp.aa_nat_nat tptp.suc N)) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 K)))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.bit_se2923211474154528505it_int N) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int K)))) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))))) (forall ((N tptp.nat)) (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) (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 ((N tptp.nat)) (= (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_se545348938243370406it_int N) (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int)) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) N)))) (forall ((B tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.log2 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)) Y) (tptp.aa_real_real _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.powr_real B) (tptp.aa_real_real tptp.uminus_uminus_real Y))))))))))) (forall ((P tptp.fun_int_bool) (K tptp.int)) (=> (tptp.pp (tptp.aa_int_bool P tptp.zero_zero_int)) (=> (tptp.pp (tptp.aa_int_bool P (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int))) (=> (forall ((K3 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool P K3)) (=> (not (= K3 tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool P (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int K3) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one)))))))) (=> (forall ((K3 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool P K3)) (=> (not (= K3 (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int))) (tptp.pp (tptp.aa_int_bool P (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int tptp.one_one_int) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int K3) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))))))))) (tptp.pp (tptp.aa_int_bool P K))))))) (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) N))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.uminus_uminus_int _let_1)) K)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int K) _let_1)) (= (tptp.aa_int_int (tptp.bit_ri631733984087533419it_int N) K) K))))) (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) N))) (= (= (tptp.aa_int_int (tptp.bit_ri631733984087533419it_int N) K) K) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.uminus_uminus_int _let_1)) K)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int K) _let_1)))))) (forall ((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.numeral_numeral_real N))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.one_one_real) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) (tptp.aa_num_nat tptp.numeral_numeral_nat N)))))) (forall ((N tptp.nat)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (let ((_let_2 (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1))) (let ((_let_3 (tptp.aa_rea7340605660300375871l_real tptp.log2 (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.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.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 ((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 ((K tptp.int) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) N))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) K)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int K) _let_1)) (= (tptp.aa_int_int (tptp.bit_se2923211474154528505it_int N) (tptp.aa_int_int tptp.uminus_uminus_int K)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int _let_1) K)))))) (forall ((X tptp.real)) (=> (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 ((B tptp.nat) (N tptp.nat) (K tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat 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.archim6058952711729229775r_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.log2 (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 ((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_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 ((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.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 ((N tptp.nat) (K tptp.num)) (= (tptp.aa_int_int (tptp.bit_ri631733984087533419it_int (tptp.aa_nat_nat tptp.suc N)) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit1 K)))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.bit_ri631733984087533419it_int N) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int K))) tptp.one_one_int))) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one)))) tptp.one_one_int))) (forall ((X tptp.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.numeral_numeral_real _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.times_times_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 ((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.numeral_numeral_real _let_1))))))))) (forall ((N tptp.nat) (K tptp.num)) (= (tptp.aa_int_int (tptp.bit_ri631733984087533419it_int (tptp.aa_nat_nat tptp.suc N)) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.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 ((X32 tptp.num) (Y32 tptp.num)) (= (= (tptp.aa_num_num tptp.bit1 X32) (tptp.aa_num_num tptp.bit1 Y32)) (= X32 Y32))) (forall ((M tptp.num) (N tptp.num)) (= (= (tptp.aa_num_num tptp.bit1 M) (tptp.aa_num_num tptp.bit1 N)) (= M 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.num) (N tptp.num)) (not (= (tptp.aa_num_num tptp.bit1 M) (tptp.aa_num_num tptp.bit0 N)))) (forall ((N tptp.num)) (not (= tptp.one (tptp.aa_num_num tptp.bit1 N)))) (forall ((M tptp.num)) (not (= (tptp.aa_num_num tptp.bit1 M) tptp.one))) (forall ((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))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.pp (tptp.aa_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.ord_less_num M) N)))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.pp (tptp.aa_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.ord_less_eq_num M) N)))) (= (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))) (= (tptp.aa_real_real tptp.real_V1803761363581548252l_real tptp.one_one_real) tptp.one_one_real) (= (tptp.real_V4546457046886955230omplex tptp.one_one_real) tptp.one_one_complex) (forall ((X tptp.real)) (= (= (tptp.aa_real_real tptp.real_V1803761363581548252l_real X) tptp.one_one_real) (= X tptp.one_one_real))) (forall ((X tptp.real)) (= (= (tptp.real_V4546457046886955230omplex X) tptp.one_one_complex) (= X tptp.one_one_real))) (forall ((X tptp.real) (Y tptp.real)) (= (tptp.aa_real_real tptp.real_V1803761363581548252l_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real X) Y)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real tptp.real_V1803761363581548252l_real X)) (tptp.aa_real_real tptp.real_V1803761363581548252l_real Y)))) (forall ((X tptp.real) (Y tptp.real)) (= (tptp.real_V4546457046886955230omplex (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real X) Y)) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.real_V4546457046886955230omplex X)) (tptp.real_V4546457046886955230omplex Y)))) (forall ((W tptp.num)) (let ((_let_1 (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.numeral_numeral_real W)) (tptp.numera6690914467698888265omplex W))) (forall ((Z tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int tptp.abs_abs_int Z)) tptp.one_one_int)) (= Z tptp.zero_zero_int))) (forall ((X tptp.real) (Y tptp.real)) (= (tptp.aa_real_real tptp.real_V1803761363581548252l_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real X) Y)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real tptp.real_V1803761363581548252l_real X)) (tptp.aa_real_real tptp.real_V1803761363581548252l_real Y)))) (forall ((X tptp.real) (Y tptp.real)) (= (tptp.real_V4546457046886955230omplex (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real X) Y)) (tptp.divide1717551699836669952omplex (tptp.real_V4546457046886955230omplex X) (tptp.real_V4546457046886955230omplex Y)))) (forall ((X tptp.real) (Y tptp.real)) (= (tptp.aa_real_real tptp.real_V1803761363581548252l_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) Y)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real tptp.real_V1803761363581548252l_real X)) (tptp.aa_real_real tptp.real_V1803761363581548252l_real Y)))) (forall ((X tptp.real) (Y tptp.real)) (= (tptp.real_V4546457046886955230omplex (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) Y)) (tptp.plus_plus_complex (tptp.real_V4546457046886955230omplex X) (tptp.real_V4546457046886955230omplex Y)))) (forall ((X tptp.real) (N tptp.nat)) (= (tptp.aa_real_real tptp.real_V1803761363581548252l_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_V1803761363581548252l_real X)) N))) (forall ((X tptp.real) (N tptp.nat)) (= (tptp.real_V4546457046886955230omplex (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) N)) (tptp.aa_nat_complex (tptp.power_power_complex (tptp.real_V4546457046886955230omplex X)) N))) (forall ((X tptp.real) (Y tptp.real)) (= (tptp.aa_real_real tptp.real_V1803761363581548252l_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real X) Y)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real tptp.real_V1803761363581548252l_real X)) (tptp.aa_real_real tptp.real_V1803761363581548252l_real Y)))) (forall ((X tptp.real) (Y tptp.real)) (= (tptp.real_V4546457046886955230omplex (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real X) Y)) (tptp.minus_minus_complex (tptp.real_V4546457046886955230omplex X) (tptp.real_V4546457046886955230omplex Y)))) (forall ((M tptp.num) (N tptp.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.plus_plus_num M N)))) (forall ((M tptp.num) (N tptp.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.plus_plus_num M N)))) (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 ((M tptp.num) (N tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit1 M))) (= (tptp.times_times_num _let_1 (tptp.aa_num_num tptp.bit0 N)) (tptp.aa_num_num tptp.bit0 (tptp.times_times_num _let_1 N))))) (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit1 N))) (= (tptp.times_times_num (tptp.aa_num_num tptp.bit0 M) _let_1) (tptp.aa_num_num tptp.bit0 (tptp.times_times_num M _let_1))))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.pp (tptp.aa_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.ord_less_num M) N)))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.pp (tptp.aa_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.ord_less_eq_num M) N)))) (forall ((N tptp.num)) (tptp.pp (tptp.aa_num_bool (tptp.ord_less_num tptp.one) (tptp.aa_num_num tptp.bit1 N)))) (forall ((M tptp.num)) (not (tptp.pp (tptp.aa_num_bool (tptp.ord_less_eq_num (tptp.aa_num_num tptp.bit1 M)) tptp.one)))) (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 ((N tptp.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.plus_plus_num tptp.one (tptp.aa_num_num tptp.bit1 N)) (tptp.aa_num_num tptp.bit0 (tptp.plus_plus_num N tptp.one)))) (forall ((M tptp.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.plus_plus_num (tptp.aa_num_num tptp.bit1 M) tptp.one) (tptp.aa_num_num tptp.bit0 (tptp.plus_plus_num M tptp.one)))) (forall ((M tptp.num) (N tptp.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.plus_plus_num (tptp.plus_plus_num M N) tptp.one)))) (forall ((M tptp.num) (N tptp.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.plus_plus_num (tptp.plus_plus_num M N) (tptp.aa_num_num tptp.bit0 (tptp.times_times_num M N)))))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.pp (tptp.aa_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.ord_less_num M) N)))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.pp (tptp.aa_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.ord_less_eq_num M) N)))) (forall ((W tptp.num)) (let ((_let_1 (tptp.aa_real_real tptp.uminus_uminus_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.numeral_numeral_real W))) (tptp.uminus1482373934393186551omplex (tptp.numera6690914467698888265omplex W)))) (forall ((M tptp.nat) (V tptp.num)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat V))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat tptp.suc M)))) _let_1) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 tptp.one))) M)) _let_1)))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat M))) (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat tptp.suc N)))) (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 tptp.one))) N))))) (forall ((M tptp.nat) (V tptp.num)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat V))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat tptp.suc M)))) _let_1) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 tptp.one))) M)) _let_1)))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat M))) (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat tptp.suc N)))) (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 tptp.one))) N))))) (forall ((X tptp.real)) (= (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)) tptp.one_one_real)) (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) tptp.one_one_real)))) (forall ((X tptp.real)) (= (tptp.real_V1022390504157884413omplex (tptp.plus_plus_complex (tptp.real_V4546457046886955230omplex X) tptp.one_one_complex)) (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) tptp.one_one_real)))) (forall ((X tptp.real) (B tptp.num)) (let ((_let_1 (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.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.numeral_numeral_real B))))) (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 ((X2 tptp.num) (X32 tptp.num)) (not (= (tptp.aa_num_num tptp.bit0 X2) (tptp.aa_num_num tptp.bit1 X32)))) (forall ((X32 tptp.num)) (not (= tptp.one (tptp.aa_num_num tptp.bit1 X32)))) (forall ((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 ((Y tptp.num)) (=> (not (= Y tptp.one)) (=> (forall ((X22 tptp.num)) (not (= Y (tptp.aa_num_num tptp.bit0 X22)))) (not (forall ((X33 tptp.num)) (not (= Y (tptp.aa_num_num tptp.bit1 X33)))))))) (forall ((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 ((Y tptp.int) (X tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int Y) X)) (= (tptp.aa_int_int tptp.abs_abs_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int X) Y)) (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 Y))))) (forall ((K tptp.int) (L tptp.int)) (=> (= (tptp.aa_int_int tptp.sgn_sgn_int K) (tptp.aa_int_int 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 ((Y tptp.real) (X tptp.real)) (=> (not (= Y 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) Y)) (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 Y))))) (forall ((Y tptp.real) (X tptp.real)) (=> (not (= Y tptp.zero_zero_real)) (= (tptp.real_V4546457046886955230omplex (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real X) Y)) (tptp.divide1717551699836669952omplex (tptp.real_V4546457046886955230omplex X) (tptp.real_V4546457046886955230omplex Y))))) (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.numeral_numeral_real N))) (= (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.numeral_numeral_rat N))) (= (tptp.numeral_numeral_rat (tptp.aa_num_num tptp.bit1 N)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat _let_1) _let_1)) tptp.one_one_rat)))) (forall ((N tptp.num)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat N))) (= (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 N)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat _let_1) _let_1)) tptp.one_one_nat)))) (forall ((N tptp.num)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int N))) (= (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit1 N)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int _let_1) _let_1)) tptp.one_one_int)))) (forall ((N tptp.num)) (= (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 N)) (tptp.aa_nat_nat tptp.suc (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 N))))) (forall ((M tptp.num) (Q2 tptp.num) (N tptp.num)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 Q2)))) (not (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 M))) _let_1) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 N))) _let_1))))) (forall ((M tptp.num) (Q2 tptp.num) (N tptp.num)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 Q2)))) (not (= (tptp.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.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 M))) _let_1) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 N))) _let_1))))) (forall ((M tptp.num) (Q2 tptp.num) (N tptp.num)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 Q2)))) (not (= (tptp.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.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 M))) _let_2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 N))) _let_2)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_num_nat tptp.numeral_numeral_nat M)) _let_1) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_num_nat tptp.numeral_numeral_nat N)) _let_1)))))) (forall ((M tptp.num) (Q2 tptp.num) (N tptp.num)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int Q2))) (let ((_let_2 (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 Q2)))) (= (= (tptp.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 ((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.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.uminus_uminus_rat X)) _let_1) (tptp.uminus_uminus_rat (tptp.aa_nat_rat (tptp.power_power_rat 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 ((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 ((X tptp.real)) (let ((_let_1 (tptp.aa_real_real tptp.real_V7735802525324610683m_real X))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real _let_1) (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 _let_1)) tptp.one_one_real)))))) (forall ((X tptp.complex)) (let ((_let_1 (tptp.real_V1022390504157884413omplex X))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real _let_1) (tptp.real_V1022390504157884413omplex (tptp.plus_plus_complex (tptp.real_V4546457046886955230omplex _let_1) tptp.one_one_complex)))))) (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 ((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 ((N tptp.num) (Q2 tptp.num)) (not (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 N))) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 Q2))) tptp.zero_zero_nat))) (forall ((N tptp.num) (Q2 tptp.num)) (not (= (tptp.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.complex)) (= (tptp.aa_nat_complex (tptp.power_power_complex A) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 tptp.one))) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_complex_complex (tptp.times_times_complex A) A)) A))) (forall ((A tptp.real)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real A) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 tptp.one))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) A)) A))) (forall ((A tptp.rat)) (= (tptp.aa_nat_rat (tptp.power_power_rat A) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 tptp.one))) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) A)) A))) (forall ((A tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 tptp.one))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) A)) A))) (forall ((A tptp.int)) (= (tptp.aa_nat_int (tptp.power_power_int A) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 tptp.one))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) A)) A))) (= (tptp.aa_num_nat tptp.numeral_numeral_nat _let_89) (tptp.aa_nat_nat tptp.suc _let_85)) (forall ((N tptp.nat)) (= (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat tptp.suc N))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 tptp.one))) N))) (forall ((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 ((V tptp.int) (K tptp.int) (L tptp.int)) (let ((_let_1 (tptp.aa_int_int tptp.abs_abs_int L))) (let ((_let_2 (tptp.aa_int_int tptp.abs_abs_int K))) (let ((_let_3 (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int tptp.sgn_sgn_int V)))) (=> (not (= V tptp.zero_zero_int)) (= (tptp.aa_int_int (tptp.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.aa_int_int tptp.sgn_sgn_int K)) (tptp.aa_int_int 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 ((X32 tptp.num)) (= (tptp.size_num (tptp.aa_num_num tptp.bit1 X32)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.size_num X32)) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)))) (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.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 ((Q2 tptp.num) (N tptp.num)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 Q2)))) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_num_nat tptp.numeral_numeral_nat tptp.one)) _let_1) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 N))) _let_1)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_num_nat tptp.numeral_numeral_nat N)) (tptp.aa_num_nat tptp.numeral_numeral_nat Q2)) tptp.zero_zero_nat)))) (forall ((Q2 tptp.num) (N tptp.num)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 Q2)))) (= (= (tptp.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.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 M))) _let_1) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_num_nat tptp.numeral_numeral_nat tptp.one)) _let_1)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_num_nat tptp.numeral_numeral_nat M)) (tptp.aa_num_nat tptp.numeral_numeral_nat Q2)) tptp.zero_zero_nat)))) (forall ((M tptp.num) (Q2 tptp.num)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 Q2)))) (= (= (tptp.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 ((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)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat tptp.suc M)))) N) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 tptp.one))) M)) N))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat tptp.suc M)))) N) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 tptp.one))) M)) N))) (forall ((M tptp.nat) (N tptp.nat) (F tptp.fun_nat_int) (K tptp.int)) (=> (forall ((I2 tptp.nat)) (=> (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) I2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I2) 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 I2))) (tptp.aa_nat_int F I2)))) 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 ((I2 tptp.nat)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) I2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I2) N)) (= (tptp.aa_nat_int F I2) K)))))))) (forall ((D tptp.int) (Z tptp.int) (X tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) D)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Z) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int X) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int tptp.abs_abs_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int X) Z))) tptp.one_one_int)) D)))))) (forall ((D tptp.int) (X tptp.int) (Z tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.minus_minus_int X))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) D)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int tptp.abs_abs_int (tptp.aa_int_int _let_1 Z))) tptp.one_one_int)) D))) Z))))) (forall ((M tptp.nat)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (let ((_let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat M) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 _let_1))))) (or (= _let_2 tptp.zero_zero_nat) (= _let_2 tptp.one_one_nat) (= _let_2 (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1)) (= _let_2 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 tptp.one))))))) (forall ((L tptp.int) (K tptp.int)) (=> (not (= L tptp.zero_zero_int)) (=> (not (= (tptp.aa_int_int tptp.sgn_sgn_int K) (tptp.aa_int_int 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) (F tptp.fun_nat_int) (K tptp.int)) (=> (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_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 I2))) (tptp.aa_nat_int F I2)))) 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 ((I2 tptp.nat)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I2) N)) (= (tptp.aa_nat_int F I2) K))))))) (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.real_V1022390504157884413omplex (tptp.plus_plus_complex B A))) (tptp.real_V1022390504157884413omplex B))) (tptp.real_V1022390504157884413omplex A)))) (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.aa_nat_fun_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.aa_nat_fun_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 ((N tptp.nat) (F tptp.fun_nat_int) (K tptp.int)) (=> (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_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 I2) tptp.one_one_nat))) (tptp.aa_nat_int F I2)))) 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 ((I2 tptp.nat)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I2) N)) (= (tptp.aa_nat_int F I2) K))))))) (forall ((X tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real X)) tptp.one_one_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.abs_abs_real Y)) tptp.one_one_real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real tptp.arctan X)) (tptp.aa_real_real tptp.arctan Y)) (tptp.aa_real_real tptp.arctan (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) Y)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real tptp.one_one_real) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real X) Y)))))))) (forall ((N tptp.nat)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (let ((_let_2 (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1))) (=> (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat N) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 _let_1))) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 tptp.one))) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat _let_2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat))) _let_2)))))))) (forall ((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.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_44) (tptp.aa_real_real tptp.uminus_uminus_real _let_90)) (= (tptp.neg_nu3811975205180677377ec_int _let_57) (tptp.aa_int_int tptp.uminus_uminus_int _let_106)) (= (tptp.neg_nu6511756317524482435omplex _let_79) (tptp.uminus1482373934393186551omplex _let_108)) (= (tptp.neg_nu3179335615603231917ec_rat _let_56) (tptp.uminus_uminus_rat _let_107)) (= (tptp.neg_nu7757733837767384882nteger _let_65) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.numera6620942414471956472nteger _let_89))) (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.inc 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_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.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))) (= (tptp.neg_nu8557863876264182079omplex tptp.one_one_complex) _let_108) (= (tptp.aa_real_real tptp.neg_nu8295874005876285629c_real tptp.one_one_real) _let_90) (= (tptp.neg_nu5219082963157363817nc_rat tptp.one_one_rat) _let_107) (= (tptp.neg_nu5851722552734809277nc_int tptp.one_one_int) _let_106) (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.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))) (tptp.aa_real_real tptp.arctan X))))) (= (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.neg_nu3179335615603231917ec_rat tptp.one_one_rat) tptp.one_one_rat) (= (tptp.neg_nu3811975205180677377ec_int tptp.one_one_int) tptp.one_one_int) (= (tptp.pred_numeral tptp.one) tptp.zero_zero_nat) (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.pred_numeral K)))) (forall ((K tptp.num) (N tptp.nat)) (= (= (tptp.aa_num_nat tptp.numeral_numeral_nat K) (tptp.aa_nat_nat tptp.suc N)) (= (tptp.pred_numeral K) N))) (= (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.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.pred_numeral (tptp.inc K)) (tptp.aa_num_nat tptp.numeral_numeral_nat K))) (= (tptp.aa_real_real tptp.neg_nu8295874005876285629c_real _let_44) _let_44) (= (tptp.neg_nu5851722552734809277nc_int _let_57) _let_57) (= (tptp.neg_nu8557863876264182079omplex _let_79) _let_79) (= (tptp.neg_nu5219082963157363817nc_rat _let_56) _let_56) (= (tptp.neg_nu5831290666863070958nteger _let_65) _let_65) (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.numeral_numeral_real K)) (tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit1 K)))) (forall ((K tptp.num)) (= (tptp.neg_nu5219082963157363817nc_rat (tptp.numeral_numeral_rat K)) (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 ((K tptp.num)) (= (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 ((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.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_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.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.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.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.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.pred_numeral K)) N))) (= (tptp.aa_real_real tptp.neg_nu6075765906172075777c_real tptp.zero_zero_real) _let_44) (= (tptp.neg_nu3811975205180677377ec_int tptp.zero_zero_int) _let_57) (= (tptp.neg_nu6511756317524482435omplex tptp.zero_zero_complex) _let_79) (= (tptp.neg_nu3179335615603231917ec_rat tptp.zero_zero_rat) _let_56) (= (tptp.neg_nu7757733837767384882nteger tptp.zero_z3403309356797280102nteger) _let_65) (forall ((K tptp.num)) (let ((_let_1 (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.numeral_numeral_rat K))) (= (tptp.neg_nu3179335615603231917ec_rat (tptp.uminus_uminus_rat _let_1)) (tptp.uminus_uminus_rat (tptp.neg_nu5219082963157363817nc_rat _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.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.numeral_numeral_rat K))) (= (tptp.neg_nu5219082963157363817nc_rat (tptp.uminus_uminus_rat _let_1)) (tptp.uminus_uminus_rat (tptp.neg_nu3179335615603231917ec_rat _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 ((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.numeral_numeral_real N))) (tptp.aa_real_real tptp.uminus_uminus_real (tptp.numeral_numeral_real (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.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.inc N))))) (forall ((N tptp.num)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.uminus_uminus_rat tptp.one_one_rat)) (tptp.uminus_uminus_rat (tptp.numeral_numeral_rat N))) (tptp.uminus_uminus_rat (tptp.numeral_numeral_rat (tptp.inc N))))) (forall ((N tptp.num)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger 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.inc N))))) (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.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.numeral_numeral_real (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.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.inc M))))) (forall ((M tptp.num)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.uminus_uminus_rat (tptp.numeral_numeral_rat M))) (tptp.uminus_uminus_rat tptp.one_one_rat)) (tptp.uminus_uminus_rat (tptp.numeral_numeral_rat (tptp.inc M))))) (forall ((M tptp.num)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger 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.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.numeral_numeral_real N)) (tptp.aa_real_real tptp.uminus_uminus_real (tptp.numeral_numeral_real (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.inc N))))) (forall ((N tptp.num)) (= (tptp.minus_minus_complex (tptp.uminus1482373934393186551omplex tptp.one_one_complex) (tptp.numera6690914467698888265omplex N)) (tptp.uminus1482373934393186551omplex (tptp.numera6690914467698888265omplex (tptp.inc N))))) (forall ((N tptp.num)) (= (tptp.minus_minus_rat (tptp.uminus_uminus_rat tptp.one_one_rat) (tptp.numeral_numeral_rat N)) (tptp.uminus_uminus_rat (tptp.numeral_numeral_rat (tptp.inc N))))) (forall ((N tptp.num)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.minus_8373710615458151222nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (tptp.numera6620942414471956472nteger N)) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.numera6620942414471956472nteger (tptp.inc N))))) (forall ((M tptp.num)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.numeral_numeral_real M)) (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)) (tptp.numeral_numeral_real (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.inc M)))) (forall ((M tptp.num)) (= (tptp.minus_minus_complex (tptp.numera6690914467698888265omplex M) (tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (tptp.numera6690914467698888265omplex (tptp.inc M)))) (forall ((M tptp.num)) (= (tptp.minus_minus_rat (tptp.numeral_numeral_rat M) (tptp.uminus_uminus_rat tptp.one_one_rat)) (tptp.numeral_numeral_rat (tptp.inc M)))) (forall ((M tptp.num)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.minus_8373710615458151222nteger (tptp.numera6620942414471956472nteger M)) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (tptp.numera6620942414471956472nteger (tptp.inc M)))) (forall ((L tptp.num) (K tptp.num)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_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.aa_nat_fun_nat_nat tptp.bit_se547839408752420682it_nat (tptp.pred_numeral L)) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 K))))) (forall ((L tptp.num) (K tptp.num)) (= (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_se545348938243370406it_int (tptp.aa_num_nat tptp.numeral_numeral_nat L)) (tptp.aa_num_int tptp.numeral_numeral_int K)) (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_se545348938243370406it_int (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_Cod1783974652533396728nteger (tptp.aa_nat6383147911832638789nteger tptp.bit_se7788150548672797655nteger (tptp.aa_num_nat tptp.numeral_numeral_nat L)) (tptp.numera6620942414471956472nteger K)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_nat6383147911832638789nteger tptp.bit_se7788150548672797655nteger (tptp.pred_numeral L)) (tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 K))))) (forall ((L tptp.num) (K tptp.num)) (= (tptp.aa_Cod4272041906116450446atural (tptp.aa_nat5282697797315388251atural tptp.bit_se6611745700429515170atural (tptp.aa_num_nat tptp.numeral_numeral_nat L)) (tptp.numera5444537566228673987atural K)) (tptp.aa_Cod4272041906116450446atural (tptp.aa_nat5282697797315388251atural tptp.bit_se6611745700429515170atural (tptp.pred_numeral L)) (tptp.numera5444537566228673987atural (tptp.aa_num_num tptp.bit0 K))))) (forall ((L tptp.num) (K tptp.num)) (= (tptp.aa_int_int (tptp.aa_nat_fun_int_int 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.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_se545348938243370406it_int (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 ((L tptp.num) (K tptp.num)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_nat6383147911832638789nteger tptp.bit_se7788150548672797655nteger (tptp.aa_num_nat tptp.numeral_numeral_nat L)) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.numera6620942414471956472nteger K))) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_nat6383147911832638789nteger tptp.bit_se7788150548672797655nteger (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.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.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.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 ((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.inc X3))))) (tptp.pp (tptp.aa_num_bool P X))))) (forall ((X tptp.num) (Y tptp.num)) (= (tptp.plus_plus_num X (tptp.inc Y)) (tptp.inc (tptp.plus_plus_num X Y)))) (forall ((K tptp.num)) (= (tptp.aa_num_nat tptp.numeral_numeral_nat K) (tptp.aa_nat_nat tptp.suc (tptp.pred_numeral K)))) (= (tptp.inc tptp.one) _let_1) (forall ((X tptp.num)) (= (tptp.inc (tptp.aa_num_num tptp.bit1 X)) (tptp.aa_num_num tptp.bit0 (tptp.inc X)))) (forall ((X tptp.num)) (= (tptp.inc (tptp.aa_num_num tptp.bit0 X)) (tptp.aa_num_num tptp.bit1 X))) (forall ((X tptp.num)) (= (tptp.plus_plus_num X tptp.one) (tptp.inc X))) (forall ((X tptp.num) (Y tptp.num)) (= (tptp.times_times_num X (tptp.inc Y)) (tptp.plus_plus_num (tptp.times_times_num X Y) X))) (forall ((K tptp.num)) (= (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 ((X tptp.num)) (= (tptp.numera6690914467698888265omplex (tptp.inc X)) (tptp.plus_plus_complex (tptp.numera6690914467698888265omplex X) tptp.one_one_complex))) (forall ((X tptp.num)) (= (tptp.numeral_numeral_real (tptp.inc X)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.numeral_numeral_real X)) tptp.one_one_real))) (forall ((X tptp.num)) (= (tptp.numeral_numeral_rat (tptp.inc X)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.numeral_numeral_rat X)) tptp.one_one_rat))) (forall ((X tptp.num)) (= (tptp.aa_num_nat tptp.numeral_numeral_nat (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.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 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.pi) _let_63)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real _let_46) tptp.pi)) (not (= _let_48 _let_46)) (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.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 ((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.pred_numeral K))))) (forall ((K tptp.num)) (= (tptp.aa_nat_rat tptp.semiri773545260158071498ct_rat (tptp.aa_num_nat tptp.numeral_numeral_nat K)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.numeral_numeral_rat K)) (tptp.aa_nat_rat tptp.semiri773545260158071498ct_rat (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.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.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.numeral_numeral_real K)) (tptp.aa_nat_real tptp.semiri2265585572941072030t_real (tptp.pred_numeral K))))) (not (= _let_48 tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real _let_48) _let_46)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real _let_48) _let_46)) (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.pred_numeral L)) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.inc K))))) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one)))) tptp.one_one_int))) (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.neg_nu3179335615603231917ec_rat X) (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))) (tptp.pp (tptp.aa_real_bool _let_105 _let_48)) (tptp.pp (tptp.aa_real_bool _let_104 _let_48)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.uminus_uminus_real _let_84)) tptp.pi)) (forall ((Y tptp.real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.arctan Y)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) (tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))))) (= (tptp.aa_real_real tptp.arctan tptp.one_one_real) _let_64) (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.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.aa_nat_fun_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.aa_nat_fun_nat_nat tptp.bit_se2925701944663578781it_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.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real _let_52) tptp.zero_zero_real)) (forall ((Y tptp.real)) (let ((_let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) (tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_2 (tptp.aa_real_real tptp.arctan Y))) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.uminus_uminus_real _let_1)) _let_2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real _let_2) _let_1)))))) (forall ((Y tptp.real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) (tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))))) (tptp.aa_real_real tptp.arctan Y)))) (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.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))))) (= (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_103) (tptp.aa_real_real tptp.arctan (tptp.aa_real_real _let_87 (tptp.numeral_numeral_real _let_102))))) (tptp.aa_real_real _let_62 (tptp.aa_real_real tptp.arctan (tptp.aa_real_real _let_97 (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_41))))))))) _let_64) (= _let_64 (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_63) (tptp.aa_real_real tptp.arctan (tptp.aa_real_real _let_87 _let_103)))) (tptp.aa_real_real tptp.arctan (tptp.aa_real_real _let_87 (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_102)))))))))) (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.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.aa_nat_fun_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.aa_nat_fun_nat_nat tptp.bit_se2925701944663578781it_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 ((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.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 ((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.numeral_numeral_real _let_1))) tptp.zero_zero_real))) (forall ((X tptp.real)) (= (= (tptp.aa_real_real tptp.cos_real X) tptp.zero_zero_real) (or (exists ((N5 tptp.nat)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (and (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1)) N5))) (= X (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N5)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) (tptp.numeral_numeral_real _let_1))))))) (exists ((N5 tptp.nat)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (and (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1)) N5))) (= X (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N5)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) (tptp.numeral_numeral_real _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.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.pi)) (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.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.numeral_numeral_real _let_1)))))))))) (forall ((X tptp.real)) (= (= (tptp.aa_real_real tptp.sin_real X) tptp.zero_zero_real) (or (exists ((N5 tptp.nat)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1)) N5)) (= X (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N5)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) (tptp.numeral_numeral_real _let_1))))))) (exists ((N5 tptp.nat)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1)) N5)) (= X (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N5)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) (tptp.numeral_numeral_real _let_1))))))))))) (= (tptp.aa_real_real tptp.sin_real tptp.zero_zero_real) tptp.zero_zero_real) (= (tptp.aa_real_real tptp.cot_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) (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))) (= (tptp.aa_real_real tptp.sin_real _let_100) tptp.zero_zero_real) (= (tptp.sin_complex _let_80) tptp.zero_zero_complex) (= (tptp.aa_real_real tptp.cos_real tptp.pi) _let_44) (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.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.plus_plus_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.plus_plus_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.aa_real_real tptp.sin_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real tptp.pi) X)) (tptp.aa_real_real tptp.uminus_uminus_real (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.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)))) (= (tptp.aa_real_real tptp.cos_real _let_100) _let_44) (= (tptp.cos_complex _let_80) _let_79) (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 ((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_real_real tptp.cos_real _let_48) tptp.zero_zero_real) (= (tptp.aa_real_real tptp.sin_real _let_84) tptp.zero_zero_real) (= (tptp.aa_real_real tptp.sin_real _let_48) tptp.one_one_real) (= (tptp.aa_real_real tptp.cos_real _let_84) 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.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.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.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))) tptp.pi)) X)) (tptp.aa_real_real tptp.cos_real X))) (forall ((N tptp.nat)) (= (tptp.aa_real_real tptp.cos_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real tptp.pi) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)) N))) (forall ((N tptp.nat)) (= (tptp.aa_real_real tptp.cos_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N)) tptp.pi)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)) N))) (forall ((X tptp.real)) (= (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.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))) tptp.pi))) (tptp.aa_real_real tptp.cot_real X))) (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 ((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))) (= (tptp.aa_real_real tptp.cos_real _let_101) tptp.zero_zero_real) (= (tptp.cos_complex _let_99) tptp.zero_zero_complex) (= (tptp.aa_real_real tptp.sin_real _let_101) tptp.one_one_real) (= (tptp.sin_complex _let_99) 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.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.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.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))) tptp.pi)) X)) (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_real_real tptp.sin_real X)))) (= (tptp.aa_real_real tptp.cos_real _let_98) tptp.zero_zero_real) (= (tptp.aa_real_real tptp.sin_real _let_98) _let_44) (forall ((X tptp.real) (Y tptp.real)) (= (tptp.aa_real_real tptp.sin_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) Y)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real tptp.sin_real X)) (tptp.aa_real_real tptp.cos_real Y))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real tptp.cos_real X)) (tptp.aa_real_real tptp.sin_real Y))))) (forall ((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 ((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 ((X tptp.real) (Y tptp.real)) (exists ((R2 tptp.real) (A3 tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.times_times_real R2))) (and (= X (tptp.aa_real_real _let_1 (tptp.aa_real_real tptp.cos_real A3))) (= Y (tptp.aa_real_real _let_1 (tptp.aa_real_real tptp.sin_real A3))))))) (forall ((X tptp.real) (Y tptp.real)) (= (tptp.aa_real_real tptp.sin_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real X) Y)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real tptp.sin_real X)) (tptp.aa_real_real tptp.cos_real Y))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real tptp.cos_real X)) (tptp.aa_real_real tptp.sin_real Y))))) (forall ((X tptp.real) (Y tptp.real)) (= (tptp.aa_real_real tptp.cos_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) Y)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real tptp.cos_real X)) (tptp.aa_real_real tptp.cos_real Y))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real tptp.sin_real X)) (tptp.aa_real_real tptp.sin_real Y))))) (forall ((X tptp.real) (Y tptp.real)) (= (tptp.aa_real_real tptp.cos_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real X) Y)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real tptp.cos_real X)) (tptp.aa_real_real tptp.cos_real Y))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real tptp.sin_real X)) (tptp.aa_real_real tptp.sin_real Y))))) (forall ((X tptp.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.real_V1022390504157884413omplex (tptp.cos_complex X)) tptp.one_one_real))) (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.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)) (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) (Y tptp.real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real tptp.sin_real X)) (tptp.aa_real_real tptp.sin_real Y))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real tptp.cos_real X)) (tptp.aa_real_real tptp.cos_real Y))))) tptp.one_one_real))) (forall ((X tptp.complex)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.aa_nat_complex (tptp.power_power_complex (tptp.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.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.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 ((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.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.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.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.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.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.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.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 ((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.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.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 ((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.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 ((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.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))))))) (not (= _let_96 tptp.zero_zero_real)) (forall ((Y tptp.real) (X tptp.real)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) Y)) (=> (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) _let_1)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Y) _let_1)) tptp.one_one_real) (exists ((T2 tptp.real)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) T2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real T2) tptp.pi)) (= X (tptp.aa_real_real tptp.cos_real T2)) (= Y (tptp.aa_real_real tptp.sin_real T2)))))))) (forall ((X tptp.real) (M tptp.nat)) (let ((_let_1 (tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X))) (= (tptp.aa_real_real tptp.sin_real (tptp.aa_real_real _let_2 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real (tptp.aa_nat_nat tptp.suc M))) tptp.pi)) _let_1))) (tptp.aa_real_real tptp.cos_real (tptp.aa_real_real _let_2 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real M)) tptp.pi)) _let_1))))))) (forall ((X tptp.real) (M tptp.nat)) (let ((_let_1 (tptp.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.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))) (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real tptp.sin_real X))))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real _let_96) 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.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.aa_real_real tptp.cos_real X3) tptp.zero_zero_real) (forall ((Y4 tptp.real)) (=> (and (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.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.aa_real_real tptp.cos_real Y4) tptp.zero_zero_real)) (= Y4 X3))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real _let_96) tptp.zero_zero_real)) (forall ((Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)) Y)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y) tptp.one_one_real)) (exists ((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) Y) (forall ((Y4 tptp.real)) (=> (and (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.pi)) (= (tptp.aa_real_real tptp.cos_real Y4) Y)) (= Y4 X3)))))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool _let_2 X)) (=> (tptp.pp (tptp.aa_real_bool _let_2 Y)) (=> (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) _let_1)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Y) _let_1)) tptp.one_one_real) (exists ((T2 tptp.real)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) T2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real T2) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) (tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))))) (= X (tptp.aa_real_real tptp.cos_real T2)) (= Y (tptp.aa_real_real tptp.sin_real T2)))))))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) _let_1)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Y) _let_1)) tptp.one_one_real) (exists ((T2 tptp.real)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) T2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real T2) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))) tptp.pi))) (= X (tptp.aa_real_real tptp.cos_real T2)) (= Y (tptp.aa_real_real tptp.sin_real T2))))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) _let_1)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Y) _let_1)) tptp.one_one_real) (not (forall ((T2 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) T2)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real T2) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))) tptp.pi))) (=> (= X (tptp.aa_real_real tptp.cos_real T2)) (not (= Y (tptp.aa_real_real tptp.sin_real T2))))))))))) (forall ((N tptp.nat)) (=> (not (= N tptp.zero_zero_nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_real_real tptp.sin_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N))))))) (forall ((W tptp.complex) (Z tptp.complex)) (= (tptp.aa_complex_complex (tptp.times_times_complex (tptp.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.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.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.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.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.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_94) _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.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 ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) (tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_2 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real _let_1)))) (=> (tptp.pp (tptp.aa_real_bool _let_2 X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) _let_1)) (=> (tptp.pp (tptp.aa_real_bool _let_2 Y)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y) _let_1)) (=> (= (tptp.aa_real_real tptp.sin_real X) (tptp.aa_real_real tptp.sin_real Y)) (= X Y))))))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X))) (let ((_let_2 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) (tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_3 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real _let_2)))) (=> (tptp.pp (tptp.aa_real_bool _let_3 X)) (=> (tptp.pp (tptp.aa_real_bool _let_1 _let_2)) (=> (tptp.pp (tptp.aa_real_bool _let_3 Y)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y) _let_2)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.sin_real X)) (tptp.aa_real_real tptp.sin_real Y))) (tptp.pp (tptp.aa_real_bool _let_1 Y))))))))))) (forall ((Y tptp.real) (X tptp.real)) (let ((_let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) (tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real _let_1)) Y)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) _let_1)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.sin_real Y)) (tptp.aa_real_real tptp.sin_real X)))))))) (= (tptp.aa_real_real tptp.cos_real _let_93) _let_88) (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.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.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.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.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.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.sin_real X)) tptp.zero_zero_real))))) (forall ((Y tptp.real) (X tptp.real)) (let ((_let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) (tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real _let_1)) Y)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) _let_1)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.sin_real Y)) (tptp.aa_real_real tptp.sin_real X)))))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) (tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_2 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real _let_1)))) (=> (tptp.pp (tptp.aa_real_bool _let_2 X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) _let_1)) (=> (tptp.pp (tptp.aa_real_bool _let_2 Y)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y) _let_1)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.sin_real X)) (tptp.aa_real_real tptp.sin_real Y))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Y)))))))))) (forall ((Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)) Y)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y) tptp.one_one_real)) (exists ((X3 tptp.real)) (let ((_let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) (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) Y) (forall ((Y4 tptp.real)) (let ((_let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) (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)) 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 Y4) Y)) (= Y4 X3)))))))))) (forall ((X tptp.real)) (let ((_let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) (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.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.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.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)) (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.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.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.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.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 ((Z tptp.complex)) (=> (= (tptp.real_V1022390504157884413omplex Z) tptp.one_one_real) (not (forall ((T2 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) T2)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real T2) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_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 T2) (tptp.aa_real_real tptp.sin_real T2)))))))))) (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.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 ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y))) (let ((_let_2 (tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) tptp.one_one_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.pi)) _let_2)) Y)) (=> (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) _let_2))) (= (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real tptp.arcsin X))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.sin_real Y)) X)))))))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X))) (let ((_let_2 (tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)) X)) (=> (tptp.pp (tptp.aa_real_bool _let_1 tptp.one_one_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.pi)) _let_2)) Y)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) _let_2))) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.arcsin X)) Y)) (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real tptp.sin_real Y))))))))))) (forall ((Y tptp.real)) (let ((_let_1 (tptp.aa_real_real tptp.arcsin Y))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)) Y)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y) tptp.one_one_real)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) (tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))))) _let_1)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real _let_1) tptp.pi)) (= (tptp.aa_real_real tptp.sin_real _let_1) Y)))))) (forall ((W tptp.int) (Z tptp.int)) (= (= (tptp.ring_1_of_int_real W) (tptp.ring_1_of_int_real Z)) (= W Z))) (forall ((W tptp.int) (Z tptp.int)) (= (= (tptp.ring_1_of_int_rat W) (tptp.ring_1_of_int_rat Z)) (= W Z))) (= (tptp.aa_real_real tptp.tan_real tptp.zero_zero_real) tptp.zero_zero_real) (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.pi)) (tptp.aa_real_real tptp.tan_real X))) (forall ((X tptp.real)) (= (= (tptp.ring_1_of_int_real (tptp.archim6058952711729229775r_real X)) X) (exists ((N5 tptp.int)) (= X (tptp.ring_1_of_int_real N5))))) (forall ((X tptp.rat)) (= (= (tptp.ring_1_of_int_rat (tptp.archim3151403230148437115or_rat X)) X) (exists ((N5 tptp.int)) (= X (tptp.ring_1_of_int_rat N5))))) (forall ((Z tptp.int)) (= (tptp.archim6058952711729229775r_real (tptp.ring_1_of_int_real Z)) Z)) (forall ((Z tptp.int)) (= (tptp.archim3151403230148437115or_rat (tptp.ring_1_of_int_rat Z)) Z)) (forall ((X tptp.rat)) (= (= (tptp.ring_1_of_int_rat (tptp.archim2889992004027027881ng_rat X)) X) (exists ((N5 tptp.int)) (= X (tptp.ring_1_of_int_rat N5))))) (forall ((X tptp.real)) (= (= (tptp.ring_1_of_int_real (tptp.archim7802044766580827645g_real X)) X) (exists ((N5 tptp.int)) (= X (tptp.ring_1_of_int_real N5))))) (forall ((Z tptp.int)) (= (tptp.archim2889992004027027881ng_rat (tptp.ring_1_of_int_rat Z)) Z)) (forall ((Z tptp.int)) (= (tptp.archim7802044766580827645g_real (tptp.ring_1_of_int_real Z)) Z)) (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.ring_1_of_int_real Z) tptp.zero_zero_real) (= Z tptp.zero_zero_int))) (forall ((Z tptp.int)) (= (= (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.ring_1_of_int_real Z)) (= Z tptp.zero_zero_int))) (forall ((Z tptp.int)) (= (= tptp.zero_zero_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.ring_1_of_int_real tptp.zero_zero_int) tptp.zero_zero_real) (= (tptp.ring_1_of_int_rat tptp.zero_zero_int) tptp.zero_zero_rat) (forall ((W tptp.int) (Z tptp.int)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.ring_1_of_int_real W)) (tptp.ring_1_of_int_real Z))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int W) Z)))) (forall ((W tptp.int) (Z tptp.int)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.ring_1_of_int_rat W)) (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 ((K tptp.num)) (= (tptp.ring_17405671764205052669omplex (tptp.aa_num_int tptp.numeral_numeral_int K)) (tptp.numera6690914467698888265omplex K))) (forall ((K tptp.num)) (= (tptp.ring_1_of_int_real (tptp.aa_num_int tptp.numeral_numeral_int K)) (tptp.numeral_numeral_real K))) (forall ((K tptp.num)) (= (tptp.ring_1_of_int_rat (tptp.aa_num_int tptp.numeral_numeral_int K)) (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 ((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.ring_1_of_int_real Z) (tptp.numeral_numeral_real N)) (= Z (tptp.aa_num_int tptp.numeral_numeral_int N)))) (forall ((Z tptp.int) (N tptp.num)) (= (= (tptp.ring_1_of_int_rat Z) (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 ((W tptp.int) (Z tptp.int)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.ring_1_of_int_real W)) (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.ring_1_of_int_rat W)) (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)))) (= (tptp.ring_17405671764205052669omplex tptp.one_one_int) tptp.one_one_complex) (= (tptp.ring_1_of_int_int tptp.one_one_int) tptp.one_one_int) (= (tptp.ring_1_of_int_real tptp.one_one_int) tptp.one_one_real) (= (tptp.ring_1_of_int_rat tptp.one_one_int) tptp.one_one_rat) (forall ((Z tptp.int)) (= (= (tptp.ring_17405671764205052669omplex Z) tptp.one_one_complex) (= Z tptp.one_one_int))) (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.ring_1_of_int_real Z) tptp.one_one_real) (= Z tptp.one_one_int))) (forall ((Z tptp.int)) (= (= (tptp.ring_1_of_int_rat Z) tptp.one_one_rat) (= Z tptp.one_one_int))) (forall ((W tptp.int) (Z tptp.int)) (= (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.ring_1_of_int_real W)) (tptp.ring_1_of_int_real Z)))) (forall ((W tptp.int) (Z tptp.int)) (= (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.ring_1_of_int_rat W)) (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.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.ring_1_of_int_real W)) (tptp.ring_1_of_int_real Z)))) (forall ((W tptp.int) (Z tptp.int)) (= (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.ring_1_of_int_rat W)) (tptp.ring_1_of_int_rat Z)))) (forall ((Z tptp.int)) (= (tptp.ring_1_of_int_real (tptp.aa_int_int tptp.uminus_uminus_int Z)) (tptp.aa_real_real tptp.uminus_uminus_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_1_of_int_rat (tptp.aa_int_int tptp.uminus_uminus_int Z)) (tptp.uminus_uminus_rat (tptp.ring_1_of_int_rat 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 ((W tptp.int) (Z tptp.int)) (= (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.ring_1_of_int_real W)) (tptp.ring_1_of_int_real Z)))) (forall ((W tptp.int) (Z tptp.int)) (= (tptp.ring_1_of_int_rat (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int W) Z)) (tptp.minus_minus_rat (tptp.ring_1_of_int_rat W) (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.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.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.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.ring_1_of_int_real (tptp.aa_int_int tptp.abs_abs_int X)) (tptp.aa_real_real tptp.abs_abs_real (tptp.ring_1_of_int_real X)))) (forall ((X tptp.int)) (= (tptp.ring_1_of_int_rat (tptp.aa_int_int tptp.abs_abs_int X)) (tptp.abs_abs_rat (tptp.ring_1_of_int_rat X)))) (forall ((Z tptp.int) (N tptp.nat)) (= (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.ring_1_of_int_rat Z)) N))) (forall ((Z tptp.int) (N tptp.nat)) (= (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.ring_1_of_int_real 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.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))) (forall ((B tptp.int) (W tptp.nat) (X tptp.int)) (= (= (tptp.aa_nat_rat (tptp.power_power_rat (tptp.ring_1_of_int_rat B)) W) (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_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.ring_1_of_int_real B)) W) (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_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_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 ((X tptp.int) (B tptp.int) (W tptp.nat)) (= (= (tptp.ring_1_of_int_rat X) (tptp.aa_nat_rat (tptp.power_power_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_real X) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_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_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.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 ((P tptp.bool)) (= (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_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))) (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 ((Z tptp.int)) (= (tptp.archim6058952711729229775r_real (tptp.aa_real_real tptp.uminus_uminus_real (tptp.ring_1_of_int_real Z))) (tptp.aa_int_int tptp.uminus_uminus_int Z))) (forall ((Z tptp.int)) (= (tptp.archim3151403230148437115or_rat (tptp.uminus_uminus_rat (tptp.ring_1_of_int_rat Z))) (tptp.aa_int_int tptp.uminus_uminus_int Z))) (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.numeral_numeral_real N)) tptp.pi))) (tptp.aa_real_real tptp.tan_real X))) (forall ((X tptp.rat) (Z tptp.int)) (= (tptp.archim2889992004027027881ng_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat X) (tptp.ring_1_of_int_rat Z))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.archim2889992004027027881ng_rat X)) Z))) (forall ((X tptp.real) (Z tptp.int)) (= (tptp.archim7802044766580827645g_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) (tptp.ring_1_of_int_real Z))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.archim7802044766580827645g_real X)) Z))) (forall ((X tptp.real) (Z tptp.int)) (= (tptp.archim6058952711729229775r_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real X) (tptp.ring_1_of_int_real Z))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.archim6058952711729229775r_real X)) Z))) (forall ((X tptp.rat) (Z tptp.int)) (= (tptp.archim3151403230148437115or_rat (tptp.minus_minus_rat X (tptp.ring_1_of_int_rat Z))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.archim3151403230148437115or_rat X)) Z))) (forall ((X tptp.rat) (Z tptp.int)) (= (tptp.archim2889992004027027881ng_rat (tptp.minus_minus_rat X (tptp.ring_1_of_int_rat Z))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.archim2889992004027027881ng_rat X)) Z))) (forall ((X tptp.real) (Z tptp.int)) (= (tptp.archim7802044766580827645g_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real X) (tptp.ring_1_of_int_real Z))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.archim7802044766580827645g_real X)) Z))) (forall ((X tptp.real) (N tptp.nat)) (= (tptp.aa_real_real tptp.tan_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N)) tptp.pi))) (tptp.aa_real_real tptp.tan_real X))) (forall ((X tptp.real) (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.ring_1_of_int_real I)) tptp.pi))) (tptp.aa_real_real tptp.tan_real X))) (forall ((Z tptp.int)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_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.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.zero_zero_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_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_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_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.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.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.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 ((Z tptp.int) (N tptp.num)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.ring_1_of_int_real Z)) (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_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.ring_1_of_int_rat Z)) (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 ((N tptp.num) (Z tptp.int)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.numeral_numeral_real N)) (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 ((N tptp.num) (Z tptp.int)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.numeral_numeral_rat N)) (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 ((Z tptp.int) (N tptp.num)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.ring_1_of_int_real Z)) (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.ring_1_of_int_rat Z)) (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.numeral_numeral_real N)) (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.numeral_numeral_rat N)) (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_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_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.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.one_one_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_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.one_one_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_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.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.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.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 ((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.ring_1_of_int_real X)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_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 ((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.ring_1_of_int_rat X)) (tptp.aa_nat_rat (tptp.power_power_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 ((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.ring_1_of_int_real B)) W)) (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 ((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.ring_1_of_int_rat B)) W)) (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 ((X tptp.num) (N tptp.nat) (Y tptp.int)) (= (= (tptp.aa_nat_complex (tptp.power_power_complex (tptp.numera6690914467698888265omplex X)) N) (tptp.ring_17405671764205052669omplex Y)) (= (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int X)) N) Y))) (forall ((X tptp.num) (N tptp.nat) (Y tptp.int)) (= (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.numeral_numeral_real X)) N) (tptp.ring_1_of_int_real Y)) (= (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int X)) N) Y))) (forall ((X tptp.num) (N tptp.nat) (Y tptp.int)) (= (= (tptp.aa_nat_rat (tptp.power_power_rat (tptp.numeral_numeral_rat X)) N) (tptp.ring_1_of_int_rat Y)) (= (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int X)) N) Y))) (forall ((X tptp.num) (N tptp.nat) (Y tptp.int)) (let ((_let_1 (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int X)) N))) (= (= _let_1 (tptp.ring_1_of_int_int Y)) (= _let_1 Y)))) (forall ((Y tptp.int) (X tptp.num) (N tptp.nat)) (= (= (tptp.ring_17405671764205052669omplex Y) (tptp.aa_nat_complex (tptp.power_power_complex (tptp.numera6690914467698888265omplex X)) N)) (= Y (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int X)) N)))) (forall ((Y tptp.int) (X tptp.num) (N tptp.nat)) (= (= (tptp.ring_1_of_int_real Y) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.numeral_numeral_real X)) N)) (= Y (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int X)) N)))) (forall ((Y tptp.int) (X tptp.num) (N tptp.nat)) (= (= (tptp.ring_1_of_int_rat Y) (tptp.aa_nat_rat (tptp.power_power_rat (tptp.numeral_numeral_rat X)) N)) (= Y (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int X)) N)))) (forall ((Y 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 Y) _let_1) (= Y _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.ring_1_of_int_real X)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_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.ring_1_of_int_rat X)) (tptp.aa_nat_rat (tptp.power_power_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.ring_1_of_int_real B)) W)) (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.ring_1_of_int_rat B)) W)) (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 ((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.ring_1_of_int_real N))) tptp.zero_zero_real)) (forall ((Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)) Y)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y) tptp.one_one_real)) (= (tptp.aa_real_real tptp.sin_real (tptp.aa_real_real tptp.arcsin Y)) Y)))) (forall ((T tptp.real)) (= (tptp.real_V1022390504157884413omplex (tptp.complex2 (tptp.aa_real_real tptp.cos_real T) (tptp.aa_real_real tptp.sin_real T))) tptp.one_one_real)) (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.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))) tptp.pi))) (tptp.aa_real_real tptp.tan_real X))) (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.numeral_numeral_real X)) N)) (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 ((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.numeral_numeral_rat X)) N)) (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 ((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.ring_1_of_int_real A)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_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 ((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.ring_1_of_int_rat A)) (tptp.aa_nat_rat (tptp.power_power_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 ((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.numeral_numeral_real X)) N)) (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.numeral_numeral_rat X)) N)) (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 ((A tptp.int) (X tptp.num) (N tptp.nat)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.ring_1_of_int_real A)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_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.ring_1_of_int_rat A)) (tptp.aa_nat_rat (tptp.power_power_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) (Y 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.numeral_numeral_real X))) N) (tptp.ring_1_of_int_real Y)) (= (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) Y))) (forall ((X tptp.num) (N tptp.nat) (Y 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 Y)) (= _let_1 Y)))) (forall ((X tptp.num) (N tptp.nat) (Y tptp.int)) (= (= (tptp.aa_nat_complex (tptp.power_power_complex (tptp.uminus1482373934393186551omplex (tptp.numera6690914467698888265omplex X))) N) (tptp.ring_17405671764205052669omplex Y)) (= (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) Y))) (forall ((X tptp.num) (N tptp.nat) (Y tptp.int)) (= (= (tptp.aa_nat_rat (tptp.power_power_rat (tptp.uminus_uminus_rat (tptp.numeral_numeral_rat X))) N) (tptp.ring_1_of_int_rat Y)) (= (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) Y))) (forall ((X tptp.num) (N tptp.nat) (Y tptp.int)) (= (= (tptp.power_8256067586552552935nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.numera6620942414471956472nteger X)) N) (tptp.ring_18347121197199848620nteger Y)) (= (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) Y))) (forall ((Y tptp.int) (X tptp.num) (N tptp.nat)) (= (= (tptp.ring_1_of_int_real Y) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real tptp.uminus_uminus_real (tptp.numeral_numeral_real X))) N)) (= Y (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 ((Y 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 Y) _let_1) (= Y _let_1)))) (forall ((Y tptp.int) (X tptp.num) (N tptp.nat)) (= (= (tptp.ring_17405671764205052669omplex Y) (tptp.aa_nat_complex (tptp.power_power_complex (tptp.uminus1482373934393186551omplex (tptp.numera6690914467698888265omplex X))) N)) (= Y (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 ((Y tptp.int) (X tptp.num) (N tptp.nat)) (= (= (tptp.ring_1_of_int_rat Y) (tptp.aa_nat_rat (tptp.power_power_rat (tptp.uminus_uminus_rat (tptp.numeral_numeral_rat X))) N)) (= Y (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 ((Y tptp.int) (X tptp.num) (N tptp.nat)) (= (= (tptp.ring_18347121197199848620nteger Y) (tptp.power_8256067586552552935nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.numera6620942414471956472nteger X)) N)) (= Y (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.aa_real_real tptp.arcsin tptp.one_one_real) _let_48) (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.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))) tptp.pi)) (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.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))) tptp.pi)) (tptp.ring_1_of_int_real N))) tptp.one_one_real)) (= (tptp.aa_real_real tptp.arcsin _let_44) _let_52) (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.numeral_numeral_real X))) N)) (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 ((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.uminus_uminus_rat (tptp.numeral_numeral_rat X))) N)) (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 ((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.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.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_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.ring_1_of_int_rat A)) (tptp.aa_nat_rat (tptp.power_power_rat (tptp.uminus_uminus_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 ((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.numeral_numeral_real X))) N)) (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_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_nat_rat (tptp.power_power_rat (tptp.uminus_uminus_rat (tptp.numeral_numeral_rat X))) N)) (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.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 ((A tptp.int) (X tptp.num) (N tptp.nat)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_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.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_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.ring_1_of_int_rat A)) (tptp.aa_nat_rat (tptp.power_power_rat (tptp.uminus_uminus_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 ((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 ((X tptp.real)) (exists ((Z4 tptp.int)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) (tptp.ring_1_of_int_real Z4))))) (forall ((X tptp.rat)) (exists ((Z4 tptp.int)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) (tptp.ring_1_of_int_rat Z4))))) (forall ((X tptp.real)) (exists ((Z4 tptp.int)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) (tptp.ring_1_of_int_real Z4))))) (forall ((X tptp.rat)) (exists ((Z4 tptp.int)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) (tptp.ring_1_of_int_rat Z4))))) (forall ((X tptp.real)) (exists ((Z4 tptp.int)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.ring_1_of_int_real Z4)) X)))) (forall ((X tptp.rat)) (exists ((Z4 tptp.int)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.ring_1_of_int_rat Z4)) X)))) (forall ((X tptp.int) (Y tptp.real)) (let ((_let_1 (tptp.ring_1_of_int_real X))) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real _let_1) Y) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real Y) _let_1)))) (forall ((X tptp.int) (Y tptp.rat)) (let ((_let_1 (tptp.ring_1_of_int_rat X))) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat _let_1) Y) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat Y) _let_1)))) (forall ((X tptp.int) (Y 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) Y) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int Y) _let_1)))) (forall ((X tptp.real) (Y tptp.real) (R tptp.real)) (= (tptp.aa_complex_complex (tptp.times_times_complex (tptp.complex2 X Y)) (tptp.real_V4546457046886955230omplex R)) (tptp.complex2 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real X) R) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real Y) R)))) (forall ((R tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.times_times_real R))) (= (tptp.aa_complex_complex (tptp.times_times_complex (tptp.real_V4546457046886955230omplex R)) (tptp.complex2 X Y)) (tptp.complex2 (tptp.aa_real_real _let_1 X) (tptp.aa_real_real _let_1 Y))))) (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 ((X tptp.real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.ring_1_of_int_real (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.ring_1_of_int_rat (tptp.archim3151403230148437115or_rat X))) X))) (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 ((X tptp.real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) (tptp.ring_1_of_int_real (tptp.archim7802044766580827645g_real X))))) (forall ((X tptp.rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) (tptp.ring_1_of_int_rat (tptp.archim2889992004027027881ng_rat X))))) (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 ((N tptp.nat) (K tptp.int)) (let ((_let_1 (tptp.aa_nat_fun_int_int tptp.bit_se545348938243370406it_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 ((N tptp.nat) (K tptp.int)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_nat6383147911832638789nteger tptp.bit_se7788150548672797655nteger N) (tptp.ring_18347121197199848620nteger K)) (tptp.ring_18347121197199848620nteger (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_se545348938243370406it_int N) K)))) (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (= (tptp.plus_plus_complex (tptp.complex2 A B) (tptp.complex2 C D)) (tptp.complex2 (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) (Y tptp.real) (R tptp.real)) (= (tptp.plus_plus_complex (tptp.complex2 X Y) (tptp.real_V4546457046886955230omplex R)) (tptp.complex2 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) R) Y))) (forall ((R tptp.real) (X tptp.real) (Y tptp.real)) (= (tptp.plus_plus_complex (tptp.real_V4546457046886955230omplex R) (tptp.complex2 X Y)) (tptp.complex2 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real R) X) Y))) (forall ((M tptp.int) (X tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.times_times_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.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.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.ring_1_of_int_real M)) 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.archim6058952711729229775r_real X))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_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.archim3151403230148437115or_rat X))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.ring_1_of_int_rat Z)) X)))) (forall ((X tptp.real) (Z tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.archim6058952711729229775r_real X)) Z)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) (tptp.ring_1_of_int_real Z))))) (forall ((X tptp.rat) (Z tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.archim3151403230148437115or_rat X)) Z)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) (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.archim7802044766580827645g_real X)) Z)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) (tptp.ring_1_of_int_real Z))))) (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.archim2889992004027027881ng_rat X)) Z)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) (tptp.ring_1_of_int_rat Z))))) (forall ((X tptp.real) (A tptp.int)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) (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.archim7802044766580827645g_real X)) A)))) (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.ring_1_of_int_rat A))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.archim2889992004027027881ng_rat X)) A)))) (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.archim2889992004027027881ng_rat X))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.ring_1_of_int_rat Z)) X)))) (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.archim7802044766580827645g_real X))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.ring_1_of_int_real Z)) X)))) (forall ((Z tptp.int) (X tptp.real)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int Z) (tptp.archim6058952711729229775r_real X)) (tptp.archim6058952711729229775r_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.ring_1_of_int_real Z)) X)))) (forall ((Z tptp.int) (X tptp.rat)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int Z) (tptp.archim3151403230148437115or_rat X)) (tptp.archim3151403230148437115or_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.ring_1_of_int_rat Z)) X)))) (forall ((X tptp.real) (Z tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.archim6058952711729229775r_real X)) Z) (tptp.archim6058952711729229775r_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) (tptp.ring_1_of_int_real Z))))) (forall ((X tptp.rat) (Z tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.archim3151403230148437115or_rat X)) Z) (tptp.archim3151403230148437115or_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat X) (tptp.ring_1_of_int_rat Z))))) (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 ((N tptp.int) (X tptp.int)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_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.ring_1_of_int_real N)) (tptp.ring_1_of_int_real X))))) (forall ((K tptp.int) (L tptp.int)) (= (tptp.archim6058952711729229775r_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.ring_1_of_int_real K)) (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.archim3151403230148437115or_rat (tptp.divide_divide_rat (tptp.ring_1_of_int_rat K) (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.archim6058952711729229775r_real X))) (=> (= X (tptp.ring_1_of_int_real _let_1)) (= (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.archim3151403230148437115or_rat X))) (=> (= X (tptp.ring_1_of_int_rat _let_1)) (= (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 ((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 ((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.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.ring_1_of_int_real N)) (tptp.ring_1_of_int_real D))))) (forall ((X tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) Y)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y) tptp.one_one_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.arcsin X)) (tptp.aa_real_real tptp.arcsin Y))))))) (forall ((X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) tptp.one_one_real)) (= (tptp.aa_real_real tptp.arcsin (tptp.aa_real_real tptp.uminus_uminus_real X)) (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_real_real tptp.arcsin X)))))) (forall ((X tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real X)) tptp.one_one_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real Y)) tptp.one_one_real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.arcsin X)) (tptp.aa_real_real tptp.arcsin Y))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) Y)))))) (forall ((X tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real X)) tptp.one_one_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real Y)) tptp.one_one_real)) (= (= (tptp.aa_real_real tptp.arcsin X) (tptp.aa_real_real tptp.arcsin Y)) (= X Y))))) (forall ((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 ((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.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.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_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 ((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.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.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 ((N tptp.int) (X tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.abs_abs_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 ((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.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.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.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.abs_abs_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.real)) (exists ((X3 tptp.int)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_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.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 ((Y4 tptp.int)) (=> (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.ring_1_of_int_real Y4)) X)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) (tptp.ring_1_of_int_real (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int Y4) tptp.one_one_int))))) (= Y4 X3)))))) (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.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.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 ((Y4 tptp.int)) (=> (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.ring_1_of_int_rat Y4)) X)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) (tptp.ring_1_of_int_rat (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int Y4) tptp.one_one_int))))) (= Y4 X3)))))) (forall ((X tptp.real)) (exists ((Z4 tptp.int)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.ring_1_of_int_real Z4)) X)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) (tptp.ring_1_of_int_real (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int Z4) tptp.one_one_int))))))) (forall ((X tptp.rat)) (exists ((Z4 tptp.int)) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.ring_1_of_int_rat Z4)) X)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) (tptp.ring_1_of_int_rat (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int Z4) tptp.one_one_int))))))) (forall ((R tptp.real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.ring_1_of_int_real (tptp.archim7802044766580827645g_real R))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real R) tptp.one_one_real)))) (forall ((R tptp.rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.ring_1_of_int_rat (tptp.archim2889992004027027881ng_rat R))) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat R) tptp.one_one_rat)))) (forall ((K tptp.num)) (= (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.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_1_of_int_rat (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int K))) (tptp.uminus_uminus_rat (tptp.numeral_numeral_rat 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 ((R tptp.real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.ring_1_of_int_real (tptp.archim7802044766580827645g_real R))) tptp.one_one_real)) R))) (forall ((R tptp.rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.minus_minus_rat (tptp.ring_1_of_int_rat (tptp.archim2889992004027027881ng_rat R)) tptp.one_one_rat)) R))) (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.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.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.ring_1_of_int_real N)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_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.ring_1_of_int_real N)) tptp.one_one_real)) (tptp.ring_1_of_int_real M))))) (forall ((A tptp.int) (B tptp.int)) (= (tptp.archim7802044766580827645g_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.ring_1_of_int_real A)) (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.archim2889992004027027881ng_rat (tptp.divide_divide_rat (tptp.ring_1_of_int_rat A) (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 ((I4 tptp.int)) (= X (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.ring_1_of_int_real I4)) tptp.pi))))) (forall ((X tptp.real)) (let ((_let_1 (tptp.archim6058952711729229775r_real X))) (let ((_let_2 (tptp.archim7802044766580827645g_real X))) (let ((_let_3 (= X (tptp.ring_1_of_int_real _let_1)))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (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.archim3151403230148437115or_rat X))) (let ((_let_2 (tptp.archim2889992004027027881ng_rat X))) (let ((_let_3 (= X (tptp.ring_1_of_int_rat _let_1)))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int _let_1) tptp.one_one_int)))))))) (forall ((X tptp.int) (D tptp.int)) (let ((_let_1 (tptp.ring_1_of_int_real D))) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.ring_1_of_int_real X)) _let_1) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_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.ring_1_of_int_real (tptp.modulo_modulo_int X D))) _let_1))))) (forall ((R tptp.real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real R) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.ring_1_of_int_real (tptp.archim6058952711729229775r_real R))) tptp.one_one_real)))) (forall ((N tptp.int) (X tptp.real)) (let ((_let_1 (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.archim6058952711729229775r_real X) N))))) (forall ((R tptp.real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real R) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.ring_1_of_int_real (tptp.archim6058952711729229775r_real R))) tptp.one_one_real)))) (forall ((R tptp.real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real R) tptp.one_one_real)) (tptp.ring_1_of_int_real (tptp.archim6058952711729229775r_real R))))) (forall ((R tptp.real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real R) tptp.one_one_real)) (tptp.ring_1_of_int_real (tptp.archim6058952711729229775r_real R))))) (forall ((X tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Y)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y) tptp.one_one_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.arcsin X)) (tptp.aa_real_real tptp.arcsin Y))))))) (forall ((X tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real X)) tptp.one_one_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real Y)) tptp.one_one_real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.arcsin X)) (tptp.aa_real_real tptp.arcsin Y))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Y)))))) (forall ((P tptp.fun_int_bool) (T tptp.real)) (= (tptp.pp (tptp.aa_int_bool P (tptp.archim6058952711729229775r_real T))) (forall ((I4 tptp.int)) (let ((_let_1 (tptp.ring_1_of_int_real I4))) (=> (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 I4))))))) (forall ((P tptp.fun_int_bool) (T tptp.rat)) (= (tptp.pp (tptp.aa_int_bool P (tptp.archim3151403230148437115or_rat T))) (forall ((I4 tptp.int)) (let ((_let_1 (tptp.ring_1_of_int_rat I4))) (=> (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 I4))))))) (forall ((X tptp.real) (A tptp.int)) (let ((_let_1 (tptp.ring_1_of_int_real A))) (= (= (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.ring_1_of_int_rat A))) (= (= (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.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.archim6058952711729229775r_real X) Z))))) (forall ((Z tptp.int) (X tptp.rat)) (let ((_let_1 (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.archim3151403230148437115or_rat X) Z))))) (forall ((X tptp.real)) (let ((_let_1 (tptp.ring_1_of_int_real (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 ((X tptp.rat)) (let ((_let_1 (tptp.ring_1_of_int_rat (tptp.archim2889992004027027881ng_rat X)))) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_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 ((Z tptp.int) (X tptp.real)) (let ((_let_1 (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.archim7802044766580827645g_real X) Z))))) (forall ((Z tptp.int) (X tptp.rat)) (let ((_let_1 (tptp.ring_1_of_int_rat Z))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_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.archim2889992004027027881ng_rat X) Z))))) (forall ((X tptp.real) (A tptp.int)) (let ((_let_1 (tptp.ring_1_of_int_real A))) (= (= (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 ((X tptp.rat) (A tptp.int)) (let ((_let_1 (tptp.ring_1_of_int_rat A))) (= (= (tptp.archim2889992004027027881ng_rat X) A) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_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 ((P tptp.fun_int_bool) (T tptp.real)) (= (tptp.pp (tptp.aa_int_bool P (tptp.archim7802044766580827645g_real T))) (forall ((I4 tptp.int)) (let ((_let_1 (tptp.ring_1_of_int_real I4))) (=> (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 I4))))))) (forall ((P tptp.fun_int_bool) (T tptp.rat)) (= (tptp.pp (tptp.aa_int_bool P (tptp.archim2889992004027027881ng_rat T))) (forall ((I4 tptp.int)) (let ((_let_1 (tptp.ring_1_of_int_rat I4))) (=> (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_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 I4))))))) (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.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.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.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.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.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.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.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.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.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.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_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.minus_minus_rat (tptp.ring_1_of_int_rat Z) tptp.one_one_rat))))) (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.archim2889992004027027881ng_rat X))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.minus_minus_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.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.ring_1_of_int_real Z)) tptp.one_one_real)) X)))) (forall ((X tptp.real)) (let ((_let_1 (tptp.archim6058952711729229775r_real X))) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_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.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.archim3151403230148437115or_rat X))) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_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.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.ring_1_of_int_real N)) (tptp.ring_1_of_int_real X))) (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.ring_1_of_int_real N)) (tptp.ring_1_of_int_real X))) (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.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.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.archim6058952711729229775r_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real A) (tptp.ring_1_of_int_real B))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int (tptp.archim6058952711729229775r_real A)) B)))) (forall ((Q2 tptp.real) (P2 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.ring_1_of_int_real (tptp.archim6058952711729229775r_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real P2) Q2)))) Q2)) P2)))) (forall ((Q2 tptp.rat) (P2 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.ring_1_of_int_rat (tptp.archim3151403230148437115or_rat (tptp.divide_divide_rat P2 Q2)))) Q2)) P2)))) (forall ((Q2 tptp.real) (P2 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 P2) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.ring_1_of_int_real (tptp.archim7802044766580827645g_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real P2) Q2)))) Q2))))) (forall ((Q2 tptp.rat) (P2 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 P2) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.ring_1_of_int_rat (tptp.archim2889992004027027881ng_rat (tptp.divide_divide_rat P2 Q2)))) Q2))))) (= (tptp.aa_real_real tptp.tan_real _let_64) tptp.one_one_real) (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 ((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 ((Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) Y)) (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.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y) (tptp.aa_real_real tptp.tan_real 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.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 ((Q2 tptp.real) (P2 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 P2) (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.ring_1_of_int_real (tptp.archim6058952711729229775r_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real P2) Q2)))) tptp.one_one_real)) Q2))))) (forall ((Q2 tptp.rat) (P2 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 P2) (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.ring_1_of_int_rat (tptp.archim3151403230148437115or_rat (tptp.divide_divide_rat P2 Q2)))) tptp.one_one_rat)) Q2))))) (forall ((Q2 tptp.real) (P2 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.ring_1_of_int_real (tptp.archim7802044766580827645g_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real P2) Q2)))) tptp.one_one_real)) Q2)) P2)))) (forall ((Q2 tptp.rat) (P2 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.minus_minus_rat (tptp.ring_1_of_int_rat (tptp.archim2889992004027027881ng_rat (tptp.divide_divide_rat P2 Q2))) tptp.one_one_rat)) Q2)) P2)))) (forall ((Y tptp.real)) (exists ((X3 tptp.real)) (let ((_let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) (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) Y))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X))) (let ((_let_2 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) (tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_3 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.uminus_uminus_real _let_2)))) (=> (tptp.pp (tptp.aa_real_bool _let_3 X)) (=> (tptp.pp (tptp.aa_real_bool _let_1 _let_2)) (=> (tptp.pp (tptp.aa_real_bool _let_3 Y)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y) _let_2)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.tan_real X)) (tptp.aa_real_real tptp.tan_real Y))) (tptp.pp (tptp.aa_real_bool _let_1 Y))))))))))) (forall ((Y tptp.real) (X tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y))) (let ((_let_2 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) (tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_3 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.uminus_uminus_real _let_2)))) (=> (tptp.pp (tptp.aa_real_bool _let_3 Y)) (=> (tptp.pp (tptp.aa_real_bool _let_1 _let_2)) (=> (tptp.pp (tptp.aa_real_bool _let_3 X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) _let_2)) (= (tptp.pp (tptp.aa_real_bool _let_1 X)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.tan_real Y)) (tptp.aa_real_real tptp.tan_real X)))))))))))) (forall ((Y tptp.real) (X tptp.real)) (let ((_let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) (tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.uminus_uminus_real _let_1)) Y)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) _let_1)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.tan_real Y)) (tptp.aa_real_real tptp.tan_real X)))))))) (forall ((Y tptp.real)) (exists ((X3 tptp.real)) (let ((_let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) (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) Y) (forall ((Y4 tptp.real)) (let ((_let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) (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)) Y4)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y4) _let_1)) (= (tptp.aa_real_real tptp.tan_real Y4) Y)) (= Y4 X3)))))))) (= (tptp.aa_real_real tptp.tan_real (tptp.aa_real_real tptp.uminus_uminus_real _let_64)) _let_44) (forall ((Y tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.one_one_real) (tptp.aa_real_real tptp.tan_real Y)) (tptp.aa_real_real tptp.tan_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) (tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))) Y)))) (forall ((N tptp.int) (X tptp.real)) (let ((_let_1 (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.archim7802044766580827645g_real 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.rat)) (let ((_let_1 (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.archim2889992004027027881ng_rat 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.ring_1_of_int_real X5)) (tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))) tptp.pi))))) (forall ((X tptp.complex) (Y tptp.complex)) (let ((_let_1 (tptp.cos_complex Y))) (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 Y)) (tptp.divide1717551699836669952omplex (tptp.sin_complex (tptp.plus_plus_complex X Y)) (tptp.aa_complex_complex (tptp.times_times_complex _let_2) _let_1)))))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_real_real tptp.cos_real Y))) (let ((_let_2 (tptp.aa_real_real tptp.cos_real X))) (=> (not (= _let_2 tptp.zero_zero_real)) (=> (not (= _let_1 tptp.zero_zero_real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real tptp.tan_real X)) (tptp.aa_real_real tptp.tan_real Y)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real tptp.sin_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) Y))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real _let_2) _let_1)))))))) (forall ((X tptp.real)) (= (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.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))) X)) (tptp.aa_real_real tptp.cot_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_real X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) (tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))))) (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real tptp.tan_real X))))))) (forall ((Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) Y)) (exists ((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.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.aa_real_real tptp.tan_real X3) Y))))) (forall ((X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.pi)) (tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.tan_real X)) tptp.zero_zero_real))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) (tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.uminus_uminus_real _let_1)) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) Y)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y) _let_1)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.tan_real X)) (tptp.aa_real_real tptp.tan_real Y)))))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) (tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_2 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.uminus_uminus_real _let_1)))) (=> (tptp.pp (tptp.aa_real_bool _let_2 X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) _let_1)) (=> (tptp.pp (tptp.aa_real_bool _let_2 Y)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y) _let_1)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.tan_real X)) (tptp.aa_real_real tptp.tan_real Y))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) Y)))))))))) (forall ((X tptp.real)) (=> (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.numeral_numeral_real (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit0 tptp.one)))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_real_real tptp.tan_real X))) tptp.one_one_real)))) (forall ((Y tptp.real)) (let ((_let_1 (tptp.aa_real_real tptp.arctan Y))) (let ((_let_2 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) (tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))))) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.uminus_uminus_real _let_2)) _let_1)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real _let_1) _let_2)) (= (tptp.aa_real_real tptp.tan_real _let_1) Y))))) (forall ((X tptp.real)) (let ((_let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) (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 ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) (tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.uminus_uminus_real _let_1)) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) _let_1)) (=> (= (tptp.aa_real_real tptp.tan_real X) Y) (= (tptp.aa_real_real tptp.arctan Y) X)))))) (forall ((X tptp.complex) (Y tptp.complex)) (let ((_let_1 (tptp.tan_complex Y))) (let ((_let_2 (tptp.tan_complex X))) (let ((_let_3 (tptp.plus_plus_complex X Y))) (=> (not (= (tptp.cos_complex X) tptp.zero_zero_complex)) (=> (not (= (tptp.cos_complex Y) 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) (Y tptp.real)) (let ((_let_1 (tptp.aa_real_real tptp.tan_real Y))) (let ((_let_2 (tptp.aa_real_real tptp.tan_real X))) (let ((_let_3 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) Y))) (=> (not (= (tptp.aa_real_real tptp.cos_real X) tptp.zero_zero_real)) (=> (not (= (tptp.aa_real_real tptp.cos_real Y) tptp.zero_zero_real)) (=> (not (= (tptp.aa_real_real tptp.cos_real _let_3) tptp.zero_zero_real)) (= (tptp.aa_real_real tptp.tan_real _let_3) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real _let_2) _let_1)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real tptp.one_one_real) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real _let_2) _let_1))))))))))) (forall ((X tptp.complex) (Y tptp.complex)) (let ((_let_1 (tptp.tan_complex Y))) (let ((_let_2 (tptp.tan_complex X))) (let ((_let_3 (tptp.minus_minus_complex X Y))) (=> (not (= (tptp.cos_complex X) tptp.zero_zero_complex)) (=> (not (= (tptp.cos_complex Y) 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) (Y tptp.real)) (let ((_let_1 (tptp.aa_real_real tptp.tan_real Y))) (let ((_let_2 (tptp.aa_real_real tptp.tan_real X))) (let ((_let_3 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real X) Y))) (=> (not (= (tptp.aa_real_real tptp.cos_real X) tptp.zero_zero_real)) (=> (not (= (tptp.aa_real_real tptp.cos_real Y) tptp.zero_zero_real)) (=> (not (= (tptp.aa_real_real tptp.cos_real _let_3) tptp.zero_zero_real)) (= (tptp.aa_real_real tptp.tan_real _let_3) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real _let_2) _let_1)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real tptp.one_one_real) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real _let_2) _let_1))))))))))) (forall ((X tptp.complex) (Y tptp.complex)) (let ((_let_1 (tptp.cos_complex Y))) (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 Y))) (tptp.divide1717551699836669952omplex (tptp.cos_complex (tptp.plus_plus_complex X Y)) (tptp.aa_complex_complex (tptp.times_times_complex _let_2) _let_1)))))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_real_real tptp.cos_real Y))) (let ((_let_2 (tptp.aa_real_real tptp.cos_real X))) (=> (not (= _let_2 tptp.zero_zero_real)) (=> (not (= _let_1 tptp.zero_zero_real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real tptp.one_one_real) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real tptp.tan_real X)) (tptp.aa_real_real tptp.tan_real Y))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real tptp.cos_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) Y))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real _let_2) _let_1)))))))) (forall ((X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.abs_abs_real X)) tptp.one_one_real)) (exists ((Z4 tptp.real)) (let ((_let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) (tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit0 tptp.one)))))) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.uminus_uminus_real _let_1)) Z4)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Z4) _let_1)) (= (tptp.aa_real_real tptp.tan_real Z4) X)))))) (forall ((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.archim6058952711729229775r_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.log2 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.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.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 ((Y tptp.real)) (let ((_let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) (tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_2 (tptp.aa_real_real tptp.arcsin Y))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)) Y)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y) tptp.one_one_real)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.uminus_uminus_real _let_1)) _let_2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real _let_2) _let_1)))))))) (forall ((Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)) Y)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y) tptp.one_one_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) (tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))))) (tptp.aa_real_real tptp.arcsin Y)))))) (forall ((Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)) Y)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y) tptp.one_one_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.arcsin Y)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) (tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))))))) (forall ((Y tptp.real)) (let ((_let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) (tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_2 (tptp.aa_real_real tptp.arcsin Y))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)) Y)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y) tptp.one_one_real)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real _let_1)) _let_2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real _let_2) _let_1)))))))) (forall ((X tptp.real)) (let ((_let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) (tptp.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.real)) (= (= (tptp.aa_real_real tptp.cos_real X) tptp.zero_zero_real) (exists ((I4 tptp.int)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (and (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_num_int tptp.numeral_numeral_int _let_1)) I4))) (= X (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.ring_1_of_int_real I4)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) (tptp.numeral_numeral_real _let_1))))))))) (forall ((X tptp.real)) (= (= (tptp.aa_real_real tptp.sin_real X) tptp.zero_zero_real) (exists ((I4 tptp.int)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_num_int tptp.numeral_numeral_int _let_1)) I4)) (= X (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.ring_1_of_int_real I4)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) (tptp.numeral_numeral_real _let_1))))))))) (forall ((X tptp.complex)) (let ((_let_1 (tptp.aa_complex_complex (tptp.times_times_complex (tptp.numera6690914467698888265omplex (tptp.aa_num_num tptp.bit0 tptp.one))) X))) (= (tptp.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.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 ((Y tptp.real)) (let ((_let_1 (tptp.aa_real_real tptp.arcsin Y))) (let ((_let_2 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) (tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)) Y)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y) tptp.one_one_real)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real _let_2)) _let_1)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real _let_1) _let_2)) (= (tptp.aa_real_real tptp.sin_real _let_1) Y))))))) (forall ((X tptp.real) (Y tptp.int)) (let ((_let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.one_one_real) (tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_2 (tptp.ring_1_of_int_real Y))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.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.archim8280529875227126926d_real X) Y)))))) (forall ((X tptp.rat) (Y tptp.int)) (let ((_let_1 (tptp.divide_divide_rat tptp.one_one_rat (tptp.numeral_numeral_rat (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_2 (tptp.ring_1_of_int_rat Y))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_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.archim7778729529865785530nd_rat X) Y)))))) (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.ring_1_of_int_real N)))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.one_one_real) (tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (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.abs_abs_rat (tptp.minus_minus_rat X (tptp.ring_1_of_int_rat N)))) (tptp.divide_divide_rat tptp.one_one_rat (tptp.numeral_numeral_rat (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.archim7778729529865785530nd_rat X) 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 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.ring_1_of_int_real (tptp.archim8280529875227126926d_real X))) X))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.one_one_real) (tptp.numeral_numeral_real (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.abs_abs_rat (tptp.minus_minus_rat (tptp.ring_1_of_int_rat (tptp.archim7778729529865785530nd_rat X)) X))) (tptp.divide_divide_rat tptp.one_one_rat (tptp.numeral_numeral_rat (tptp.aa_num_num tptp.bit0 tptp.one)))))) (forall ((X tptp.real)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (let ((_let_2 (tptp.aa_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.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.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 ((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.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))))) (tptp.ring_1_of_int_real (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.minus_minus_rat X (tptp.divide_divide_rat tptp.one_one_rat (tptp.numeral_numeral_rat (tptp.aa_num_num tptp.bit0 tptp.one))))) (tptp.ring_1_of_int_rat (tptp.archim7778729529865785530nd_rat X))))) (forall ((X tptp.real) (Y tptp.real)) (= (= (tptp.aa_real_real tptp.sqrt X) (tptp.aa_real_real tptp.sqrt Y)) (= X Y))) (= (tptp.aa_real_real tptp.sqrt tptp.zero_zero_real) tptp.zero_zero_real) (forall ((X tptp.real)) (= (= (tptp.aa_real_real tptp.sqrt X) tptp.zero_zero_real) (= X tptp.zero_zero_real))) (forall ((X tptp.real) (Y tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.sqrt X)) (tptp.aa_real_real tptp.sqrt Y))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Y)))) (forall ((X tptp.real) (Y tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.sqrt X)) (tptp.aa_real_real tptp.sqrt Y))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) Y)))) (= (tptp.aa_real_real tptp.sqrt tptp.one_one_real) tptp.one_one_real) (forall ((X tptp.real)) (= (= (tptp.aa_real_real tptp.sqrt X) tptp.one_one_real) (= X tptp.one_one_real))) (forall ((N tptp.int)) (= (tptp.archim8280529875227126926d_real (tptp.ring_1_of_int_real N)) N)) (forall ((N tptp.int)) (= (tptp.archim7778729529865785530nd_rat (tptp.ring_1_of_int_rat N)) N)) (forall ((X tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.sqrt X)) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) tptp.zero_zero_real)))) (forall ((Y tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real))) (= (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real tptp.sqrt Y))) (tptp.pp (tptp.aa_real_bool _let_1 Y))))) (forall ((Y tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (= (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real tptp.sqrt Y))) (tptp.pp (tptp.aa_real_bool _let_1 Y))))) (forall ((X tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.sqrt X)) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) tptp.zero_zero_real)))) (forall ((Y tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real))) (= (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real tptp.sqrt Y))) (tptp.pp (tptp.aa_real_bool _let_1 Y))))) (forall ((X tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.sqrt X)) tptp.one_one_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) tptp.one_one_real)))) (forall ((Y tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.one_one_real))) (= (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real tptp.sqrt Y))) (tptp.pp (tptp.aa_real_bool _let_1 Y))))) (forall ((X tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.sqrt X)) tptp.one_one_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) tptp.one_one_real)))) (forall ((A tptp.real)) (let ((_let_1 (tptp.aa_real_real tptp.sqrt A))) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real _let_1) _let_1) (tptp.aa_real_real tptp.abs_abs_real A)))) (forall ((X tptp.real)) (= (tptp.aa_real_real tptp.sqrt (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real X) X)) (tptp.aa_real_real tptp.abs_abs_real X))) (= (tptp.archim8280529875227126926d_real tptp.zero_zero_real) tptp.zero_zero_int) (= (tptp.archim7778729529865785530nd_rat tptp.zero_zero_rat) tptp.zero_zero_int) (forall ((N tptp.num)) (= (tptp.archim8280529875227126926d_real (tptp.numeral_numeral_real N)) (tptp.aa_num_int tptp.numeral_numeral_int N))) (forall ((N tptp.num)) (= (tptp.archim7778729529865785530nd_rat (tptp.numeral_numeral_rat N)) (tptp.aa_num_int tptp.numeral_numeral_int N))) (= (tptp.archim8280529875227126926d_real tptp.one_one_real) tptp.one_one_int) (= (tptp.archim7778729529865785530nd_rat tptp.one_one_rat) tptp.one_one_int) (forall ((N tptp.nat)) (= (tptp.archim8280529875227126926d_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N)) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N))) (forall ((N tptp.nat)) (= (tptp.archim7778729529865785530nd_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat N)) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N))) (= (tptp.aa_real_real tptp.sqrt _let_63) _let_46) (forall ((N tptp.num)) (= (tptp.archim8280529875227126926d_real (tptp.aa_real_real tptp.uminus_uminus_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.archim7778729529865785530nd_rat (tptp.uminus_uminus_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.real)) (= (tptp.aa_real_real tptp.sqrt (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (tptp.aa_real_real tptp.abs_abs_real X))) (forall ((X tptp.real)) (= (= (tptp.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) (Y 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 Y) _let_1))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real 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 ((X tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Y)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.sqrt X)) (tptp.aa_real_real tptp.sqrt Y))))) (forall ((X tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) Y)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.sqrt X)) (tptp.aa_real_real tptp.sqrt Y))))) (forall ((X tptp.real) (Y tptp.real)) (= (tptp.aa_real_real tptp.sqrt (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real X) Y)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real tptp.sqrt X)) (tptp.aa_real_real tptp.sqrt Y)))) (forall ((X tptp.real) (Y tptp.real)) (= (tptp.aa_real_real tptp.sqrt (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real X) Y)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real tptp.sqrt X)) (tptp.aa_real_real tptp.sqrt Y)))) (forall ((X tptp.real) (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.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool _let_1 X)) (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real tptp.sqrt X)))))) (forall ((X tptp.real)) (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)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.one_one_real))) (=> (tptp.pp (tptp.aa_real_bool _let_1 X)) (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real tptp.sqrt X)))))) (forall ((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) (Y tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool _let_1 X)) (=> (tptp.pp (tptp.aa_real_bool _let_1 Y)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.sqrt (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) Y))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real tptp.sqrt X)) (tptp.aa_real_real tptp.sqrt Y)))))))) (forall ((X tptp.real) (Y tptp.real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) (tptp.aa_real_real tptp.sqrt (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real X) X)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real Y) Y)))))) (forall ((X tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) Y)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.archim7778729529865785530nd_rat X)) (tptp.archim7778729529865785530nd_rat Y))))) (forall ((X tptp.real)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.archim6058952711729229775r_real X)) (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.archim3151403230148437115or_rat X)) (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.archim8280529875227126926d_real X)) (tptp.archim7802044766580827645g_real X)))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real _let_71) _let_46)) (forall ((X tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) Y)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) (tptp.aa_real_real tptp.sqrt Y))))) (forall ((X tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) Y)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) (tptp.aa_real_real tptp.sqrt Y))))) (forall ((X tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.sqrt X)) Y)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Y) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))))) (= (tptp.aa_real_real tptp.tan_real _let_93) _let_91) (forall ((Y tptp.real) (X tptp.real)) (=> (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Y) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) X) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) Y)) (= (tptp.aa_real_real tptp.sqrt X) Y)))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool _let_1 X)) (=> (tptp.pp (tptp.aa_real_bool _let_1 Y)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Y) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.sqrt X)) Y))))))) (forall ((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.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))))) U)))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (= (tptp.aa_real_real tptp.sqrt (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) _let_1)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Y) _let_1))) Y) (= X tptp.zero_zero_real)))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (= (tptp.aa_real_real tptp.sqrt (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) _let_1)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Y) _let_1))) X) (= Y tptp.zero_zero_real)))) (forall ((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 ((Y tptp.real) (X tptp.real)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y) (tptp.aa_real_real tptp.sqrt (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) _let_1)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Y) _let_1))))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) (tptp.aa_real_real tptp.sqrt (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) _let_1)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Y) _let_1))))))) (forall ((X tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real X)) (tptp.aa_real_real tptp.sqrt Y))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) Y)))) (= (tptp.aa_real_real tptp.cos_real _let_64) _let_95) (= (tptp.aa_real_real tptp.sin_real _let_64) _let_95) (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.ring_1_of_int_real (tptp.archim8280529875227126926d_real Z))))) (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_real_real _let_1 (tptp.ring_1_of_int_real M))))))) (forall ((Z tptp.rat) (M tptp.int)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.abs_abs_rat (tptp.minus_minus_rat Z (tptp.ring_1_of_int_rat (tptp.archim7778729529865785530nd_rat Z))))) (tptp.abs_abs_rat (tptp.minus_minus_rat Z (tptp.ring_1_of_int_rat M)))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool _let_1 X)) (=> (tptp.pp (tptp.aa_real_bool _let_1 Y)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Y) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.sqrt X)) Y))))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool _let_2 X)) (=> (tptp.pp (tptp.aa_real_bool _let_2 Y)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.sqrt (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) _let_1)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Y) _let_1)))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) Y)))))))) (= (tptp.aa_real_real tptp.tan_real _let_94) (tptp.aa_real_real _let_87 _let_91)) (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.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real X)) (tptp.aa_real_real tptp.sqrt (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) _let_1)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Y) _let_1))))))) (forall ((Y tptp.real) (X tptp.real)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real Y)) (tptp.aa_real_real tptp.sqrt (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) _let_1)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Y) _let_1))))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.sqrt (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) _let_1)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Y) _let_1)))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real tptp.abs_abs_real X)) (tptp.aa_real_real tptp.abs_abs_real Y)))))) (forall ((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.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)))))))) (= (tptp.aa_real_real tptp.cos_real _let_94) _let_92) (= (tptp.aa_real_real tptp.sin_real _let_93) _let_92) (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 ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.real_V1022390504157884413omplex (tptp.complex2 X Y)) (tptp.aa_real_real tptp.sqrt (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) _let_1)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Y) _let_1)))))) (forall ((X tptp.real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) (tptp.aa_real_real tptp.sqrt (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) tptp.one_one_real)))))) (forall ((X tptp.real) (Y tptp.real) (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 Y) _let_1))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real 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) (Y tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool _let_1 X)) (=> (tptp.pp (tptp.aa_real_bool _let_1 Y)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.sqrt (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real X) Y))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) Y)) (tptp.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_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.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))) (tptp.aa_real_real tptp.sqrt X)))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real X) (tptp.aa_real_real tptp.sqrt (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) _let_1)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Y) _let_1)))))) tptp.one_one_real)))) (forall ((X tptp.real) (U tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (let ((_let_2 (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1))) (let ((_let_3 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real U) (tptp.aa_real_real tptp.sqrt (tptp.numeral_numeral_real _let_1))))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.abs_abs_real X)) _let_3)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.abs_abs_real Y)) _let_3)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.sqrt (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) _let_2)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Y) _let_2)))) U)))))))) (forall ((X tptp.real)) (=> (tptp.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 ((X tptp.real)) (= (tptp.aa_real_real tptp.cos_real (tptp.aa_real_real tptp.arctan X)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.one_one_real) (tptp.aa_real_real tptp.sqrt (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real tptp.one_one_real) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))))))) (forall ((X tptp.real)) (= (tptp.aa_real_real tptp.sin_real (tptp.aa_real_real tptp.arctan X)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real X) (tptp.aa_real_real tptp.sqrt (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real tptp.one_one_real) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))))))) (forall ((X tptp.real) (U tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (let ((_let_2 (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1))) (let ((_let_3 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (let ((_let_4 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real U) (tptp.numeral_numeral_real _let_1)))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) _let_4)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y) _let_4)) (=> (tptp.pp (tptp.aa_real_bool _let_3 X)) (=> (tptp.pp (tptp.aa_real_bool _let_3 Y)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.sqrt (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) _let_2)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Y) _let_2)))) U))))))))))) (forall ((X tptp.real)) (let ((_let_1 (tptp.aa_real_real tptp.sin_real X))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) _let_1)) (= _let_1 (tptp.aa_real_real tptp.sqrt (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real tptp.one_one_real) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real tptp.cos_real X)) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))))))) (forall ((X tptp.real)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (let ((_let_2 (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real tptp.one_one_real))) (= (tptp.aa_real_real tptp.arctan X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.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 ((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 ((X tptp.real)) (= (tptp.archim8280529875227126926d_real X) (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.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))))))) (forall ((X tptp.rat)) (= (tptp.archim7778729529865785530nd_rat X) (tptp.archim3151403230148437115or_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat X) (tptp.divide_divide_rat tptp.one_one_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.ring_1_of_int_real (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.numeral_numeral_real (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.ring_1_of_int_rat (tptp.archim7778729529865785530nd_rat X))) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat X) (tptp.divide_divide_rat tptp.one_one_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.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.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))))) (tptp.ring_1_of_int_real (tptp.archim8280529875227126926d_real X))))) (forall ((X tptp.rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.minus_minus_rat X (tptp.divide_divide_rat tptp.one_one_rat (tptp.numeral_numeral_rat (tptp.aa_num_num tptp.bit0 tptp.one))))) (tptp.ring_1_of_int_rat (tptp.archim7778729529865785530nd_rat X))))) (forall ((X tptp.real)) (let ((_let_1 (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.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.archim7802044766580827645g_real X))) (=> (not _let_2) (= _let_1 (tptp.archim6058952711729229775r_real X))))))) (forall ((X tptp.rat)) (let ((_let_1 (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.divide_divide_rat tptp.one_one_rat (tptp.numeral_numeral_rat (tptp.aa_num_num tptp.bit0 tptp.one)))) (tptp.archimedean_frac_rat X))))) (and (=> _let_2 (= _let_1 (tptp.archim2889992004027027881ng_rat X))) (=> (not _let_2) (= _let_1 (tptp.archim3151403230148437115or_rat X))))))) (forall ((Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real Y)) tptp.one_one_real)) (= (tptp.aa_real_real tptp.sin_real (tptp.aa_real_real tptp.arccos Y)) (tptp.aa_real_real tptp.sqrt (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real tptp.one_one_real) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Y) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))))))) (forall ((X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) tptp.one_one_real)) (= (tptp.aa_real_real tptp.sin_real (tptp.aa_real_real tptp.arccos X)) (tptp.aa_real_real tptp.sqrt (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real tptp.one_one_real) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))))))) (forall ((Theta tptp.real)) (not (forall ((K3 tptp.int)) (not (= (tptp.aa_real_real tptp.arccos (tptp.aa_real_real tptp.cos_real Theta)) (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real Theta) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.ring_1_of_int_real K3)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))) tptp.pi))))))))) (forall ((X tptp.real)) (let ((_let_1 (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.log2 _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)))))) (= (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 ((X tptp.real)) (= (= (tptp.aa_real_real tptp.exp_real X) tptp.one_one_real) (= X tptp.zero_zero_real))) (= (tptp.aa_real_real tptp.arccos tptp.one_one_real) tptp.zero_zero_real) (forall ((Z tptp.int)) (= (tptp.aa_real_real tptp.archim2898591450579166408c_real (tptp.ring_1_of_int_real Z)) tptp.zero_zero_real)) (forall ((Z tptp.int)) (= (tptp.archimedean_frac_rat (tptp.ring_1_of_int_rat Z)) tptp.zero_zero_rat)) (forall ((X tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real) (tptp.aa_real_real tptp.exp_real X))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) X)))) (forall ((X tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.exp_real X)) tptp.one_one_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) tptp.zero_zero_real)))) (forall ((X tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.one_one_real) (tptp.aa_real_real tptp.exp_real X))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) X)))) (forall ((X tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.exp_real X)) tptp.one_one_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) tptp.zero_zero_real)))) (= (tptp.aa_real_real tptp.arccos _let_44) tptp.pi) (forall ((Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)) Y)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y) tptp.one_one_real)) (= (tptp.aa_real_real tptp.cos_real (tptp.aa_real_real tptp.arccos Y)) Y)))) (= (tptp.aa_real_real tptp.arccos tptp.zero_zero_real) _let_48) (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 ((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 ((X tptp.complex) (Y tptp.complex)) (= (tptp.aa_complex_complex (tptp.times_times_complex (tptp.exp_complex X)) (tptp.exp_complex Y)) (tptp.exp_complex (tptp.plus_plus_complex X Y)))) (forall ((X tptp.real) (Y tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real tptp.exp_real X)) (tptp.aa_real_real tptp.exp_real Y)) (tptp.aa_real_real tptp.exp_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) Y)))) (forall ((X tptp.complex) (Y tptp.complex)) (=> (= (tptp.aa_complex_complex (tptp.times_times_complex X) Y) (tptp.aa_complex_complex (tptp.times_times_complex Y) X)) (= (tptp.exp_complex (tptp.plus_plus_complex X Y)) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.exp_complex X)) (tptp.exp_complex Y))))) (forall ((X tptp.real) (Y tptp.real)) (=> (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real X) Y) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real Y) X)) (= (tptp.aa_real_real tptp.exp_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) Y)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real tptp.exp_real X)) (tptp.aa_real_real tptp.exp_real Y))))) (forall ((X tptp.complex) (Y tptp.complex)) (= (tptp.exp_complex (tptp.minus_minus_complex X Y)) (tptp.divide1717551699836669952omplex (tptp.exp_complex X) (tptp.exp_complex Y)))) (forall ((X tptp.real) (Y tptp.real)) (= (tptp.aa_real_real tptp.exp_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real X) Y)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real tptp.exp_real X)) (tptp.aa_real_real tptp.exp_real Y)))) (forall ((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)))) (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.archimedean_frac_rat X)))) (forall ((X tptp.real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.archim2898591450579166408c_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.archimedean_frac_rat X)) tptp.one_one_rat))) (forall ((X tptp.real)) (= (tptp.aa_real_real tptp.archim2898591450579166408c_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) tptp.one_one_real)) (tptp.aa_real_real tptp.archim2898591450579166408c_real X))) (forall ((X tptp.rat)) (= (tptp.archimedean_frac_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat X) tptp.one_one_rat)) (tptp.archimedean_frac_rat 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)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real tptp.one_one_real) X)) (tptp.aa_real_real tptp.exp_real X)))) (forall ((X tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real tptp.exp_real X)) (tptp.aa_real_real tptp.exp_real (tptp.aa_real_real tptp.uminus_uminus_real X))) tptp.one_one_real)) (forall ((X tptp.complex)) (= (tptp.aa_complex_complex (tptp.times_times_complex (tptp.exp_complex X)) (tptp.exp_complex (tptp.uminus1482373934393186551omplex X))) tptp.one_one_complex)) (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 ((X tptp.real)) (= (tptp.aa_real_real tptp.ln_ln_real X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.log2 (tptp.aa_real_real tptp.exp_real tptp.one_one_real)) X))) (forall ((X tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) Y)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y) tptp.one_one_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.arccos Y)) (tptp.aa_real_real tptp.arccos X))))))) (forall ((X tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real X)) tptp.one_one_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real Y)) tptp.one_one_real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.arccos X)) (tptp.aa_real_real tptp.arccos Y))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y) X)))))) (forall ((X tptp.real) (Y tptp.real)) (=> (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real X)) tptp.one_one_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real Y)) tptp.one_one_real))) (= (= (tptp.aa_real_real tptp.arccos X) (tptp.aa_real_real tptp.arccos Y)) (= X Y)))) (forall ((X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) X)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real tptp.one_one_real) X)) (tptp.aa_real_real tptp.exp_real X))))) (forall ((Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.one_one_real) Y)) (exists ((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 Y) tptp.one_one_real))) (= (tptp.aa_real_real tptp.exp_real X3) Y))))) (forall ((X tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.exp_real tptp.one_one_real)) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) Y)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real tptp.ln_ln_real Y)) Y)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real tptp.ln_ln_real X)) X)))))) (forall ((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.ring_1_of_int_real (tptp.archim6058952711729229775r_real X))))) (forall ((X tptp.rat)) (= (tptp.archimedean_frac_rat X) (tptp.minus_minus_rat X (tptp.ring_1_of_int_rat (tptp.archim3151403230148437115or_rat X))))) (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 ((Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)) Y)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y) tptp.one_one_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_real_real tptp.arccos Y)))))) (forall ((X tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Y)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y) tptp.one_one_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.arccos Y)) (tptp.aa_real_real tptp.arccos X))))))) (forall ((X tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real X)) tptp.one_one_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real Y)) tptp.one_one_real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.arccos X)) (tptp.aa_real_real tptp.arccos Y))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y) X)))))) (forall ((Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)) Y)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y) tptp.one_one_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.arccos Y)) tptp.pi))))) (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_90)) (forall ((Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real Y)) tptp.one_one_real)) (= (tptp.aa_real_real tptp.cos_real (tptp.aa_real_real tptp.arccos Y)) Y))) (forall ((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 ((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.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) (Y 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 Y)))) (let ((_let_2 (tptp.aa_real_real tptp.archim2898591450579166408c_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) Y)))) (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) (Y tptp.rat)) (let ((_let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.archimedean_frac_rat X)) (tptp.archimedean_frac_rat Y)))) (let ((_let_2 (tptp.archimedean_frac_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat X) Y)))) (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.minus_minus_rat _let_1 tptp.one_one_rat)))))))) (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)))))) (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_46)) (forall ((Y tptp.real)) (let ((_let_1 (tptp.aa_real_real tptp.arccos Y))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)) Y)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y) tptp.one_one_real)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) _let_1)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real _let_1) tptp.pi))))))) (forall ((Y tptp.real)) (let ((_let_1 (tptp.aa_real_real tptp.arccos Y))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)) Y)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y) tptp.one_one_real)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) _let_1)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real _let_1) tptp.pi))))))) (forall ((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 ((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.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 ((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 ((Y tptp.real)) (let ((_let_1 (tptp.aa_real_real tptp.arccos Y))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)) Y)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y) tptp.one_one_real)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) _let_1)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real _let_1) tptp.pi)) (= (tptp.aa_real_real tptp.cos_real _let_1) Y)))))) (forall ((Z tptp.real)) (let ((_let_1 (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.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.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.real_V1022390504157884413omplex (tptp.exp_complex Z))) _let_1))))) (forall ((X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real X)) tptp.one_one_real)) (= (tptp.aa_real_real tptp.arccos (tptp.aa_real_real tptp.uminus_uminus_real X)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real tptp.pi) (tptp.aa_real_real tptp.arccos X))))) (forall ((X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_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) (Y tptp.real)) (let ((_let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.archim6058952711729229775r_real X)) (tptp.archim6058952711729229775r_real Y)))) (let ((_let_2 (tptp.archim6058952711729229775r_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) Y)))) (let ((_let_3 (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.archim2898591450579166408c_real X)) (tptp.aa_real_real tptp.archim2898591450579166408c_real Y))) tptp.one_one_real)))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int _let_1) tptp.one_one_int)))))))) (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.archim3151403230148437115or_rat X)) (tptp.archim3151403230148437115or_rat Y)))) (let ((_let_2 (tptp.archim3151403230148437115or_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat X) Y)))) (let ((_let_3 (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.archimedean_frac_rat X)) (tptp.archimedean_frac_rat Y))) tptp.one_one_rat)))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int _let_1) tptp.one_one_int)))))))) (forall ((X tptp.real)) (let ((_let_1 (tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.one_one_real) _let_1))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.exp_real X)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real tptp.one_one_real) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real _let_1) X)))))))) (forall ((N tptp.nat) (X tptp.real)) (let ((_let_1 (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real _let_1)) X)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real tptp.one_one_real) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real X) _let_1))) N)) (tptp.aa_real_real tptp.exp_real X))))))) (forall ((X tptp.real) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) _let_1)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real tptp.one_one_real) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real X) _let_1))) N)) (tptp.aa_real_real tptp.exp_real (tptp.aa_real_real tptp.uminus_uminus_real X)))))))) (forall ((Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) Y)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y) tptp.one_one_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.arccos Y)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) (tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))))))) (forall ((Z tptp.real)) (let ((_let_1 (tptp.aa_real_real tptp.real_V7735802525324610683m_real Z))) (let ((_let_2 (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.real_V1022390504157884413omplex Z))) (let ((_let_2 (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.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 ((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.numeral_numeral_real _let_1)))) (tptp.aa_real_real tptp.exp_real X)))))) (forall ((X tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.log2 (tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit0 tptp.one))))))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) X)) (= (tptp.aa_real_real _let_1 X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real _let_1 (tptp.aa_real_real tptp.exp_real tptp.one_one_real))) (tptp.aa_real_real tptp.ln_ln_real X)))))) (forall ((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.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 ((L tptp.int) (K tptp.int)) (let ((_let_1 (tptp.aa_int_int tptp.abs_abs_int L))) (let ((_let_2 (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_int_nat tptp.nat2 (tptp.aa_int_int tptp.abs_abs_int K))) (tptp.aa_int_nat tptp.nat2 _let_1))))) (let ((_let_3 (tptp.aa_int_int tptp.sgn_sgn_int L))) (let ((_let_4 (tptp.aa_int_fun_int_int tptp.times_times_int _let_3))) (let ((_let_5 (tptp.modulo_modulo_int K L))) (let ((_let_6 (= (tptp.aa_int_int tptp.sgn_sgn_int K) _let_3))) (let ((_let_7 (= L tptp.zero_zero_int))) (and (=> _let_7 (= _let_5 K)) (=> (not _let_7) (and (=> _let_6 (= _let_5 (tptp.aa_int_int _let_4 _let_2))) (=> (not _let_6) (= _let_5 (tptp.aa_int_int _let_4 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int _let_1) (tptp.aa_bool_int tptp.zero_n2684676970156552555ol_int (tptp.aa_bool_bool tptp.fNot (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int L) K))))) _let_2))))))))))))))) (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.aa_int_int tptp.sgn_sgn_int K) (tptp.aa_int_int tptp.sgn_sgn_int L)))) (let ((_let_4 (= L tptp.zero_zero_int))) (and (=> _let_4 (= _let_2 tptp.zero_zero_int)) (=> (not _let_4) (and (=> _let_3 (= _let_2 (tptp.aa_nat_int tptp.semiri1314217659103216013at_int _let_1))) (=> (not _let_3) (= _let_2 (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat _let_1) (tptp.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) (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 ((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.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.pred_numeral N)))))) (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.ring_1_of_int_real I)))) (let ((_let_3 (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) I)))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) X)) (and (=> _let_3 (= _let_2 (tptp.aa_nat_real _let_1 (tptp.aa_int_nat tptp.nat2 I)))) (=> (not _let_3) (= _let_2 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.one_one_real) (tptp.aa_nat_real _let_1 (tptp.aa_int_nat tptp.nat2 (tptp.aa_int_int tptp.uminus_uminus_int I)))))))))))) (forall ((N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat))) (= (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat tptp.bit_se2002935070580805687sk_nat N))) (tptp.pp (tptp.aa_nat_bool _let_1 N))))) (forall ((N tptp.nat)) (= (tptp.aa_int_nat tptp.nat2 (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N)) N)) (forall ((K tptp.num)) (= (tptp.aa_int_nat tptp.nat2 (tptp.aa_num_int tptp.numeral_numeral_int K)) (tptp.aa_num_nat tptp.numeral_numeral_nat K))) (= (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 ((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 ((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)))) (= _let_86 _let_11) (= (tptp.aa_nat_nat tptp.bit_se2002935070580805687sk_nat _let_11) tptp.one_one_nat) (= (tptp.aa_nat_int tptp.bit_se2000444600071755411sk_int _let_11) tptp.one_one_int) (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 ((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 ((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.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.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 ((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 ((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 ((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.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.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 ((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.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.pred_numeral 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 ((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.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.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 ((X tptp.num) (N tptp.nat) (Y tptp.int)) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat X)) N) (tptp.aa_int_nat tptp.nat2 Y)) (= (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int X)) N) Y))) (forall ((Y tptp.int) (X tptp.num) (N tptp.nat)) (= (= (tptp.aa_int_nat tptp.nat2 Y) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat X)) N)) (= Y (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int X)) N)))) (forall ((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.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.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 ((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 ((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 ((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.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.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.code_natural) (N tptp.nat)) (let ((_let_1 (tptp.numera5444537566228673987atural (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.pp (tptp.aa_nat_bool (tptp.bit_se8040316288895769887atural (tptp.modulo8411746178871703098atural A _let_1)) N)) (and (= N tptp.zero_zero_nat) (not (tptp.pp (tptp.dvd_dvd_Code_natural _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.aa_nat_fun_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))))))) (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.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat X)) N)) (tptp.aa_int_nat tptp.nat2 A))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int X)) N)) A)))) (forall ((A tptp.int) (X tptp.num) (N tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_int_nat tptp.nat2 A)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat X)) N))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int X)) N))))) (forall ((X tptp.num) (N tptp.nat) (A tptp.int)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat X)) N)) (tptp.aa_int_nat tptp.nat2 A))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int X)) N)) A)))) (forall ((A tptp.int) (X tptp.num) (N tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_int_nat tptp.nat2 A)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat X)) N))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int X)) N))))) (forall ((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 ((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 ((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 ((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 ((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 ((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 ((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)) (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.aa_nat_fun_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)))) (= tptp.zero_zero_nat (tptp.aa_int_nat tptp.nat2 tptp.zero_zero_int)) (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 ((X tptp.int) (Y tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X) Y)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_int_nat tptp.nat2 X)) (tptp.aa_int_nat tptp.nat2 Y))))) (forall ((P tptp.fun_nat_bool)) (= (exists ((X_13 tptp.nat)) (tptp.pp (tptp.aa_nat_bool P X_13))) (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 ((P tptp.fun_nat_bool)) (= (forall ((X_13 tptp.nat)) (tptp.pp (tptp.aa_nat_bool P X_13))) (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 ((Z tptp.int) (Z5 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.pp (tptp.aa_int_bool _let_1 Z)) (=> (tptp.pp (tptp.aa_int_bool _let_1 Z5)) (= (= (tptp.aa_int_nat tptp.nat2 Z) (tptp.aa_int_nat tptp.nat2 Z5)) (= Z Z5)))))) (= tptp.one_one_nat _let_86) (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 ((Z tptp.complex)) (exists ((A3 tptp.complex) (R2 tptp.real)) (= Z (tptp.aa_complex_complex (tptp.times_times_complex (tptp.real_V4546457046886955230omplex R2)) (tptp.exp_complex A3))))) (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 ((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 ((N tptp.nat) (K tptp.int)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se547839408752420682it_nat N) (tptp.aa_int_nat tptp.nat2 K)) (tptp.aa_int_nat tptp.nat2 (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_se545348938243370406it_int N) K)))) (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 ((R tptp.real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real R) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real (tptp.aa_int_nat tptp.nat2 (tptp.archim7802044766580827645g_real R)))))) (forall ((R tptp.rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat R) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat (tptp.aa_int_nat tptp.nat2 (tptp.archim2889992004027027881ng_rat R)))))) (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 ((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 ((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 ((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 ((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 ((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 ((M tptp.nat) (K 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_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 ((N tptp.nat) (A tptp.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 ((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.archim7802044766580827645g_real X)))))) (forall ((N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)) N)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N) (tptp.aa_nat_nat tptp.bit_se2002935070580805687sk_nat N))))) (forall ((R tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) R)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real (tptp.aa_int_nat tptp.nat2 (tptp.archim6058952711729229775r_real R)))) R)))) (forall ((R tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) R)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat (tptp.aa_int_nat tptp.nat2 (tptp.archim3151403230148437115or_rat R)))) R)))) (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 ((N5 tptp.nat)) (=> (= I (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N5)) (tptp.pp (tptp.aa_nat_bool P N5)))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int I) tptp.zero_zero_int)) (tptp.pp (tptp.aa_nat_bool P tptp.zero_zero_nat)))))) (forall ((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.archim6058952711729229775r_real A))) (tptp.aa_int_nat tptp.nat2 (tptp.archim6058952711729229775r_real B)))) (tptp.aa_int_nat tptp.nat2 (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.archim3151403230148437115or_rat A))) (tptp.aa_int_nat tptp.nat2 (tptp.archim3151403230148437115or_rat B)))) (tptp.aa_int_nat tptp.nat2 (tptp.archim3151403230148437115or_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) B)))))) (forall ((K tptp.int) (N tptp.nat)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) K)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N) (tptp.aa_int_nat tptp.nat2 K))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N)) K))))) (forall ((Z tptp.int) (Z5 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.pp (tptp.aa_int_bool _let_1 Z)) (=> (tptp.pp (tptp.aa_int_bool _let_1 Z5)) (= (tptp.aa_int_nat tptp.nat2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int Z) Z5)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_int_nat tptp.nat2 Z)) (tptp.aa_int_nat tptp.nat2 Z5))))))) (forall ((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 ((Z tptp.int) (Z5 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) Z)) (= (tptp.aa_int_nat tptp.nat2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int Z) Z5)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_int_nat tptp.nat2 Z)) (tptp.aa_int_nat tptp.nat2 Z5))))) (forall ((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 ((Z5 tptp.int) (Z tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) Z5)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Z5) Z)) (= (tptp.aa_int_nat tptp.nat2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int Z) Z5)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_int_nat tptp.nat2 Z)) (tptp.aa_int_nat tptp.nat2 Z5)))))) (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.pp (tptp.aa_int_bool _let_1 X)) (=> (tptp.pp (tptp.aa_int_bool _let_1 Y)) (= (tptp.aa_int_nat tptp.nat2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int X) Y)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_int_nat tptp.nat2 X)) (tptp.aa_int_nat tptp.nat2 Y))))))) (forall ((K tptp.int) (L tptp.int)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_int_nat tptp.nat2 (tptp.aa_int_int tptp.abs_abs_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int K) L)))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_int_nat tptp.nat2 (tptp.aa_int_int tptp.abs_abs_int K))) (tptp.aa_int_nat tptp.nat2 (tptp.aa_int_int tptp.abs_abs_int L)))))) (forall ((Y tptp.int) (X tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) Y)) (= (tptp.aa_int_nat tptp.nat2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int X) Y)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_int_nat tptp.nat2 X)) (tptp.aa_int_nat tptp.nat2 Y))))) (forall ((X tptp.int) (Y tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) X)) (= (tptp.aa_int_nat tptp.nat2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int X) Y)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_int_nat tptp.nat2 X)) (tptp.aa_int_nat tptp.nat2 Y))))) (forall ((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 ((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.archim6058952711729229775r_real X)) tptp.zero_zero_nat))) (forall ((Z tptp.int) (N tptp.nat)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) Z)) (= (tptp.aa_int_nat tptp.nat2 (tptp.aa_nat_int (tptp.power_power_int Z) N)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_int_nat tptp.nat2 Z)) N)))) (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.pp (tptp.aa_int_bool _let_1 X)) (=> (tptp.pp (tptp.aa_int_bool _let_1 Y)) (= (tptp.aa_int_nat tptp.nat2 (tptp.modulo_modulo_int X Y)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_int_nat tptp.nat2 X)) (tptp.aa_int_nat tptp.nat2 Y))))))) (forall ((K tptp.int) (L tptp.int)) (let ((_let_1 (tptp.aa_int_int tptp.abs_abs_int L))) (let ((_let_2 (tptp.aa_int_int tptp.abs_abs_int K))) (= (tptp.aa_int_int (tptp.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))))))) (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.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.archim6058952711729229775r_real A)))))) (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.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_int_nat tptp.nat2 _let_2)) (tptp.aa_int_nat tptp.nat2 _let_1))))))) (forall ((K tptp.int) (N tptp.nat)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) K)) (= (tptp.aa_int_nat tptp.nat2 (tptp.aa_int_int (tptp.bit_se2923211474154528505it_int N) K)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se2925701944663578781it_nat N) (tptp.aa_int_nat tptp.nat2 K))))) (forall ((K tptp.int) (N tptp.nat)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) K)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se2925701944663578781it_nat N) (tptp.aa_int_nat tptp.nat2 K)) (tptp.aa_int_nat tptp.nat2 (tptp.aa_int_int (tptp.bit_se2923211474154528505it_int N) K))))) (forall ((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.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N) tptp.zero_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) (N tptp.nat)) (let ((_let_1 (tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger 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 ((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.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger 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))) (= (tptp.aa_int_nat tptp.nat2 _let_68) _let_85) (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 ((K tptp.int)) (not (forall ((N2 tptp.nat)) (let ((_let_1 (tptp.bit_se1146084159140164899it_int K))) (=> (forall ((M3 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) M3)) (= (tptp.pp (tptp.aa_nat_bool _let_1 M3)) (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 ((Z tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) Z)) (= (tptp.aa_nat_nat tptp.suc (tptp.aa_int_nat tptp.nat2 Z)) (tptp.aa_int_nat tptp.nat2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int tptp.one_one_int) Z))))) (forall ((W tptp.int) (M tptp.nat)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) W)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_int_nat tptp.nat2 W)) M)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int W) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int M)))))) (forall ((Z tptp.int) (Z5 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Z) tptp.zero_zero_int)) (= (tptp.aa_int_nat tptp.nat2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int Z) Z5)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_int_nat tptp.nat2 (tptp.aa_int_int tptp.uminus_uminus_int Z))) (tptp.aa_int_nat tptp.nat2 (tptp.aa_int_int tptp.uminus_uminus_int Z5)))))) (forall ((A tptp.nat) (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 ((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.archim6058952711729229775r_real X)) 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 A) N)) (not (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer _let_1) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger 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.aa_nat_fun_nat_nat tptp.power_power_nat _let_1) N)))))))) (forall ((N tptp.nat)) (= (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat tptp.bit_se2002935070580805687sk_nat N)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N))) (forall ((N tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat tptp.bit_se2002935070580805687sk_nat N)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N)))) (forall ((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.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.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.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 ((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 ((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 ((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 ((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.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger 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.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger 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 ((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_nat tptp.bit_se2002935070580805687sk_nat N) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N)) tptp.one_one_nat))) (forall ((N tptp.nat)) (= (tptp.aa_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 ((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.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger 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.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger 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)) (= (tptp.aa_nat_nat tptp.bit_se2002935070580805687sk_nat N) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N)) tptp.one_one_nat))) (forall ((N tptp.nat)) (= (tptp.aa_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 ((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)) (= (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.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 ((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) (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.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)))))))))))) (= (tptp.cis _let_84) tptp.one_one_complex) (= (tptp.exp_complex (tptp.aa_complex_complex (tptp.times_times_complex (tptp.aa_complex_complex (tptp.times_times_complex _let_83) _let_80)) tptp.imaginary_unit)) tptp.one_one_complex) (= (tptp.exp_complex (tptp.aa_complex_complex _let_81 (tptp.aa_complex_complex _let_82 _let_83))) tptp.one_one_complex) (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 ((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.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.aa_nat_fun_nat_nat tptp.bit_se727722235901077358nd_nat A) A) A)) (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.aa_nat_fun_nat_nat 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) (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.aa_nat_fun_nat_nat tptp.bit_se727722235901077358nd_nat A) B))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se727722235901077358nd_nat _let_1) B) _let_1))) (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_78 _let_77 _let_76 (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)))) (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))) (= (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.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.aa_nat_fun_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.aa_nat_fun_nat_nat tptp.bit_se727722235901077358nd_nat A) tptp.zero_zero_nat) tptp.zero_zero_nat)) (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.uminus_uminus_rat A)) (tptp.uminus_uminus_rat (tptp.aa_rat_rat tptp.inverse_inverse_rat A)))) (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.divide_divide_rat A B)) (tptp.divide_divide_rat B A))) (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.abs_abs_rat (tptp.aa_rat_rat tptp.inverse_inverse_rat A)) (tptp.aa_rat_rat tptp.inverse_inverse_rat (tptp.abs_abs_rat A)))) (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.sgn_sgn_rat (tptp.aa_rat_rat tptp.inverse_inverse_rat A)) (tptp.aa_rat_rat tptp.inverse_inverse_rat (tptp.sgn_sgn_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.sgn_sgn_rat A))) (= (tptp.aa_rat_rat tptp.inverse_inverse_rat _let_1) _let_1))) (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.aa_nat_fun_nat_nat tptp.bit_se2925701944663578781it_nat N))) (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se727722235901077358nd_nat A) B)) (tptp.aa_nat_nat (tptp.aa_nat_fun_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.nat) (B tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.bit_se547839408752420682it_nat N))) (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se727722235901077358nd_nat A) B)) (tptp.aa_nat_nat (tptp.aa_nat_fun_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)) (let ((_let_1 (tptp.aa_nat_fun_int_int tptp.bit_se545348938243370406it_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.code_integer) (B tptp.code_integer)) (let ((_let_1 (tptp.aa_nat6383147911832638789nteger tptp.bit_se7788150548672797655nteger N))) (= (tptp.aa_Cod1783974652533396728nteger _let_1 (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.bit_se3949692690581998587nteger A) B)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.bit_se3949692690581998587nteger (tptp.aa_Cod1783974652533396728nteger _let_1 A)) (tptp.aa_Cod1783974652533396728nteger _let_1 B))))) (forall ((N tptp.nat) (A tptp.code_natural) (B tptp.code_natural)) (let ((_let_1 (tptp.aa_nat5282697797315388251atural tptp.bit_se6611745700429515170atural N))) (= (tptp.aa_Cod4272041906116450446atural _let_1 (tptp.bit_se2773287842338716102atural A B)) (tptp.bit_se2773287842338716102atural (tptp.aa_Cod4272041906116450446atural _let_1 A) (tptp.aa_Cod4272041906116450446atural _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) (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 ((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)) (= (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)) (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.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 ((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 ((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 ((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))))) (= (tptp.real_V1022390504157884413omplex tptp.imaginary_unit) tptp.one_one_real) (forall ((A tptp.real)) (= (tptp.real_V1022390504157884413omplex (tptp.cis A)) tptp.one_one_real)) (= (tptp.cis tptp.zero_zero_real) tptp.one_one_complex) (forall ((X tptp.complex)) (= (tptp.divide1717551699836669952omplex X tptp.imaginary_unit) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.uminus1482373934393186551omplex tptp.imaginary_unit)) X))) (forall ((X tptp.complex)) (let ((_let_1 (tptp.times_times_complex tptp.imaginary_unit))) (= (tptp.aa_complex_complex _let_1 (tptp.aa_complex_complex _let_1 X)) (tptp.uminus1482373934393186551omplex X)))) (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) (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)) (=> (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.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.numeral_numeral_rat W))) (= (tptp.aa_rat_rat tptp.inverse_inverse_rat _let_1) (tptp.divide_divide_rat tptp.one_one_rat _let_1)))) (forall ((Y 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 Y))) tptp.one_one_int)) (forall ((Y tptp.num)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se727722235901077358nd_nat tptp.one_one_nat) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 Y))) 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.aa_nat_fun_nat_nat tptp.bit_se727722235901077358nd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 X))) tptp.one_one_nat) tptp.one_one_nat)) (= (tptp.cis tptp.pi) _let_79) (= (tptp.aa_complex_complex _let_81 tptp.imaginary_unit) _let_79) (forall ((Z tptp.complex) (N tptp.num)) (let ((_let_1 (tptp.numera6690914467698888265omplex N))) (= (tptp.divide1717551699836669952omplex Z (tptp.aa_complex_complex (tptp.times_times_complex _let_1) tptp.imaginary_unit)) (tptp.divide1717551699836669952omplex (tptp.uminus1482373934393186551omplex (tptp.aa_complex_complex (tptp.times_times_complex tptp.imaginary_unit) Z)) _let_1)))) (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.aa_nat_fun_nat_nat tptp.bit_se727722235901077358nd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 X))) tptp.one_one_nat) tptp.zero_zero_nat)) (forall ((Y 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 Y))) tptp.zero_zero_int)) (forall ((Y tptp.num)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se727722235901077358nd_nat tptp.one_one_nat) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 Y))) tptp.zero_zero_nat)) (forall ((W tptp.num)) (let ((_let_1 (tptp.aa_real_real tptp.uminus_uminus_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.uminus_uminus_rat (tptp.numeral_numeral_rat W)))) (= (tptp.aa_rat_rat tptp.inverse_inverse_rat _let_1) (tptp.divide_divide_rat tptp.one_one_rat _let_1)))) (forall ((X tptp.num) (Y 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 Y))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.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 Y))))) (forall ((X tptp.num) (Y tptp.num)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se727722235901077358nd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 X))) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 Y))) (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.aa_nat_fun_nat_nat tptp.bit_se727722235901077358nd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat X)) (tptp.aa_num_nat tptp.numeral_numeral_nat Y))))) (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 ((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 ((X tptp.num) (Y 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 Y))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.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 Y))))) (forall ((X tptp.num) (Y tptp.num)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se727722235901077358nd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 X))) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 Y))) (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.aa_nat_fun_nat_nat tptp.bit_se727722235901077358nd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat X)) (tptp.aa_num_nat tptp.numeral_numeral_nat Y))))) (forall ((X tptp.num) (Y 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 Y))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.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 Y))))) (forall ((X tptp.num) (Y tptp.num)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se727722235901077358nd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 X))) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 Y))) (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.aa_nat_fun_nat_nat tptp.bit_se727722235901077358nd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat X)) (tptp.aa_num_nat tptp.numeral_numeral_nat Y))))) (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)) (= (tptp.aa_nat_complex (tptp.power_power_complex tptp.imaginary_unit) _let_2) _let_79) (= (tptp.cis _let_48) tptp.imaginary_unit) (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))) (forall ((X tptp.num) (Y 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 Y))) (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 Y)))))) (forall ((X tptp.num) (Y tptp.num)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se727722235901077358nd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 X))) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 Y))) (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.aa_nat_fun_nat_nat tptp.bit_se727722235901077358nd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat X)) (tptp.aa_num_nat tptp.numeral_numeral_nat Y)))))) (= (tptp.exp_complex (tptp.aa_complex_complex _let_82 tptp.imaginary_unit)) _let_79) (= (tptp.exp_complex (tptp.aa_complex_complex _let_81 _let_80)) _let_79) (= (tptp.cis _let_52) _let_72) (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.aa_nat_fun_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)) (= (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)))) _let_78 _let_77 _let_76 (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))) (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)) (=> (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)) (=> (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 ((Y tptp.real) (X tptp.real)) (let ((_let_1 (tptp.aa_real_real tptp.inverse_inverse_real Y))) (let ((_let_2 (tptp.aa_rea7340605660300375871l_real tptp.times_times_real X))) (=> (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real Y) X) (tptp.aa_real_real _let_2 Y)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real _let_1) X) (tptp.aa_real_real _let_2 _let_1)))))) (forall ((Y tptp.complex) (X tptp.complex)) (let ((_let_1 (tptp.invers8013647133539491842omplex Y))) (let ((_let_2 (tptp.times_times_complex X))) (=> (= (tptp.aa_complex_complex (tptp.times_times_complex Y) X) (tptp.aa_complex_complex _let_2 Y)) (= (tptp.aa_complex_complex (tptp.times_times_complex _let_1) X) (tptp.aa_complex_complex _let_2 _let_1)))))) (forall ((Y tptp.rat) (X tptp.rat)) (let ((_let_1 (tptp.aa_rat_rat tptp.inverse_inverse_rat Y))) (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 Y) X) (tptp.aa_rat_rat _let_2 Y)) (= (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 ((M tptp.nat) (N tptp.nat)) (= (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_nat (tptp.aa_nat_fun_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.aa_nat_fun_nat_nat tptp.bit_se727722235901077358nd_nat M) N)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se727722235901077358nd_nat (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat M)) (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat N)))) (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 ((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.aa_nat_fun_nat_nat tptp.bit_se727722235901077358nd_nat A))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_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.aa_nat_fun_nat_nat tptp.bit_se727722235901077358nd_nat B) 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.aa_nat_fun_nat_nat tptp.bit_se727722235901077358nd_nat A) B) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se727722235901077358nd_nat B) A))) (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.aa_nat_fun_nat_nat tptp.bit_se727722235901077358nd_nat B))) (let ((_let_2 (tptp.aa_nat_fun_nat_nat 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.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.real_V1022390504157884413omplex (tptp.invers8013647133539491842omplex A)) (tptp.aa_real_real tptp.inverse_inverse_real (tptp.real_V1022390504157884413omplex A))))) (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.inverse_inverse_real A)) N) (tptp.aa_real_real tptp.inverse_inverse_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real A) N)))) (forall ((A tptp.complex) (N tptp.nat)) (= (tptp.aa_nat_complex (tptp.power_power_complex (tptp.invers8013647133539491842omplex A)) N) (tptp.invers8013647133539491842omplex (tptp.aa_nat_complex (tptp.power_power_complex A) N)))) (forall ((A tptp.rat) (N tptp.nat)) (= (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_rat_rat tptp.inverse_inverse_rat A)) N) (tptp.aa_rat_rat tptp.inverse_inverse_rat (tptp.aa_nat_rat (tptp.power_power_rat A) N)))) (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 ((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 ((B tptp.real)) (= (tptp.cis B) (tptp.exp_complex (tptp.aa_complex_complex (tptp.times_times_complex tptp.imaginary_unit) (tptp.real_V4546457046886955230omplex B))))) (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)))) (not (= tptp.imaginary_unit tptp.one_one_complex)) (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 ((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)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.bit_se1148574629649215175it_nat (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)) (tptp.aa_nat_nat tptp.suc N))))) (forall ((N tptp.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 ((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.uminus_uminus_rat A)) (tptp.uminus_uminus_rat (tptp.aa_rat_rat tptp.inverse_inverse_rat A))))) (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))) (= (tptp.aa_real_real tptp.inverse_inverse_real _let_75) _let_75) (= (tptp.invers8013647133539491842omplex _let_74) _let_74) (= (tptp.aa_rat_rat tptp.inverse_inverse_rat _let_73) _let_73) (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.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.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.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.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.abs_abs_rat (tptp.aa_rat_rat tptp.inverse_inverse_rat A)) (tptp.aa_rat_rat tptp.inverse_inverse_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.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.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.int) (Y tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.pp (tptp.aa_int_bool _let_1 X)) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se725231765392027082nd_int X) Y)))))) (forall ((X tptp.int) (Y tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) X)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se725231765392027082nd_int X) Y)) X)))) (forall ((Y tptp.int) (X tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) Y)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se725231765392027082nd_int X) Y)) Y)))) (forall ((Y tptp.int) (Z tptp.int) (Ya tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) Y)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Y) Z)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se725231765392027082nd_int Y) Ya)) Z))))) (forall ((Y tptp.int) (Z tptp.int) (X tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) Y)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Y) Z)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se725231765392027082nd_int X) Y)) Z))))) (forall ((X tptp.real) (Y tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real X) Y) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real X) (tptp.aa_real_real tptp.inverse_inverse_real Y)))) (forall ((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.aa_nat_fun_nat_nat tptp.bit_se2925701944663578781it_nat N) A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se727722235901077358nd_nat A) (tptp.aa_nat_nat tptp.bit_se2002935070580805687sk_nat N)))) (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 ((A tptp.real) (B tptp.real)) (= (tptp.aa_complex_complex (tptp.times_times_complex (tptp.cis A)) (tptp.cis B)) (tptp.cis (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) B)))) (forall ((W tptp.complex) (Z tptp.complex)) (let ((_let_1 (tptp.times_times_complex tptp.imaginary_unit))) (= (= (tptp.aa_complex_complex _let_1 W) Z) (= W (tptp.uminus1482373934393186551omplex (tptp.aa_complex_complex _let_1 Z)))))) (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 ((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 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 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 ((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)) (=> (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.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) (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.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.minus_minus_rat B A))) _let_1))))))) (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.divide_divide_rat tptp.one_one_rat A)))) (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 ((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 ((Y tptp.int) (Z tptp.int) (Ya tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) Y)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Y) Z)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se725231765392027082nd_int Y) Ya)) Z))))) (forall ((Y tptp.int) (Z tptp.int) (X tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) Y)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Y) 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) Y)) Z))))) (forall ((M tptp.nat) (Q2 tptp.nat) (N tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.bit_se1148574629649215175it_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se547839408752420682it_nat M) Q2)) N)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.bit_se1148574629649215175it_nat Q2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) M)))))) (= tptp.imaginary_unit (tptp.complex2 tptp.zero_zero_real tptp.one_one_real)) (forall ((X tptp.real) (Y tptp.real)) (= (= (tptp.complex2 X Y) tptp.imaginary_unit) (and (= X tptp.zero_zero_real) (= Y tptp.one_one_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.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.aa_nat_fun_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)))))) (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 ((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 ((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.minus_minus_rat _let_2 _let_1) (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.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.real) (B tptp.real)) (= (tptp.aa_complex_complex (tptp.times_times_complex tptp.imaginary_unit) (tptp.complex2 A B)) (tptp.complex2 (tptp.aa_real_real tptp.uminus_uminus_real B) A))) (forall ((A tptp.real) (B tptp.real)) (= (tptp.aa_complex_complex (tptp.times_times_complex (tptp.complex2 A B)) tptp.imaginary_unit) (tptp.complex2 (tptp.aa_real_real tptp.uminus_uminus_real B) 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.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se727722235901077358nd_nat A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se547839408752420682it_nat N) tptp.one_one_nat)) tptp.zero_zero_nat)))) (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.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_se545348938243370406it_int N) tptp.one_one_int)) tptp.zero_zero_int)))) (forall ((A tptp.code_integer) (N tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.bit_se9216721137139052372nteger A) N)) (not (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.bit_se3949692690581998587nteger A) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_nat6383147911832638789nteger tptp.bit_se7788150548672797655nteger N) tptp.one_one_Code_integer)) tptp.zero_z3403309356797280102nteger)))) (forall ((A tptp.code_natural) (N tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.bit_se8040316288895769887atural A) N)) (not (= (tptp.bit_se2773287842338716102atural A (tptp.aa_Cod4272041906116450446atural (tptp.aa_nat5282697797315388251atural tptp.bit_se6611745700429515170atural N) tptp.one_one_Code_natural)) tptp.zero_z2226904508553997617atural)))) (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 ((P tptp.fun_real_bool) (E tptp.real)) (=> (forall ((D2 tptp.real) (E2 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real D2) E2)) (=> (tptp.pp (tptp.aa_real_bool P D2)) (tptp.pp (tptp.aa_real_bool P E2))))) (=> (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_real_bool P (tptp.aa_real_real tptp.inverse_inverse_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real (tptp.aa_nat_nat tptp.suc N2)))))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) E)) (tptp.pp (tptp.aa_real_bool P E)))))) (forall ((P tptp.fun_real_bool) (E tptp.real)) (=> (forall ((D2 tptp.real) (E2 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real D2) E2)) (=> (tptp.pp (tptp.aa_real_bool P D2)) (tptp.pp (tptp.aa_real_bool P E2))))) (=> (forall ((N2 tptp.nat)) (=> (not (= N2 tptp.zero_zero_nat)) (tptp.pp (tptp.aa_real_bool P (tptp.aa_real_real tptp.inverse_inverse_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N2)))))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) E)) (tptp.pp (tptp.aa_real_bool P E)))))) (forall ((E tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) E)) (exists ((N5 tptp.nat)) (let ((_let_1 (tptp.aa_real_real tptp.inverse_inverse_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N5)))) (and (not (= N5 tptp.zero_zero_nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) _let_1)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real _let_1) E))))))) (forall ((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 ((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 ((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.code_natural)) (= (tptp.bit_se2773287842338716102atural A tptp.one_one_Code_natural) (tptp.modulo8411746178871703098atural A (tptp.numera5444537566228673987atural (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.aa_nat_fun_nat_nat tptp.bit_se727722235901077358nd_nat A) tptp.one_one_nat) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (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.code_natural)) (= (tptp.bit_se2773287842338716102atural tptp.one_one_Code_natural A) (tptp.modulo8411746178871703098atural A (tptp.numera5444537566228673987atural (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.aa_nat_fun_nat_nat tptp.bit_se727722235901077358nd_nat tptp.one_one_nat) A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (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 ((R tptp.real)) (= (tptp.aa_complex_complex (tptp.times_times_complex (tptp.real_V4546457046886955230omplex R)) tptp.imaginary_unit) (tptp.complex2 tptp.zero_zero_real R))) (forall ((R tptp.real)) (= (tptp.aa_complex_complex (tptp.times_times_complex tptp.imaginary_unit) (tptp.real_V4546457046886955230omplex R)) (tptp.complex2 tptp.zero_zero_real R))) (forall ((A tptp.real) (X tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.log2 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 ((A tptp.real) (B tptp.real)) (= (tptp.complex2 A B) (tptp.plus_plus_complex (tptp.real_V4546457046886955230omplex A) (tptp.aa_complex_complex (tptp.times_times_complex tptp.imaginary_unit) (tptp.real_V4546457046886955230omplex B))))) (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.aa_nat_fun_nat_nat tptp.bit_se727722235901077358nd_nat A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N)) tptp.zero_zero_nat) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.bit_se1148574629649215175it_nat A) 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.bit_se1148574629649215175it_nat M) N)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat _let_1) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat M) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat _let_1) N)))))))) (forall ((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.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 ((Z tptp.complex)) (exists ((R2 tptp.real) (A3 tptp.real)) (= Z (tptp.aa_complex_complex (tptp.times_times_complex (tptp.real_V4546457046886955230omplex R2)) (tptp.plus_plus_complex (tptp.real_V4546457046886955230omplex (tptp.aa_real_real tptp.cos_real A3)) (tptp.aa_complex_complex (tptp.times_times_complex tptp.imaginary_unit) (tptp.real_V4546457046886955230omplex (tptp.aa_real_real tptp.sin_real A3)))))))) (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.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) (tptp.aa_real_real tptp.inverse_inverse_real X)))))) (forall ((X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) X)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real tptp.inverse_inverse_real (tptp.aa_real_real tptp.sqrt X))) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_real_real tptp.inverse_inverse_real X)))) (forall ((X tptp.real)) (= (tptp.aa_real_real tptp.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.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 ((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 ((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.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))))))) (forall ((X tptp.real)) (let ((_let_1 (tptp.aa_real_real tptp.exp_real X))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real X)) (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real _let_1) (tptp.aa_real_real tptp.inverse_inverse_real _let_1))) (tptp.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 ((A tptp.real)) (= (tptp.real_V1022390504157884413omplex (tptp.plus_plus_complex (tptp.real_V4546457046886955230omplex (tptp.aa_real_real tptp.cos_real A)) (tptp.aa_complex_complex (tptp.times_times_complex tptp.imaginary_unit) (tptp.real_V4546457046886955230omplex (tptp.aa_real_real tptp.sin_real A))))) tptp.one_one_real)) (forall ((R tptp.real) (A tptp.real)) (= (tptp.real_V1022390504157884413omplex (tptp.aa_complex_complex (tptp.times_times_complex (tptp.real_V4546457046886955230omplex R)) (tptp.plus_plus_complex (tptp.real_V4546457046886955230omplex (tptp.aa_real_real tptp.cos_real A)) (tptp.aa_complex_complex (tptp.times_times_complex tptp.imaginary_unit) (tptp.real_V4546457046886955230omplex (tptp.aa_real_real tptp.sin_real A)))))) (tptp.aa_real_real tptp.abs_abs_real R))) (= (tptp.arg _let_72) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.pi)) _let_46)) (= (tptp.csqrt tptp.imaginary_unit) (tptp.divide1717551699836669952omplex (tptp.plus_plus_complex tptp.one_one_complex tptp.imaginary_unit) (tptp.real_V4546457046886955230omplex _let_71))) (= (tptp.arg tptp.imaginary_unit) _let_48) (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.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))))) (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.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))) tptp.pi)) N)) tptp.one_one_complex))) (= (tptp.aa_real_real tptp.sinh_real tptp.zero_zero_real) tptp.zero_zero_real) (forall ((X tptp.real)) (= (tptp.member_real (tptp.aa_real_real tptp.archim2898591450579166408c_real X) tptp.ring_1_Ints_real) (tptp.member_real X tptp.ring_1_Ints_real))) (forall ((Z tptp.complex)) (= (= (tptp.csqrt Z) tptp.one_one_complex) (= Z tptp.one_one_complex))) (= (tptp.csqrt tptp.one_one_complex) tptp.one_one_complex) (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.archimedean_frac_rat X) tptp.zero_zero_rat) (tptp.member_rat X tptp.ring_1_Ints_rat))) (forall ((X tptp.real) (Y tptp.real)) (=> (or (tptp.member_real X tptp.ring_1_Ints_real) (tptp.member_real Y tptp.ring_1_Ints_real)) (= (tptp.archim6058952711729229775r_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) Y)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.archim6058952711729229775r_real X)) (tptp.archim6058952711729229775r_real Y))))) (forall ((X tptp.rat) (Y tptp.rat)) (=> (or (tptp.member_rat X tptp.ring_1_Ints_rat) (tptp.member_rat Y tptp.ring_1_Ints_rat)) (= (tptp.archim3151403230148437115or_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat X) Y)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.archim3151403230148437115or_rat X)) (tptp.archim3151403230148437115or_rat Y))))) (forall ((X tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) (tptp.aa_real_real tptp.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.archimedean_frac_rat X))) (not (tptp.member_rat X tptp.ring_1_Ints_rat)))) (forall ((Y tptp.num)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se727722235901077358nd_nat (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 Y))) tptp.zero_zero_nat)) (forall ((X tptp.num)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se727722235901077358nd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 X))) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)) tptp.zero_zero_nat)) (forall ((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 ((Y tptp.num)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se727722235901077358nd_nat (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 Y))) tptp.one_one_nat)) (forall ((X tptp.num)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se727722235901077358nd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 X))) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)) tptp.one_one_nat)) (forall ((N tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se727722235901077358nd_nat N) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat N) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (forall ((N tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se727722235901077358nd_nat (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)) N) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat N) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (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.numeral_numeral_real N) tptp.ring_1_Ints_real)) (forall ((N tptp.num)) (tptp.member_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)))) (tptp.member_complex tptp.one_one_complex tptp.ring_1_Ints_complex) (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) (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)))) (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.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 ((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.rat)) (= (tptp.member_rat (tptp.uminus_uminus_rat X) tptp.ring_1_Ints_rat) (tptp.member_rat X tptp.ring_1_Ints_rat))) (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 ((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.rat)) (=> (tptp.member_rat A tptp.ring_1_Ints_rat) (tptp.member_rat (tptp.uminus_uminus_rat A) tptp.ring_1_Ints_rat))) (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 ((X tptp.complex) (Y tptp.complex)) (= (tptp.divide1717551699836669952omplex X Y) (tptp.aa_complex_complex (tptp.times_times_complex X) (tptp.invers8013647133539491842omplex Y)))) (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.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.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 ((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 ((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.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_complex (tptp.ring_17405671764205052669omplex Z) tptp.ring_1_Ints_complex)) (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.ring_1_of_int_real Z) tptp.ring_1_Ints_real)) (forall ((Z tptp.int)) (tptp.member_rat (tptp.ring_1_of_int_rat Z) tptp.ring_1_Ints_rat)) (forall ((Q2 tptp.complex) (P tptp.fun_complex_bool)) (=> (tptp.member_complex Q2 tptp.ring_1_Ints_complex) (=> (forall ((Z4 tptp.int)) (tptp.pp (tptp.aa_complex_bool P (tptp.ring_17405671764205052669omplex Z4)))) (tptp.pp (tptp.aa_complex_bool P Q2))))) (forall ((Q2 tptp.int) (P tptp.fun_int_bool)) (=> (tptp.member_int Q2 tptp.ring_1_Ints_int) (=> (forall ((Z4 tptp.int)) (tptp.pp (tptp.aa_int_bool P (tptp.ring_1_of_int_int Z4)))) (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 ((Z4 tptp.int)) (tptp.pp (tptp.aa_real_bool P (tptp.ring_1_of_int_real Z4)))) (tptp.pp (tptp.aa_real_bool P Q2))))) (forall ((Q2 tptp.rat) (P tptp.fun_rat_bool)) (=> (tptp.member_rat Q2 tptp.ring_1_Ints_rat) (=> (forall ((Z4 tptp.int)) (tptp.pp (tptp.aa_rat_bool P (tptp.ring_1_of_int_rat Z4)))) (tptp.pp (tptp.aa_rat_bool P Q2))))) (forall ((Q2 tptp.complex)) (=> (tptp.member_complex Q2 tptp.ring_1_Ints_complex) (not (forall ((Z4 tptp.int)) (not (= Q2 (tptp.ring_17405671764205052669omplex Z4))))))) (forall ((Q2 tptp.int)) (=> (tptp.member_int Q2 tptp.ring_1_Ints_int) (not (forall ((Z4 tptp.int)) (not (= Q2 (tptp.ring_1_of_int_int Z4))))))) (forall ((Q2 tptp.real)) (=> (tptp.member_real Q2 tptp.ring_1_Ints_real) (not (forall ((Z4 tptp.int)) (not (= Q2 (tptp.ring_1_of_int_real Z4))))))) (forall ((Q2 tptp.rat)) (=> (tptp.member_rat Q2 tptp.ring_1_Ints_rat) (not (forall ((Z4 tptp.int)) (not (= Q2 (tptp.ring_1_of_int_rat Z4))))))) (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 ((M tptp.nat) (N tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se727722235901077358nd_nat M) N) (tptp.aa_int_nat tptp.nat2 (tptp.aa_int_int (tptp.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 ((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.ring_1_of_int_real A)) (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.divide_divide_rat (tptp.ring_1_of_int_rat A) (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)) (=> (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.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.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.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.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.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) (Y tptp.code_integer)) (=> (tptp.member_Code_integer X tptp.ring_11222124179247155820nteger) (=> (tptp.member_Code_integer Y tptp.ring_11222124179247155820nteger) (= (= X Y) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.abs_abs_Code_integer (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.minus_8373710615458151222nteger X) Y))) tptp.one_one_Code_integer)))))) (forall ((X tptp.real) (Y tptp.real)) (=> (tptp.member_real X tptp.ring_1_Ints_real) (=> (tptp.member_real Y tptp.ring_1_Ints_real) (= (= X Y) (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))) tptp.one_one_real)))))) (forall ((X tptp.rat) (Y tptp.rat)) (=> (tptp.member_rat X tptp.ring_1_Ints_rat) (=> (tptp.member_rat Y tptp.ring_1_Ints_rat) (= (= X Y) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.abs_abs_rat (tptp.minus_minus_rat X Y))) tptp.one_one_rat)))))) (forall ((X tptp.int) (Y tptp.int)) (=> (tptp.member_int X tptp.ring_1_Ints_int) (=> (tptp.member_int Y tptp.ring_1_Ints_int) (= (= X Y) (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) Y))) 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)) (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.archimedean_frac_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.minus_minus_rat tptp.one_one_rat (tptp.archimedean_frac_rat X)))))))) (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.ring_1_of_int_real (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.archim6058952711729229775r_real A)) (tptp.archim6058952711729229775r_real B)))) (tptp.ring_1_of_int_real (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_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.ring_1_of_int_rat (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.archim6058952711729229775r_real A)) (tptp.archim6058952711729229775r_real B)))) (tptp.ring_1_of_int_rat (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.archim6058952711729229775r_real A)) (tptp.archim6058952711729229775r_real B)))) (tptp.ring_1_of_int_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_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.ring_1_of_int_real (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.archim3151403230148437115or_rat A)) (tptp.archim3151403230148437115or_rat B)))) (tptp.ring_1_of_int_real (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_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.ring_1_of_int_rat (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.archim3151403230148437115or_rat A)) (tptp.archim3151403230148437115or_rat B)))) (tptp.ring_1_of_int_rat (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.archim3151403230148437115or_rat A)) (tptp.archim3151403230148437115or_rat B)))) (tptp.ring_1_of_int_int (tptp.archim3151403230148437115or_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) B)))))))) (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 ((X tptp.rat) (A tptp.rat)) (= (= (tptp.archimedean_frac_rat X) A) (and (tptp.member_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 ((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.ring_1_of_int_real (tptp.archim7802044766580827645g_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) B)))) (tptp.ring_1_of_int_real (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.archim7802044766580827645g_real A)) (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_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.ring_1_of_int_rat (tptp.archim7802044766580827645g_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) B)))) (tptp.ring_1_of_int_rat (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.archim7802044766580827645g_real A)) (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.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.archim7802044766580827645g_real A)) (tptp.archim7802044766580827645g_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.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.ring_1_of_int_real (tptp.archim2889992004027027881ng_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) B)))) (tptp.ring_1_of_int_real (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.archim2889992004027027881ng_rat A)) (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_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.ring_1_of_int_rat (tptp.archim2889992004027027881ng_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) B)))) (tptp.ring_1_of_int_rat (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.archim2889992004027027881ng_rat A)) (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.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.archim2889992004027027881ng_rat A)) (tptp.archim2889992004027027881ng_rat B)))))))) (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.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.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.aa_nat_fun_nat_nat tptp.bit_se727722235901077358nd_nat M) N))) (let ((_let_3 (or (= M tptp.zero_zero_nat) (= N tptp.zero_zero_nat)))) (and (=> _let_3 (= _let_2 tptp.zero_zero_nat)) (=> (not _let_3) (= _let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat M) _let_1)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat N) _let_1))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat _let_1) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se727722235901077358nd_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat M) _let_1)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat N) _let_1))))))))))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat _let_1))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se727722235901077358nd_nat M) N) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.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.aa_nat_fun_nat_nat tptp.bit_se727722235901077358nd_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat M) _let_1)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat N) _let_1)))))))) (forall ((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 ((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.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 ((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.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))))) (forall ((N tptp.nat)) (let ((_let_1 (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se6528837805403552850or_nat N) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N) (tptp.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.aa_nat_fun_nat_nat tptp.bit_se6528837805403552850or_nat (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)) N) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N) (tptp.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.divide_divide_rat A (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat K))) (tptp.aa_nat_rat (tptp.gbinomial_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 ((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.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 ((X tptp.int) (Y 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 Y)) Y))) (forall ((A tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_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.aa_nat_fun_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.aa_nat_fun_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 ((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.aa_nat_fun_nat_nat tptp.bit_se2925701944663578781it_nat N))) (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se6528837805403552850or_nat A) B)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se6528837805403552850or_nat (tptp.aa_nat_nat _let_1 A)) (tptp.aa_nat_nat _let_1 B))))) (forall ((N tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.bit_se547839408752420682it_nat N))) (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se6528837805403552850or_nat A) B)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se6528837805403552850or_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)) (let ((_let_1 (tptp.aa_nat_fun_int_int tptp.bit_se545348938243370406it_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.code_integer) (B tptp.code_integer)) (let ((_let_1 (tptp.aa_nat6383147911832638789nteger tptp.bit_se7788150548672797655nteger N))) (= (tptp.aa_Cod1783974652533396728nteger _let_1 (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.bit_se3222712562003087583nteger A) B)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.bit_se3222712562003087583nteger (tptp.aa_Cod1783974652533396728nteger _let_1 A)) (tptp.aa_Cod1783974652533396728nteger _let_1 B))))) (forall ((N tptp.nat) (A tptp.code_natural) (B tptp.code_natural)) (let ((_let_1 (tptp.aa_nat5282697797315388251atural tptp.bit_se6611745700429515170atural N))) (= (tptp.aa_Cod4272041906116450446atural _let_1 (tptp.bit_se2046307713759805098atural A B)) (tptp.bit_se2046307713759805098atural (tptp.aa_Cod4272041906116450446atural _let_1 A) (tptp.aa_Cod4272041906116450446atural _let_1 B))))) (= (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 ((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.aa_nat_fun_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.aa_nat_fun_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.num) (Y tptp.num)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se6528837805403552850or_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 X))) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 Y))) (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.aa_nat_fun_nat_nat tptp.bit_se6528837805403552850or_nat (tptp.aa_num_nat tptp.numeral_numeral_nat X)) (tptp.aa_num_nat tptp.numeral_numeral_nat Y))))) (forall ((X tptp.num) (Y 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 Y))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.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 Y))))) (forall ((X tptp.num)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se6528837805403552850or_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 X))) tptp.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)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se6528837805403552850or_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 X))) tptp.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 ((Y tptp.num)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se6528837805403552850or_nat tptp.one_one_nat) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 Y))) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 Y)))) (forall ((Y tptp.num)) (= (tptp.aa_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 Y))) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 Y)))) (forall ((Y tptp.num)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se6528837805403552850or_nat tptp.one_one_nat) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 Y))) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 Y)))) (forall ((Y 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 Y))) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit1 Y)))) (forall ((X tptp.num) (Y tptp.num)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se6528837805403552850or_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 X))) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 Y))) (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.aa_nat_fun_nat_nat tptp.bit_se6528837805403552850or_nat (tptp.aa_num_nat tptp.numeral_numeral_nat X)) (tptp.aa_num_nat tptp.numeral_numeral_nat Y))))) (forall ((X tptp.num) (Y 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 Y))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.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 Y))))) (forall ((X tptp.num)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se6528837805403552850or_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 X))) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 X)))) (forall ((X tptp.num)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se6528837805403552850or_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 X))) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 X)))) (forall ((Y tptp.num)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se6528837805403552850or_nat (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 Y))) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 Y)))) (forall ((Y tptp.num)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se6528837805403552850or_nat (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 Y))) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 Y)))) (forall ((X tptp.num) (Y tptp.num)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se6528837805403552850or_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 X))) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 Y))) (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.aa_nat_fun_nat_nat tptp.bit_se6528837805403552850or_nat (tptp.aa_num_nat tptp.numeral_numeral_nat X)) (tptp.aa_num_nat tptp.numeral_numeral_nat Y)))))) (forall ((X tptp.num) (Y 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 Y))) (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 Y)))))) (forall ((X tptp.num) (Y tptp.num)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se6528837805403552850or_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 X))) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 Y))) (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.aa_nat_fun_nat_nat tptp.bit_se6528837805403552850or_nat (tptp.aa_num_nat tptp.numeral_numeral_nat X)) (tptp.aa_num_nat tptp.numeral_numeral_nat Y)))))) (forall ((X tptp.num) (Y 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 Y))) (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 Y)))))) (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)))) (forall ((N tptp.nat) (K tptp.nat)) (= (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex (tptp.aa_nat_nat (tptp.aa_nat_fun_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.aa_nat_fun_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.aa_nat_fun_nat_nat tptp.gbinomial_nat N) K)) (tptp.aa_nat_rat (tptp.gbinomial_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat N)) K))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.bit_se6528837805403552850or_nat A))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_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.aa_nat_fun_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.nat) (B tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se6528837805403552850or_nat A) B) (tptp.aa_nat_nat (tptp.aa_nat_fun_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 ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.bit_se6528837805403552850or_nat B))) (let ((_let_2 (tptp.aa_nat_fun_nat_nat 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 ((M tptp.nat) (N tptp.nat)) (= (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se6528837805403552850or_nat M) N)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.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.aa_nat_fun_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 ((X tptp.int) (Y 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 Y) Z)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se6526347334894502574or_int (tptp.aa_int_int _let_1 Y)) (tptp.aa_int_int _let_1 Z))))) (forall ((Y 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 Y) 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 Y) X)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se725231765392027082nd_int Z) X)))) (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.aa_nat_fun_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 ((X tptp.real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.one_one_real) (tptp.aa_real_real tptp.cosh_real X)))) (forall ((N tptp.nat) (K tptp.nat)) (= (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex (tptp.aa_nat_nat (tptp.aa_nat_fun_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.aa_nat_fun_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.aa_nat_fun_nat_nat tptp.binomial N) K)) (tptp.aa_nat_rat (tptp.gbinomial_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat N)) K))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se2161824704523386999it_nat M) N) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se6528837805403552850or_nat N) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se547839408752420682it_nat M) tptp.one_one_nat)))) (forall ((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 ((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.bit_se6528837805403552850or_nat A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se547839408752420682it_nat N) tptp.one_one_nat)))) (forall ((N tptp.nat) (A tptp.int)) (= (tptp.bit_se2159334234014336723it_int N A) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se6526347334894502574or_int A) (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_se545348938243370406it_int N) tptp.one_one_int)))) (forall ((N tptp.nat) (A tptp.code_integer)) (= (tptp.bit_se1345352211410354436nteger N A) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.bit_se3222712562003087583nteger A) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_nat6383147911832638789nteger tptp.bit_se7788150548672797655nteger N) tptp.one_one_Code_integer)))) (forall ((N tptp.nat) (A tptp.code_natural)) (= (tptp.bit_se168947363167071951atural N A) (tptp.bit_se2046307713759805098atural A (tptp.aa_Cod4272041906116450446atural (tptp.aa_nat5282697797315388251atural tptp.bit_se6611745700429515170atural N) tptp.one_one_Code_natural)))) (forall ((X tptp.real) (Y tptp.real)) (= (tptp.aa_real_real tptp.sinh_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) Y)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real tptp.sinh_real X)) (tptp.aa_real_real tptp.cosh_real Y))) (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 Y))))) (forall ((X tptp.real) (Y tptp.real)) (= (tptp.aa_real_real tptp.cosh_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) Y)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real tptp.cosh_real X)) (tptp.aa_real_real tptp.cosh_real Y))) (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 Y))))) (forall ((X tptp.real) (Y tptp.real)) (= (tptp.aa_real_real tptp.sinh_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real X) Y)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real tptp.sinh_real X)) (tptp.aa_real_real tptp.cosh_real Y))) (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 Y))))) (forall ((X tptp.real) (Y tptp.real)) (= (tptp.aa_real_real tptp.cosh_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real X) Y)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real tptp.cosh_real X)) (tptp.aa_real_real tptp.cosh_real Y))) (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 Y))))) (forall ((X tptp.complex)) (= (tptp.plus_plus_complex (tptp.sinh_complex X) (tptp.cosh_complex X)) (tptp.exp_complex X))) (forall ((X tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real tptp.sinh_real X)) (tptp.aa_real_real tptp.cosh_real X)) (tptp.aa_real_real tptp.exp_real X))) (forall ((X tptp.complex)) (= (tptp.plus_plus_complex (tptp.cosh_complex X) (tptp.sinh_complex X)) (tptp.exp_complex X))) (forall ((X tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real tptp.cosh_real X)) (tptp.aa_real_real tptp.sinh_real X)) (tptp.aa_real_real tptp.exp_real X))) (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 ((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.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)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.minus_minus_rat A (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.minus_minus_rat A tptp.one_one_rat)) K)))) (forall ((K tptp.nat) (A tptp.real)) (let ((_let_1 (tptp.aa_nat_real tptp.semiri5074537144036343181t_real K))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real _let_1) A)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real A) _let_1)) K)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.gbinomial_real A) K)))))) (forall ((K tptp.nat) (A tptp.rat)) (let ((_let_1 (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat K))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat _let_1) A)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat (tptp.power_power_rat (tptp.divide_divide_rat A _let_1)) K)) (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.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 ((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.aa_nat_fun_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)) (= (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.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 ((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.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.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 ((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.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 ((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.divide_divide_rat _let_2 (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat _let_1))))))) (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.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)) (= (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.uminus_uminus_rat tptp.one_one_rat)) K)) (tptp.aa_nat_rat (tptp.gbinomial_rat (tptp.minus_minus_rat (tptp.minus_minus_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat K) A) tptp.one_one_rat)) K)))) (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.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.minus_minus_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.minus_minus_rat (tptp.uminus_uminus_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat K)) tptp.one_one_rat)) N))))) (forall ((X tptp.complex) (Y tptp.complex)) (let ((_let_1 (tptp.tanh_complex Y))) (let ((_let_2 (tptp.tanh_complex X))) (=> (not (= (tptp.cosh_complex X) tptp.zero_zero_complex)) (=> (not (= (tptp.cosh_complex Y) tptp.zero_zero_complex)) (= (tptp.tanh_complex (tptp.plus_plus_complex X Y)) (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) (Y tptp.real)) (let ((_let_1 (tptp.aa_real_real tptp.tanh_real Y))) (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 Y) tptp.zero_zero_real)) (= (tptp.aa_real_real tptp.tanh_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) Y)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real _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 ((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.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.uminus_uminus_rat tptp.one_one_rat)) K)) (tptp.aa_nat_rat (tptp.gbinomial_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 ((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.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.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.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.uminus_uminus_rat tptp.one_one_rat)) K)) (tptp.aa_nat_rat (tptp.comm_s4028243227959126397er_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_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 ((A tptp.rat) (K tptp.nat)) (= (tptp.aa_nat_rat (tptp.gbinomial_rat A) K) (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.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 ((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.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 ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se6528837805403552850or_nat M) N))) (let ((_let_3 (= N tptp.zero_zero_nat))) (let ((_let_4 (= M tptp.zero_zero_nat))) (and (=> _let_4 (= _let_2 N)) (=> (not _let_4) (and (=> _let_3 (= _let_2 M)) (=> (not _let_3) (= _let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat M) _let_1)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat N) _let_1))) _let_1)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat _let_1) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se6528837805403552850or_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat M) _let_1)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat N) _let_1)))))))))))))) (forall ((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)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat _let_1))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se6528837805403552850or_nat M) N) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.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.aa_nat_fun_nat_nat tptp.bit_se6528837805403552850or_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat M) _let_1)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat N) _let_1)))))))) (forall ((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.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.minus_8373710615458151222nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger 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.aa_nat_fun_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 ((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.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.minus_8373710615458151222nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger 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.aa_nat_fun_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 ((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 ((X7 tptp.fun_nat_real)) (= (tptp.topolo4055970368930404560y_real X7) (forall ((J3 tptp.nat)) (exists ((M7 tptp.nat)) (forall ((M6 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M7) M6)) (forall ((N5 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M7) N5)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_nat_real X7 M6)) (tptp.aa_nat_real X7 N5)))) (tptp.aa_real_real tptp.inverse_inverse_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real (tptp.aa_nat_nat tptp.suc J3))))))))))))) (forall ((Z tptp.complex)) (= (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.real_V1022390504157884413omplex Z)) (tptp.re Z))) (tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))))) (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.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 ((X tptp.complex)) (= (tptp.sinh_complex X) (tptp.real_V2046097035970521341omplex (tptp.aa_real_real tptp.inverse_inverse_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.cosh_real X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.real_V1485227260804924795R_real (tptp.aa_real_real tptp.inverse_inverse_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 ((X tptp.complex)) (= (tptp.cosh_complex X) (tptp.real_V2046097035970521341omplex (tptp.aa_real_real tptp.inverse_inverse_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 ((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.real_V1022390504157884413omplex B)) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))))) (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) (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)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.real_V1485227260804924795R_real A) tptp.zero_zero_real) tptp.zero_zero_real)) (forall ((A tptp.real)) (= (tptp.real_V2046097035970521341omplex A tptp.zero_zero_complex) tptp.zero_zero_complex)) (forall ((X tptp.real) (A tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.times_times_real X))) (let ((_let_2 (tptp.aa_rea7340605660300375871l_real tptp.real_V1485227260804924795R_real A))) (= (tptp.aa_real_real _let_1 (tptp.aa_real_real _let_2 Y)) (tptp.aa_real_real _let_2 (tptp.aa_real_real _let_1 Y)))))) (forall ((X tptp.complex) (A tptp.real) (Y tptp.complex)) (let ((_let_1 (tptp.times_times_complex X))) (= (tptp.aa_complex_complex _let_1 (tptp.real_V2046097035970521341omplex A Y)) (tptp.real_V2046097035970521341omplex A (tptp.aa_complex_complex _let_1 Y))))) (forall ((A tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.real_V1485227260804924795R_real A))) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real _let_1 X)) Y) (tptp.aa_real_real _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real X) Y))))) (forall ((A tptp.real) (X tptp.complex) (Y tptp.complex)) (= (tptp.aa_complex_complex (tptp.times_times_complex (tptp.real_V2046097035970521341omplex A X)) Y) (tptp.real_V2046097035970521341omplex A (tptp.aa_complex_complex (tptp.times_times_complex X) Y)))) (forall ((X tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.real_V1485227260804924795R_real tptp.one_one_real) X) X)) (forall ((X tptp.complex)) (= (tptp.real_V2046097035970521341omplex tptp.one_one_real X) 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 ((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 ((N tptp.nat)) (= (tptp.re (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex N)) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N))) (forall ((X tptp.complex) (Y tptp.complex)) (= (tptp.cnj (tptp.aa_complex_complex (tptp.times_times_complex X) Y)) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.cnj X)) (tptp.cnj Y)))) (forall ((Z tptp.complex)) (= (= (tptp.cnj Z) tptp.one_one_complex) (= Z tptp.one_one_complex))) (= (tptp.cnj tptp.one_one_complex) tptp.one_one_complex) (forall ((X tptp.complex) (N tptp.nat)) (= (tptp.cnj (tptp.aa_nat_complex (tptp.power_power_complex X) N)) (tptp.aa_nat_complex (tptp.power_power_complex (tptp.cnj X)) N))) (forall ((X tptp.complex) (Y tptp.complex)) (= (tptp.cnj (tptp.plus_plus_complex X Y)) (tptp.plus_plus_complex (tptp.cnj X) (tptp.cnj Y)))) (forall ((X tptp.complex) (Y tptp.complex)) (= (tptp.cnj (tptp.minus_minus_complex X Y)) (tptp.minus_minus_complex (tptp.cnj X) (tptp.cnj Y)))) (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 ((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 ((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 ((X tptp.complex)) (= (tptp.real_V2046097035970521341omplex tptp.zero_zero_real X) tptp.zero_zero_complex)) (forall ((B tptp.real) (U tptp.real) (A tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.real_V1485227260804924795R_real U))) (= (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real B) (tptp.aa_real_real _let_1 A)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) (tptp.aa_real_real _let_1 B))) (or (= A B) (= U tptp.one_one_real))))) (forall ((B tptp.complex) (U tptp.real) (A tptp.complex)) (= (= (tptp.plus_plus_complex B (tptp.real_V2046097035970521341omplex U A)) (tptp.plus_plus_complex A (tptp.real_V2046097035970521341omplex U B))) (or (= A B) (= U tptp.one_one_real)))) (forall ((X tptp.real) (Y 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.real_V1485227260804924795R_real X) Y)) N) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.real_V1485227260804924795R_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) N)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Y) N)))) (forall ((X tptp.real) (Y tptp.complex) (N tptp.nat)) (= (tptp.aa_nat_complex (tptp.power_power_complex (tptp.real_V2046097035970521341omplex X Y)) N) (tptp.real_V2046097035970521341omplex (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) N) (tptp.aa_nat_complex (tptp.power_power_complex Y) N)))) (forall ((Z tptp.complex)) (= (tptp.re (tptp.sgn_sgn_complex Z)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.re Z)) (tptp.real_V1022390504157884413omplex Z)))) (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 ((X tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.real_V1485227260804924795R_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)) X) (tptp.aa_real_real tptp.uminus_uminus_real X))) (forall ((X tptp.complex)) (= (tptp.real_V2046097035970521341omplex (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real) X) (tptp.uminus1482373934393186551omplex X))) (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 ((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 ((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 ((A tptp.real) (X tptp.complex)) (= (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.real_V1022390504157884413omplex X)))) (forall ((Z tptp.complex) (N tptp.nat)) (= (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.re Z)) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N)))) (forall ((Z tptp.complex) (R tptp.real)) (= (tptp.re (tptp.divide1717551699836669952omplex Z (tptp.real_V4546457046886955230omplex R))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.re Z)) R))) (forall ((U tptp.num) (W tptp.num) (A tptp.real)) (let ((_let_1 (tptp.numeral_numeral_real W))) (let ((_let_2 (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 ((U tptp.num) (W tptp.num) (A tptp.complex)) (let ((_let_1 (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.numeral_numeral_real W)) A)))) (forall ((Z tptp.complex) (W tptp.num)) (= (tptp.re (tptp.divide1717551699836669952omplex Z (tptp.numera6690914467698888265omplex W))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.re Z)) (tptp.numeral_numeral_real W)))) (forall ((V tptp.num) (W tptp.num) (A tptp.real)) (let ((_let_1 (tptp.numeral_numeral_real V))) (let ((_let_2 (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 ((V tptp.num) (W tptp.num) (A tptp.complex)) (let ((_let_1 (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.numeral_numeral_real W)) _let_1) A)))) (forall ((U tptp.num) (V tptp.num) (W tptp.num) (A tptp.real)) (let ((_let_1 (tptp.numeral_numeral_real V))) (let ((_let_2 (tptp.numeral_numeral_real W))) (let ((_let_3 (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 ((U tptp.num) (V tptp.num) (W tptp.num) (A tptp.complex)) (let ((_let_1 (tptp.numeral_numeral_real V))) (let ((_let_2 (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.numeral_numeral_real W))) _let_1) 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.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 ((A tptp.complex)) (= (tptp.real_V2046097035970521341omplex (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.one_one_real) (tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.plus_plus_complex A A)) A)) (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 ((A tptp.real) (X tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.real_V1485227260804924795R_real A) X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) X))) (forall ((X tptp.real) (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 ((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 ((A tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.real_V1485227260804924795R_real A))) (= (tptp.aa_real_real _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) Y)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real _let_1 X)) (tptp.aa_real_real _let_1 Y))))) (forall ((A tptp.real) (X tptp.complex) (Y tptp.complex)) (= (tptp.real_V2046097035970521341omplex A (tptp.plus_plus_complex X Y)) (tptp.plus_plus_complex (tptp.real_V2046097035970521341omplex A X) (tptp.real_V2046097035970521341omplex A Y)))) (forall ((A tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.real_V1485227260804924795R_real A))) (= (tptp.aa_real_real _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real X) Y)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real _let_1 X)) (tptp.aa_real_real _let_1 Y))))) (forall ((A tptp.real) (X tptp.complex) (Y tptp.complex)) (= (tptp.real_V2046097035970521341omplex A (tptp.minus_minus_complex X Y)) (tptp.minus_minus_complex (tptp.real_V2046097035970521341omplex A X) (tptp.real_V2046097035970521341omplex A Y)))) (forall ((R tptp.real) (X tptp.complex)) (= (tptp.re (tptp.real_V2046097035970521341omplex R X)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real R) (tptp.re X)))) (forall ((A tptp.complex) (B tptp.complex)) (= (= (tptp.re (tptp.divide1717551699836669952omplex A B)) tptp.zero_zero_real) (= (tptp.re (tptp.aa_complex_complex (tptp.times_times_complex A) (tptp.cnj B))) tptp.zero_zero_real))) (forall ((Z tptp.complex)) (= (tptp.real_V1022390504157884413omplex Z) (tptp.aa_real_real tptp.sqrt (tptp.re (tptp.aa_complex_complex (tptp.times_times_complex Z) (tptp.cnj Z)))))) (forall ((A tptp.complex) (B tptp.complex)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_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.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.re (tptp.divide1717551699836669952omplex A B)))) (tptp.pp (tptp.aa_real_bool _let_1 (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.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.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.re (tptp.divide1717551699836669952omplex A B)))) (tptp.pp (tptp.aa_real_bool _let_1 (tptp.re (tptp.aa_complex_complex (tptp.times_times_complex A) (tptp.cnj B)))))))) (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.pp (tptp.aa_int_bool _let_1 X)) (=> (tptp.pp (tptp.aa_int_bool _let_1 Y)) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se6526347334894502574or_int X) Y))))))) (forall ((X tptp.real) (Y 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.plus_plus_real X) Y)) Xa) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_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 Y) Xa)))) (forall ((X tptp.real) (Y tptp.real) (Xa tptp.complex)) (= (tptp.real_V2046097035970521341omplex (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) Y) Xa) (tptp.plus_plus_complex (tptp.real_V2046097035970521341omplex X Xa) (tptp.real_V2046097035970521341omplex Y Xa)))) (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.plus_plus_real A) B)) X) (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) X)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.real_V1485227260804924795R_real B) X)))) (forall ((A tptp.real) (B tptp.real) (X tptp.complex)) (= (tptp.real_V2046097035970521341omplex (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) B) X) (tptp.plus_plus_complex (tptp.real_V2046097035970521341omplex A X) (tptp.real_V2046097035970521341omplex B X)))) (forall ((R tptp.real) (X tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.real_V1485227260804924795R_real R) X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real tptp.real_V1803761363581548252l_real R)) X))) (forall ((R tptp.real) (X tptp.complex)) (= (tptp.real_V2046097035970521341omplex R X) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.real_V4546457046886955230omplex R)) X))) (forall ((R tptp.real)) (= (tptp.aa_real_real tptp.real_V1803761363581548252l_real R) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.real_V1485227260804924795R_real R) tptp.one_one_real))) (forall ((R tptp.real)) (= (tptp.real_V4546457046886955230omplex R) (tptp.real_V2046097035970521341omplex R tptp.one_one_complex))) (forall ((X tptp.real) (Y 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) Y)) 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 Y) Xa)))) (forall ((X tptp.real) (Y tptp.real) (Xa tptp.complex)) (= (tptp.real_V2046097035970521341omplex (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real X) Y) Xa) (tptp.minus_minus_complex (tptp.real_V2046097035970521341omplex X Xa) (tptp.real_V2046097035970521341omplex Y Xa)))) (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 ((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 ((R tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.times_times_real R))) (= (tptp.real_V2046097035970521341omplex R (tptp.complex2 A B)) (tptp.complex2 (tptp.aa_real_real _let_1 A) (tptp.aa_real_real _let_1 B))))) (= (tptp.re tptp.one_one_complex) tptp.one_one_real) (forall ((X tptp.complex) (Y tptp.complex)) (= (tptp.re (tptp.plus_plus_complex X Y)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.re X)) (tptp.re Y)))) (forall ((X tptp.complex) (Y tptp.complex)) (= (tptp.re (tptp.minus_minus_complex X Y)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.re X)) (tptp.re Y)))) (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 ((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 ((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.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.re Z))))) (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 ((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 ((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 ((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 ((A tptp.real) (E 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) E)) 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) E)) D))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real C) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.real_V1485227260804924795R_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real B) A)) E)) D))))) (forall ((A tptp.real) (E 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) E)) 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) E)) D))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.real_V1485227260804924795R_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A) B)) E)) C)) D)))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se6528837805403552850or_nat M) N) (tptp.aa_int_nat tptp.nat2 (tptp.aa_int_int (tptp.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 ((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.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.re _let_1)))))) (forall ((N tptp.nat) (K tptp.int)) (= (tptp.bit_se2159334234014336723it_int N K) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se6526347334894502574or_int K) (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_se545348938243370406it_int N) tptp.one_one_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.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)) (=> (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 ((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) (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)) (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) (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))) (=> (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) (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) (B tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool (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) Y)) (=> (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) Y))))))))) (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.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.real_V1485227260804924795R_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 ((X tptp.complex)) (= (tptp.real_V2046097035970521341omplex (tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)) X) (tptp.plus_plus_complex X X))) (forall ((M tptp.real) (Y 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)) (= (= Y (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 Y)) (tptp.aa_real_real _let_1 C)) X))))) (forall ((M tptp.real) (Y 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)) (= (= Y (tptp.plus_plus_complex (tptp.real_V2046097035970521341omplex M X) C)) (= (tptp.minus_minus_complex (tptp.real_V2046097035970521341omplex _let_1 Y) (tptp.real_V2046097035970521341omplex _let_1 C)) X))))) (forall ((M tptp.real) (X tptp.real) (C tptp.real) (Y 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) Y) (= X (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real _let_1 Y)) (tptp.aa_real_real _let_1 C))))))) (forall ((M tptp.real) (X tptp.complex) (C tptp.complex) (Y 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) Y) (= X (tptp.minus_minus_complex (tptp.real_V2046097035970521341omplex _let_1 Y) (tptp.real_V2046097035970521341omplex _let_1 C))))))) (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 ((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 ((Z tptp.complex)) (let ((_let_1 (tptp.real_V1022390504157884413omplex Z))) (let ((_let_2 (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.re (tptp.aa_nat_complex (tptp.power_power_complex (tptp.cis A)) N)))) (forall ((Z tptp.complex)) (= (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.real_V1022390504157884413omplex Z)) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (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 ((M6 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M7) M6)) (forall ((N5 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M7) N5)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.real_V1022390504157884413omplex (tptp.minus_minus_complex (tptp.aa_nat_complex X7 M6) (tptp.aa_nat_complex X7 N5)))) 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 ((M6 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M7) M6)) (forall ((N5 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M7) N5)) (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 M6)) (tptp.aa_nat_real X7 N5)))) E3))))))))))) (forall ((X7 tptp.fun_nat_complex)) (=> (forall ((E2 tptp.real)) (=> (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 ((N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M8) N2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.real_V1022390504157884413omplex (tptp.minus_minus_complex (tptp.aa_nat_complex X7 M2) (tptp.aa_nat_complex X7 N2)))) E2))))))))) (tptp.topolo6517432010174082258omplex X7))) (forall ((X7 tptp.fun_nat_real)) (=> (forall ((E2 tptp.real)) (=> (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 ((N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M8) 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 M2)) (tptp.aa_nat_real X7 N2)))) E2))))))))) (tptp.topolo4055970368930404560y_real X7))) (forall ((X7 tptp.fun_nat_complex) (E tptp.real)) (=> (tptp.topolo6517432010174082258omplex X7) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) E)) (exists ((M9 tptp.nat)) (forall ((M3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M9) M3)) (forall ((N6 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M9) N6)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.real_V1022390504157884413omplex (tptp.minus_minus_complex (tptp.aa_nat_complex X7 M3) (tptp.aa_nat_complex X7 N6)))) E)))))))))) (forall ((X7 tptp.fun_nat_real) (E tptp.real)) (=> (tptp.topolo4055970368930404560y_real X7) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) E)) (exists ((M9 tptp.nat)) (forall ((M3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M9) M3)) (forall ((N6 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M9) 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 M3)) (tptp.aa_nat_real X7 N6)))) E)))))))))) (forall ((X tptp.int) (N tptp.nat) (Y tptp.int)) (let ((_let_1 (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) N))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) X)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) _let_1)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Y) _let_1)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se6526347334894502574or_int X) Y)) _let_1))))))) (forall ((Z tptp.complex)) (= (tptp.real_V4546457046886955230omplex (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_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 ((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.complex)) (let ((_let_1 (tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.re Z))) (let ((_let_3 (tptp.real_V1022390504157884413omplex Z))) (let ((_let_4 (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.im Z))) (= (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.real_V1022390504157884413omplex Z)) (tptp.re Z))) (tptp.numeral_numeral_real (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 ((X tptp.complex)) (let ((_let_1 (tptp.re X))) (=> (= (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) (Y tptp.complex)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.im Y))) (let ((_let_3 (tptp.re Y))) (let ((_let_4 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real _let_3) _let_1)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real _let_2) _let_1)))) (let ((_let_5 (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.re X)))) (let ((_let_6 (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.im X)))) (= (tptp.divide1717551699836669952omplex X Y) (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 ((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) (Y tptp.int)) (= (= (tptp.aa_int_int tptp.bit_ri7919022796975470100ot_int X) (tptp.aa_int_int tptp.bit_ri7919022796975470100ot_int Y)) (= X Y))) (forall ((X tptp.int) (Y 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)) Y) (tptp.aa_int_int tptp.bit_ri7919022796975470100ot_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se6526347334894502574or_int X) Y)))) (forall ((X tptp.int) (Y 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 Y)) (tptp.aa_int_int tptp.bit_ri7919022796975470100ot_int (tptp.aa_int_int _let_1 Y))))) (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)) (forall ((X tptp.complex) (N tptp.nat)) (=> (= (tptp.im X) tptp.zero_zero_real) (= (tptp.im (tptp.aa_nat_complex (tptp.power_power_complex X) N)) tptp.zero_zero_real))) (= (tptp.aa_Cod1783974652533396728nteger tptp.bit_ri7632146776885996613nteger tptp.zero_z3403309356797280102nteger) _let_65) (= _let_66 _let_57) (= (tptp.aa_Cod1783974652533396728nteger tptp.bit_ri7632146776885996613nteger _let_65) tptp.zero_z3403309356797280102nteger) (= (tptp.aa_int_int tptp.bit_ri7919022796975470100ot_int _let_57) tptp.zero_zero_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 ((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.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.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 ((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.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.inc N)))) (forall ((Z tptp.complex)) (= (tptp.im (tptp.aa_complex_complex (tptp.times_times_complex Z) (tptp.cnj Z))) tptp.zero_zero_real)) (forall ((Z tptp.complex)) (= (tptp.im (tptp.aa_complex_complex (tptp.times_times_complex tptp.imaginary_unit) Z)) (tptp.re Z))) (forall ((Z tptp.complex) (R tptp.real)) (= (tptp.im (tptp.divide1717551699836669952omplex Z (tptp.real_V4546457046886955230omplex R))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.im Z)) R))) (forall ((Z tptp.complex)) (= (tptp.im (tptp.sgn_sgn_complex Z)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.im Z)) (tptp.real_V1022390504157884413omplex Z)))) (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.aa_int_int (tptp.aa_nat_fun_int_int 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)))) (forall ((N tptp.nat)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_nat6383147911832638789nteger 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 ((X tptp.complex) (N tptp.nat)) (=> (= (tptp.im X) tptp.zero_zero_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.re X)) N)))) (forall ((Z tptp.complex)) (= (tptp.re (tptp.aa_complex_complex (tptp.times_times_complex tptp.imaginary_unit) Z)) (tptp.aa_real_real tptp.uminus_uminus_real (tptp.im Z)))) (forall ((Z tptp.complex) (W tptp.num)) (= (tptp.im (tptp.divide1717551699836669952omplex Z (tptp.numera6690914467698888265omplex W))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.im Z)) (tptp.numeral_numeral_real W)))) (forall ((Z tptp.complex) (N tptp.nat)) (= (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.im Z)) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N)))) (= (tptp.aa_Cod1783974652533396728nteger tptp.bit_ri7632146776885996613nteger tptp.one_one_Code_integer) _let_70) (= _let_67 _let_69) (forall ((X tptp.complex)) (let ((_let_1 (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.re X))))) (= (tptp.csqrt (tptp.uminus1482373934393186551omplex X)) (tptp.aa_complex_complex (tptp.times_times_complex tptp.imaginary_unit) (tptp.csqrt X)))))) (forall ((R tptp.real) (X tptp.complex)) (= (tptp.im (tptp.real_V2046097035970521341omplex R X)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real R) (tptp.im X)))) (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 ((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 ((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.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 ((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))) (= (tptp.im tptp.imaginary_unit) tptp.one_one_real) (= (tptp.im tptp.one_one_complex) tptp.zero_zero_real) (forall ((X tptp.complex) (Y tptp.complex)) (= (tptp.im (tptp.plus_plus_complex X Y)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.im X)) (tptp.im Y)))) (forall ((X tptp.complex) (Y tptp.complex)) (= (tptp.im (tptp.minus_minus_complex X Y)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.im X)) (tptp.im Y)))) (forall ((A tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger 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.uminus1351360451143612070nteger A) (tptp.aa_Cod1783974652533396728nteger tptp.bit_ri7632146776885996613nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger 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 ((A tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger tptp.bit_ri7632146776885996613nteger A) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger 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 ((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_67) tptp.zero_zero_int) (forall ((R tptp.real) (X tptp.complex)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.times_times_real R))) (= (tptp.real_V2046097035970521341omplex R X) (tptp.complex2 (tptp.aa_real_real _let_1 (tptp.re X)) (tptp.aa_real_real _let_1 (tptp.im X)))))) (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.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.inc N))) (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.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 ((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 ((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 ((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 ((X tptp.complex) (Y tptp.complex)) (= (tptp.im (tptp.aa_complex_complex (tptp.times_times_complex X) Y)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.re X)) (tptp.im Y))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.im X)) (tptp.re Y))))) (forall ((X tptp.complex) (Y tptp.complex)) (= (tptp.re (tptp.aa_complex_complex (tptp.times_times_complex X) Y)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.re X)) (tptp.re Y))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.im X)) (tptp.im Y))))) (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 ((A tptp.complex) (B tptp.complex)) (= (= (tptp.im (tptp.divide1717551699836669952omplex A B)) tptp.zero_zero_real) (= (tptp.im (tptp.aa_complex_complex (tptp.times_times_complex A) (tptp.cnj B))) tptp.zero_zero_real))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.aa_int_int (tptp.aa_nat_fun_int_int 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 ((M tptp.nat) (N tptp.nat)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_nat6383147911832638789nteger tptp.bit_se7788150548672797655nteger M) (tptp.bit_se2119862282449309892nteger N)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.bit_se3949692690581998587nteger (tptp.bit_se2119862282449309892nteger (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N) M))) (tptp.aa_Cod1783974652533396728nteger tptp.bit_ri7632146776885996613nteger (tptp.bit_se2119862282449309892nteger M))))) (forall ((X tptp.complex) (Y tptp.complex)) (= (tptp.plus_plus_complex X Y) (tptp.complex2 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.re X)) (tptp.re Y)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.im X)) (tptp.im Y))))) (forall ((N tptp.nat) (A tptp.code_integer)) (= (tptp.bit_se8260200283734997820nteger N A) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.bit_se3949692690581998587nteger A) (tptp.aa_Cod1783974652533396728nteger tptp.bit_ri7632146776885996613nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_nat6383147911832638789nteger 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_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.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_se545348938243370406it_int N) tptp.one_one_int))))) (forall ((X tptp.complex) (Y tptp.complex)) (= (tptp.minus_minus_complex X Y) (tptp.complex2 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.re X)) (tptp.re Y)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.im X)) (tptp.im Y))))) (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.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_se545348938243370406it_int N) tptp.one_one_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.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 ((Z tptp.complex)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_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.re Z))) (tptp.aa_real_real tptp.abs_abs_real (tptp.im Z)))))) (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.im (tptp.divide1717551699836669952omplex A B)))) (tptp.pp (tptp.aa_real_bool _let_1 (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.im (tptp.divide1717551699836669952omplex A B))) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_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.im (tptp.divide1717551699836669952omplex A B)))) (tptp.pp (tptp.aa_real_bool _let_1 (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.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.im (tptp.aa_complex_complex (tptp.times_times_complex A) (tptp.cnj B)))) tptp.zero_zero_real)))) (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.im (tptp.aa_nat_complex (tptp.power_power_complex (tptp.cis A)) N)))) (forall ((Z tptp.complex)) (= (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.re Z))) (tptp.aa_real_real tptp.cos_real (tptp.im Z))))) (forall ((Z tptp.complex)) (= (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.re Z))) (tptp.aa_real_real tptp.sin_real (tptp.im Z))))) (forall ((A tptp.complex)) (= A (tptp.plus_plus_complex (tptp.real_V4546457046886955230omplex (tptp.re A)) (tptp.aa_complex_complex (tptp.times_times_complex tptp.imaginary_unit) (tptp.real_V4546457046886955230omplex (tptp.im A)))))) (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 ((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 ((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 ((X tptp.complex) (Y tptp.complex)) (let ((_let_1 (tptp.re Y))) (let ((_let_2 (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.im X)))) (let ((_let_3 (tptp.im Y))) (let ((_let_4 (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.re X)))) (= (tptp.aa_complex_complex (tptp.times_times_complex X) Y) (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 ((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.re _let_3))) (tptp.pp (tptp.aa_real_bool _let_2 (tptp.re _let_1)))) (= (tptp.pp (tptp.aa_real_bool _let_2 (tptp.im _let_3))) (tptp.pp (tptp.aa_real_bool _let_2 (tptp.im _let_1))))))))) (forall ((Z tptp.complex)) (= (tptp.exp_complex Z) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.real_V4546457046886955230omplex (tptp.aa_real_real tptp.exp_real (tptp.re Z)))) (tptp.cis (tptp.im Z))))) (forall ((Z tptp.complex)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (= 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.re Z)) _let_1)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_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_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_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.re Z)) _let_1)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.im Z)) _let_1))))) (forall ((X tptp.complex)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (= (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.numeral_numeral_real _let_1)) (tptp.re X))) (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.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.re X)) _let_1)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_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.re Z)) _let_1)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.im Z)) _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 (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 ((Z tptp.complex)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (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.re Z)) _let_1)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.im Z)) _let_1)))))) (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 ((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.re X))) (= (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.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)))) (let ((_let_2 (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.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.im Z)) _let_2)) _let_1)) tptp.one_one_real))))) (forall ((X tptp.complex) (Y tptp.complex)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.im Y))) (let ((_let_3 (tptp.re Y))) (= (tptp.re (tptp.divide1717551699836669952omplex X Y)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.re X)) _let_3)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_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 ((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.re Z)) _let_1)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.im Z)) _let_1)))))) (forall ((W tptp.complex) (Z tptp.complex)) (let ((_let_1 (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.im W))))) (= (tptp.csqrt Z) W))))) (forall ((B tptp.complex)) (let ((_let_1 (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.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.im X))) (= (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.re X)) _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.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.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.im Z)))) tptp.imaginary_unit))) (forall ((X tptp.complex) (Y tptp.complex)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.im Y))) (let ((_let_3 (tptp.re Y))) (= (tptp.im (tptp.divide1717551699836669952omplex X Y)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.im X)) _let_3)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_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.re Z))) (tptp.aa_real_real tptp.abs_abs_real (tptp.im Z)))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real tptp.sqrt (tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))) (tptp.real_V1022390504157884413omplex Z))))) (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.im X))) (let ((_let_3 (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 ((R tptp.complex) (Z tptp.complex)) (=> (tptp.member_complex R tptp.real_V2521375963428798218omplex) (= (tptp.im (tptp.divide1717551699836669952omplex R Z)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real tptp.uminus_uminus_real (tptp.re R))) (tptp.im Z))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.real_V1022390504157884413omplex Z)) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))))) (forall ((R tptp.complex) (Z tptp.complex)) (=> (tptp.member_complex R tptp.real_V2521375963428798218omplex) (= (tptp.re (tptp.divide1717551699836669952omplex R Z)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.re R)) (tptp.re Z))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.real_V1022390504157884413omplex Z)) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))))) (forall ((X32 tptp.num)) (= (tptp.size_size_num (tptp.aa_num_num tptp.bit1 X32)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.size_size_num X32)) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)))) (forall ((X2 tptp.num)) (= (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.size_size_num X2)) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)))) (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 ((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.aa_nat_fun_nat_nat tptp.bit_se1412395901928357646or_nat A) B))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_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.aa_nat_fun_nat_nat 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.aa_nat_fun_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 A) tptp.zero_zero_int) A)) (forall ((A tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se1412395901928357646or_nat A) tptp.zero_zero_nat) 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.aa_nat_fun_nat_nat tptp.bit_se1412395901928357646or_nat tptp.zero_zero_nat) A) 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.aa_nat_fun_nat_nat tptp.bit_se2925701944663578781it_nat N))) (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se1412395901928357646or_nat A) B)) (tptp.aa_nat_nat (tptp.aa_nat_fun_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.nat) (B tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.bit_se547839408752420682it_nat N))) (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se1412395901928357646or_nat A) B)) (tptp.aa_nat_nat (tptp.aa_nat_fun_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)) (let ((_let_1 (tptp.aa_nat_fun_int_int tptp.bit_se545348938243370406it_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.code_integer) (B tptp.code_integer)) (let ((_let_1 (tptp.aa_nat6383147911832638789nteger tptp.bit_se7788150548672797655nteger N))) (= (tptp.aa_Cod1783974652533396728nteger _let_1 (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.bit_se1080825931792720795nteger A) B)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.bit_se1080825931792720795nteger (tptp.aa_Cod1783974652533396728nteger _let_1 A)) (tptp.aa_Cod1783974652533396728nteger _let_1 B))))) (forall ((N tptp.nat) (A tptp.code_natural) (B tptp.code_natural)) (let ((_let_1 (tptp.aa_nat5282697797315388251atural tptp.bit_se6611745700429515170atural N))) (= (tptp.aa_Cod4272041906116450446atural _let_1 (tptp.bit_se9127793120404214118atural A B)) (tptp.bit_se9127793120404214118atural (tptp.aa_Cod4272041906116450446atural _let_1 A) (tptp.aa_Cod4272041906116450446atural _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 ((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) (Y 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) Y)) (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 Y)))) (forall ((X tptp.int) (Y 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) Y)) (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 Y)))) (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.aa_nat_fun_nat_nat tptp.bit_se1412395901928357646or_nat _let_1) tptp.one_one_nat) _let_1))) (forall ((Y tptp.num)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit1 Y)))) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se1409905431419307370or_int tptp.one_one_int) _let_1) _let_1))) (forall ((Y tptp.num)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 Y)))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se1412395901928357646or_nat tptp.one_one_nat) _let_1) _let_1))) (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 ((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 ((R tptp.complex) (Z tptp.complex)) (=> (tptp.member_complex R tptp.real_V2521375963428798218omplex) (= (tptp.re (tptp.divide1717551699836669952omplex Z R)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.re Z)) (tptp.re R))))) (forall ((Y tptp.complex) (X tptp.complex)) (=> (tptp.member_complex Y tptp.real_V2521375963428798218omplex) (=> (tptp.member_complex X tptp.real_V2521375963428798218omplex) (= (= (tptp.aa_complex_complex (tptp.times_times_complex tptp.imaginary_unit) Y) X) (and (= X tptp.zero_zero_complex) (= Y tptp.zero_zero_complex)))))) (forall ((Y tptp.complex) (X tptp.complex)) (=> (tptp.member_complex Y tptp.real_V2521375963428798218omplex) (=> (tptp.member_complex X tptp.real_V2521375963428798218omplex) (= (= X (tptp.aa_complex_complex (tptp.times_times_complex tptp.imaginary_unit) Y)) (and (= X tptp.zero_zero_complex) (= Y tptp.zero_zero_complex)))))) (forall ((X tptp.num) (Y 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 Y))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.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 Y))))) (forall ((X tptp.num) (Y tptp.num)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se1412395901928357646or_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 X))) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 Y))) (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.aa_nat_fun_nat_nat tptp.bit_se1412395901928357646or_nat (tptp.aa_num_nat tptp.numeral_numeral_nat X)) (tptp.aa_num_nat tptp.numeral_numeral_nat Y))))) (forall ((Y 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 Y))) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit1 Y)))) (forall ((Y tptp.num)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se1412395901928357646or_nat tptp.one_one_nat) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 Y))) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 Y)))) (forall ((X tptp.num)) (= (tptp.aa_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.aa_nat_fun_nat_nat tptp.bit_se1412395901928357646or_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 X))) tptp.one_one_nat) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 X)))) (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 ((R tptp.complex) (Z tptp.complex)) (=> (tptp.member_complex R tptp.real_V2521375963428798218omplex) (= (tptp.im (tptp.divide1717551699836669952omplex Z R)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.im Z)) (tptp.re R))))) (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 ((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 ((X tptp.num) (Y 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 Y))) (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 Y)))))) (forall ((X tptp.num) (Y tptp.num)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se1412395901928357646or_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 X))) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 Y))) (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.aa_nat_fun_nat_nat tptp.bit_se1412395901928357646or_nat (tptp.aa_num_nat tptp.numeral_numeral_nat X)) (tptp.aa_num_nat tptp.numeral_numeral_nat Y)))))) (forall ((X tptp.num) (Y 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 Y))) (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 Y)))))) (forall ((X tptp.num) (Y tptp.num)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se1412395901928357646or_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 X))) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 Y))) (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.aa_nat_fun_nat_nat tptp.bit_se1412395901928357646or_nat (tptp.aa_num_nat tptp.numeral_numeral_nat X)) (tptp.aa_num_nat tptp.numeral_numeral_nat Y)))))) (forall ((X tptp.num) (Y 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 Y))) (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 Y)))))) (forall ((X tptp.num) (Y tptp.num)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se1412395901928357646or_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 X))) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 Y))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.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.aa_nat_fun_nat_nat tptp.bit_se1412395901928357646or_nat (tptp.aa_num_nat tptp.numeral_numeral_nat X)) (tptp.aa_num_nat tptp.numeral_numeral_nat Y)))))) (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.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.aa_nat_fun_nat_nat tptp.bit_se1412395901928357646or_nat M) N)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se1412395901928357646or_nat (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat M)) (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat N)))) (forall ((W tptp.num)) (tptp.member_complex (tptp.numera6690914467698888265omplex W) tptp.real_V2521375963428798218omplex)) (forall ((W tptp.num)) (tptp.member_real (tptp.numeral_numeral_real W) 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.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)))) (tptp.member_real tptp.one_one_real tptp.real_V470468836141973256s_real) (tptp.member_complex tptp.one_one_complex 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.plus_plus_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.plus_plus_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.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.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.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.aa_nat_fun_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 ((X tptp.list_VEBT_VEBT) (Y tptp.list_VEBT_VEBT)) (=> (not (= (tptp.size_s6755466524823107622T_VEBT X) (tptp.size_s6755466524823107622T_VEBT Y))) (not (= X Y)))) (forall ((X tptp.list_bool) (Y tptp.list_bool)) (=> (not (= (tptp.size_size_list_bool X) (tptp.size_size_list_bool Y))) (not (= X Y)))) (forall ((X tptp.list_nat) (Y tptp.list_nat)) (=> (not (= (tptp.size_size_list_nat X) (tptp.size_size_list_nat Y))) (not (= X Y)))) (forall ((X tptp.list_int) (Y tptp.list_int)) (=> (not (= (tptp.size_size_list_int X) (tptp.size_size_list_int Y))) (not (= X Y)))) (forall ((X tptp.num) (Y tptp.num)) (=> (not (= (tptp.size_size_num X) (tptp.size_size_num Y))) (not (= X Y)))) (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.aa_nat_fun_nat_nat tptp.bit_se1412395901928357646or_nat B))) (let ((_let_2 (tptp.aa_nat_fun_nat_nat 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.aa_nat_fun_nat_nat tptp.bit_se1412395901928357646or_nat A) B) (tptp.aa_nat_nat (tptp.aa_nat_fun_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.aa_nat_fun_nat_nat tptp.bit_se1412395901928357646or_nat A))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_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.aa_nat_fun_nat_nat tptp.bit_se1412395901928357646or_nat B) C))))) (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.aa_nat_fun_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)) (= (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 ((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 ((Y 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 Y) 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 Y) X)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se1409905431419307370or_int Z) X)))) (forall ((Y 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 Y) 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 Y) X)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se725231765392027082nd_int Z) X)))) (forall ((X tptp.int) (Y 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 Y) Z)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se725231765392027082nd_int (tptp.aa_int_int _let_1 Y)) (tptp.aa_int_int _let_1 Z))))) (forall ((X tptp.int) (Y 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 Y) Z)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se1409905431419307370or_int (tptp.aa_int_int _let_1 Y)) (tptp.aa_int_int _let_1 Z))))) (tptp.member_real tptp.zero_zero_real tptp.real_V470468836141973256s_real) (tptp.member_complex tptp.zero_zero_complex tptp.real_V2521375963428798218omplex) (forall ((A tptp.real) (N tptp.nat)) (=> (tptp.member_real A tptp.real_V470468836141973256s_real) (tptp.member_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real A) N) tptp.real_V470468836141973256s_real))) (forall ((A tptp.complex) (N tptp.nat)) (=> (tptp.member_complex A tptp.real_V2521375963428798218omplex) (tptp.member_complex (tptp.aa_nat_complex (tptp.power_power_complex A) N) tptp.real_V2521375963428798218omplex))) (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 ((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) (Y tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.pp (tptp.aa_int_bool _let_1 X)) (=> (tptp.pp (tptp.aa_int_bool _let_1 Y)) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se1409905431419307370or_int X) Y))))))) (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.aa_nat_fun_nat_nat tptp.bit_se1412395901928357646or_nat A) B)))) (forall ((X tptp.int) (Y tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se725231765392027082nd_int X) Y)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se1409905431419307370or_int X) Y)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int X) Y))) (forall ((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 ((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 ((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)))) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se1409905431419307370or_int tptp.one_one_int) _let_67) _let_66) (forall ((X tptp.int) (Y tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se6526347334894502574or_int X) Y) (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) Y)) (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 Y))))) (forall ((X tptp.int) (Y tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se6526347334894502574or_int X) Y) (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 Y))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se725231765392027082nd_int (tptp.aa_int_int tptp.bit_ri7919022796975470100ot_int X)) Y)))) (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.aa_nat_fun_nat_nat tptp.bit_se1412395901928357646or_nat A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se547839408752420682it_nat N) tptp.one_one_nat)))) (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.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_se545348938243370406it_int N) tptp.one_one_int)))) (forall ((N tptp.nat) (A tptp.code_integer)) (= (tptp.bit_se2793503036327961859nteger N A) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.bit_se1080825931792720795nteger A) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_nat6383147911832638789nteger tptp.bit_se7788150548672797655nteger N) tptp.one_one_Code_integer)))) (forall ((N tptp.nat) (A tptp.code_natural)) (= (tptp.bit_se1617098188084679374atural N A) (tptp.bit_se9127793120404214118atural A (tptp.aa_Cod4272041906116450446atural (tptp.aa_nat5282697797315388251atural tptp.bit_se6611745700429515170atural N) tptp.one_one_Code_natural)))) (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 ((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.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_se545348938243370406it_int N) L)))) (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.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_se545348938243370406it_int N) tptp.one_one_int)))) (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.aa_nat_fun_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) (Y 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 Y) tptp.zero_z3403309356797280102nteger) (=> (= (tptp.aa_Cod1783974652533396728nteger _let_2 Y) _let_1) (= X Y))))))))) (forall ((A tptp.int) (X tptp.int) (Y 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 Y) tptp.zero_zero_int) (=> (= (tptp.aa_int_int _let_2 Y) _let_1) (= X Y))))))))) (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 ((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))) (= (tptp.size_size_num tptp.one) tptp.zero_zero_nat) (forall ((X tptp.code_integer) (Y tptp.code_integer)) (=> (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.bit_se3949692690581998587nteger X) Y) tptp.zero_z3403309356797280102nteger) (=> (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.bit_se1080825931792720795nteger X) Y) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (= (tptp.aa_Cod1783974652533396728nteger tptp.bit_ri7632146776885996613nteger X) Y)))) (forall ((X tptp.int) (Y tptp.int)) (=> (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se725231765392027082nd_int X) Y) tptp.zero_zero_int) (=> (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se1409905431419307370or_int X) Y) (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int)) (= (tptp.aa_int_int tptp.bit_ri7919022796975470100ot_int X) Y)))) (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 ((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)) (= (tptp.aa_nat_nat tptp.bit_se2002935070580805687sk_nat (tptp.aa_nat_nat tptp.suc N)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se1412395901928357646or_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.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.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger 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.aa_nat_fun_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.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger 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.aa_nat_fun_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.aa_nat_fun_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) (Y tptp.int)) (let ((_let_1 (tptp.aa_nat_int (tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) N))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) X)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) _let_1)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Y) _let_1)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se1409905431419307370or_int X) Y)) _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) (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 ((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 ((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_65 tptp.bit_se3222712562003087583nteger) (tptp.boolea8527374999097803216ff_int tptp.bit_se725231765392027082nd_int tptp.bit_se1409905431419307370or_int tptp.bit_ri7919022796975470100ot_int tptp.zero_zero_int _let_57 tptp.bit_se6526347334894502574or_int) (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.bit_or_not_num_neg M (tptp.aa_num_num tptp.bit0 N)))))) (forall ((N tptp.num) (M tptp.num)) (= (tptp.aa_int_int (tptp.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.bit_or_not_num_neg M (tptp.aa_num_num tptp.bit0 N)))))) (forall ((A tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.ord_max_int A) A) A)) (forall ((A tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat A) A) A)) (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.ord_max_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.aa_nat_fun_nat_nat tptp.ord_max_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) (B tptp.int)) (let ((_let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.ord_max_int A) B))) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.ord_max_int _let_1) B) _let_1))) (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))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat _let_1) B) _let_1))) (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.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.ord_less_eq_num (tptp.ord_max_num B C)) A)) (and (tptp.pp (tptp.aa_num_bool (tptp.ord_less_eq_num B) A)) (tptp.pp (tptp.aa_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 ((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.ord_max_rat A B) B))) (forall ((A tptp.num) (B tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.ord_less_eq_num A) B)) (= (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 ((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.ord_max_rat A B) A))) (forall ((B tptp.num) (A tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.ord_less_eq_num B) A)) (= (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 ((X tptp.real) (Y tptp.real) (Z tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.ord_max_real X) Y)) Z)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Z)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y) Z))))) (forall ((X tptp.rat) (Y tptp.rat) (Z tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.ord_max_rat X Y)) Z)) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) Z)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Y) Z))))) (forall ((X tptp.num) (Y tptp.num) (Z tptp.num)) (= (tptp.pp (tptp.aa_num_bool (tptp.ord_less_num (tptp.ord_max_num X Y)) Z)) (and (tptp.pp (tptp.aa_num_bool (tptp.ord_less_num X) Z)) (tptp.pp (tptp.aa_num_bool (tptp.ord_less_num Y) Z))))) (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat X) Y)) Z)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Z)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Y) Z))))) (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.ord_max_int X) Y)) Z)) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) Z)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Y) Z))))) (forall ((A tptp.real) (B tptp.real)) (=> (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.ord_max_real 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_rat A) B)) (= (tptp.ord_max_rat A B) B))) (forall ((A tptp.num) (B tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.ord_less_num A) B)) (= (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_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_int A) B)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.ord_max_int A) B) B))) (forall ((B tptp.real) (A tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B) A)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.ord_max_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_rat B) A)) (= (tptp.ord_max_rat A B) A))) (forall ((B tptp.num) (A tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.ord_less_num B) A)) (= (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_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_int B) A)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.ord_max_int 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.numeral_numeral_real U))) (let ((_let_2 (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.numeral_numeral_rat U))) (let ((_let_2 (tptp.numeral_numeral_rat V))) (let ((_let_3 (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 ((X tptp.num)) (let ((_let_1 (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.numeral_numeral_rat X))) (= (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.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.numeral_numeral_rat X))) (= (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.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_real_real (tptp.aa_rea7340605660300375871l_real tptp.ord_max_real tptp.zero_zero_real) tptp.one_one_real) tptp.one_one_real) (= (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) (forall ((X tptp.num)) (let ((_let_1 (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.numeral_numeral_rat X))) (= (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.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.numeral_numeral_rat X))) (= (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_real_real tptp.uminus_uminus_real (tptp.numeral_numeral_real U)))) (let ((_let_2 (tptp.aa_real_real tptp.uminus_uminus_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.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.uminus_uminus_rat (tptp.numeral_numeral_rat U)))) (let ((_let_2 (tptp.uminus_uminus_rat (tptp.numeral_numeral_rat V)))) (let ((_let_3 (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.numeral_numeral_real U)))) (let ((_let_2 (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.uminus_uminus_rat (tptp.numeral_numeral_rat U)))) (let ((_let_2 (tptp.numeral_numeral_rat V))) (let ((_let_3 (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.numeral_numeral_real U))) (let ((_let_2 (tptp.aa_real_real tptp.uminus_uminus_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.numeral_numeral_rat U))) (let ((_let_2 (tptp.uminus_uminus_rat (tptp.numeral_numeral_rat V)))) (let ((_let_3 (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 ((X tptp.num)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 X)))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se1412395901928357646or_nat _let_1) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)) _let_1))) (forall ((Y tptp.num)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 Y)))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se1412395901928357646or_nat (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)) _let_1) _let_1))) (forall ((X tptp.num)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se1412395901928357646or_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 X))) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 X)))) (forall ((Y tptp.num)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se1412395901928357646or_nat (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 Y))) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 Y)))) (forall ((X tptp.int) (Y tptp.int)) (= (tptp.ring_1_of_int_real (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.ord_max_int X) Y)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.ord_max_real (tptp.ring_1_of_int_real X)) (tptp.ring_1_of_int_real Y)))) (forall ((X tptp.int) (Y tptp.int)) (= (tptp.ring_1_of_int_rat (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.ord_max_int X) Y)) (tptp.ord_max_rat (tptp.ring_1_of_int_rat X) (tptp.ring_1_of_int_rat Y)))) (forall ((X tptp.int) (Y tptp.int)) (= (tptp.ring_1_of_int_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.ord_max_int X) Y)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.ord_max_int (tptp.ring_1_of_int_int X)) (tptp.ring_1_of_int_int Y)))) (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat C))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 B)) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.ord_max_rat A B)))))) (forall ((C tptp.num) (B tptp.num) (A tptp.num)) (let ((_let_1 (tptp.ord_less_eq_num C))) (=> (tptp.pp (tptp.aa_num_bool _let_1 B)) (tptp.pp (tptp.aa_num_bool _let_1 (tptp.ord_max_num A B)))))) (forall ((C tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat C))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 B)) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat A) B)))))) (forall ((C tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int C))) (=> (tptp.pp (tptp.aa_int_bool _let_1 B)) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.ord_max_int A) B)))))) (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat C))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 A)) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.ord_max_rat A B)))))) (forall ((C tptp.num) (A tptp.num) (B tptp.num)) (let ((_let_1 (tptp.ord_less_eq_num C))) (=> (tptp.pp (tptp.aa_num_bool _let_1 A)) (tptp.pp (tptp.aa_num_bool _let_1 (tptp.ord_max_num A B)))))) (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat C))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 A)) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat A) B)))))) (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int C))) (=> (tptp.pp (tptp.aa_int_bool _let_1 A)) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.ord_max_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)) (= (tptp.ord_max_rat A B) B))) (forall ((A tptp.num) (B tptp.num)) (= (tptp.pp (tptp.aa_num_bool (tptp.ord_less_eq_num A) B)) (= (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 ((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.ord_max_rat A B) A))) (forall ((B tptp.num) (A tptp.num)) (= (tptp.pp (tptp.aa_num_bool (tptp.ord_less_eq_num B) A)) (= (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 ((Z tptp.rat) (X tptp.rat) (Y tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat Z))) (= (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.ord_max_rat X Y))) (or (tptp.pp (tptp.aa_rat_bool _let_1 X)) (tptp.pp (tptp.aa_rat_bool _let_1 Y)))))) (forall ((Z tptp.num) (X tptp.num) (Y tptp.num)) (let ((_let_1 (tptp.ord_less_eq_num Z))) (= (tptp.pp (tptp.aa_num_bool _let_1 (tptp.ord_max_num X Y))) (or (tptp.pp (tptp.aa_num_bool _let_1 X)) (tptp.pp (tptp.aa_num_bool _let_1 Y)))))) (forall ((Z tptp.nat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Z))) (= (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat X) Y))) (or (tptp.pp (tptp.aa_nat_bool _let_1 X)) (tptp.pp (tptp.aa_nat_bool _let_1 Y)))))) (forall ((Z tptp.int) (X tptp.int) (Y tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Z))) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.ord_max_int X) Y))) (or (tptp.pp (tptp.aa_int_bool _let_1 X)) (tptp.pp (tptp.aa_int_bool _let_1 Y)))))) (forall ((B tptp.rat) (A tptp.rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) (tptp.ord_max_rat A B)))) (forall ((B tptp.num) (A tptp.num)) (tptp.pp (tptp.aa_num_bool (tptp.ord_less_eq_num B) (tptp.ord_max_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_eq_nat B) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_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_eq_int B) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.ord_max_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) (tptp.ord_max_rat A B)))) (forall ((A tptp.num) (B tptp.num)) (tptp.pp (tptp.aa_num_bool (tptp.ord_less_eq_num A) (tptp.ord_max_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) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_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) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.ord_max_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_eq_rat B) A)) (= A (tptp.ord_max_rat A B)))) (forall ((B tptp.num) (A tptp.num)) (= (tptp.pp (tptp.aa_num_bool (tptp.ord_less_eq_num B) A)) (= A (tptp.ord_max_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_eq_nat B) A)) (= A (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_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_eq_int B) A)) (= A (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.ord_max_int A) 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) A)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.ord_max_rat B C)) A))))) (forall ((B tptp.num) (A tptp.num) (C tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.ord_less_eq_num B) A)) (=> (tptp.pp (tptp.aa_num_bool (tptp.ord_less_eq_num C) A)) (tptp.pp (tptp.aa_num_bool (tptp.ord_less_eq_num (tptp.ord_max_num B 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_eq_nat B) A)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat C) A)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat B) 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_eq_int B) A)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int C) A)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.ord_max_int B) 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.ord_max_rat B C)) A)) (not (=> (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 C) A))))))) (forall ((B tptp.num) (C tptp.num) (A tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.ord_less_eq_num (tptp.ord_max_num B C)) A)) (not (=> (tptp.pp (tptp.aa_num_bool (tptp.ord_less_eq_num B) A)) (not (tptp.pp (tptp.aa_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)) (not (=> (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 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)) (not (=> (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 C) A))))))) (forall ((A tptp.rat) (B tptp.rat)) (=> (= A (tptp.ord_max_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 (tptp.ord_max_num A B)) (tptp.pp (tptp.aa_num_bool (tptp.ord_less_eq_num B) A)))) (forall ((A tptp.nat) (B tptp.nat)) (=> (= A (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_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 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.ord_max_int A) B)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_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_eq_rat B) A)) (= A (tptp.ord_max_rat A B)))) (forall ((B tptp.num) (A tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.ord_less_eq_num B) A)) (= A (tptp.ord_max_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_eq_nat B) A)) (= A (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_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_eq_int B) A)) (= A (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.ord_max_int A) B)))) (forall ((C tptp.rat) (A tptp.rat) (D tptp.rat) (B tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat C) A)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat D) B)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.ord_max_rat C D)) (tptp.ord_max_rat A B)))))) (forall ((C tptp.num) (A tptp.num) (D tptp.num) (B tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.ord_less_eq_num C) A)) (=> (tptp.pp (tptp.aa_num_bool (tptp.ord_less_eq_num D) B)) (tptp.pp (tptp.aa_num_bool (tptp.ord_less_eq_num (tptp.ord_max_num C D)) (tptp.ord_max_num A B)))))) (forall ((C tptp.nat) (A tptp.nat) (D tptp.nat) (B tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat C) A)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat D) 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.ord_max_nat C) D)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat A) B)))))) (forall ((C tptp.int) (A tptp.int) (D tptp.int) (B tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int C) A)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int D) 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.ord_max_int C) D)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.ord_max_int A) B)))))) (forall ((C tptp.real) (B tptp.real) (A tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real C))) (=> (tptp.pp (tptp.aa_real_bool _let_1 B)) (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.ord_max_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_rat C))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 B)) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.ord_max_rat A B)))))) (forall ((C tptp.num) (B tptp.num) (A tptp.num)) (let ((_let_1 (tptp.ord_less_num C))) (=> (tptp.pp (tptp.aa_num_bool _let_1 B)) (tptp.pp (tptp.aa_num_bool _let_1 (tptp.ord_max_num A B)))))) (forall ((C tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat C))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 B)) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat A) B)))))) (forall ((C tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_int C))) (=> (tptp.pp (tptp.aa_int_bool _let_1 B)) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.ord_max_int A) B)))))) (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real C))) (=> (tptp.pp (tptp.aa_real_bool _let_1 A)) (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.ord_max_real A) B)))))) (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat C))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 A)) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.ord_max_rat A B)))))) (forall ((C tptp.num) (A tptp.num) (B tptp.num)) (let ((_let_1 (tptp.ord_less_num C))) (=> (tptp.pp (tptp.aa_num_bool _let_1 A)) (tptp.pp (tptp.aa_num_bool _let_1 (tptp.ord_max_num A B)))))) (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat C))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 A)) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat A) B)))))) (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_int C))) (=> (tptp.pp (tptp.aa_int_bool _let_1 A)) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.ord_max_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 (= A (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.ord_max_real A) B)) (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 (= A (tptp.ord_max_rat A B)) (not (= A B))))) (forall ((B tptp.num) (A tptp.num)) (= (tptp.pp (tptp.aa_num_bool (tptp.ord_less_num B) A)) (and (= A (tptp.ord_max_num A B)) (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 (= A (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat A) B)) (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 (= A (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.ord_max_int A) B)) (not (= A B))))) (forall ((B tptp.real) (C tptp.real) (A tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.ord_max_real B) C)) A)) (not (=> (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 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_rat (tptp.ord_max_rat B C)) A)) (not (=> (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 C) A))))))) (forall ((B tptp.num) (C tptp.num) (A tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.ord_less_num (tptp.ord_max_num B C)) A)) (not (=> (tptp.pp (tptp.aa_num_bool (tptp.ord_less_num B) A)) (not (tptp.pp (tptp.aa_num_bool (tptp.ord_less_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_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat B) C)) A)) (not (=> (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 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_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.ord_max_int B) C)) A)) (not (=> (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 C) A))))))) (forall ((Z tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Z))) (= (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.ord_max_real X) Y))) (or (tptp.pp (tptp.aa_real_bool _let_1 X)) (tptp.pp (tptp.aa_real_bool _let_1 Y)))))) (forall ((Z tptp.rat) (X tptp.rat) (Y tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Z))) (= (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.ord_max_rat X Y))) (or (tptp.pp (tptp.aa_rat_bool _let_1 X)) (tptp.pp (tptp.aa_rat_bool _let_1 Y)))))) (forall ((Z tptp.num) (X tptp.num) (Y tptp.num)) (let ((_let_1 (tptp.ord_less_num Z))) (= (tptp.pp (tptp.aa_num_bool _let_1 (tptp.ord_max_num X Y))) (or (tptp.pp (tptp.aa_num_bool _let_1 X)) (tptp.pp (tptp.aa_num_bool _let_1 Y)))))) (forall ((Z tptp.nat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Z))) (= (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat X) Y))) (or (tptp.pp (tptp.aa_nat_bool _let_1 X)) (tptp.pp (tptp.aa_nat_bool _let_1 Y)))))) (forall ((Z tptp.int) (X tptp.int) (Y tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_int Z))) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.ord_max_int X) Y))) (or (tptp.pp (tptp.aa_int_bool _let_1 X)) (tptp.pp (tptp.aa_int_bool _let_1 Y)))))) (forall ((X tptp.real) (Y tptp.real) (Z tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X))) (= (tptp.aa_real_real _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.ord_max_real Y) Z)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.ord_max_real (tptp.aa_real_real _let_1 Y)) (tptp.aa_real_real _let_1 Z))))) (forall ((X tptp.rat) (Y tptp.rat) (Z tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat X))) (= (tptp.aa_rat_rat _let_1 (tptp.ord_max_rat Y Z)) (tptp.ord_max_rat (tptp.aa_rat_rat _let_1 Y) (tptp.aa_rat_rat _let_1 Z))))) (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.plus_plus_int X))) (= (tptp.aa_int_int _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.ord_max_int Y) Z)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.ord_max_int (tptp.aa_int_int _let_1 Y)) (tptp.aa_int_int _let_1 Z))))) (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat X))) (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat Y) Z)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat (tptp.aa_nat_nat _let_1 Y)) (tptp.aa_nat_nat _let_1 Z))))) (forall ((X tptp.real) (Y tptp.real) (Z tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.ord_max_real X) Y)) Z) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.ord_max_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) Z)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real Y) Z)))) (forall ((X tptp.rat) (Y tptp.rat) (Z tptp.rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.ord_max_rat X Y)) Z) (tptp.ord_max_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat X) Z) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat Y) Z)))) (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.ord_max_int X) Y)) 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 Y) Z)))) (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat X) Y)) Z) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat X) Z)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Y) Z)))) (forall ((X tptp.real) (Y tptp.real) (Z tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.ord_max_real X) Y)) Z) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.ord_max_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real X) Z)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real Y) Z)))) (forall ((X tptp.rat) (Y tptp.rat) (Z tptp.rat)) (= (tptp.minus_minus_rat (tptp.ord_max_rat X Y) Z) (tptp.ord_max_rat (tptp.minus_minus_rat X Z) (tptp.minus_minus_rat Y Z)))) (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.ord_max_int X) Y)) 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 Y) Z)))) (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.ord_max_int A))) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.ord_max_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.ord_max_int B) C))))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat A))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_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.ord_max_nat B) C))))) (forall ((A tptp.int) (B tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.ord_max_int A) B) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.ord_max_int B) 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.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat B) A))) (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.ord_max_int B))) (let ((_let_2 (tptp.aa_int_fun_int_int tptp.ord_max_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.aa_nat_fun_nat_nat tptp.ord_max_nat B))) (let ((_let_2 (tptp.aa_nat_fun_nat_nat tptp.ord_max_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 ((X tptp.nat) (Y tptp.nat)) (= (tptp.aa_nat_real tptp.semiri5074537144036343181t_real (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat X) Y)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.ord_max_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real X)) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real Y)))) (forall ((X tptp.nat) (Y tptp.nat)) (= (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat X) Y)) (tptp.ord_max_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat X) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat Y)))) (forall ((X tptp.nat) (Y tptp.nat)) (= (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat X) Y)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat X)) (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat Y)))) (forall ((X tptp.nat) (Y tptp.nat)) (= (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat X) Y)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.ord_max_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int X)) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int Y)))) (= (tptp.bit_or_not_num_neg tptp.one tptp.one) tptp.one) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se7882103937844011126it_nat M) N) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se1412395901928357646or_nat N) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se547839408752420682it_nat M) tptp.one_one_nat)))) (forall ((N tptp.num)) (= (tptp.bit_or_not_num_neg (tptp.aa_num_num tptp.bit0 N) tptp.one) (tptp.aa_num_num tptp.bit0 tptp.one))) (forall ((N tptp.num) (M tptp.num)) (= (tptp.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.bit_or_not_num_neg N M)))) (forall ((N tptp.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.bit_or_not_num_neg tptp.one _let_1) _let_1))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se1412395901928357646or_nat M) N) (tptp.aa_int_nat tptp.nat2 (tptp.aa_int_int (tptp.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.num)) (= (tptp.bit_or_not_num_neg tptp.one (tptp.aa_num_num tptp.bit0 M)) (tptp.aa_num_num tptp.bit1 M))) (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.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.bit_or_not_num_neg N M))))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.aa_num_int tptp.numeral_numeral_int (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.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se1412395901928357646or_nat (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)) N) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N) (tptp.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.aa_nat_fun_nat_nat tptp.bit_se1412395901928357646or_nat N) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N) (tptp.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 ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat _let_1))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se1412395901928357646or_nat M) N) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.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.aa_nat_fun_nat_nat tptp.bit_se1412395901928357646or_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat M) _let_1)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat N) _let_1)))))))) (forall ((N tptp.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.bit_or_not_num_neg tptp.one (tptp.bitM 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.bit_or_not_num_neg tptp.one (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.aa_nat_fun_nat_nat tptp.bit_se1412395901928357646or_nat M) N))) (let ((_let_3 (= N tptp.zero_zero_nat))) (let ((_let_4 (= M tptp.zero_zero_nat))) (and (=> _let_4 (= _let_2 N)) (=> (not _let_4) (and (=> _let_3 (= _let_2 M)) (=> (not _let_3) (= _let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat M) _let_1)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat N) _let_1))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat _let_1) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se1412395901928357646or_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat M) _let_1)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat N) _let_1)))))))))))))) (forall ((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 ((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.neg_nu6511756317524482435omplex (tptp.numera6690914467698888265omplex K)) (tptp.numera6690914467698888265omplex (tptp.bitM K)))) (forall ((K tptp.num)) (= (tptp.aa_real_real tptp.neg_nu6075765906172075777c_real (tptp.numeral_numeral_real K)) (tptp.numeral_numeral_real (tptp.bitM K)))) (forall ((K tptp.num)) (= (tptp.neg_nu3179335615603231917ec_rat (tptp.numeral_numeral_rat K)) (tptp.numeral_numeral_rat (tptp.bitM K)))) (forall ((K tptp.num)) (= (tptp.neg_nu3811975205180677377ec_int (tptp.aa_num_int tptp.numeral_numeral_int K)) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.bitM K)))) (forall ((K tptp.num)) (= (tptp.pred_numeral (tptp.aa_num_num tptp.bit0 K)) (tptp.aa_num_nat tptp.numeral_numeral_nat (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.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.pred_numeral K))))) (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.bit_or_not_num_neg M (tptp.bitM 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.bit0 N)))) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.bit_or_not_num_neg M (tptp.bitM N)))))) (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.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.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat M) N)) Q2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) Q2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N) Q2)))) (forall ((M tptp.nat) (N tptp.nat) (Q2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M))) (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat N) Q2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat (tptp.aa_nat_nat _let_1 N)) (tptp.aa_nat_nat _let_1 Q2))))) (= (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.bitM (tptp.aa_num_num tptp.bit0 N)) (tptp.aa_num_num tptp.bit1 (tptp.bitM N)))) (forall ((N tptp.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.bit_or_not_num_neg (tptp.aa_num_num tptp.bit0 N) (tptp.aa_num_num tptp.bit0 M)) (tptp.bitM (tptp.bit_or_not_num_neg N M)))) (forall ((N tptp.num)) (= (tptp.inc (tptp.bitM N)) (tptp.aa_num_num tptp.bit0 N))) (forall ((N tptp.num) (M tptp.num)) (= (tptp.bit_or_not_num_neg (tptp.aa_num_num tptp.bit1 N) (tptp.aa_num_num tptp.bit1 M)) (tptp.bitM (tptp.bit_or_not_num_neg N M)))) (forall ((N tptp.num)) (= (tptp.bitM (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.bitM N))))) (forall ((N tptp.num)) (= (tptp.plus_plus_num tptp.one (tptp.bitM N)) (tptp.aa_num_num tptp.bit0 N))) (forall ((N tptp.num)) (= (tptp.plus_plus_num (tptp.bitM N) tptp.one) (tptp.aa_num_num tptp.bit0 N))) (forall ((N tptp.num) (M tptp.num)) (= (tptp.bit_or_not_num_neg (tptp.aa_num_num tptp.bit1 N) (tptp.aa_num_num tptp.bit0 M)) (tptp.bitM (tptp.bit_or_not_num_neg N M)))) (forall ((N tptp.num)) (= (tptp.numera6690914467698888265omplex (tptp.bitM N)) (tptp.minus_minus_complex (tptp.numera6690914467698888265omplex (tptp.aa_num_num tptp.bit0 N)) tptp.one_one_complex))) (forall ((N tptp.num)) (= (tptp.numeral_numeral_real (tptp.bitM N)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 N))) tptp.one_one_real))) (forall ((N tptp.num)) (= (tptp.numeral_numeral_rat (tptp.bitM N)) (tptp.minus_minus_rat (tptp.numeral_numeral_rat (tptp.aa_num_num tptp.bit0 N)) tptp.one_one_rat))) (forall ((N tptp.num)) (= (tptp.aa_num_int tptp.numeral_numeral_int (tptp.bitM N)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 N))) tptp.one_one_int))) (forall ((W 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.bitM W)))))) (forall ((W 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.bitM W)))))) (forall ((W 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.bitM W)))))) (forall ((N tptp.num)) (= (tptp.aa_Cod1783974652533396728nteger tptp.bit_ri7632146776885996613nteger (tptp.numera6620942414471956472nteger (tptp.bitM N))) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 N))))) (forall ((N tptp.num)) (= (tptp.aa_int_int tptp.bit_ri7919022796975470100ot_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.bitM N))) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 N))))) (forall ((X tptp.num) (Xa tptp.num) (Y tptp.num)) (let ((_let_1 (= Xa tptp.one))) (let ((_let_2 (=> _let_1 (not (= Y tptp.one))))) (let ((_let_3 (= X tptp.one))) (=> (= (tptp.bit_or_not_num_neg X Xa) Y) (=> (=> _let_3 _let_2) (=> (=> _let_3 (forall ((M2 tptp.num)) (=> (= Xa (tptp.aa_num_num tptp.bit0 M2)) (not (= Y (tptp.aa_num_num tptp.bit1 M2)))))) (=> (=> _let_3 (forall ((M2 tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit1 M2))) (=> (= Xa _let_1) (not (= Y _let_1)))))) (=> (=> (exists ((N2 tptp.num)) (= X (tptp.aa_num_num tptp.bit0 N2))) (=> _let_1 (not (= Y (tptp.aa_num_num tptp.bit0 tptp.one))))) (=> (forall ((N2 tptp.num)) (=> (= X (tptp.aa_num_num tptp.bit0 N2)) (forall ((M2 tptp.num)) (=> (= Xa (tptp.aa_num_num tptp.bit0 M2)) (not (= Y (tptp.bitM (tptp.bit_or_not_num_neg N2 M2)))))))) (=> (forall ((N2 tptp.num)) (=> (= X (tptp.aa_num_num tptp.bit0 N2)) (forall ((M2 tptp.num)) (=> (= Xa (tptp.aa_num_num tptp.bit1 M2)) (not (= Y (tptp.aa_num_num tptp.bit0 (tptp.bit_or_not_num_neg N2 M2)))))))) (=> (=> (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 ((M2 tptp.num)) (=> (= Xa (tptp.aa_num_num tptp.bit0 M2)) (not (= Y (tptp.bitM (tptp.bit_or_not_num_neg N2 M2)))))))) (not (forall ((N2 tptp.num)) (=> (= X (tptp.aa_num_num tptp.bit1 N2)) (forall ((M2 tptp.num)) (=> (= Xa (tptp.aa_num_num tptp.bit1 M2)) (not (= Y (tptp.bitM (tptp.bit_or_not_num_neg N2 M2)))))))))))))))))))))) (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 ((Xs tptp.list_VEBT_VEBT)) (= (tptp.size_s8217280938318005548T_VEBT (tptp.subseqs_VEBT_VEBT Xs)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.size_s6755466524823107622T_VEBT Xs)))) (forall ((Xs tptp.list_bool)) (= (tptp.size_s9193230429364170767t_bool (tptp.subseqs_bool Xs)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.size_size_list_bool Xs)))) (forall ((Xs tptp.list_nat)) (= (tptp.size_s3023201423986296836st_nat (tptp.subseqs_nat Xs)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.size_size_list_nat Xs)))) (forall ((Xs tptp.list_int)) (= (tptp.size_s533118279054570080st_int (tptp.subseqs_int Xs)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.size_size_list_int Xs)))) (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.pred_numeral L) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.inc K)))))) (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.aa_nat_fun_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.aa_nat_fun_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 ((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.aa_nat_fun_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.aa_nat_fun_nat_nat tptp.bit_se8570568707652914677it_nat M) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se8570568707652914677it_nat N) A)) (tptp.aa_nat_nat (tptp.aa_nat_fun_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)) (= (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.aa_nat_fun_nat_nat tptp.bit_se8570568707652914677it_nat N))) (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se727722235901077358nd_nat A) B)) (tptp.aa_nat_nat (tptp.aa_nat_fun_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.aa_nat_fun_nat_nat tptp.bit_se8570568707652914677it_nat N))) (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se1412395901928357646or_nat A) B)) (tptp.aa_nat_nat (tptp.aa_nat_fun_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.aa_nat_fun_nat_nat tptp.bit_se8570568707652914677it_nat N))) (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se6528837805403552850or_nat A) B)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se6528837805403552850or_nat (tptp.aa_nat_nat _let_1 A)) (tptp.aa_nat_nat _let_1 B))))) (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.aa_nat_fun_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 ((N tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se8570568707652914677it_nat N) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)) (tptp.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) (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 ((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.aa_nat_fun_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.aa_nat_fun_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.aa_nat_fun_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.aa_nat_fun_nat_nat tptp.bit_se8570568707652914677it_nat N) (tptp.aa_num_nat tptp.numeral_numeral_nat K)))) (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.aa_nat_fun_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 ((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.pred_numeral L) (tptp.aa_num_int tptp.numeral_numeral_int K)))) (forall ((L tptp.num) (K tptp.num)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_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.aa_nat_fun_nat_nat tptp.bit_se8570568707652914677it_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.pred_numeral L) (tptp.aa_num_int tptp.numeral_numeral_int K)))) (forall ((L tptp.num) (K tptp.num)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_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.aa_nat_fun_nat_nat tptp.bit_se8570568707652914677it_nat (tptp.pred_numeral L)) (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_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.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.inc K)))))) (forall ((N tptp.nat) (K tptp.int)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se8570568707652914677it_nat N) (tptp.aa_int_nat tptp.nat2 K)) (tptp.aa_int_nat tptp.nat2 (tptp.bit_se8568078237143864401it_int N K)))) (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.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.aa_nat_fun_nat_nat 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.aa_nat_fun_nat_nat tptp.bit_se8570568707652914677it_nat N) M)))) (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat 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 ((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.aa_nat_fun_nat_nat tptp.bit_se2925701944663578781it_nat N) A) A) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_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.aa_int_int (tptp.aa_nat_fun_int_int 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.aa_int_int (tptp.aa_nat_fun_int_int 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.aa_nat_fun_nat_nat tptp.bit_se8570568707652914677it_nat N))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_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.aa_nat_fun_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.aa_nat_fun_nat_nat tptp.bit_se8570568707652914677it_nat M))) (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se2925701944663578781it_nat N) A)) (tptp.aa_nat_nat (tptp.aa_nat_fun_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))))) (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.aa_nat_fun_nat_nat tptp.bit_se547839408752420682it_nat N) tptp.one_one_nat)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se8570568707652914677it_nat N) A))) (forall ((A tptp.int) (N tptp.nat)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A) (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_se545348938243370406it_int N) tptp.one_one_int)) (tptp.bit_se8568078237143864401it_int N A))) (forall ((A tptp.code_integer) (N tptp.nat)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.divide6298287555418463151nteger A) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_nat6383147911832638789nteger tptp.bit_se7788150548672797655nteger N) tptp.one_one_Code_integer)) (tptp.bit_se3928097537394005634nteger N A))) (forall ((A tptp.code_natural) (N tptp.nat)) (= (tptp.aa_Cod4272041906116450446atural (tptp.aa_Cod5141017464274028979atural tptp.divide5121882707175180666atural A) (tptp.aa_Cod4272041906116450446atural (tptp.aa_nat5282697797315388251atural tptp.bit_se6611745700429515170atural N) tptp.one_one_Code_natural)) (tptp.bit_se2751692689150723149atural N A))) (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.aa_nat_fun_nat_nat tptp.bit_se727722235901077358nd_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se8570568707652914677it_nat N) A)) tptp.one_one_nat) tptp.one_one_nat))) (forall ((N tptp.nat) (A tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_nat6383147911832638789nteger tptp.bit_se7788150548672797655nteger N) (tptp.bit_se3928097537394005634nteger N A))) (tptp.bit_se1745604003318907178nteger N A)) A)) (forall ((N tptp.nat) (A tptp.code_natural)) (= (tptp.aa_Cod4272041906116450446atural (tptp.aa_Cod5141017464274028979atural tptp.plus_p4538020629002901425atural (tptp.aa_Cod4272041906116450446atural (tptp.aa_nat5282697797315388251atural tptp.bit_se6611745700429515170atural N) (tptp.bit_se2751692689150723149atural N A))) (tptp.bit_se569199155075624693atural N A)) A)) (forall ((N tptp.nat) (A tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_nat_fun_int_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.aa_nat_fun_nat_nat tptp.bit_se547839408752420682it_nat N) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se8570568707652914677it_nat N) A))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se2925701944663578781it_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.aa_nat_fun_nat_nat 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 ((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.aa_nat_fun_nat_nat tptp.bit_se8570568707652914677it_nat N) A) A))) (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 ((N tptp.nat) (M tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se8570568707652914677it_nat N) M) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat M) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N)))) (forall ((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.aa_nat_fun_nat_nat tptp.bit_se8570568707652914677it_nat (tptp.aa_nat_nat tptp.suc N)) A) (tptp.aa_nat_nat (tptp.aa_nat_fun_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.aa_nat_fun_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.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N)))) (forall ((A tptp.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.aa_nat_fun_nat_nat tptp.bit_se8570568707652914677it_nat N) A)))))) (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.aa_nat_fun_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 ((N tptp.nat) (M tptp.nat) (A tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_nat6383147911832638789nteger tptp.bit_se7788150548672797655nteger N) (tptp.bit_se1745604003318907178nteger M (tptp.bit_se3928097537394005634nteger N A))) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.bit_se3949692690581998587nteger A) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.bit_se3949692690581998587nteger (tptp.bit_se2119862282449309892nteger (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) N))) (tptp.aa_Cod1783974652533396728nteger tptp.bit_ri7632146776885996613nteger (tptp.bit_se2119862282449309892nteger N)))))) (forall ((N tptp.nat) (M tptp.nat) (A tptp.int)) (= (tptp.aa_int_int (tptp.aa_nat_fun_int_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 ((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_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.aa_nat_set_nat (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_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 ((N tptp.nat) (Xs tptp.list_VEBT_VEBT)) (let ((_let_1 (tptp.size_s6755466524823107622T_VEBT Xs))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N) _let_1)) (= (tptp.nth_VEBT_VEBT (tptp.rotate1_VEBT_VEBT Xs) N) (tptp.nth_VEBT_VEBT Xs (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat tptp.suc N)) _let_1)))))) (forall ((N tptp.nat) (Xs tptp.list_bool)) (let ((_let_1 (tptp.size_size_list_bool Xs))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N) _let_1)) (= (tptp.pp (tptp.aa_nat_bool (tptp.nth_bool (tptp.rotate1_bool Xs)) N)) (tptp.pp (tptp.aa_nat_bool (tptp.nth_bool Xs) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat tptp.suc N)) _let_1))))))) (forall ((N tptp.nat) (Xs tptp.list_nat)) (let ((_let_1 (tptp.size_size_list_nat Xs))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N) _let_1)) (= (tptp.aa_nat_nat (tptp.nth_nat (tptp.rotate1_nat Xs)) N) (tptp.aa_nat_nat (tptp.nth_nat Xs) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat tptp.suc N)) _let_1)))))) (forall ((N tptp.nat) (Xs tptp.list_int)) (let ((_let_1 (tptp.size_size_list_int Xs))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N) _let_1)) (= (tptp.aa_nat_int (tptp.nth_int (tptp.rotate1_int Xs)) N) (tptp.aa_nat_int (tptp.nth_int Xs) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat tptp.suc N)) _let_1)))))) (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.neg_numeral_sub_int N tptp.one)))))) (forall ((N tptp.nat)) (= (tptp.aa_real_real (tptp.aa_nat_fun_real_real tptp.root N) tptp.zero_zero_real) tptp.zero_zero_real)) (forall ((X tptp.real)) (= (tptp.aa_real_real (tptp.aa_nat_fun_real_real tptp.root (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)) X) X)) (forall ((X tptp.real)) (= (tptp.aa_real_real (tptp.aa_nat_fun_real_real tptp.root tptp.zero_zero_nat) X) tptp.zero_zero_real)) (forall ((N tptp.nat) (X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_nat_fun_real_real tptp.root N))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (= (= (tptp.aa_real_real _let_1 X) (tptp.aa_real_real _let_1 Y)) (= X Y))))) (= (tptp.neg_numeral_sub_real tptp.one tptp.one) tptp.zero_zero_real) (= (tptp.neg_numeral_sub_rat tptp.one tptp.one) tptp.zero_zero_rat) (= (tptp.neg_numeral_sub_int tptp.one tptp.one) tptp.zero_zero_int) (forall ((M tptp.num) (N tptp.num)) (= (tptp.minus_minus_complex (tptp.numera6690914467698888265omplex M) (tptp.numera6690914467698888265omplex N)) (tptp.neg_nu8416839295433526191omplex M N))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.numeral_numeral_real M)) (tptp.numeral_numeral_real N)) (tptp.neg_numeral_sub_real M N))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.minus_minus_rat (tptp.numeral_numeral_rat M) (tptp.numeral_numeral_rat N)) (tptp.neg_numeral_sub_rat 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_num_int tptp.numeral_numeral_int N)) (tptp.neg_numeral_sub_int M N))) (forall ((K tptp.num) (L tptp.num)) (= (tptp.neg_numeral_sub_int (tptp.aa_num_num tptp.bit0 K) (tptp.aa_num_num tptp.bit0 L)) (tptp.neg_numeral_dbl_int (tptp.neg_numeral_sub_int K L)))) (forall ((K tptp.num) (L tptp.num)) (= (tptp.neg_numeral_sub_int (tptp.aa_num_num tptp.bit1 K) (tptp.aa_num_num tptp.bit1 L)) (tptp.neg_numeral_dbl_int (tptp.neg_numeral_sub_int K L)))) (forall ((V tptp.num) (W tptp.num) (Y tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real tptp.uminus_uminus_real (tptp.numeral_numeral_real V))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.numeral_numeral_real W)) Y)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.neg_numeral_sub_real W V)) Y))) (forall ((V tptp.num) (W tptp.num) (Y tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int V))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_num_int tptp.numeral_numeral_int W)) Y)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.neg_numeral_sub_int W V)) Y))) (forall ((V tptp.num) (W tptp.num) (Y tptp.complex)) (= (tptp.plus_plus_complex (tptp.uminus1482373934393186551omplex (tptp.numera6690914467698888265omplex V)) (tptp.plus_plus_complex (tptp.numera6690914467698888265omplex W) Y)) (tptp.plus_plus_complex (tptp.neg_nu8416839295433526191omplex W V) Y))) (forall ((V tptp.num) (W tptp.num) (Y tptp.rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.uminus_uminus_rat (tptp.numeral_numeral_rat V))) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.numeral_numeral_rat W)) Y)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.neg_numeral_sub_rat W V)) Y))) (forall ((V tptp.num) (W tptp.num) (Y tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.numera6620942414471956472nteger V))) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.plus_p5714425477246183910nteger (tptp.numera6620942414471956472nteger W)) Y)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.plus_p5714425477246183910nteger (tptp.neg_nu5755505904847501662nteger W V)) Y))) (forall ((V tptp.num) (W tptp.num) (Y tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_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.numeral_numeral_real W))) Y)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.neg_numeral_sub_real V W)) Y))) (forall ((V tptp.num) (W tptp.num) (Y tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_num_int tptp.numeral_numeral_int V)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int W))) Y)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.neg_numeral_sub_int V W)) Y))) (forall ((V tptp.num) (W tptp.num) (Y tptp.complex)) (= (tptp.plus_plus_complex (tptp.numera6690914467698888265omplex V) (tptp.plus_plus_complex (tptp.uminus1482373934393186551omplex (tptp.numera6690914467698888265omplex W)) Y)) (tptp.plus_plus_complex (tptp.neg_nu8416839295433526191omplex V W) Y))) (forall ((V tptp.num) (W tptp.num) (Y tptp.rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.numeral_numeral_rat V)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.uminus_uminus_rat (tptp.numeral_numeral_rat W))) Y)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.neg_numeral_sub_rat V W)) Y))) (forall ((V tptp.num) (W tptp.num) (Y tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.plus_p5714425477246183910nteger (tptp.numera6620942414471956472nteger V)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.numera6620942414471956472nteger W))) Y)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.plus_p5714425477246183910nteger (tptp.neg_nu5755505904847501662nteger V W)) Y))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real tptp.uminus_uminus_real (tptp.numeral_numeral_real M))) (tptp.numeral_numeral_real N)) (tptp.neg_numeral_sub_real N M))) (forall ((M tptp.num) (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.aa_num_int tptp.numeral_numeral_int M))) (tptp.aa_num_int tptp.numeral_numeral_int N)) (tptp.neg_numeral_sub_int N M))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.plus_plus_complex (tptp.uminus1482373934393186551omplex (tptp.numera6690914467698888265omplex M)) (tptp.numera6690914467698888265omplex N)) (tptp.neg_nu8416839295433526191omplex N M))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.uminus_uminus_rat (tptp.numeral_numeral_rat M))) (tptp.numeral_numeral_rat N)) (tptp.neg_numeral_sub_rat N M))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.numera6620942414471956472nteger M))) (tptp.numera6620942414471956472nteger N)) (tptp.neg_nu5755505904847501662nteger N M))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.numeral_numeral_real M)) (tptp.aa_real_real tptp.uminus_uminus_real (tptp.numeral_numeral_real N))) (tptp.neg_numeral_sub_real 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_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int N))) (tptp.neg_numeral_sub_int M N))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.plus_plus_complex (tptp.numera6690914467698888265omplex M) (tptp.uminus1482373934393186551omplex (tptp.numera6690914467698888265omplex N))) (tptp.neg_nu8416839295433526191omplex M N))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.numeral_numeral_rat M)) (tptp.uminus_uminus_rat (tptp.numeral_numeral_rat N))) (tptp.neg_numeral_sub_rat M N))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.plus_p5714425477246183910nteger (tptp.numera6620942414471956472nteger M)) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.numera6620942414471956472nteger N))) (tptp.neg_nu5755505904847501662nteger M 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.aa_real_real (tptp.aa_nat_fun_real_real tptp.root N) X) tptp.zero_zero_real) (= X tptp.zero_zero_real)))) (forall ((N tptp.nat) (X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_nat_fun_real_real tptp.root N))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real _let_1 X)) (tptp.aa_real_real _let_1 Y))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Y)))))) (forall ((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.numeral_numeral_real M))) (tptp.aa_real_real tptp.uminus_uminus_real (tptp.numeral_numeral_real N))) (tptp.neg_numeral_sub_real N M))) (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_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int N))) (tptp.neg_numeral_sub_int N M))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.minus_minus_complex (tptp.uminus1482373934393186551omplex (tptp.numera6690914467698888265omplex M)) (tptp.uminus1482373934393186551omplex (tptp.numera6690914467698888265omplex N))) (tptp.neg_nu8416839295433526191omplex N M))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.minus_minus_rat (tptp.uminus_uminus_rat (tptp.numeral_numeral_rat M)) (tptp.uminus_uminus_rat (tptp.numeral_numeral_rat N))) (tptp.neg_numeral_sub_rat N M))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.minus_8373710615458151222nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.numera6620942414471956472nteger M))) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.numera6620942414471956472nteger N))) (tptp.neg_nu5755505904847501662nteger N M))) (forall ((N tptp.nat) (X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_nat_fun_real_real tptp.root N))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real _let_1 X)) (tptp.aa_real_real _let_1 Y))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) Y)))))) (forall ((N tptp.nat) (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)) (=> (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 ((Xs tptp.list_VEBT_VEBT)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.size_s6755466524823107622T_VEBT Xs)) tptp.one_one_nat)) (= (tptp.rotate1_VEBT_VEBT Xs) Xs))) (forall ((Xs tptp.list_bool)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.size_size_list_bool Xs)) tptp.one_one_nat)) (= (tptp.rotate1_bool Xs) Xs))) (forall ((Xs tptp.list_nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.size_size_list_nat Xs)) tptp.one_one_nat)) (= (tptp.rotate1_nat Xs) Xs))) (forall ((Xs tptp.list_int)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.size_size_list_int Xs)) tptp.one_one_nat)) (= (tptp.rotate1_int Xs) Xs))) (forall ((K tptp.num) (L tptp.num)) (= (tptp.neg_numeral_sub_int (tptp.aa_num_num tptp.bit0 K) (tptp.aa_num_num tptp.bit1 L)) (tptp.neg_nu3811975205180677377ec_int (tptp.neg_numeral_sub_int K L)))) (forall ((K tptp.num) (L tptp.num)) (= (tptp.neg_numeral_sub_int (tptp.aa_num_num tptp.bit1 K) (tptp.aa_num_num tptp.bit0 L)) (tptp.neg_nu5851722552734809277nc_int (tptp.neg_numeral_sub_int K L)))) (forall ((N tptp.num)) (= (tptp.minus_minus_complex tptp.one_one_complex (tptp.numera6690914467698888265omplex N)) (tptp.neg_nu8416839295433526191omplex tptp.one N))) (forall ((N tptp.num)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real tptp.one_one_real) (tptp.numeral_numeral_real N)) (tptp.neg_numeral_sub_real tptp.one N))) (forall ((N tptp.num)) (= (tptp.minus_minus_rat tptp.one_one_rat (tptp.numeral_numeral_rat N)) (tptp.neg_numeral_sub_rat 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_num_int tptp.numeral_numeral_int N)) (tptp.neg_numeral_sub_int tptp.one N))) (forall ((M tptp.num)) (= (tptp.minus_minus_complex (tptp.numera6690914467698888265omplex M) tptp.one_one_complex) (tptp.neg_nu8416839295433526191omplex M tptp.one))) (forall ((M tptp.num)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.numeral_numeral_real M)) tptp.one_one_real) (tptp.neg_numeral_sub_real M tptp.one))) (forall ((M tptp.num)) (= (tptp.minus_minus_rat (tptp.numeral_numeral_rat M) tptp.one_one_rat) (tptp.neg_numeral_sub_rat M tptp.one))) (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.one_one_int) (tptp.neg_numeral_sub_int M tptp.one))) (forall ((N tptp.nat) (Y tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (= (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real (tptp.aa_nat_fun_real_real tptp.root N) Y))) (tptp.pp (tptp.aa_real_bool _let_1 Y)))))) (forall ((N tptp.nat) (X tptp.real)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_nat_fun_real_real tptp.root N) X)) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) tptp.zero_zero_real))))) (forall ((N tptp.nat) (Y tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (= (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real (tptp.aa_nat_fun_real_real tptp.root N) Y))) (tptp.pp (tptp.aa_real_bool _let_1 Y)))))) (forall ((N tptp.nat) (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 ((K tptp.num)) (= (tptp.neg_nu8416839295433526191omplex (tptp.aa_num_num tptp.bit1 K) tptp.one) (tptp.numera6690914467698888265omplex (tptp.aa_num_num tptp.bit0 K)))) (forall ((K tptp.num)) (= (tptp.neg_numeral_sub_real (tptp.aa_num_num tptp.bit1 K) tptp.one) (tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 K)))) (forall ((K tptp.num)) (= (tptp.neg_numeral_sub_rat (tptp.aa_num_num tptp.bit1 K) tptp.one) (tptp.numeral_numeral_rat (tptp.aa_num_num tptp.bit0 K)))) (forall ((K tptp.num)) (= (tptp.neg_numeral_sub_int (tptp.aa_num_num tptp.bit1 K) tptp.one) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 K)))) (forall ((N tptp.nat) (Y tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (= (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real (tptp.aa_nat_fun_real_real tptp.root N) Y))) (tptp.pp (tptp.aa_real_bool _let_1 Y)))))) (forall ((N tptp.nat) (X tptp.real)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_nat_fun_real_real tptp.root N) X)) tptp.one_one_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) tptp.one_one_real))))) (forall ((N tptp.nat) (Y tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.one_one_real))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (= (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real (tptp.aa_nat_fun_real_real tptp.root N) Y))) (tptp.pp (tptp.aa_real_bool _let_1 Y)))))) (forall ((N tptp.nat) (X tptp.real)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.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.num)) (= (tptp.aa_Cod1783974652533396728nteger tptp.bit_ri7632146776885996613nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.numera6620942414471956472nteger N))) (tptp.neg_nu5755505904847501662nteger N tptp.one))) (forall ((N tptp.num)) (= (tptp.aa_int_int tptp.bit_ri7919022796975470100ot_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int N))) (tptp.neg_numeral_sub_int N tptp.one))) (forall ((K tptp.num)) (= (tptp.neg_nu8416839295433526191omplex (tptp.aa_num_num tptp.bit0 K) tptp.one) (tptp.numera6690914467698888265omplex (tptp.bitM K)))) (forall ((K tptp.num)) (= (tptp.neg_numeral_sub_real (tptp.aa_num_num tptp.bit0 K) tptp.one) (tptp.numeral_numeral_real (tptp.bitM K)))) (forall ((K tptp.num)) (= (tptp.neg_numeral_sub_rat (tptp.aa_num_num tptp.bit0 K) tptp.one) (tptp.numeral_numeral_rat (tptp.bitM K)))) (forall ((K tptp.num)) (= (tptp.neg_numeral_sub_int (tptp.aa_num_num tptp.bit0 K) tptp.one) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.bitM K)))) (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.numeral_numeral_real N)) (tptp.neg_numeral_sub_real N tptp.one))) (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_num_int tptp.numeral_numeral_int N)) (tptp.neg_numeral_sub_int N tptp.one))) (forall ((N tptp.num)) (= (tptp.plus_plus_complex (tptp.uminus1482373934393186551omplex tptp.one_one_complex) (tptp.numera6690914467698888265omplex N)) (tptp.neg_nu8416839295433526191omplex N tptp.one))) (forall ((N tptp.num)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.uminus_uminus_rat tptp.one_one_rat)) (tptp.numeral_numeral_rat N)) (tptp.neg_numeral_sub_rat N tptp.one))) (forall ((N tptp.num)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (tptp.numera6620942414471956472nteger N)) (tptp.neg_nu5755505904847501662nteger N tptp.one))) (forall ((M tptp.num)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.numeral_numeral_real M)) (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)) (tptp.neg_numeral_sub_real M tptp.one))) (forall ((M 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_int_int tptp.uminus_uminus_int tptp.one_one_int)) (tptp.neg_numeral_sub_int M tptp.one))) (forall ((M tptp.num)) (= (tptp.plus_plus_complex (tptp.numera6690914467698888265omplex M) (tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (tptp.neg_nu8416839295433526191omplex M tptp.one))) (forall ((M tptp.num)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.numeral_numeral_rat M)) (tptp.uminus_uminus_rat tptp.one_one_rat)) (tptp.neg_numeral_sub_rat M tptp.one))) (forall ((M tptp.num)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.plus_p5714425477246183910nteger (tptp.numera6620942414471956472nteger M)) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (tptp.neg_nu5755505904847501662nteger M tptp.one))) (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.numeral_numeral_real M))) tptp.one_one_real) (tptp.neg_numeral_sub_real tptp.one 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.one_one_int) (tptp.neg_numeral_sub_int tptp.one M))) (forall ((M tptp.num)) (= (tptp.plus_plus_complex (tptp.uminus1482373934393186551omplex (tptp.numera6690914467698888265omplex M)) tptp.one_one_complex) (tptp.neg_nu8416839295433526191omplex tptp.one M))) (forall ((M tptp.num)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.uminus_uminus_rat (tptp.numeral_numeral_rat M))) tptp.one_one_rat) (tptp.neg_numeral_sub_rat tptp.one M))) (forall ((M tptp.num)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.numera6620942414471956472nteger M))) tptp.one_one_Code_integer) (tptp.neg_nu5755505904847501662nteger tptp.one M))) (forall ((M tptp.num)) (= (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.numeral_numeral_real M))) (tptp.neg_numeral_sub_real tptp.one M))) (forall ((M tptp.num)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int tptp.one_one_int) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int M))) (tptp.neg_numeral_sub_int tptp.one M))) (forall ((M tptp.num)) (= (tptp.plus_plus_complex tptp.one_one_complex (tptp.uminus1482373934393186551omplex (tptp.numera6690914467698888265omplex M))) (tptp.neg_nu8416839295433526191omplex tptp.one M))) (forall ((M tptp.num)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat tptp.one_one_rat) (tptp.uminus_uminus_rat (tptp.numeral_numeral_rat M))) (tptp.neg_numeral_sub_rat tptp.one M))) (forall ((M tptp.num)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.numera6620942414471956472nteger M))) (tptp.neg_nu5755505904847501662nteger tptp.one M))) (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.numeral_numeral_real M))) (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)) (tptp.neg_numeral_sub_real tptp.one M))) (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.aa_int_int tptp.uminus_uminus_int tptp.one_one_int)) (tptp.neg_numeral_sub_int tptp.one M))) (forall ((M tptp.num)) (= (tptp.minus_minus_complex (tptp.uminus1482373934393186551omplex (tptp.numera6690914467698888265omplex M)) (tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (tptp.neg_nu8416839295433526191omplex tptp.one M))) (forall ((M tptp.num)) (= (tptp.minus_minus_rat (tptp.uminus_uminus_rat (tptp.numeral_numeral_rat M)) (tptp.uminus_uminus_rat tptp.one_one_rat)) (tptp.neg_numeral_sub_rat tptp.one M))) (forall ((M tptp.num)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.minus_8373710615458151222nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.numera6620942414471956472nteger M))) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (tptp.neg_nu5755505904847501662nteger tptp.one 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_real_real tptp.uminus_uminus_real (tptp.numeral_numeral_real N))) (tptp.neg_numeral_sub_real N tptp.one))) (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_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int N))) (tptp.neg_numeral_sub_int N tptp.one))) (forall ((N tptp.num)) (= (tptp.minus_minus_complex (tptp.uminus1482373934393186551omplex tptp.one_one_complex) (tptp.uminus1482373934393186551omplex (tptp.numera6690914467698888265omplex N))) (tptp.neg_nu8416839295433526191omplex N tptp.one))) (forall ((N tptp.num)) (= (tptp.minus_minus_rat (tptp.uminus_uminus_rat tptp.one_one_rat) (tptp.uminus_uminus_rat (tptp.numeral_numeral_rat N))) (tptp.neg_numeral_sub_rat N tptp.one))) (forall ((N tptp.num)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.minus_8373710615458151222nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.numera6620942414471956472nteger N))) (tptp.neg_nu5755505904847501662nteger N tptp.one))) (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.neg_numeral_sub_real M tptp.one))) tptp.one_one_real) (tptp.aa_real_real tptp.uminus_uminus_real (tptp.numeral_numeral_real M)))) (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.neg_numeral_sub_int M tptp.one))) 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)) (= (tptp.minus_minus_complex (tptp.uminus1482373934393186551omplex (tptp.neg_nu8416839295433526191omplex M tptp.one)) tptp.one_one_complex) (tptp.uminus1482373934393186551omplex (tptp.numera6690914467698888265omplex M)))) (forall ((M tptp.num)) (= (tptp.minus_minus_rat (tptp.uminus_uminus_rat (tptp.neg_numeral_sub_rat M tptp.one)) tptp.one_one_rat) (tptp.uminus_uminus_rat (tptp.numeral_numeral_rat M)))) (forall ((M tptp.num)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.minus_8373710615458151222nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.neg_nu5755505904847501662nteger M tptp.one))) tptp.one_one_Code_integer) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.numera6620942414471956472nteger M)))) (forall ((L tptp.num)) (= (tptp.neg_numeral_sub_real tptp.one (tptp.aa_num_num tptp.bit1 L)) (tptp.aa_real_real tptp.uminus_uminus_real (tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 L))))) (forall ((L tptp.num)) (= (tptp.neg_numeral_sub_int tptp.one (tptp.aa_num_num tptp.bit1 L)) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 L))))) (forall ((L tptp.num)) (= (tptp.neg_nu8416839295433526191omplex tptp.one (tptp.aa_num_num tptp.bit1 L)) (tptp.uminus1482373934393186551omplex (tptp.numera6690914467698888265omplex (tptp.aa_num_num tptp.bit0 L))))) (forall ((L tptp.num)) (= (tptp.neg_numeral_sub_rat tptp.one (tptp.aa_num_num tptp.bit1 L)) (tptp.uminus_uminus_rat (tptp.numeral_numeral_rat (tptp.aa_num_num tptp.bit0 L))))) (forall ((L tptp.num)) (= (tptp.neg_nu5755505904847501662nteger tptp.one (tptp.aa_num_num tptp.bit1 L)) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 L))))) (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 ((L tptp.num)) (= (tptp.neg_numeral_sub_real tptp.one (tptp.aa_num_num tptp.bit0 L)) (tptp.aa_real_real tptp.uminus_uminus_real (tptp.numeral_numeral_real (tptp.bitM L))))) (forall ((L tptp.num)) (= (tptp.neg_numeral_sub_int tptp.one (tptp.aa_num_num tptp.bit0 L)) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.bitM L))))) (forall ((L tptp.num)) (= (tptp.neg_nu8416839295433526191omplex tptp.one (tptp.aa_num_num tptp.bit0 L)) (tptp.uminus1482373934393186551omplex (tptp.numera6690914467698888265omplex (tptp.bitM L))))) (forall ((L tptp.num)) (= (tptp.neg_numeral_sub_rat tptp.one (tptp.aa_num_num tptp.bit0 L)) (tptp.uminus_uminus_rat (tptp.numeral_numeral_rat (tptp.bitM L))))) (forall ((L tptp.num)) (= (tptp.neg_nu5755505904847501662nteger tptp.one (tptp.aa_num_num tptp.bit0 L)) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.numera6620942414471956472nteger (tptp.bitM L))))) (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.neg_numeral_sub_int N tptp.one)) K)))) (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) (Y tptp.real)) (let ((_let_1 (tptp.aa_nat_fun_real_real tptp.root N))) (= (tptp.aa_real_real _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real X) Y)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real _let_1 X)) (tptp.aa_real_real _let_1 Y))))) (forall ((N tptp.nat) (X tptp.real)) (let ((_let_1 (tptp.aa_nat_fun_real_real tptp.root N))) (= (tptp.aa_real_real _let_1 (tptp.aa_real_real tptp.uminus_uminus_real X)) (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_real_real _let_1 X))))) (forall ((M tptp.nat) (N tptp.nat) (X tptp.real)) (let ((_let_1 (tptp.aa_nat_fun_real_real tptp.root M))) (let ((_let_2 (tptp.aa_nat_fun_real_real tptp.root N))) (= (tptp.aa_real_real _let_1 (tptp.aa_real_real _let_2 X)) (tptp.aa_real_real _let_2 (tptp.aa_real_real _let_1 X)))))) (forall ((N tptp.nat) (X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_nat_fun_real_real tptp.root N))) (= (tptp.aa_real_real _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real X) Y)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real _let_1 X)) (tptp.aa_real_real _let_1 Y))))) (forall ((X tptp.real) (N tptp.nat)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool _let_1 X)) (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real (tptp.aa_nat_fun_real_real tptp.root N) X)))))) (forall ((K tptp.num) (L tptp.num)) (= (tptp.neg_nu8416839295433526191omplex K L) (tptp.minus_minus_complex (tptp.numera6690914467698888265omplex K) (tptp.numera6690914467698888265omplex L)))) (forall ((K tptp.num) (L tptp.num)) (= (tptp.neg_numeral_sub_real K L) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.numeral_numeral_real K)) (tptp.numeral_numeral_real L)))) (forall ((K tptp.num) (L tptp.num)) (= (tptp.neg_numeral_sub_rat K L) (tptp.minus_minus_rat (tptp.numeral_numeral_rat K) (tptp.numeral_numeral_rat L)))) (forall ((K tptp.num) (L tptp.num)) (= (tptp.neg_numeral_sub_int K L) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_num_int tptp.numeral_numeral_int K)) (tptp.aa_num_int tptp.numeral_numeral_int L)))) (forall ((N tptp.nat) (X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_nat_fun_real_real tptp.root N))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Y)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real _let_1 X)) (tptp.aa_real_real _let_1 Y))))))) (forall ((N tptp.nat) (X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_nat_fun_real_real tptp.root N))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) Y)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real _let_1 X)) (tptp.aa_real_real _let_1 Y))))))) (forall ((N tptp.nat) (X tptp.real) (K tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_real_real tptp.root N))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (= (tptp.aa_real_real _let_1 (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) K)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real _let_1 X)) K))))) (forall ((N tptp.nat) (X tptp.real)) (let ((_let_1 (tptp.aa_nat_fun_real_real tptp.root N))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (= (tptp.aa_real_real _let_1 (tptp.aa_real_real tptp.abs_abs_real X)) (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_real_real _let_1 X)))))) (forall ((X tptp.real) (Xs tptp.list_real)) (=> (tptp.member_real X (tptp.set_real2 Xs)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.size_size_list_real Xs))))) (forall ((X tptp.complex) (Xs tptp.list_complex)) (=> (tptp.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.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) (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.num) (M tptp.num)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.neg_numeral_sub_real N M))) (tptp.pp (tptp.aa_num_bool (tptp.ord_less_eq_num M) N)))) (forall ((N tptp.num) (M tptp.num)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.neg_numeral_sub_rat N M))) (tptp.pp (tptp.aa_num_bool (tptp.ord_less_eq_num M) N)))) (forall ((N tptp.num) (M tptp.num)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.neg_numeral_sub_int N M))) (tptp.pp (tptp.aa_num_bool (tptp.ord_less_eq_num M) N)))) (forall ((N tptp.num) (M tptp.num)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.neg_numeral_sub_real N M)) tptp.zero_zero_real)) (tptp.pp (tptp.aa_num_bool (tptp.ord_less_eq_num N) M)))) (forall ((N tptp.num) (M tptp.num)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.neg_numeral_sub_rat N M)) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_num_bool (tptp.ord_less_eq_num N) M)))) (forall ((N tptp.num) (M tptp.num)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.neg_numeral_sub_int N M)) tptp.zero_zero_int)) (tptp.pp (tptp.aa_num_bool (tptp.ord_less_eq_num N) M)))) (forall ((N tptp.num) (M tptp.num)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.neg_numeral_sub_real N M)) tptp.zero_zero_real)) (tptp.pp (tptp.aa_num_bool (tptp.ord_less_num N) M)))) (forall ((N tptp.num) (M tptp.num)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.neg_numeral_sub_rat N M)) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_num_bool (tptp.ord_less_num N) M)))) (forall ((N tptp.num) (M tptp.num)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.neg_numeral_sub_int N M)) tptp.zero_zero_int)) (tptp.pp (tptp.aa_num_bool (tptp.ord_less_num N) M)))) (forall ((N tptp.num) (M tptp.num)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) (tptp.neg_numeral_sub_real N M))) (tptp.pp (tptp.aa_num_bool (tptp.ord_less_num M) N)))) (forall ((N tptp.num) (M tptp.num)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) (tptp.neg_numeral_sub_rat N M))) (tptp.pp (tptp.aa_num_bool (tptp.ord_less_num M) N)))) (forall ((N tptp.num) (M tptp.num)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) (tptp.neg_numeral_sub_int N M))) (tptp.pp (tptp.aa_num_bool (tptp.ord_less_num M) N)))) (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) (N4 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) N4)) (=> (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 N4) 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) (Y tptp.real)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (= (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_real_real (tptp.aa_nat_fun_real_real tptp.root N) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Y) N))) (tptp.aa_real_real tptp.abs_abs_real Y)))) (forall ((N tptp.nat) (X tptp.real)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) X)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_real_real (tptp.aa_nat_fun_real_real tptp.root N) X)))))) (forall ((N tptp.nat) (N4 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) N4)) (=> (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 N4) X)))))))) (forall ((N tptp.nat) (N4 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) N4)) (=> (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 N4) X)) (tptp.aa_real_real (tptp.aa_nat_fun_real_real tptp.root N) X))))))) (forall ((N tptp.nat) (X tptp.real)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) X)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real (tptp.aa_nat_fun_real_real tptp.root N) X)) N) X)))) (forall ((N tptp.nat) (Y tptp.real) (X tptp.real)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) Y)) (=> (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Y) N) X) (= (tptp.aa_real_real (tptp.aa_nat_fun_real_real tptp.root N) X) Y))))) (forall ((N tptp.nat) (X tptp.real)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) X)) (= (tptp.aa_real_real (tptp.aa_nat_fun_real_real tptp.root N) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) N)) X)))) (forall ((N tptp.nat) (X tptp.real)) (=> (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N))) (= (tptp.aa_real_real (tptp.aa_nat_fun_real_real tptp.root N) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) N)) X))) (forall ((N tptp.nat) (Y tptp.real) (X tptp.real)) (=> (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N))) (=> (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Y) N) X) (= (tptp.aa_real_real (tptp.aa_nat_fun_real_real tptp.root N) X) Y)))) (forall ((N tptp.nat) (X tptp.real)) (=> (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N))) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real (tptp.aa_nat_fun_real_real tptp.root N) X)) N) X))) (forall ((N tptp.nat) (N4 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) N4)) (=> (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 N4) X)))))))) (forall ((N tptp.num)) (= (tptp.neg_numeral_sub_int (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.neg_numeral_sub_int N tptp.one)))) (forall ((N tptp.nat) (Y tptp.real)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (= (tptp.aa_real_real (tptp.aa_nat_fun_real_real tptp.root N) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real tptp.sgn_sgn_real Y)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real tptp.abs_abs_real Y)) N))) Y))) (forall ((N tptp.nat) (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.log2 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.log2 (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.log2 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 ((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.inc (tptp.aa_nat_num tptp.num_of_nat N)))) (=> (not _let_2) (= _let_1 tptp.one)))))) (forall ((X tptp.num) (Y tptp.num)) (= (tptp.pow X (tptp.aa_num_num tptp.bit1 Y)) (tptp.times_times_num (tptp.sqr (tptp.pow X Y)) X))) (forall ((Q2 tptp.num)) (= (tptp.aa_nat_num tptp.num_of_nat (tptp.aa_num_nat tptp.numeral_numeral_nat Q2)) Q2)) (forall ((N tptp.num)) (= (tptp.sqr (tptp.aa_num_num tptp.bit0 N)) (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit0 (tptp.sqr N))))) (= (tptp.sqr tptp.one) tptp.one) (forall ((X tptp.num)) (= (tptp.sqr X) (tptp.times_times_num X X))) (= (tptp.aa_nat_num tptp.num_of_nat tptp.zero_zero_nat) tptp.one) (forall ((N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (= (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_nat_num tptp.num_of_nat N)) N))) (forall ((N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N) tptp.one_one_nat)) (= (tptp.aa_nat_num tptp.num_of_nat N) tptp.one))) (forall ((X tptp.num) (Y tptp.num)) (= (tptp.pow X (tptp.aa_num_num tptp.bit0 Y)) (tptp.sqr (tptp.pow X Y)))) (forall ((N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (= (tptp.aa_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.plus_plus_num (tptp.aa_nat_num tptp.num_of_nat M) (tptp.aa_nat_num tptp.num_of_nat N))))))) (forall ((N tptp.num)) (= (tptp.sqr (tptp.aa_num_num tptp.bit1 N)) (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit0 (tptp.plus_plus_num (tptp.sqr N) N))))) (forall ((X tptp.int) (Xa tptp.int) (Y tptp.int)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int _let_1))) (let ((_let_3 (tptp.aa_bool_int tptp.zero_n2684676970156552555ol_int (tptp.aa_bool_bool (tptp.fconj (tptp.aa_bool_bool tptp.fNot (tptp.aa_int_bool _let_2 X))) (tptp.aa_bool_bool tptp.fNot (tptp.aa_int_bool _let_2 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) Y) (and (=> _let_5 (= Y (tptp.aa_int_int tptp.uminus_uminus_int _let_3))) (=> (not _let_5) (= Y (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int _let_3) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int _let_1) (tptp.aa_int_int (tptp.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)))) (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 ((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.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.pred_numeral K)) N)))) (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)) (= (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) (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) (K tptp.int) (L tptp.int) (R tptp.int)) (= (tptp.aa_int_int (tptp.bit_concat_bit M (tptp.aa_int_int (tptp.bit_concat_bit N K) L)) R) (tptp.aa_int_int (tptp.bit_concat_bit (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_min_nat M) N) K) (tptp.aa_int_int (tptp.bit_concat_bit (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) N) L) R)))) (forall ((M tptp.nat) (N tptp.nat) (K tptp.int) (L tptp.int)) (= (tptp.aa_int_int (tptp.bit_se2923211474154528505it_int M) (tptp.aa_int_int (tptp.bit_concat_bit N K) L)) (tptp.aa_int_int (tptp.bit_concat_bit (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_min_nat M) N) K) (tptp.aa_int_int (tptp.bit_se2923211474154528505it_int (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) N)) L)))) (= (tptp.aa_nat_set_nat tptp.nat_set_decode tptp.zero_zero_nat) tptp.bot_bot_set_nat) (forall ((N tptp.nat) (Z tptp.nat)) (let ((_let_1 (tptp.aa_nat_set_nat tptp.nat_set_decode Z))) (=> (not (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat N) _let_1))) (= (tptp.aa_nat_set_nat tptp.nat_set_decode (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N)) Z)) (tptp.insert_nat N _let_1))))) (forall ((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) (Y 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) Y) (=> _let_1 (not (=> (and (=> _let_6 (= Y (tptp.aa_int_int tptp.uminus_uminus_int _let_4))) (=> (not _let_6) (= Y (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int _let_4) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int _let_2) (tptp.aa_int_int (tptp.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)))))))))))) (= tptp.bot_bot_nat tptp.zero_zero_nat) (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 ((K3 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 K3 L2)) (=> (=> (not (and (tptp.member_int K3 _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 K3) _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 K3) L2))))))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool P A0) A1))))) (forall ((Q2 tptp.int) (R tptp.int)) (= (tptp.adjust_div (tptp.product_Pair_int_int Q2 R)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int Q2) (tptp.aa_bool_int tptp.zero_n2684676970156552555ol_int (tptp.aa_bool_bool tptp.fNot (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.fequal_int R) tptp.zero_zero_int)))))) (forall ((B tptp.int) (A tptp.int) (Q2 tptp.int) (R tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))))) (=> (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 R)) (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 R)) tptp.one_one_int))))))) (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 ((I2 tptp.int) (J2 tptp.int)) (=> (tptp.accp_P1096762738010456898nt_int tptp.upto_rel (tptp.product_Pair_int_int I2 J2)) (=> (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int I2) 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 I2) tptp.one_one_int)) J2))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool P I2) J2))))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool P A0) A1))))) (forall ((A tptp.int) (B tptp.int) (Q2 tptp.int) (R tptp.int) (Q4 tptp.int) (R4 tptp.int)) (=> (tptp.eucl_rel_int A B (tptp.product_Pair_int_int Q2 R)) (=> (tptp.eucl_rel_int A B (tptp.product_Pair_int_int Q4 R4)) (= R R4)))) (forall ((A tptp.int) (B tptp.int) (Q2 tptp.int) (R tptp.int) (Q4 tptp.int) (R4 tptp.int)) (=> (tptp.eucl_rel_int A B (tptp.product_Pair_int_int Q2 R)) (=> (tptp.eucl_rel_int A B (tptp.product_Pair_int_int Q4 R4)) (= Q2 Q4)))) (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 ((M2 tptp.num)) (not (= X (tptp.product_Pair_num_num (tptp.aa_num_num tptp.bit0 M2) tptp.one)))) (=> (forall ((M2 tptp.num) (N2 tptp.num)) (not (= X (tptp.product_Pair_num_num (tptp.aa_num_num tptp.bit0 M2) (tptp.aa_num_num tptp.bit0 N2))))) (=> (forall ((M2 tptp.num) (N2 tptp.num)) (not (= X (tptp.product_Pair_num_num (tptp.aa_num_num tptp.bit0 M2) (tptp.aa_num_num tptp.bit1 N2))))) (=> (forall ((M2 tptp.num)) (not (= X (tptp.product_Pair_num_num (tptp.aa_num_num tptp.bit1 M2) tptp.one)))) (=> (forall ((M2 tptp.num) (N2 tptp.num)) (not (= X (tptp.product_Pair_num_num (tptp.aa_num_num tptp.bit1 M2) (tptp.aa_num_num tptp.bit0 N2))))) (not (forall ((M2 tptp.num) (N2 tptp.num)) (not (= X (tptp.product_Pair_num_num (tptp.aa_num_num tptp.bit1 M2) (tptp.aa_num_num tptp.bit1 N2))))))))))))))) (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) (R tptp.int)) (=> (tptp.eucl_rel_int K L (tptp.product_Pair_int_int Q2 R)) (= (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) (R tptp.int)) (=> (tptp.eucl_rel_int K L (tptp.product_Pair_int_int Q2 R)) (= (tptp.modulo_modulo_int K L) R))) (forall ((L tptp.int) (K tptp.int) (Q2 tptp.int)) (=> (not (= L tptp.zero_zero_int)) (=> (= K (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int Q2) L)) (tptp.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 ((A tptp.int) (B tptp.int) (Q2 tptp.int) (R tptp.int)) (let ((_let_1 (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.fequal_int R) tptp.zero_zero_int))) (let ((_let_2 (tptp.aa_int_int tptp.uminus_uminus_int Q2))) (=> (tptp.eucl_rel_int A B (tptp.product_Pair_int_int Q2 R)) (=> (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) R))))))))) (forall ((K tptp.int) (L tptp.int) (Q2 tptp.int) (R tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_int L))) (let ((_let_2 (tptp.pp (tptp.aa_int_bool _let_1 tptp.zero_zero_int)))) (let ((_let_3 (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) L)))) (= (tptp.eucl_rel_int K L (tptp.product_Pair_int_int Q2 R)) (and (= K (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int L) Q2)) R)) (=> _let_3 (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) R)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int R) L)))) (=> (not _let_3) (and (=> _let_2 (and (tptp.pp (tptp.aa_int_bool _let_1 R)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int R) tptp.zero_zero_int)))) (=> (not _let_2) (= Q2 tptp.zero_zero_int)))))))))) (forall ((R tptp.int) (L tptp.int) (K tptp.int) (Q2 tptp.int)) (=> (= (tptp.aa_int_int tptp.sgn_sgn_int R) (tptp.aa_int_int tptp.sgn_sgn_int L)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int tptp.abs_abs_int R)) (tptp.aa_int_int tptp.abs_abs_int L))) (=> (= K (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int Q2) L)) R)) (tptp.eucl_rel_int K L (tptp.product_Pair_int_int Q2 R)))))) (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 ((Q6 tptp.int)) (=> (= A32 (tptp.product_Pair_int_int Q6 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 Q6) A22)))))) (not (forall ((R2 tptp.int) (Q6 tptp.int)) (=> (= A32 (tptp.product_Pair_int_int Q6 R2)) (=> (= (tptp.aa_int_int tptp.sgn_sgn_int R2) (tptp.aa_int_int tptp.sgn_sgn_int A22)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int tptp.abs_abs_int R2)) (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 Q6) A22)) R2)))))))))))) (forall ((A1 tptp.int) (A22 tptp.int) (A32 tptp.product_prod_int_int)) (= (tptp.eucl_rel_int A1 A22 A32) (or (exists ((K2 tptp.int)) (and (= A1 K2) (= A22 tptp.zero_zero_int) (= A32 (tptp.product_Pair_int_int tptp.zero_zero_int K2)))) (exists ((L3 tptp.int) (K2 tptp.int) (Q5 tptp.int)) (and (= A1 K2) (= A22 L3) (= A32 (tptp.product_Pair_int_int Q5 tptp.zero_zero_int)) (not (= L3 tptp.zero_zero_int)) (= K2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int Q5) L3)))) (exists ((R5 tptp.int) (L3 tptp.int) (K2 tptp.int) (Q5 tptp.int)) (and (= A1 K2) (= A22 L3) (= A32 (tptp.product_Pair_int_int Q5 R5)) (= (tptp.aa_int_int tptp.sgn_sgn_int R5) (tptp.aa_int_int 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))) (= K2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int Q5) L3)) R5))))))) (forall ((B tptp.int) (A tptp.int) (Q2 tptp.int) (R tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_2 (tptp.aa_int_fun_int_int tptp.plus_plus_int tptp.one_one_int))) (=> (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 R)) (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 R))))))))) (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 ((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 ((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 ((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 ((M tptp.num)) (= (tptp.unique5052692396658037445od_int (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 ((M tptp.num) (N tptp.num)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat N))) (let ((_let_2 (tptp.aa_num_nat tptp.numeral_numeral_nat M))) (= (tptp.unique5055182867167087721od_nat M N) (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat _let_2) _let_1)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat _let_2) _let_1)))))) (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (tptp.aa_num_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 ((X tptp.nat)) (= (tptp.bezw X tptp.zero_zero_nat) (tptp.product_Pair_int_int tptp.one_one_int tptp.zero_zero_int))) (forall ((R tptp.real) (A tptp.real)) (= (tptp.invers8013647133539491842omplex (tptp.rcis R A)) (tptp.rcis (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.one_one_real) R) (tptp.aa_real_real tptp.uminus_uminus_real A)))) (forall ((K5 tptp.set_int)) (let ((_let_1 (tptp.gcd_Gcd_int K5))) (= (tptp.aa_int_int tptp.abs_abs_int _let_1) _let_1))) (forall ((R tptp.real) (A tptp.real)) (= (tptp.re (tptp.rcis R A)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real R) (tptp.aa_real_real tptp.cos_real A)))) (forall ((R tptp.real) (A tptp.real)) (= (tptp.im (tptp.rcis R A)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real R) (tptp.aa_real_real tptp.sin_real A)))) (forall ((X tptp.product_prod_nat_nat)) (not (forall ((K3 tptp.nat) (M2 tptp.nat)) (not (= X (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat K3) M2)))))) (forall ((A2 tptp.set_int) (A tptp.int)) (=> (forall ((B3 tptp.int)) (=> (tptp.member_int B3 A2) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int A) B3)))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int A) (tptp.gcd_Gcd_int A2))))) (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 ((N4 tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat tptp.one_one_nat) N4)) (= (tptp.gcd_Gcd_nat N4) tptp.one_one_nat))) (forall ((A2 tptp.set_nat) (A tptp.nat)) (=> (forall ((B3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat B3) A2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat A) B3)))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat A) (tptp.gcd_Gcd_nat A2))))) (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 ((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 ((A tptp.real)) (= (tptp.cis A) (tptp.rcis tptp.one_one_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 ((R tptp.real) (A tptp.real)) (= (tptp.rcis R A) (tptp.aa_complex_complex (tptp.times_times_complex (tptp.real_V4546457046886955230omplex R)) (tptp.cis A)))) (forall ((R tptp.real) (A tptp.real) (N tptp.nat)) (= (tptp.aa_nat_complex (tptp.power_power_complex (tptp.rcis R A)) N) (tptp.rcis (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real R) 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) (K tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc K))) (let ((_let_2 (tptp.aa_nat7603221163087113075at_nat (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.aa_nat7603221163087113075at_nat (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) (Y tptp.product_prod_nat_nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc X))) (let ((_let_2 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Xa) X)))) (=> (= (tptp.aa_nat7603221163087113075at_nat (tptp.nat_prod_decode_aux X) Xa) Y) (and (=> _let_2 (= Y (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) (= Y (tptp.aa_nat7603221163087113075at_nat (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 ((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.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)) (tptp.aa_num_nat tptp.numeral_numeral_nat K)) (tptp.product_snd_nat_nat (tptp.unique5055182867167087721od_nat tptp.one K)))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.product_snd_nat_nat (tptp.divmod_nat M N)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat M) N))) (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 ((Y tptp.nat) (X tptp.nat)) (let ((_let_1 (tptp.bezw Y (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat X) Y)))) (let ((_let_2 (tptp.product_snd_int_int _let_1))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) Y)) (= (tptp.bezw X Y) (tptp.product_Pair_int_int _let_2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.product_fst_int_int _let_1)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int _let_2) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat X) Y)))))))))) (forall ((Y tptp.nat) (X tptp.nat)) (let ((_let_1 (tptp.bezw Y (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat X) Y)))) (let ((_let_2 (tptp.product_snd_int_int _let_1))) (let ((_let_3 (tptp.bezw X Y))) (let ((_let_4 (= Y tptp.zero_zero_nat))) (and (=> _let_4 (= _let_3 (tptp.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) Y))))))))))))) (forall ((X tptp.nat) (Xa tptp.nat) (Y tptp.product_prod_int_int)) (let ((_let_1 (tptp.bezw Xa (tptp.aa_nat_nat (tptp.aa_nat_fun_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) Y) (and (=> _let_3 (= Y (tptp.product_Pair_int_int tptp.one_one_int tptp.zero_zero_int))) (=> (not _let_3) (= Y (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 ((M tptp.nat) (N tptp.nat)) (= (tptp.divmod_nat M N) (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat M) N)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat M) N)))) (forall ((N tptp.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 ((R tptp.int) (L tptp.int)) (let ((_let_1 (tptp.adjust_mod L R))) (let ((_let_2 (= R 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) R))))))) (forall ((X tptp.nat) (Xa tptp.nat) (Y 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.aa_nat_fun_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) Y) (=> _let_1 (not (=> (and (=> _let_4 (= Y (tptp.product_Pair_int_int tptp.one_one_int tptp.zero_zero_int))) (=> (not _let_4) (= Y (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 ((K tptp.nat) (M tptp.nat)) (= (tptp.aa_Pro4243173770044397973at_nat tptp.nat_prod_encode (tptp.aa_nat7603221163087113075at_nat (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))) (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (tptp.bezw X Y))) (= (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.gcd_gcd_nat X) Y)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.product_fst_int_int _let_1)) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int X))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.product_snd_int_int _let_1)) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int Y)))))) (forall ((X tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.gcd_gcd_nat X) X) X)) (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (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 _let_1) B) _let_1))) (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.gcd_gcd_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.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.gcd_gcd_nat A) A) A)) (forall ((X tptp.product_prod_nat_nat) (Y tptp.product_prod_nat_nat)) (= (= (tptp.aa_Pro4243173770044397973at_nat tptp.nat_prod_encode X) (tptp.aa_Pro4243173770044397973at_nat tptp.nat_prod_encode Y)) (= X Y))) (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 ((M tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.gcd_gcd_nat M) tptp.one_one_nat) tptp.one_one_nat)) (forall ((Y tptp.nat) (X tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat Y) X)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.gcd_gcd_nat X) Y) Y))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat X) Y)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.gcd_gcd_nat X) Y) X))) (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 ((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)) (=> (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 ((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 ((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 ((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) (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 ((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 ((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) (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 ((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) (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) (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)) (= (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 ((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 (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 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) (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) (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 ((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)) (=> (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 ((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)) (=> (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) (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 ((X tptp.nat) (Y tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.gcd_gcd_nat X) Y) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.gcd_gcd_nat Y) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat X) Y)))) (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 ((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 ((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 ((Y tptp.nat) (X tptp.nat)) (=> (not (= Y tptp.zero_zero_nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.gcd_gcd_nat X) Y) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.gcd_gcd_nat Y) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat X) Y))))) (forall ((Y tptp.nat) (X tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.gcd_gcd_nat X) Y))) (let ((_let_2 (= Y tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 X)) (=> (not _let_2) (= _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.gcd_gcd_nat Y) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat X) Y)))))))) (forall ((X tptp.nat) (Xa tptp.nat) (Y 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) Y) (and (=> _let_1 (= Y X)) (=> (not _let_1) (= Y (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.gcd_gcd_nat Xa) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat X) Xa)))))))) (forall ((A2 tptp.set_nat)) (=> (forall ((A3 tptp.nat) (B3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat A3) A2)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat B3) A2)) (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.gcd_gcd_nat A3) B3)) A2))))) (=> (not (= A2 tptp.bot_bot_set_nat)) (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat (tptp.gcd_Gcd_nat A2)) A2))))) (forall ((A tptp.nat) (B tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (exists ((X3 tptp.nat) (Y3 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) Y3)) (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) (Y3 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 Y3))) (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 Y3))) (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 ((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 ((X tptp.nat) (Xa tptp.nat) (Y 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.aa_nat7603221163087113075at_nat (tptp.nat_prod_decode_aux X) Xa) Y) (=> _let_1 (not (=> (and (=> _let_3 (= Y (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) (= Y (tptp.aa_nat7603221163087113075at_nat (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.nat) (Xa tptp.nat) (Y 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) Y) (=> _let_1 (not (=> (and (=> _let_2 (= Y X)) (=> (not _let_2) (= Y (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.gcd_gcd_nat Xa) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat X) Xa))))) (not _let_1)))))))) (forall ((M tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.gcd_gcd_int M) tptp.one_one_int) tptp.one_one_int)) (forall ((X tptp.int) (Y tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.gcd_gcd_int (tptp.aa_int_int tptp.uminus_uminus_int X)) Y) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.gcd_gcd_int X) Y))) (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.gcd_gcd_int X))) (= (tptp.aa_int_int _let_1 (tptp.aa_int_int tptp.uminus_uminus_int Y)) (tptp.aa_int_int _let_1 Y)))) (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.gcd_gcd_int X) Y))) (= (tptp.aa_int_int tptp.abs_abs_int _let_1) _let_1))) (forall ((X tptp.int) (Y tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.gcd_gcd_int (tptp.aa_int_int tptp.abs_abs_int X)) Y) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.gcd_gcd_int X) Y))) (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.gcd_gcd_int X))) (= (tptp.aa_int_int _let_1 (tptp.aa_int_int tptp.abs_abs_int Y)) (tptp.aa_int_int _let_1 Y)))) (forall ((M tptp.int) (N tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.gcd_gcd_int M) N))) (or (not (= M tptp.zero_zero_int)) (not (= N tptp.zero_zero_int))))) (forall ((X tptp.int) (N tptp.num)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int N))) (let ((_let_2 (tptp.aa_int_fun_int_int tptp.gcd_gcd_int X))) (= (tptp.aa_int_int _let_2 (tptp.aa_int_int tptp.uminus_uminus_int _let_1)) (tptp.aa_int_int _let_2 _let_1))))) (forall ((N tptp.num) (X tptp.int)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int N))) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.gcd_gcd_int (tptp.aa_int_int tptp.uminus_uminus_int _let_1)) X) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.gcd_gcd_int _let_1) X)))) (forall ((X tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.gcd_gcd_int X) tptp.zero_zero_int) (tptp.aa_int_int tptp.abs_abs_int X))) (forall ((X tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.gcd_gcd_int tptp.zero_zero_int) X) (tptp.aa_int_int tptp.abs_abs_int X))) (forall ((X tptp.int) (Y tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int X) Y)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.gcd_gcd_int X) Y) (tptp.aa_int_int tptp.abs_abs_int X)))) (forall ((Y tptp.int) (X tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int Y) X)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.gcd_gcd_int X) Y) (tptp.aa_int_int tptp.abs_abs_int Y)))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int 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.aa_int_int (tptp.aa_int_fun_int_int 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.aa_int_int (tptp.aa_int_fun_int_int tptp.gcd_gcd_int K) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N))))) (forall ((X tptp.int) (Y tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.gcd_gcd_int X) Y) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.gcd_gcd_int Y) (tptp.modulo_modulo_int X Y)))) (forall ((X tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.gcd_gcd_int X) X) (tptp.aa_int_int tptp.abs_abs_int X))) (forall ((X tptp.int) (Y tptp.int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.gcd_gcd_int X) Y)))) (forall ((X tptp.int) (Y tptp.int)) (exists ((U2 tptp.int) (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) Y)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.gcd_gcd_int X) Y)))) (forall ((K tptp.int) (M tptp.int) (N tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.times_times_int K))) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int tptp.abs_abs_int K)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.gcd_gcd_int M) N)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.gcd_gcd_int (tptp.aa_int_int _let_1 M)) (tptp.aa_int_int _let_1 N))))) (forall ((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.aa_int_int (tptp.aa_int_fun_int_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.aa_int_int (tptp.aa_int_fun_int_int tptp.gcd_gcd_int A) B)) B)))) (forall ((X tptp.int) (Y tptp.int) (P tptp.fun_int_bool)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.gcd_gcd_int X))) (let ((_let_2 (tptp.pp (tptp.aa_int_bool P (tptp.aa_int_int _let_1 Y))))) (let ((_let_3 (tptp.aa_int_int tptp.uminus_uminus_int Y))) (let ((_let_4 (tptp.aa_int_fun_int_int tptp.gcd_gcd_int (tptp.aa_int_int tptp.uminus_uminus_int X)))) (let ((_let_5 (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Y) tptp.zero_zero_int)))) (let ((_let_6 (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X) tptp.zero_zero_int)))) (let ((_let_7 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_8 (tptp.pp (tptp.aa_int_bool _let_7 Y)))) (let ((_let_9 (tptp.pp (tptp.aa_int_bool _let_7 X)))) (=> (=> _let_9 (=> _let_8 _let_2)) (=> (=> _let_9 (=> _let_5 (tptp.pp (tptp.aa_int_bool P (tptp.aa_int_int _let_1 _let_3))))) (=> (=> _let_6 (=> _let_8 (tptp.pp (tptp.aa_int_bool P (tptp.aa_int_int _let_4 Y))))) (=> (=> _let_6 (=> _let_5 (tptp.pp (tptp.aa_int_bool P (tptp.aa_int_int _let_4 _let_3))))) _let_2)))))))))))))) (forall ((D tptp.int) (A tptp.int) (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.aa_int_int (tptp.aa_int_fun_int_int tptp.gcd_gcd_int A) B))))) (forall ((Y tptp.int) (X tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) Y)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.gcd_gcd_int X) Y) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.gcd_gcd_int Y) (tptp.modulo_modulo_int X Y))))) (forall ((K tptp.int) (L tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_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.aa_int_int (tptp.aa_int_fun_int_int 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.int) (Y tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.gcd_gcd_int X) Y) (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 Y)))))) (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.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.ring_1_of_int_real N)) (tptp.power_int_real X N))))) (forall ((Z tptp.complex)) (= (tptp.member_complex Z tptp.semiri3842193898606819883omplex) (and (= (tptp.im Z) tptp.zero_zero_real) (exists ((I4 tptp.nat)) (= (tptp.re Z) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real I4)))))) (forall ((D3 tptp.int) (P tptp.fun_int_bool) (P3 tptp.fun_int_bool) (B4 tptp.set_int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) 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 P3 X3)))))) (=> (forall ((X3 tptp.int)) (=> (forall ((Xa2 tptp.int)) (=> (tptp.member_int Xa2 (tptp.set_or1266510415728281911st_int tptp.one_one_int D3)) (forall ((Xb2 tptp.int)) (=> (tptp.member_int Xb2 B4) (not (= X3 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int Xb2) 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) (K3 tptp.int)) (= (tptp.pp (tptp.aa_int_bool P3 X3)) (tptp.pp (tptp.aa_int_bool P3 (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 K3) D3)))))) (= (exists ((X_13 tptp.int)) (tptp.pp (tptp.aa_int_bool P X_13))) (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 P3 X5)))) (exists ((X5 tptp.int)) (and (tptp.member_int X5 (tptp.set_or1266510415728281911st_int tptp.one_one_int D3)) (exists ((Xa3 tptp.int)) (and (tptp.member_int Xa3 B4) (tptp.pp (tptp.aa_int_bool P (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int Xa3) X5)))))))))))))) (forall ((D3 tptp.int) (P tptp.fun_int_bool) (P3 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 P3 X3)))))) (=> (forall ((X3 tptp.int)) (=> (forall ((Xa2 tptp.int)) (=> (tptp.member_int Xa2 (tptp.set_or1266510415728281911st_int tptp.one_one_int D3)) (forall ((Xb2 tptp.int)) (=> (tptp.member_int Xb2 A2) (not (= X3 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int Xb2) 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) (K3 tptp.int)) (= (tptp.pp (tptp.aa_int_bool P3 X3)) (tptp.pp (tptp.aa_int_bool P3 (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 K3) D3)))))) (= (exists ((X_13 tptp.int)) (tptp.pp (tptp.aa_int_bool P X_13))) (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 P3 X5)))) (exists ((X5 tptp.int)) (and (tptp.member_int X5 (tptp.set_or1266510415728281911st_int tptp.one_one_int D3)) (exists ((Xa3 tptp.int)) (and (tptp.member_int Xa3 A2) (tptp.pp (tptp.aa_int_bool P (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int Xa3) X5)))))))))))))) (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 ((Xb2 tptp.int)) (=> (tptp.member_int Xb2 A2) (not (= X3 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int Xb2) 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 ((Xb2 tptp.int)) (=> (tptp.member_int Xb2 A2) (not (= X3 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int Xb2) 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 ((Xa4 tptp.int)) (=> (tptp.member_int Xa4 (tptp.set_or1266510415728281911st_int tptp.one_one_int D3)) (forall ((Xb3 tptp.int)) (=> (tptp.member_int Xb3 A2) (not (= X4 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int Xb3) Xa4))))))) (=> (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 ((Xb2 tptp.int)) (=> (tptp.member_int Xb2 A2) (not (= X3 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int Xb2) 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 ((Xb2 tptp.int)) (=> (tptp.member_int Xb2 A2) (not (= X3 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int Xb2) 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 ((Xa4 tptp.int)) (=> (tptp.member_int Xa4 (tptp.set_or1266510415728281911st_int tptp.one_one_int D3)) (forall ((Xb3 tptp.int)) (=> (tptp.member_int Xb3 A2) (not (= X4 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int Xb3) Xa4))))))) (=> (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) (B4 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 ((Xb2 tptp.int)) (=> (tptp.member_int Xb2 B4) (not (= X3 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int Xb2) 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 ((Xb2 tptp.int)) (=> (tptp.member_int Xb2 B4) (not (= X3 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int Xb2) 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 ((Xa4 tptp.int)) (=> (tptp.member_int Xa4 (tptp.set_or1266510415728281911st_int tptp.one_one_int D3)) (forall ((Xb3 tptp.int)) (=> (tptp.member_int Xb3 B4) (not (= X4 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int Xb3) Xa4))))))) (=> (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) (B4 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 ((Xb2 tptp.int)) (=> (tptp.member_int Xb2 B4) (not (= X3 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int Xb2) 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 ((Xb2 tptp.int)) (=> (tptp.member_int Xb2 B4) (not (= X3 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int Xb2) 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 ((Xa4 tptp.int)) (=> (tptp.member_int Xa4 (tptp.set_or1266510415728281911st_int tptp.one_one_int D3)) (forall ((Xb3 tptp.int)) (=> (tptp.member_int Xb3 B4) (not (= X4 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int Xb3) Xa4))))))) (=> (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 ((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 ((Xa4 tptp.int)) (=> (tptp.member_int Xa4 (tptp.set_or1266510415728281911st_int tptp.one_one_int D3)) (forall ((Xb3 tptp.int)) (=> (tptp.member_int Xb3 A2) (not (= X4 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int Xb3) Xa4))))))) (=> (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) (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 ((Xa4 tptp.int)) (=> (tptp.member_int Xa4 (tptp.set_or1266510415728281911st_int tptp.one_one_int D3)) (forall ((Xb3 tptp.int)) (=> (tptp.member_int Xb3 A2) (not (= X4 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int Xb3) Xa4))))))) (=> (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) (B4 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 ((Xa4 tptp.int)) (=> (tptp.member_int Xa4 (tptp.set_or1266510415728281911st_int tptp.one_one_int D3)) (forall ((Xb3 tptp.int)) (=> (tptp.member_int Xb3 B4) (not (= X4 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int Xb3) Xa4))))))) (=> (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) (B4 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 ((Xa4 tptp.int)) (=> (tptp.member_int Xa4 (tptp.set_or1266510415728281911st_int tptp.one_one_int D3)) (forall ((Xb3 tptp.int)) (=> (tptp.member_int Xb3 B4) (not (= X4 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int Xb3) Xa4))))))) (=> (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 ((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 ((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) (K3 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 K3) D)))))) (= (exists ((X_13 tptp.int)) (tptp.pp (tptp.aa_int_bool P X_13))) (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) (B4 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) B4) (forall ((X4 tptp.int)) (=> (forall ((Xa4 tptp.int)) (=> (tptp.member_int Xa4 (tptp.set_or1266510415728281911st_int tptp.one_one_int D3)) (forall ((Xb3 tptp.int)) (=> (tptp.member_int Xb3 B4) (not (= X4 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int Xb3) Xa4))))))) (=> (= 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) (B4 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 B4) (forall ((X4 tptp.int)) (=> (forall ((Xa4 tptp.int)) (=> (tptp.member_int Xa4 (tptp.set_or1266510415728281911st_int tptp.one_one_int D3)) (forall ((Xb3 tptp.int)) (=> (tptp.member_int Xb3 B4) (not (= X4 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int Xb3) Xa4))))))) (=> (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) (B4 tptp.set_int) (T tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) D3)) (forall ((X4 tptp.int)) (=> (forall ((Xa4 tptp.int)) (=> (tptp.member_int Xa4 (tptp.set_or1266510415728281911st_int tptp.one_one_int D3)) (forall ((Xb3 tptp.int)) (=> (tptp.member_int Xb3 B4) (not (= X4 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int Xb3) Xa4))))))) (=> (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) (B4 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 B4) (forall ((X4 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_int T))) (=> (forall ((Xa4 tptp.int)) (=> (tptp.member_int Xa4 (tptp.set_or1266510415728281911st_int tptp.one_one_int D3)) (forall ((Xb3 tptp.int)) (=> (tptp.member_int Xb3 B4) (not (= X4 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int Xb3) Xa4))))))) (=> (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 ((Xa4 tptp.int)) (=> (tptp.member_int Xa4 (tptp.set_or1266510415728281911st_int tptp.one_one_int D3)) (forall ((Xb3 tptp.int)) (=> (tptp.member_int Xb3 A2) (not (= X4 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int Xb3) Xa4))))))) (=> (= 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 ((Xa4 tptp.int)) (=> (tptp.member_int Xa4 (tptp.set_or1266510415728281911st_int tptp.one_one_int D3)) (forall ((Xb3 tptp.int)) (=> (tptp.member_int Xb3 A2) (not (= X4 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int Xb3) Xa4))))))) (=> (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 ((Xa4 tptp.int)) (=> (tptp.member_int Xa4 (tptp.set_or1266510415728281911st_int tptp.one_one_int D3)) (forall ((Xb3 tptp.int)) (=> (tptp.member_int Xb3 A2) (not (= X4 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int Xb3) Xa4))))))) (=> (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 ((Xa4 tptp.int)) (=> (tptp.member_int Xa4 (tptp.set_or1266510415728281911st_int tptp.one_one_int D3)) (forall ((Xb3 tptp.int)) (=> (tptp.member_int Xb3 A2) (not (= X4 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int Xb3) Xa4))))))) (=> (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 ((J tptp.int) (I tptp.int)) (let ((_let_1 (tptp.set_or1266510415728281911st_int I J))) (let ((_let_2 (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int J) I)))) (and (=> _let_2 (= _let_1 tptp.bot_bot_set_int)) (=> (not _let_2) (= _let_1 (tptp.insert_int I (tptp.set_or1266510415728281911st_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int I) tptp.one_one_int) J)))))))) (forall ((D3 tptp.int) (B4 tptp.set_int) (T tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) D3)) (forall ((X4 tptp.int)) (=> (forall ((Xa4 tptp.int)) (=> (tptp.member_int Xa4 (tptp.set_or1266510415728281911st_int tptp.one_one_int D3)) (forall ((Xb3 tptp.int)) (=> (tptp.member_int Xb3 B4) (not (= X4 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int Xb3) Xa4))))))) (=> (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) (B4 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) B4) (forall ((X4 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int T))) (=> (forall ((Xa4 tptp.int)) (=> (tptp.member_int Xa4 (tptp.set_or1266510415728281911st_int tptp.one_one_int D3)) (forall ((Xb3 tptp.int)) (=> (tptp.member_int Xb3 B4) (not (= X4 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int Xb3) Xa4))))))) (=> (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 ((Xa4 tptp.int)) (=> (tptp.member_int Xa4 (tptp.set_or1266510415728281911st_int tptp.one_one_int D3)) (forall ((Xb3 tptp.int)) (=> (tptp.member_int Xb3 A2) (not (= X4 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int Xb3) Xa4))))))) (=> (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 ((Xa4 tptp.int)) (=> (tptp.member_int Xa4 (tptp.set_or1266510415728281911st_int tptp.one_one_int D3)) (forall ((Xb3 tptp.int)) (=> (tptp.member_int Xb3 A2) (not (= X4 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int Xb3) Xa4))))))) (=> (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 ((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 ((X tptp.real) (Y tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.real_V975177566351809787t_real X) Y) (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real X) Y)))) (forall ((X tptp.complex) (Y tptp.complex)) (= (tptp.real_V3694042436643373181omplex X Y) (tptp.real_V1022390504157884413omplex (tptp.minus_minus_complex X Y)))) (forall ((Q2 tptp.int) (P2 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Q2) tptp.zero_zero_int)) (= (tptp.normalize (tptp.product_Pair_int_int P2 Q2)) (tptp.normalize (tptp.product_Pair_int_int (tptp.aa_int_int tptp.uminus_uminus_int P2) (tptp.aa_int_int tptp.uminus_uminus_int Q2)))))) (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 ((P2 tptp.int)) (= (tptp.normalize (tptp.product_Pair_int_int P2 tptp.zero_zero_int)) (tptp.product_Pair_int_int tptp.zero_zero_int tptp.one_one_int))) (forall ((K tptp.num)) (= (tptp.quotient_of (tptp.uminus_uminus_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))) (= (tptp.quotient_of tptp.one_one_rat) _let_38) (= (tptp.quotient_of tptp.zero_zero_rat) _let_37) (= (tptp.quotient_of _let_56) (tptp.product_Pair_int_int _let_57 tptp.one_one_int)) (forall ((K tptp.num)) (= (tptp.quotient_of (tptp.numeral_numeral_rat K)) (tptp.product_Pair_int_int (tptp.aa_num_int tptp.numeral_numeral_int K) tptp.one_one_int))) (forall ((Q2 tptp.rat) (R tptp.rat)) (= (tptp.minus_minus_rat Q2 R) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat Q2) (tptp.uminus_uminus_rat R)))) (forall ((A tptp.rat)) (let ((_let_1 (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.uminus_uminus_rat tptp.one_one_rat)))))))))) (forall ((R tptp.rat) (P2 tptp.int) (Q2 tptp.int)) (=> (= (tptp.quotient_of R) (tptp.product_Pair_int_int P2 Q2)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) Q2)))) (forall ((R tptp.rat)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) (tptp.product_snd_int_int (tptp.quotient_of R))))) (forall ((R tptp.product_prod_int_int) (P2 tptp.int) (Q2 tptp.int)) (=> (= (tptp.normalize R) (tptp.product_Pair_int_int P2 Q2)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) Q2)))) (forall ((Q2 tptp.int) (S tptp.int) (P2 tptp.int) (R tptp.int)) (=> (not (= Q2 tptp.zero_zero_int)) (=> (not (= S tptp.zero_zero_int)) (=> (= (tptp.normalize (tptp.product_Pair_int_int P2 Q2)) (tptp.normalize (tptp.product_Pair_int_int R S))) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int P2) S) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int R) Q2)))))) (forall ((P2 tptp.rat)) (= (tptp.quotient_of (tptp.sgn_sgn_rat P2)) (tptp.product_Pair_int_int (tptp.aa_int_int tptp.sgn_sgn_int (tptp.product_fst_int_int (tptp.quotient_of P2))) tptp.one_one_int))) (forall ((A tptp.int)) (= (tptp.quotient_of (tptp.of_int A)) (tptp.product_Pair_int_int A tptp.one_one_int))) (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.divide_divide_rat tptp.one_one_rat (tptp.numeral_numeral_rat K)))) (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.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.divide_divide_rat (tptp.numeral_numeral_rat K) (tptp.numeral_numeral_rat L)))) (forall ((L tptp.nat) (U tptp.nat)) (= (tptp.finite_card_nat (tptp.aa_nat_set_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.nat) (U tptp.nat)) (= (tptp.finite_card_nat (tptp.aa_nat_set_nat (tptp.set_or5834768355832116004an_nat L) U)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat U) (tptp.aa_nat_nat tptp.suc L)))) (forall ((Q2 tptp.rat) (R tptp.rat)) (= (tptp.divide_divide_rat Q2 R) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat Q2) (tptp.aa_rat_rat tptp.inverse_inverse_rat R)))) (forall ((R tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) R)) (not (forall ((S3 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) S3)) (forall ((T2 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) T2)) (not (= R (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat S3) T2)))))))))) (forall ((N tptp.nat) (P tptp.fun_nat_bool)) (= (forall ((M6 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M6) N)) (tptp.pp (tptp.aa_nat_bool P M6)))) (forall ((X5 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X5) (tptp.aa_nat_set_nat (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 ((M6 tptp.nat)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M6) N)) (tptp.pp (tptp.aa_nat_bool P M6)))) (exists ((X5 tptp.nat)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X5) (tptp.aa_nat_set_nat (tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N))) (tptp.pp (tptp.aa_nat_bool P X5)))))) (forall ((N tptp.nat)) (let ((_let_1 (tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat))) (let ((_let_2 (tptp.aa_nat_nat tptp.suc N))) (= (tptp.aa_nat_set_nat _let_1 _let_2) (tptp.insert_nat _let_2 (tptp.aa_nat_set_nat _let_1 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_set_nat (tptp.set_or1269000886237332187st_nat M) N) (tptp.insert_nat M (tptp.aa_nat_set_nat (tptp.set_or1269000886237332187st_nat (tptp.aa_nat_nat tptp.suc M)) N))))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.set_or1269000886237332187st_nat M))) (let ((_let_2 (tptp.aa_nat_nat tptp.suc N))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) _let_2)) (= (tptp.aa_nat_set_nat _let_1 _let_2) (tptp.insert_nat _let_2 (tptp.aa_nat_set_nat _let_1 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.aa_nat_set_nat (tptp.set_or1269000886237332187st_nat (tptp.aa_nat_nat tptp.suc M)) N)) (tptp.aa_nat_set_nat (tptp.set_or1269000886237332187st_nat M) N)))) (forall ((X tptp.real)) (tptp.member_real (tptp.aa_real_real tptp.tanh_real X) (tptp.set_or1633881224788618240n_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real) tptp.one_one_real))) (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)) (= (tptp.frct _let_38) tptp.one_one_rat) (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 ((I tptp.nat) (J tptp.nat)) (= (tptp.image_nat_nat tptp.suc (tptp.aa_nat_set_nat (tptp.set_or1269000886237332187st_nat I) J)) (tptp.aa_nat_set_nat (tptp.set_or1269000886237332187st_nat (tptp.aa_nat_nat tptp.suc I)) (tptp.aa_nat_nat tptp.suc J)))) (forall ((K5 tptp.set_int)) (= (tptp.gcd_Gcd_int (tptp.image_int_int tptp.abs_abs_int K5)) (tptp.gcd_Gcd_int K5))) (forall ((N tptp.nat)) (= (tptp.finite_card_nat (tptp.collect_nat (tptp.aa_nat_fun_nat_bool tptp.aTP_Lamm_af N))) (tptp.aa_nat_nat tptp.suc N))) (forall ((N4 tptp.set_nat)) (= (tptp.gcd_Gcd_int (tptp.image_nat_int tptp.semiri1314217659103216013at_int N4)) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.gcd_Gcd_nat N4)))) (forall ((K5 tptp.set_int)) (= (tptp.gcd_Gcd_nat (tptp.image_int_nat tptp.aTP_Lamm_ag K5)) (tptp.aa_int_nat tptp.nat2 (tptp.gcd_Gcd_int K5)))) (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 ((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_ah M10) I))) tptp.zero_zero_nat)))) (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_ai M10) I)))) (tptp.finite_card_nat (tptp.collect_nat (tptp.aa_nat_fun_nat_bool (tptp.aTP_Lamm_ah M10) I)))))) (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_ai M10) I))) (tptp.finite_card_nat (tptp.collect_nat (tptp.aa_nat_fun_nat_bool (tptp.aTP_Lamm_ah M10) I)))))) (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.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.aa_nat_fun_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 ((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_aj 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 ((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 ((A tptp.nat) (B tptp.nat)) (= (tptp.image_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_set_nat (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 ((Z5 tptp.int) (Z tptp.int)) (let ((_let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int Z) Z5))) (let ((_let_2 (tptp.aa_int_nat tptp.nat2 Z))) (let ((_let_3 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat _let_2) (tptp.aa_int_nat tptp.nat2 Z5)))) (let ((_let_4 (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Z5) tptp.zero_zero_int)))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.if_nat (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int _let_1) tptp.zero_zero_int)) tptp.zero_zero_nat) (tptp.aa_int_nat tptp.nat2 _let_1)))))))))) (forall ((N tptp.nat)) (let ((_let_1 (tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat))) (= (tptp.aa_nat_set_nat _let_1 (tptp.aa_nat_nat tptp.suc N)) (tptp.insert_nat tptp.zero_zero_nat (tptp.image_nat_nat tptp.suc (tptp.aa_nat_set_nat _let_1 N)))))) (forall ((X tptp.nat)) (= (tptp.aa_nat_set_nat tptp.nat_set_decode X) (tptp.collect_nat (tptp.aa_nat_fun_nat_bool tptp.aTP_Lamm_al X)))) (forall ((P2 tptp.product_prod_int_int)) (let ((_let_1 (tptp.product_snd_int_int P2))) (let ((_let_2 (tptp.product_fst_int_int P2))) (let ((_let_3 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.gcd_gcd_int _let_2) _let_1))) (let ((_let_4 (tptp.aa_int_int tptp.uminus_uminus_int _let_3))) (let ((_let_5 (tptp.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 P2))) (let ((_let_8 (= _let_1 tptp.zero_zero_int))) (let ((_let_9 (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) _let_1)))) (and (=> _let_9 (= _let_7 (tptp.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 ((N tptp.nat) (TreeList tptp.list_VEBT_VEBT) (X tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_V5917875025757280293ildren N TreeList) X)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions (tptp.nth_VEBT_VEBT TreeList (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high X) N))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low X) N))))) (forall ((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_am X)))) (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_an (tptp.aa_nat_set_nat (tptp.set_or1269000886237332187st_nat (tptp.aa_nat_nat tptp.suc 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.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) tptp.one_one_real)) (tptp.topolo6980174941875973593q_real (tptp.aa_real_fun_nat_real tptp.power_power_real X))))) (forall ((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_an (tptp.aa_nat_set_nat (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 ((I tptp.nat) (J tptp.nat)) (= (tptp.groups705719431365010083at_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_set_nat (tptp.set_or1269000886237332187st_nat I) J)) (tptp.groups1705073143266064639nt_int tptp.aTP_Lamm_ao (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.aa_nat_set_nat (tptp.set_or1269000886237332187st_nat I) _let_1)) (tptp.groups1705073143266064639nt_int tptp.aTP_Lamm_ao (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_real tptp.zero_zero_real) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) (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_ap 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 X)) tptp.one_one_real)) (= (tptp.aa_real_real tptp.arctan X) (tptp.suminf_real (tptp.aa_real_fun_nat_real tptp.aTP_Lamm_aq 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.real_V1022390504157884413omplex C)))) (tptp.cis (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_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_aj C) N)))))) (= _let_64 (tptp.suminf_real tptp.aTP_Lamm_ar)) (forall ((M10 tptp.set_nat) (N4 tptp.set_nat)) (= (tptp.pp (tptp.aa_set_nat_bool (tptp.bij_betw_nat_nat tptp.suc M10) N4)) (= (tptp.image_nat_nat tptp.suc M10) N4))) (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_aq X)))) (forall ((N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (tptp.bij_betw_nat_complex (tptp.aTP_Lamm_as N) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N) (tptp.collect_complex (tptp.aTP_Lamm_ak N))))) (forall ((X tptp.real)) (tptp.pp (tptp.aa_real_bool (tptp.sums_real (tptp.aa_real_fun_nat_real tptp.aTP_Lamm_at X)) (tptp.aa_real_real tptp.sin_real X)))) (= (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat tptp.zero_zero_nat) tptp.bot_bot_set_nat) (forall ((K tptp.nat)) (= (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat (tptp.aa_nat_nat tptp.suc K)) (tptp.insert_nat K (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat K)))) (forall ((N tptp.nat)) (= (= (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N) tptp.bot_bot_set_nat) (= N tptp.zero_zero_nat))) (forall ((K tptp.num)) (let ((_let_1 (tptp.pred_numeral K))) (= (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat (tptp.aa_num_nat tptp.numeral_numeral_nat K)) (tptp.insert_nat _let_1 (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat _let_1))))) (forall ((N tptp.nat)) (= (tptp.image_nat_nat tptp.suc (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N)) (tptp.aa_nat_set_nat (tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N))) (forall ((N tptp.nat)) (= (tptp.aa_nat_set_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.aa_nat_set_nat tptp.set_ord_lessThan_nat N))))) (forall ((F tptp.fun_nat_real) (Z tptp.real)) (=> (forall ((I2 tptp.nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_nat_real F I2)) tptp.one_one_real))) (=> (forall ((I2 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 I2)))) (=> (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_au F) Z))))))) (tptp.pp (tptp.aa_real_bool (tptp.sums_real tptp.aTP_Lamm_av) 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_aw G)) X)))) (forall ((G tptp.fun_nat_real) (X tptp.real) (F tptp.fun_nat_real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.sums_real G) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.sums_real F) Y)) (tptp.pp (tptp.aa_real_bool (tptp.sums_real (tptp.aa_fun1839206346889086768t_real (tptp.aTP_Lamm_ax G) F)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) Y)))))) (forall ((X tptp.real)) (tptp.pp (tptp.aa_real_bool (tptp.sums_real (tptp.aa_real_fun_nat_real tptp.aTP_Lamm_ay X)) (tptp.aa_real_real tptp.cos_real 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 X) tptp.zero_zero_real)) (exists ((T2 tptp.real)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) T2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real T2) tptp.zero_zero_real)) (= (tptp.aa_real_real tptp.cos_real X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real tptp.aTP_Lamm_az X) (tptp.aa_nat_set_nat 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 T2) (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.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 ((T2 tptp.real)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) T2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real T2) X)) (= (tptp.aa_real_real tptp.cos_real X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real tptp.aTP_Lamm_az X) (tptp.aa_nat_set_nat 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 T2) (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.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 ((T2 tptp.real)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) T2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real T2) X)) (= (tptp.aa_real_real tptp.sin_real X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real tptp.aTP_Lamm_ba X) (tptp.aa_nat_set_nat 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 T2) (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.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.groups6591440286371151544t_real tptp.aTP_Lamm_bb (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat (tptp.aa_nat_nat tptp.suc N))) tptp.one_one_real)) (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 ((B6 tptp.real)) (= (tptp.aa_real_real F H) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.groups6591440286371151544t_real (tptp.aa_fun1839206346889086768t_real (tptp.aTP_Lamm_bc H) J) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real B6) (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.aa_nat_set_nat tptp.set_ord_lessThan_nat N))) (= (tptp.groups6591440286371151544t_real (tptp.aa_fun1839206346889086768t_real (tptp.aTP_Lamm_bd F) G) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.groups6591440286371151544t_real (tptp.aTP_Lamm_be F) _let_1)) (tptp.groups6591440286371151544t_real (tptp.aTP_Lamm_bf G) _let_1))))) (forall ((X tptp.real) (N tptp.nat)) (exists ((T2 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 T2)) (tptp.aa_real_real tptp.abs_abs_real X))) (= (tptp.aa_real_real tptp.exp_real X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real tptp.aTP_Lamm_bg X) (tptp.aa_nat_set_nat 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 T2)) (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.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real tptp.aTP_Lamm_ba X) (tptp.aa_nat_set_nat 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.groups6591440286371151544t_real F (tptp.aa_nat_set_nat 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 ((T2 tptp.real)) (let ((_let_1 (tptp.aa_real_real tptp.abs_abs_real T2))) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) _let_1)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real _let_1) (tptp.aa_real_real tptp.abs_abs_real X))) (= (tptp.aa_real_real tptp.exp_real X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real tptp.aTP_Lamm_bg X) (tptp.aa_nat_set_nat 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 T2)) (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 ((T2 tptp.real)) (= (tptp.aa_real_real tptp.sin_real X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real tptp.aTP_Lamm_ba X) (tptp.aa_nat_set_nat 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 T2) (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.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 ((T2 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 T2)) (tptp.aa_real_real tptp.abs_abs_real X))) (= (tptp.aa_real_real tptp.sin_real X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real tptp.aTP_Lamm_ba X) (tptp.aa_nat_set_nat 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 T2) (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.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 ((T2 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 T2)) (tptp.aa_real_real tptp.abs_abs_real X))) (= (tptp.aa_real_real tptp.cos_real X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real tptp.aTP_Lamm_az X) (tptp.aa_nat_set_nat 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 T2) (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.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 ((T2 tptp.real)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) T2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real T2) X)) (= (tptp.aa_real_real tptp.sin_real X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real tptp.aTP_Lamm_ba X) (tptp.aa_nat_set_nat 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 T2) (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.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 ((U tptp.nat)) (= (tptp.finite_card_nat (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat U)) (tptp.aa_nat_nat tptp.suc U))) (= (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat tptp.zero_zero_nat) (tptp.insert_nat tptp.zero_zero_nat tptp.bot_bot_set_nat)) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_nat_fun_nat_nat tptp.aTP_Lamm_bh M)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial (tptp.aa_nat_nat tptp.suc N)) (tptp.aa_nat_nat tptp.suc M)))) (forall ((N tptp.nat) (M tptp.nat)) (= (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_nat_fun_nat_nat tptp.aTP_Lamm_bi N)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat M)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N) M)) tptp.one_one_nat)) M))) (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N))) (= (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_nat_fun_nat_nat tptp.aTP_Lamm_bi N)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat M)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat _let_1 M)) tptp.one_one_nat)) (tptp.aa_nat_nat _let_1 tptp.one_one_nat))))) (forall ((R tptp.nat) (N tptp.nat)) (= (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_nat_fun_nat_nat tptp.aTP_Lamm_bj R)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat R) N))) N))) (forall ((N tptp.nat)) (= (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N) (tptp.aa_nat_set_nat (tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N))) (forall ((K tptp.nat)) (= (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat (tptp.aa_nat_nat tptp.suc K)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat K))) (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_bk M) N)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat M)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial (tptp.aa_nat_nat tptp.suc N)) M)))) (forall ((M tptp.nat) (N tptp.nat) (R tptp.nat)) (= (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_nat_fun_nat_nat (tptp.aa_nat3783148529270815480at_nat (tptp.aTP_Lamm_bl M) N) R)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat R)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) N)) R))) (forall ((K tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc K))) (= (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat _let_1) (tptp.insert_nat _let_1 (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat K))))) (forall ((N tptp.nat)) (= (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_nat_fun_nat_nat tptp.binomial N)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N))) (forall ((A tptp.nat) (B tptp.nat) (N tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) B)) N) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_nat_fun_nat_nat (tptp.aa_nat3783148529270815480at_nat (tptp.aTP_Lamm_bm A) B) N)) (tptp.aa_nat_set_nat 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 ((I2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) I2)) (= (tptp.aa_nat_nat A I2) 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_bn A) X)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat M))) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_nat_fun_nat_nat (tptp.aTP_Lamm_bn B) X)) (tptp.aa_nat_set_nat 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_bp A) B) X)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) N))))))) (forall ((N tptp.nat)) (= (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_nat_fun_nat_nat tptp.aTP_Lamm_bq N)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N)) N))) (forall ((K tptp.num)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat K))) (= (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat _let_1) (tptp.insert_nat _let_1 (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat (tptp.pred_numeral K)))))) (forall ((M tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat _let_1) M))) (= (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_nat_fun_nat_nat tptp.binomial (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat _let_2) tptp.one_one_nat))) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat M)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat _let_1) _let_2))))) (forall ((N tptp.nat)) (= (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_nat_fun_nat_nat tptp.aTP_Lamm_br N)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat N) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) tptp.one_one_nat))))) (forall ((N tptp.nat)) (= (tptp.image_nat_nat tptp.suc (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N)) (tptp.aa_nat_set_nat (tptp.set_or1269000886237332187st_nat tptp.one_one_nat) (tptp.aa_nat_nat tptp.suc N)))) (forall ((N tptp.nat)) (= (tptp.aa_nat_set_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.aa_nat_set_nat tptp.set_ord_atMost_nat N))))) (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_bs (tptp.collect_complex (tptp.aa_com1553036987509291606x_bool (tptp.aTP_Lamm_bt N) C))) tptp.zero_zero_complex))) (forall ((N tptp.nat)) (= (tptp.aa_nat_set_nat (tptp.set_or1269000886237332187st_nat (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)) N) (tptp.minus_minus_set_nat (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N) (tptp.insert_nat tptp.zero_zero_nat tptp.bot_bot_set_nat)))) (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_bs (tptp.collect_complex (tptp.aTP_Lamm_ak N))) tptp.zero_zero_complex))) (forall ((N tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat _let_1 N)) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat _let_1) (tptp.collect_nat (tptp.aa_nat_fun_nat_bool tptp.aTP_Lamm_bu N)))))) (forall ((N tptp.nat)) (= (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat tptp.aTP_Lamm_an) (tptp.aa_nat_set_nat (tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat 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_bv A) D)) (tptp.aa_nat_set_nat (tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (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_an) (tptp.aa_nat_set_nat (tptp.set_or1269000886237332187st_nat M) N)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat N) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N) tptp.one_one_nat))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat M) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) tptp.one_one_nat)))) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (forall ((M tptp.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_ao (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 ((T tptp.vEBT_VEBT)) (= (tptp.vEBT_set_vebt T) (tptp.collect_nat (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions T)))) (forall ((P2 tptp.rat) (Q2 tptp.rat)) (= (tptp.quotient_of (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat P2) Q2)) (tptp.produc4245557441103728435nt_int (tptp.aTP_Lamm_bx Q2) (tptp.quotient_of P2)))) (forall ((P2 tptp.rat) (Q2 tptp.rat)) (= (tptp.quotient_of (tptp.divide_divide_rat P2 Q2)) (tptp.produc4245557441103728435nt_int (tptp.aTP_Lamm_bz Q2) (tptp.quotient_of P2)))) (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_ca) (tptp.divmod_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) N) N)))))))) (forall ((P2 tptp.rat) (Q2 tptp.rat)) (= (tptp.quotient_of (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat P2) Q2)) (tptp.produc4245557441103728435nt_int (tptp.aTP_Lamm_cc Q2) (tptp.quotient_of P2)))) (forall ((P2 tptp.rat) (Q2 tptp.rat)) (= (tptp.quotient_of (tptp.minus_minus_rat P2 Q2)) (tptp.produc4245557441103728435nt_int (tptp.aTP_Lamm_ce Q2) (tptp.quotient_of P2)))) (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_cf L)) Qr))) (forall ((P2 tptp.rat)) (= (tptp.quotient_of (tptp.aa_rat_rat tptp.inverse_inverse_rat P2)) (tptp.produc4245557441103728435nt_int tptp.aTP_Lamm_cg (tptp.quotient_of P2)))) (forall ((L tptp.num) (Qr tptp.product_prod_int_int)) (= (tptp.unique5024387138958732305ep_int L Qr) (tptp.produc4245557441103728435nt_int (tptp.aTP_Lamm_ch L) Qr))) (forall ((Uy tptp.option4927543243414619207at_nat) (V tptp.nat) (TreeList tptp.list_VEBT_VEBT) (S tptp.vEBT_VEBT) (X tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc V))) (let ((_let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat _let_1) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_3 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high X) _let_2))) (let ((_let_4 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_3) (tptp.size_s6755466524823107622T_VEBT TreeList))))) (= (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_V5719532721284313246member (tptp.vEBT_Node Uy _let_1 TreeList S)) X)) (and (=> _let_4 (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_V5719532721284313246member (tptp.nth_VEBT_VEBT TreeList _let_3)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low X) _let_2)))) _let_4))))))) (forall ((Y tptp.real)) (= (tptp.aa_real_real tptp.arctan Y) (tptp.the_real (tptp.aa_rea7809428808904475482l_bool tptp.aTP_Lamm_ci Y)))) (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)))) (= _let_48 _let_61) (= tptp.pi (tptp.aa_real_real _let_62 _let_61)) (forall ((Y tptp.real)) (= (tptp.aa_real_real tptp.arcsin Y) (tptp.the_real (tptp.aa_rea7809428808904475482l_bool tptp.aTP_Lamm_ck Y)))) (forall ((X tptp.vEBT_VEBT) (Xa tptp.nat) (Y tptp.bool)) (let ((_let_1 (tptp.pp Y))) (=> (= (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_V5719532721284313246member X) Xa)) _let_1) (=> (forall ((A3 tptp.bool) (B3 tptp.bool)) (let ((_let_1 (= Xa tptp.one_one_nat))) (let ((_let_2 (= Xa tptp.zero_zero_nat))) (=> (= X (tptp.vEBT_Leaf A3 B3)) (= (tptp.pp Y) (not (and (=> _let_2 (tptp.pp A3)) (=> (not _let_2) (and (=> _let_1 (tptp.pp B3)) _let_1))))))))) (=> (=> (exists ((Uu2 tptp.option4927543243414619207at_nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (= X (tptp.vEBT_Node Uu2 tptp.zero_zero_nat Uv2 Uw2))) _let_1) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (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.aa_nat_fun_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 Y) (not (and (=> _let_3 (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_V5719532721284313246member (tptp.nth_VEBT_VEBT TreeList2 _let_2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low 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) (B3 tptp.bool)) (let ((_let_1 (= Xa tptp.one_one_nat))) (let ((_let_2 (= Xa tptp.zero_zero_nat))) (=> (= X (tptp.vEBT_Leaf A3 B3)) (not (and (=> _let_2 (tptp.pp A3)) (=> (not _let_2) (and (=> _let_1 (tptp.pp B3)) _let_1)))))))) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (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.aa_nat_fun_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.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low Xa) _let_1)))) _let_3))))))))))) (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 ((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)) (forall ((Y tptp.vEBT_VEBT)) (=> (forall ((X112 tptp.option4927543243414619207at_nat) (X122 tptp.nat) (X132 tptp.list_VEBT_VEBT) (X142 tptp.vEBT_VEBT)) (not (= Y (tptp.vEBT_Node X112 X122 X132 X142)))) (not (forall ((X212 tptp.bool) (X223 tptp.bool)) (not (= Y (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 ((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) (Deg tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (Deg2 tptp.nat)) (not (= X (tptp.produc738532404422230701BT_nat (tptp.vEBT_Node Mima Deg TreeList2 Summary) Deg2))))))) (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)))) (= (tptp.vEBT_vebt_buildup tptp.zero_zero_nat) _let_60) (forall ((X tptp.produc9072475918466114483BT_nat)) (=> (forall ((A3 tptp.bool) (B3 tptp.bool) (X3 tptp.nat)) (not (= X (tptp.produc738532404422230701BT_nat (tptp.vEBT_Leaf A3 B3) 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)))))))) (= (tptp.vEBT_vebt_buildup _let_11) _let_60) (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))))))) (= tptp.nat_prod_encode (tptp.produc6842872674320459806at_nat tptp.aTP_Lamm_cl)) (forall ((X tptp.vEBT_VEBT) (Xa tptp.nat)) (=> (not (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_V5719532721284313246member X) Xa))) (=> (forall ((A3 tptp.bool) (B3 tptp.bool)) (let ((_let_1 (= Xa tptp.one_one_nat))) (let ((_let_2 (= Xa tptp.zero_zero_nat))) (=> (= X (tptp.vEBT_Leaf A3 B3)) (and (=> _let_2 (tptp.pp A3)) (=> (not _let_2) (and (=> _let_1 (tptp.pp B3)) _let_1))))))) (=> (forall ((Uu2 tptp.option4927543243414619207at_nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (not (= X (tptp.vEBT_Node Uu2 tptp.zero_zero_nat Uv2 Uw2)))) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (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.aa_nat_fun_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.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low Xa) _let_1)))) _let_3))))))))))) (forall ((Mi tptp.nat) (Ma tptp.nat) (V tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Vc tptp.vEBT_VEBT) (X tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc V))) (let ((_let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat _let_1) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_3 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high X) _let_2))) (let ((_let_4 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_3) (tptp.size_s6755466524823107622T_VEBT TreeList))))) (= (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_VEBT_membermima (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Mi) Ma)) _let_1 TreeList Vc)) X)) (or (= X Mi) (= X Ma) (and (=> _let_4 (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_VEBT_membermima (tptp.nth_VEBT_VEBT TreeList _let_3)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low X) _let_2)))) _let_4)))))))) (forall ((V tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Vd tptp.vEBT_VEBT) (X tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc V))) (let ((_let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat _let_1) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_3 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high X) _let_2))) (let ((_let_4 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_3) (tptp.size_s6755466524823107622T_VEBT TreeList))))) (= (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_VEBT_membermima (tptp.vEBT_Node tptp.none_P5556105721700978146at_nat _let_1 TreeList Vd)) X)) (and (=> _let_4 (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_VEBT_membermima (tptp.nth_VEBT_VEBT TreeList _let_3)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low X) _let_2)))) _let_4))))))) (forall ((A tptp.int) (B tptp.int)) (tptp.finite_finite_int (tptp.collect_int (tptp.aa_int_fun_int_bool (tptp.aTP_Lamm_cm 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_cn 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_co 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_cp 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_bt N) C))))) (forall ((N tptp.nat)) (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat (tptp.aa_nat_set_nat tptp.nat_set_decode N)))) (forall ((X tptp.produc9072475918466114483BT_nat)) (=> (forall ((Uu2 tptp.bool) (Uv2 tptp.bool) (Uw2 tptp.nat)) (not (= X (tptp.produc738532404422230701BT_nat (tptp.vEBT_Leaf Uu2 Uv2) Uw2)))) (=> (forall ((Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT) (Uz tptp.nat)) (not (= X (tptp.produc738532404422230701BT_nat (tptp.vEBT_Node tptp.none_P5556105721700978146at_nat tptp.zero_zero_nat Ux2 Uy2) Uz)))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va2 tptp.list_VEBT_VEBT) (Vb 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 Va2 Vb) X3)))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (V3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Vc2 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 Vc2) X3)))) (not (forall ((V3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Vd2 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 Vd2) X3)))))))))) (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_cq I))))) (forall ((Ux tptp.list_VEBT_VEBT) (Uy tptp.vEBT_VEBT) (Uz2 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)) Uz2)))) (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_cr M)))))) (forall ((N4 tptp.set_nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat N4) (tptp.aa_nat_set_nat (tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N))) (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat N4)))) (forall ((Mi tptp.nat) (Ma tptp.nat) (Va3 tptp.list_VEBT_VEBT) (Vb2 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 Va3 Vb2)) X)) (or (= X Mi) (= X Ma)))) (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 ((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 ((Va2 tptp.list_VEBT_VEBT) (Vb 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 Va2 Vb))) (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.aa_nat_fun_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 ((Vc2 tptp.vEBT_VEBT)) (= X (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Mi2) Ma2)) (tptp.aa_nat_nat tptp.suc V3) TreeList2 Vc2))) (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.aa_nat_fun_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.aa_nat_fun_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 ((Vd2 tptp.vEBT_VEBT)) (= X (tptp.vEBT_Node tptp.none_P5556105721700978146at_nat (tptp.aa_nat_nat tptp.suc V3) TreeList2 Vd2))) (not (and (=> _let_3 (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_VEBT_membermima (tptp.nth_VEBT_VEBT TreeList2 _let_2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low Xa) _let_1)))) _let_3)))))))))))) (forall ((X tptp.vEBT_VEBT) (Xa tptp.nat) (Y tptp.bool)) (let ((_let_1 (tptp.pp Y))) (=> (= (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 ((Va2 tptp.list_VEBT_VEBT) (Vb 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 Va2 Vb))) (= (tptp.pp Y) (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.aa_nat_fun_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 ((Vc2 tptp.vEBT_VEBT)) (= X (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Mi2) Ma2)) (tptp.aa_nat_nat tptp.suc V3) TreeList2 Vc2))) (= (tptp.pp Y) (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.aa_nat_fun_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.aa_nat_fun_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 ((Vd2 tptp.vEBT_VEBT)) (= X (tptp.vEBT_Node tptp.none_P5556105721700978146at_nat (tptp.aa_nat_nat tptp.suc V3) TreeList2 Vd2))) (= (tptp.pp Y) (not (and (=> _let_3 (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_VEBT_membermima (tptp.nth_VEBT_VEBT TreeList2 _let_2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low Xa) _let_1)))) _let_3)))))))))))))))) (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 ((Va2 tptp.list_VEBT_VEBT) (Vb 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 Va2 Vb))) (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.aa_nat_fun_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 ((Vc2 tptp.vEBT_VEBT)) (= X (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Mi2) Ma2)) (tptp.aa_nat_nat tptp.suc V3) TreeList2 Vc2))) (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.aa_nat_fun_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.aa_nat_fun_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 ((Vd2 tptp.vEBT_VEBT)) (= X (tptp.vEBT_Node tptp.none_P5556105721700978146at_nat (tptp.aa_nat_nat tptp.suc V3) TreeList2 Vd2))) (and (=> _let_3 (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_VEBT_membermima (tptp.nth_VEBT_VEBT TreeList2 _let_2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low Xa) _let_1)))) _let_3))))))))))))) (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) (B7 tptp.bool)) (= A1 (tptp.vEBT_Leaf A5 B7))) (= A22 (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat))) (exists ((TreeList3 tptp.list_VEBT_VEBT) (N5 tptp.nat) (Summary2 tptp.vEBT_VEBT)) (and (= A1 (tptp.vEBT_Node tptp.none_P5556105721700978146at_nat A22 TreeList3 Summary2)) (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) N5)))) (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt Summary2) N5)) (= (tptp.size_s6755466524823107622T_VEBT TreeList3) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N5)) (= A22 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N5) N5)) (not (exists ((X_13 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions Summary2) X_13)))) (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_13 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions X5) X_13)))))))) (exists ((TreeList3 tptp.list_VEBT_VEBT) (N5 tptp.nat) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N5))) (and (= A1 (tptp.vEBT_Node tptp.none_P5556105721700978146at_nat A22 TreeList3 Summary2)) (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) N5)))) (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt Summary2) _let_1)) (= (tptp.size_s6755466524823107622T_VEBT TreeList3) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) _let_1)) (= A22 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N5) _let_1)) (not (exists ((X_13 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions Summary2) X_13)))) (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_13 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions X5) X_13))))))))) (exists ((TreeList3 tptp.list_VEBT_VEBT) (N5 tptp.nat) (Summary2 tptp.vEBT_VEBT) (Mi3 tptp.nat) (Ma3 tptp.nat)) (let ((_let_1 (= Mi3 Ma3))) (let ((_let_2 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (and (= A1 (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Mi3) Ma3)) A22 TreeList3 Summary2)) (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) N5)))) (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt Summary2) N5)) (= (tptp.size_s6755466524823107622T_VEBT TreeList3) (tptp.aa_nat_nat _let_2 N5)) (= A22 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N5) N5)) (forall ((I4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I4) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N5))) (= (exists ((X_13 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions (tptp.nth_VEBT_VEBT TreeList3 I4)) X_13))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions Summary2) I4))))) (=> _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_13 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions X5) X_13))))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Mi3) Ma3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Ma3) (tptp.aa_nat_nat _let_2 A22))) (=> (not _let_1) (forall ((I4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I4) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N5))) (and (=> (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high Ma3) N5) I4) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions (tptp.nth_VEBT_VEBT TreeList3 I4)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low Ma3) N5)))) (forall ((X5 tptp.nat)) (=> (and (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high X5) N5) I4) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions (tptp.nth_VEBT_VEBT TreeList3 I4)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low X5) N5)))) (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) (N5 tptp.nat) (Summary2 tptp.vEBT_VEBT) (Mi3 tptp.nat) (Ma3 tptp.nat)) (let ((_let_1 (= Mi3 Ma3))) (let ((_let_2 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_3 (tptp.aa_nat_nat tptp.suc N5))) (and (= A1 (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Mi3) Ma3)) A22 TreeList3 Summary2)) (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) N5)))) (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt Summary2) _let_3)) (= (tptp.size_s6755466524823107622T_VEBT TreeList3) (tptp.aa_nat_nat _let_2 _let_3)) (= A22 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N5) _let_3)) (forall ((I4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I4) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_nat_nat tptp.suc N5)))) (= (exists ((X_13 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions (tptp.nth_VEBT_VEBT TreeList3 I4)) X_13))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions Summary2) I4))))) (=> _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_13 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions X5) X_13))))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Mi3) Ma3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Ma3) (tptp.aa_nat_nat _let_2 A22))) (=> (not _let_1) (forall ((I4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I4) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_nat_nat tptp.suc N5)))) (and (=> (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high Ma3) N5) I4) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions (tptp.nth_VEBT_VEBT TreeList3 I4)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low Ma3) N5)))) (forall ((X5 tptp.nat)) (=> (and (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high X5) N5) I4) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions (tptp.nth_VEBT_VEBT TreeList3 I4)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low X5) N5)))) (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 ((A1 tptp.vEBT_VEBT) (A22 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt A1) A22)) (=> (=> (exists ((A3 tptp.bool) (B3 tptp.bool)) (= A1 (tptp.vEBT_Leaf A3 B3))) (not (= A22 (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)))) (=> (forall ((TreeList2 tptp.list_VEBT_VEBT) (N2 tptp.nat) (Summary tptp.vEBT_VEBT) (M2 tptp.nat) (Deg tptp.nat)) (=> (= A1 (tptp.vEBT_Node tptp.none_P5556105721700978146at_nat Deg TreeList2 Summary)) (=> (= A22 Deg) (=> (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 Summary) M2)) (=> (= (tptp.size_s6755466524823107622T_VEBT TreeList2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) M2)) (=> (= M2 N2) (=> (= Deg (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N2) M2)) (=> (not (exists ((X_1 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions Summary) X_1)))) (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_1 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions X4) X_1)))))))))))))))) (=> (forall ((TreeList2 tptp.list_VEBT_VEBT) (N2 tptp.nat) (Summary tptp.vEBT_VEBT) (M2 tptp.nat) (Deg tptp.nat)) (=> (= A1 (tptp.vEBT_Node tptp.none_P5556105721700978146at_nat Deg TreeList2 Summary)) (=> (= A22 Deg) (=> (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 Summary) M2)) (=> (= (tptp.size_s6755466524823107622T_VEBT TreeList2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) M2)) (=> (= M2 (tptp.aa_nat_nat tptp.suc N2)) (=> (= Deg (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N2) M2)) (=> (not (exists ((X_1 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions Summary) X_1)))) (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_1 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions X4) X_1)))))))))))))))) (=> (forall ((TreeList2 tptp.list_VEBT_VEBT) (N2 tptp.nat) (Summary tptp.vEBT_VEBT) (M2 tptp.nat) (Deg tptp.nat) (Mi2 tptp.nat) (Ma2 tptp.nat)) (let ((_let_1 (= Mi2 Ma2))) (let ((_let_2 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (=> (= A1 (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Mi2) Ma2)) Deg TreeList2 Summary)) (=> (= A22 Deg) (=> (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 Summary) M2)) (=> (= (tptp.size_s6755466524823107622T_VEBT TreeList2) (tptp.aa_nat_nat _let_2 M2)) (=> (= M2 N2) (=> (= Deg (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N2) M2)) (=> (forall ((I3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I3) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) M2))) (= (exists ((X_13 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions (tptp.nth_VEBT_VEBT TreeList2 I3)) X_13))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions Summary) I3))))) (=> (=> _let_1 (forall ((X4 tptp.vEBT_VEBT)) (=> (tptp.pp (tptp.aa_set8260762808118238015T_bool (tptp.aa_VEB289770264548726718T_bool tptp.member_VEBT_VEBT X4) (tptp.set_VEBT_VEBT2 TreeList2))) (not (exists ((X_1 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions X4) X_1))))))) (=> (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 Deg))) (not (=> (not _let_1) (forall ((I3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I3) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) M2))) (and (=> (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high Ma2) N2) I3) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions (tptp.nth_VEBT_VEBT TreeList2 I3)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low Ma2) N2)))) (forall ((X4 tptp.nat)) (=> (and (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high X4) N2) I3) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions (tptp.nth_VEBT_VEBT TreeList2 I3)) (tptp.aa_nat_nat (tptp.aa_nat_fun_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) (Summary tptp.vEBT_VEBT) (M2 tptp.nat) (Deg tptp.nat) (Mi2 tptp.nat) (Ma2 tptp.nat)) (let ((_let_1 (= Mi2 Ma2))) (let ((_let_2 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (=> (= A1 (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Mi2) Ma2)) Deg TreeList2 Summary)) (=> (= A22 Deg) (=> (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 Summary) M2)) (=> (= (tptp.size_s6755466524823107622T_VEBT TreeList2) (tptp.aa_nat_nat _let_2 M2)) (=> (= M2 (tptp.aa_nat_nat tptp.suc N2)) (=> (= Deg (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N2) M2)) (=> (forall ((I3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I3) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) M2))) (= (exists ((X_13 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions (tptp.nth_VEBT_VEBT TreeList2 I3)) X_13))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions Summary) I3))))) (=> (=> _let_1 (forall ((X4 tptp.vEBT_VEBT)) (=> (tptp.pp (tptp.aa_set8260762808118238015T_bool (tptp.aa_VEB289770264548726718T_bool tptp.member_VEBT_VEBT X4) (tptp.set_VEBT_VEBT2 TreeList2))) (not (exists ((X_1 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions X4) X_1))))))) (=> (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 Deg))) (not (=> (not _let_1) (forall ((I3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I3) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) M2))) (and (=> (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high Ma2) N2) I3) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions (tptp.nth_VEBT_VEBT TreeList2 I3)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low Ma2) N2)))) (forall ((X4 tptp.nat)) (=> (and (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high X4) N2) I3) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions (tptp.nth_VEBT_VEBT TreeList2 I3)) (tptp.aa_nat_nat (tptp.aa_nat_fun_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 ((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)))) (forall ((TreeList tptp.list_VEBT_VEBT) (N tptp.nat) (Summary3 tptp.vEBT_VEBT) (M tptp.nat) (Deg3 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 Summary3) M)) (=> (= (tptp.size_s6755466524823107622T_VEBT TreeList) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) M)) (=> (= M N) (=> (= Deg3 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N) M)) (=> (not (exists ((X_12 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions Summary3) X_12)))) (=> (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_12 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions X3) X_12)))))) (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt (tptp.vEBT_Node tptp.none_P5556105721700978146at_nat Deg3 TreeList Summary3)) Deg3)))))))))) (forall ((TreeList tptp.list_VEBT_VEBT) (N tptp.nat) (Summary3 tptp.vEBT_VEBT) (M tptp.nat) (Deg3 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 Summary3) M)) (=> (= (tptp.size_s6755466524823107622T_VEBT TreeList) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) M)) (=> (= M (tptp.aa_nat_nat tptp.suc N)) (=> (= Deg3 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N) M)) (=> (not (exists ((X_12 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions Summary3) X_12)))) (=> (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_12 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions X3) X_12)))))) (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt (tptp.vEBT_Node tptp.none_P5556105721700978146at_nat Deg3 TreeList Summary3)) Deg3)))))))))) (forall ((TreeList tptp.list_VEBT_VEBT) (N tptp.nat) (Summary3 tptp.vEBT_VEBT) (M tptp.nat) (Deg3 tptp.nat) (Mi tptp.nat) (Ma tptp.nat)) (let ((_let_1 (= Mi Ma))) (let ((_let_2 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (=> (forall ((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 Summary3) M)) (=> (= (tptp.size_s6755466524823107622T_VEBT TreeList) (tptp.aa_nat_nat _let_2 M)) (=> (= M N) (=> (= Deg3 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N) M)) (=> (forall ((I2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) M))) (= (exists ((X_13 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions (tptp.nth_VEBT_VEBT TreeList I2)) X_13))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions Summary3) I2))))) (=> (=> _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_12 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions X3) X_12))))))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Mi) Ma)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Ma) (tptp.aa_nat_nat _let_2 Deg3))) (=> (=> (not _let_1) (forall ((I2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) M))) (and (=> (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high Ma) N) I2) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions (tptp.nth_VEBT_VEBT TreeList I2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low Ma) N)))) (forall ((X3 tptp.nat)) (=> (and (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high X3) N) I2) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions (tptp.nth_VEBT_VEBT TreeList I2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_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)) Deg3 TreeList Summary3)) Deg3))))))))))))))) (forall ((TreeList tptp.list_VEBT_VEBT) (N tptp.nat) (Summary3 tptp.vEBT_VEBT) (M tptp.nat) (Deg3 tptp.nat) (Mi tptp.nat) (Ma tptp.nat)) (let ((_let_1 (= Mi Ma))) (let ((_let_2 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (=> (forall ((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 Summary3) M)) (=> (= (tptp.size_s6755466524823107622T_VEBT TreeList) (tptp.aa_nat_nat _let_2 M)) (=> (= M (tptp.aa_nat_nat tptp.suc N)) (=> (= Deg3 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N) M)) (=> (forall ((I2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) M))) (= (exists ((X_13 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions (tptp.nth_VEBT_VEBT TreeList I2)) X_13))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions Summary3) I2))))) (=> (=> _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_12 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions X3) X_12))))))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Mi) Ma)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Ma) (tptp.aa_nat_nat _let_2 Deg3))) (=> (=> (not _let_1) (forall ((I2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) M))) (and (=> (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high Ma) N) I2) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions (tptp.nth_VEBT_VEBT TreeList I2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low Ma) N)))) (forall ((X3 tptp.nat)) (=> (and (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high X3) N) I2) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions (tptp.nth_VEBT_VEBT TreeList I2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_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)) Deg3 TreeList Summary3)) Deg3))))))))))))))) (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.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N)) (tptp.aa_set_nat_nat tptp.nat_set_encode A2)))))) (forall ((X tptp.nat) (Y tptp.vEBT_VEBT)) (let ((_let_1 (not (= Y (tptp.vEBT_Leaf tptp.fFalse tptp.fFalse))))) (=> (= (tptp.vEBT_vebt_buildup X) Y) (=> (=> (= X tptp.zero_zero_nat) _let_1) (=> (=> (= X (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)) _let_1) (not (forall ((Va tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat tptp.suc Va)))) (let ((_let_3 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat _let_2) _let_1))) (let ((_let_4 (tptp.aa_nat_nat tptp.suc _let_3))) (let ((_let_5 (tptp.vEBT_vebt_buildup _let_3))) (let ((_let_6 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat _let_1))) (let ((_let_7 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat _let_1) _let_2)))) (=> (= X _let_2) (not (and (=> _let_7 (= Y (tptp.vEBT_Node tptp.none_P5556105721700978146at_nat _let_2 (tptp.replicate_VEBT_VEBT (tptp.aa_nat_nat _let_6 _let_3) _let_5) _let_5))) (=> (not _let_7) (= Y (tptp.vEBT_Node tptp.none_P5556105721700978146at_nat _let_2 (tptp.replicate_VEBT_VEBT (tptp.aa_nat_nat _let_6 _let_4) _let_5) (tptp.vEBT_vebt_buildup _let_4))))))))))))))))))))) (forall ((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) (Va2 tptp.list_VEBT_VEBT) (Vb 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 Va2 Vb))) (=> (= 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) (Vc2 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.aa_nat_fun_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 Vc2))) (=> (= 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.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low Xa) _let_2)))) _let_4)))))))))) (not (forall ((V3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Vd2 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.aa_nat_fun_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 Vd2))) (=> (= 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.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low Xa) _let_2)))) _let_4))))))))))))))))) (forall ((N tptp.nat)) (= (tptp.aa_set_nat_nat tptp.nat_set_encode (tptp.aa_nat_set_nat tptp.nat_set_decode N)) N)) (= (tptp.aa_set_nat_nat tptp.nat_set_encode tptp.bot_bot_set_nat) tptp.zero_zero_nat) (forall ((A2 tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A2)) (= (tptp.aa_nat_set_nat tptp.nat_set_decode (tptp.aa_set_nat_nat tptp.nat_set_encode A2)) A2))) (forall ((A2 tptp.set_nat) (B4 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 B4)) (= (= (tptp.aa_set_nat_nat tptp.nat_set_encode A2) (tptp.aa_set_nat_nat tptp.nat_set_encode B4)) (= A2 B4))))) (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))) (= tptp.nat_set_encode (tptp.groups3542108847815614940at_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat _let_2))) (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 ((Va3 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 Va3)))) (let ((_let_3 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat _let_2) _let_1))) (let ((_let_4 (tptp.aa_nat_nat tptp.suc _let_3))) (let ((_let_5 (tptp.vEBT_vebt_buildup _let_3))) (let ((_let_6 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat _let_1))) (let ((_let_7 (tptp.vEBT_vebt_buildup _let_2))) (let ((_let_8 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat _let_1) _let_2)))) (and (=> _let_8 (= _let_7 (tptp.vEBT_Node tptp.none_P5556105721700978146at_nat _let_2 (tptp.replicate_VEBT_VEBT (tptp.aa_nat_nat _let_6 _let_3) _let_5) _let_5))) (=> (not _let_8) (= _let_7 (tptp.vEBT_Node tptp.none_P5556105721700978146at_nat _let_2 (tptp.replicate_VEBT_VEBT (tptp.aa_nat_nat _let_6 _let_4) _let_5) (tptp.vEBT_vebt_buildup _let_4)))))))))))))) (forall ((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) (Va2 tptp.list_VEBT_VEBT) (Vb 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 Va2 Vb))) (=> (= 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) (Vc2 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.aa_nat_fun_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 Vc2))) (=> (= 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.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low Xa) _let_2)))) _let_4))))))))))) (not (forall ((V3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Vd2 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.aa_nat_fun_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 Vd2))) (=> (= 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.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low Xa) _let_2)))) _let_4)))))))))))))))) (forall ((X tptp.vEBT_VEBT) (Xa tptp.nat) (Y tptp.bool)) (=> (= (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_VEBT_membermima X) Xa)) (tptp.pp Y)) (=> (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 Y)) (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 Y)) (not (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel (tptp.produc738532404422230701BT_nat _let_1 Xa))))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va2 tptp.list_VEBT_VEBT) (Vb 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 Va2 Vb))) (=> (= X _let_1) (=> (= (tptp.pp Y) (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) (Vc2 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 Vc2))) (let ((_let_3 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat _let_1) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_4 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high 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 Y) (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.aa_nat_fun_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) (Vd2 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 Vd2))) (let ((_let_3 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat _let_1) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_4 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high 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 Y) (and (=> _let_5 (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_VEBT_membermima (tptp.nth_VEBT_VEBT TreeList2 _let_4)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low Xa) _let_3)))) _let_5)) (not (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel (tptp.produc738532404422230701BT_nat _let_2 Xa))))))))))))))))))) (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) (B3 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 B3))) (=> (= 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 B3)) _let_1))))))))) (=> (forall ((Uu2 tptp.option4927543243414619207at_nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (let ((_let_1 (tptp.vEBT_Node Uu2 tptp.zero_zero_nat Uv2 Uw2))) (=> (= X _let_1) (not (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel (tptp.produc738532404422230701BT_nat _let_1 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.aa_nat_fun_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.aa_nat_fun_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) (B3 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 B3))) (=> (= 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 B3)) _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.aa_nat_fun_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.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low Xa) _let_2)))) _let_4))))))))))))))) (forall ((X tptp.vEBT_VEBT) (Xa tptp.nat) (Y tptp.bool)) (=> (= (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_V5719532721284313246member X) Xa)) (tptp.pp Y)) (=> (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel (tptp.produc738532404422230701BT_nat X Xa)) (=> (forall ((A3 tptp.bool) (B3 tptp.bool)) (let ((_let_1 (tptp.vEBT_Leaf A3 B3))) (let ((_let_2 (= Xa tptp.one_one_nat))) (let ((_let_3 (= Xa tptp.zero_zero_nat))) (=> (= X _let_1) (=> (= (tptp.pp Y) (and (=> _let_3 (tptp.pp A3)) (=> (not _let_3) (and (=> _let_2 (tptp.pp B3)) _let_2)))) (not (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel (tptp.produc738532404422230701BT_nat _let_1 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 Y)) (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.aa_nat_fun_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 Y) (and (=> _let_5 (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_V5719532721284313246member (tptp.nth_VEBT_VEBT TreeList2 _let_4)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low Xa) _let_3)))) _let_5)) (not (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel (tptp.produc738532404422230701BT_nat _let_2 Xa))))))))))))))))) (forall ((X tptp.nat) (Y tptp.vEBT_VEBT)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat))) (let ((_let_2 (tptp.accp_nat tptp.vEBT_v4011308405150292612up_rel))) (let ((_let_3 (= Y (tptp.vEBT_Leaf tptp.fFalse tptp.fFalse)))) (=> (= (tptp.vEBT_vebt_buildup X) Y) (=> (tptp.pp (tptp.aa_nat_bool _let_2 X)) (=> (=> (= X tptp.zero_zero_nat) (=> _let_3 (not (tptp.pp (tptp.aa_nat_bool _let_2 tptp.zero_zero_nat))))) (=> (=> (= X _let_1) (=> _let_3 (not (tptp.pp (tptp.aa_nat_bool _let_2 _let_1))))) (not (forall ((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.aa_nat_fun_nat_nat tptp.power_power_nat _let_2))) (let ((_let_7 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat _let_2) _let_1)))) (=> (= X _let_1) (=> (and (=> _let_7 (= Y (tptp.vEBT_Node tptp.none_P5556105721700978146at_nat _let_1 (tptp.replicate_VEBT_VEBT (tptp.aa_nat_nat _let_6 _let_3) _let_5) _let_5))) (=> (not _let_7) (= Y (tptp.vEBT_Node tptp.none_P5556105721700978146at_nat _let_1 (tptp.replicate_VEBT_VEBT (tptp.aa_nat_nat _let_6 _let_4) _let_5) (tptp.vEBT_vebt_buildup _let_4))))) (not (tptp.pp (tptp.aa_nat_bool (tptp.accp_nat tptp.vEBT_v4011308405150292612up_rel) _let_1)))))))))))))))))))))) (forall ((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 ((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 ((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_an) (tptp.aa_nat_set_nat (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 ((I tptp.nat) (J tptp.nat)) (= (tptp.image_nat_nat tptp.suc (tptp.aa_nat_set_nat (tptp.set_or4665077453230672383an_nat I) J)) (tptp.aa_nat_set_nat (tptp.set_or4665077453230672383an_nat (tptp.aa_nat_nat tptp.suc I)) (tptp.aa_nat_nat tptp.suc J)))) (forall ((L tptp.nat) (U tptp.nat)) (= (tptp.finite_card_nat (tptp.aa_nat_set_nat (tptp.set_or4665077453230672383an_nat L) U)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat U) L))) (forall ((M tptp.nat)) (= (tptp.aa_nat_set_nat (tptp.set_or4665077453230672383an_nat M) (tptp.aa_nat_nat tptp.suc M)) (tptp.insert_nat M tptp.bot_bot_set_nat))) (forall ((N tptp.nat) (P tptp.fun_nat_bool)) (= (exists ((M6 tptp.nat)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M6) N)) (tptp.pp (tptp.aa_nat_bool P M6)))) (exists ((X5 tptp.nat)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X5) (tptp.aa_nat_set_nat (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 ((M6 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M6) N)) (tptp.pp (tptp.aa_nat_bool P M6)))) (forall ((X5 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X5) (tptp.aa_nat_set_nat (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.aa_nat_set_nat (tptp.set_or4665077453230672383an_nat L) (tptp.aa_nat_nat tptp.suc U)) (tptp.aa_nat_set_nat (tptp.set_or1269000886237332187st_nat L) U))) (forall ((N tptp.nat)) (= (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N) (tptp.aa_nat_set_nat (tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N))) (forall ((M tptp.nat)) (= (tptp.aa_nat_set_nat (tptp.set_or4665077453230672383an_nat M) tptp.zero_zero_nat) tptp.bot_bot_set_nat)) (forall ((L tptp.nat) (U tptp.nat)) (= (tptp.aa_nat_set_nat (tptp.set_or4665077453230672383an_nat (tptp.aa_nat_nat tptp.suc L)) U) (tptp.aa_nat_set_nat (tptp.set_or5834768355832116004an_nat L) U))) (forall ((N tptp.nat)) (let ((_let_1 (tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat))) (= (tptp.aa_nat_set_nat _let_1 (tptp.aa_nat_nat tptp.suc N)) (tptp.insert_nat N (tptp.aa_nat_set_nat _let_1 N))))) (forall ((N4 tptp.set_nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat N4) (tptp.aa_nat_set_nat (tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N))) (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat N4)))) (forall ((A2 tptp.set_nat) (K tptp.nat)) (let ((_let_1 (tptp.aa_nat_set_nat (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.nat) (N tptp.nat)) (let ((_let_1 (tptp.set_or4665077453230672383an_nat M))) (let ((_let_2 (tptp.aa_nat_set_nat _let_1 (tptp.aa_nat_nat tptp.suc N)))) (let ((_let_3 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N)))) (and (=> _let_3 (= _let_2 (tptp.insert_nat N (tptp.aa_nat_set_nat _let_1 N)))) (=> (not _let_3) (= _let_2 tptp.bot_bot_set_nat))))))) (forall ((N tptp.nat)) (let ((_let_1 (tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat))) (= (tptp.aa_nat_set_nat _let_1 (tptp.aa_nat_nat tptp.suc N)) (tptp.insert_nat tptp.zero_zero_nat (tptp.image_nat_nat tptp.suc (tptp.aa_nat_set_nat _let_1 N)))))) (forall ((N tptp.nat)) (= (tptp.groups708209901874060359at_nat tptp.suc (tptp.aa_nat_set_nat (tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N)) (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat N))) (forall ((N tptp.nat)) (= (tptp.groups708209901874060359at_nat tptp.suc (tptp.aa_nat_set_nat (tptp.set_or4665077453230672383an_nat (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)) N)) (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat N))) (forall ((N4 tptp.set_nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat N4) (tptp.aa_nat_set_nat (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 N4)) N)))) (forall ((S2 tptp.set_nat)) (let ((_let_1 (tptp.groups3542108847815614940at_nat tptp.aTP_Lamm_an))) (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.aa_nat_set_nat (tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) (tptp.finite_card_nat S2)))) (tptp.aa_set_nat_nat _let_1 S2))))) (forall ((M tptp.nat) (K tptp.num)) (let ((_let_1 (tptp.set_or4665077453230672383an_nat M))) (let ((_let_2 (tptp.aa_nat_set_nat _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat K)))) (let ((_let_3 (tptp.pred_numeral K))) (let ((_let_4 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) _let_3)))) (and (=> _let_4 (= _let_2 (tptp.insert_nat _let_3 (tptp.aa_nat_set_nat _let_1 _let_3)))) (=> (not _let_4) (= _let_2 tptp.bot_bot_set_nat)))))))) (forall ((C tptp.nat) (Y tptp.nat) (X tptp.nat)) (let ((_let_1 (tptp.image_nat_nat (tptp.aa_nat_fun_nat_nat tptp.aTP_Lamm_cs C) (tptp.aa_nat_set_nat (tptp.set_or4665077453230672383an_nat X) Y)))) (let ((_let_2 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Y)))) (let ((_let_3 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat C) Y)))) (and (=> _let_3 (= _let_1 (tptp.aa_nat_set_nat (tptp.set_or4665077453230672383an_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat X) C)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Y) C)))) (=> (not _let_3) (and (=> _let_2 (= _let_1 (tptp.insert_nat tptp.zero_zero_nat tptp.bot_bot_set_nat))) (=> (not _let_2) (= _let_1 tptp.bot_bot_set_nat))))))))) (forall ((N tptp.nat)) (= (tptp.aa_nat_set_nat (tptp.set_or4665077453230672383an_nat (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)) N) (tptp.minus_minus_set_nat (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N) (tptp.insert_nat tptp.zero_zero_nat tptp.bot_bot_set_nat)))) (forall ((K tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat _let_1) (tptp.aa_nat_set_nat (tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) K)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat _let_1 K)) tptp.one_one_nat)))) (forall ((N tptp.nat) (A tptp.fun_nat_nat) (B tptp.fun_nat_nat)) (let ((_let_1 (tptp.aa_nat_set_nat (tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N))) (=> (forall ((I2 tptp.nat) (J2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I2) 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 I2)) (tptp.aa_nat_nat A J2)))))) (=> (forall ((I2 tptp.nat) (J2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I2) 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 I2)))))) (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_ct 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 ((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 ((U tptp.int)) (tptp.finite_finite_int (tptp.set_or4662586982721622107an_int tptp.zero_zero_int U))) (forall ((L tptp.int) (U tptp.int)) (= (tptp.set_or4662586982721622107an_int L (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int U) tptp.one_one_int)) (tptp.set_or1266510415728281911st_int L U))) (forall ((A tptp.nat) (B tptp.nat)) (= (tptp.image_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_set_nat (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 ((U tptp.int)) (= (tptp.finite_card_int (tptp.set_or4662586982721622107an_int tptp.zero_zero_int U)) (tptp.aa_int_nat tptp.nat2 U))) (forall ((L tptp.int) (U tptp.int)) (= (tptp.set_or4662586982721622107an_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int L) tptp.one_one_int) U) (tptp.set_or5832277885323065728an_int L U))) (forall ((L tptp.int) (U tptp.int)) (= (tptp.image_int_int (tptp.aTP_Lamm_cu 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 ((X21 tptp.bool) (X222 tptp.bool)) (= (tptp.aa_VEBT_VEBT_nat tptp.vEBT_size_VEBT (tptp.vEBT_Leaf X21 X222)) tptp.zero_zero_nat)) (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.aa_nat_set_nat tptp.set_ord_lessThan_nat (tptp.aa_int_nat tptp.nat2 U)))))) (= tptp.code_T6385005292777649522of_nat tptp.semiri1314217659103216013at_int) (= tptp.code_Target_positive tptp.numeral_numeral_int) (forall ((L tptp.num) (Qr tptp.produc8923325533196201883nteger)) (= (tptp.unique4921790084139445826nteger L Qr) (tptp.produc6916734918728496179nteger (tptp.aTP_Lamm_cv L) Qr))) (forall ((K tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.minus_8373710615458151222nteger K) tptp.zero_z3403309356797280102nteger) K)) (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.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.plus_p5714425477246183910nteger tptp.zero_z3403309356797280102nteger) L) L)) (forall ((K tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.plus_p5714425477246183910nteger 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 ((L tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.minus_8373710615458151222nteger tptp.zero_z3403309356797280102nteger) L) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger L))) (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_cw) 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_cx) Nat)))) (= tptp.zero_zero_nat tptp.zero_zero_nat) (= tptp.zero_zero_int tptp.zero_zero_int) (= tptp.one_one_int tptp.one_one_int) (= tptp.one_one_nat 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_eq_nat (tptp.aa_nat_nat tptp.suc M)) N)) (tptp.pp (tptp.aa_nat_bool (tptp.case_nat_bool tptp.fFalse (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M)) N)))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat M) _let_1) (tptp.aa_nat_nat (tptp.case_nat_nat _let_1 (tptp.aa_nat_fun_nat_nat tptp.aTP_Lamm_cy N)) M)))) (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat _let_1) M) (tptp.aa_nat_nat (tptp.case_nat_nat _let_1 (tptp.aa_nat_fun_nat_nat tptp.aTP_Lamm_cz 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_an) (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.ord_min_nat M) (tptp.aa_nat_nat tptp.suc N)) (tptp.aa_nat_nat (tptp.case_nat_nat tptp.zero_zero_nat (tptp.aa_nat_fun_nat_nat tptp.aTP_Lamm_da 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.aa_nat_fun_nat_nat tptp.aTP_Lamm_db N)) M))) (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.aa_int_Code_integer 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.aa_int_Code_integer tptp.code_integer_of_int K))) (let ((_let_5 (= K tptp.zero_zero_int))) (let ((_let_6 (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int K) tptp.zero_zero_int)))) (and (=> _let_6 (= _let_4 (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_int_Code_integer tptp.code_integer_of_int (tptp.aa_int_int tptp.uminus_uminus_int K))))) (=> (not _let_6) (and (=> _let_5 (= _let_4 tptp.zero_z3403309356797280102nteger)) (=> (not _let_5) (= _let_4 (tptp.if_Code_integer (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.fequal_int (tptp.modulo_modulo_int K _let_2)) tptp.zero_zero_int) _let_3 (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.plus_p5714425477246183910nteger _let_3) 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.bit1 N)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.plus_p5714425477246183910nteger _let_1) _let_1)) tptp.one_one_Code_integer)))) (forall ((Xa tptp.nat) (X tptp.int)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_nat6383147911832638789nteger tptp.bit_se7788150548672797655nteger Xa) (tptp.aa_int_Code_integer tptp.code_integer_of_int X)) (tptp.aa_int_Code_integer tptp.code_integer_of_int (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_se545348938243370406it_int Xa) X)))) (= tptp.zero_z3403309356797280102nteger (tptp.aa_int_Code_integer tptp.code_integer_of_int tptp.zero_zero_int)) (forall ((Xa tptp.int) (X tptp.int)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.divide6298287555418463151nteger (tptp.aa_int_Code_integer tptp.code_integer_of_int Xa)) (tptp.aa_int_Code_integer tptp.code_integer_of_int X)) (tptp.aa_int_Code_integer tptp.code_integer_of_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int Xa) X)))) (forall ((K tptp.code_integer) (L tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger 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.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.gcd_gcd_Code_integer L) (tptp.modulo364778990260209775nteger (tptp.abs_abs_Code_integer K) (tptp.abs_abs_Code_integer L))))))) (forall ((Xa tptp.int) (X tptp.int)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.gcd_gcd_Code_integer (tptp.aa_int_Code_integer tptp.code_integer_of_int Xa)) (tptp.aa_int_Code_integer tptp.code_integer_of_int X)) (tptp.aa_int_Code_integer tptp.code_integer_of_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.gcd_gcd_int Xa) X)))) (forall ((Xa tptp.int) (X tptp.int)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.plus_p5714425477246183910nteger (tptp.aa_int_Code_integer tptp.code_integer_of_int Xa)) (tptp.aa_int_Code_integer tptp.code_integer_of_int X)) (tptp.aa_int_Code_integer tptp.code_integer_of_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int Xa) X)))) (forall ((Xa tptp.int) (X tptp.int)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_int_Code_integer tptp.code_integer_of_int Xa)) (tptp.aa_int_Code_integer tptp.code_integer_of_int X)) (tptp.aa_int_Code_integer tptp.code_integer_of_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int Xa) X)))) (= tptp.one_one_Code_integer (tptp.aa_int_Code_integer tptp.code_integer_of_int tptp.one_one_int)) (forall ((Xa tptp.int) (X tptp.int)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.minus_8373710615458151222nteger (tptp.aa_int_Code_integer tptp.code_integer_of_int Xa)) (tptp.aa_int_Code_integer tptp.code_integer_of_int X)) (tptp.aa_int_Code_integer tptp.code_integer_of_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int Xa) X)))) (forall ((X tptp.rat)) (= (tptp.archim3151403230148437115or_rat X) (tptp.the_int (tptp.aTP_Lamm_dc X)))) (= (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.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.plus_p5714425477246183910nteger _let_1) _let_1)))) (= (tptp.code_integer_of_num _let_1) _let_59) (forall ((X tptp.real)) (= (tptp.archim6058952711729229775r_real X) (tptp.the_int (tptp.aTP_Lamm_dd X)))) (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_de K) (tptp.code_divmod_abs K (tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one)))))))))) (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.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger 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 ((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_an) 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 (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_df 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_dg L) _let_1)))))))))))))))))) (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 ((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_dh L) _let_1))))))))))))) (forall ((K tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger K) tptp.zero_z3403309356797280102nteger)) (= (tptp.code_nat_of_integer K) tptp.zero_zero_nat))) (forall ((N tptp.nat)) (= (tptp.compow_fun_nat_nat N tptp.suc) (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N))) (= _let_58 _let_58) (= (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.code_nat_of_integer tptp.one_one_Code_integer) tptp.one_one_nat) (= tptp.code_Target_negative (tptp.comp_int_int_num tptp.uminus_uminus_int tptp.numeral_numeral_int)) (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_di (tptp.code_divmod_integer K (tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one)))))))))) (tptp.fun_is_measure_int _let_18) (tptp.semila1623282765462674594er_nat tptp.ord_max_nat tptp.zero_zero_nat tptp.aTP_Lamm_af tptp.aTP_Lamm_bu) (tptp.semila1623282765462674594er_nat tptp.gcd_gcd_nat tptp.zero_zero_nat tptp.dvd_dvd_nat tptp.aTP_Lamm_dj) (forall ((K tptp.code_integer)) (let ((_let_1 (tptp.aa_Code_integer_int 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.aa_Code_integer_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_dk (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_dm) Xa) X)))) (forall ((N tptp.nat)) (= (tptp.aa_Code_integer_int tptp.code_int_of_integer (tptp.semiri4939895301339042750nteger N)) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N))) (= (tptp.aa_Code_integer_int tptp.code_int_of_integer tptp.zero_z3403309356797280102nteger) tptp.zero_zero_int) (forall ((K tptp.num)) (= (tptp.aa_Code_integer_int 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.aa_Code_integer_int tptp.code_int_of_integer (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.plus_p5714425477246183910nteger X) Xa)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_Code_integer_int tptp.code_int_of_integer X)) (tptp.aa_Code_integer_int tptp.code_int_of_integer Xa)))) (forall ((X tptp.code_integer) (Xa tptp.code_integer)) (= (tptp.aa_Code_integer_int 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.aa_Code_integer_int tptp.code_int_of_integer X)) (tptp.aa_Code_integer_int tptp.code_int_of_integer Xa)))) (= (tptp.aa_Code_integer_int tptp.code_int_of_integer tptp.one_one_Code_integer) tptp.one_one_int) (forall ((X tptp.code_integer) (Xa tptp.code_integer)) (= (tptp.aa_Code_integer_int tptp.code_int_of_integer (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.minus_8373710615458151222nteger X) Xa)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_Code_integer_int tptp.code_int_of_integer X)) (tptp.aa_Code_integer_int tptp.code_int_of_integer Xa)))) (forall ((X tptp.code_integer) (Xa tptp.code_integer)) (= (tptp.aa_Code_integer_int tptp.code_int_of_integer (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.divide6298287555418463151nteger X) Xa)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int (tptp.aa_Code_integer_int tptp.code_int_of_integer X)) (tptp.aa_Code_integer_int tptp.code_int_of_integer Xa)))) (forall ((Z tptp.int)) (not (forall ((X3 tptp.nat) (Y3 tptp.nat)) (not (= Z (tptp.aa_Pro4240683299535347697at_int tptp.abs_Integ (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat X3) Y3))))))) (forall ((P tptp.fun_int_bool) (X tptp.int)) (=> (forall ((Y3 tptp.product_prod_nat_nat)) (tptp.pp (tptp.aa_int_bool P (tptp.aa_Pro4240683299535347697at_int tptp.abs_Integ Y3)))) (tptp.pp (tptp.aa_int_bool P X)))) (forall ((X tptp.code_integer) (Xa tptp.code_integer)) (= (tptp.aa_Code_integer_int tptp.code_int_of_integer (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.gcd_gcd_Code_integer X) Xa)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.gcd_gcd_int (tptp.aa_Code_integer_int tptp.code_int_of_integer X)) (tptp.aa_Code_integer_int tptp.code_int_of_integer Xa)))) (forall ((X tptp.nat) (Xa tptp.code_integer)) (= (tptp.aa_Code_integer_int tptp.code_int_of_integer (tptp.aa_Cod1783974652533396728nteger (tptp.aa_nat6383147911832638789nteger tptp.bit_se7788150548672797655nteger X) Xa)) (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_se545348938243370406it_int X) (tptp.aa_Code_integer_int tptp.code_int_of_integer Xa)))) (= tptp.zero_zero_int (tptp.aa_Pro4240683299535347697at_int tptp.abs_Integ _let_32)) (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_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.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_dn) X)))) (= tptp.one_one_int (tptp.aa_Pro4240683299535347697at_int tptp.abs_Integ _let_29)) (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_dp) 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_dr) 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_dt) 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_dv) Xa) X)))) (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.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.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.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.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.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.sgn_sgn_rat (tptp.aa_int_rat (tptp.aa_int_fun_int_rat tptp.fract A) B)) (tptp.ring_1_of_int_rat (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int tptp.sgn_sgn_int A)) (tptp.aa_int_int tptp.sgn_sgn_int 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 ((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 ((P tptp.fun_rat_bool) (Q2 tptp.rat)) (=> (forall ((A3 tptp.int) (B3 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) B3)) (tptp.pp (tptp.aa_rat_bool P (tptp.aa_int_rat (tptp.aa_int_fun_int_rat tptp.fract A3) B3))))) (tptp.pp (tptp.aa_rat_bool P Q2)))) (forall ((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 ((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))) (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 ((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 ((A tptp.int) (B tptp.int)) (let ((_let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int 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)))) (= tptp.one_one_rat (tptp.aa_int_rat (tptp.aa_int_fun_int_rat tptp.fract tptp.one_one_int) tptp.one_one_int)) (forall ((K tptp.int)) (= (tptp.aa_int_rat (tptp.aa_int_fun_int_rat tptp.fract K) tptp.one_one_int) (tptp.ring_1_of_int_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 ((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.numeral_numeral_rat W))) (forall ((K tptp.num)) (= (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 ((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.aa_nat_set_nat (tptp.set_or5834768355832116004an_nat I) J)) (tptp.cons_nat _let_1 (tptp.linord2614967742042102400et_nat (tptp.aa_nat_set_nat (tptp.set_or5834768355832116004an_nat _let_1) J))))))) (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))))) (= (tptp.aa_int_rat (tptp.aa_int_fun_int_rat tptp.fract _let_57) tptp.one_one_int) _let_56) (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.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.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.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 ((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 ((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.uminus_uminus_rat (tptp.numeral_numeral_rat W)))) (forall ((K tptp.num)) (= (tptp.uminus_uminus_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 ((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.aa_nat_set_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 ((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_dr) (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_dp) (tptp.aa_int1417691210696471063at_nat tptp.rep_Integ X)) (tptp.aa_int1417691210696471063at_nat tptp.rep_Integ Xa))))) (= tptp.inf_inf_nat tptp.ord_min_nat) (= tptp.inf_inf_int tptp.ord_min_int) (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)))) (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 ((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.aa_nat_set_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.aa_nat_set_nat (tptp.set_or6659071591806873216st_nat L) U)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat U) L))) (forall ((X tptp.list_nat) (Y tptp.list_nat)) (= (= (tptp.aa_list_nat_nat tptp.nat_list_encode X) (tptp.aa_list_nat_nat tptp.nat_list_encode Y)) (= X Y))) (forall ((L tptp.nat) (U tptp.nat)) (= (tptp.aa_nat_set_nat (tptp.set_or1269000886237332187st_nat (tptp.aa_nat_nat tptp.suc L)) U) (tptp.aa_nat_set_nat (tptp.set_or6659071591806873216st_nat L) U))) (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.aa_nat_set_nat (tptp.set_or6659071591806873216st_nat I) J)) (tptp.cons_nat _let_1 (tptp.linord2614967742042102400et_nat (tptp.aa_nat_set_nat (tptp.set_or6659071591806873216st_nat _let_1) J))))))) (forall ((X tptp.list_nat) (Y tptp.nat)) (=> (= (tptp.aa_list_nat_nat tptp.nat_list_encode X) Y) (=> (=> (= X tptp.nil_nat) (not (= Y tptp.zero_zero_nat))) (not (forall ((X3 tptp.nat) (Xs2 tptp.list_nat)) (=> (= X (tptp.cons_nat X3 Xs2)) (not (= Y (tptp.aa_nat_nat tptp.suc (tptp.aa_Pro4243173770044397973at_nat tptp.nat_prod_encode (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat X3) (tptp.aa_list_nat_nat tptp.nat_list_encode Xs2)))))))))))) (= tptp.uminus_uminus_int (tptp.aa_fun8399641135911395862nt_int _let_55 _let_31)) (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_dw M) (tptp.bit_take_bit_num _let_1 N))))) (forall ((M tptp.num)) (= (tptp.bit_take_bit_num tptp.zero_zero_nat M) tptp.none_num)) (forall ((N tptp.nat)) (= (tptp.bit_take_bit_num (tptp.aa_nat_nat tptp.suc N) tptp.one) (tptp.some_num tptp.one))) (forall ((R tptp.num)) (= (tptp.bit_take_bit_num (tptp.aa_num_nat tptp.numeral_numeral_nat R) tptp.one) (tptp.some_num tptp.one))) (forall ((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 ((N tptp.nat)) (= (tptp.bit_take_bit_num N tptp.one) (tptp.case_nat_option_num tptp.none_num tptp.aTP_Lamm_dx N))) (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 ((L tptp.int) (U tptp.int)) (= (tptp.set_or1266510415728281911st_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int L) tptp.one_one_int) U) (tptp.set_or6656581121297822940st_int L U))) (forall ((N tptp.nat) (M tptp.num)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se2925701944663578781it_nat N) (tptp.aa_num_nat tptp.numeral_numeral_nat M)))) (let ((_let_2 (tptp.bit_take_bit_num N M))) (let ((_let_3 (= _let_1 tptp.zero_zero_nat))) (and (=> _let_3 (= _let_2 tptp.none_num)) (=> (not _let_3) (= _let_2 (tptp.some_num (tptp.aa_nat_num tptp.num_of_nat _let_1))))))))) (forall ((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.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.bitM 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 ((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_dy (tptp.bit_take_bit_num N M)))) (forall ((R tptp.num) (M tptp.num)) (= (tptp.bit_take_bit_num (tptp.aa_num_nat tptp.numeral_numeral_nat R) (tptp.aa_num_num tptp.bit1 M)) (tptp.some_num (tptp.case_option_num_num tptp.one tptp.bit1 (tptp.bit_take_bit_num (tptp.pred_numeral R) M))))) (forall ((R tptp.num) (M tptp.num)) (= (tptp.bit_take_bit_num (tptp.aa_num_nat tptp.numeral_numeral_nat R) (tptp.aa_num_num tptp.bit0 M)) (tptp.case_o6005452278849405969um_num tptp.none_num tptp.aTP_Lamm_dy (tptp.bit_take_bit_num (tptp.pred_numeral R) 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.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_dz (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.bit0 N)) (tptp.some_num tptp.one))) (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.bit1 N)) tptp.none_num)) (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_ea 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_eb 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_int_int tptp.bit_ri7919022796975470100ot_int (tptp.aa_num_int tptp.numeral_numeral_int M))) (tptp.aa_num_int tptp.numeral_numeral_int N)) (tptp.case_option_int_num tptp.zero_zero_int tptp.numeral_numeral_int (tptp.bit_and_not_num N M)))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.aa_int_int (tptp.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)))) (= tptp.times_times_int (tptp.map_fu8294830438409148311nt_int tptp.rep_Integ _let_55 _let_34)) (= tptp.minus_minus_int (tptp.map_fu8294830438409148311nt_int tptp.rep_Integ _let_55 _let_25)) (= tptp.plus_plus_int (tptp.map_fu8294830438409148311nt_int tptp.rep_Integ _let_55 _let_23)) (forall ((X tptp.int) (Xa tptp.int) (Y 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) Y) (=> _let_1 (not (=> (and (=> _let_2 (= Y (tptp.cons_int X (tptp.upto (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int X) tptp.one_one_int) Xa)))) (=> (not _let_2) (= Y tptp.nil_int))) (not _let_1)))))))) (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 ((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 ((K tptp.nat)) (= (tptp.linord2614967742042102400et_nat (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat (tptp.aa_nat_nat tptp.suc K))) (tptp.append_nat (tptp.linord2614967742042102400et_nat (tptp.aa_nat_set_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.aa_nat_set_nat tptp.set_ord_atMost_nat _let_1)) (tptp.append_nat (tptp.linord2614967742042102400et_nat (tptp.aa_nat_set_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_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_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_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 ((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) (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)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int I) J)) (= (tptp.upto I J) (tptp.append_int (tptp.upto I (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int J) tptp.one_one_int)) (tptp.cons_int J tptp.nil_int))))) (forall ((I tptp.int) (J tptp.int) (K tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int I) J)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int J) K)) (= (tptp.upto I K) (tptp.append_int (tptp.upto I (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int J) tptp.one_one_int)) (tptp.cons_int J (tptp.upto (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int J) tptp.one_one_int) K))))))) (forall ((I tptp.int) (J tptp.int)) (= (tptp.set_or4662586982721622107an_int I J) (tptp.set_int2 (tptp.upto I (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int J) tptp.one_one_int))))) (forall ((I tptp.int) (J tptp.int)) (= (tptp.set_or6656581121297822940st_int I J) (tptp.set_int2 (tptp.upto (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int I) tptp.one_one_int) J)))) (forall ((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) (Y tptp.list_int)) (let ((_let_1 (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X) Xa)))) (=> (= (tptp.upto X Xa) Y) (and (=> _let_1 (= Y (tptp.cons_int X (tptp.upto (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int X) tptp.one_one_int) Xa)))) (=> (not _let_1) (= Y tptp.nil_int)))))) (forall ((I tptp.int) (J tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int I) J)) (= (tptp.upto I J) (tptp.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.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 ((X tptp.num) (Xa tptp.num) (Y tptp.option_num)) (let ((_let_1 (not (= Y tptp.none_num)))) (let ((_let_2 (= X tptp.one))) (=> (= (tptp.bit_and_not_num X Xa) Y) (=> (=> _let_2 (=> (= Xa tptp.one) _let_1)) (=> (=> _let_2 (=> (exists ((N2 tptp.num)) (= Xa (tptp.aa_num_num tptp.bit0 N2))) (not (= Y (tptp.some_num tptp.one))))) (=> (=> _let_2 (=> (exists ((N2 tptp.num)) (= Xa (tptp.aa_num_num tptp.bit1 N2))) _let_1)) (=> (forall ((M2 tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 M2))) (=> (= X _let_1) (=> (= Xa tptp.one) (not (= Y (tptp.some_num _let_1))))))) (=> (forall ((M2 tptp.num)) (=> (= X (tptp.aa_num_num tptp.bit0 M2)) (forall ((N2 tptp.num)) (=> (= Xa (tptp.aa_num_num tptp.bit0 N2)) (not (= Y (tptp.map_option_num_num tptp.bit0 (tptp.bit_and_not_num M2 N2)))))))) (=> (forall ((M2 tptp.num)) (=> (= X (tptp.aa_num_num tptp.bit0 M2)) (forall ((N2 tptp.num)) (=> (= Xa (tptp.aa_num_num tptp.bit1 N2)) (not (= Y (tptp.map_option_num_num tptp.bit0 (tptp.bit_and_not_num M2 N2)))))))) (=> (forall ((M2 tptp.num)) (=> (= X (tptp.aa_num_num tptp.bit1 M2)) (=> (= Xa tptp.one) (not (= Y (tptp.some_num (tptp.aa_num_num tptp.bit0 M2))))))) (=> (forall ((M2 tptp.num)) (=> (= X (tptp.aa_num_num tptp.bit1 M2)) (forall ((N2 tptp.num)) (=> (= Xa (tptp.aa_num_num tptp.bit0 N2)) (not (= Y (tptp.case_o6005452278849405969um_num (tptp.some_num tptp.one) tptp.aTP_Lamm_dz (tptp.bit_and_not_num M2 N2)))))))) (not (forall ((M2 tptp.num)) (=> (= X (tptp.aa_num_num tptp.bit1 M2)) (forall ((N2 tptp.num)) (=> (= Xa (tptp.aa_num_num tptp.bit1 N2)) (not (= Y (tptp.map_option_num_num tptp.bit0 (tptp.bit_and_not_num M2 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.bit0 M) (tptp.aa_num_num tptp.bit1 N)) (tptp.map_option_num_num tptp.bit0 (tptp.bit_and_not_num M N)))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.bit_and_not_num (tptp.aa_num_num tptp.bit1 M) (tptp.aa_num_num tptp.bit1 N)) (tptp.map_option_num_num tptp.bit0 (tptp.bit_and_not_num M N)))) (forall ((X tptp.num) (Xa tptp.num) (Y tptp.option_num)) (let ((_let_1 (not (= Y (tptp.some_num tptp.one))))) (let ((_let_2 (= Xa tptp.one))) (let ((_let_3 (=> _let_2 _let_1))) (let ((_let_4 (not (= Y tptp.none_num)))) (let ((_let_5 (= X tptp.one))) (=> (= (tptp.aa_num_option_num (tptp.aa_num6390622462783740633on_num tptp.bit_un7362597486090784418nd_num X) Xa) Y) (=> (=> _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 ((M2 tptp.num)) (= X (tptp.aa_num_num tptp.bit0 M2))) (=> _let_2 _let_4)) (=> (forall ((M2 tptp.num)) (=> (= X (tptp.aa_num_num tptp.bit0 M2)) (forall ((N2 tptp.num)) (=> (= Xa (tptp.aa_num_num tptp.bit0 N2)) (not (= Y (tptp.map_option_num_num tptp.bit0 (tptp.aa_num_option_num (tptp.aa_num6390622462783740633on_num tptp.bit_un7362597486090784418nd_num M2) N2)))))))) (=> (forall ((M2 tptp.num)) (=> (= X (tptp.aa_num_num tptp.bit0 M2)) (forall ((N2 tptp.num)) (=> (= Xa (tptp.aa_num_num tptp.bit1 N2)) (not (= Y (tptp.map_option_num_num tptp.bit0 (tptp.aa_num_option_num (tptp.aa_num6390622462783740633on_num tptp.bit_un7362597486090784418nd_num M2) N2)))))))) (=> (=> (exists ((M2 tptp.num)) (= X (tptp.aa_num_num tptp.bit1 M2))) _let_3) (=> (forall ((M2 tptp.num)) (=> (= X (tptp.aa_num_num tptp.bit1 M2)) (forall ((N2 tptp.num)) (=> (= Xa (tptp.aa_num_num tptp.bit0 N2)) (not (= Y (tptp.map_option_num_num tptp.bit0 (tptp.aa_num_option_num (tptp.aa_num6390622462783740633on_num tptp.bit_un7362597486090784418nd_num M2) N2)))))))) (not (forall ((M2 tptp.num)) (=> (= X (tptp.aa_num_num tptp.bit1 M2)) (forall ((N2 tptp.num)) (=> (= Xa (tptp.aa_num_num tptp.bit1 N2)) (not (= Y (tptp.case_o6005452278849405969um_num (tptp.some_num tptp.one) tptp.aTP_Lamm_dz (tptp.aa_num_option_num (tptp.aa_num6390622462783740633on_num tptp.bit_un7362597486090784418nd_num M2) N2)))))))))))))))))))))))) (forall ((X tptp.num) (Xa tptp.num) (Y tptp.option_num)) (let ((_let_1 (= X tptp.one))) (=> (= (tptp.aa_num_option_num (tptp.aa_num6390622462783740633on_num tptp.bit_un2480387367778600638or_num X) Xa) Y) (=> (=> _let_1 (=> (= Xa tptp.one) (not (= Y tptp.none_num)))) (=> (=> _let_1 (forall ((N2 tptp.num)) (=> (= Xa (tptp.aa_num_num tptp.bit0 N2)) (not (= Y (tptp.some_num (tptp.aa_num_num tptp.bit1 N2))))))) (=> (=> _let_1 (forall ((N2 tptp.num)) (=> (= Xa (tptp.aa_num_num tptp.bit1 N2)) (not (= Y (tptp.some_num (tptp.aa_num_num tptp.bit0 N2))))))) (=> (forall ((M2 tptp.num)) (=> (= X (tptp.aa_num_num tptp.bit0 M2)) (=> (= Xa tptp.one) (not (= Y (tptp.some_num (tptp.aa_num_num tptp.bit1 M2))))))) (=> (forall ((M2 tptp.num)) (=> (= X (tptp.aa_num_num tptp.bit0 M2)) (forall ((N2 tptp.num)) (=> (= Xa (tptp.aa_num_num tptp.bit0 N2)) (not (= Y (tptp.map_option_num_num tptp.bit0 (tptp.aa_num_option_num (tptp.aa_num6390622462783740633on_num tptp.bit_un2480387367778600638or_num M2) N2)))))))) (=> (forall ((M2 tptp.num)) (=> (= X (tptp.aa_num_num tptp.bit0 M2)) (forall ((N2 tptp.num)) (=> (= Xa (tptp.aa_num_num tptp.bit1 N2)) (not (= Y (tptp.some_num (tptp.case_option_num_num tptp.one tptp.bit1 (tptp.aa_num_option_num (tptp.aa_num6390622462783740633on_num tptp.bit_un2480387367778600638or_num M2) N2))))))))) (=> (forall ((M2 tptp.num)) (=> (= X (tptp.aa_num_num tptp.bit1 M2)) (=> (= Xa tptp.one) (not (= Y (tptp.some_num (tptp.aa_num_num tptp.bit0 M2))))))) (=> (forall ((M2 tptp.num)) (=> (= X (tptp.aa_num_num tptp.bit1 M2)) (forall ((N2 tptp.num)) (=> (= Xa (tptp.aa_num_num tptp.bit0 N2)) (not (= Y (tptp.some_num (tptp.case_option_num_num tptp.one tptp.bit1 (tptp.aa_num_option_num (tptp.aa_num6390622462783740633on_num tptp.bit_un2480387367778600638or_num M2) N2))))))))) (not (forall ((M2 tptp.num)) (=> (= X (tptp.aa_num_num tptp.bit1 M2)) (forall ((N2 tptp.num)) (=> (= Xa (tptp.aa_num_num tptp.bit1 N2)) (not (= Y (tptp.map_option_num_num tptp.bit0 (tptp.aa_num_option_num (tptp.aa_num6390622462783740633on_num tptp.bit_un2480387367778600638or_num M2) 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 ((N tptp.num)) (= (tptp.aa_num_option_num (tptp.aa_num6390622462783740633on_num tptp.bit_un7362597486090784418nd_num tptp.one) (tptp.aa_num_num tptp.bit1 N)) (tptp.some_num tptp.one))) (forall ((M tptp.num)) (= (tptp.aa_num_option_num (tptp.aa_num6390622462783740633on_num tptp.bit_un7362597486090784418nd_num (tptp.aa_num_num tptp.bit1 M)) tptp.one) (tptp.some_num tptp.one))) (forall ((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)) (= (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 ((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 ((M tptp.num)) (= (tptp.aa_num_option_num (tptp.aa_num6390622462783740633on_num tptp.bit_un2480387367778600638or_num (tptp.aa_num_num tptp.bit1 M)) tptp.one) (tptp.some_num (tptp.aa_num_num tptp.bit0 M)))) (forall ((M tptp.num)) (= (tptp.aa_num_option_num (tptp.aa_num6390622462783740633on_num tptp.bit_un2480387367778600638or_num (tptp.aa_num_num tptp.bit0 M)) tptp.one) (tptp.some_num (tptp.aa_num_num tptp.bit1 M)))) (forall ((N tptp.num)) (= (tptp.aa_num_option_num (tptp.aa_num6390622462783740633on_num tptp.bit_un2480387367778600638or_num tptp.one) (tptp.aa_num_num tptp.bit1 N)) (tptp.some_num (tptp.aa_num_num tptp.bit0 N)))) (forall ((N tptp.num)) (= (tptp.aa_num_option_num (tptp.aa_num6390622462783740633on_num tptp.bit_un2480387367778600638or_num tptp.one) (tptp.aa_num_num tptp.bit0 N)) (tptp.some_num (tptp.aa_num_num tptp.bit1 N)))) (forall ((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_dz (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.bit0 M)) (tptp.aa_num_num tptp.bit1 N)) (tptp.some_num (tptp.case_option_num_num tptp.one tptp.bit1 (tptp.aa_num_option_num (tptp.aa_num6390622462783740633on_num tptp.bit_un2480387367778600638or_num M) N))))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.aa_num_option_num (tptp.aa_num6390622462783740633on_num tptp.bit_un2480387367778600638or_num (tptp.aa_num_num tptp.bit1 M)) (tptp.aa_num_num tptp.bit0 N)) (tptp.some_num (tptp.case_option_num_num tptp.one tptp.bit1 (tptp.aa_num_option_num (tptp.aa_num6390622462783740633on_num tptp.bit_un2480387367778600638or_num M) N))))) (= 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_ef (tptp.product_Pair_nat_num N M)))) (= tptp.semiri1316708129612266289at_nat tptp.id_nat) (= tptp.ord_less_int (tptp.map_fu2743658913401090412t_bool tptp.rep_Integ _let_54 _let_28)) (= tptp.ord_less_eq_int (tptp.map_fu2743658913401090412t_bool tptp.rep_Integ _let_54 _let_26)) (= tptp.nat2 (tptp.map_fu2345160673673942751at_nat tptp.rep_Integ tptp.id_nat _let_30)) (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))))) (forall ((X tptp.list_nat) (Y tptp.nat)) (let ((_let_1 (tptp.accp_list_nat tptp.nat_list_encode_rel))) (=> (= (tptp.aa_list_nat_nat tptp.nat_list_encode X) Y) (=> (tptp.pp (tptp.aa_list_nat_bool _let_1 X)) (=> (=> (= X tptp.nil_nat) (=> (= Y tptp.zero_zero_nat) (not (tptp.pp (tptp.aa_list_nat_bool _let_1 tptp.nil_nat))))) (not (forall ((X3 tptp.nat) (Xs2 tptp.list_nat)) (let ((_let_1 (tptp.cons_nat X3 Xs2))) (=> (= X _let_1) (=> (= Y (tptp.aa_nat_nat tptp.suc (tptp.aa_Pro4243173770044397973at_nat tptp.nat_prod_encode (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat 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 ((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_eg (tptp.code_divmod_integer K (tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one)))))))))) (forall ((X tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool tptp.positive X)) (=> (tptp.pp (tptp.aa_rat_bool tptp.positive Y)) (tptp.pp (tptp.aa_rat_bool tptp.positive (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat X) Y)))))) (forall ((X tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool tptp.positive X)) (=> (tptp.pp (tptp.aa_rat_bool tptp.positive Y)) (tptp.pp (tptp.aa_rat_bool tptp.positive (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat X) Y)))))) (forall ((X tptp.rat) (Y tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) Y)) (tptp.pp (tptp.aa_rat_bool tptp.positive (tptp.minus_minus_rat Y 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))))))) (= tptp.positive (tptp.map_fu5118516228767806217l_bool tptp.rep_Rat tptp.id_bool tptp.aTP_Lamm_eh)) (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 ((M tptp.nat) (N tptp.nat)) (= (tptp.tl_nat (tptp.upt M N)) (tptp.upt (tptp.aa_nat_nat tptp.suc M) N))) (forall ((M tptp.nat) (I tptp.nat) (J tptp.nat)) (= (tptp.drop_nat M (tptp.upt I J)) (tptp.upt (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat I) M) J))) (forall ((I tptp.nat) (J tptp.nat)) (= (tptp.size_size_list_nat (tptp.upt I J)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat J) I))) (forall ((I tptp.nat) (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 ((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 ((I tptp.nat) (K tptp.nat) (J tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat I) K))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_1) J)) (= (tptp.aa_nat_nat (tptp.nth_nat (tptp.upt I J)) K) _let_1)))) (tptp.order_mono_nat_nat tptp.suc) (forall ((N tptp.nat) (M tptp.nat)) (= (tptp.aa_nat_set_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.aa_nat_set_nat tptp.set_ord_lessThan_nat N) (tptp.set_nat2 (tptp.upt tptp.zero_zero_nat 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)) (= (tptp.upt I tptp.zero_zero_nat) tptp.nil_nat)) (forall ((N tptp.nat) (M tptp.nat)) (= (tptp.aa_nat_set_nat (tptp.set_or6659071591806873216st_nat N) M) (tptp.set_nat2 (tptp.upt (tptp.aa_nat_nat tptp.suc N) (tptp.aa_nat_nat tptp.suc M))))) (forall ((N tptp.nat) (M tptp.nat)) (= (tptp.aa_nat_set_nat (tptp.set_or5834768355832116004an_nat N) M) (tptp.set_nat2 (tptp.upt (tptp.aa_nat_nat tptp.suc N) M)))) (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 ((N tptp.nat)) (= (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N) (tptp.set_nat2 (tptp.upt tptp.zero_zero_nat (tptp.aa_nat_nat tptp.suc N))))) (forall ((I tptp.nat) (J tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I) J)) (= (tptp.upt I J) (tptp.cons_nat I (tptp.upt (tptp.aa_nat_nat tptp.suc I) J))))) (forall ((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 ((I tptp.nat) (J tptp.nat) (X tptp.nat) (Xs tptp.list_nat)) (= (= (tptp.upt I J) (tptp.cons_nat X Xs)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I) J)) (= I X) (= (tptp.upt (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat I) tptp.one_one_nat) J) Xs)))) (forall ((I tptp.nat) (J tptp.nat)) (let ((_let_1 (tptp.upt I J))) (let ((_let_2 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I) J)))) (and (=> _let_2 (= _let_1 (tptp.cons_nat I (tptp.upt (tptp.aa_nat_nat tptp.suc I) J)))) (=> (not _let_2) (= _let_1 tptp.nil_nat)))))) (forall ((K tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) K)) (tptp.order_mono_nat_nat (tptp.aa_nat_fun_nat_nat tptp.aTP_Lamm_ei K)))) (forall ((I tptp.nat) (J tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I) J)) (= (tptp.upt I (tptp.aa_nat_nat tptp.suc J)) (tptp.append_nat (tptp.upt I J) (tptp.cons_nat J tptp.nil_nat))))) (forall ((I tptp.nat) (J tptp.nat)) (let ((_let_1 (tptp.upt I (tptp.aa_nat_nat tptp.suc J)))) (let ((_let_2 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I) J)))) (and (=> _let_2 (= _let_1 (tptp.append_nat (tptp.upt I J) (tptp.cons_nat J tptp.nil_nat)))) (=> (not _let_2) (= _let_1 tptp.nil_nat)))))) (forall ((X tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Y)) (exists ((Q6 tptp.rat)) (let ((_let_1 (tptp.aa_rat_real tptp.field_7254667332652039916t_real Q6))) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) _let_1)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real _let_1) Y))))))) (forall ((N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (= (tptp.image_nat_nat (tptp.aa_nat_fun_nat_nat tptp.aTP_Lamm_ej N) tptp.top_top_set_nat) (tptp.aa_nat_set_nat (tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N)))) (= tptp.top_top_set_nat (tptp.insert_nat tptp.zero_zero_nat _let_51)) (= tptp.plus_plus_rat (tptp.map_fu5968964422797239547at_rat tptp.rep_Rat _let_53 tptp.aTP_Lamm_ek)) (= (tptp.finite410649719033368117t_unit tptp.top_to1996260823553986621t_unit) tptp.one_one_nat) (forall ((A tptp.real)) (let ((_let_1 (tptp.image_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) tptp.top_top_set_real))) (let ((_let_2 (= A tptp.zero_zero_real))) (and (=> _let_2 (= _let_1 (tptp.insert_real tptp.zero_zero_real tptp.bot_bot_set_real))) (=> (not _let_2) (= _let_1 tptp.top_top_set_real)))))) (= (tptp.image_int_int tptp.abs_abs_int tptp.top_top_set_int) tptp.semiring_1_Nats_int) (= (tptp.finite_card_bool tptp.top_top_set_bool) _let_2) (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)))) (not (tptp.finite_finite_int tptp.top_top_set_int)) (= (tptp.image_list_nat_nat tptp.nat_list_encode tptp.top_top_set_list_nat) tptp.top_top_set_nat) (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_2486076414777270412at_nat tptp.nat_prod_encode tptp.top_to4669805908274784177at_nat) tptp.top_top_set_nat) (tptp.pp (tptp.aa_set_nat_bool (tptp.bij_be5333170631980326235at_nat tptp.nat_prod_encode tptp.top_to4669805908274784177at_nat) tptp.top_top_set_nat)) (forall ((N tptp.nat) (M tptp.nat)) (= (tptp.map_nat_nat (tptp.aa_nat_fun_nat_nat tptp.aTP_Lamm_el 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 ((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 ((M tptp.nat) (N tptp.nat)) (= (tptp.map_nat_nat tptp.aTP_Lamm_em (tptp.upt (tptp.aa_nat_nat tptp.suc M) (tptp.aa_nat_nat tptp.suc N))) (tptp.upt M N))) (= tptp.one_one_rat (tptp.aa_Pro6166618844887768661nt_rat tptp.abs_Rat _let_38)) (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_37)) (= tptp.times_times_rat (tptp.map_fu5968964422797239547at_rat tptp.rep_Rat _let_53 tptp.aTP_Lamm_en)) (= tptp.inverse_inverse_rat (tptp.aa_fun7041730090766645614at_rat _let_53 tptp.aTP_Lamm_eo)) (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_ep N)) X))))))) (= (tptp.finite_card_char tptp.top_top_set_char) _let_42) (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) (Y tptp.product_prod_int_int)) (let ((_let_1 (tptp.product_snd_int_int X))) (let ((_let_2 (tptp.product_snd_int_int Y))) (= (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.aa_Pro1534211998248933470t_bool tptp.ratrel X) Y)) (and (not (= _let_1 tptp.zero_zero_int)) (not (= _let_2 tptp.zero_zero_int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.product_fst_int_int X)) _let_2) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.product_fst_int_int Y)) _let_1))))))) (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.aa_Pro1534211998248933470t_bool tptp.ratrel _let_38) _let_38)) (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.aa_Pro1534211998248933470t_bool tptp.ratrel _let_37) _let_37)) (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 ((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))))))) (= tptp.top_top_set_char (tptp.image_nat_char tptp.unique3096191561947761185of_nat _let_43)) (forall ((X1 tptp.bool) (X2 tptp.bool) (X32 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 X32 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_43) (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.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger 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) (X32 tptp.bool) (X42 tptp.bool) (X52 tptp.bool) (X62 tptp.bool) (X72 tptp.bool) (X8 tptp.bool)) (= (tptp.size_char (tptp.char2 X1 X2 X32 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.aa_nat_fun_nat_nat tptp.bit_se2925701944663578781it_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit1 tptp.one)))) (tptp.aa_char_nat tptp.comm_s629917340098488124ar_nat C)))) (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) (S2 tptp.set_real)) (=> (tptp.has_fi5821293074295781190e_real F L (tptp.topolo2177554685111907308n_real X S2)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real L) tptp.zero_zero_real)) (exists ((D2 tptp.real)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) D2)) (forall ((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 S2) (=> (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) (S2 tptp.set_real)) (=> (tptp.has_fi5821293074295781190e_real F L (tptp.topolo2177554685111907308n_real X S2)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) L)) (exists ((D2 tptp.real)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) D2)) (forall ((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 S2) (=> (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) (S2 tptp.set_real)) (=> (tptp.has_fi5821293074295781190e_real F L (tptp.topolo2177554685111907308n_real X S2)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) L)) (exists ((D2 tptp.real)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) D2)) (forall ((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 S2) (=> (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) (S2 tptp.set_real)) (=> (tptp.has_fi5821293074295781190e_real F L (tptp.topolo2177554685111907308n_real X S2)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real L) tptp.zero_zero_real)) (exists ((D2 tptp.real)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) D2)) (forall ((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 S2) (=> (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 ((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 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 ((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 X)) (tptp.aa_real_real F (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_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 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 ((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 ((Z4 tptp.real)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) Z4)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Z4) 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 Z4)))))))) (forall ((F tptp.fun_real_real) (L tptp.real) (X tptp.real) (D tptp.real)) (=> (tptp.has_fi5821293074295781190e_real F L (tptp.topolo2177554685111907308n_real X tptp.top_top_set_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) D)) (=> (forall ((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))) D)) (= (tptp.aa_real_real F X) (tptp.aa_real_real F Y3)))) (= L tptp.zero_zero_real))))) (forall ((A tptp.real) (B tptp.real) (V tptp.fun_real_real) (K tptp.real)) (let ((_let_1 (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 ((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))) D)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real F Y3)) (tptp.aa_real_real F X))))) (= L tptp.zero_zero_real))))) (forall ((F tptp.fun_real_real) (L tptp.real) (X tptp.real) (D tptp.real)) (=> (tptp.has_fi5821293074295781190e_real F L (tptp.topolo2177554685111907308n_real X tptp.top_top_set_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) D)) (=> (forall ((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))) 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 Y3))))) (= L tptp.zero_zero_real))))) (forall ((X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) X)) (tptp.has_fi5821293074295781190e_real tptp.ln_ln_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.one_one_real) X) (tptp.topolo2177554685111907308n_real X tptp.top_top_set_real)))) (forall ((N tptp.nat) (X tptp.real) (S tptp.set_real)) (tptp.has_fi5821293074295781190e_real (tptp.aa_nat_fun_real_real tptp.aTP_Lamm_eq N) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)))) (tptp.topolo2177554685111907308n_real X S))) (forall ((G tptp.fun_real_real) (M tptp.real) (X tptp.real) (N tptp.nat)) (let ((_let_1 (tptp.topolo2177554685111907308n_real X tptp.top_top_set_real))) (=> (tptp.has_fi5821293074295781190e_real G M _let_1) (tptp.has_fi5821293074295781190e_real (tptp.aa_nat_fun_real_real (tptp.aTP_Lamm_er G) N) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real G X)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) tptp.one_one_nat)))) M) _let_1)))) (forall ((Z tptp.real) (R tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) Z)) (tptp.has_fi5821293074295781190e_real (tptp.aa_rea7340605660300375871l_real tptp.aTP_Lamm_es R) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real R) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.powr_real Z) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real R) tptp.one_one_real))) (tptp.topolo2177554685111907308n_real Z tptp.top_top_set_real)))) (forall ((X tptp.real) (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.log2 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) (R tptp.real)) (let ((_let_1 (tptp.topolo2177554685111907308n_real X tptp.top_top_set_real))) (let ((_let_2 (tptp.aa_real_real G X))) (=> (tptp.has_fi5821293074295781190e_real G M _let_1) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) _let_2)) (tptp.has_fi5821293074295781190e_real (tptp.aa_rea7340605660300375871l_real (tptp.aTP_Lamm_et G) R) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real R) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.powr_real _let_2) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real R) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real tptp.one_one_nat))))) M) _let_1)))))) (forall ((G tptp.fun_real_real) (M tptp.real) (X tptp.real) (F tptp.fun_real_real) (R tptp.real)) (let ((_let_1 (tptp.topolo2177554685111907308n_real X tptp.top_top_set_real))) (let ((_let_2 (tptp.aa_real_real G X))) (let ((_let_3 (tptp.aa_real_real F X))) (=> (tptp.has_fi5821293074295781190e_real G M _let_1) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) _let_2)) (=> (tptp.has_fi5821293074295781190e_real F R _let_1) (tptp.has_fi5821293074295781190e_real (tptp.aa_fun6946558556880649704l_real (tptp.aTP_Lamm_eu G) F) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.powr_real _let_2) _let_3)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real R) (tptp.aa_real_real tptp.ln_ln_real _let_2))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real M) _let_3)) _let_2))) _let_1)))))))) (forall ((X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) X)) (tptp.has_fi5821293074295781190e_real tptp.sqrt (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real tptp.inverse_inverse_real (tptp.aa_real_real tptp.sqrt X))) (tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.topolo2177554685111907308n_real X 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_ev 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) (Y3 tptp.real)) (let ((_let_1 (tptp.set_or1633881224788618240n_real A B))) (=> (tptp.member_real X3 _let_1) (=> (tptp.member_real Y3 _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 Y3) 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) Y3))))))))) (tptp.has_fi5821293074295781190e_real (tptp.aTP_Lamm_ew F) (tptp.suminf_real _let_1) (tptp.topolo2177554685111907308n_real X0 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.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 ((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 ((R3 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 R3) R3)) (tptp.summable_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_ex F) X3)))) (=> (tptp.member_real X0 (tptp.set_or1633881224788618240n_real (tptp.aa_real_real tptp.uminus_uminus_real R3) R3)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) R3)) (tptp.has_fi5821293074295781190e_real (tptp.aTP_Lamm_ez F) (tptp.suminf_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_ex 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 ((M2 tptp.nat) (X3 tptp.real)) (tptp.has_fi5821293074295781190e_real (tptp.aa_nat_fun_real_real Diff M2) (tptp.aa_real_real (tptp.aa_nat_fun_real_real Diff (tptp.aa_nat_nat tptp.suc M2)) X3) (tptp.topolo2177554685111907308n_real X3 tptp.top_top_set_real)))) (exists ((T2 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 T2)) (tptp.aa_real_real tptp.abs_abs_real X))) (= (tptp.aa_real_real F X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_fa Diff) X) (tptp.aa_nat_set_nat 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) T2)) (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 ((M2 tptp.nat) (X3 tptp.real)) (tptp.has_fi5821293074295781190e_real (tptp.aa_nat_fun_real_real Diff M2) (tptp.aa_real_real (tptp.aa_nat_fun_real_real Diff (tptp.aa_nat_nat tptp.suc M2)) X3) (tptp.topolo2177554685111907308n_real X3 tptp.top_top_set_real))) (exists ((T2 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 T2)) (tptp.aa_real_real tptp.abs_abs_real X))) (= (tptp.aa_real_real F X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_fa Diff) X) (tptp.aa_nat_set_nat 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) T2)) (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 ((M2 tptp.nat) (T2 tptp.real)) (=> (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 H) T2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real T2) tptp.zero_zero_real))) (tptp.has_fi5821293074295781190e_real (tptp.aa_nat_fun_real_real Diff M2) (tptp.aa_real_real (tptp.aa_nat_fun_real_real Diff (tptp.aa_nat_nat tptp.suc M2)) T2) (tptp.topolo2177554685111907308n_real T2 tptp.top_top_set_real)))) (exists ((T2 tptp.real)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real H) T2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real T2) tptp.zero_zero_real)) (= (tptp.aa_real_real F H) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.groups6591440286371151544t_real (tptp.aa_fun1113820866546176217t_real (tptp.aTP_Lamm_fb H) Diff) (tptp.aa_nat_set_nat 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) T2)) (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 ((M2 tptp.nat) (T2 tptp.real)) (=> (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) T2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real T2) H))) (tptp.has_fi5821293074295781190e_real (tptp.aa_nat_fun_real_real Diff M2) (tptp.aa_real_real (tptp.aa_nat_fun_real_real Diff (tptp.aa_nat_nat tptp.suc M2)) T2) (tptp.topolo2177554685111907308n_real T2 tptp.top_top_set_real)))) (exists ((T2 tptp.real)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) T2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real T2) H)) (= (tptp.aa_real_real F H) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.groups6591440286371151544t_real (tptp.aa_fun1113820866546176217t_real (tptp.aTP_Lamm_fb H) Diff) (tptp.aa_nat_set_nat 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) T2)) (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 ((M2 tptp.nat) (T2 tptp.real)) (=> (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) T2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real T2) H))) (tptp.has_fi5821293074295781190e_real (tptp.aa_nat_fun_real_real Diff M2) (tptp.aa_real_real (tptp.aa_nat_fun_real_real Diff (tptp.aa_nat_nat tptp.suc M2)) T2) (tptp.topolo2177554685111907308n_real T2 tptp.top_top_set_real)))) (exists ((T2 tptp.real)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) T2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real T2) H)) (= (tptp.aa_real_real F H) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.groups6591440286371151544t_real (tptp.aa_fun1113820866546176217t_real (tptp.aTP_Lamm_fb H) Diff) (tptp.aa_nat_set_nat 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) T2)) (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 ((M2 tptp.nat) (X3 tptp.real)) (tptp.has_fi5821293074295781190e_real (tptp.aa_nat_fun_real_real Diff M2) (tptp.aa_real_real (tptp.aa_nat_fun_real_real Diff (tptp.aa_nat_nat tptp.suc M2)) X3) (tptp.topolo2177554685111907308n_real X3 tptp.top_top_set_real))) (exists ((T2 tptp.real)) (let ((_let_1 (tptp.aa_real_real tptp.abs_abs_real T2))) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) _let_1)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real _let_1) (tptp.aa_real_real tptp.abs_abs_real X))) (= (tptp.aa_real_real F X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_fa Diff) X) (tptp.aa_nat_set_nat 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) T2)) (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 ((M2 tptp.nat) (T2 tptp.real)) (=> (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.aa_real_real tptp.abs_abs_real T2)) (tptp.aa_real_real tptp.abs_abs_real X)))) (tptp.has_fi5821293074295781190e_real (tptp.aa_nat_fun_real_real Diff M2) (tptp.aa_real_real (tptp.aa_nat_fun_real_real Diff (tptp.aa_nat_nat tptp.suc M2)) T2) (tptp.topolo2177554685111907308n_real T2 tptp.top_top_set_real)))) (exists ((T2 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 T2)) (tptp.aa_real_real tptp.abs_abs_real X))) (= (tptp.aa_real_real F X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_fa Diff) X) (tptp.aa_nat_set_nat 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) T2)) (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 ((M2 tptp.nat) (T2 tptp.real)) (=> (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 A) T2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real T2) B))) (tptp.has_fi5821293074295781190e_real (tptp.aa_nat_fun_real_real Diff M2) (tptp.aa_real_real (tptp.aa_nat_fun_real_real Diff (tptp.aa_nat_nat tptp.suc M2)) T2) (tptp.topolo2177554685111907308n_real T2 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 ((T2 tptp.real)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) T2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real T2) C)) (= (tptp.aa_real_real F A) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real (tptp.aa_rea7841385751566875788t_real (tptp.aTP_Lamm_fc Diff) A) C) (tptp.aa_nat_set_nat 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) T2)) (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 ((M2 tptp.nat) (T2 tptp.real)) (=> (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 A) T2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real T2) B))) (tptp.has_fi5821293074295781190e_real (tptp.aa_nat_fun_real_real Diff M2) (tptp.aa_real_real (tptp.aa_nat_fun_real_real Diff (tptp.aa_nat_nat tptp.suc M2)) T2) (tptp.topolo2177554685111907308n_real T2 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 ((T2 tptp.real)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real C) T2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real T2) B)) (= (tptp.aa_real_real F B) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real (tptp.aa_rea7841385751566875788t_real (tptp.aTP_Lamm_fc Diff) B) C) (tptp.aa_nat_set_nat 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) T2)) (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 ((M2 tptp.nat) (T2 tptp.real)) (=> (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 A) T2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real T2) B))) (tptp.has_fi5821293074295781190e_real (tptp.aa_nat_fun_real_real Diff M2) (tptp.aa_real_real (tptp.aa_nat_fun_real_real Diff (tptp.aa_nat_nat tptp.suc M2)) T2) (tptp.topolo2177554685111907308n_real T2 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 ((T2 tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real T2))) (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 T2)) (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) T2)) (tptp.pp (tptp.aa_real_bool _let_1 X)))) (= (tptp.aa_real_real F X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real (tptp.aa_rea7841385751566875788t_real (tptp.aTP_Lamm_fd Diff) C) X) (tptp.aa_nat_set_nat 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) T2)) (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) (B4 tptp.real)) (=> (forall ((M2 tptp.nat) (T2 tptp.real)) (=> (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) T2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real T2) H))) (tptp.has_fi5821293074295781190e_real (tptp.aa_nat_fun_real_real Diff M2) (tptp.aa_real_real (tptp.aa_nat_fun_real_real Diff (tptp.aa_nat_nat tptp.suc M2)) T2) (tptp.topolo2177554685111907308n_real T2 tptp.top_top_set_real)))) (=> (= N (tptp.aa_nat_nat tptp.suc K)) (forall ((M3 tptp.nat) (T3 tptp.real)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc M3))) (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 M3) 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 (tptp.aa_rea1103652080130114956l_real (tptp.aa_fun2567993205388704171l_real (tptp.aTP_Lamm_ff N) Diff) B4) M3) (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) T3)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real (tptp.aa_nat1308781354268537904t_real (tptp.aTP_Lamm_fg Diff) M3) T3) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat _let_2))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real B4) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real T3) _let_2)) (tptp.aa_nat_real tptp.semiri2265585572941072030t_real _let_2))))) (tptp.topolo2177554685111907308n_real T3 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_fh (tptp.suminf_real (tptp.aa_real_fun_nat_real tptp.aTP_Lamm_fi 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 ((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 ((R2 tptp.real)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) R2)) (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))) R2))) (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 ((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 ((R2 tptp.real)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) R2)) (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))) R2))) (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 L) tptp.zero_zero_real)) (exists ((R2 tptp.real)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) R2)) (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))) R2))) (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 ((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 ((X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real) X)) (tptp.topolo4422821103128117721l_real (tptp.topolo2177554685111907308n_real X tptp.top_top_set_real) tptp.arcosh_real))) (tptp.filterlim_real_real tptp.aTP_Lamm_fj _let_49 (tptp.topolo2177554685111907308n_real _let_48 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.topolo4422821103128117721l_real (tptp.topolo2177554685111907308n_real X tptp.top_top_set_real) tptp.arccos)))) (forall ((X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) tptp.one_one_real)) (tptp.topolo4422821103128117721l_real (tptp.topolo2177554685111907308n_real X tptp.top_top_set_real) tptp.arcsin)))) (forall ((X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) tptp.one_one_real)) (tptp.topolo4422821103128117721l_real (tptp.topolo2177554685111907308n_real X tptp.top_top_set_real) tptp.artanh_real)))) (forall ((D tptp.real) (X tptp.real) (G tptp.fun_real_real) (F tptp.fun_real_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) D)) (=> (forall ((Z4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real Z4) X))) D)) (= (tptp.aa_real_real G (tptp.aa_real_real F Z4)) Z4))) (=> (forall ((Z4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real Z4) X))) D)) (tptp.topolo4422821103128117721l_real (tptp.topolo2177554685111907308n_real Z4 tptp.top_top_set_real) F))) (tptp.topolo4422821103128117721l_real (tptp.topolo2177554685111907308n_real (tptp.aa_real_real F X) tptp.top_top_set_real) G))))) (forall ((A tptp.real) (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 ((Z4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) Z4)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Z4) B)) (tptp.topolo4422821103128117721l_real (tptp.topolo2177554685111907308n_real Z4 tptp.top_top_set_real) F)))) (=> (forall ((Z4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) Z4)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Z4) B)) (tptp.topolo4422821103128117721l_real (tptp.topolo2177554685111907308n_real Z4 tptp.top_top_set_real) G)))) (=> (forall ((Z4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) Z4)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Z4) B)) (tptp.has_fi5821293074295781190e_real G (tptp.aa_real_real G2 Z4) (tptp.topolo2177554685111907308n_real Z4 tptp.top_top_set_real))))) (=> (forall ((Z4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) Z4)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Z4) B)) (tptp.has_fi5821293074295781190e_real F (tptp.aa_real_real F2 Z4) (tptp.topolo2177554685111907308n_real Z4 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_fk A))) (tptp.member_real (tptp.suminf_real _let_2) (tptp.set_or1222579329274155063t_real (tptp.groups6591440286371151544t_real _let_2 (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat _let_1) tptp.one_one_nat))) (tptp.groups6591440286371151544t_real _let_2 (tptp.aa_nat_set_nat 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_fk A))) (tptp.member_real (tptp.suminf_real _let_2) (tptp.set_or1222579329274155063t_real (tptp.groups6591440286371151544t_real _let_2 (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat _let_1)) (tptp.groups6591440286371151544t_real _let_2 (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat _let_1) tptp.one_one_nat)))))))))))) (forall ((C tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) C)) (tptp.filterlim_nat_nat (tptp.aa_nat_fun_nat_nat tptp.aTP_Lamm_fl 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))) (tptp.filterlim_nat_real tptp.aTP_Lamm_fm _let_50 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_fn 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))))))))) (tptp.filterlim_nat_real tptp.aTP_Lamm_fo _let_49 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_fp C) (tptp.topolo2815343760600316023s_real tptp.one_one_real) tptp.at_top_nat))) (tptp.filterlim_nat_real tptp.aTP_Lamm_fq _let_49 tptp.at_top_nat) (forall ((R tptp.real)) (tptp.filterlim_nat_real (tptp.aa_real_fun_nat_real tptp.aTP_Lamm_fr R) (tptp.topolo2815343760600316023s_real R) tptp.at_top_nat)) (forall ((F tptp.fun_nat_real) (L tptp.real)) (=> (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_nat_real F N2)) (tptp.aa_nat_real F (tptp.aa_nat_nat tptp.suc N2))))) (=> (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_nat_real F N2)) L))) (=> (forall ((E2 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) E2)) (exists ((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)) E2)))))) (tptp.filterlim_nat_real F (tptp.topolo2815343760600316023s_real L) tptp.at_top_nat))))) (forall ((X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) tptp.one_one_real)) (tptp.filterlim_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) (tptp.topolo2815343760600316023s_real tptp.zero_zero_real) tptp.at_top_nat)))) (forall ((X tptp.real) (A tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real) X)) (tptp.filterlim_nat_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_fs X) A) (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 ((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 ((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_ft X) (tptp.topolo2815343760600316023s_real tptp.zero_zero_real) tptp.at_top_nat))) (forall ((R tptp.real)) (tptp.filterlim_nat_real (tptp.aa_real_fun_nat_real tptp.aTP_Lamm_fu R) (tptp.topolo2815343760600316023s_real R) tptp.at_top_nat)) (forall ((X tptp.real)) (tptp.filterlim_nat_real (tptp.aa_real_fun_nat_real tptp.aTP_Lamm_fv X) (tptp.topolo2815343760600316023s_real (tptp.aa_real_real tptp.exp_real X)) tptp.at_top_nat)) (forall ((R tptp.real)) (tptp.filterlim_nat_real (tptp.aa_real_fun_nat_real tptp.aTP_Lamm_fw R) (tptp.topolo2815343760600316023s_real R) tptp.at_top_nat)) (forall ((A tptp.fun_nat_real)) (=> (tptp.filterlim_nat_real A (tptp.topolo2815343760600316023s_real tptp.zero_zero_real) tptp.at_top_nat) (=> (tptp.topolo6980174941875973593q_real A) (tptp.summable_real (tptp.aTP_Lamm_fk 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_fk A)))))) (forall ((Theta tptp.fun_nat_real) (Theta2 tptp.real)) (=> (tptp.filterlim_nat_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_fx Theta) Theta2) (tptp.topolo2815343760600316023s_real tptp.one_one_real) tptp.at_top_nat) (not (forall ((K3 tptp.fun_nat_int)) (not (tptp.filterlim_nat_real (tptp.aa_fun4551936527957760560t_real (tptp.aTP_Lamm_fy Theta) K3) (tptp.topolo2815343760600316023s_real Theta2) tptp.at_top_nat)))))) (forall ((Theta tptp.fun_nat_real)) (=> (tptp.filterlim_nat_real (tptp.aTP_Lamm_fz Theta) (tptp.topolo2815343760600316023s_real tptp.one_one_real) tptp.at_top_nat) (exists ((K3 tptp.fun_nat_int)) (tptp.filterlim_nat_real (tptp.aa_fun4551936527957760560t_real (tptp.aTP_Lamm_fy Theta) K3) (tptp.topolo2815343760600316023s_real tptp.zero_zero_real) tptp.at_top_nat)))) (forall ((A tptp.fun_nat_real)) (=> (tptp.filterlim_nat_real A (tptp.topolo2815343760600316023s_real tptp.zero_zero_real) tptp.at_top_nat) (=> (tptp.topolo6980174941875973593q_real A) (tptp.filterlim_nat_real (tptp.aTP_Lamm_ga A) (tptp.topolo2815343760600316023s_real (tptp.suminf_real (tptp.aTP_Lamm_fk 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_am 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_fk A))) (=> (tptp.filterlim_nat_real A (tptp.topolo2815343760600316023s_real tptp.zero_zero_real) tptp.at_top_nat) (=> (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_nat_real A N2)))) (=> (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_nat_real A (tptp.aa_nat_nat tptp.suc N2))) (tptp.aa_nat_real A N2)))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.groups6591440286371151544t_real _let_1 (tptp.aa_nat_set_nat 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_ga A) (tptp.topolo2815343760600316023s_real (tptp.suminf_real (tptp.aTP_Lamm_fk 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.groups6591440286371151544t_real (tptp.aTP_Lamm_fk A) (tptp.aa_nat_set_nat 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_ga 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.groups6591440286371151544t_real (tptp.aTP_Lamm_fk A) (tptp.aa_nat_set_nat 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_gb 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_gb A) (tptp.topolo2815343760600316023s_real (tptp.suminf_real (tptp.aTP_Lamm_fk 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_gb A) (tptp.topolo2815343760600316023s_real (tptp.suminf_real (tptp.aTP_Lamm_fk A))) tptp.at_top_nat))))) (forall ((A tptp.fun_nat_real) (N tptp.nat)) (let ((_let_1 (tptp.aTP_Lamm_fk A))) (=> (tptp.filterlim_nat_real A (tptp.topolo2815343760600316023s_real tptp.zero_zero_real) tptp.at_top_nat) (=> (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_nat_real A N2)))) (=> (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_nat_real A (tptp.aa_nat_nat tptp.suc N2))) (tptp.aa_nat_real A N2)))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.suminf_real _let_1)) (tptp.groups6591440286371151544t_real _let_1 (tptp.aa_nat_set_nat 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 ((C4 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) C4)))))) (tptp.filterlim_nat_nat tptp.suc tptp.at_top_nat tptp.at_top_nat) (tptp.filterlim_real_real tptp.arctan (tptp.topolo2815343760600316023s_real _let_52) tptp.at_bot_real) (forall ((X tptp.real)) (tptp.filterlim_real_real (tptp.aa_rea7340605660300375871l_real tptp.aTP_Lamm_gc 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.artanh_real tptp.at_bot_real (tptp.topolo2177554685111907308n_real _let_44 (tptp.set_or5849166863359141190n_real _let_44))) (tptp.filterlim_real_real tptp.tan_real tptp.at_bot_real (tptp.topolo2177554685111907308n_real _let_52 (tptp.set_or5849166863359141190n_real _let_52))) (tptp.filterlim_real_real tptp.tanh_real (tptp.topolo2815343760600316023s_real _let_44) tptp.at_bot_real) (tptp.filterlim_real_real tptp.arcosh_real _let_49 (tptp.topolo2177554685111907308n_real tptp.one_one_real (tptp.set_or5849166863359141190n_real tptp.one_one_real))) (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_gd N) F) tptp.at_bot_real F3))))) (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_gd N) F) tptp.at_top_real F3))))) (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_nat_real tptp.semiri5074537144036343181t_real tptp.at_infinity_real tptp.at_top_nat) (= (tptp.aa_nat_set_nat tptp.set_or1210151606488870762an_nat tptp.zero_zero_nat) _let_51) (tptp.filterlim_real_real tptp.tanh_real _let_50 tptp.at_top_real) (tptp.filterlim_real_real tptp.artanh_real tptp.at_top_real (tptp.topolo2177554685111907308n_real tptp.one_one_real (tptp.set_or5984915006950818249n_real tptp.one_one_real))) (forall ((K tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc K))) (= (tptp.aa_nat_set_nat tptp.set_or1210151606488870762an_nat _let_1) (tptp.minus_minus_set_nat (tptp.aa_nat_set_nat tptp.set_or1210151606488870762an_nat K) (tptp.insert_nat _let_1 tptp.bot_bot_set_nat))))) (tptp.filterlim_real_real tptp.aTP_Lamm_ge _let_49 tptp.at_top_real) (forall ((F tptp.fun_real_real) (Y tptp.real)) (let ((_let_1 (tptp.topolo2815343760600316023s_real Y))) (=> (tptp.order_mono_real_real F) (=> (tptp.filterlim_nat_real (tptp.aTP_Lamm_gf F) _let_1 tptp.at_top_nat) (tptp.filterlim_real_real F _let_1 tptp.at_top_real))))) (forall ((K tptp.nat)) (tptp.filterlim_real_real (tptp.aa_nat_fun_real_real tptp.aTP_Lamm_gg 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_gh X) (tptp.topolo2815343760600316023s_real (tptp.aa_real_real tptp.exp_real X)) tptp.at_top_real)) (tptp.filterlim_real_real tptp.tan_real tptp.at_top_real (tptp.topolo2177554685111907308n_real _let_48 (tptp.set_or5984915006950818249n_real _let_48))) (tptp.filterlim_real_real tptp.arctan (tptp.topolo2815343760600316023s_real _let_48) 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) (Y tptp.real)) (let ((_let_1 (tptp.topolo2177554685111907308n_real X (tptp.set_or5849166863359141190n_real X)))) (let ((_let_2 (tptp.topolo2815343760600316023s_real Y))) (=> (tptp.filterlim_real_real G tptp.at_top_real _let_1) (=> (tptp.eventually_real (tptp.aTP_Lamm_gi G2) _let_1) (=> (tptp.eventually_real (tptp.aa_fun9137271176455094897l_bool (tptp.aTP_Lamm_gj F) F2) _let_1) (=> (tptp.eventually_real (tptp.aa_fun9137271176455094897l_bool (tptp.aTP_Lamm_gj G) G2) _let_1) (=> (tptp.filterlim_real_real (tptp.aa_fun6946558556880649704l_real (tptp.aTP_Lamm_gk G2) F2) _let_2 _let_1) (tptp.filterlim_real_real (tptp.aa_fun6946558556880649704l_real (tptp.aTP_Lamm_gk 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 ((P tptp.fun_nat_bool) (K tptp.nat)) (= (tptp.eventually_nat (tptp.aa_nat_fun_nat_bool (tptp.aTP_Lamm_gm P) K) tptp.at_top_nat) (tptp.eventually_nat P tptp.at_top_nat))) (forall ((P tptp.fun_nat_bool) (K tptp.nat)) (=> (tptp.eventually_nat P tptp.at_top_nat) (tptp.eventually_nat (tptp.aa_nat_fun_nat_bool (tptp.aTP_Lamm_gm P) K) 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_gn P) A) (tptp.topolo2177554685111907308n_real tptp.zero_zero_real (tptp.set_or5849166863359141190n_real tptp.zero_zero_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.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_gj F) F2) _let_1) (=> (tptp.eventually_real (tptp.aa_fun9137271176455094897l_bool (tptp.aTP_Lamm_gj G) G2) _let_1) (=> (tptp.filterlim_real_real (tptp.aa_fun6946558556880649704l_real (tptp.aTP_Lamm_go F2) G2) tptp.at_top_real _let_1) (tptp.filterlim_real_real (tptp.aa_fun6946558556880649704l_real (tptp.aTP_Lamm_go 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_top_real _let_1) (=> (tptp.eventually_real (tptp.aa_fun9137271176455094897l_bool (tptp.aTP_Lamm_gj F) F2) _let_1) (=> (tptp.eventually_real (tptp.aa_fun9137271176455094897l_bool (tptp.aTP_Lamm_gj G) G2) _let_1) (=> (tptp.filterlim_real_real (tptp.aa_fun6946558556880649704l_real (tptp.aTP_Lamm_go F2) G2) tptp.at_top_real _let_1) (tptp.filterlim_real_real (tptp.aa_fun6946558556880649704l_real (tptp.aTP_Lamm_go 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_gi G) _let_1) (=> (tptp.eventually_real (tptp.aTP_Lamm_gi G2) _let_1) (=> (tptp.eventually_real (tptp.aa_fun9137271176455094897l_bool (tptp.aTP_Lamm_gj F) F2) _let_1) (=> (tptp.eventually_real (tptp.aa_fun9137271176455094897l_bool (tptp.aTP_Lamm_gj G) G2) _let_1) (=> (tptp.filterlim_real_real (tptp.aa_fun6946558556880649704l_real (tptp.aTP_Lamm_gk G2) F2) F3 _let_1) (tptp.filterlim_real_real (tptp.aa_fun6946558556880649704l_real (tptp.aTP_Lamm_go 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_gi G) _let_1) (=> (tptp.eventually_real (tptp.aTP_Lamm_gi G2) _let_1) (=> (tptp.eventually_real (tptp.aa_fun9137271176455094897l_bool (tptp.aTP_Lamm_gj F) F2) _let_1) (=> (tptp.eventually_real (tptp.aa_fun9137271176455094897l_bool (tptp.aTP_Lamm_gj G) G2) _let_1) (=> (tptp.filterlim_real_real (tptp.aa_fun6946558556880649704l_real (tptp.aTP_Lamm_gk G2) F2) F3 _let_1) (tptp.filterlim_real_real (tptp.aa_fun6946558556880649704l_real (tptp.aTP_Lamm_go 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_gj F) F2) _let_1) (=> (tptp.eventually_real (tptp.aa_fun9137271176455094897l_bool (tptp.aTP_Lamm_gj G) G2) _let_1) (=> (tptp.filterlim_real_real (tptp.aa_fun6946558556880649704l_real (tptp.aTP_Lamm_go F2) G2) tptp.at_top_real _let_1) (tptp.filterlim_real_real (tptp.aa_fun6946558556880649704l_real (tptp.aTP_Lamm_go 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.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_gj F) F2) _let_1) (=> (tptp.eventually_real (tptp.aa_fun9137271176455094897l_bool (tptp.aTP_Lamm_gj G) G2) _let_1) (=> (tptp.filterlim_real_real (tptp.aa_fun6946558556880649704l_real (tptp.aTP_Lamm_go F2) G2) tptp.at_bot_real _let_1) (tptp.filterlim_real_real (tptp.aa_fun6946558556880649704l_real (tptp.aTP_Lamm_go 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.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_gj F) F2) _let_1) (=> (tptp.eventually_real (tptp.aa_fun9137271176455094897l_bool (tptp.aTP_Lamm_gj G) G2) _let_1) (=> (tptp.filterlim_real_real (tptp.aa_fun6946558556880649704l_real (tptp.aTP_Lamm_go F2) G2) tptp.at_bot_real _let_1) (tptp.filterlim_real_real (tptp.aa_fun6946558556880649704l_real (tptp.aTP_Lamm_go 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) (Y tptp.real)) (let ((_let_1 (tptp.topolo2177554685111907308n_real X tptp.top_top_set_real))) (let ((_let_2 (tptp.topolo2815343760600316023s_real Y))) (=> (tptp.filterlim_real_real G tptp.at_top_real _let_1) (=> (tptp.eventually_real (tptp.aTP_Lamm_gi G2) _let_1) (=> (tptp.eventually_real (tptp.aa_fun9137271176455094897l_bool (tptp.aTP_Lamm_gj F) F2) _let_1) (=> (tptp.eventually_real (tptp.aa_fun9137271176455094897l_bool (tptp.aTP_Lamm_gj G) G2) _let_1) (=> (tptp.filterlim_real_real (tptp.aa_fun6946558556880649704l_real (tptp.aTP_Lamm_gk G2) F2) _let_2 _let_1) (tptp.filterlim_real_real (tptp.aa_fun6946558556880649704l_real (tptp.aTP_Lamm_gk 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.topolo2815343760600316023s_real X))) (=> (tptp.filterlim_real_real G tptp.at_top_real tptp.at_top_real) (=> (tptp.eventually_real (tptp.aTP_Lamm_gi G2) tptp.at_top_real) (=> (tptp.eventually_real (tptp.aa_fun9137271176455094897l_bool (tptp.aTP_Lamm_gj F) F2) tptp.at_top_real) (=> (tptp.eventually_real (tptp.aa_fun9137271176455094897l_bool (tptp.aTP_Lamm_gj G) G2) tptp.at_top_real) (=> (tptp.filterlim_real_real (tptp.aa_fun6946558556880649704l_real (tptp.aTP_Lamm_gk G2) F2) _let_1 tptp.at_top_real) (tptp.filterlim_real_real (tptp.aa_fun6946558556880649704l_real (tptp.aTP_Lamm_gk 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) (Y tptp.real)) (let ((_let_1 (tptp.topolo2177554685111907308n_real X (tptp.set_or5984915006950818249n_real X)))) (let ((_let_2 (tptp.topolo2815343760600316023s_real Y))) (=> (tptp.filterlim_real_real G tptp.at_top_real _let_1) (=> (tptp.eventually_real (tptp.aTP_Lamm_gi G2) _let_1) (=> (tptp.eventually_real (tptp.aa_fun9137271176455094897l_bool (tptp.aTP_Lamm_gj F) F2) _let_1) (=> (tptp.eventually_real (tptp.aa_fun9137271176455094897l_bool (tptp.aTP_Lamm_gj G) G2) _let_1) (=> (tptp.filterlim_real_real (tptp.aa_fun6946558556880649704l_real (tptp.aTP_Lamm_gk G2) F2) _let_2 _let_1) (tptp.filterlim_real_real (tptp.aa_fun6946558556880649704l_real (tptp.aTP_Lamm_gk G) F) _let_2 _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_gi G) _let_1) (=> (tptp.eventually_real (tptp.aTP_Lamm_gi G2) _let_1) (=> (tptp.eventually_real (tptp.aa_fun9137271176455094897l_bool (tptp.aTP_Lamm_gj F) F2) _let_1) (=> (tptp.eventually_real (tptp.aa_fun9137271176455094897l_bool (tptp.aTP_Lamm_gj G) G2) _let_1) (=> (tptp.filterlim_real_real (tptp.aa_fun6946558556880649704l_real (tptp.aTP_Lamm_gk G2) F2) F3 _let_1) (tptp.filterlim_real_real (tptp.aa_fun6946558556880649704l_real (tptp.aTP_Lamm_go F) G) F3 _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_gi G0) _let_1) (=> (tptp.eventually_real (tptp.aTP_Lamm_gi G2) _let_1) (=> (tptp.eventually_real (tptp.aa_fun9137271176455094897l_bool (tptp.aTP_Lamm_gj F0) F2) _let_1) (=> (tptp.eventually_real (tptp.aa_fun9137271176455094897l_bool (tptp.aTP_Lamm_gj G0) G2) _let_1) (=> (tptp.filterlim_real_real (tptp.aa_fun6946558556880649704l_real (tptp.aTP_Lamm_gk G2) F2) F3 _let_1) (tptp.filterlim_real_real (tptp.aa_fun6946558556880649704l_real (tptp.aTP_Lamm_go F0) G0) 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_gj F) F2) _let_1) (=> (tptp.eventually_real (tptp.aa_fun9137271176455094897l_bool (tptp.aTP_Lamm_gj G) G2) _let_1) (=> (tptp.filterlim_real_real (tptp.aa_fun6946558556880649704l_real (tptp.aTP_Lamm_go F2) G2) tptp.at_bot_real _let_1) (tptp.filterlim_real_real (tptp.aa_fun6946558556880649704l_real (tptp.aTP_Lamm_go F) G) tptp.at_bot_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.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_gi G2) _let_1) (=> (tptp.eventually_real (tptp.aa_fun9137271176455094897l_bool (tptp.aTP_Lamm_gj F) F2) _let_1) (=> (tptp.eventually_real (tptp.aa_fun9137271176455094897l_bool (tptp.aTP_Lamm_gj G) G2) _let_1) (=> (tptp.filterlim_real_real (tptp.aa_fun6946558556880649704l_real (tptp.aTP_Lamm_gk G2) F2) _let_2 _let_1) (tptp.filterlim_real_real (tptp.aa_fun6946558556880649704l_real (tptp.aTP_Lamm_gk G) F) _let_2 _let_1))))))))) (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 ((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 ((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) (Z4 tptp.real)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) Z4)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Z4) B)) (tptp.has_fi5821293074295781190e_real F L2 (tptp.topolo2177554685111907308n_real Z4 tptp.top_top_set_real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real F 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_gp F))))) (tptp.topolo5044208981011980120l_real _let_45 tptp.arccos) (tptp.topolo5044208981011980120l_real _let_45 tptp.arcsin) (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 ((A2 tptp.set_real) (F tptp.fun_real_real)) (=> (tptp.topolo5044208981011980120l_real A2 F) (=> (forall ((X3 tptp.real)) (=> (tptp.member_real X3 A2) (tptp.member_real (tptp.aa_real_real F X3) (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.aTP_Lamm_gq F))))) (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 ((M tptp.nat) (N4 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_gr M) N4))) (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_gs M) N4)))) (tptp.finite_card_list_nat (tptp.collect_list_nat (tptp.aa_nat2079453845469346690t_bool (tptp.aTP_Lamm_gt M) N4))))))) (forall ((M tptp.nat) (N4 tptp.nat)) (= (tptp.finite_card_list_nat (tptp.collect_list_nat (tptp.aa_nat2079453845469346690t_bool (tptp.aTP_Lamm_gr M) N4))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N4) M)) tptp.one_one_nat)) N4))) (= (tptp.image_int_nat tptp.nat_int_encode tptp.top_top_set_int) tptp.top_top_set_nat) (forall ((X tptp.int) (Y tptp.int)) (= (= (tptp.aa_int_nat tptp.nat_int_encode X) (tptp.aa_int_nat tptp.nat_int_encode Y)) (= X Y))) (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.complete_Sup_Sup_nat tptp.bot_bot_set_nat) tptp.zero_zero_nat) (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 ((N tptp.nat) (K tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial N) K) (tptp.finite_card_set_nat (tptp.collect_set_nat (tptp.aa_nat8857836526276733660t_bool (tptp.aTP_Lamm_gu N) K))))) (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_ep 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 ((X tptp.int)) (= (tptp.aa_nat_int tptp.nat_int_decode (tptp.aa_int_nat tptp.nat_int_encode X)) X)) (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.nat) (Y tptp.nat)) (= (= (tptp.aa_nat_int tptp.nat_int_decode X) (tptp.aa_nat_int tptp.nat_int_decode Y)) (= X Y))) (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.log2 B) (tptp.set_or5849166863359141190n_real tptp.zero_zero_real)))) (forall ((A2 tptp.set_nat)) (tptp.pp (tptp.aa_set_nat_bool (tptp.inj_on_nat_int tptp.nat_int_decode) A2))) (forall ((N4 tptp.set_nat)) (tptp.pp (tptp.aa_set_nat_bool (tptp.inj_on_nat_nat tptp.suc) N4))) (forall ((A2 tptp.set_Pr1261947904930325089at_nat)) (tptp.inj_on2178005380612969504at_nat tptp.nat_prod_encode A2)) (forall ((A2 tptp.set_list_nat)) (tptp.inj_on_list_nat_nat tptp.nat_list_encode A2)) (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 ((N4 tptp.set_nat) (K tptp.nat)) (=> (forall ((N2 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat N2) N4)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) N2)))) (tptp.pp (tptp.aa_set_nat_bool (tptp.inj_on_nat_nat (tptp.aa_nat_fun_nat_nat tptp.aTP_Lamm_cs K)) N4)))) (tptp.pp (tptp.aa_set_nat_bool (tptp.inj_on_nat_char tptp.unique3096191561947761185of_nat) _let_43)) (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_cr N))) N))) (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat J) K))) (let ((_let_2 (tptp.set_or4665077453230672383an_nat I))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I) J)) (= (tptp.aa_nat_set_nat _let_2 _let_1) (tptp.sup_sup_set_nat (tptp.aa_nat_set_nat _let_2 J) (tptp.aa_nat_set_nat (tptp.set_or4665077453230672383an_nat J) _let_1))))))) (forall ((S2 tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat S2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.finite_card_nat S2)) (tptp.aa_nat_nat tptp.suc (tptp.lattic8265883725875713057ax_nat S2)))))) (forall ((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_gv 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_gw 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_gx M10)))))))) (forall ((X tptp.rat)) (= (tptp.quotient_of X) (tptp.the_Pr4378521158711661632nt_int (tptp.aTP_Lamm_gy 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 ((N tptp.int)) (=> (not (= N tptp.zero_zero_int)) (= (tptp.lattic8263393255366662781ax_int (tptp.collect_int (tptp.aa_int_fun_int_bool tptp.aTP_Lamm_cq N))) (tptp.aa_int_int tptp.abs_abs_int N)))) (forall ((Q2 tptp.int) (P2 tptp.int)) (let ((_let_1 (tptp.product_Pair_int_int P2 Q2))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) Q2)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.algebr932160517623751201me_int P2) Q2)) (= (tptp.normalize _let_1) _let_1))))) (= tptp.sup_sup_nat tptp.ord_max_nat) (= tptp.sup_sup_int tptp.ord_max_int) (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 ((Q2 tptp.rat)) (not (forall ((A3 tptp.int) (B3 tptp.int)) (=> (= Q2 (tptp.aa_int_rat (tptp.aa_int_fun_int_rat tptp.fract A3) B3)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) B3)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.algebr932160517623751201me_int A3) B3)))))))) (forall ((P tptp.fun_rat_bool) (Q2 tptp.rat)) (=> (forall ((A3 tptp.int) (B3 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) B3)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.algebr932160517623751201me_int A3) B3)) (tptp.pp (tptp.aa_rat_bool P (tptp.aa_int_rat (tptp.aa_int_fun_int_rat tptp.fract A3) B3)))))) (tptp.pp (tptp.aa_rat_bool P Q2)))) (forall ((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 ((N tptp.int) (M tptp.int)) (=> (not (= N tptp.zero_zero_int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.gcd_gcd_int M) N) (tptp.lattic8263393255366662781ax_int (tptp.collect_int (tptp.aa_int_fun_int_bool (tptp.aTP_Lamm_gz N) M)))))) (forall ((Q2 tptp.rat)) (=> (forall ((A3 tptp.int) (B3 tptp.int)) (=> (= Q2 (tptp.aa_int_rat (tptp.aa_int_fun_int_rat tptp.fract A3) B3)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) B3)) (=> (not (= A3 tptp.zero_zero_int)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.algebr932160517623751201me_int A3) B3))))))) (= Q2 tptp.zero_zero_rat))) (forall ((R tptp.rat)) (exists ((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 (= R (tptp.aa_int_rat (tptp.aa_int_fun_int_rat tptp.fract _let_2) _let_1)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) _let_1)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.algebr932160517623751201me_int _let_2) _let_1)) (forall ((Y4 tptp.product_prod_int_int)) (let ((_let_1 (tptp.product_snd_int_int Y4))) (let ((_let_2 (tptp.product_fst_int_int Y4))) (=> (and (= R (tptp.aa_int_rat (tptp.aa_int_fun_int_rat tptp.fract _let_2) _let_1)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) _let_1)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.algebr932160517623751201me_int _let_2) _let_1))) (= Y4 X3)))))))))) (tptp.bNF_re1394333895916556125l_bool tptp.ratrel tptp.fequal_bool tptp.aTP_Lamm_eh tptp.aTP_Lamm_eh) (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 ((M tptp.nat) (N tptp.nat)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.algebr932160517623751201me_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int M)) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.algebr934650988132801477me_nat M) N)))) (forall ((N tptp.nat) (K tptp.int)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.algebr934650988132801477me_nat N) (tptp.aa_int_nat tptp.nat2 (tptp.aa_int_int tptp.abs_abs_int K)))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.algebr932160517623751201me_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N)) K)))) (forall ((K tptp.int) (N tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.algebr934650988132801477me_nat (tptp.aa_int_nat tptp.nat2 (tptp.aa_int_int tptp.abs_abs_int K))) N)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.algebr932160517623751201me_int K) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N))))) (forall ((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 N) (tptp.aa_nat_nat tptp.suc N)))) (forall ((N tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.algebr934650988132801477me_nat (tptp.aa_nat_nat tptp.suc 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 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) (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 ((X tptp.real)) (=> (tptp.member_real X tptp.field_5140801741446780682s_real) (not (forall ((M2 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 M2)) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N2))) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.algebr934650988132801477me_nat M2) N2))))))))) (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) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Y)) (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) Y)))))) (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))))) (forall ((N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.algebr934650988132801477me_nat N) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) tptp.one_one_nat))))) (forall ((N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.algebr934650988132801477me_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N) tptp.one_one_nat)) N)))) (forall ((X tptp.num) (Xa tptp.num) (Y tptp.option_num)) (let ((_let_1 (= X tptp.one))) (=> (= (tptp.bit_and_not_num X Xa) Y) (=> (tptp.accp_P3113834385874906142um_num tptp.bit_and_not_num_rel (tptp.product_Pair_num_num X Xa)) (=> (=> _let_1 (=> (= Xa tptp.one) (=> (= Y 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) (=> (= Y (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) (=> (= Y tptp.none_num) (not (tptp.accp_P3113834385874906142um_num tptp.bit_and_not_num_rel (tptp.product_Pair_num_num tptp.one _let_1)))))))) (=> (forall ((M2 tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 M2))) (=> (= X _let_1) (=> (= Xa tptp.one) (=> (= Y (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 ((M2 tptp.num)) (=> (= X (tptp.aa_num_num tptp.bit0 M2)) (forall ((N2 tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 N2))) (=> (= Xa _let_1) (=> (= Y (tptp.map_option_num_num tptp.bit0 (tptp.bit_and_not_num M2 N2))) (not (tptp.accp_P3113834385874906142um_num tptp.bit_and_not_num_rel (tptp.product_Pair_num_num (tptp.aa_num_num tptp.bit0 M2) _let_1))))))))) (=> (forall ((M2 tptp.num)) (=> (= X (tptp.aa_num_num tptp.bit0 M2)) (forall ((N2 tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit1 N2))) (=> (= Xa _let_1) (=> (= Y (tptp.map_option_num_num tptp.bit0 (tptp.bit_and_not_num M2 N2))) (not (tptp.accp_P3113834385874906142um_num tptp.bit_and_not_num_rel (tptp.product_Pair_num_num (tptp.aa_num_num tptp.bit0 M2) _let_1))))))))) (=> (forall ((M2 tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit1 M2))) (=> (= X _let_1) (=> (= Xa tptp.one) (=> (= Y (tptp.some_num (tptp.aa_num_num tptp.bit0 M2))) (not (tptp.accp_P3113834385874906142um_num tptp.bit_and_not_num_rel (tptp.product_Pair_num_num _let_1 tptp.one)))))))) (=> (forall ((M2 tptp.num)) (=> (= X (tptp.aa_num_num tptp.bit1 M2)) (forall ((N2 tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 N2))) (=> (= Xa _let_1) (=> (= Y (tptp.case_o6005452278849405969um_num (tptp.some_num tptp.one) tptp.aTP_Lamm_dz (tptp.bit_and_not_num M2 N2))) (not (tptp.accp_P3113834385874906142um_num tptp.bit_and_not_num_rel (tptp.product_Pair_num_num (tptp.aa_num_num tptp.bit1 M2) _let_1))))))))) (not (forall ((M2 tptp.num)) (=> (= X (tptp.aa_num_num tptp.bit1 M2)) (forall ((N2 tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit1 N2))) (=> (= Xa _let_1) (=> (= Y (tptp.map_option_num_num tptp.bit0 (tptp.bit_and_not_num M2 N2))) (not (tptp.accp_P3113834385874906142um_num tptp.bit_and_not_num_rel (tptp.product_Pair_num_num (tptp.aa_num_num tptp.bit1 M2) _let_1)))))))))))))))))))))) (tptp.bNF_re4734134812813710757nt_int tptp.ratrel _let_39 tptp.aTP_Lamm_en tptp.aTP_Lamm_en) (tptp.bNF_re6650684261131312217nt_int tptp.fequal_nat tptp.fequal_int tptp.semiri1314217659103216013at_int tptp.semiri1314217659103216013at_int) (tptp.bNF_re6378542964492772123um_int tptp.fequal_num (tptp.bNF_re1822329894187522285nt_int tptp.fequal_num tptp.fequal_int) tptp.aTP_Lamm_ha tptp.aTP_Lamm_ha) (tptp.pp (tptp.aa_fun_int_int_bool (tptp.aa_fun3770596143487498376t_bool _let_16 tptp.aTP_Lamm_hb) tptp.aTP_Lamm_hb)) (tptp.bNF_re5717476210804479843nt_int tptp.fequal_int _let_16 tptp.plus_plus_int tptp.plus_plus_int) (tptp.bNF_re5162689864697376059at_nat tptp.fequal_nat _let_40 tptp.plus_plus_nat tptp.plus_plus_nat) (tptp.pp (tptp.aa_fun_nat_nat_bool (tptp.aa_fun3185460345579526648t_bool _let_40 tptp.suc) tptp.suc)) (tptp.bNF_re5717476210804479843nt_int tptp.fequal_int _let_16 tptp.times_times_int tptp.times_times_int) (tptp.bNF_re5162689864697376059at_nat tptp.fequal_nat _let_40 tptp.times_times_nat tptp.times_times_nat) (tptp.bNF_re5162689864697376059at_nat tptp.fequal_nat _let_40 tptp.minus_minus_nat tptp.minus_minus_nat) (tptp.bNF_re5717476210804479843nt_int tptp.fequal_int _let_16 tptp.minus_minus_int tptp.minus_minus_int) (tptp.bNF_re5162689864697376059at_nat tptp.fequal_nat _let_40 tptp.bit_se547839408752420682it_nat tptp.bit_se547839408752420682it_nat) (tptp.bNF_re5651586111134833323nt_int tptp.fequal_nat _let_16 tptp.bit_se545348938243370406it_int tptp.bit_se545348938243370406it_int) (tptp.bNF_re5162689864697376059at_nat tptp.fequal_nat _let_40 tptp.divide_divide_nat tptp.divide_divide_nat) (tptp.bNF_re5717476210804479843nt_int tptp.fequal_int _let_16 tptp.divide_divide_int tptp.divide_divide_int) (tptp.bNF_re5717476210804479843nt_int tptp.fequal_int _let_16 tptp.gcd_gcd_int tptp.gcd_gcd_int) (tptp.bNF_re4808202430149235895nt_int tptp.fequal_int (tptp.bNF_re6250860962936578807nt_int tptp.fequal_int tptp.ratrel) tptp.aTP_Lamm_hc tptp.aTP_Lamm_hc) (tptp.bNF_re4734134812813710757nt_int tptp.ratrel _let_39 tptp.aTP_Lamm_ek tptp.aTP_Lamm_ek) (tptp.pp (tptp.aa_fun1403452029515102102t_bool (tptp.aa_fun8298786006102058668t_bool _let_39 tptp.aTP_Lamm_eo) tptp.aTP_Lamm_eo)) (forall ((X tptp.num) (Xa tptp.num) (Y tptp.option_num)) (let ((_let_1 (= X tptp.one))) (=> (= (tptp.aa_num_option_num (tptp.aa_num6390622462783740633on_num tptp.bit_un7362597486090784418nd_num X) Xa) Y) (=> (tptp.accp_P3113834385874906142um_num tptp.bit_un4731106466462545111um_rel (tptp.product_Pair_num_num X Xa)) (=> (=> _let_1 (=> (= Xa tptp.one) (=> (= Y (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) (=> (= Y 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) (=> (= Y (tptp.some_num tptp.one)) (not (tptp.accp_P3113834385874906142um_num tptp.bit_un4731106466462545111um_rel (tptp.product_Pair_num_num tptp.one _let_1)))))))) (=> (forall ((M2 tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 M2))) (=> (= X _let_1) (=> (= Xa tptp.one) (=> (= Y tptp.none_num) (not (tptp.accp_P3113834385874906142um_num tptp.bit_un4731106466462545111um_rel (tptp.product_Pair_num_num _let_1 tptp.one)))))))) (=> (forall ((M2 tptp.num)) (=> (= X (tptp.aa_num_num tptp.bit0 M2)) (forall ((N2 tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 N2))) (=> (= Xa _let_1) (=> (= Y (tptp.map_option_num_num tptp.bit0 (tptp.aa_num_option_num (tptp.aa_num6390622462783740633on_num tptp.bit_un7362597486090784418nd_num M2) N2))) (not (tptp.accp_P3113834385874906142um_num tptp.bit_un4731106466462545111um_rel (tptp.product_Pair_num_num (tptp.aa_num_num tptp.bit0 M2) _let_1))))))))) (=> (forall ((M2 tptp.num)) (=> (= X (tptp.aa_num_num tptp.bit0 M2)) (forall ((N2 tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit1 N2))) (=> (= Xa _let_1) (=> (= Y (tptp.map_option_num_num tptp.bit0 (tptp.aa_num_option_num (tptp.aa_num6390622462783740633on_num tptp.bit_un7362597486090784418nd_num M2) N2))) (not (tptp.accp_P3113834385874906142um_num tptp.bit_un4731106466462545111um_rel (tptp.product_Pair_num_num (tptp.aa_num_num tptp.bit0 M2) _let_1))))))))) (=> (forall ((M2 tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit1 M2))) (=> (= X _let_1) (=> (= Xa tptp.one) (=> (= Y (tptp.some_num tptp.one)) (not (tptp.accp_P3113834385874906142um_num tptp.bit_un4731106466462545111um_rel (tptp.product_Pair_num_num _let_1 tptp.one)))))))) (=> (forall ((M2 tptp.num)) (=> (= X (tptp.aa_num_num tptp.bit1 M2)) (forall ((N2 tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 N2))) (=> (= Xa _let_1) (=> (= Y (tptp.map_option_num_num tptp.bit0 (tptp.aa_num_option_num (tptp.aa_num6390622462783740633on_num tptp.bit_un7362597486090784418nd_num M2) N2))) (not (tptp.accp_P3113834385874906142um_num tptp.bit_un4731106466462545111um_rel (tptp.product_Pair_num_num (tptp.aa_num_num tptp.bit1 M2) _let_1))))))))) (not (forall ((M2 tptp.num)) (=> (= X (tptp.aa_num_num tptp.bit1 M2)) (forall ((N2 tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit1 N2))) (=> (= Xa _let_1) (=> (= Y (tptp.case_o6005452278849405969um_num (tptp.some_num tptp.one) tptp.aTP_Lamm_dz (tptp.aa_num_option_num (tptp.aa_num6390622462783740633on_num tptp.bit_un7362597486090784418nd_num M2) N2))) (not (tptp.accp_P3113834385874906142um_num tptp.bit_un4731106466462545111um_rel (tptp.product_Pair_num_num (tptp.aa_num_num tptp.bit1 M2) _let_1)))))))))))))))))))))) (forall ((X tptp.num) (Xa tptp.num) (Y tptp.option_num)) (let ((_let_1 (= X tptp.one))) (=> (= (tptp.aa_num_option_num (tptp.aa_num6390622462783740633on_num tptp.bit_un2480387367778600638or_num X) Xa) Y) (=> (tptp.accp_P3113834385874906142um_num tptp.bit_un2901131394128224187um_rel (tptp.product_Pair_num_num X Xa)) (=> (=> _let_1 (=> (= Xa tptp.one) (=> (= Y 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) (=> (= Y (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) (=> (= Y (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 ((M2 tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 M2))) (=> (= X _let_1) (=> (= Xa tptp.one) (=> (= Y (tptp.some_num (tptp.aa_num_num tptp.bit1 M2))) (not (tptp.accp_P3113834385874906142um_num tptp.bit_un2901131394128224187um_rel (tptp.product_Pair_num_num _let_1 tptp.one)))))))) (=> (forall ((M2 tptp.num)) (=> (= X (tptp.aa_num_num tptp.bit0 M2)) (forall ((N2 tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 N2))) (=> (= Xa _let_1) (=> (= Y (tptp.map_option_num_num tptp.bit0 (tptp.aa_num_option_num (tptp.aa_num6390622462783740633on_num tptp.bit_un2480387367778600638or_num M2) N2))) (not (tptp.accp_P3113834385874906142um_num tptp.bit_un2901131394128224187um_rel (tptp.product_Pair_num_num (tptp.aa_num_num tptp.bit0 M2) _let_1))))))))) (=> (forall ((M2 tptp.num)) (=> (= X (tptp.aa_num_num tptp.bit0 M2)) (forall ((N2 tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit1 N2))) (=> (= Xa _let_1) (=> (= Y (tptp.some_num (tptp.case_option_num_num tptp.one tptp.bit1 (tptp.aa_num_option_num (tptp.aa_num6390622462783740633on_num tptp.bit_un2480387367778600638or_num M2) N2)))) (not (tptp.accp_P3113834385874906142um_num tptp.bit_un2901131394128224187um_rel (tptp.product_Pair_num_num (tptp.aa_num_num tptp.bit0 M2) _let_1))))))))) (=> (forall ((M2 tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit1 M2))) (=> (= X _let_1) (=> (= Xa tptp.one) (=> (= Y (tptp.some_num (tptp.aa_num_num tptp.bit0 M2))) (not (tptp.accp_P3113834385874906142um_num tptp.bit_un2901131394128224187um_rel (tptp.product_Pair_num_num _let_1 tptp.one)))))))) (=> (forall ((M2 tptp.num)) (=> (= X (tptp.aa_num_num tptp.bit1 M2)) (forall ((N2 tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 N2))) (=> (= Xa _let_1) (=> (= Y (tptp.some_num (tptp.case_option_num_num tptp.one tptp.bit1 (tptp.aa_num_option_num (tptp.aa_num6390622462783740633on_num tptp.bit_un2480387367778600638or_num M2) N2)))) (not (tptp.accp_P3113834385874906142um_num tptp.bit_un2901131394128224187um_rel (tptp.product_Pair_num_num (tptp.aa_num_num tptp.bit1 M2) _let_1))))))))) (not (forall ((M2 tptp.num)) (=> (= X (tptp.aa_num_num tptp.bit1 M2)) (forall ((N2 tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit1 N2))) (=> (= Xa _let_1) (=> (= Y (tptp.map_option_num_num tptp.bit0 (tptp.aa_num_option_num (tptp.aa_num6390622462783740633on_num tptp.bit_un2480387367778600638or_num M2) N2))) (not (tptp.accp_P3113834385874906142um_num tptp.bit_un2901131394128224187um_rel (tptp.product_Pair_num_num (tptp.aa_num_num tptp.bit1 M2) _let_1)))))))))))))))))))))) (forall ((X tptp.num) (Xa tptp.num) (Y tptp.num)) (let ((_let_1 (= X tptp.one))) (=> (= (tptp.bit_or_not_num_neg X Xa) Y) (=> (tptp.accp_P3113834385874906142um_num tptp.bit_or3848514188828904588eg_rel (tptp.product_Pair_num_num X Xa)) (=> (=> _let_1 (=> (= Xa tptp.one) (=> (= Y tptp.one) (not (tptp.accp_P3113834385874906142um_num tptp.bit_or3848514188828904588eg_rel (tptp.product_Pair_num_num tptp.one tptp.one)))))) (=> (=> _let_1 (forall ((M2 tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 M2))) (=> (= Xa _let_1) (=> (= Y (tptp.aa_num_num tptp.bit1 M2)) (not (tptp.accp_P3113834385874906142um_num tptp.bit_or3848514188828904588eg_rel (tptp.product_Pair_num_num tptp.one _let_1)))))))) (=> (=> _let_1 (forall ((M2 tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit1 M2))) (=> (= Xa _let_1) (=> (= Y _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) (=> (= Y (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 ((M2 tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 M2))) (=> (= Xa _let_1) (=> (= Y (tptp.bitM (tptp.bit_or_not_num_neg N2 M2))) (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 ((M2 tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit1 M2))) (=> (= Xa _let_1) (=> (= Y (tptp.aa_num_num tptp.bit0 (tptp.bit_or_not_num_neg N2 M2))) (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) (=> (= Y 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 ((M2 tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 M2))) (=> (= Xa _let_1) (=> (= Y (tptp.bitM (tptp.bit_or_not_num_neg N2 M2))) (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 ((M2 tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit1 M2))) (=> (= Xa _let_1) (=> (= Y (tptp.bitM (tptp.bit_or_not_num_neg N2 M2))) (not (tptp.accp_P3113834385874906142um_num tptp.bit_or3848514188828904588eg_rel (tptp.product_Pair_num_num (tptp.aa_num_num tptp.bit1 N2) _let_1)))))))))))))))))))))) (= tptp.bit_un2901131394128224187um_rel tptp.bit_un3595099601533988841um_rel) (= tptp.bit_un4731106466462545111um_rel tptp.bit_un5425074673868309765um_rel) (tptp.bNF_re6323452265856231590at_rat tptp.pcr_rat _let_36 tptp.aTP_Lamm_ek tptp.plus_plus_rat) (tptp.pp (tptp.aa_rat_bool (tptp.aa_Pro6332413336323567195t_bool tptp.pcr_rat _let_38) tptp.one_one_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_Pro6332413336323567195t_bool tptp.pcr_rat _let_37) tptp.zero_zero_rat)) (tptp.bNF_re2486238095283335024nt_rat tptp.fequal_int (tptp.bNF_re2214769303045360666nt_rat tptp.fequal_int tptp.pcr_rat) tptp.aTP_Lamm_hc tptp.fract) (tptp.bNF_re6323452265856231590at_rat tptp.pcr_rat _let_36 tptp.aTP_Lamm_en tptp.times_times_rat) (tptp.bNF_re3535474257078034868l_bool tptp.pcr_rat tptp.fequal_bool tptp.aTP_Lamm_eh tptp.positive) (tptp.pp (tptp.aa_fun_rat_rat_bool (tptp.aa_fun2103967415933125506t_bool _let_36 tptp.aTP_Lamm_eo) tptp.inverse_inverse_rat)) (tptp.bNF_re8869769828555196650nt_int tptp.pcr_int _let_35 _let_34 tptp.times_times_int) (tptp.pp (tptp.aa_int_bool (tptp.aa_Pro2928840338864870335t_bool tptp.pcr_int _let_32) tptp.zero_zero_int)) (tptp.bNF_re6830278522597306478at_int tptp.fequal_nat tptp.pcr_int tptp.aTP_Lamm_hd tptp.semiri1314217659103216013at_int) (tptp.pp (tptp.aa_fun_int_int_bool (tptp.aa_fun7527181275634263258t_bool _let_35 _let_31) tptp.uminus_uminus_int)) (tptp.bNF_re4555766996558763186at_nat tptp.pcr_int tptp.fequal_nat _let_30 tptp.nat2) (tptp.pp (tptp.aa_int_bool (tptp.aa_Pro2928840338864870335t_bool tptp.pcr_int _let_29) tptp.one_one_int)) (tptp.bNF_re2632563231991741785t_bool tptp.pcr_int _let_33 _let_28 tptp.ord_less_int) (tptp.bNF_re2632563231991741785t_bool tptp.pcr_int _let_33 _let_26 tptp.ord_less_eq_int) (tptp.bNF_re8869769828555196650nt_int tptp.pcr_int _let_35 _let_23 tptp.plus_plus_int) (tptp.bNF_re8869769828555196650nt_int tptp.pcr_int _let_35 _let_25 tptp.minus_minus_int) (tptp.bNF_re6214786843070381989at_nat tptp.intrel _let_24 _let_34 _let_34) (forall ((X tptp.nat) (Y tptp.nat) (U tptp.nat) (V tptp.nat)) (= (tptp.pp (tptp.aa_Pro2232559814647311250t_bool (tptp.aa_Pro595088089689268830t_bool tptp.intrel (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat X) Y)) (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat U) V))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat X) V) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat U) Y)))) (tptp.bNF_re2632563231991741785t_bool tptp.pcr_int _let_33 tptp.intrel tptp.fequal_int) (forall ((X tptp.product_prod_nat_nat) (Y tptp.product_prod_nat_nat)) (= (= (tptp.aa_Pro4240683299535347697at_int tptp.abs_Integ X) (tptp.aa_Pro4240683299535347697at_int tptp.abs_Integ Y)) (tptp.pp (tptp.aa_Pro2232559814647311250t_bool (tptp.aa_Pro595088089689268830t_bool tptp.intrel X) Y)))) (tptp.pp (tptp.aa_Pro2232559814647311250t_bool (tptp.aa_Pro595088089689268830t_bool tptp.intrel _let_32) _let_32)) (tptp.pp (tptp.aa_fun4519828053337421206t_bool (tptp.aa_fun2399787666232550060t_bool _let_24 _let_31) _let_31)) (tptp.bNF_re8246922863344978751at_nat tptp.intrel tptp.fequal_nat _let_30 _let_30) (tptp.pp (tptp.aa_Pro2232559814647311250t_bool (tptp.aa_Pro595088089689268830t_bool tptp.intrel _let_29) _let_29)) (forall ((A2 tptp.set_nat) (M tptp.nat)) (= (tptp.produc457027306803732586at_nat A2 (tptp.aTP_Lamm_he M)) (tptp.sup_su6327502436637775413at_nat (tptp.produc457027306803732586at_nat A2 (tptp.aTP_Lamm_hf M)) (tptp.produc457027306803732586at_nat A2 (tptp.aTP_Lamm_hg M))))) (= tptp.intrel (tptp.produc5023667602222594023t_bool tptp.aTP_Lamm_hi)) (forall ((M tptp.nat)) (= (tptp.collec3392354462482085612at_nat (tptp.produc8955392012077580105t_bool (tptp.aTP_Lamm_hj M))) (tptp.produc457027306803732586at_nat (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat M) (tptp.aTP_Lamm_hf M)))) (tptp.bNF_re2219331435504962769t_bool tptp.intrel _let_27 _let_28 _let_28) (tptp.bNF_re2219331435504962769t_bool tptp.intrel _let_27 _let_26 _let_26) (tptp.bNF_re6214786843070381989at_nat tptp.intrel _let_24 _let_25 _let_25) (tptp.bNF_re6214786843070381989at_nat tptp.intrel _let_24 _let_23 _let_23) (= tptp.field_5140801741446780682s_real (tptp.collect_real tptp.aTP_Lamm_hk)) (forall ((P2 tptp.rat) (Q2 tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat P2) Q2)) (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.produc8560705615207772305t_bool (tptp.aTP_Lamm_hm Q2)) (tptp.quotient_of P2))))) (forall ((P2 tptp.rat)) (= (tptp.archim3151403230148437115or_rat P2) (tptp.produc8211389475949308722nt_int tptp.divide_divide_int (tptp.quotient_of P2)))) (forall ((P2 tptp.rat) (Q2 tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat P2) Q2)) (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.produc8560705615207772305t_bool (tptp.aTP_Lamm_ho Q2)) (tptp.quotient_of P2))))) (= tptp.field_5140801741446780682s_real (tptp.collect_real tptp.aTP_Lamm_hp)) (forall ((Qr tptp.product_prod_int_int)) (= (tptp.adjust_div Qr) (tptp.produc8211389475949308722nt_int tptp.aTP_Lamm_hq Qr))) (forall ((D tptp.int)) (= (tptp.int_ge_less_than D) (tptp.collec213857154873943460nt_int (tptp.produc8560705615207772305t_bool (tptp.aTP_Lamm_hr D))))) (forall ((D tptp.int)) (= (tptp.int_ge_less_than2 D) (tptp.collec213857154873943460nt_int (tptp.produc8560705615207772305t_bool (tptp.aTP_Lamm_hs D))))) (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) (Deg tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Deg) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat Deg) _let_1)))) (=> (= X (tptp.vEBT_Node Mima Deg TreeList2 Summary)) (and (= Deg 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 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 TreeList2) (tptp.aa_nat_nat (tptp.aa_nat_fun_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 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_ht Deg) TreeList2) Summary)) 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) (Deg tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Deg) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat Deg) _let_1)))) (=> (= X (tptp.vEBT_Node Mima Deg TreeList2 Summary)) (not (and (= Deg 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 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 TreeList2) (tptp.aa_nat_nat (tptp.aa_nat_fun_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 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_ht Deg) TreeList2) Summary)) Mima))))))))))) (forall ((Mima2 tptp.option4927543243414619207at_nat) (Deg3 tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary3 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 Deg3) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat Deg3) _let_1)))) (= (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_VEBT_valid (tptp.vEBT_Node Mima2 Deg3 TreeList Summary3)) Deg4)) (and (= Deg3 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 Deg3) (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 Summary3) _let_2)) (= (tptp.size_s6755466524823107622T_VEBT TreeList) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat _let_1) _let_2)) (tptp.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 Summary3)))) (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_ht Deg3) TreeList) Summary3)) Mima2)))))) (forall ((X tptp.vEBT_VEBT) (Xa tptp.nat) (Y tptp.bool)) (let ((_let_1 (tptp.pp Y))) (=> (= (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) (Deg tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Deg) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat Deg) _let_1)))) (=> (= X (tptp.vEBT_Node Mima Deg TreeList2 Summary)) (= (tptp.pp Y) (not (and (= Deg 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 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 TreeList2) (tptp.aa_nat_nat (tptp.aa_nat_fun_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 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_ht Deg) TreeList2) Summary)) Mima))))))))))))) (forall ((X tptp.vEBT_VEBT) (Xa tptp.nat) (Y tptp.bool)) (=> (= (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_VEBT_valid X) Xa)) (tptp.pp Y)) (=> (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 Y) (= 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) (Deg tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (tptp.vEBT_Node Mima Deg TreeList2 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.minus_minus_nat Deg) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat Deg) _let_2)))) (=> (= X _let_1) (=> (= (tptp.pp Y) (and (= Deg 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 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_3)) (= (tptp.size_s6755466524823107622T_VEBT TreeList2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat _let_2) _let_3)) (tptp.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 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_ht Deg) TreeList2) Summary)) Mima))) (not (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel (tptp.produc738532404422230701BT_nat _let_1 Xa)))))))))))))) (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) (Deg tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Deg) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat Deg) _let_1)))) (let ((_let_3 (tptp.vEBT_Node Mima Deg TreeList2 Summary))) (=> (= X _let_3) (=> (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel (tptp.produc738532404422230701BT_nat _let_3 Xa)) (not (and (= Deg 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 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 TreeList2) (tptp.aa_nat_nat (tptp.aa_nat_fun_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 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_ht Deg) TreeList2) Summary)) 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) (Deg tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Deg) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat Deg) _let_1)))) (let ((_let_3 (tptp.vEBT_Node Mima Deg TreeList2 Summary))) (=> (= X _let_3) (=> (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel (tptp.produc738532404422230701BT_nat _let_3 Xa)) (and (= Deg 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 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 TreeList2) (tptp.aa_nat_nat (tptp.aa_nat_fun_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 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_ht Deg) TreeList2) Summary)) Mima))))))))))))) (tptp.bNF_re2717234250851183977l_bool tptp.realrel tptp.fequal_bool tptp.aTP_Lamm_hu tptp.aTP_Lamm_hu) (tptp.pp (tptp.aa_fun_nat_rat_bool (tptp.aa_fun6650786570619099624t_bool tptp.realrel tptp.aTP_Lamm_hv) tptp.aTP_Lamm_hv)) (tptp.pp (tptp.aa_fun_nat_rat_bool (tptp.aa_fun6650786570619099624t_bool tptp.realrel tptp.aTP_Lamm_hw) tptp.aTP_Lamm_hw)) (tptp.bNF_re769765379126235449at_rat tptp.realrel _let_22 tptp.aTP_Lamm_hx tptp.aTP_Lamm_hx) (tptp.bNF_re769765379126235449at_rat tptp.realrel _let_22 tptp.aTP_Lamm_hy tptp.aTP_Lamm_hy) (tptp.pp (tptp.aa_fun1696419067750587730t_bool (tptp.aa_fun4901480949278917796t_bool _let_22 tptp.aTP_Lamm_hz) tptp.aTP_Lamm_hz)) (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))) (tptp.pp (tptp.aa_fun1696419067750587730t_bool (tptp.aa_fun4901480949278917796t_bool _let_22 tptp.aTP_Lamm_ib) tptp.aTP_Lamm_ib)) (= (tptp.aa_nat_set_nat tptp.set_ord_atLeast_nat tptp.zero_zero_nat) tptp.top_top_set_nat) (forall ((C tptp.rat)) (= (tptp.pp (tptp.vanishes (tptp.aTP_Lamm_ic C))) (= C tptp.zero_zero_rat))) (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 ((K tptp.nat)) (= (tptp.aa_nat_set_nat tptp.set_ord_atLeast_nat (tptp.aa_nat_nat tptp.suc K)) (tptp.aa_nat_set_nat tptp.set_or1210151606488870762an_nat K))) (forall ((X7 tptp.fun_nat_rat)) (=> (tptp.pp (tptp.vanishes X7)) (tptp.pp (tptp.vanishes (tptp.aa_fun765758790203053448at_rat tptp.aTP_Lamm_hz X7))))) (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) (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_id X7) Y6)))))) (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 ((K2 tptp.nat)) (forall ((N5 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K2) N5)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.abs_abs_rat (tptp.aa_nat_rat X7 N5))) R5))))))))) (forall ((X7 tptp.fun_nat_rat)) (=> (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)) (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.abs_abs_rat (tptp.aa_nat_rat X7 N2))) R2))))))) (tptp.pp (tptp.vanishes X7)))) (forall ((X7 tptp.fun_nat_rat) (R 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) R)) (exists ((K3 tptp.nat)) (forall ((N6 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K3) N6)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.abs_abs_rat (tptp.aa_nat_rat X7 N6))) R)))))))) (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.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_hy X7) Y6)))))) (forall ((K tptp.nat)) (= (tptp.aa_nat_set_nat tptp.set_ord_atLeast_nat (tptp.aa_nat_nat tptp.suc K)) (tptp.minus_minus_set_nat (tptp.aa_nat_set_nat tptp.set_ord_atLeast_nat K) (tptp.insert_nat K tptp.bot_bot_set_nat)))) (tptp.pp (tptp.aa_fun9137951878280015556l_bool (tptp.aa_fun9159459243913713430l_bool _let_21 tptp.aTP_Lamm_ib) tptp.inverse_inverse_real)) (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_hv (tptp.aTP_Lamm_ia X)))))) (= tptp.one_one_real (tptp.aa_fun_nat_rat_real tptp.real2 tptp.aTP_Lamm_hw)) (forall ((P tptp.fun_real_bool) (X tptp.real)) (=> (forall ((Y3 tptp.fun_nat_rat)) (=> (tptp.pp (tptp.aa_fun_nat_rat_bool (tptp.aa_fun6650786570619099624t_bool tptp.realrel Y3) Y3)) (tptp.pp (tptp.aa_real_bool P (tptp.aa_fun_nat_rat_real tptp.real2 Y3))))) (tptp.pp (tptp.aa_real_bool P 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_ic X)))) (= tptp.zero_zero_real (tptp.aa_fun_nat_rat_real tptp.real2 tptp.aTP_Lamm_hv)) (tptp.bNF_re8935275315890131625l_bool tptp.pcr_real _let_20 tptp.realrel tptp.fequal_real) (forall ((X tptp.int)) (= (tptp.ring_1_of_int_real X) (tptp.aa_fun_nat_rat_real tptp.real2 (tptp.aTP_Lamm_ie X)))) (tptp.pp (tptp.aa_real_bool (tptp.aa_fun5258240734392065441l_bool tptp.pcr_real tptp.aTP_Lamm_hv) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_fun5258240734392065441l_bool tptp.pcr_real tptp.aTP_Lamm_hw) tptp.one_one_real)) (forall ((X tptp.nat)) (= (tptp.aa_nat_real tptp.semiri5074537144036343181t_real X) (tptp.aa_fun_nat_rat_real tptp.real2 (tptp.aTP_Lamm_if X)))) (tptp.pp (tptp.aa_fun9137951878280015556l_bool (tptp.aa_fun9159459243913713430l_bool _let_21 tptp.aTP_Lamm_hz) tptp.uminus_uminus_real)) (tptp.bNF_re1162444993429354318l_real tptp.pcr_real _let_21 tptp.aTP_Lamm_hx tptp.plus_plus_real) (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_hz X))))) (tptp.bNF_re1162444993429354318l_real tptp.pcr_real _let_21 tptp.aTP_Lamm_hy tptp.times_times_real) (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_hy Xa) X)))))) (tptp.pp (tptp.aa_fun3352386287069783311l_bool (tptp.aa_fun7221085148252759141l_bool _let_20 tptp.aTP_Lamm_hu) tptp.positive2)) (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 ((K2 tptp.nat)) (forall ((N5 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K2) N5)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat R5) (tptp.aa_nat_rat X N5))))))))))) (forall ((X tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool tptp.positive2 X)) (=> (tptp.pp (tptp.aa_real_bool tptp.positive2 Y)) (tptp.pp (tptp.aa_real_bool tptp.positive2 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real X) Y)))))) (forall ((X tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool tptp.positive2 X)) (=> (tptp.pp (tptp.aa_real_bool tptp.positive2 Y)) (tptp.pp (tptp.aa_real_bool tptp.positive2 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) Y)))))) (not (tptp.pp (tptp.aa_real_bool tptp.positive2 tptp.zero_zero_real))) (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)))))) (forall ((X tptp.real) (Y tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Y)) (tptp.pp (tptp.aa_real_bool tptp.positive2 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real Y) X))))) (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 ((K2 tptp.nat)) (forall ((N5 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K2) N5)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat X7 N5)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_nat_rat Y6 N5)) R5)))))))))))) (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 ((K2 tptp.nat)) (forall ((N5 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K2) N5)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat R5) (tptp.aa_nat_rat (tptp.aa_real_fun_nat_rat tptp.rep_real X) N5)))))))))) (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) (Y6 tptp.fun_nat_rat)) (=> (tptp.cauchy X7) (=> (tptp.cauchy Y6) (tptp.cauchy (tptp.aa_fun765758790203053448at_rat (tptp.aTP_Lamm_id 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.aa_fun3638354034882855594at_rat tptp.aTP_Lamm_hy 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.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_hz X7)))) (forall ((X tptp.rat)) (tptp.cauchy (tptp.aTP_Lamm_ic X))) (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 ((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 ((X7 tptp.fun_nat_rat)) (=> (tptp.cauchy X7) (=> (not (tptp.pp (tptp.vanishes X7))) (tptp.cauchy (tptp.aTP_Lamm_ia X7))))) (forall ((X7 tptp.fun_nat_rat)) (=> (tptp.cauchy X7) (exists ((B3 tptp.rat)) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) B3)) (forall ((N6 tptp.nat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.abs_abs_rat (tptp.aa_nat_rat X7 N6))) B3))))))) (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 ((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) (Y 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))) Y))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_fun_nat_rat_real tptp.real2 X7)) Y))))) (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_hz 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_hy 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_id 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_id 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_id 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_id X7) Y6))) (tptp.pp (tptp.vanishes (tptp.aa_fun765758790203053448at_rat (tptp.aTP_Lamm_ig 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_id X4) Xa2)))))) (forall ((X7 tptp.fun_nat_rat)) (=> (tptp.cauchy X7) (=> (not (tptp.pp (tptp.vanishes X7))) (exists ((B3 tptp.rat)) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) B3)) (exists ((K3 tptp.nat)) (or (forall ((N6 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K3) N6)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B3) (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 K3) N6)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B3) (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 ((K2 tptp.nat)) (forall ((N5 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K2) N5)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat R5) (tptp.aa_nat_rat X7 N5))))))))))) (forall ((X7 tptp.fun_nat_rat)) (=> (tptp.cauchy X7) (=> (not (tptp.pp (tptp.vanishes X7))) (exists ((B3 tptp.rat)) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) B3)) (exists ((K3 tptp.nat)) (forall ((N6 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K3) N6)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B3) (tptp.abs_abs_rat (tptp.aa_nat_rat X7 N6)))))))))))) (forall ((X7 tptp.fun_nat_rat) (R 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) R)) (exists ((K3 tptp.nat)) (forall ((M3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K3) M3)) (forall ((N6 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K3) N6)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.abs_abs_rat (tptp.minus_minus_rat (tptp.aa_nat_rat X7 M3) (tptp.aa_nat_rat X7 N6)))) R)))))))))) (forall ((X7 tptp.fun_nat_rat)) (=> (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)) (exists ((K4 tptp.nat)) (forall ((M2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K4) M2)) (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.abs_abs_rat (tptp.minus_minus_rat (tptp.aa_nat_rat X7 M2) (tptp.aa_nat_rat X7 N2)))) R2))))))))) (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 ((K2 tptp.nat)) (forall ((M6 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K2) M6)) (forall ((N5 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K2) N5)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.abs_abs_rat (tptp.minus_minus_rat (tptp.aa_nat_rat X7 M6) (tptp.aa_nat_rat X7 N5)))) 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_ia 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 ((K2 tptp.nat)) (forall ((N5 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K2) N5)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat X7 N5)) R5)))))))))) (= tptp.positive2 (tptp.map_fu1722713901878115497l_bool tptp.rep_real tptp.id_bool tptp.aTP_Lamm_hu)) (= tptp.inverse_inverse_real (tptp.aa_fun8686829112900759002l_real _let_19 tptp.aTP_Lamm_ib)) (= tptp.uminus_uminus_real (tptp.aa_fun8686829112900759002l_real _let_19 tptp.aTP_Lamm_hz)) (= tptp.times_times_real (tptp.map_fu2502140041903272327l_real tptp.rep_real _let_19 tptp.aTP_Lamm_hy)) (= tptp.plus_plus_real (tptp.map_fu2502140041903272327l_real tptp.rep_real _let_19 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.pcr_real tptp.cr_real) (forall ((F tptp.fun_nat_real) (M10 tptp.nat)) (=> (tptp.bfun_nat_real (tptp.aa_nat_fun_nat_real (tptp.aTP_Lamm_ih F) M10) tptp.at_top_nat) (=> (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M10) M2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M2) 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 M2)))))) (tptp.topolo7531315842566124627t_real F)))) (forall ((F tptp.fun_nat_real) (M10 tptp.nat)) (=> (tptp.bfun_nat_real (tptp.aa_nat_fun_nat_real (tptp.aTP_Lamm_ih F) M10) tptp.at_top_nat) (=> (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M10) M2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M2) N2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_nat_real F M2)) (tptp.aa_nat_real F N2)))))) (tptp.topolo7531315842566124627t_real F)))) (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 ((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 ((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.aa_nat_set_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.aa_nat_set_nat tptp.nat_set_decode X)))) (= tptp.euclid4777050414544973029ze_nat tptp.id_nat) (= tptp.euclid4774559944035922753ze_int _let_18) (forall ((K tptp.int)) (= (tptp.aa_int_int tptp.abs_abs_int (tptp.euclid3395696857347342551nt_int K)) tptp.one_one_int)) (forall ((K tptp.int)) (=> (not (= K tptp.zero_zero_int)) (= (tptp.euclid3395696857347342551nt_int K) (tptp.aa_int_int tptp.sgn_sgn_int K)))) (forall ((N tptp.nat)) (= (tptp.aa_nat_nat tptp.euclid3398187327856392827nt_nat N) tptp.one_one_nat)) (forall ((K tptp.int)) (let ((_let_1 (tptp.euclid3395696857347342551nt_int K))) (let ((_let_2 (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) K)))) (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))))))) (tptp.transp_fun_nat_rat tptp.realrel) (tptp.pp (tptp.aa_nat_bool (tptp.ordering_top_nat tptp.aTP_Lamm_af tptp.aTP_Lamm_bu) tptp.zero_zero_nat)) (forall ((F tptp.fun_nat_nat) (N tptp.nat)) (=> (tptp.order_5726023648592871131at_nat F) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N) (tptp.aa_nat_nat F N))))) (tptp.pp (tptp.aa_nat_bool (tptp.ordering_top_nat tptp.dvd_dvd_nat tptp.aTP_Lamm_dj) tptp.zero_zero_nat)) (forall ((K tptp.nat) (M tptp.nat)) (= (tptp.aa_nat7603221163087113075at_nat tptp.nat_prod_decode (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat tptp.nat_triangle K)) M)) (tptp.aa_nat7603221163087113075at_nat (tptp.nat_prod_decode_aux K) M))) (forall ((X tptp.nat) (Y tptp.nat)) (= (= (tptp.aa_nat7603221163087113075at_nat tptp.nat_prod_decode X) (tptp.aa_nat7603221163087113075at_nat tptp.nat_prod_decode Y)) (= X Y))) (forall ((X tptp.product_prod_nat_nat)) (= (tptp.aa_nat7603221163087113075at_nat tptp.nat_prod_decode (tptp.aa_Pro4243173770044397973at_nat tptp.nat_prod_encode X)) X)) (forall ((N tptp.nat)) (= (tptp.aa_Pro4243173770044397973at_nat tptp.nat_prod_encode (tptp.aa_nat7603221163087113075at_nat tptp.nat_prod_decode N)) N)) (forall ((A2 tptp.set_nat)) (tptp.pp (tptp.aa_set_nat_bool (tptp.inj_on5538052773655684606at_nat tptp.nat_prod_decode) A2))) (= tptp.nat_prod_decode (tptp.nat_prod_decode_aux tptp.zero_zero_nat)) (= (tptp.image_5846123807819985514at_nat tptp.nat_prod_decode tptp.top_top_set_nat) tptp.top_to4669805908274784177at_nat) (tptp.bij_be8693218025023041337at_nat tptp.nat_prod_decode tptp.top_top_set_nat tptp.top_to4669805908274784177at_nat) (forall ((A0 tptp.nat) (P tptp.fun_nat_bool)) (let ((_let_1 (tptp.accp_nat tptp.nat_list_decode_rel))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 A0)) (=> (=> (tptp.pp (tptp.aa_nat_bool _let_1 tptp.zero_zero_nat)) (tptp.pp (tptp.aa_nat_bool P tptp.zero_zero_nat))) (=> (forall ((N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N2))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.accp_nat tptp.nat_list_decode_rel) _let_1)) (=> (forall ((X4 tptp.nat) (Y4 tptp.nat)) (=> (= (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat X4) Y4) (tptp.aa_nat7603221163087113075at_nat tptp.nat_prod_decode N2)) (tptp.pp (tptp.aa_nat_bool P Y4)))) (tptp.pp (tptp.aa_nat_bool P _let_1)))))) (tptp.pp (tptp.aa_nat_bool P A0))))))) (forall ((X tptp.nat) (Y tptp.list_nat)) (=> (= (tptp.aa_nat_list_nat tptp.nat_list_decode X) Y) (=> (=> (= X tptp.zero_zero_nat) (not (= Y tptp.nil_nat))) (not (forall ((N2 tptp.nat)) (=> (= X (tptp.aa_nat_nat tptp.suc N2)) (not (= Y (tptp.produc2761476792215241774st_nat tptp.aTP_Lamm_ii (tptp.aa_nat7603221163087113075at_nat tptp.nat_prod_decode N2)))))))))) (forall ((X tptp.list_nat)) (= (tptp.aa_nat_list_nat tptp.nat_list_decode (tptp.aa_list_nat_nat tptp.nat_list_encode X)) X)) (forall ((N tptp.nat)) (= (tptp.aa_list_nat_nat tptp.nat_list_encode (tptp.aa_nat_list_nat tptp.nat_list_decode N)) N)) (forall ((X tptp.nat) (Y tptp.nat)) (= (= (tptp.aa_nat_list_nat tptp.nat_list_decode X) (tptp.aa_nat_list_nat tptp.nat_list_decode Y)) (= X Y))) (forall ((A2 tptp.set_nat)) (tptp.pp (tptp.aa_set_nat_bool (tptp.inj_on_nat_list_nat tptp.nat_list_decode) A2))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.accp_nat tptp.nat_list_decode_rel) tptp.zero_zero_nat)) _let_17) _let_17 (forall ((N tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.accp_nat tptp.nat_list_decode_rel) _let_1)) (= (tptp.aa_nat_list_nat tptp.nat_list_decode _let_1) (tptp.produc2761476792215241774st_nat tptp.aTP_Lamm_ii (tptp.aa_nat7603221163087113075at_nat tptp.nat_prod_decode N)))))) (tptp.bij_be6293887246118711976st_nat tptp.nat_list_decode tptp.top_top_set_nat tptp.top_top_set_list_nat) (= (tptp.image_nat_list_nat tptp.nat_list_decode tptp.top_top_set_nat) tptp.top_top_set_list_nat) (forall ((N tptp.nat)) (= (tptp.aa_nat_list_nat tptp.nat_list_decode (tptp.aa_nat_nat tptp.suc N)) (tptp.produc2761476792215241774st_nat tptp.aTP_Lamm_ii (tptp.aa_nat7603221163087113075at_nat tptp.nat_prod_decode N)))) (forall ((X tptp.nat) (Y tptp.list_nat)) (let ((_let_1 (tptp.accp_nat tptp.nat_list_decode_rel))) (=> (= (tptp.aa_nat_list_nat tptp.nat_list_decode X) Y) (=> (tptp.pp (tptp.aa_nat_bool _let_1 X)) (=> (=> (= X tptp.zero_zero_nat) (=> (= Y tptp.nil_nat) (not (tptp.pp (tptp.aa_nat_bool _let_1 tptp.zero_zero_nat))))) (not (forall ((N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N2))) (=> (= X _let_1) (=> (= Y (tptp.produc2761476792215241774st_nat tptp.aTP_Lamm_ii (tptp.aa_nat7603221163087113075at_nat tptp.nat_prod_decode N2))) (not (tptp.pp (tptp.aa_nat_bool (tptp.accp_nat tptp.nat_list_decode_rel) _let_1))))))))))))) (forall ((B tptp.real) (I tptp.real)) (let ((_let_1 (tptp.aa_rea7683167438103758690t_real (tptp.aTP_Lamm_ij B) I))) (let ((_let_2 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.powr_real2 B) I))) (let ((_let_3 (tptp.archim6058952711729229775r_real I))) (let ((_let_4 (= (tptp.ring_1_of_int_real _let_3) I))) (let ((_let_5 (tptp.aa_real_fun_nat_real tptp.power_power_real B))) (let ((_let_6 (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) I)))) (let ((_let_7 (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real B) tptp.zero_zero_real)))) (and (=> _let_7 (= _let_2 (tptp.abort_real (tptp.literal2 tptp.fFalse tptp.fFalse tptp.fFalse tptp.fFalse tptp.fTrue tptp.fTrue tptp.fTrue (tptp.literal2 tptp.fTrue tptp.fTrue tptp.fTrue tptp.fTrue tptp.fFalse tptp.fTrue tptp.fTrue (tptp.literal2 tptp.fTrue tptp.fTrue tptp.fTrue tptp.fFalse tptp.fTrue tptp.fTrue tptp.fTrue (tptp.literal2 tptp.fFalse tptp.fTrue tptp.fFalse tptp.fFalse tptp.fTrue tptp.fTrue tptp.fTrue (tptp.literal2 tptp.fTrue tptp.fTrue tptp.fTrue tptp.fTrue tptp.fTrue tptp.fFalse tptp.fTrue (tptp.literal2 tptp.fFalse tptp.fTrue tptp.fFalse tptp.fFalse tptp.fTrue tptp.fTrue tptp.fTrue (tptp.literal2 tptp.fTrue tptp.fFalse tptp.fTrue tptp.fFalse tptp.fFalse tptp.fTrue tptp.fTrue (tptp.literal2 tptp.fTrue tptp.fFalse tptp.fFalse tptp.fFalse tptp.fFalse tptp.fTrue tptp.fTrue (tptp.literal2 tptp.fFalse tptp.fFalse tptp.fTrue tptp.fTrue tptp.fFalse tptp.fTrue tptp.fTrue (tptp.literal2 tptp.fFalse tptp.fFalse tptp.fFalse tptp.fFalse tptp.fFalse tptp.fTrue tptp.fFalse (tptp.literal2 tptp.fTrue tptp.fTrue tptp.fTrue tptp.fFalse tptp.fTrue tptp.fTrue tptp.fTrue (tptp.literal2 tptp.fTrue tptp.fFalse tptp.fFalse tptp.fTrue tptp.fFalse tptp.fTrue tptp.fTrue (tptp.literal2 tptp.fFalse tptp.fFalse tptp.fTrue tptp.fFalse tptp.fTrue tptp.fTrue tptp.fTrue (tptp.literal2 tptp.fFalse tptp.fFalse tptp.fFalse tptp.fTrue tptp.fFalse tptp.fTrue tptp.fTrue (tptp.literal2 tptp.fFalse tptp.fFalse tptp.fFalse tptp.fFalse tptp.fFalse tptp.fTrue tptp.fFalse (tptp.literal2 tptp.fFalse tptp.fTrue tptp.fTrue tptp.fTrue tptp.fFalse tptp.fTrue tptp.fTrue (tptp.literal2 tptp.fTrue tptp.fTrue tptp.fTrue tptp.fTrue tptp.fFalse tptp.fTrue tptp.fTrue (tptp.literal2 tptp.fFalse tptp.fTrue tptp.fTrue tptp.fTrue tptp.fFalse tptp.fTrue tptp.fTrue (tptp.literal2 tptp.fFalse tptp.fFalse tptp.fFalse tptp.fFalse tptp.fTrue tptp.fTrue tptp.fTrue (tptp.literal2 tptp.fTrue tptp.fTrue tptp.fTrue tptp.fTrue tptp.fFalse tptp.fTrue tptp.fTrue (tptp.literal2 tptp.fTrue tptp.fTrue tptp.fFalse tptp.fFalse tptp.fTrue tptp.fTrue tptp.fTrue (tptp.literal2 tptp.fTrue tptp.fFalse tptp.fFalse tptp.fTrue tptp.fFalse tptp.fTrue tptp.fTrue (tptp.literal2 tptp.fFalse tptp.fFalse tptp.fTrue tptp.fFalse tptp.fTrue tptp.fTrue tptp.fTrue (tptp.literal2 tptp.fTrue tptp.fFalse tptp.fFalse tptp.fTrue tptp.fFalse tptp.fTrue tptp.fTrue (tptp.literal2 tptp.fFalse tptp.fTrue tptp.fTrue tptp.fFalse tptp.fTrue tptp.fTrue tptp.fTrue (tptp.literal2 tptp.fTrue tptp.fFalse tptp.fTrue tptp.fFalse tptp.fFalse tptp.fTrue tptp.fTrue (tptp.literal2 tptp.fFalse tptp.fFalse tptp.fFalse tptp.fFalse tptp.fFalse tptp.fTrue tptp.fFalse (tptp.literal2 tptp.fFalse tptp.fTrue tptp.fFalse tptp.fFalse tptp.fFalse tptp.fTrue tptp.fTrue (tptp.literal2 tptp.fTrue tptp.fFalse tptp.fFalse tptp.fFalse tptp.fFalse tptp.fTrue tptp.fTrue (tptp.literal2 tptp.fTrue tptp.fTrue tptp.fFalse tptp.fFalse tptp.fTrue tptp.fTrue tptp.fTrue (tptp.literal2 tptp.fTrue tptp.fFalse tptp.fTrue tptp.fFalse tptp.fFalse tptp.fTrue tptp.fTrue tptp.zero_zero_literal))))))))))))))))))))))))))))))) _let_1))) (=> (not _let_7) (and (=> _let_4 (and (=> _let_6 (= _let_2 (tptp.aa_nat_real _let_5 (tptp.aa_int_nat tptp.nat2 _let_3)))) (=> (not _let_6) (= _let_2 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.one_one_real) (tptp.aa_nat_real _let_5 (tptp.aa_int_nat tptp.nat2 (tptp.archim6058952711729229775r_real (tptp.aa_real_real tptp.uminus_uminus_real I))))))))) (=> (not _let_4) (= _let_2 (tptp.abort_real (tptp.literal2 tptp.fFalse tptp.fFalse tptp.fFalse tptp.fFalse tptp.fTrue tptp.fTrue tptp.fTrue (tptp.literal2 tptp.fTrue tptp.fTrue tptp.fTrue tptp.fTrue tptp.fFalse tptp.fTrue tptp.fTrue (tptp.literal2 tptp.fTrue tptp.fTrue tptp.fTrue tptp.fFalse tptp.fTrue tptp.fTrue tptp.fTrue (tptp.literal2 tptp.fFalse tptp.fTrue tptp.fFalse tptp.fFalse tptp.fTrue tptp.fTrue tptp.fTrue (tptp.literal2 tptp.fTrue tptp.fTrue tptp.fTrue tptp.fTrue tptp.fTrue tptp.fFalse tptp.fTrue (tptp.literal2 tptp.fFalse tptp.fTrue tptp.fFalse tptp.fFalse tptp.fTrue tptp.fTrue tptp.fTrue (tptp.literal2 tptp.fTrue tptp.fFalse tptp.fTrue tptp.fFalse tptp.fFalse tptp.fTrue tptp.fTrue (tptp.literal2 tptp.fTrue tptp.fFalse tptp.fFalse tptp.fFalse tptp.fFalse tptp.fTrue tptp.fTrue (tptp.literal2 tptp.fFalse tptp.fFalse tptp.fTrue tptp.fTrue tptp.fFalse tptp.fTrue tptp.fTrue (tptp.literal2 tptp.fFalse tptp.fFalse tptp.fFalse tptp.fFalse tptp.fFalse tptp.fTrue tptp.fFalse (tptp.literal2 tptp.fTrue tptp.fTrue tptp.fTrue tptp.fFalse tptp.fTrue tptp.fTrue tptp.fTrue (tptp.literal2 tptp.fTrue tptp.fFalse tptp.fFalse tptp.fTrue tptp.fFalse tptp.fTrue tptp.fTrue (tptp.literal2 tptp.fFalse tptp.fFalse tptp.fTrue tptp.fFalse tptp.fTrue tptp.fTrue tptp.fTrue (tptp.literal2 tptp.fFalse tptp.fFalse tptp.fFalse tptp.fTrue tptp.fFalse tptp.fTrue tptp.fTrue (tptp.literal2 tptp.fFalse tptp.fFalse tptp.fFalse tptp.fFalse tptp.fFalse tptp.fTrue tptp.fFalse (tptp.literal2 tptp.fFalse tptp.fTrue tptp.fTrue tptp.fTrue tptp.fFalse tptp.fTrue tptp.fTrue (tptp.literal2 tptp.fTrue tptp.fTrue tptp.fTrue tptp.fTrue tptp.fFalse tptp.fTrue tptp.fTrue (tptp.literal2 tptp.fFalse tptp.fTrue tptp.fTrue tptp.fTrue tptp.fFalse tptp.fTrue tptp.fTrue (tptp.literal2 tptp.fTrue tptp.fFalse tptp.fTrue tptp.fTrue tptp.fFalse tptp.fTrue tptp.fFalse (tptp.literal2 tptp.fTrue tptp.fFalse tptp.fFalse tptp.fTrue tptp.fFalse tptp.fTrue tptp.fTrue (tptp.literal2 tptp.fFalse tptp.fTrue tptp.fTrue tptp.fTrue tptp.fFalse tptp.fTrue tptp.fTrue (tptp.literal2 tptp.fFalse tptp.fFalse tptp.fTrue tptp.fFalse tptp.fTrue tptp.fTrue tptp.fTrue (tptp.literal2 tptp.fTrue tptp.fFalse tptp.fTrue tptp.fFalse tptp.fFalse tptp.fTrue tptp.fTrue (tptp.literal2 tptp.fTrue tptp.fTrue tptp.fTrue tptp.fFalse tptp.fFalse tptp.fTrue tptp.fTrue (tptp.literal2 tptp.fTrue tptp.fFalse tptp.fTrue tptp.fFalse tptp.fFalse tptp.fTrue tptp.fTrue (tptp.literal2 tptp.fFalse tptp.fTrue tptp.fFalse tptp.fFalse tptp.fTrue tptp.fTrue tptp.fTrue (tptp.literal2 tptp.fFalse tptp.fFalse tptp.fFalse tptp.fFalse tptp.fFalse tptp.fTrue tptp.fFalse (tptp.literal2 tptp.fTrue tptp.fFalse tptp.fTrue tptp.fFalse tptp.fFalse tptp.fTrue tptp.fTrue (tptp.literal2 tptp.fFalse tptp.fFalse tptp.fFalse tptp.fTrue tptp.fTrue tptp.fTrue tptp.fTrue (tptp.literal2 tptp.fFalse tptp.fFalse tptp.fFalse tptp.fFalse tptp.fTrue tptp.fTrue tptp.fTrue (tptp.literal2 tptp.fTrue tptp.fTrue tptp.fTrue tptp.fTrue tptp.fFalse tptp.fTrue tptp.fTrue (tptp.literal2 tptp.fFalse tptp.fTrue tptp.fTrue tptp.fTrue tptp.fFalse tptp.fTrue tptp.fTrue (tptp.literal2 tptp.fTrue tptp.fFalse tptp.fTrue tptp.fFalse tptp.fFalse tptp.fTrue tptp.fTrue (tptp.literal2 tptp.fFalse tptp.fTrue tptp.fTrue tptp.fTrue tptp.fFalse tptp.fTrue tptp.fTrue (tptp.literal2 tptp.fFalse tptp.fFalse tptp.fTrue tptp.fFalse tptp.fTrue tptp.fTrue tptp.fTrue tptp.zero_zero_literal))))))))))))))))))))))))))))))))))) _let_1)))))))))))))) (forall ((N tptp.nat)) (= (tptp.aa_Code_integer_int tptp.code_int_of_integer (tptp.aa_nat_Code_integer tptp.code_integer_of_nat N)) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N))) (forall ((X tptp.nat)) (= (tptp.aa_Code_integer_int tptp.code_int_of_integer (tptp.aa_nat_Code_integer tptp.code_integer_of_nat X)) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int X))) (= (tptp.aa_nat_Code_integer tptp.code_integer_of_nat tptp.zero_zero_nat) tptp.zero_z3403309356797280102nteger) (forall ((X tptp.nat)) (= (tptp.aa_nat_Code_integer tptp.code_integer_of_nat X) (tptp.aa_int_Code_integer tptp.code_integer_of_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int X)))) (forall ((N tptp.num)) (= (tptp.aa_nat_Code_integer tptp.code_integer_of_nat (tptp.aa_num_nat tptp.numeral_numeral_nat N)) (tptp.numera6620942414471956472nteger N))) (= (tptp.aa_nat_Code_integer tptp.code_integer_of_nat tptp.one_one_nat) tptp.one_one_Code_integer) (= tptp.code_integer_of_nat (tptp.map_fu6290471996055670595nteger tptp.id_nat tptp.code_integer_of_int tptp.semiri1314217659103216013at_int)) (forall ((Xs tptp.list_int)) (= (tptp.gcd_Gcd_int (tptp.set_int2 Xs)) (tptp.fold_int_int tptp.gcd_gcd_int Xs tptp.zero_zero_int))) (forall ((M tptp.num) (N tptp.nat)) (= (tptp.ord_le2932123472753598470d_enat (tptp.numera1916890842035813515d_enat M) (tptp.extended_enat2 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)) N)))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.plus_p3455044024723400733d_enat (tptp.extended_enat2 M) (tptp.extended_enat2 N)) (tptp.extended_enat2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) N)))) (forall ((N tptp.extended_enat)) (let ((_let_1 (tptp.extended_enat2 tptp.zero_zero_nat))) (= (tptp.minus_3235023915231533773d_enat _let_1 N) _let_1))) (forall ((N tptp.extended_enat)) (= (tptp.minus_3235023915231533773d_enat N (tptp.extended_enat2 tptp.zero_zero_nat)) N)) (forall ((A tptp.nat) (B tptp.nat)) (= (tptp.minus_3235023915231533773d_enat (tptp.extended_enat2 A) (tptp.extended_enat2 B)) (tptp.extended_enat2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat A) B)))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.times_7803423173614009249d_enat (tptp.extended_enat2 M) (tptp.extended_enat2 N)) (tptp.extended_enat2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat M) N)))) (forall ((M tptp.num) (N tptp.nat)) (= (tptp.ord_le72135733267957522d_enat (tptp.numera1916890842035813515d_enat M) (tptp.extended_enat2 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)) N)))) (forall ((X tptp.nat)) (= (= tptp.zero_z5237406670263579293d_enat (tptp.extended_enat2 X)) (= X tptp.zero_zero_nat))) (forall ((X tptp.nat)) (= (= (tptp.extended_enat2 X) tptp.zero_z5237406670263579293d_enat) (= X tptp.zero_zero_nat))) (= tptp.zero_z5237406670263579293d_enat (tptp.extended_enat2 tptp.zero_zero_nat)) (forall ((K tptp.num)) (= (tptp.numera1916890842035813515d_enat K) (tptp.extended_enat2 (tptp.aa_num_nat tptp.numeral_numeral_nat K)))) (= tptp.one_on7984719198319812577d_enat (tptp.extended_enat2 tptp.one_one_nat)) (forall ((X tptp.nat)) (= (= (tptp.extended_enat2 X) tptp.one_on7984719198319812577d_enat) (= X tptp.one_one_nat))) (forall ((X tptp.nat)) (= (= tptp.one_on7984719198319812577d_enat (tptp.extended_enat2 X)) (= X tptp.one_one_nat))) (forall ((M tptp.nat) (N tptp.extended_enat)) (= (tptp.ord_le2932123472753598470d_enat (tptp.extended_enat2 (tptp.aa_nat_nat tptp.suc M)) N) (tptp.ord_le72135733267957522d_enat (tptp.extended_enat2 M) N))) (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_ik D) (tptp.topolo2177554685111907308n_real A (tptp.set_or5849166863359141190n_real A))) (tptp.topolo2177554685111907308n_real _let_1 (tptp.set_or5849166863359141190n_real _let_1))))) (forall ((X tptp.extended_enat) (Y tptp.extended_enat) (N tptp.nat)) (= (tptp.ord_le2932123472753598470d_enat (tptp.plus_p3455044024723400733d_enat X Y) (tptp.extended_enat2 N)) (exists ((Y7 tptp.nat) (X10 tptp.nat)) (and (= X (tptp.extended_enat2 X10)) (= Y (tptp.extended_enat2 Y7)) (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 X10) Y7)) N)))))) (forall ((A tptp.real)) (= (tptp.topolo2177554685111907308n_real A (tptp.set_or5849166863359141190n_real A)) (tptp.filtermap_real_real (tptp.aa_rea7340605660300375871l_real tptp.aTP_Lamm_il A) (tptp.topolo2177554685111907308n_real tptp.zero_zero_real (tptp.set_or5849166863359141190n_real tptp.zero_zero_real))))) (forall ((Xs tptp.list_nat)) (= (tptp.gcd_Gcd_nat (tptp.set_nat2 Xs)) (tptp.aa_nat_nat (tptp.fold_nat_nat tptp.gcd_gcd_nat Xs) tptp.zero_zero_nat))) (forall ((M tptp.nat)) (let ((_let_1 (tptp.times_7803423173614009249d_enat (tptp.extended_enat2 M) tptp.extend5688581933313929465d_enat))) (let ((_let_2 (= M tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.zero_z5237406670263579293d_enat)) (=> (not _let_2) (= _let_1 tptp.extend5688581933313929465d_enat)))))) (forall ((N tptp.nat)) (let ((_let_1 (tptp.times_7803423173614009249d_enat tptp.extend5688581933313929465d_enat (tptp.extended_enat2 N)))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.zero_z5237406670263579293d_enat)) (=> (not _let_2) (= _let_1 tptp.extend5688581933313929465d_enat)))))) (forall ((Q2 tptp.extended_enat)) (= (tptp.plus_p3455044024723400733d_enat tptp.extend5688581933313929465d_enat Q2) tptp.extend5688581933313929465d_enat)) (forall ((Q2 tptp.extended_enat)) (= (tptp.plus_p3455044024723400733d_enat Q2 tptp.extend5688581933313929465d_enat) tptp.extend5688581933313929465d_enat)) (forall ((N tptp.extended_enat)) (= (tptp.minus_3235023915231533773d_enat tptp.extend5688581933313929465d_enat N) tptp.extend5688581933313929465d_enat)) (= (tptp.times_7803423173614009249d_enat tptp.extend5688581933313929465d_enat tptp.extend5688581933313929465d_enat) tptp.extend5688581933313929465d_enat) (forall ((N tptp.extended_enat)) (=> (not (= N tptp.extend5688581933313929465d_enat)) (= (tptp.minus_3235023915231533773d_enat N N) tptp.zero_z5237406670263579293d_enat))) (forall ((X tptp.extended_enat) (Y tptp.extended_enat)) (=> (not (= X tptp.extend5688581933313929465d_enat)) (= (tptp.minus_3235023915231533773d_enat (tptp.plus_p3455044024723400733d_enat X Y) X) Y))) (forall ((A tptp.nat)) (= (tptp.minus_3235023915231533773d_enat (tptp.extended_enat2 A) tptp.extend5688581933313929465d_enat) tptp.zero_z5237406670263579293d_enat)) (forall ((A tptp.extended_enat) (B tptp.extended_enat) (C tptp.extended_enat)) (= (tptp.ord_le2932123472753598470d_enat (tptp.plus_p3455044024723400733d_enat A B) (tptp.plus_p3455044024723400733d_enat A C)) (or (= A tptp.extend5688581933313929465d_enat) (tptp.ord_le2932123472753598470d_enat B C)))) (forall ((A tptp.extended_enat) (B tptp.extended_enat) (C tptp.extended_enat)) (= (tptp.ord_le72135733267957522d_enat (tptp.plus_p3455044024723400733d_enat A B) (tptp.plus_p3455044024723400733d_enat A C)) (and (not (= A tptp.extend5688581933313929465d_enat)) (tptp.ord_le72135733267957522d_enat B C)))) (not (= tptp.extend5688581933313929465d_enat tptp.one_on7984719198319812577d_enat)) (forall ((A tptp.extended_enat) (B tptp.extended_enat) (C tptp.extended_enat)) (= (= (tptp.plus_p3455044024723400733d_enat A B) (tptp.plus_p3455044024723400733d_enat A C)) (or (= A tptp.extend5688581933313929465d_enat) (= B C)))) (forall ((M tptp.extended_enat) (N tptp.extended_enat)) (= (= (tptp.plus_p3455044024723400733d_enat M N) tptp.extend5688581933313929465d_enat) (or (= M tptp.extend5688581933313929465d_enat) (= N tptp.extend5688581933313929465d_enat)))) (forall ((A tptp.extended_enat) (B tptp.extended_enat)) (= (= (tptp.times_7803423173614009249d_enat A B) tptp.extend5688581933313929465d_enat) (or (and (= A tptp.extend5688581933313929465d_enat) (not (= B tptp.zero_z5237406670263579293d_enat))) (and (= B tptp.extend5688581933313929465d_enat) (not (= A tptp.zero_z5237406670263579293d_enat)))))) (forall ((N tptp.extended_enat)) (=> (tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat N) (= (tptp.times_7803423173614009249d_enat N tptp.extend5688581933313929465d_enat) tptp.extend5688581933313929465d_enat))) (forall ((N tptp.extended_enat)) (=> (tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat N) (= (tptp.times_7803423173614009249d_enat tptp.extend5688581933313929465d_enat N) tptp.extend5688581933313929465d_enat))) (forall ((M tptp.extended_enat) (N tptp.extended_enat)) (= (tptp.times_7803423173614009249d_enat M N) (tptp.extend3600170679010898289d_enat (tptp.aTP_Lamm_in N) (tptp.if_Extended_enat (tptp.fequal_Extended_enat N tptp.zero_z5237406670263579293d_enat) tptp.zero_z5237406670263579293d_enat tptp.extend5688581933313929465d_enat) M))) (forall ((A tptp.extended_enat) (B tptp.extended_enat)) (= (tptp.minus_3235023915231533773d_enat A B) (tptp.extend3600170679010898289d_enat (tptp.aTP_Lamm_ip B) tptp.extend5688581933313929465d_enat A))) (forall ((M tptp.extended_enat) (N tptp.extended_enat)) (= (tptp.plus_p3455044024723400733d_enat M N) (tptp.extend3600170679010898289d_enat (tptp.aTP_Lamm_ir N) tptp.extend5688581933313929465d_enat M))) (forall ((I tptp.extended_enat)) (= (tptp.extended_eSuc I) (tptp.extend3600170679010898289d_enat tptp.aTP_Lamm_is tptp.extend5688581933313929465d_enat I))) (forall ((K tptp.num)) (= (tptp.extended_eSuc (tptp.numera1916890842035813515d_enat K)) (tptp.numera1916890842035813515d_enat (tptp.plus_plus_num K tptp.one)))) (forall ((N tptp.extended_enat) (M tptp.extended_enat)) (= (tptp.minus_3235023915231533773d_enat (tptp.extended_eSuc N) (tptp.extended_eSuc M)) (tptp.minus_3235023915231533773d_enat N M))) (forall ((N tptp.extended_enat)) (= (tptp.minus_3235023915231533773d_enat (tptp.extended_eSuc N) tptp.one_on7984719198319812577d_enat) N)) (forall ((N tptp.nat)) (= (tptp.extended_eSuc (tptp.extended_enat2 N)) (tptp.extended_enat2 (tptp.aa_nat_nat tptp.suc N)))) (forall ((X tptp.extended_enat) (Y tptp.nat)) (= (= (tptp.extended_eSuc X) (tptp.extended_enat2 Y)) (exists ((N5 tptp.nat)) (and (= Y (tptp.aa_nat_nat tptp.suc N5)) (= X (tptp.extended_enat2 N5)))))) (forall ((Y tptp.nat) (X tptp.extended_enat)) (= (= (tptp.extended_enat2 Y) (tptp.extended_eSuc X)) (exists ((N5 tptp.nat)) (and (= Y (tptp.aa_nat_nat tptp.suc N5)) (= (tptp.extended_enat2 N5) X))))) (forall ((M tptp.extended_enat) (N tptp.extended_enat)) (= (tptp.plus_p3455044024723400733d_enat (tptp.extended_eSuc M) N) (tptp.extended_eSuc (tptp.plus_p3455044024723400733d_enat M N)))) (forall ((M tptp.extended_enat) (N tptp.extended_enat)) (= (tptp.plus_p3455044024723400733d_enat M (tptp.extended_eSuc N)) (tptp.extended_eSuc (tptp.plus_p3455044024723400733d_enat M N)))) (= tptp.one_on7984719198319812577d_enat (tptp.extended_eSuc tptp.zero_z5237406670263579293d_enat)) (forall ((M tptp.extended_enat) (N tptp.extended_enat)) (= (tptp.times_7803423173614009249d_enat (tptp.extended_eSuc M) N) (tptp.plus_p3455044024723400733d_enat N (tptp.times_7803423173614009249d_enat M N)))) (forall ((M tptp.extended_enat) (N tptp.extended_enat)) (= (tptp.times_7803423173614009249d_enat M (tptp.extended_eSuc N)) (tptp.plus_p3455044024723400733d_enat M (tptp.times_7803423173614009249d_enat M N)))) (forall ((N tptp.extended_enat)) (= (tptp.extended_eSuc N) (tptp.plus_p3455044024723400733d_enat N tptp.one_on7984719198319812577d_enat))) (forall ((Q2 tptp.extended_enat)) (= (tptp.plus_p3455044024723400733d_enat tptp.one_on7984719198319812577d_enat Q2) (tptp.extended_eSuc Q2))) (forall ((Q2 tptp.extended_enat)) (= (tptp.plus_p3455044024723400733d_enat Q2 tptp.one_on7984719198319812577d_enat) (tptp.extended_eSuc Q2))) (tptp.quotie6870213296501934825t_real tptp.realrel tptp.real2 tptp.rep_real tptp.cr_real) (forall ((Net tptp.filter_real)) (tptp.has_ve631408500373753343e_real tptp.aTP_Lamm_it tptp.one_one_real Net)) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.gcd_lcm_Code_integer A) B) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.divide6298287555418463151nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.abs_abs_Code_integer A)) (tptp.abs_abs_Code_integer B))) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.gcd_gcd_Code_integer A) B)))) (forall ((M tptp.nat) (N tptp.nat)) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.gcd_lcm_nat M) N) tptp.zero_zero_nat) (or (= M tptp.zero_zero_nat) (= N tptp.zero_zero_nat)))) (forall ((M tptp.int) (N tptp.int)) (= (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.gcd_lcm_int M) N) tptp.zero_zero_int) (or (= M tptp.zero_zero_int) (= N tptp.zero_zero_int)))) (forall ((M tptp.nat) (N tptp.nat)) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.gcd_lcm_nat M) N) M) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat N) M)))) (forall ((M tptp.nat) (N tptp.nat)) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.gcd_lcm_nat M) N) N) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat M) N)))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat X) Y)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.gcd_lcm_nat Y) X) Y))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat X) Y)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.gcd_lcm_nat X) Y) Y))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.gcd_lcm_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_lcm_nat M) N)))) (forall ((I tptp.int) (J tptp.int)) (let ((_let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.gcd_lcm_int I) J))) (= (tptp.aa_int_int tptp.abs_abs_int _let_1) _let_1))) (forall ((X tptp.int) (Y tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.gcd_lcm_int (tptp.aa_int_int tptp.abs_abs_int X)) Y) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.gcd_lcm_int X) Y))) (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.gcd_lcm_int X))) (= (tptp.aa_int_int _let_1 (tptp.aa_int_int tptp.abs_abs_int Y)) (tptp.aa_int_int _let_1 Y)))) (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.gcd_lcm_nat M) N) _let_1) (and (= M _let_1) (= N _let_1))))) (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.gcd_lcm_int M) N) tptp.one_one_int) (and (or (= M tptp.one_one_int) (= M _let_1)) (or (= N tptp.one_one_int) (= N _let_1)))))) (forall ((X tptp.int) (Y tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int X) Y)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.gcd_lcm_int X) Y) (tptp.aa_int_int tptp.abs_abs_int Y)))) (forall ((X tptp.int) (Y tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int X) Y)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.gcd_lcm_int Y) X) (tptp.aa_int_int tptp.abs_abs_int Y)))) (forall ((M tptp.int) (N tptp.int)) (= (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.gcd_lcm_int M) N) (tptp.aa_int_int tptp.abs_abs_int N)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int M) N)))) (forall ((M tptp.int) (N tptp.int)) (= (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.gcd_lcm_int M) N) (tptp.aa_int_int tptp.abs_abs_int M)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int N) M)))) (forall ((K tptp.int) (N tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.gcd_lcm_nat (tptp.aa_int_nat tptp.nat2 (tptp.aa_int_int tptp.abs_abs_int K))) N) (tptp.aa_int_nat tptp.nat2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.gcd_lcm_int K) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N))))) (forall ((N tptp.nat) (K tptp.int)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.gcd_lcm_nat N) (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.aa_int_fun_int_int tptp.gcd_lcm_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N)) K)))) (forall ((D tptp.int) (A tptp.int) (B tptp.int)) (= (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 (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int A) D)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int B) D)) (forall ((E3 tptp.int)) (=> (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int A) E3)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int B) E3))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int D) E3))))) (= D (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.gcd_lcm_int A) B)))) (forall ((M tptp.nat) (N tptp.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.aa_nat_fun_nat_nat tptp.gcd_gcd_nat M) N)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.gcd_lcm_nat M) N)))) (forall ((X tptp.code_integer) (Xa tptp.code_integer)) (= (tptp.aa_Code_integer_int tptp.code_int_of_integer (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.gcd_lcm_Code_integer X) Xa)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.gcd_lcm_int (tptp.aa_Code_integer_int tptp.code_int_of_integer X)) (tptp.aa_Code_integer_int tptp.code_int_of_integer Xa)))) (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 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.gcd_lcm_nat M) N)))))) (forall ((K tptp.nat) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat K))) (=> (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.gcd_lcm_nat M) N)))))) (forall ((A tptp.nat) (D tptp.nat) (B tptp.nat)) (= (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat A) D)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat B) D)) (forall ((E3 tptp.nat)) (=> (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat A) E3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat B) E3))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat D) E3))))) (= D (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.gcd_lcm_nat A) B)))) (forall ((I tptp.int) (M tptp.int) (N tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int I))) (=> (tptp.pp (tptp.aa_int_bool _let_1 M)) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.gcd_lcm_int M) N)))))) (forall ((I tptp.int) (N tptp.int) (M tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int I))) (=> (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.gcd_lcm_int M) N)))))) (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.gcd_lcm_int X))) (= (tptp.aa_int_int _let_1 (tptp.aa_int_int tptp.uminus_uminus_int Y)) (tptp.aa_int_int _let_1 Y)))) (forall ((X tptp.int) (Y tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.gcd_lcm_int (tptp.aa_int_int tptp.uminus_uminus_int X)) Y) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.gcd_lcm_int X) Y))) (forall ((Xa tptp.int) (X tptp.int)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.gcd_lcm_Code_integer (tptp.aa_int_Code_integer tptp.code_integer_of_int Xa)) (tptp.aa_int_Code_integer tptp.code_integer_of_int X)) (tptp.aa_int_Code_integer tptp.code_integer_of_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.gcd_lcm_int Xa) X)))) (forall ((X tptp.int) (Y tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.gcd_lcm_int X) Y) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.gcd_lcm_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 Y)))))) (tptp.bNF_re5717476210804479843nt_int tptp.fequal_int _let_16 tptp.gcd_lcm_int tptp.gcd_lcm_int) (forall ((M tptp.int) (N tptp.int)) (=> (not (= M tptp.zero_zero_int)) (=> (not (= N 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.gcd_lcm_int 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 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.gcd_lcm_nat M) N))))))) (forall ((X tptp.int) (Y tptp.int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.gcd_lcm_int X) Y)))) (forall ((X tptp.int) (Y tptp.int) (P tptp.fun_int_bool)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.gcd_lcm_int X))) (let ((_let_2 (tptp.pp (tptp.aa_int_bool P (tptp.aa_int_int _let_1 Y))))) (let ((_let_3 (tptp.aa_int_int tptp.uminus_uminus_int Y))) (let ((_let_4 (tptp.aa_int_fun_int_int tptp.gcd_lcm_int (tptp.aa_int_int tptp.uminus_uminus_int X)))) (let ((_let_5 (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Y) tptp.zero_zero_int)))) (let ((_let_6 (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X) tptp.zero_zero_int)))) (let ((_let_7 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_8 (tptp.pp (tptp.aa_int_bool _let_7 Y)))) (let ((_let_9 (tptp.pp (tptp.aa_int_bool _let_7 X)))) (=> (=> _let_9 (=> _let_8 _let_2)) (=> (=> _let_9 (=> _let_5 (tptp.pp (tptp.aa_int_bool P (tptp.aa_int_int _let_1 _let_3))))) (=> (=> _let_6 (=> _let_8 (tptp.pp (tptp.aa_int_bool P (tptp.aa_int_int _let_4 Y))))) (=> (=> _let_6 (=> _let_5 (tptp.pp (tptp.aa_int_bool P (tptp.aa_int_int _let_4 _let_3))))) _let_2)))))))))))))) (forall ((X tptp.nat) (Y tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.gcd_lcm_nat X) Y) (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 X) Y)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.gcd_gcd_nat X) Y)))) (forall ((M tptp.int) (N tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int tptp.abs_abs_int M)) (tptp.aa_int_int tptp.abs_abs_int 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.gcd_gcd_int M) N)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.gcd_lcm_int M) N)))) (forall ((A tptp.int) (B tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.gcd_lcm_int A) 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.times_times_int (tptp.aa_int_int tptp.abs_abs_int A)) (tptp.aa_int_int tptp.abs_abs_int B))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.gcd_gcd_int A) B)))) (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))) (=> (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat M2) M10)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat N2) M10)) (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.gcd_lcm_nat M2) N2)) M10))))) (= (tptp.gcd_Lcm_nat M10) (tptp.lattic8265883725875713057ax_nat M10))))))) (forall ((Xs tptp.list_int)) (= (tptp.gcd_Lcm_int (tptp.set_int2 Xs)) (tptp.fold_int_int tptp.gcd_lcm_int Xs tptp.one_one_int))) (forall ((A2 tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat tptp.zero_zero_nat) A2)) (= (tptp.gcd_Lcm_nat A2) tptp.zero_zero_nat))) (forall ((K5 tptp.set_int)) (let ((_let_1 (tptp.gcd_Lcm_int K5))) (= (tptp.aa_int_int tptp.abs_abs_int _let_1) _let_1))) (forall ((A2 tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A2)) (= (= (tptp.gcd_Lcm_nat A2) tptp.zero_zero_nat) (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat tptp.zero_zero_nat) A2))))) (forall ((K5 tptp.set_int)) (= (tptp.gcd_Lcm_int (tptp.image_int_int tptp.abs_abs_int K5)) (tptp.gcd_Lcm_int K5))) (forall ((N4 tptp.set_nat)) (= (tptp.gcd_Lcm_int (tptp.image_nat_int tptp.semiri1314217659103216013at_int N4)) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.gcd_Lcm_nat N4)))) (forall ((K5 tptp.set_int)) (= (tptp.gcd_Lcm_nat (tptp.image_int_nat tptp.aTP_Lamm_ag K5)) (tptp.aa_int_nat tptp.nat2 (tptp.gcd_Lcm_int K5)))) (forall ((M10 tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat M10)) (=> (not (= M10 tptp.bot_bot_set_nat)) (=> (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat M2) M10)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat N2) M10)) (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.gcd_lcm_nat M2) N2)) M10))))) (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat (tptp.gcd_Lcm_nat M10)) M10)))))) (forall ((N tptp.nat) (M10 tptp.set_nat)) (= (tptp.gcd_Lcm_nat (tptp.insert_nat N M10)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.gcd_lcm_nat N) (tptp.gcd_Lcm_nat M10)))) (= (tptp.gcd_Lcm_nat tptp.bot_bot_set_nat) tptp.one_one_nat) (forall ((M10 tptp.set_nat) (N tptp.nat)) (=> (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) M10)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat X3) N)))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.gcd_Lcm_nat M10)) N)))) (forall ((M tptp.nat) (M10 tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat M) M10)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat M) (tptp.gcd_Lcm_nat M10))))) (forall ((M tptp.int) (M10 tptp.set_int)) (=> (tptp.member_int M M10) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int M) (tptp.gcd_Lcm_int M10))))) (forall ((A2 tptp.set_int) (A tptp.int)) (=> (forall ((B3 tptp.int)) (=> (tptp.member_int B3 A2) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int B3) A)))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.gcd_Lcm_int A2)) A)))) (forall ((M10 tptp.set_nat)) (=> (not (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat M10))) (= (tptp.gcd_Lcm_nat M10) tptp.zero_zero_nat))) (forall ((K5 tptp.set_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.gcd_Lcm_int K5)))) (forall ((M10 tptp.set_nat)) (= (tptp.gcd_Gcd_nat M10) (tptp.gcd_Lcm_nat (tptp.collect_nat (tptp.aTP_Lamm_iu M10))))) (forall ((K5 tptp.set_int)) (= (tptp.gcd_Lcm_int K5) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.gcd_Lcm_nat (tptp.image_int_nat (tptp.comp_int_nat_int tptp.nat2 tptp.abs_abs_int) K5))))) (forall ((Xs tptp.list_nat)) (= (tptp.gcd_Lcm_nat (tptp.set_nat2 Xs)) (tptp.aa_nat_nat (tptp.fold_nat_nat tptp.gcd_lcm_nat Xs) tptp.one_one_nat))) (forall ((M10 tptp.set_nat)) (let ((_let_1 (tptp.gcd_Lcm_nat M10))) (let ((_let_2 (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat M10)))) (and (=> _let_2 (= _let_1 (tptp.lattic7826324295020591184_F_nat tptp.gcd_lcm_nat tptp.one_one_nat M10))) (=> (not _let_2) (= _let_1 tptp.zero_zero_nat)))))) (= tptp.normal571682499473568032ze_int tptp.abs_abs_int) (= tptp.normal574172969982618308ze_nat tptp.id_nat) (forall ((X4 tptp.product_prod_nat_nat)) (= (tptp.aa_Pro2928840338864870335t_bool tptp.cr_int X4) (tptp.aa_int_fun_int_bool tptp.fequal_int (tptp.aa_Pro4240683299535347697at_int tptp.abs_Integ X4)))) (= tptp.pcr_int tptp.cr_int) (tptp.quotie1194848508323700631at_int tptp.intrel tptp.abs_Integ tptp.rep_Integ tptp.cr_int) (tptp.pp (tptp.aa_nat_bool (tptp.semila9081495762789891438tr_nat tptp.gcd_gcd_nat) tptp.zero_zero_nat)) (tptp.pp (tptp.aa_nat_bool (tptp.semila9081495762789891438tr_nat tptp.ord_max_nat) tptp.zero_zero_nat)) (forall ((F tptp.fun_real_real) (R tptp.real) (B tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.times_times_real R))) (=> (tptp.real_V4572627801940501177l_real F) (= (tptp.aa_real_real F (tptp.aa_real_real _let_1 B)) (tptp.aa_real_real _let_1 (tptp.aa_real_real F B)))))) (forall ((F tptp.fun_real_real)) (=> (tptp.real_V4572627801940501177l_real F) (not (forall ((C3 tptp.real)) (not (= F (tptp.aa_rea7340605660300375871l_real tptp.times_times_real C3))))))) (tptp.filterlim_nat_int tptp.semiri1314217659103216013at_int tptp.at_top_int tptp.at_top_nat) (forall ((Xa tptp.num) (X tptp.num)) (= (tptp.aa_num_Code_integer (tptp.aa_num5808785979904431436nteger tptp.code_sub Xa) X) (tptp.aa_int_Code_integer tptp.code_integer_of_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_num_int tptp.numeral_numeral_int Xa)) (tptp.aa_num_int tptp.numeral_numeral_int X))))) (forall ((X tptp.num) (Xa tptp.num)) (= (tptp.aa_Code_integer_int tptp.code_int_of_integer (tptp.aa_num_Code_integer (tptp.aa_num5808785979904431436nteger tptp.code_sub X) Xa)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_num_int tptp.numeral_numeral_int X)) (tptp.aa_num_int tptp.numeral_numeral_int Xa)))) (= (tptp.aa_num_Code_integer (tptp.aa_num5808785979904431436nteger tptp.code_sub tptp.one) tptp.one) tptp.zero_z3403309356797280102nteger) (forall ((M tptp.num) (N tptp.num)) (= (tptp.aa_num_Code_integer (tptp.aa_num5808785979904431436nteger tptp.code_sub (tptp.aa_num_num tptp.bit0 M)) (tptp.aa_num_num tptp.bit1 N)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.minus_8373710615458151222nteger (tptp.aa_Cod1783974652533396728nteger tptp.code_dup (tptp.aa_num_Code_integer (tptp.aa_num5808785979904431436nteger tptp.code_sub M) N))) tptp.one_one_Code_integer))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.aa_num_Code_integer (tptp.aa_num5808785979904431436nteger tptp.code_sub (tptp.aa_num_num tptp.bit1 M)) (tptp.aa_num_num tptp.bit0 N)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger tptp.code_dup (tptp.aa_num_Code_integer (tptp.aa_num5808785979904431436nteger tptp.code_sub M) N))) tptp.one_one_Code_integer))) (forall ((X tptp.code_integer)) (let ((_let_1 (tptp.aa_Code_integer_int tptp.code_int_of_integer X))) (= (tptp.aa_Code_integer_int tptp.code_int_of_integer (tptp.aa_Cod1783974652533396728nteger tptp.code_dup X)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int _let_1) _let_1)))) (forall ((X tptp.int)) (= (tptp.aa_Cod1783974652533396728nteger tptp.code_dup (tptp.aa_int_Code_integer tptp.code_integer_of_int X)) (tptp.aa_int_Code_integer tptp.code_integer_of_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int X) X)))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.aa_num_Code_integer (tptp.aa_num5808785979904431436nteger tptp.code_sub (tptp.aa_num_num tptp.bit0 M)) (tptp.aa_num_num tptp.bit0 N)) (tptp.aa_Cod1783974652533396728nteger tptp.code_dup (tptp.aa_num_Code_integer (tptp.aa_num5808785979904431436nteger tptp.code_sub M) N)))) (forall ((N tptp.num)) (= (tptp.aa_num_Code_integer (tptp.aa_num5808785979904431436nteger tptp.code_sub tptp.one) (tptp.aa_num_num tptp.bit0 N)) (tptp.code_Neg (tptp.bitM N)))) (= tptp.code_dup (tptp.aa_fun8964553180794676938nteger _let_15 tptp.aTP_Lamm_hb)) (forall ((N tptp.num)) (= (tptp.aa_Cod1783974652533396728nteger tptp.code_dup (tptp.code_Neg N)) (tptp.code_Neg (tptp.aa_num_num tptp.bit0 N)))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.plus_p5714425477246183910nteger (tptp.code_Neg M)) (tptp.code_Neg N)) (tptp.code_Neg (tptp.plus_plus_num M N)))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.minus_8373710615458151222nteger (tptp.code_Neg M)) (tptp.code_Neg N)) (tptp.aa_num_Code_integer (tptp.aa_num5808785979904431436nteger tptp.code_sub N) M))) (forall ((N tptp.num)) (= (tptp.aa_num_Code_integer (tptp.aa_num5808785979904431436nteger tptp.code_sub tptp.one) (tptp.aa_num_num tptp.bit1 N)) (tptp.code_Neg (tptp.aa_num_num tptp.bit0 N)))) (= tptp.bit_se7788150548672797655nteger (tptp.map_fu214667362969451334nteger tptp.id_nat _let_15 tptp.bit_se545348938243370406it_int)) (= tptp.gcd_lcm_Code_integer (tptp.map_fu1034890151506530863nteger tptp.code_int_of_integer _let_15 tptp.gcd_lcm_int)) (= tptp.plus_p5714425477246183910nteger (tptp.map_fu1034890151506530863nteger tptp.code_int_of_integer _let_15 tptp.plus_plus_int)) (= tptp.times_3573771949741848930nteger (tptp.map_fu1034890151506530863nteger tptp.code_int_of_integer _let_15 tptp.times_times_int)) (= tptp.minus_8373710615458151222nteger (tptp.map_fu1034890151506530863nteger tptp.code_int_of_integer _let_15 tptp.minus_minus_int)) (= tptp.divide6298287555418463151nteger (tptp.map_fu1034890151506530863nteger tptp.code_int_of_integer _let_15 tptp.divide_divide_int)) (= tptp.gcd_gcd_Code_integer (tptp.map_fu1034890151506530863nteger tptp.code_int_of_integer _let_15 tptp.gcd_gcd_int)) (forall ((M tptp.num)) (= (tptp.aa_num_Code_integer (tptp.aa_num5808785979904431436nteger tptp.code_sub (tptp.aa_num_num tptp.bit0 M)) tptp.one) (tptp.code_Pos (tptp.bitM M)))) (forall ((M tptp.num)) (= (tptp.aa_num_Code_integer (tptp.aa_num5808785979904431436nteger tptp.code_sub (tptp.aa_num_num tptp.bit1 M)) tptp.one) (tptp.code_Pos (tptp.aa_num_num tptp.bit0 M)))) (forall ((N tptp.num)) (= (tptp.aa_Cod1783974652533396728nteger tptp.code_dup (tptp.code_Pos N)) (tptp.code_Pos (tptp.aa_num_num tptp.bit0 N)))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.code_Pos M)) (tptp.code_Pos N)) (tptp.code_Pos (tptp.times_times_num M N)))) (= tptp.one_one_Code_integer _let_13) (= _let_14 _let_13) (forall ((K tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 K))) (= (tptp.numera6620942414471956472nteger _let_1) (tptp.code_Pos _let_1)))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.plus_p5714425477246183910nteger (tptp.code_Pos M)) (tptp.code_Pos N)) (tptp.code_Pos (tptp.plus_plus_num M N)))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.minus_8373710615458151222nteger (tptp.code_Pos M)) (tptp.code_Pos N)) (tptp.aa_num_Code_integer (tptp.aa_num5808785979904431436nteger tptp.code_sub M) N))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.minus_8373710615458151222nteger (tptp.code_Pos M)) (tptp.code_Neg N)) (tptp.code_Pos (tptp.plus_plus_num M N)))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.minus_8373710615458151222nteger (tptp.code_Neg M)) (tptp.code_Pos N)) (tptp.code_Neg (tptp.plus_plus_num M N)))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.code_Neg M)) (tptp.code_Neg N)) (tptp.code_Pos (tptp.times_times_num M N)))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.code_Neg M)) (tptp.code_Pos N)) (tptp.code_Neg (tptp.times_times_num M N)))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.code_Pos M)) (tptp.code_Neg N)) (tptp.code_Neg (tptp.times_times_num M N)))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.plus_p5714425477246183910nteger (tptp.code_Pos M)) (tptp.code_Neg N)) (tptp.aa_num_Code_integer (tptp.aa_num5808785979904431436nteger tptp.code_sub M) N))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.plus_p5714425477246183910nteger (tptp.code_Neg M)) (tptp.code_Pos N)) (tptp.aa_num_Code_integer (tptp.aa_num5808785979904431436nteger tptp.code_sub N) M))) (tptp.pp (tptp.aa_nat_bool (tptp.monoid_nat tptp.ord_max_nat) tptp.zero_zero_nat)) (tptp.pp (tptp.aa_nat_bool (tptp.monoid_nat tptp.gcd_gcd_nat) tptp.zero_zero_nat)) (forall ((X7 tptp.set_real)) (= (tptp.comple1385675409528146559p_real X7) (tptp.ord_Least_real (tptp.aTP_Lamm_iv X7)))) (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)) (=> (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 ((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 ((K3 tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool P (tptp.aa_nat_nat tptp.suc K3))) (tptp.pp (tptp.aa_nat_bool Q K3)))) (= (tptp.ord_Least_nat P) (tptp.aa_nat_nat tptp.suc (tptp.ord_Least_nat Q)))))))) (= (tptp.aa_nat_nat tptp.unit_f2748546683901255202or_nat tptp.zero_zero_nat) tptp.zero_zero_nat) (forall ((N tptp.nat)) (= (tptp.aa_nat_nat tptp.unit_f2748546683901255202or_nat (tptp.aa_nat_nat tptp.suc N)) tptp.one_one_nat)) (= tptp.unit_f2746056213392204926or_int tptp.sgn_sgn_int) (forall ((N tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.unit_f2748546683901255202or_nat N))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.zero_zero_nat)) (=> (not _let_2) (= _let_1 tptp.one_one_nat)))))) (tptp.pp (tptp.aa_nat_bool (tptp.comm_monoid_nat tptp.gcd_gcd_nat) tptp.zero_zero_nat)) (tptp.pp (tptp.aa_nat_bool (tptp.comm_monoid_nat tptp.ord_max_nat) tptp.zero_zero_nat)) (forall ((M tptp.num) (N tptp.num)) (= (tptp.times_times_num M N) (tptp.aa_nat_num tptp.num_of_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.nat_of_num M)) (tptp.aa_num_nat tptp.nat_of_num N))))) (forall ((M tptp.num)) (= (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.bit_un6697907153464112080or_num (tptp.aa_num_num tptp.bit0 M)) tptp.one) (tptp.aa_num_num tptp.bit1 M))) (forall ((X tptp.num)) (let ((_let_1 (tptp.aa_num_nat tptp.nat_of_num X))) (= (tptp.aa_num_nat tptp.nat_of_num (tptp.sqr X)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat _let_1) _let_1)))) (forall ((N tptp.num)) (let ((_let_1 (tptp.aa_num_nat tptp.nat_of_num N))) (= (tptp.aa_num_nat tptp.nat_of_num (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 ((M tptp.num) (N tptp.num)) (= (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.bit_un6697907153464112080or_num (tptp.aa_num_num tptp.bit1 M)) (tptp.aa_num_num tptp.bit0 N)) (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.bit_un6697907153464112080or_num M) N)))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.bit_un6697907153464112080or_num (tptp.aa_num_num tptp.bit0 M)) (tptp.aa_num_num tptp.bit1 N)) (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.bit_un6697907153464112080or_num M) N)))) (forall ((M tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit1 M))) (= (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.bit_un6697907153464112080or_num _let_1) tptp.one) _let_1))) (forall ((N tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit1 N))) (= (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.bit_un6697907153464112080or_num tptp.one) _let_1) _let_1))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.pp (tptp.aa_num_bool (tptp.ord_less_eq_num M) N)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_num_nat tptp.nat_of_num M)) (tptp.aa_num_nat tptp.nat_of_num N))))) (forall ((X tptp.num) (Y tptp.num)) (= (tptp.aa_num_nat tptp.nat_of_num (tptp.plus_plus_num X Y)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_num_nat tptp.nat_of_num X)) (tptp.aa_num_nat tptp.nat_of_num Y)))) (forall ((X tptp.num)) (let ((_let_1 (tptp.aa_num_nat tptp.nat_of_num X))) (= (tptp.aa_num_nat tptp.nat_of_num (tptp.aa_num_num tptp.bit0 X)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat _let_1) _let_1)))) (forall ((X tptp.num)) (= (tptp.aa_nat_num tptp.num_of_nat (tptp.aa_num_nat tptp.nat_of_num X)) X)) (forall ((M tptp.num) (N tptp.num)) (= (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.bit_un6697907153464112080or_num (tptp.aa_num_num tptp.bit1 M)) (tptp.aa_num_num tptp.bit1 N)) (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.bit_un6697907153464112080or_num M) N)))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.bit_un6697907153464112080or_num (tptp.aa_num_num tptp.bit0 M)) (tptp.aa_num_num tptp.bit0 N)) (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.bit_un6697907153464112080or_num M) N)))) (forall ((X tptp.num) (Y tptp.num)) (= (= X Y) (= (tptp.aa_num_nat tptp.nat_of_num X) (tptp.aa_num_nat tptp.nat_of_num Y)))) (= (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.bit_un6697907153464112080or_num tptp.one) tptp.one) tptp.one) (= tptp.nat_of_num tptp.numeral_numeral_nat) (= _let_12 tptp.one_one_nat) (forall ((M tptp.num) (N tptp.num)) (= (tptp.pp (tptp.aa_num_bool (tptp.ord_less_num M) N)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_num_nat tptp.nat_of_num M)) (tptp.aa_num_nat tptp.nat_of_num N))))) (forall ((X tptp.num) (Y tptp.num)) (= (tptp.aa_num_nat tptp.nat_of_num (tptp.times_times_num X Y)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.nat_of_num X)) (tptp.aa_num_nat tptp.nat_of_num Y)))) (forall ((X tptp.num)) (= (tptp.aa_num_nat tptp.nat_of_num (tptp.inc X)) (tptp.aa_nat_nat tptp.suc (tptp.aa_num_nat tptp.nat_of_num X)))) (forall ((X 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.nat_of_num X)))) (forall ((X tptp.num)) (not (= (tptp.aa_num_nat tptp.nat_of_num X) tptp.zero_zero_nat))) (= _let_12 _let_11) (forall ((X tptp.num)) (let ((_let_1 (tptp.aa_num_nat tptp.nat_of_num X))) (= (tptp.aa_num_nat tptp.nat_of_num (tptp.aa_num_num tptp.bit1 X)) (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat _let_1) _let_1))))) (forall ((N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (= (tptp.aa_num_nat tptp.nat_of_num (tptp.aa_nat_num tptp.num_of_nat N)) N))) (forall ((N tptp.num)) (let ((_let_1 (tptp.aa_num_nat tptp.nat_of_num N))) (= (tptp.aa_num_nat tptp.nat_of_num (tptp.aa_num_num tptp.bit1 N)) (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat _let_1) _let_1))))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.plus_plus_num M N) (tptp.aa_nat_num tptp.num_of_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_num_nat tptp.nat_of_num M)) (tptp.aa_num_nat tptp.nat_of_num N))))) (forall ((X tptp.num) (Xa tptp.num) (Y tptp.num)) (let ((_let_1 (= X tptp.one))) (=> (= (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.bit_un6697907153464112080or_num X) Xa) Y) (=> (=> _let_1 (=> (= Xa tptp.one) (not (= Y tptp.one)))) (=> (=> _let_1 (forall ((N2 tptp.num)) (=> (= Xa (tptp.aa_num_num tptp.bit0 N2)) (not (= Y (tptp.aa_num_num tptp.bit1 N2)))))) (=> (=> _let_1 (forall ((N2 tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit1 N2))) (=> (= Xa _let_1) (not (= Y _let_1)))))) (=> (forall ((M2 tptp.num)) (=> (= X (tptp.aa_num_num tptp.bit0 M2)) (=> (= Xa tptp.one) (not (= Y (tptp.aa_num_num tptp.bit1 M2)))))) (=> (forall ((M2 tptp.num)) (=> (= X (tptp.aa_num_num tptp.bit0 M2)) (forall ((N2 tptp.num)) (=> (= Xa (tptp.aa_num_num tptp.bit0 N2)) (not (= Y (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.bit_un6697907153464112080or_num M2) N2)))))))) (=> (forall ((M2 tptp.num)) (=> (= X (tptp.aa_num_num tptp.bit0 M2)) (forall ((N2 tptp.num)) (=> (= Xa (tptp.aa_num_num tptp.bit1 N2)) (not (= Y (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.bit_un6697907153464112080or_num M2) N2)))))))) (=> (forall ((M2 tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit1 M2))) (=> (= X _let_1) (=> (= Xa tptp.one) (not (= Y _let_1)))))) (=> (forall ((M2 tptp.num)) (=> (= X (tptp.aa_num_num tptp.bit1 M2)) (forall ((N2 tptp.num)) (=> (= Xa (tptp.aa_num_num tptp.bit0 N2)) (not (= Y (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.bit_un6697907153464112080or_num M2) N2)))))))) (not (forall ((M2 tptp.num)) (=> (= X (tptp.aa_num_num tptp.bit1 M2)) (forall ((N2 tptp.num)) (=> (= Xa (tptp.aa_num_num tptp.bit1 N2)) (not (= Y (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.bit_un6697907153464112080or_num M2) N2)))))))))))))))))))) (forall ((N tptp.num)) (= (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.bit_un6697907153464112080or_num tptp.one) (tptp.aa_num_num tptp.bit0 N)) (tptp.aa_num_num tptp.bit1 N))) (forall ((X tptp.num) (Xa tptp.num) (Y tptp.num)) (let ((_let_1 (= X tptp.one))) (=> (= (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.bit_un6697907153464112080or_num X) Xa) Y) (=> (tptp.accp_P3113834385874906142um_num tptp.bit_un4773296044027857193um_rel (tptp.product_Pair_num_num X Xa)) (=> (=> _let_1 (=> (= Xa tptp.one) (=> (= Y tptp.one) (not (tptp.accp_P3113834385874906142um_num tptp.bit_un4773296044027857193um_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) (=> (= Y (tptp.aa_num_num tptp.bit1 N2)) (not (tptp.accp_P3113834385874906142um_num tptp.bit_un4773296044027857193um_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) (=> (= Y _let_1) (not (tptp.accp_P3113834385874906142um_num tptp.bit_un4773296044027857193um_rel (tptp.product_Pair_num_num tptp.one _let_1)))))))) (=> (forall ((M2 tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 M2))) (=> (= X _let_1) (=> (= Xa tptp.one) (=> (= Y (tptp.aa_num_num tptp.bit1 M2)) (not (tptp.accp_P3113834385874906142um_num tptp.bit_un4773296044027857193um_rel (tptp.product_Pair_num_num _let_1 tptp.one)))))))) (=> (forall ((M2 tptp.num)) (=> (= X (tptp.aa_num_num tptp.bit0 M2)) (forall ((N2 tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 N2))) (=> (= Xa _let_1) (=> (= Y (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.bit_un6697907153464112080or_num M2) N2))) (not (tptp.accp_P3113834385874906142um_num tptp.bit_un4773296044027857193um_rel (tptp.product_Pair_num_num (tptp.aa_num_num tptp.bit0 M2) _let_1))))))))) (=> (forall ((M2 tptp.num)) (=> (= X (tptp.aa_num_num tptp.bit0 M2)) (forall ((N2 tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit1 N2))) (=> (= Xa _let_1) (=> (= Y (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.bit_un6697907153464112080or_num M2) N2))) (not (tptp.accp_P3113834385874906142um_num tptp.bit_un4773296044027857193um_rel (tptp.product_Pair_num_num (tptp.aa_num_num tptp.bit0 M2) _let_1))))))))) (=> (forall ((M2 tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit1 M2))) (=> (= X _let_1) (=> (= Xa tptp.one) (=> (= Y _let_1) (not (tptp.accp_P3113834385874906142um_num tptp.bit_un4773296044027857193um_rel (tptp.product_Pair_num_num _let_1 tptp.one)))))))) (=> (forall ((M2 tptp.num)) (=> (= X (tptp.aa_num_num tptp.bit1 M2)) (forall ((N2 tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 N2))) (=> (= Xa _let_1) (=> (= Y (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.bit_un6697907153464112080or_num M2) N2))) (not (tptp.accp_P3113834385874906142um_num tptp.bit_un4773296044027857193um_rel (tptp.product_Pair_num_num (tptp.aa_num_num tptp.bit1 M2) _let_1))))))))) (not (forall ((M2 tptp.num)) (=> (= X (tptp.aa_num_num tptp.bit1 M2)) (forall ((N2 tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit1 N2))) (=> (= Xa _let_1) (=> (= Y (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.bit_un6697907153464112080or_num M2) N2))) (not (tptp.accp_P3113834385874906142um_num tptp.bit_un4773296044027857193um_rel (tptp.product_Pair_num_num (tptp.aa_num_num tptp.bit1 M2) _let_1)))))))))))))))))))))) (= tptp.bit_un6697907153464112080or_num tptp.bit_un2785000775030745342or_num) (= tptp.bit_un4773296044027857193um_rel tptp.bit_un6909899581280750971um_rel) (forall ((X tptp.rat)) (= (tptp.archim6058952711729229775r_real (tptp.aa_rat_real tptp.ratreal X)) (tptp.archim3151403230148437115or_rat X))) (forall ((X tptp.rat) (Y tptp.rat)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_rat_real tptp.ratreal X)) (tptp.aa_rat_real tptp.ratreal Y)) (tptp.aa_rat_real tptp.ratreal (tptp.minus_minus_rat X Y)))) (forall ((X tptp.rat)) (= (tptp.aa_real_real tptp.inverse_inverse_real (tptp.aa_rat_real tptp.ratreal X)) (tptp.aa_rat_real tptp.ratreal (tptp.aa_rat_rat tptp.inverse_inverse_rat X)))) (forall ((X tptp.rat) (Y tptp.rat)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_rat_real tptp.ratreal X)) (tptp.aa_rat_real tptp.ratreal Y)) (tptp.aa_rat_real tptp.ratreal (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat X) Y)))) (= tptp.one_one_real (tptp.aa_rat_real tptp.ratreal tptp.one_one_rat)) (= tptp.zero_zero_real (tptp.aa_rat_real tptp.ratreal tptp.zero_zero_rat)) (forall ((X tptp.rat) (Y tptp.rat)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_rat_real tptp.ratreal X)) (tptp.aa_rat_real tptp.ratreal Y))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) Y)))) (= tptp.ratreal tptp.field_7254667332652039916t_real) (forall ((X tptp.rat)) (= (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_rat_real tptp.ratreal X)) (tptp.aa_rat_real tptp.ratreal (tptp.uminus_uminus_rat X)))) (forall ((X tptp.rat) (Y tptp.rat)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_rat_real tptp.ratreal X)) (tptp.aa_rat_real tptp.ratreal Y))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) Y)))) (forall ((X tptp.rat) (Y tptp.rat)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_rat_real tptp.ratreal X)) (tptp.aa_rat_real tptp.ratreal Y)) (tptp.aa_rat_real tptp.ratreal (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat X) Y)))) (forall ((X tptp.rat) (Y tptp.rat)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_rat_real tptp.ratreal X)) (tptp.aa_rat_real tptp.ratreal Y)) (tptp.aa_rat_real tptp.ratreal (tptp.divide_divide_rat X Y)))) (tptp.semila1248733672344298208er_nat tptp.gcd_gcd_nat tptp.dvd_dvd_nat tptp.aTP_Lamm_dj) (forall ((N tptp.code_natural)) (let ((_let_1 (tptp.aa_Code_natural_nat tptp.code_nat_of_natural N))) (=> (not (= N tptp.zero_z2226904508553997617atural)) (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 _let_1) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat))) _let_1))))) (forall ((K tptp.num)) (= (tptp.aa_Code_natural_nat tptp.code_nat_of_natural (tptp.numera5444537566228673987atural K)) (tptp.aa_num_nat tptp.numeral_numeral_nat K))) (forall ((X tptp.code_natural) (Xa tptp.code_natural)) (= (tptp.aa_Code_natural_nat tptp.code_nat_of_natural (tptp.aa_Cod4272041906116450446atural (tptp.aa_Cod5141017464274028979atural tptp.plus_p4538020629002901425atural X) Xa)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_Code_natural_nat tptp.code_nat_of_natural X)) (tptp.aa_Code_natural_nat tptp.code_nat_of_natural Xa)))) (forall ((X tptp.code_natural) (Xa tptp.code_natural)) (= (tptp.aa_Code_natural_nat tptp.code_nat_of_natural (tptp.aa_Cod4272041906116450446atural (tptp.aa_Cod5141017464274028979atural tptp.minus_7197305767214868737atural X) Xa)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_Code_natural_nat tptp.code_nat_of_natural X)) (tptp.aa_Code_natural_nat tptp.code_nat_of_natural Xa)))) (forall ((X tptp.code_natural) (Xa tptp.code_natural)) (= (tptp.aa_Code_natural_nat tptp.code_nat_of_natural (tptp.aa_Cod4272041906116450446atural (tptp.aa_Cod5141017464274028979atural tptp.times_2397367101498566445atural X) Xa)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_Code_natural_nat tptp.code_nat_of_natural X)) (tptp.aa_Code_natural_nat tptp.code_nat_of_natural Xa)))) (= (tptp.aa_Code_natural_nat tptp.code_nat_of_natural tptp.one_one_Code_natural) tptp.one_one_nat) (forall ((X tptp.code_natural) (Xa tptp.code_natural)) (= (tptp.aa_Code_natural_nat tptp.code_nat_of_natural (tptp.aa_Cod4272041906116450446atural (tptp.aa_Cod5141017464274028979atural tptp.divide5121882707175180666atural X) Xa)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_Code_natural_nat tptp.code_nat_of_natural X)) (tptp.aa_Code_natural_nat tptp.code_nat_of_natural Xa)))) (= (tptp.aa_Code_natural_nat tptp.code_nat_of_natural tptp.zero_z2226904508553997617atural) tptp.zero_zero_nat) (forall ((X tptp.nat) (Xa tptp.code_natural)) (= (tptp.aa_Code_natural_nat tptp.code_nat_of_natural (tptp.aa_Cod4272041906116450446atural (tptp.aa_nat5282697797315388251atural tptp.bit_se6611745700429515170atural X) Xa)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se547839408752420682it_nat X) (tptp.aa_Code_natural_nat tptp.code_nat_of_natural Xa)))) (= (tptp.aa_Cod4272041906116450446atural (tptp.aa_Cod5141017464274028979atural tptp.minus_7197305767214868737atural tptp.zero_z2226904508553997617atural) tptp.one_one_Code_natural) tptp.zero_z2226904508553997617atural) (forall ((X tptp.code_natural)) (= (tptp.aa_Code_integer_int tptp.code_int_of_integer (tptp.aa_Cod5448446754359732931nteger tptp.code_i5400310926305786745atural X)) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_Code_natural_nat tptp.code_nat_of_natural X)))) (forall ((N tptp.code_natural)) (= (tptp.aa_Code_integer_int tptp.code_int_of_integer (tptp.aa_Cod5448446754359732931nteger tptp.code_i5400310926305786745atural N)) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_Code_natural_nat tptp.code_nat_of_natural N)))) (forall ((V tptp.code_natural) (W tptp.code_natural)) (let ((_let_1 (tptp.aa_num_num tptp.bit1 tptp.one))) (let ((_let_2 (tptp.aa_num_num tptp.bit1 _let_1))) (let ((_let_3 (tptp.aa_num_num tptp.bit0 _let_1))) (let ((_let_4 (tptp.numera5444537566228673987atural (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit0 (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_3)))))))))))))))) (let ((_let_5 (tptp.aa_num_num tptp.bit0 tptp.one))) (let ((_let_6 (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_5)))))) (let ((_let_7 (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.bit1 (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.bit1 (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.bit1 (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.bit1 _let_2)))))))))))))))))))))) (let ((_let_8 (tptp.minus_shift (tptp.numera5444537566228673987atural (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit1 (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_7))))))))) (tptp.aa_Cod4272041906116450446atural (tptp.aa_Cod5141017464274028979atural tptp.times_2397367101498566445atural (tptp.modulo8411746178871703098atural W _let_4)) (tptp.numera5444537566228673987atural (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit0 (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 (tptp.aa_num_num tptp.bit1 _let_6)))))))))))) (tptp.aa_Cod4272041906116450446atural (tptp.aa_Cod5141017464274028979atural tptp.times_2397367101498566445atural (tptp.aa_Cod4272041906116450446atural (tptp.aa_Cod5141017464274028979atural tptp.divide5121882707175180666atural W) _let_4)) (tptp.numera5444537566228673987atural (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 (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit0 _let_2)))))))))))))) (let ((_let_9 (tptp.numera5444537566228673987atural (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit1 _let_3)))))))))))))))) (let ((_let_10 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit1 _let_7))))))))) (let ((_let_11 (tptp.minus_shift (tptp.numera5444537566228673987atural (tptp.aa_num_num tptp.bit1 _let_10)) (tptp.aa_Cod4272041906116450446atural (tptp.aa_Cod5141017464274028979atural tptp.times_2397367101498566445atural (tptp.modulo8411746178871703098atural V _let_9)) (tptp.numera5444537566228673987atural (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit0 _let_6)))))))))))) (tptp.aa_Cod4272041906116450446atural (tptp.aa_Cod5141017464274028979atural tptp.times_2397367101498566445atural (tptp.aa_Cod4272041906116450446atural (tptp.aa_Cod5141017464274028979atural tptp.divide5121882707175180666atural V) _let_9)) (tptp.numera5444537566228673987atural (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit0 (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.bit1 _let_5))))))))))))))))) (= (tptp.aa_Pro7165575656943818355atural tptp.next (tptp.produc3574140220909816553atural V W)) (tptp.aa_Pro7165575656943818355atural (tptp.produc6639722614265839536atural (tptp.aa_Cod4272041906116450446atural (tptp.aa_Cod5141017464274028979atural tptp.plus_p4538020629002901425atural (tptp.minus_shift (tptp.numera5444537566228673987atural (tptp.aa_num_num tptp.bit0 _let_10)) _let_11 (tptp.aa_Cod4272041906116450446atural (tptp.aa_Cod5141017464274028979atural tptp.plus_p4538020629002901425atural _let_8) tptp.one_one_Code_natural))) tptp.one_one_Code_natural)) (tptp.produc3574140220909816553atural _let_11 _let_8))))))))))))))) (forall ((B tptp.code_natural) (I tptp.code_natural)) (let ((_let_1 (tptp.log B I))) (let ((_let_2 (or (tptp.ord_le1926595141338095240atural B tptp.one_one_Code_natural) (tptp.ord_le5570908160329646204atural I B)))) (and (=> _let_2 (= _let_1 tptp.one_one_Code_natural)) (=> (not _let_2) (= _let_1 (tptp.aa_Cod4272041906116450446atural (tptp.aa_Cod5141017464274028979atural tptp.plus_p4538020629002901425atural tptp.one_one_Code_natural) (tptp.log B (tptp.aa_Cod4272041906116450446atural (tptp.aa_Cod5141017464274028979atural tptp.divide5121882707175180666atural I) B))))))))) (forall ((K tptp.code_natural) (L tptp.code_natural) (R tptp.code_natural)) (let ((_let_1 (tptp.minus_shift R K L))) (let ((_let_2 (tptp.ord_le5570908160329646204atural K L))) (and (=> _let_2 (= _let_1 (tptp.aa_Cod4272041906116450446atural (tptp.aa_Cod5141017464274028979atural tptp.minus_7197305767214868737atural (tptp.aa_Cod4272041906116450446atural (tptp.aa_Cod5141017464274028979atural tptp.plus_p4538020629002901425atural R) K)) L))) (=> (not _let_2) (= _let_1 (tptp.aa_Cod4272041906116450446atural (tptp.aa_Cod5141017464274028979atural tptp.minus_7197305767214868737atural K) L))))))) (forall ((X tptp.code_natural) (Xa tptp.code_natural) (Y tptp.code_natural)) (let ((_let_1 (or (tptp.ord_le1926595141338095240atural X tptp.one_one_Code_natural) (tptp.ord_le5570908160329646204atural Xa X)))) (=> (= (tptp.log X Xa) Y) (and (=> _let_1 (= Y tptp.one_one_Code_natural)) (=> (not _let_1) (= Y (tptp.aa_Cod4272041906116450446atural (tptp.aa_Cod5141017464274028979atural tptp.plus_p4538020629002901425atural tptp.one_one_Code_natural) (tptp.log X (tptp.aa_Cod4272041906116450446atural (tptp.aa_Cod5141017464274028979atural tptp.divide5121882707175180666atural Xa) X))))))))) (forall ((S tptp.produc7822875418678951345atural)) (= (tptp.split_seed S) (tptp.produc8282080750456430313atural (tptp.aTP_Lamm_ix S) S))) (forall ((K tptp.code_natural)) (= (tptp.range K) (tptp.produc5538323210962509403atural (tptp.iterat8892046348760725948atural (tptp.log (tptp.numera5444537566228673987atural (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit0 (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.bit1 (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.bit1 (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.bit1 (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.bit1 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit1 tptp.one))))))))))))))))))))))))))))))) K) tptp.aTP_Lamm_iz tptp.one_one_Code_natural) (tptp.aTP_Lamm_ja K)))) (forall ((V tptp.code_natural) (K tptp.code_natural)) (let ((_let_1 (tptp.inc_shift V K))) (let ((_let_2 (= V K))) (and (=> _let_2 (= _let_1 tptp.one_one_Code_natural)) (=> (not _let_2) (= _let_1 (tptp.aa_Cod4272041906116450446atural (tptp.aa_Cod5141017464274028979atural tptp.plus_p4538020629002901425atural K) tptp.one_one_Code_natural))))))) (forall ((X tptp.code_natural) (Xa tptp.code_natural) (Y tptp.code_natural)) (let ((_let_1 (tptp.accp_P8126237942716283194atural tptp.log_rel (tptp.produc3574140220909816553atural X Xa)))) (let ((_let_2 (or (tptp.ord_le1926595141338095240atural X tptp.one_one_Code_natural) (tptp.ord_le5570908160329646204atural Xa X)))) (=> (= (tptp.log X Xa) Y) (=> _let_1 (not (=> (and (=> _let_2 (= Y tptp.one_one_Code_natural)) (=> (not _let_2) (= Y (tptp.aa_Cod4272041906116450446atural (tptp.aa_Cod5141017464274028979atural tptp.plus_p4538020629002901425atural tptp.one_one_Code_natural) (tptp.log X (tptp.aa_Cod4272041906116450446atural (tptp.aa_Cod5141017464274028979atural tptp.divide5121882707175180666atural Xa) X)))))) (not _let_1)))))))) (forall ((Xa tptp.nat) (X tptp.nat)) (= (tptp.aa_Cod4272041906116450446atural (tptp.aa_Cod5141017464274028979atural tptp.divide5121882707175180666atural (tptp.aa_nat_Code_natural tptp.code_natural_of_nat Xa)) (tptp.aa_nat_Code_natural tptp.code_natural_of_nat X)) (tptp.aa_nat_Code_natural tptp.code_natural_of_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat Xa) X)))) (forall ((Xa tptp.nat) (X tptp.nat)) (= (tptp.aa_Cod4272041906116450446atural (tptp.aa_nat5282697797315388251atural tptp.bit_se6611745700429515170atural Xa) (tptp.aa_nat_Code_natural tptp.code_natural_of_nat X)) (tptp.aa_nat_Code_natural tptp.code_natural_of_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se547839408752420682it_nat Xa) X)))) (forall ((Xa tptp.nat) (X tptp.nat)) (= (tptp.aa_Cod4272041906116450446atural (tptp.aa_Cod5141017464274028979atural tptp.times_2397367101498566445atural (tptp.aa_nat_Code_natural tptp.code_natural_of_nat Xa)) (tptp.aa_nat_Code_natural tptp.code_natural_of_nat X)) (tptp.aa_nat_Code_natural tptp.code_natural_of_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat Xa) X)))) (= tptp.one_one_Code_natural (tptp.aa_nat_Code_natural tptp.code_natural_of_nat tptp.one_one_nat)) (forall ((Xa tptp.nat) (X tptp.nat)) (= (tptp.aa_Cod4272041906116450446atural (tptp.aa_Cod5141017464274028979atural tptp.plus_p4538020629002901425atural (tptp.aa_nat_Code_natural tptp.code_natural_of_nat Xa)) (tptp.aa_nat_Code_natural tptp.code_natural_of_nat X)) (tptp.aa_nat_Code_natural tptp.code_natural_of_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Xa) X)))) (forall ((Xa tptp.nat) (X tptp.nat)) (= (tptp.aa_Cod4272041906116450446atural (tptp.aa_Cod5141017464274028979atural tptp.minus_7197305767214868737atural (tptp.aa_nat_Code_natural tptp.code_natural_of_nat Xa)) (tptp.aa_nat_Code_natural tptp.code_natural_of_nat X)) (tptp.aa_nat_Code_natural tptp.code_natural_of_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Xa) X)))) (= tptp.zero_z2226904508553997617atural (tptp.aa_nat_Code_natural tptp.code_natural_of_nat tptp.zero_zero_nat)) (forall ((X tptp.nat)) (= (tptp.aa_Cod5448446754359732931nteger tptp.code_i5400310926305786745atural (tptp.aa_nat_Code_natural tptp.code_natural_of_nat X)) (tptp.aa_int_Code_integer tptp.code_integer_of_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int X)))) (= tptp.code_i5400310926305786745atural (tptp.map_fu2787874002554666395nteger tptp.code_nat_of_natural tptp.code_integer_of_int tptp.semiri1314217659103216013at_int)) (forall ((X tptp.code_natural)) (= (tptp.aa_Code_natural_nat tptp.code_nat_of_natural (tptp.aa_Cod4272041906116450446atural tptp.code_Suc X)) (tptp.aa_nat_nat tptp.suc (tptp.aa_Code_natural_nat tptp.code_nat_of_natural X)))) (forall ((N tptp.code_natural)) (= (tptp.aa_Cod4272041906116450446atural (tptp.aa_Cod5141017464274028979atural tptp.minus_7197305767214868737atural (tptp.aa_Cod4272041906116450446atural tptp.code_Suc N)) tptp.one_one_Code_natural) N)) (forall ((X tptp.nat)) (= (tptp.aa_Cod4272041906116450446atural tptp.code_Suc (tptp.aa_nat_Code_natural tptp.code_natural_of_nat X)) (tptp.aa_nat_Code_natural tptp.code_natural_of_nat (tptp.aa_nat_nat tptp.suc X)))) (= tptp.code_Suc (tptp.aa_fun5114738747585492520atural _let_10 tptp.suc)) (tptp.quotie6776551016481293500at_int tptp.intrel tptp.abs_Integ tptp.rep_Integ) (= tptp.bit_se6611745700429515170atural (tptp.map_fu5588224966615042724atural tptp.id_nat _let_10 tptp.bit_se547839408752420682it_nat)) (= tptp.divide5121882707175180666atural (tptp.map_fu7613509917203888380atural tptp.code_nat_of_natural _let_10 tptp.divide_divide_nat)) (= tptp.plus_p4538020629002901425atural (tptp.map_fu7613509917203888380atural tptp.code_nat_of_natural _let_10 tptp.plus_plus_nat)) (= tptp.minus_7197305767214868737atural (tptp.map_fu7613509917203888380atural tptp.code_nat_of_natural _let_10 tptp.minus_minus_nat)) (= tptp.times_2397367101498566445atural (tptp.map_fu7613509917203888380atural tptp.code_nat_of_natural _let_10 tptp.times_times_nat)) (tptp.bNF_re4520166952630509772nteger tptp.fequal_num (tptp.bNF_re6501075790457514782nteger tptp.fequal_num tptp.code_pcr_integer) tptp.aTP_Lamm_ha tptp.code_sub) (tptp.bNF_re4578097776928471693nteger tptp.fequal_nat _let_9 tptp.bit_se545348938243370406it_int tptp.bit_se7788150548672797655nteger) (tptp.bNF_re9130850084932126070nteger tptp.code_pcr_integer _let_9 tptp.divide_divide_int tptp.divide6298287555418463151nteger) (tptp.bNF_re9130850084932126070nteger tptp.code_pcr_integer _let_9 tptp.minus_minus_int tptp.minus_8373710615458151222nteger) (tptp.bNF_re9130850084932126070nteger tptp.code_pcr_integer _let_9 tptp.times_times_int tptp.times_3573771949741848930nteger) (tptp.bNF_re9130850084932126070nteger tptp.code_pcr_integer _let_9 tptp.plus_plus_int tptp.plus_p5714425477246183910nteger) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_int3865899974016033897r_bool tptp.code_pcr_integer tptp.one_one_int) tptp.one_one_Code_integer)) (tptp.pp (tptp.aa_fun7169572220525660642r_bool (tptp.aa_fun4674266849241344294r_bool _let_9 tptp.aTP_Lamm_hb) tptp.code_dup)) (tptp.bNF_re4153400068438556298nteger tptp.fequal_nat tptp.code_pcr_integer tptp.semiri1314217659103216013at_int tptp.code_integer_of_nat) (tptp.bNF_re9130850084932126070nteger tptp.code_pcr_integer _let_9 tptp.gcd_gcd_int tptp.gcd_gcd_Code_integer) (tptp.bNF_re9130850084932126070nteger tptp.code_pcr_integer _let_9 tptp.gcd_lcm_int tptp.gcd_lcm_Code_integer) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_int3865899974016033897r_bool tptp.code_pcr_integer tptp.zero_zero_int) tptp.zero_z3403309356797280102nteger)) (tptp.bNF_re5252274238750452962nteger tptp.code_pcr_natural tptp.code_pcr_integer tptp.semiri1314217659103216013at_int tptp.code_i5400310926305786745atural) (tptp.pp (tptp.aa_fun857525882259921228l_bool (tptp.aa_fun1838662137086867784l_bool _let_8 tptp.suc) tptp.code_Suc)) (tptp.bNF_re1400205106991740995atural tptp.code_pcr_natural _let_8 tptp.divide_divide_nat tptp.divide5121882707175180666atural) (tptp.bNF_re728283343719287275atural tptp.fequal_nat _let_8 tptp.bit_se547839408752420682it_nat tptp.bit_se6611745700429515170atural) (tptp.bNF_re1400205106991740995atural tptp.code_pcr_natural _let_8 tptp.minus_minus_nat tptp.minus_7197305767214868737atural) (tptp.bNF_re1400205106991740995atural tptp.code_pcr_natural _let_8 tptp.times_times_nat tptp.times_2397367101498566445atural) (tptp.bNF_re1400205106991740995atural tptp.code_pcr_natural _let_8 tptp.plus_plus_nat tptp.plus_p4538020629002901425atural) (forall ((K tptp.num) (L tptp.num)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.neg K)) (tptp.neg L))) (tptp.pp (tptp.aa_num_bool (tptp.ord_less_eq_num L) K)))) (forall ((L 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.neg L))))) (forall ((K tptp.num)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.neg K)) tptp.zero_zero_int))) (tptp.pp (tptp.aa_Code_natural_bool (tptp.aa_nat4473165201473010874l_bool tptp.code_pcr_natural tptp.zero_zero_nat) tptp.zero_z2226904508553997617atural)) (forall ((K tptp.num)) (= (tptp.aa_int_nat tptp.nat2 (tptp.neg K)) tptp.zero_zero_nat)) (forall ((K tptp.num) (L tptp.num)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.neg K)) (tptp.neg L))) (tptp.pp (tptp.aa_num_bool (tptp.ord_less_num L) K)))) (tptp.pp (tptp.aa_Code_natural_bool (tptp.aa_nat4473165201473010874l_bool tptp.code_pcr_natural tptp.one_one_nat) tptp.one_one_Code_natural)) (forall ((M tptp.num) (N tptp.num)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.neg M)) (tptp.neg N)) (tptp.neg (tptp.plus_plus_num M N)))) (forall ((L tptp.num)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) (tptp.neg L))))) (forall ((K tptp.num)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.neg K)) tptp.zero_zero_int))) (forall ((N tptp.num)) (= (tptp.sub tptp.one (tptp.aa_num_num tptp.bit0 N)) (tptp.neg (tptp.bitM N)))) (forall ((N tptp.num)) (= (tptp.sub tptp.one (tptp.aa_num_num tptp.bit1 N)) (tptp.neg (tptp.aa_num_num tptp.bit0 N)))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.sub M N) (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_num_int tptp.numeral_numeral_int N)))) (= (tptp.sub tptp.one tptp.one) tptp.zero_zero_int) (forall ((M tptp.num) (N tptp.num)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.neg M)) (tptp.neg N)) (tptp.sub N M))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.sub (tptp.aa_num_num tptp.bit0 M) (tptp.aa_num_num tptp.bit1 N)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.dup (tptp.sub M N))) tptp.one_one_int))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.sub (tptp.aa_num_num tptp.bit1 M) (tptp.aa_num_num tptp.bit0 N)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.dup (tptp.sub M N))) tptp.one_one_int))) (= (tptp.dup tptp.zero_zero_int) tptp.zero_zero_int) (forall ((K tptp.int)) (= (tptp.dup K) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int K) K))) (forall ((N tptp.num)) (= (tptp.dup (tptp.neg N)) (tptp.neg (tptp.aa_num_num tptp.bit0 N)))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.sub (tptp.aa_num_num tptp.bit0 M) (tptp.aa_num_num tptp.bit0 N)) (tptp.dup (tptp.sub M N)))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.sub (tptp.aa_num_num tptp.bit1 M) (tptp.aa_num_num tptp.bit1 N)) (tptp.dup (tptp.sub M N)))) (forall ((M tptp.num)) (= (tptp.sub (tptp.aa_num_num tptp.bit0 M) tptp.one) (tptp.aa_num_int tptp.pos (tptp.bitM M)))) (forall ((M tptp.num)) (= (tptp.sub (tptp.aa_num_num tptp.bit1 M) tptp.one) (tptp.aa_num_int tptp.pos (tptp.aa_num_num tptp.bit0 M)))) (forall ((N tptp.num)) (= (tptp.dup (tptp.aa_num_int tptp.pos N)) (tptp.aa_num_int tptp.pos (tptp.aa_num_num tptp.bit0 N)))) (forall ((K tptp.num) (L 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.pos K)) (tptp.neg L))))) (forall ((K tptp.num) (L tptp.num)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.neg K)) (tptp.aa_num_int tptp.pos L)))) (forall ((N tptp.num)) (= (tptp.neg N) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.pos N)))) (forall ((M tptp.num)) (= (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.pos M)) (tptp.neg M))) (forall ((M tptp.num)) (= (tptp.aa_int_int tptp.uminus_uminus_int (tptp.neg M)) (tptp.aa_num_int tptp.pos M))) (forall ((K tptp.num) (L tptp.num)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.neg K)) (tptp.aa_num_int tptp.pos L)))) (forall ((K tptp.num) (L tptp.num)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_num_int tptp.pos K)) (tptp.neg L))))) (forall ((K tptp.num)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_num_int tptp.pos K)) tptp.zero_zero_int)))) (forall ((L 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.pos L)))) (= tptp.pos tptp.numeral_numeral_int) (= tptp.one_one_int (tptp.aa_num_int tptp.pos tptp.one)) (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.pos M)) (tptp.aa_num_int tptp.pos N)) (tptp.aa_num_int tptp.pos (tptp.plus_plus_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.pos M)) (tptp.aa_num_int tptp.pos N)) (tptp.aa_num_int tptp.pos (tptp.times_times_num M N)))) (forall ((K tptp.num) (L tptp.num)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_num_int tptp.pos K)) (tptp.aa_num_int tptp.pos L))) (tptp.pp (tptp.aa_num_bool (tptp.ord_less_num K) L)))) (forall ((K tptp.num)) (= (tptp.aa_int_nat tptp.nat2 (tptp.aa_num_int tptp.pos K)) (tptp.aa_num_nat tptp.nat_of_num K))) (forall ((L 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.pos L)))) (forall ((K 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.pos K)) tptp.zero_zero_int)))) (forall ((K tptp.num) (L tptp.num)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_num_int tptp.pos K)) (tptp.aa_num_int tptp.pos L))) (tptp.pp (tptp.aa_num_bool (tptp.ord_less_eq_num K) L)))) (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.pos M)) (tptp.aa_num_int tptp.pos N)) (tptp.sub M N))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.neg M)) (tptp.aa_num_int tptp.pos N)) (tptp.neg (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.pos M)) (tptp.neg N)) (tptp.aa_num_int tptp.pos (tptp.plus_plus_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.neg M)) (tptp.neg N)) (tptp.aa_num_int tptp.pos (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.neg M)) (tptp.aa_num_int tptp.pos N)) (tptp.neg (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.pos M)) (tptp.neg N)) (tptp.neg (tptp.times_times_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.pos M)) (tptp.neg N)) (tptp.sub M N))) (forall ((M tptp.num) (N tptp.num)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.neg M)) (tptp.aa_num_int tptp.pos N)) (tptp.sub N M))) (forall ((X tptp.sum_sum_nat_nat)) (= (tptp.aa_Sum8073061460641146765at_nat tptp.nat_sum_encode X) (tptp.sum_ca6763686470577984908at_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.aTP_Lamm_jb X))) (tptp.quotie8981163687542601860t_real tptp.realrel tptp.real2 tptp.rep_real) (forall ((X tptp.sum_sum_nat_nat) (Y tptp.sum_sum_nat_nat)) (= (= (tptp.aa_Sum8073061460641146765at_nat tptp.nat_sum_encode X) (tptp.aa_Sum8073061460641146765at_nat tptp.nat_sum_encode Y)) (= X Y))) (tptp.pp (tptp.aa_set_nat_bool (tptp.bij_be5432664580149595207at_nat tptp.nat_sum_encode tptp.top_to6661820994512907621at_nat) tptp.top_top_set_nat)) (= (tptp.image_1320371278474632150at_nat tptp.nat_sum_encode tptp.top_to6661820994512907621at_nat) tptp.top_top_set_nat) (forall ((A2 tptp.set_Sum_sum_nat_nat)) (tptp.inj_on6343450744447823682at_nat tptp.nat_sum_encode A2)) (forall ((I tptp.int)) (= (tptp.aa_int_nat tptp.nat_int_encode I) (tptp.aa_Sum8073061460641146765at_nat tptp.nat_sum_encode (tptp.if_Sum_sum_nat_nat (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) I) (tptp.sum_Inl_nat_nat (tptp.aa_int_nat tptp.nat2 I)) (tptp.sum_Inr_nat_nat (tptp.aa_int_nat tptp.nat2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_int_int tptp.uminus_uminus_int I)) tptp.one_one_int))))))) (forall ((N tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat N) _let_1))) (let ((_let_3 (tptp.aa_nat7431386967378518541at_nat tptp.nat_sum_decode N))) (let ((_let_4 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat _let_1) N)))) (and (=> _let_4 (= _let_3 (tptp.sum_Inl_nat_nat _let_2))) (=> (not _let_4) (= _let_3 (tptp.sum_Inr_nat_nat _let_2))))))))) (forall ((X tptp.sum_sum_nat_nat)) (= (tptp.aa_nat7431386967378518541at_nat tptp.nat_sum_decode (tptp.aa_Sum8073061460641146765at_nat tptp.nat_sum_encode X)) X)) (forall ((N tptp.nat)) (= (tptp.aa_Sum8073061460641146765at_nat tptp.nat_sum_encode (tptp.aa_nat7431386967378518541at_nat tptp.nat_sum_decode N)) N)) (forall ((A2 tptp.set_nat)) (tptp.pp (tptp.aa_set_nat_bool (tptp.inj_on5701776251185195458at_nat tptp.nat_sum_decode) A2))) (= (tptp.image_678696785212003926at_nat tptp.nat_sum_decode tptp.top_top_set_nat) tptp.top_to6661820994512907621at_nat) (tptp.bij_be4790990086886966983at_nat tptp.nat_sum_decode tptp.top_top_set_nat tptp.top_to6661820994512907621at_nat) (forall ((X tptp.nat) (Y tptp.nat)) (= (= (tptp.aa_nat7431386967378518541at_nat tptp.nat_sum_decode X) (tptp.aa_nat7431386967378518541at_nat tptp.nat_sum_decode Y)) (= X Y))) (forall ((A0 tptp.nat) (P tptp.fun_nat_bool)) (let ((_let_1 (tptp.accp_nat tptp.nth_item_rel))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 A0)) (=> (=> (tptp.pp (tptp.aa_nat_bool _let_1 tptp.zero_zero_nat)) (tptp.pp (tptp.aa_nat_bool P tptp.zero_zero_nat))) (=> (forall ((N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N2))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.accp_nat tptp.nth_item_rel) _let_1)) (=> (forall ((A6 tptp.nat) (Aa tptp.nat)) (=> (= (tptp.aa_nat7431386967378518541at_nat tptp.nat_sum_decode N2) (tptp.sum_Inl_nat_nat A6)) (=> (= (tptp.aa_nat7431386967378518541at_nat tptp.nat_sum_decode A6) (tptp.sum_Inl_nat_nat Aa)) (tptp.pp (tptp.aa_nat_bool P Aa))))) (=> (forall ((A6 tptp.nat) (B8 tptp.nat)) (=> (= (tptp.aa_nat7431386967378518541at_nat tptp.nat_sum_decode N2) (tptp.sum_Inl_nat_nat A6)) (=> (= (tptp.aa_nat7431386967378518541at_nat tptp.nat_sum_decode A6) (tptp.sum_Inr_nat_nat B8)) (tptp.pp (tptp.aa_nat_bool P B8))))) (=> (forall ((B8 tptp.nat) (Ba tptp.nat) (X4 tptp.nat) (Y4 tptp.nat)) (=> (= (tptp.aa_nat7431386967378518541at_nat tptp.nat_sum_decode N2) (tptp.sum_Inr_nat_nat B8)) (=> (= (tptp.aa_nat7431386967378518541at_nat tptp.nat_sum_decode B8) (tptp.sum_Inr_nat_nat Ba)) (=> (= (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat X4) Y4) (tptp.aa_nat7603221163087113075at_nat tptp.nat_prod_decode Ba)) (tptp.pp (tptp.aa_nat_bool P X4)))))) (=> (forall ((B8 tptp.nat) (Ba tptp.nat) (X4 tptp.nat) (Y4 tptp.nat)) (=> (= (tptp.aa_nat7431386967378518541at_nat tptp.nat_sum_decode N2) (tptp.sum_Inr_nat_nat B8)) (=> (= (tptp.aa_nat7431386967378518541at_nat tptp.nat_sum_decode B8) (tptp.sum_Inr_nat_nat Ba)) (=> (= (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat X4) Y4) (tptp.aa_nat7603221163087113075at_nat tptp.nat_prod_decode Ba)) (tptp.pp (tptp.aa_nat_bool P Y4)))))) (tptp.pp (tptp.aa_nat_bool P _let_1))))))))) (tptp.pp (tptp.aa_nat_bool P A0))))))) (forall ((N tptp.nat)) (= (tptp.aa_nat_int tptp.nat_int_decode N) (tptp.sum_ca7763040182479039464nt_nat tptp.semiri1314217659103216013at_int tptp.aTP_Lamm_jc (tptp.aa_nat7431386967378518541at_nat tptp.nat_sum_decode N)))) (forall ((Uu tptp.product_prod_int_int)) (let ((_let_1 (tptp.product_fst_int_int Uu))) (= (tptp.aa_Pro6970504127699319548nt_int tptp.aTP_Lamm_eo 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_ib Uu) (tptp.if_fun_nat_rat (tptp.vanishes Uu) tptp.aTP_Lamm_hv (tptp.aTP_Lamm_ia Uu)))) (forall ((Uu tptp.nat)) (= (tptp.aa_nat_real tptp.aTP_Lamm_ar 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_av 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.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_cj 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.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_int tptp.aTP_Lamm_jc Uu) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int Uu))) tptp.one_one_int))) (forall ((Uu tptp.nat)) (= (tptp.aa_nat_real tptp.aTP_Lamm_bb 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_fj 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_ge 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_fm 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_em 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.int)) (= (tptp.aa_int_int tptp.aTP_Lamm_hb Uu) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int Uu) Uu))) (forall ((Uu tptp.nat)) (= (tptp.aa_nat7603221163087113075at_nat tptp.aTP_Lamm_hd 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_eh 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.code_natural)) (= (tptp.aa_Cod6352003912080677724atural tptp.aTP_Lamm_iz Uu) (tptp.produc5538323210962509403atural tptp.next (tptp.aTP_Lamm_iy Uu)))) (forall ((Uu tptp.nat)) (= (tptp.aa_nat_real tptp.aTP_Lamm_fo 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.nat)) (= (tptp.aa_nat_nat tptp.aTP_Lamm_jb Uu) (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))) Uu)))) (forall ((Uu tptp.real)) (= (tptp.aa_real_real tptp.aTP_Lamm_fh Uu) (tptp.suminf_real (tptp.aa_real_fun_nat_real tptp.aTP_Lamm_aq Uu)))) (forall ((Uu tptp.nat)) (= (tptp.aa_nat_set_nat tptp.aTP_Lamm_gx Uu) (tptp.collect_nat (tptp.aa_nat_fun_nat_bool tptp.aTP_Lamm_cr Uu)))) (forall ((Uu tptp.nat)) (= (tptp.aa_nat_real tptp.aTP_Lamm_fq 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_dz Uu) (tptp.some_num (tptp.aa_num_num tptp.bit1 Uu)))) (forall ((Uu tptp.num)) (= (tptp.aa_num_option_num tptp.aTP_Lamm_dy Uu) (tptp.some_num (tptp.aa_num_num tptp.bit0 Uu)))) (forall ((Uu tptp.nat)) (= (tptp.aa_nat8803788312118491388at_nat tptp.aTP_Lamm_ca Uu) (tptp.product_Pair_nat_nat (tptp.aa_nat_nat tptp.suc Uu)))) (forall ((Uu tptp.nat)) (= (tptp.aa_nat_Extended_enat tptp.aTP_Lamm_is Uu) (tptp.extended_enat2 (tptp.aa_nat_nat tptp.suc Uu)))) (forall ((Uu tptp.int)) (= (tptp.aa_int_nat tptp.aTP_Lamm_ag Uu) (tptp.aa_int_nat tptp.nat2 (tptp.aa_int_int tptp.abs_abs_int Uu)))) (forall ((Uu tptp.fun_nat_rat)) (= (tptp.pp (tptp.aa_fun_nat_rat_bool tptp.aTP_Lamm_hu 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 ((K2 tptp.nat)) (forall ((N5 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K2) N5)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat R5) (tptp.aa_nat_rat Uu N5)))))))))) (forall ((Uu tptp.real)) (= (tptp.pp (tptp.aa_real_bool tptp.aTP_Lamm_hk Uu)) (exists ((I4 tptp.int) (N5 tptp.nat)) (and (= Uu (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.ring_1_of_int_real I4)) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N5))) (not (= N5 tptp.zero_zero_nat)))))) (forall ((Uu tptp.real)) (= (tptp.pp (tptp.aa_real_bool tptp.aTP_Lamm_hp Uu)) (exists ((I4 tptp.int) (J3 tptp.int)) (and (= Uu (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.ring_1_of_int_real I4)) (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_dx Uu) (tptp.some_num tptp.one))) (forall ((Uu tptp.num) (Uua tptp.nat)) (= (tptp.aa_nat_option_num (tptp.aTP_Lamm_ee Uu) Uua) (tptp.case_num_option_num (tptp.some_num tptp.one) (tptp.aTP_Lamm_ec Uua) (tptp.aTP_Lamm_ed 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_aw 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.aa_Code_integer_int tptp.code_int_of_integer Uu)))) (= (tptp.aa_Code_integer_int (tptp.aa_Cod1242632294114111009er_int tptp.aTP_Lamm_dk 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.plus_plus_num _let_1 _let_1))) (= (tptp.aa_Code_integer_num (tptp.aa_Cod6128727250572145423er_num tptp.aTP_Lamm_eg Uu) Uua) (tptp.if_num (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.fequal_Code_integer Uua) tptp.zero_z3403309356797280102nteger) _let_2 (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_di Uu) Uua) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.if_nat (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.fequal_Code_integer Uua) tptp.zero_z3403309356797280102nteger)) _let_2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat _let_2) tptp.one_one_nat)))))) (forall ((Uu tptp.int) (Uua tptp.int)) (= (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.aTP_Lamm_cg 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.aa_int_int tptp.sgn_sgn_int Uu)) Uua) (tptp.aa_int_int tptp.abs_abs_int Uu))))) (forall ((Uu tptp.int) (Uua tptp.int)) (= (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.aTP_Lamm_hc 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.extended_enat) (Uua tptp.nat)) (= (tptp.aa_nat_Extended_enat (tptp.aTP_Lamm_in Uu) Uua) (tptp.extend3600170679010898289d_enat (tptp.aTP_Lamm_im Uua) (tptp.if_Extended_enat (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.fequal_nat Uua) tptp.zero_zero_nat) tptp.zero_z5237406670263579293d_enat tptp.extend5688581933313929465d_enat) Uu))) (forall ((Uu tptp.extended_enat) (Uua tptp.nat)) (= (tptp.aa_nat_Extended_enat (tptp.aTP_Lamm_ir Uu) Uua) (tptp.extend3600170679010898289d_enat (tptp.aTP_Lamm_iq Uua) tptp.extend5688581933313929465d_enat Uu))) (forall ((Uu tptp.extended_enat) (Uua tptp.nat)) (= (tptp.aa_nat_Extended_enat (tptp.aTP_Lamm_ip Uu) Uua) (tptp.extend3600170679010898289d_enat (tptp.aTP_Lamm_io Uua) tptp.zero_z5237406670263579293d_enat Uu))) (forall ((Uu tptp.nat) (Uua tptp.num)) (= (tptp.aa_num_option_num (tptp.aa_nat3713591252005393295on_num tptp.aTP_Lamm_ef Uu) Uua) (tptp.case_nat_option_num tptp.none_num (tptp.aTP_Lamm_ee Uua) Uu))) (forall ((Uu tptp.nat) (Uua tptp.num)) (= (tptp.aa_num_option_num (tptp.aTP_Lamm_ec Uu) Uua) (tptp.case_o6005452278849405969um_num tptp.none_num tptp.aTP_Lamm_dy (tptp.bit_take_bit_num Uu Uua)))) (forall ((Uu tptp.num) (Uua tptp.nat)) (= (tptp.aa_nat_option_num (tptp.aTP_Lamm_ea Uu) Uua) (tptp.case_o6005452278849405969um_num tptp.none_num tptp.aTP_Lamm_dy (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_ek 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_ap 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_at 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_ay 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.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.aTP_Lamm_ck 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.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.aTP_Lamm_ci 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.product_prod_int_int) (Uua tptp.product_prod_int_int)) (= (tptp.aa_Pro6970504127699319548nt_int (tptp.aa_Pro4124234152028750080nt_int tptp.aTP_Lamm_en 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_dd Uu) Uua)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_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.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_dc Uu) Uua)) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_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.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_aq 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_fi 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_fk 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_gy 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_dj 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.aa_nat_fun_nat_nat tptp.aTP_Lamm_bq Uu) Uua) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial Uu) Uua)) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (forall ((Uu tptp.real) (Uua tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.aTP_Lamm_bg 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_gg 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_hg Uu) Uua) (tptp.aa_nat_set_nat (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.aa_nat_fun_nat_nat tptp.aTP_Lamm_ei Uu) Uua) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat Uu) Uua)) Uua))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.aTP_Lamm_bi Uu) Uua) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Uu) Uua)) Uu))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.aTP_Lamm_bj Uu) Uua) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Uu) Uua)) Uua))) (forall ((Uu tptp.nat) (Uua tptp.complex)) (= (tptp.pp (tptp.aa_complex_bool (tptp.aTP_Lamm_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_fv 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_gc 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_gh 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_am 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.fun_nat_real) (Uua tptp.nat)) (= (tptp.aa_nat_real (tptp.aTP_Lamm_gb Uu) Uua) (tptp.groups6591440286371151544t_real (tptp.aTP_Lamm_fk Uu) (tptp.aa_nat_set_nat 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_ga Uu) Uua) (tptp.groups6591440286371151544t_real (tptp.aTP_Lamm_fk Uu) (tptp.aa_nat_set_nat 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_cl 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_dw 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_ep 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_ba 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_az 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_ha 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.aa_nat_fun_nat_nat tptp.aTP_Lamm_br Uu) Uua) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat Uua) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial Uu) Uua)))) (forall ((Uu tptp.real) (Uua tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.aTP_Lamm_fw 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_hq 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_fu 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_fr 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.nat) (Uua tptp.nat)) (= (tptp.aa_nat_list_nat (tptp.aa_nat6157064778417537467st_nat tptp.aTP_Lamm_ii Uu) Uua) (tptp.cons_nat Uu (tptp.aa_nat_list_nat tptp.nat_list_decode Uua)))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.aTP_Lamm_af 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.aa_nat_fun_nat_nat tptp.aTP_Lamm_ej Uu) Uua) (tptp.aa_nat_nat (tptp.aa_nat_fun_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_bu 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.aa_nat_fun_nat_nat tptp.aTP_Lamm_fl 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_ik 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.aa_nat_fun_nat_nat tptp.aTP_Lamm_cs 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_eq 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_il 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.aa_nat_fun_nat_nat tptp.aTP_Lamm_el 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_cu 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_es 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_cr 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_cq 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_dn 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.aa_nat_fun_nat_nat tptp.aTP_Lamm_bh Uu) Uua) (tptp.aa_nat_nat (tptp.aa_nat_fun_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_fp 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_bf 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_be 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_real) (Uua tptp.nat)) (= (tptp.aa_nat_real (tptp.aTP_Lamm_gf 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_ed 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_eb 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_hi Uu) Uua) (tptp.produc8955392012077580105t_bool (tptp.aa_nat8637530788439456283t_bool (tptp.aTP_Lamm_hh Uu) Uua)))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat7997280740862404369at_nat (tptp.aa_nat5682243440470347102at_nat tptp.aTP_Lamm_dv Uu) Uua) (tptp.produc2626176000494625587at_nat (tptp.aa_nat4158579785191972357at_nat (tptp.aTP_Lamm_du Uu) Uua)))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat7997280740862404369at_nat (tptp.aa_nat5682243440470347102at_nat tptp.aTP_Lamm_dt Uu) Uua) (tptp.produc2626176000494625587at_nat (tptp.aa_nat4158579785191972357at_nat (tptp.aTP_Lamm_ds Uu) Uua)))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat4401263874371387303t_bool (tptp.aa_nat4909001760120733684t_bool tptp.aTP_Lamm_dr Uu) Uua) (tptp.produc8955392012077580105t_bool (tptp.aa_nat8637530788439456283t_bool (tptp.aTP_Lamm_dq Uu) Uua)))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat4401263874371387303t_bool (tptp.aa_nat4909001760120733684t_bool tptp.aTP_Lamm_dp Uu) Uua) (tptp.produc8955392012077580105t_bool (tptp.aa_nat8637530788439456283t_bool (tptp.aTP_Lamm_do Uu) Uua)))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat7997280740862404369at_nat (tptp.aa_nat5682243440470347102at_nat tptp.aTP_Lamm_dm Uu) Uua) (tptp.produc2626176000494625587at_nat (tptp.aa_nat4158579785191972357at_nat (tptp.aTP_Lamm_dl Uu) Uua)))) (forall ((Uu tptp.fun_nat_real) (Uua tptp.real)) (= (tptp.aa_real_real (tptp.aTP_Lamm_ez Uu) Uua) (tptp.suminf_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_ey Uu) Uua)))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat_complex (tptp.aTP_Lamm_as 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.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_gi 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_al Uu) Uua)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat _let_1) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat Uu) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat _let_1) Uua)))))))) (forall ((Uu tptp.code_natural) (Uua tptp.code_natural)) (= (tptp.aa_Cod6352003912080677724atural (tptp.aTP_Lamm_iy Uu) Uua) (tptp.produc6639722614265839536atural (tptp.aa_Cod4272041906116450446atural (tptp.aa_Cod5141017464274028979atural tptp.plus_p4538020629002901425atural Uua) (tptp.aa_Cod4272041906116450446atural (tptp.aa_Cod5141017464274028979atural tptp.times_2397367101498566445atural Uu) (tptp.numera5444537566228673987atural (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit0 (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.bit1 (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.bit1 (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.bit1 (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.bit1 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit1 tptp.one)))))))))))))))))))))))))))))))))))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat_set_nat (tptp.aTP_Lamm_hf Uu) Uua) (tptp.aa_nat_set_nat 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_ft 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.code_natural) (Uua tptp.code_natural)) (= (tptp.aa_Cod6352003912080677724atural (tptp.aTP_Lamm_ja Uu) Uua) (tptp.produc6639722614265839536atural (tptp.modulo8411746178871703098atural Uua Uu)))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat_Extended_enat (tptp.aTP_Lamm_im Uu) Uua) (tptp.extended_enat2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat Uu) Uua)))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat_Extended_enat (tptp.aTP_Lamm_io Uu) Uua) (tptp.extended_enat2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uu) Uua)))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat_Extended_enat (tptp.aTP_Lamm_iq Uu) Uua) (tptp.extended_enat2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Uu) Uua)))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.aTP_Lamm_db Uu) Uua) (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_min_nat Uu) Uua)))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.aTP_Lamm_da Uu) Uua) (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_min_nat Uua) Uu)))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.aTP_Lamm_cz Uu) Uua) (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat Uu) Uua)))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.aTP_Lamm_cy 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_rat) (Uua tptp.nat)) (= (tptp.aa_nat_rat (tptp.aTP_Lamm_ia 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_hz Uu) Uua) (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_gq Uu) Uua) (tptp.aa_real_real tptp.artanh_real (tptp.aa_real_real Uu Uua)))) (forall ((Uu tptp.fun_real_real) (Uua tptp.real)) (= (tptp.aa_real_real (tptp.aTP_Lamm_gp 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_fz 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_ew 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_iv 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.set_nat) (Uua tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aTP_Lamm_iu Uu) Uua)) (forall ((X5 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X5) Uu)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat Uua) X5)))))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat_set_nat (tptp.aTP_Lamm_he Uu) Uua) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat Uu))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat_rat (tptp.aTP_Lamm_if Uu) Uua) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat Uu))) (forall ((Uu tptp.int) (Uua tptp.nat)) (= (tptp.aa_nat_rat (tptp.aTP_Lamm_ie Uu) Uua) (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_ax 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_bd 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_cv Uu) Uua) Uub) (tptp.if_Pro6119634080678213985nteger (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger _let_2) Uub) (tptp.produc1086072967326762835nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.plus_p5714425477246183910nteger _let_1) tptp.one_one_Code_integer) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger 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_cf 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_ch 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_dg 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.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.minus_8373710615458151222nteger _let_1) tptp.one_one_Code_integer) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger 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_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.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.minus_8373710615458151222nteger _let_1) tptp.one_one_Code_integer) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger 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_df 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.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.minus_8373710615458151222nteger _let_1) tptp.one_one_Code_integer) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger 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_gj 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_ev 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_de 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.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger 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.produc7822875418678951345atural) (Uua tptp.code_natural) (Uub tptp.code_natural)) (= (tptp.aa_Cod6808739660676082561atural (tptp.aa_Cod4292056611156568242atural (tptp.aTP_Lamm_ix Uu) Uua) Uub) (tptp.produc8282080750456430313atural (tptp.aa_Cod8811915439870959971atural (tptp.aTP_Lamm_iw Uua) Uub) (tptp.produc6591912806276919810atural (tptp.aa_Pro7165575656943818355atural tptp.next 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_ho Uu) Uua) Uub)) (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.produc8560705615207772305t_bool (tptp.aa_int2327297053056786951t_bool (tptp.aTP_Lamm_hn 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_hm Uu) Uua) Uub)) (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.produc8560705615207772305t_bool (tptp.aa_int2327297053056786951t_bool (tptp.aTP_Lamm_hl 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_ce Uu) Uua) Uub) (tptp.produc4245557441103728435nt_int (tptp.aa_int1966403025003302569nt_int (tptp.aTP_Lamm_cd 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_cc Uu) Uua) Uub) (tptp.produc4245557441103728435nt_int (tptp.aa_int1966403025003302569nt_int (tptp.aTP_Lamm_cb 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_bz Uu) Uua) Uub) (tptp.produc4245557441103728435nt_int (tptp.aa_int1966403025003302569nt_int (tptp.aTP_Lamm_by 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_bx Uu) Uua) Uub) (tptp.produc4245557441103728435nt_int (tptp.aa_int1966403025003302569nt_int (tptp.aTP_Lamm_bw 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_fa 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_fb 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_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.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_bc 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_gs 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_gt 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_gr 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_ai 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_gu Uu) Uua) Uub)) (and (tptp.member_set_nat Uub (tptp.pow_nat (tptp.aa_nat_set_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_ah 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_bk Uu) Uua) Uub) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uua) Uub)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uu) Uub)))) (forall ((Uu tptp.int) (Uua tptp.int) (Uub tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool (tptp.aTP_Lamm_hr 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_cm 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_hs 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_co 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_cp 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_cn 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_gw 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_gz 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_gv 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_hj 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.nat) (Uua tptp.complex) (Uub tptp.complex)) (= (tptp.pp (tptp.aa_complex_bool (tptp.aa_com1553036987509291606x_bool (tptp.aTP_Lamm_bt 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_aj 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_fy 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.ring_1_of_int_real (tptp.aa_nat_int Uua Uub))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_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_ey 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_au 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_bn Uu) Uua) Uub) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat Uu Uub)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat Uua) Uub)))) (forall ((Uu tptp.fun_real_real) (Uua tptp.fun_real_real) (Uub tptp.real)) (= (tptp.aa_real_real (tptp.aa_fun6946558556880649704l_real (tptp.aTP_Lamm_go 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_gk 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_hy 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_ct 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_fn 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_id Uu) Uua) Uub) (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_eu 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_real_real) (Uua tptp.nat) (Uub tptp.real)) (= (tptp.aa_real_real (tptp.aa_nat_fun_real_real (tptp.aTP_Lamm_er 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_gd 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_et 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_ig Uu) Uua) Uub) (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_fs 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_bv Uu) Uua) Uub) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Uu) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat Uub) Uua)))) (forall ((Uu tptp.real) (Uua tptp.real) (Uub tptp.product_unit)) (= (tptp.aa_Product_unit_real (tptp.aa_rea7683167438103758690t_real (tptp.aTP_Lamm_ij Uu) Uua) Uub) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.powr_real2 Uu) 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_gn 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_ih Uu) Uua) Uub) (tptp.aa_nat_real Uu (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Uub) Uua)))) (forall ((Uu tptp.fun_nat_bool) (Uua tptp.nat) (Uub tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool (tptp.aTP_Lamm_gm Uu) Uua) Uub)) (tptp.pp (tptp.aa_nat_bool Uu (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Uub) Uua))))) (forall ((Uu tptp.fun_nat_real) (Uua tptp.real) (Uub tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_fx 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_bp 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_bo Uu) Uua) Uuc)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat Uuc))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat Uub) Uuc)))) (forall ((Uu tptp.fun_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_fg 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_fe 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_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 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_fc 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.code_natural) (Uua tptp.code_natural) (Uub tptp.code_natural) (Uuc tptp.code_natural)) (let ((_let_1 (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.bit1 (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.bit1 (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.bit1 (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.bit1 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit1 tptp.one)))))))))))))))))))))))) (= (tptp.aa_Cod6808739660676082561atural (tptp.aa_Cod4292056611156568242atural (tptp.aa_Cod8811915439870959971atural (tptp.aTP_Lamm_iw Uu) Uua) Uub) Uuc) (tptp.produc4480994950612372183atural (tptp.produc3574140220909816553atural (tptp.inc_shift (tptp.numera5444537566228673987atural (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit1 _let_1))))))))) Uu) Uuc) (tptp.produc3574140220909816553atural Uub (tptp.inc_shift (tptp.numera5444537566228673987atural (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit1 (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_1))))))))) Uua)))))) (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_dl 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_bm Uu) Uua) Uub) Uuc) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial Uub) Uuc))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat Uu) Uuc))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat Uua) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uub) Uuc))))) (forall ((Uu tptp.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_bl Uu) Uua) Uub) Uuc) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial Uu) Uuc)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial Uua) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uub) Uuc))))) (forall ((Uu tptp.int) (Uua tptp.int) (Uub tptp.int) (Uuc tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool (tptp.aa_int2327297053056786951t_bool (tptp.aTP_Lamm_hn 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_dq 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_hl 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_do 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_ds 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_du 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_hh 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_bo 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_cd 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_cb 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_bw 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_by 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_ff Uu) Uua) Uub) Uuc) Uud) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real (tptp.aa_nat_fun_real_real Uua Uuc) Uud)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real (tptp.aa_nat1308781354268537904t_real (tptp.aTP_Lamm_fe Uua) Uuc) Uud) (tptp.aa_nat_set_nat 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_ht Uu) Uua) Uub) Uuc) Uud)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Uuc) Uud)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Uud) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat _let_1) Uu))) (forall ((I4 tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I4) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat _let_1) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uu) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat Uu) _let_1))))) (= (exists ((X_13 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions (tptp.nth_VEBT_VEBT Uua I4)) X_13))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions Uub) I4)))))) (=> _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_13 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions X5) X_13))))))) (=> (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.aa_nat_fun_nat_nat tptp.power_power_nat _let_1) Uu))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_V5917875025757280293ildren (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat Uu) _let_1) Uua) 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_ic Uu) Uua) Uu)) (forall ((Uu tptp.complex)) (= (tptp.aa_complex_complex tptp.aTP_Lamm_bs Uu) Uu)) (forall ((Uu tptp.real)) (= (tptp.aa_real_real tptp.aTP_Lamm_it Uu) Uu)) (forall ((Uu tptp.nat)) (= (tptp.aa_nat_nat tptp.aTP_Lamm_an Uu) Uu)) (forall ((Uu tptp.int)) (= (tptp.aa_int_int tptp.aTP_Lamm_ao Uu) Uu)) (forall ((Uu tptp.nat)) (= (tptp.aa_nat_rat tptp.aTP_Lamm_hv Uu) tptp.zero_zero_rat)) (forall ((Uu tptp.nat)) (= (tptp.aa_nat_rat tptp.aTP_Lamm_hw Uu) tptp.one_one_rat)) (forall ((Uu tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool tptp.aTP_Lamm_cx Uu)) false)) (forall ((Uu tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool tptp.aTP_Lamm_cw Uu)) true)) (forall ((P tptp.bool)) (or (tptp.pp P) (tptp.pp (tptp.aa_bool_bool tptp.fNot P)))) (forall ((P tptp.bool)) (or (not (tptp.pp (tptp.aa_bool_bool tptp.fNot P))) (not (tptp.pp P)))) (tptp.pp tptp.fTrue) (forall ((P tptp.bool) (Q tptp.bool)) (or (not (tptp.pp (tptp.aa_bool_bool (tptp.fconj P) Q))) (tptp.pp Q))) (forall ((P tptp.bool) (Q tptp.bool)) (or (not (tptp.pp (tptp.aa_bool_bool (tptp.fconj P) Q))) (tptp.pp P))) (forall ((P tptp.bool) (Q tptp.bool)) (or (not (tptp.pp P)) (not (tptp.pp Q)) (tptp.pp (tptp.aa_bool_bool (tptp.fconj P) Q)))) (forall ((P tptp.bool) (Q tptp.bool)) (or (not (tptp.pp (tptp.aa_bool_bool (tptp.fdisj P) Q))) (tptp.pp P) (tptp.pp Q))) (forall ((Q tptp.bool) (P tptp.bool)) (or (not (tptp.pp Q)) (tptp.pp (tptp.aa_bool_bool (tptp.fdisj P) Q)))) (forall ((P tptp.bool) (Q tptp.bool)) (or (not (tptp.pp P)) (tptp.pp (tptp.aa_bool_bool (tptp.fdisj P) Q)))) (not (tptp.pp tptp.fFalse)) (forall ((P tptp.bool) (Q tptp.bool)) (or (not (tptp.pp (tptp.aa_bool_bool (tptp.aa_boo8970175072276269406l_bool tptp.fimplies P) Q))) (not (tptp.pp P)) (tptp.pp Q))) (forall ((Q tptp.bool) (P tptp.bool)) (or (not (tptp.pp Q)) (tptp.pp (tptp.aa_bool_bool (tptp.aa_boo8970175072276269406l_bool tptp.fimplies P) Q)))) (forall ((P tptp.bool) (Q tptp.bool)) (or (tptp.pp P) (tptp.pp (tptp.aa_bool_bool (tptp.aa_boo8970175072276269406l_bool tptp.fimplies P) Q)))) (forall ((X tptp.int) (Y tptp.int)) (= (tptp.if_int tptp.fFalse X Y) Y)) (forall ((X tptp.int) (Y tptp.int)) (= (tptp.if_int tptp.fTrue X Y) X)) (forall ((X tptp.nat) (Y tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.if_nat tptp.fFalse) X) Y) Y)) (forall ((X tptp.nat) (Y tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.if_nat tptp.fTrue) X) Y) X)) (forall ((X tptp.num) (Y tptp.num)) (= (tptp.if_num tptp.fFalse X Y) Y)) (forall ((X tptp.num) (Y tptp.num)) (= (tptp.if_num tptp.fTrue X Y) X)) (forall ((P tptp.fun_nat_bool) (X tptp.nat)) (or (not (tptp.pp (tptp.aa_nat_bool P X))) (tptp.pp (tptp.aa_fun_nat_bool_bool tptp.fEx_nat P)))) (forall ((X tptp.real) (Y tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real (tptp.if_real tptp.fFalse) X) Y) Y)) (forall ((X tptp.real) (Y tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real (tptp.if_real tptp.fTrue) X) Y) X)) (forall ((X tptp.int) (Y tptp.int)) (or (not (= X Y)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.fequal_int X) Y)))) (forall ((X tptp.int) (Y tptp.int)) (or (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.fequal_int X) Y))) (= X Y))) (forall ((X tptp.nat) (Y tptp.nat)) (or (not (= X Y)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.fequal_nat X) Y)))) (forall ((X tptp.nat) (Y tptp.nat)) (or (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.fequal_nat X) Y))) (= X Y))) (forall ((X tptp.num) (Y tptp.num)) (or (not (= X Y)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.fequal_num X) Y)))) (forall ((X tptp.num) (Y tptp.num)) (or (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.fequal_num X) Y))) (= X Y))) (forall ((X tptp.rat) (Y tptp.rat)) (or (not (= X Y)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.fequal_rat X) Y)))) (forall ((X tptp.rat) (Y tptp.rat)) (or (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.fequal_rat X) Y))) (= X Y))) (forall ((X tptp.bool) (Y tptp.bool)) (or (not (= X Y)) (tptp.pp (tptp.aa_bool_bool (tptp.aa_boo8970175072276269406l_bool tptp.fequal_bool X) Y)))) (forall ((X tptp.bool) (Y tptp.bool)) (or (not (tptp.pp (tptp.aa_bool_bool (tptp.aa_boo8970175072276269406l_bool tptp.fequal_bool X) Y))) (= X Y))) (forall ((X tptp.real) (Y tptp.real)) (or (not (= X Y)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.fequal_real X) Y)))) (forall ((X tptp.real) (Y tptp.real)) (or (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.fequal_real X) Y))) (= X Y))) (forall ((X tptp.complex) (Y tptp.complex)) (or (not (= X Y)) (tptp.pp (tptp.aa_complex_bool (tptp.fequal_complex X) Y)))) (forall ((X tptp.complex) (Y tptp.complex)) (or (not (tptp.pp (tptp.aa_complex_bool (tptp.fequal_complex X) Y))) (= X Y))) (forall ((X tptp.extended_enat) (Y tptp.extended_enat)) (= (tptp.if_Extended_enat tptp.fFalse X Y) Y)) (forall ((X tptp.extended_enat) (Y tptp.extended_enat)) (= (tptp.if_Extended_enat tptp.fTrue X Y) X)) (forall ((X tptp.code_integer) (Y tptp.code_integer)) (= (tptp.if_Code_integer tptp.fFalse X Y) Y)) (forall ((X tptp.code_integer) (Y tptp.code_integer)) (= (tptp.if_Code_integer tptp.fTrue X Y) X)) (forall ((X tptp.extended_enat) (Y tptp.extended_enat)) (or (not (= X Y)) (tptp.pp (tptp.fequal_Extended_enat X Y)))) (forall ((X tptp.extended_enat) (Y tptp.extended_enat)) (or (not (tptp.pp (tptp.fequal_Extended_enat X Y))) (= X Y))) (forall ((P tptp.fun_VEBT_VEBT_bool) (X tptp.vEBT_VEBT)) (or (not (tptp.pp (tptp.fAll_VEBT_VEBT P))) (tptp.pp (tptp.aa_VEBT_VEBT_bool P X)))) (forall ((X tptp.code_integer) (Y tptp.code_integer)) (or (not (= X Y)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.fequal_Code_integer X) Y)))) (forall ((X tptp.code_integer) (Y tptp.code_integer)) (or (not (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.fequal_Code_integer X) Y))) (= X Y))) (forall ((X tptp.fun_int_int) (Y tptp.fun_int_int)) (= (tptp.if_fun_int_int tptp.fFalse X Y) Y)) (forall ((X tptp.fun_int_int) (Y tptp.fun_int_int)) (= (tptp.if_fun_int_int tptp.fTrue X Y) X)) (forall ((X tptp.fun_nat_rat) (Y tptp.fun_nat_rat)) (= (tptp.if_fun_nat_rat tptp.fFalse X Y) Y)) (forall ((X tptp.fun_nat_rat) (Y tptp.fun_nat_rat)) (= (tptp.if_fun_nat_rat tptp.fTrue X Y) X)) (forall ((X tptp.sum_sum_nat_nat) (Y tptp.sum_sum_nat_nat)) (= (tptp.if_Sum_sum_nat_nat tptp.fFalse X Y) Y)) (forall ((X tptp.sum_sum_nat_nat) (Y tptp.sum_sum_nat_nat)) (= (tptp.if_Sum_sum_nat_nat tptp.fTrue X Y) X)) (forall ((X tptp.product_prod_int_int) (Y tptp.product_prod_int_int)) (= (tptp.if_Pro3027730157355071871nt_int tptp.fFalse X Y) Y)) (forall ((X tptp.product_prod_int_int) (Y tptp.product_prod_int_int)) (= (tptp.if_Pro3027730157355071871nt_int tptp.fTrue X Y) X)) (forall ((X tptp.product_prod_nat_nat) (Y tptp.product_prod_nat_nat)) (= (tptp.if_Pro6206227464963214023at_nat tptp.fFalse X Y) Y)) (forall ((X tptp.product_prod_nat_nat) (Y tptp.product_prod_nat_nat)) (= (tptp.if_Pro6206227464963214023at_nat tptp.fTrue X Y) X)) (forall ((X tptp.fun_nat_fun_int_int) (Y tptp.fun_nat_fun_int_int)) (= (tptp.if_fun5757141600869472092nt_int tptp.fFalse X Y) Y)) (forall ((X tptp.fun_nat_fun_int_int) (Y tptp.fun_nat_fun_int_int)) (= (tptp.if_fun5757141600869472092nt_int tptp.fTrue X Y) X)) (forall ((X tptp.fun_nat_fun_nat_nat) (Y tptp.fun_nat_fun_nat_nat)) (= (tptp.if_fun6060303171108177060at_nat tptp.fFalse X Y) Y)) (forall ((X tptp.fun_nat_fun_nat_nat) (Y tptp.fun_nat_fun_nat_nat)) (= (tptp.if_fun6060303171108177060at_nat tptp.fTrue X Y) X)) (forall ((P tptp.fun_bool_bool) (Q tptp.fun_VEBT_VEBT_bool) (R3 tptp.vEBT_VEBT)) (= (tptp.aa_VEBT_VEBT_bool (tptp.cOMBB_3745307990312268622T_VEBT P Q) R3) (tptp.aa_bool_bool P (tptp.aa_VEBT_VEBT_bool Q R3)))) (forall ((P tptp.fun_VE2066785035971159626l_bool) (Q tptp.fun_VEBT_VEBT_bool) (R3 tptp.vEBT_VEBT)) (= (tptp.aa_VEBT_VEBT_bool (tptp.cOMBS_6222329278419335549l_bool P Q) R3) (tptp.aa_bool_bool (tptp.aa_VEB8047906998784800507l_bool P R3) (tptp.aa_VEBT_VEBT_bool Q R3)))) (forall ((P tptp.bool)) (or (= P tptp.fTrue) (= P tptp.fFalse))) (forall ((X tptp.produc8923325533196201883nteger) (Y tptp.produc8923325533196201883nteger)) (= (tptp.if_Pro6119634080678213985nteger tptp.fFalse X Y) Y)) (forall ((X tptp.produc8923325533196201883nteger) (Y tptp.produc8923325533196201883nteger)) (= (tptp.if_Pro6119634080678213985nteger tptp.fTrue X Y) X)) (forall ((P tptp.fun_fu7168253649841883962l_bool) (Q tptp.fun_VE3763956218935105199t_bool) (R3 tptp.vEBT_VEBT)) (= (tptp.aa_VEBT_VEBT_bool (tptp.cOMBB_2885587777813823575T_VEBT P Q) R3) (tptp.aa_fun_nat_bool_bool P (tptp.aa_VEB4832260192069861672t_bool Q R3)))) (forall ((P tptp.fun_bo1841576699660343469l_bool) (Q tptp.fun_VEBT_VEBT_bool) (R3 tptp.vEBT_VEBT)) (= (tptp.aa_VEB8047906998784800507l_bool (tptp.cOMBB_3438363824644082366T_VEBT P Q) R3) (tptp.aa_boo8970175072276269406l_bool P (tptp.aa_VEBT_VEBT_bool Q R3)))) (forall ((P tptp.fun_VE7346385682144900493T_bool) (Q tptp.set_VEBT_VEBT) (R3 tptp.vEBT_VEBT)) (= (tptp.aa_VEBT_VEBT_bool (tptp.cOMBC_771164880915498576T_bool P Q) R3) (tptp.aa_set8260762808118238015T_bool (tptp.aa_VEB289770264548726718T_bool P R3) Q))) _let_7 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 18.53/18.78  )
% 18.53/18.78  % SZS output end Proof for ITP220_1
% 18.53/18.78  % cvc5---1.0.5 exiting
% 18.53/18.79  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------